Rebuilding the Periodic Table

Periodic Table BanThe Periodic Table of the elements is a fascinating icon of science. It is incredibly useful and has been exploited and sexploited too in the form of a periodic table of yoga and a sexy PT. It has also been hacked apart, cut and paste into different formats, created as illuminated wall cases, woodworked into furniture, spiralled, spherized, and generally rebuilt in almost every imaginable way ever since Mendeleev first dreamed of laying out his elemental cards according to the periodicity of elemental properties.

Now, in an effort to inspire chemists to reconsider the foundations of the periodic table, chemical philosopher Eric Scerri of the University of California, Los Angeles, is building a new way to classify the chemical elements one step at a time.

Writing in the latest issue of the Journal of Chemical Education (PDF 2008, 85, 585-589), Scerri explains how the periodic table initially arose from the discovery of atomic weight triads but he now suggests that chemists should recognize the fundamental importance of atomic number triads.

This sea change in elemental attitude might enhance the periodic table by classifying the elements at a fundamental level as basic substances. As such, he and his colleagues have developed a new version of the “left-step” periodic table, which looks very different from the conventional PT. In the new layout, with its step-like pattern actinides and lanthanides are no longer relegated to a standalone box, but form the first step of the PT.

Climbing right to the transition metals (Fe, Mn, Ir, Sg et al) on the next step and then to the non- and semi-metals, such as boron carbon, oxygen, silicon etc and finally a step in which the halogens (fluorine, chlorine…), noble gases (neon, xenon…), alkali metals (potassium, sodium…) and alkaline earth metals (beryllium, calcium…) form the final highest step on the right. Hydrogen tops the halogen column and helium crowns the noble gases rather than acting as the outer beacons as with the conventional layout. (Click the graphic for a clearer, full-size view).
left step periodic style=

“The left step table has been around for some time,” Scerri told me, “but I am modifying it to accommodate two atomic number triads which would otherwise be absent. They are He, Ne, Ar which ceases to exist as a triad in the usually encountered left-step table and H, F, Cl which does not exist either in the conventional medium-long form table or the usually encountered left-step table.”

In the grander scheme of things, whatever form the Periodic Table takes in the future matters not to those of us who sing, so we end with a song, the periodic table song from Tom Lehrer (who was 80 on April 9, 2008 and gets a mention in the Official Google Blog this week), known simply as The Elements.

520 thoughts on “Rebuilding the Periodic Table”

  1. From Jess Tauber via email:

    A discussion group is now available on Yahoo Groups

    “Our group includes Eric Scerri, among others. A number of our subscribers took part in the action on David Bradley’s Rebuilding the Periodic Table thread on

    Periodic Discussion

  2. Yes, everyone, it’s way past bedtime metaphorically speaking. You’ve all had a lovely time despite the name calling and the tears (mostly mine in exasperation at having to try and keep order), and now it’s time to stop. Say g’night to your friends and promise to play nicely again tomorrow, metaphorically speaking.

    Fundamentally, there is, with current chemical understanding, no resolution to the debate to be had, it seems, despite the best efforts of each party to argue their case for the status quo, staggers and steps, relocations and the spiralling of the PT into 3D.


    (Please don’t try and put any more coins in the slot, you will lose your money).

  3. David: I thought you would have taken the ball away a long time ago. Thank you for letting us play until it got dark.

  4. Have you guys ever observed children playing ball? It usually starts off well…until a conflict of interest or a difference of opinion about the game’s rules comes to light. Then they get nasty, start calling each other names, hair pulling, fisty cuffs, and the throwing of stones often ensue.

    Inevitably, a parent must step in to take charge of the situation before someone gets hurt. The kids are asked to “play nicely”. If they continue with the bad behaviour, the ball is usually confiscated and in extreme cases they are sent to bed with no supper…

  5. Valery: Fell in love with Longman’s spiral in 1951. Dropped school chemistry after 2 years because teacher not interested in Longman or H over C. Did soil chemistry and plant biochem courses as part of forestry degree. Continued to read abour chemistry in Scientific American and New Scientist. Back to work on Longman in 2002 and read van Spronsen, Mazurs and many of their references.

  6. Prof. Bent, after Valery and I started interacting and I tried to rationalize what to ‘do’ with the spacer layers in the Adomah model (originally I’d wondered whether we could stick antielements in there!), I realized that the numbers of spheres NOT used was the same as the numbers that were utilized, and that the slice sizes were the same as well, just coming from the directly opposite edge as that of the s-block in the Adomah, and oriented perpendicularly.

    I’d always been bothered by the fact that we had to double up elements to make a regular tetrahedron. Now with equal-count and -distribution real estate one could re-assort and have all elements get one sphere each.

    A remaining problem was that this inverse Adomah set, which intercalated the first one, broke up the continuity of subperiods- that is, one edge would get, say, all the s1 electrons, and its opposite s2. In addition one still had to deal with the numerical lopsidedness of putting Z=1 on one vertex and Z=2 on another, but not 3 and 4 on the remaining two vertices (though one COULD do this and I tried it too).

    As I explored this virgin territory, I found that a number of different ways to rationally distribute the quantum numbers on vertices, edges, faces, and the tetrahedral body existed that would give symmetrical results- some were just more aesthetically pleasing than others. One particular set took the center-point of two opposing edges as the place around which to put H, He, and then 119 and 120 on the other edge. This system gave one a very symmetrical result, with all Cartesian coordinates, straight lines, and right angles for the locations of subperiods. But it still broke things up in ways I found displeasing.

    It was at that moment that, serendipitously, I realized suddenly that by switching the constructional assignment of two of the quantum numbers I could get around these subperiod discontinuities. But I was dubious- I’d already built an Adomah-style tetrahedron from wooden spheres (my young nephews built others for themselves from the remaining pile of balls). I physically counted, one by one, the spheres on the outer edge of the 120-sphere tetrahedron (which wasn’t THAT easy since I’d constructed the thing from slices and it would fall apart unless deliberately held together) and to my delight and astonishment I found that the outer ring contained exactly 28 spheres, enough for the full f block.

    So, did this carry over to the other orbital types? The next ring held 20 spheres, but there were TWO of these. The next inward had 12 spheres- it took a bit of doing to visualize that there were three of these rings, since nothing was colored, or labeled, and the slices didn’t lend themselves easily to the counts. Well, if there were THREE, then the innermost rings would be 4 spheres apiece, and there should be four of them- as there turned out to be.

    Note that the differences in sphere counts for the rings were consistently 8 different: 28, 20, 12, and 4, reflecting the fact that each ring represents two full subperiods of the same type. Having to multiply these by 1, 2, 3 and 4 respectively shows the relation to the symmetrically disposed flat Adomah system as adapted from the LSPT, and the Madelung table.

    The s-block elements directly surround a rotational axis that extends from the center of one edge to the center of the opposing edge at right angles to it. In my model the counts still increase along this axis, so there is still ‘lopsidedness’ numerically (but then this seems to be a fault of all periodic depictions). A 120-sphere tetrahedron has a continuous outer ‘jacket’ of 100 spheres surrounding a core of 20 (and as discussed over on the Yahoo Group ( everything up to Z=20 seems much more regular), so I’ve wondered whether one could actually start in the middle and move outward instead.

    Just as an aside the rule for constructing these jackets is to sum successive squares of even numbers: The core has 2 sq + 4 sq, and the outer jacket has 6 sq + 8 sq, which are oriented the same way. One can also get inverted tetrahedra by summing intermediately, so 0 sq + 2 sq gives the first four elements which can be hidden inside the 20-sphere tet. What the significance of the next sum, 4 sq + 6 sq (=52), may be, I haven’t any clue. Takers?

    I’ve also constructed periodic systems out of 4-sphere tetrahedra. Two such sets turned out to have been discovered first (to my chagrin, but then one has to take as well as one gives…) by Pierre Demers in Quebec some years ago.

    All of these models have the advantage of assigning one element to one sphere, though they otherwise vary wildly in terms of symmetry and continuity of elements from the original periodic string.

    One can also get symmetrical models utilizing the 4 vertices for symmetry, but the results are far uglier to the mind of someone used to 3D. Perhaps someone from Flatland would find such aesthetic reactions superfluous…

    Because of kinships beyond primary, secondary, tertiary and some quaternary, I still think that extra dimensions might be likely, but now made up for by ‘hidden’ dimensional quality as an offset, so no NET increase on the surface- the figure folds back on itself, negating any increase in numbers of spheres (though this would possibly mean that all elements and their properties would be combinatoric in nature from contributions from higher dimensions (i.e. extra spheres), then reduced by the back-folding (so fewer spheres). Hard to wrap one’s mind around, and I can’t find any references to such a thing. But if good enough for subatomic physics, why wouldn’t it work for us?

    Jess Tauber

  7. Henry,

    I have never built sliced up tetrahedron myself in real world. I built computer model of it using 2×7, 4×5, 6×3, 8×1 and 9×0 blocks. It surely works on computer. The last pair yields edge of the tetrahedron (line thickness of 0) with zero area and zero corresponding elements. I am not sure about irregular tetrahedron that you suggested. I have never tried that. I am sure that Alex will enjoy that. Jess told me once that he actually built physical model around 1979.

    I find it amazing, though, that in order to make regular tetrahedron work, quantum number “ms” values have to be +/-1/2 as guessed by Pauli and later confirmed by Dirac. So, the relationship between the quantum numbers “n”, “l”, “ml” and “ms” has tetrahedral character.

    I had a lot of fun while making 3D Madelung rule diagram using red and green spheres. Each red sphere has to be marked with two consecutive elements: H-He, Li-Be, B-C, N-O…. Green spheres stay unmarked. Than 3D Madelung rule diagram is built like this:

    Put first red sphere (H-He) on top of a table; then put two green spheres next to the red to form triangle and put second red sphere (Li-Be) on top of the triangle. Then put three red spheres (B…Ne) on top of table so they interlock with two green spheres, put two green spheres on top of three red and next to one red and then red sphere (Na-Mg) at the very top. Start fourth layer with 4 green spheres on top of the table next to three red. Put three red (Al….Ar) on top of four green, then two green on top of three red and then one red for K and Ca. Proceed in the same manner, alternating red and green spheres to build up bi-color tetrahedral stack of spheres of any size. The tetrahedron does not have to stop, it can grow infinitely, just like 2D Madelung rule diagram. You will notice that Janet’s dyads occure due to the presence of two types of spheres, red and green (protons and neutrons?). Jess suggested once that it could be electrons and neutrinos.

    I was amazed at first that such simple procedure of constructing bi-color stack of spheres mimics Madelung rule diagram in 3D so precisely and third dimension corresponds to number of “ml” values for each subshell exactly. I think that Alex will enjoy that!


    The many-body problem in classical mechanics and quantum mechanics are alike in one respect: Neither problem has been solved in the general case in closed form.
    Strictly speaking there is no such thing as “the earth’s orbit” about the sun.
    The earth’s motion is influenced by the locations of all the other planets.
    Of course, planet-planet interactions in our solar system are much weaker, relative to sun-planet interactions, than are electron-electron interactions in atoms, relative to nucleus-electron interactions, so, of course, the orbital approximation is much better for our planetary system than it is for atoms. Still, modern electron-density functional theory yields electron-densities for frontier orbitals that many chemists take very seriously indeed. [In my electron-density models, frontier nucleophilic (electron-pair donor) sites correspond, usually, to unshared valence-shell electron-pairs and and frontier electrophilic (electron-pair acceptor) sites correspond to the models’ “pockets”. That simple model accounts for a huge number of organic reaction mechanisms and the stereochemistry of a huge number of inter- and intra-molecular interactions. For me, those (localized molecular) orbitals are so useful I cannot imagine doing with them!]

  9. Valery, about the “one step that [I] overlooked”: I wasn’t concerned with creating a REGULAR tetrahedron, whereas I gather that has been one of your aims. In climbing up the front face of my tetrahedron, block heights increase in the order 2 4 6 8. In proceeding back across the bottom face, block widths decrease in the order 14 10 6 2. So “my” tetrahedron is an irregular tetrahedron. “Doubling up” locations changes the latter sequence to 7 5 3 1 and yields your “perimeter rule”: 2+7 = 4+5 = 6+3 = 8+1 = 9, and, in my case, the possibility of a regular tetrahedron. I’m not absolutely certain about all of that, since I’ve not yet made a model. If I mention it to one of my grandsons, Alex, I might receive one as a Christmas present. Several years ago, when I was in the midst of writing “New Ideas”, Alex gave me a magnificent framed large sheet of stainless steel and, backed by magnetic tape, 120 wood squares with burned into them the element’s symbols and atomic numbers, so that I can move elements around at will. It hangs in a location of honor in our upper hallway near my study. Alex is author of the remark, on seeing the left-step table without H and He, Z = 1 and 2, and asked where to put them, “It’s a no brainer”. Both of his parents are chemists as are three of his grandparents and assorted aunts and uncles, brain-washed, as you might suppose, regarding He and Be. Henry

  10. As for myself, my undergraduate chemistry training allowed me to work in labs whenever money was tight. I even have my name on a patent for synthesizing arachidonic acid inhibitors for a pharmaceuticals firm in the ’80’s, and my last lab position was doing adhesives research.

    The thinking was more fun than being a pair of hands, but mostly this was quashed by superiors. Because of this that last firm missed out on getting in on wound glues, at a time when they were focussed on clipping fractions off cents per pound costwise. Shortsighted would be putting it mildly. I remember telling them about the tetrahedral PT configuration too- the only response was derision.

    Jess Tauber

    writes Scerri regarding Bent’s long comments.
    Of course! Perfectly put!
    Imagine this:
    You have a theory: He/Ne (Helium belongs above neon in periodic tables). You’re holding onto it tightly when along comes a book that, line after line, paragraph after paragraph, and page after page, for over 190 pages, demolishes your theory while making the case, time and again, for an alternative theory.
    How are you going to feel about that book — or a part of it on a blog?
    “How very tedious!”
    So, too, in so many words, said a (He/Ne)-lover and reviewer of “New Ideas”.
    Another thing said: It’s “INCOMPREHENSIBLE!”
    To whom? The man in the street?
    I’ve an intelligent brother, a physicist, supportive of my campaign for He/Be, who freely admits that some arguments for He/Be — which, for a life-long chemist, seem obvious — go right over his head.
    Called to mind is a remark by a participant in an NSF/AAAS Chautauqua short course for college teachers on Thermodynamics, Art, Poetry, and the Environment. “Dr. Bent,” said the participant after a session, “I think perhaps it’s time that you retired from themodynamics for a while.” I knew what he meant. We had a rule in the department of chemistry at the University of Minnesota that the noted physical chemist and infrared spectroscopist Bryce L. Crawford should not be permitted to teach the undergraduate p. chem. course two years in a row, because by the second year everything was “obvious” to the instructor.
    No doubt PK has seen students asleep in classes because what’s being said is “tedious” because “incomprehensible”.
    To characterize an argument as “tedious” and “incomprehensible” is to run the risk, however, of being deemed uncomprehending.
    Revealed are two additional tools in our provocateur’s kit: declarations that an argument is tedious and/or incomprehensible.
    Regarding a scientific and pedagogical issue, consider –

    How do you do that for beginners?
    Can one base the construction on a set of simple axioms,
    in an Aristotelian approach to the Platonic Ideal of an axiomatized system?
    (Construction of any one table is sufficient for construction of all tables, since all satisfactory modern tables are topologically equivalent to each other, and exhibit the same Groups.) Five responses:

    (1) Tell the truth (when in doubt, said Mark Twain). Tell it as it happened: Dobereiner’s triads, Newland’s Octaves, de Chancourtois’s helix, &c.
    “Boring!” say students. To enjoy history one needs to have a history.
    History of the periodic table is for periodic table buffs, not periodic table beginners.

    (2) Use Madelung’s Rule. From where? Periodic table’s shapes. The argument is circular. Further more, exceptions to the rule exist.

    (3) Apply Table Construction Conventions to an annotated Mendeleev Line (NI, front cover), with sequences HNAE and CV (H Halogen, N Noble Gas, A Alkali Metal, E Alkaline Earth Metal; C Coinage Metal, V Volatile Metal).
    Two questions: (a) How does one know how to annotate the Line? (Historically, Tl was often put in Group I, Mg and Pb in Group II, Be and Cr in Group III.) and (b) Where do the Construction Conventions come from? Periodic table’s shapes? The argument, again, is circular — as, indeed, are all arguments that rely on true inductions.

    (4) Apply Table Construction Conventions to elements’ maximum oxidation numbers (NI, Section 11). The results are the same as in (3), if not as impressive, owing to absence of oxidation number sequences corresponding the CV sequences, owing to existence of states of oxidation of the coinage metals higher than +1.
    Methods (1), (3), and (4) have the virtue with beginners that they do not require knowledge of atomic orbitals, or even of electrons.

    (5) Apply Table Construction Conventions to atoms’ first stage ionization energies. Atomic orbitals need not be mentioned. (Even the word “electron” can be avoided, through use of an operational definition of 1st stage ionization energy.) Major and minor zig-zags in and IE vs. Z plot correspond to the HNAE and CV sequences in Method (3).

    My preferred method? Methods (3), (4), and (5), in that order.
    Said the Bellman, “What I tell you three times is true.”
    The result (arrived at in three ways) is (accordingly) a “natural” classification (Whewell).

    It might appear at first glance that the first zig-zag of an IE vs. Z plot, namely H (medium high) He (highest) Li (very low) Be (higher), places H and He above the second zig-zag’s zig: F and Ne. The COMPLETE PICTURE reveals, however, that, for maximum regularity, overall, the first zig-zag should be interpreted as two zags. Remember –

    All parts of it are related to each other through their contributions to the System’s OVERALL SHAPE.
    The overall shape of a periodic table is its most important property.
    It should be foremost in one’s mind when moving elements around in order, e.g., to “maximize the number of triads”.
    Do the moves maximize, also, the table’s TOTAL NUMBER of arithmetical regularities?

    The change H/Li and He/Be to H/F and He/Ne actually diminishes a periodic table’s total number of arithmetical regularities!
    (Arithmetical regularities arising from triads are only one part of a periodic table’s total number of arithmetical regularities.)
    Elevating a Principle of Triad Maximization over the Principle of Maximum Arithmetical Regularities elevates a part over the whole. It’s –

    unless one can argue that some regularities are more fundamental than other regularities.
    Triad regularities are, however, less fundamental than row-length regularities.
    Row-length regularities — a consequence of the Pauli Exclusion Principle and the important quantum mechanical expression (2 l + 1) — are one of the reasons for occurrence of triads, not vice-versa.
    Triads are NOT the reason for row-length regularities.
    “Maximizing number of triads” naively elevates a Triad Principle over the Pauli Exclusion Principle and the quantum mechanical principles embodied in the expression (2 l + 1).
    It gets everything backwards! It puts the cart before the horse!

    Help us understand your position on periodic tables.
    How do you construct from scratch for beginners a periodic table?
    No such method is described in your book.

    As a chemist one takes pride and as a teacher pleasure in capturing the periodic table from chemical data without reference to atomic orbitals, which, in many-electron systems, our PK may agree, are, strictly speaking, nonexistent.
    It’s philosophically unsatisfying to think that the Central Science’s Central Icon is based on a physical approximation!
    The Periodic System is explained by a physical approximation, but based on chemical inductions.
    Nonetheless, it is a fact: There exists a striking Concordance between the ordinal numbers generated by periodic tables and the integers generated by an orbital interpretation of Madelung’s Rule.

    If “right” means “extremely useful” and “real” means “so useful one cannot imagine doing without, in one’s mental map of the world, the thing asserted to be real”, then the orbital interpretation of the Periodic System comes very close indeed to allowing one to say that, for many practical purposes, “orbitals are real”.

  12. Philip,

    I admire your deep knowledge of issues connected with the peirodic law. I understand that you are not a pro also. What is your background in Chemistry?

  13. Valery: Knowing a lot of chemistry does not make you a pro; what counts is that you don’t have a vested interest to defend. It’s interesting to know how you arrived at the tetrahedron – not Platonically at all! I did a lot of work on my ‘galaxy’ with drawing pins and pieces of string.

  14. @Philip, You are “right in saying that [I] had no professional chemist’s baggage to shed”.
    The condition persists.
    I never took chemistry because of the stupid periodic table that belied the periodic law in such an obvious manner that even a mediocre high school student could see.

  15. Philip,

    I have to confess that I have some background in chemistry that goes beyond High school curriculum. I am structural engineer by profession. Chemistry and Material Science are very important parts of engineering curriculum (at least they were in former Soviet universities). I was straight “A” student. I am not well versed in organic chemistry, though.

  16. Thanks, Henry. I enjoyed reading your practical advice on how to build the tetrahedron using s,p,d,f blocks. However, there is one step that you overlooked. In order for periodic table blocks to become slices of the tetrahedron as shown at, elements have to be placed in rectangular 1/2X1 boxes in order to mimic “ml”/”ms” relationship. That is, two “ms” values for each “ml” value, since absolute value of “ms” is 1/2 and all other quantum numbers “n”, “l” and “ml” are integers.

    My initial intent was to shorten LSPT in order to place it on sheet of paper. After I cut length in half by putting element symbols in rectangular cells, I noticed that perimeters of all four LSPT blocks became equal! I was puzzled by that. I could not understan what it could possibly mean. Areas of block are related to number of the elements, but what perimeters have to do with anything? It took me more than a year before I realized that s,p,d, and f blocks, if you put them in order one behind the other, are slices of the tetrahedron.

    I had never had a goal to convert PT into tetrahedron. I am not Platonist. It was completely unexpected outcome.

  17. I left out Lieutenant Colonel W Sedgwick, a military engineer in the British Army in India, who foresaw atoms of zero valency in his book ‘Force as an Entity, with Stream, Pool and Wave Forms’ (1890). He predicted atomic weights of 20, 40, 80 and 120; correct for Ne and Ar, a bit low for Kr (84) and Xe (131).

  18. Philip wrote,

    “It is interesting to see the part that non-chemists have played in this history, starting with Beguyer de Chancourtois, Hinrichs, Janet and John D Clark (all engineers), Edgar Longman (poster artist)… And Melinda, Roy, Jess, Valery, I think I am right in saying that you had no professional chemist’s baggage to shed?”

    Let us not forget Anton van den Broek, the Dutch econometrician who first suggested the concept of atomic number.
    See a 4-5 page section in my book plus a rare photo of him obtained from his family.

    He was cited by Rutherford, Bohr, Soddy and others.

    eric scerri

  19. I love Hebe’s idea of a poster of shapes. Actually the top half of the cover of New Ideas would be along the top as a continuous strip, various tabular shapes would be arrayed along the middle, with Mendeleev’s short form on the left and Valery’s on the right. The bottom part would show various shapes that wind the continous strip into a 2D or 3D shape, including some of Janet’s intermediate forms, with his helix on four nested cylinders bottom right.

    I think that what enabled Janet to arrive at his revolutionary shape was has complete absence of any personal history in chemistry. He was born in 1849, so already 20 before Mendeleev’s table, and his career had been in mechanical engineering. His hobby had been biological form, and he had published over a hundred papers on the anatomy and physiology of animals (mainly the social insects) and plants (especially the tiny spheres of volvox), his drawings were superb.

    It was only around 1926, at the age of 77 that he turned his attention to chemistry, and specifically to the Periodic System. At first he was so new to the discipline that he thought periodicity must come from the structure of the nucleus, as seen in his first publication in 1927. Then he had this flash of insight, that if you moved the two left hand columns to the right hand side, the shape became perfectly regular. At first he balked at the idea of putting H and He over Li and Be, but after a few months hesitation, he decided that regularity had to come first, especially when he found he could derive the table from an elegant helix, passing through some strange and beautiful transformations. It was only then that he learnt of quantum theory and saw that his shape-based conclusion accorded perfectly with it.

    L. M. Simmons, a professional chemist, arrived at the Janet table in 1948, having toyed with Janet version I (H and He over F and Ne) in 1947. He knew Janet’s one article in English but did not give him due credit (forgivably; the editor had completely mangled it). Edward Mazurs championed Janet but did not give an accurate reproduction of a single one of Janet’s shapes, even the table. Jan van Spronsen had a very high regard for Janet, and in his own table (endpaper) he put H and He over Li and Be, but he moved the s block back to the left. And that’s where things stood until Hebe took up the cudgels. For a lifelong professional chemist that was a courageous thing to do.

    It is interesting to see the part that non-chemists have played in this history, starting with Beguyer de Chancourtois, Hinrichs, Janet and John D Clark (all engineers), Edgar Longman (poster artist)… And Melinda, Roy, Jess, Valery, I think I am right in saying that you had no professional chemist’s baggage to shed?


    Your correspondence with your 10th grader, Trevor Seaks, suggests the following activities for him.
    Make a copy of a conventional periodic table.
    Cut out its s-, p-, d-, and f-blocks.
    Cut off the p-block’s He appendage and add it to the s-blocks vacant site above Be.
    Make copies of the blocks.
    Arrange the blocks in the following ways:
    – the conventional arrangement: sdp(f footnoted)
    – the “long form” form of the conventional arrangement: sfdp
    – the “left-step” arrangement: fdps
    – the “left-step” arrangement rotated cw 90 degrees
    – the rotated “left-step” arrangement with its blocks centered (Adomah)
    – the “front-step” arrangements, blocks’ sheets pasted to stand-alone wood rectangles arranged as in NI Figures 50, 51, and/or 52

    Now, I’ve not thought through the following remarks carefully. To do so I’d need to make models. But –
    Suppose one centers the blocks’ sheets on stiff paper arranged, in thought, initially as in Figures 50 – 51, justified at or toward the left.
    Next, in thought, center the blocks’ sheets.
    To hold the blocks’ sheets in place, attach their four corners to four of six edges of a wire tetrahedron whose front face is a triangle resting on its base and pointing upwards and backwards and whose base is a second triangular face facing backwards. Is that structure equivalent to your “Tetrahedron”?
    From there your student might enjoy the challenge of building the corresponding “tangent sphere” model.

    Caution. You might turn this young man into a scientist or engineer.
    His parents might want to be consulted about that.

    A Concluding Remark: The hallmark of a good theory is that it works in situations for which it was not originally designed.

    Currently we have the Janet Block Theory (helium-above-beryllium) and various versions of a Scerri Block Theory, with distorted Janet Blocks. The former theory works with the Valery/Jess Tetrahedron. The latter theory does not.

    Experience with periodic tables suggests changing the warning “Seek symmetry, but distrust it” to “Seek symmetry and regularity, but distrust it UNLESS IT’S PERFECT.”

    The regularity Mendeleev sought for his short-form table was not perfect. On the other hand, the regularity achieved for an imperfectly regular Janet Table, sans H and He, is, on locating H and He above Li and Be, perfect.

    The regularity imposed by IUPAC’s 1-18 column-labeling scheme is imperfect, in that it omits the f-block, and no additions to it render it perfectly regular.

  21. Valery,
    The questions of your 10th grader, Trevor Seaks, are EXCELLENT!
    He’s the kind of student who makes teaching worthwhile.
    Your replies, in turn, have set me to thinking.
    Bohr liked to say that the opposite of a profound truth may be a profound truth.
    That periodic tables can be based on atomic structure is one of the profound truths of our age.
    Might the opposite be true?
    Might arriving at your Adomah Table without reference to atomic structure be possible?
    I believe so.
    Capture the LSTP, sans H and He, in the manner described in the caption for NI’s Fig. 1.
    Add H and He to maximize overall regularity.
    Obtained is Janet’s LSPT.
    Rotate it clockwise 90 degrees and center blocks.
    Obtained is Adomah.
    What’s the new abscissa?
    The previous ordinate, r + 2l = n + l, minus l. I.e., n.
    It’s significance?
    It’s where with increasing Z, r + l (= n) adopts a new, larger value than before.
    It’s where one enters the s-block, at an alkali metal, from a noble gas.
    It’s an index of chemical discontinuity (NI, Section 46).
    I’ve yet to absorb all the information displayed by your tetrahedral construction.

    One might tell Trevor how to construct Adomah from a conventional, sdp(f) PT.
    Elevate the f-block.
    Move the s-block to the right.
    Relocate He, to the (obviously?) vacant position above Be.
    Rotate the construction clockwise 90 degrees.
    Center the blocks.

    It’s heartening to see a student such as Trevor involved in such a mature manner with periodic tables. I imagine you may have had something to do with that. Congratulations!
    Change with regard to periodic tables may well be, when it occurs, a grassroots phenomenon.
    Planck lamented late in his life that new ideas that he could prove mathematically to be correct were seldom accepted by his peers and only entered into physics after they had died and were replaced by a younger generations that had grown up with the ideas.
    You’re on the right track. Keep up the good work!
    It’s a winner for everyone whose life it touches.
    Presumably that will include Trevor’s teacher and some of his classmates. &c. &c.
    Exponential growth looks pretty flat at first. But eventually it takes off.
    No doubt you know the old example of the lake whose lily pad population doubles every year.
    After 100 years the lake is half-covered. When is it completely covered?

  22. Eric scerri says:
    March 19, 2010 at 11:54 pm
    “How very tedious!
    “It’s not me or a few PT designers that Bent needs to convince but editors of journals and university presses.
    “Good luck doing that Henry.”

    Just practicing, Eric.
    Luck favors perfection.
    Joule had to keep returning with ever more perfect experimental results before he’d convinced journal editors to publish his results regarding the mechanical equivalent of heat.
    My recent discussion of “r” and “n” and nodal surfaces, e.g., is a “more perfect” discussion of that issue than what appears in NI, written at a time when it had never occurred to its author that any reader would deny a normalized wave function’s nodal surface at infinity!


    Philip, on March 20, 2010 at 7:23 am, you wrote:
    “David, you are incorrigible! You set us all off on this quest with your statement that you were bored with the old sdp(f) table, yet now, for your ‘Periodic Table of Science Blogs’, you have reverted to the boring shape.

    “Shape is actually something we have not talked about, so fascinated were we by the battle between Hebe and the Philosopher King.”

    I gather that none of the gang’s favorite graphical representations of the Periodic Law has been deemed sufficiently shapely to qualify for David’s final fifteen. Location of helium adjacent to beryllium probably disqualifies instantly any representation in the eyes of individuals not familiar with regularities in the Periodic System that are contingent on location of helium above beryllium. Your remark about shape has prompted the opening question (above) regarding periodic tables’ shape-determing shapes.

    The internal form of Mendeleev’s short-form table — its checkerboard character, from the bottom up — seems to have determined in Mendeleev’s mind the remarkable shape of the top of his table: namely, the highly unusual horizontal locations of B, C, N, O, and F. They’re not what one would have expected from a chemist of Mendeleev’s caliber. Janet’s gaseous helium above metallic beryllium has scarcely anything by way of first-element distinctiveness over Mendeleev’s gaseous fluorine — the most nonmetallic of the nonmetals — above solid, metallic manganese!

    Mendeleev loved regularity! That’s what his Periodic Law is about. It’s what his eka-element predictions were about: the overall shape of a periodic table shaping finer details of the table’s shape — sort of a bootstrap operation. I don’t believe that Mendeleev would have had any problem at all with helium above beryllium, if that assignment completed a table’s perfectly regular shape. Seeking a new shape of the periodic table, David? What’s wrong with Janet’s spiral and left-step graphic representations of the Periodic Law? They’re not new? True. They’ve been around for what? Almost a century?

    As a young chemist, I assumed that the traditional table’s footnoted elements were located beneath the main part of the elements’ arrangement merely to fit the wide arrangement’s shape onto a narrow page. Later I learned that there was much more to that than that.

    Some textbooks of inorganic chemistry have stated that the footnoted elements are not a regular part of the Periodic System!
    Others textbooks have depicted the footnoted elements as TWO SEPARATE SERIES, the “lanthanides” and “actinides”, shown separated from each other, vertically, by a larger gap than exists between blocks’ rows in the table above them.
    Still other authors have maintained, to this day, that all 28 lanthanides and actinides belonged in a single, super-sized group in the d-block.
    IUPAC’s old fuddy-duddies essentially ignore the lanthanides and actinides. They say, disingenuously, that IUPAC does not promote any particular form of the table, but then it often shows only the currently traditional sdp(f) table, around which its 1-18 column-labeling scheme was designed. That scheme makes no allowance whatsoever for an f-block.

    The shape of the traditional table seems to have influenced how chemists have thought about the table’s contents.

    The overall shape of the left-step periodic table, sans H and He, captured from atomic numbers and a natural set of Construction Conventions applied to information regarding memberships of named Groups, elements maximum oxidation numbers, or atoms first-stage ionization energies, determines immediately a pair of natural locations for H and He — “natural” because those same locations, above Li and Be, are indicated as well by several other considerations, including: The Triad Rules, PFED, and a Concordance between ordinal numbers generated by the Table and quantum numbers of atomic physics.

    Periodic tables’ shapes have shaped their shapes.
    Shape is a wonderful thing.
    Thing’s shapes shape all our thoughts.
    All the world’s wonders are wonderful shapes.


    P.S. I told my wife I wouldn’t spend time in a “battle between Hebe and the Philosopher King”, before realizing that as outlandish as PK’s remarks seemed (to me) to be, they might offer a unique opportunity — because uniquely outlandish — to generate in the form of a dialogue a caricature of the sociology of science and the gap between how a scientist argues and how a philosopher of science argues.

    My remarks are directed at PK’s remarks, not at PK himself, except, I suppose, as he identifies his person with his remarks — which may not be a deep identification, however, since, as you and Valery have pointed out, he reverses his remarks from time to time. I’ve done the same thing. Been there (with H and He) and done that (located them above F and Ne), for 36 years! Some people are slow learners.

    My parents wondered at one point if I’d ever learn to talk. I recall recalling that it was pleasant being around adults in one’s own private world, like a fly on the wall, hearing them talk, and not having to respond to what they were saying, pointing being sufficient for personal needs. It would be nice to be able to just point at evidence for He/Be. One might have thought that the shape of Janet’s table would have been sufficient. But chemists, instead of embracing it, as a challenge to domesticate, have rejected it as merely a physicist’s spectroscopic chart, not a periodic table at all! PK is in good company.

    Well, then, how about pointing to the “Concordance”, applicable to any periodic table? And PFED? Unfortunately for He/Be, their shapes are only visible to inner eyes. They’re not, like the Periodic Law itself, capable of being expressed by shapely graphical representations that can be comprehended by outer eyes “at a glance” (Polya). I’d thought NI’s Figures 29, 40, and 44 might serve that purpose, for the Concordance and PFED. They haven’t, at least not for PK. Something additional is needed. Time? Well, time will tell. I believe it’s on He/Be’s side. After all, He/Be has made some progress. There’s now a book about it. “And about time,” Janet might say?

    Over the past two decades He/Be has converted at least one individual, Henry Bent, to HeBe. Conversion of many souls begins with the first soul. And HB wasn’t the first. Before him was Ronald Rich, who used the LSPT in his little classic on Periodic Correlations. And before Rich was Janet.

    North Carolina proclaims on its license plates “First in Freedom” (for some obscure engagement near the start of the Revolutionary War). Was Janet the first for freedom from the mind-constraining, physics- and PFED-denying tyranny of helium-above-neon?

    Heisenberg asks, “How do you achieve a successful revolution?” His answer: “Change as little as possible.” Change He/Ne to He/Be? It revolutionizes how one looks at the periodic table — perhaps literally. For to obtain after that change the shapely tabular form of the table you endorsed March 20, rotate Janet’s tabular arrangement of blocks clockwise 90 degrees and center the blocks.

    Would it destroy the beauty of a landscape or a portrait version of your Spiral to use the space at its four corners to indicate, in an abstract manner, with a focus on shape, absent symbols of the elements: (1) the shapely spiral; (2) the spiral cut and de-spiraled to the long form of the traditional periodic table; (3) the spiral and/or the traditional table transformed to the shapely left-step table; and (4) the left-step table transformed to the even more shapely Valery table?

    What more could David ask for? I’d like to place my order for a copy right now. PK should have a copy, to show his students.

    Perhaps the transformations (1) to (2) to (3) to (4) could be the second side of a two-sided poster, so that when a wall-hanger tired of the shape(s) on one side, (s)he could turn it over.

    Yours for better posters for a better understanding of Chemical Periodicity through successive Aristotelian approximations to a Platonic Ideal, HeBe.

  24. I would like to share with all folks here my recent email exchange with a high school student that was given assignment to write about ADOMAH Periodic Table in school. I thought that his questions and my answers might have some value for this discussion. Here it is:

    On 3/19/10, Trevor Seaks wrote:
    Dear Valery Tsimmerman

    I was hoping that you could answer a few questions about the Adomah periodic table and yourself. I am presently doing a project over it for my 10th grade pre-AP chemistry class. The questions are as follows:
    How is the Adomah table different from the regular periodic table?
    What does the Adomah table display best?
    How are trends shown?
    When would the Adomah table best be used?
    What are the cons of the Adomah table? (if any)
    What else have you done?
    What was your purpose in making this table?
    When and where did you make this table?
    How is this table used?

    Trevor Seaks
    Thanks for your questions. Here are my answers:
    1. Adomah Periodic Table (APT) is based on major alternative depiction of the periodic system: Left Step Periodic Table (LSPT) that was introduced by Charles Janet in 1928-29. In APT rectangular blocks are arranged in s,p,d,f order, that correspond to angular momentum quantum number values: l=0,1,2,3. That is why both APT and LSPT are called spdf-tables. In traditional PT, that is also called sfdp-table order of blocks representing quantum number “l” is broken: l=0,3,2,1. Also, periods in traditional table are horizontal and groups are vertical. In Adomah PT periods are presented as cascades, horizontal rows represent groups of elements and vertical columns show electron shells that correspond to the values of principal quantum number “n”. As you can see, unlike traditional Periodic Table, Adomah Periodic table is built with respect to electron structure, identified with the help of spectroscopy;
    2. Adomah is the only periodic table that allows direct readout of quantum number “n”, that is the electron shells. It can be used for quick derivation of electron configurations and, at the same time, retains all important attributes of traditional periodic table, such as groups and periods;
    3. Trends are shown in following order: Rare earth metals, transition metals, metals, semi-metals, non-metals,inert gases, alkali metals and alkaline earth metals at the base of the table. All groups of Adomah PT are the same as in traditional PT and follow each other in the same order. All other trends, such as second and tertiary periodicity, electronegativity, electropositivity, first element distinctivness, atomic core radiuses, oxidation states, first and second ionization energies, etc. are well reflected by APT.
    4. Adomah Table is most useful for teaching and learning how to write electron configurations, quantum attributes of atoms, it can also be used for the same purposes as traditional PT, that is classification of chemical elements;
    5. As I stated above, APT is the only Periodic Table that allows direct readout of major quantum numbers “n” and “l”, that is electron shells and subshells. Other cons of APT are listed in previous answers and at web site;
    6. I and my partner, Jess Tauber, have also determined that periodic system is naturally symmetrical and tetrahedral and is based on Tetrahedral numbers that can be found in fourth diagonal of Pascal Triangle. That is major mathematical regularity of the Periodic System that has deep meaning and could potentially lead to new discoveries in quantum mechanics, as well as in atomic and nuclear Physics;
    7. The purpose was to create periodic table that better follows electronic structure of atoms than traditional table;
    8. I made this table at my home in Maryland, USA. I created first image of the Table in February, 2006;
    9. Go to my web page and click on User Guide button on the left side of the screen in order to see example of simplified method of writing electron configurations;

    Good luck with your project.

    Valery Tsimmerman.

  25. @Henry, Yes, the picture of Glenn Seaborg and his appreciation of the AAE was a real pleasant surprise.

    Regarding a starting place for design of a periodic table, I suppose all of us started with a flat table, such as we found on the wall of the classroom and inside the cover of our chemistry books.

    I have, as you asked, thought of returning to 2D, stimulated by a professor who indicated a preference for a periodic table that could fit in a pocket. There is nothing the AAE can’t do, I said.
    The DeskTopper, in what I call a “RoadKill” adaptation, flattens out just fine, and instead of rotating, one just pushes the segment on the right around the back to the left to see all the elements. See it at

    I returned the very same model to 3D with staples, where it can be seen as the Y/LU version at

    You are no doubt distressed that H and He are so conventionally placed on these examples. I have both a personal and a pragmatic reason for doing so.

    As the educational application of the AAE is positioned in the introduction to chemistry curriculum, scaffolding the pre-knowledge of students (of the standard table) and leaving them at the next lesson (no doubt employing the standard table), there does not appear to be a profit in the kind of convincing that I would have to do (when even the experts on this blog appear not to always be in agreement with each other – not to mention with the ‘public’ and the ‘establishment’) for potential purchasers if placing H & He other than where the students are coming from and going to. Not my job to build ”the Bridge to Nowhere”, but to try to eke out a living selling what teachers want, in order to make their lives a little easier and classroom time more effective. When IUPAC gets wise, it may have an effect on my market – and therefore, me, and my product.

    The personal reason is that I just LOVE the “Hydrogen Crown”!!

    Using it to form the whole first period allows me to start the table in the stars with most of the rest of Hydrogen (wait ‘til you see the next AAE! [ a peek at ] ). It starts connected to Li and touching both Be and He, and by looping down with a very stretched box, glancing along the top elements of the groups in the s-block (actually touching Carbon), comes to rest with a corner to Ne and a side to both F & He.

    Lord knows how many diads, triads and knights moves the trip accomplishes in, I must say, One Fell Swoop!

    When developing the AAE from lspt for you to evaluate an idea of adapting the kind of hands-on teaching, which I was interested to learn you had done, I left off H & He, as I didn’t wish to expose myself to the ongoing conflict of fact/fiction/and opinion. (This illustrated series of steps for a new product is posted at
    The symmetry of H & He atop the s-block in the first steps would be nice, but how to fly the first period to the second with a stretch He atop the p-block groups? Look at the lost Hydrogen drama! …and whatever else of the d,t, & kms that H provides.

    All the best,

    More from Hebe for our Philosopher King

    Cited earlier as evidence of PFED (the Phenomenon of First-Element Distinctiveness), denied by PK, were first-stage ionization energies of the cores of atoms of Group II: He Be Mg Ca Sr Ba. Immediately below is the same information for atoms of Group I: H Li Na K Rb Cs:
    Cores’ 1st-stage IE’s for Group I: infinite 76 47 32 26 23.
    As for Ca Sr Ba, one might called their neighbors K Rb Cs the “true” alkali metals.
    And as for Group II, first-element distinctiveness hits one between the eyes, with evidence, again, of second- and third-element distinctiveness.
    In “Principles”, Mendeleev devotes an entire chapter to Group I’s third element: sodium.

    All Groups of the p-block yield the same pattern, in so far as one can check it from known ionization energies of atomic ions.
    The pattern is similar to those established by core’s sizes (NI, p37).

    Let A, B, and C stand for the 1st-stage core IE’s of a Group’s first three elements. A measure of first-element distinctiveness is the ratio R = (A – B)/(B – C). Through the p-block, left-to-right, R increases from 2.45 for the B Group through 3.08 for the C Group, 3.60 for the N Group, 3.63 for the O Group, and 3.90 for the F Group to 4.05 for Ne Group.

    As Jensen pointed out, first-element distinctiveness increases block-to-block in the order s >> p > d > f, the block order of the left-step table, left-to-right.
    By the R-measure, first-element distinctiveness also increases left-to-right within the p-block, as illustrated, also, by core radii (NI, p37) and Allen’s electronegativities (NI, p97).
    Fact and theory seem to fit each other nicely.

    Of course, once one grants first-element-distinctiveness, particularly in the s- and p-blocks, that knocks out completely He/Ne.

    INCIDENTALLY, isn’t it inconsistent, somewhat, to state that the order of a block-to-block trend in first-element distinctiveness is s >> p > d > f, which is certainly true when H and He reside in the s-block, above Li and Be, but then to deny that helium’s natural location in periodic tables is in the s-block?

    Yes, beryllium is often cited as an instance of first-element distinctiveness.
    (The s-block’s huge first-element distinctiveness is accompanied in the s-block by distinctive second-, and even third-element distinctiveness.)
    But Be’s distinctiveness, with respect to Mg, is not nearly what H’s distinctiveness is, with respect to Li.
    Thus, one loses, with H and Be as first elements in the s-block, a trend within blocks of first-element distinctiveness, increasing from left-to-right.
    One way to save an intra-block, left-to-right trend in first-element distinctiveness in the s-block would be to remove both H and He from the s-block, as ES does.
    But then one no longer has the first part of Jensen’s block-to-block trend: s >> p,
    since the distinctiveness of, e.g., N (with respect to P) is greater than that of, say, Li (with respect to Na) [cf. NI, p37.]
    [Core radii and ionization energies yield the same conclusions regarding intra- and inter-block trends in first-element distinctiveness. The whole picture seems to hang together nicely.]
    In summary: facts and logical consistency require H/Li and He/Be.

    ADDED NOTE: He/Be Theory predicted, in a sense, the facts cited above regarding first-stage ionization energies of atomic cores, in that, owing to He/Be Theory, Hebe went looking for the cited facts, expecting to find exactly what, in fact, has been reported herein.
    The facts existed in the literature before Hebe was aware of them , or had even formulated He/Be Theory.
    The Theory came first, then knowledge, for Hebe, of supportive facts.

    That was the order of events, for the most part, throughout the writing of “New Ideas”.
    He/Be Theory told Hebe what to look for. And what was sought for was usually found.
    (It would have been nice to have had more ionization energies of atomic ions.)

    The situation calls to mind Einstein and Brownian Motion. Believing in atomic theory, Einstein predicted the motion without being aware of its existence, he claimed. That’s called what in the philosophy of science, postdiction?

    Don’t some philosophers of science consider theories’ postdictions — fitting and correlating known facts — as significant as theories’ predictions, if, indeed, logically (if not psychologically) essentially the same thing?

    In writing “New Ideas”, Hebe was constantly on the lookout for predictions based on the shape of the LSPT, particularly He’s contribution to that shape, sitting above Be. And then it would turn out that the predicted facts were already known.

    Einstein wrote of his Brownian Motion Paper — his most cited paper — that “My major aim was to find facts which would guarantee as much as possible the existence of atoms of finite size.”

    Hebe’s major aim in writing “New Ideas” was to find facts which would guarantee as much as possible the usefulness of locating helium above beryllium in periodic tables.

    Apologies, folks, for taking up so much space in this blog. The available space does seem, however, to be virtually semi-infinite. Called to mind, by way of an explanation for Hebe’s behavior, is a question one of his friends and colleagues at the University of Minnesota, professor John Overend (an Oxford graduate, originally from Wales) liked to ask: “How can you tell when a piece of research is successful?” John’s answer: “Are you encouraged to continue?”


  27. Professor Bent was referring to a telephone conversation we had, which I enjoyed very much as well.. There are many parallelisms to be found in a number of different fields where there is still contention over the nature of the systems they deal with, from basics such as how to assort, classify, or rank combinable primitives, through representation of rules of combination and contexts of usage. We see this sort of thing in linguistics all the time- in the hard sciences much more of this is already settled, but blood still gets spilled. It’s complex systems, not necessarily turtles, all the way down.

    By the way, has anyone ever considered the periodic system on a Moebius strip? Or for the more adventurous, a Klein bottle or higher-dimensional object?

    On a Moebius strip, duals can be represented continuously and as opposites simultaneously. With a Klein bottle? Perhaps different orientions of path relative to the inside/outside nexus accounts for the continuous periodic line as well as duals and increasing period lengths? A marriage of this sort of thing with the close-packed tetrahedral structure, so that s and any outermost subshell maintain direct connectivity (as they do NOT in the angled ring system after 2 and 3p).

    Jess Tauber

    Arguments for He/Ne Shot Down (NI, pp115-116)

    To the 10 invalid reasons cited in “New Ideas” for locating helium above beryllium, Scerri adds two new ones.

    Scerri Reason Number 1: Created with He/Ne is a new primary triad He Ne Ar.
    True, but at what cost?!

    Atoms in all other vertical (primary) triads have the same number of outer electrons.
    Not so He Ne Ar!

    Types of atoms’ outer electrons in all triads of the s- and p-blocks are the same.
    Not so He Ne Ar!

    Nowhere else in the Periodic System does a triad contain its column’s first element.
    Not so He Ne Ar! (and Be Mg Ca, because missing above Be is He!)

    Scerri Reason Number 2: Throughout its history in periodic tables, and to this day, helium appears above neon. That’s where everyone puts it. That’s the general consensus. Helium above beryllium would just upset people. Why rock the boat?

    Reason Number 2 is not a scientific reason.
    By that reasoning, the earth would still be flat, the sun circling it, and its God-given species invariant.

    “I accepted He/Ne,” a student might say, “until I saw your reasons for it!”

    No scientific reasons for He/Ne exist.

    On the other hand, many scientific reasons for He/Be exist.
    Not one recently cited reason for He/Be has been shown by logical reasoning to be wrong.
    (It is argued, illogically, that such reasons do not exist. Scientific evidence is denied, incompetence of its discoverer asserted. The deniers have their heads in the sand.)

    Scientific systems live dangerously.
    ONE EXCEPTION to a logical system brings the entire structure tumbling down!
    To refute He/Be Theory, one need find merely one exception to its implications!
    There’s an exercise for He/Be skeptics.
    If He/Be Theory is correct, it will keep them out of mischief forever.

    An easier challenge: State one — merely one — scientific reason in support of He/Ne.

    Failure to rise to the challenge or two execute the exercise means that the entire campaign for He/Ne against He/Be has been COMPLETELY UNPHILOSOPHICAL.

    Am I flogging a dead horse?
    It’s still galloping around the countryside.
    Evidently at this time one cannot say too often or in too many different ways that He/Ne is wrong and He/Be is right.
    The truth will out, it’s said, but sometimes very slowly indeed.
    He/Ne has been ingrained in science’s collective psyche for over a century.
    It’s removal may take a little time.
    After Lavoisier’s new theory of combustion, phlogiston theory didn’t disappear overnight.

  29. David, you are incorrigible! You set us all off on this quest with your statement that you were bored with the old sdp(f) table, yet now, for your ‘Periodic Table of Science Blogs’, you have reverted to the boring shape.

    Shape is actually something we have not talked about, so fascinated were we by the battle between Hebe and the Philosopher King. One of the problems of sdp(f) is that it is wider than it is high. It is even worse with sfdp or fdps. This means that either it has to be squeezed down to fit on a printed page, which is normally higher than it is wide, or it has to be printed sideways and the book has to be turned through 90 degrees. (Of course the same is not true of a poster or a computer screen.)

    One of the many virtues of Valery’s Adomah is that it is higher than it is wide – actually twice as high, but the boxes could be widened. It means reading the sequence of numbers downwards, but one soon gets used to that. In fact columns of numbers are frequent in scientific publications. For the computer screen, Adomah can be printed in its horizontal version.

    Most spirals are circular in outline, which is also the wrong shape. I designed my Chemical Galaxy specifically so that it would fill a sheet in the An series. (For Americans, this is a series of rectangles in which the long axis is 1.414… times the short axis, so that each size is exactly half as big as the previous one. A0 is one square metre and An is 2^n square metres; yet another reason for you to adopt the metric system!) I thought a poster would be easier to read in the ‘landscape’ version. Now, with the printed page in mind, I am designing a ‘portrait’ version.

  30. Doesn’t it bother you to think of all your students who have been and are being unnecessarily deprived of the insights into the Periodic System that are contingent on location of helium above beryllium?

    Do you present your students with BOTH SIDES OF THE STORY: the short story for He/Ne and the much longer story for He/Be; and then let them decide where they want to locate helium? That would be an honorable thing to do. Anything less than that, GIVEN WHAT WE KNOW TODAY, would be dishonorable. Teachers have a moral responsibility to be as open-minded and informed as possible.

    Just from a personal point of view, think of all your students who may some day see helium-above-beryllium in periodic tables and, after learning of the logical rationale for that relocation, wonder: Why weren’t we told about that in college?

    Take it from an old-timer. It’s always nice, in the long run, to be on the wave of the future, rather than stuck in a century-old backwater.

    This comment was edited for brevity and to remove inappropriate statements.


    I thoroughly enjoyed our conversation today. You mentioned Valery’s “Perimeter Rule”:
    For Z through 120, block depth plus half block width equals 9.
    It’s one of several mathematically equivalent ways to state periodic tables’ arithmetical regularities.

    One-half block width is (1/2)[2(2 l + 1)] = 2 l + 1.
    Block depth is 2D – 2 l, where D = the ordinal number of the LSPT’s last dyad.
    For D = 4, block depth = 8 – 2 l.
    Adding one-half a block’s width, 2 l + 1, yields 8 + 1 = 9.

    Linguist analysis adds new dimensions to one’s understanding of controversies regarding the periodic table. Revealed are insights into deep linguistic features of languages, and, perhaps along the way, into the sociology of scientists and philosophers of science.


  32. How very tedious!

    It’s not me or a few PT designers that Bent needs to convince but editors of journals and university presses.
    Good luck doing that Henry.


    (1) A CORRECTION. Scerri is, strictly speaking, right. He did not say EXACTLY what I’d said (from memory) he’d said (in Sci. Am. (?)). But really, that’s sort of beside the point, his ref. to Sci. Am., and perhaps not quite the whole truth. Here’s what he wrote in JCE, Feb. 1991, p123:

    “The proposed new fdps version shown in Figure 2 does not yield any new predictions as to chemical or physical behavior of the elements [not true by the time of the publication, 2006, of NI, subtitled “An Introduction to Leading {New} Uses of the Left-Step Periodic Table”], and this in itself argues against its adoption. Moreover, the proposed version leads to grouping together of the element helium with the alkaline earth metals, which is a little difficult to accept in chemical terms. . . NOT SURPRISINGLY [emphasis added] this proposed electronic form of the periodic table has not been generally adopted by chemists . . .”

    (2) SIGNIFICANCE OF A CHEMICAL ROUTE TO THE LSPT. One of NI’s leading contribution to chemical pedagogy may be its provision of grounds for dropping the phrase “electronic form of the periodic table”, through the book’s demonstration of chemical captures of the left-step periodic table WITHOUT REFERENCE TO ELECTRONS OR ORBITALS. That’s in the spirit of Feynman’s remark that sometimes it’s useful to see how little theoretical machinery one really needs in order to obtain a given result. Chemical capture of the LSPT is what makes the consilience between ordinal numbers generated by Chemical Periodicity and the quantum numbers of atomic physics so extraordinary.

    (3) DEFINITIONS of “n” AND “r” IN TERMS OF NODAL SURFACES. Scerri complains that I’ve introduced new definitions for quantum numbers. So I have. My book’s title is, after all, “New Ideas”. Included are new ideas (Mine and mine alone? I’m not sure.) regarding two definitions. The question is: Are the “new ideas” useful? Judge for yourselves.

    Eugen points out that Scerri and I can both use the relation n = r + l. So far so good. But that’s not the entire story.

    In my identification of n and r, n is the total number of nodal surfaces and r is the total number of radial nodal surfaces. In the alternative definitions that Scerri prefers, n is the total number of nodal surfaces NOT COUNTING THE ONE AT INFINITY and r is the total number of radial nodal surfaces NOT COUNTING THE ONE AT INFINITY. What’s the gain in that, for students? If the inelegance of the latter definitions were the only issue at hand, Scerri’s tantrum would be a tempest in a teapot, over an issue of taste. But, as with periodic tables, inelegance in this instance hides deep physical principles.

    Strictly speaking, SCERRI’S PREFERRED DEFINITIONS OF n AND r, FROM THE LITERATURE, DO NOT CORRESPOND TO PHYSICAL REALITY! That fact has an immediate kicker. (The proof of the usefulness of definitions is in the pudding.)

    I can write, in terms of nodal surfaces, that r ≥ 1 and n ≥ 1.
    Scerri must write, IN TERMS OF NODAL SURFACES, that r ≥ 0 and n ≥ 0.
    But, in fact, never is n = 0!
    And that’s only the beginning of the story. The most significant part follows.

    One of the famous relations in quantum mechanics that drops out of solutions of Schrodinger’s equation for the hydrogen atom is the relation l ≤ n – 1. It’s widely used by students in working out atoms’ electron configurations. They couldn’t get very far in Chem101 without it.

    [Consequently, it’s a huge weakness in chemical education today that that relation, l ≤ n – 1, just appears out of the blue. Students must accept it. There’s nothing else that they can do. They can’t understand it. Chem101 is a faith-based course. It may be, indeed, worse than no course at all! Students arrive fearful of what they are about to encounter and leave confirmed in their fears. “Chemical educators” should be advised: “Above all, do no harm!”]

    Both Scerri and I, to repeat, can write n = r + l. I can write, in addition, as mentioned, r ≥ 1. Add that to the previous relation. Presto! n ≥ 1 + l; i.e.: l ≤ n – 1. Q.E.D.

    [It’s that simple. If you frame definitions in strict accordance with physical reality, nice things tend to happen. If I knew that I’d pass into the history of chemistry for that derivation alone, I’d be happy. (I’ve not checked the literature to see if others have used it. I first used it in a graduate course in quantum mechanics at UConn in 1953, and later in general chemistry. Over the years many students have seen it, from me, if from no one else.)]

    What can Scerri do? Adding r ≥ 0 to n = r + l yields l ≤ n. Wrong!

    How, then, does a Scerri introduce freshmen to the relation l ≤ n – 1? With a wave of the hand? (Quantum mechanics used to be called “wave mechanics”.)

    My prediction is — if past performance is prologue — that our provocateur will respond with complete and absolute silence regarding this situation in which his choice of definitions of the quantum numbers n and r IN TERMS OF NODAL SURFACES leads to the incorrect relations n ≥ 0 and l ≤ n.

    Historical Note: I sense that it may be correct to say that the nodal-surface interpretation of the principal and radial quantum numbers “n” and “r” FOLLOWED introduction in discussions of the hydrogen atom of two integers one less than my “n” and “r”. It’s rather like He/Be following He/Ne. Science progresses. It gradually cleans up its act. I’m grateful to our provocateur for instigating what might be correctly described as a small part of that clean-up.

  34. Roy,
    That’s a beautiful picture of Glen Seaborg with the AAE!
    In constructing it, you start with the two-dimensional LSPT.
    Have you thought of returning to two-dimensions, from the AAE?
    It’s projection on a flat surface, as loops, with subsequent spreading out of its curves would yield, it would seem, one or more of various graphic representations of the Periodic Law popular with some people.

    To “domesticate” the AAE for people unfamiliar with it, one might start with the traditional s(f-footnoted)dp table and proceed through the sfdp and fdps tables to the AAE, followed by its planar projection, which, stretched out in one dimension, is Mendeleev’s Line, easily curled up to Philip’s spiral. Along the way one could branch off to step-pyramid tables, and Valery’s table, and its sequels. That might bring everybody together, and illustrate that all representations of the Periodic Law, of ordered Z-values, are topologically equivalent to each other.


    Illustrating an old adage, Philip, are your comments of March 19, 8:05 am that –

    “You [ES] have rearranged [the periodic table] by (1) removing the f block to a footnote, (2) slicing the p block in two, between groups VI and VII and (3) moving the four groups on the right of the cut to the left of the table. All that for the sake of bilateral symmetry and a couple of triads! I’m sorry, but I can’t see the point. What is a learner to make of ‘periods’ such as F-Ne-Na-Mg-[gap]-Al-Si-P-S?!


    [One thing to say for the F-Ne-Na-Mg . . . Al-Si-P-S table: It does list the most commonly named Groups first. The LSPT lists them last.]

    Sanderson’s truncated table for beginners, with both its f- and the d-blocks footnoted, and with H above Li and He above Ne, has “bilateral symmetry” — granted certain restrictions on atomic numbers. That restriction in itself suggests that such tables may not reflect fundamental features of the Period System.

    Latent in Mendeleev’s Line are several deeply significant REGULARITIES. But the Line itself exhibits no symmetry whatsoever! On the contrary, exactly contrary to what one must have for true and exact symmetry, elements occur in the Line ONLY ONCE.

    We seem to need new(?) terms to describe particularly shapely representations of the Periodic Law.

    Centering the LSPT’s dyads yields a step-pyramid table, with bilateral symmetry — if one doesn’t look closely at the Table’s entries; and, again, subject to restrictions on Z. Needed to guide the eye down a Group are vertically separated dyads tied together by tie-lines.

    Elevating the LSPT’s blocks by an amount equal to their l-values (corresponding to plotting vs. l the quantity n rather than n+l) yields Valery’s table with, again, bilateral symmetry — if, again, one doesn’t look closely at the Table’s entries; and, again, subject to restrictions on Z. Needed to guide the eye along periods are horizontally separated blocks tied together with tie-lines.

    That said, because the Periodic System’s fundamental explanation lies in atomic structure, where symmetry plays an important role, perhaps one should consider carefully Valey’s suggestion — and Jess’s — that symmetry does, indeed, become manifest in some representations of the Periodic Law.


  36. FOR SHAME!
    You’re dissimulating, Eric.
    On March 18, 2010 at 6:44 pm you wrote:
    “The person who really convinced me, at least temporarily, of the value of the LST was Gary Katz in his clear and concise article in The Chemical Educator whatever I may have said to Henry at some time.”

    A reader might wonder, however: Why would a “clear and concise” and convincing article on such an important topic as location of the s-block in periodic tables appear in an obscure journal, The Chemical Educator, rather than in the Journal of Chemical Education, location of many articles on periodic tables.

    You and I know the reason for that, Eric.
    Gary tried to get his article published in JCE, and failed.
    An unfavorable review by a referee.
    Namely? You know. Tell us. Go ahead. Tell the truth.

    This is ridiculous!
    Changing your mind all the time is one thing.
    And stating irrelevant and partial truths is another failing.
    But surely this is beyond the pale!
    It doesn’t add one iota to the advancement of science.

    With apologies to the rest of the gang for dwelling on an issue of no scientific significance whatsoever — or maybe not?
    (One likes to know, in science, how reliable one’s sources really are.)


  37. I know you guys are too busy with this one post (still) to worry about what else happens on the Sciencebase blog…but…I created a Periodic Table of Science Bloggers today. Within about 11 hours it’s almost fully populated. I just need blogger to represent the following elements to come forward and request a slot now: Zr, Nb, Ru, Rh, Pd, Ag, Hf, Au, Te, xe, Pb, Po, Hs, Nd, Pm, Tb, Ac, Np, Pu, Cf, Er, Fm, Yb and UUx elements 113-118

    Needless to say, Sciencebase is “Sb”

    The speed with which this post went viral is quite amazing, I tweeted about it first thing this morning (about 8am UK time I think it was). And like, I say only a couple of handfuls of elements yet to find bloggers. I’m only adding them if people specifically ask, so please don’t send suggestions unless they’re yours and please don’t send for any elements that are coloured bronze or gold on the PT as they’re already taken.

  38. Jess: I sense that I don’t understand fully the subtleties of your comments of March 18, 10:41 pm. For what they are worth, here are some thoughts prompted by them. They may be wide of the mark.

    Chemists have traditionally made a big deal out of Periodic TABLES vertical columns and horizontal periods. Columns have meant primary kinships: same number of valence-shell electrons of, generally, the same type. That’s what “verticality” has meant.

    The electronic interpretation of secondary kinships is: same number but different types of valence-shell electrons and, to be chemically significant, same maximum oxidation state.

    The electronic interpretation of tertiary kinships is: same number of valence-shell vacancies and hence, sometimes, same minimum oxidation state.

    “Primary”, “secondary”, and “tertiary” indicate kinship closeness, not kinship strength.

    Why are “secondary” kinships ranked “ahead” — as to closeness — of “tertiary” kinships?
    In the history of periodic tables they have been MUCH MORE IMPORTANT than tertiary kinships — at least until recently (with the helium issue).
    Also, secondary kinships FAR outnumber tertiary kinships.

    Secondary kinships create periods of different lengths.
    Periods of different lengths have led to the creation of some 700 periodic tables.
    Imagine the absence of secondary kinships.
    We’d have have one, simple, rectangular table, the same for everyone —
    except, perhaps, for the location of H and He? At the far right or the far left?.
    (Electronic structure might place them at the far left.
    Maximizing number of triads would place them at the far right.)

    I’ve never been particularly moved by “knight’s move”. The reason for it? Sort of vector addition of the traditional “diagonal relation” and the “inert-pair effect”? The first move takes one down and to the right one space, the second one to the right two spaces. The completed move: 1 down and 2 to the right (if 1 + 2 = 2). That model predicts that knight’s move is always associated with atoms that exhibit the inert-pair effect. Is that so? I’m not up on the move. What are the leading examples of it? Perhaps I need to give it more thought. I recall seeing it discussed in Scerri’s book. At the time I took that as a mark of poor judgment.


  39. Professor Bent wrote:
    “If they were logical, textbooks would go from Madelung’s Diagram, which they seem happy to accept, to your periodic table to Janet’s table to the sfdp table to their beloved s(f-footnoted)dp table, which, wrapped on a cylinder and then projected on a plane yields a Janet/Stewart spiral”

    Exactly! It is so coherent!

    Also. If they were lucky enough to notice that Madelung rule diagram, where “l” is abscissa and “n” is ordinate, could have depth, third axis: “ml”. Such “ml” axis would have negative and positive branches, that is -l,…,0,…,+l. Then, it would become unequivocal: Periodic System is tetrahedral by nature! Would they be happy to accept this fact? I do not see why not, except, it would be hard to show this on flat sheets of typical text book. However, with the help of 3D modeling that modern computers allow, this would add value and increase interest for the Madelung rule diagram, for the phenomenon of Periodicity and for the Periodic Table.

    Then, of course, they would be forced to accept He/Be and they would not like it. They rather be incoherent than to accept obvious.

  40. Eric: You are still convinced of the value of the LSPT – in Janet’s version I (with H and He over F and Ne), which he considered in April 1928 and rejected in November 1928. You have rearranged it by (1) removing the f block to a footnote, (2) slicing the p block in two, between groups VI and VII and (3) moving the four groups on the right of the cut to the left of the table. All that for the sake of bilateral symmetry and a couple of triads! I’m sorry, but I can’t see the point. What is a learner to make of ‘periods’ such as F-Ne-Na-Mg-[gap]-Al-Si-P-S?!

  41. If one accepts Prof. Bent’s classification of primary, secondary, tertiary, and quaternary kinships, and that they are mathematical/geometrical in nature, one still has the issue, in any hierarchical system (such as the periodic system), of relative ranking.

    Given knight’s moves and diagonals, aufbau anomalies, relativistic effects and various types of coupling, I’d say that the rankings must be changing in different places within the geometry of the system. Surface behavior of elements is not therefore uniform, and we have a complex featural landscape which makes things much more interesting than they otherwise might be. There is still method behind the madness, and room for primacy of the He/Ne kinship rankingwise, even if the kinship isn’t primary geometrically. I’d still put He over the alkali metals, but so what? Other elements feel much more at home in other columns too, but we don’t stack them that way.

    Jess Tauber

  42. ES, your remark “Induction in mathematics [brought up by whom?] has a different meaning than in philosophy of science [or at least in science]” is true, BUT BESIDE THE POINT.
    In his book, Polya is not talking about ordinary mathematical induction. Far from it! The remark “Polya is of very little relevance too” is irrelevant. To assume that he is talking about “induction in mathematics” is naive indeed! A glance at his two volumes would make that clear in an instant.

    [Incidentally, so that we may be certain that we are talking about the same thing, what are your two or three favorite examples of INDUCTION IN THE PHILOSOPHY OF SCIENCE?]

    Polya talks about the kind of induction featured by the Inductive Sciences. His facts are mathematical facts. His ideas are mathematical theorems. The mental tilt induced by Polya’s discussions is essentially the same, in my experience, as the mental tilt induced by my work in chemistry. That’s why I used to study Polya.

    Polya didn’t title his book “A Philosophy of Science”, but as a subtitle, that wouldn’t be far from the mark. I recall my father saying that Stadler, the University of Missouri’s leading researcher in the 1930s and 1940s, in genetics, used to require his graduate students to read Polya’s earlier classic titled “How to Solve It”. “The Role of Induction and Analogy in Mathematics”is a deeper study, a summary of years of mathematical research, for which Polya was famous, and years of teaching, students and teachers of mathematics, for which he was also famous.

    You’ve characterize some of my research as merely a “guess”. Exactly!
    Polya says: Of course, let us teach proving. But, above all, let us teach guessing!
    In research in mathematics as in theoretical research in the sciences, guessing comes first, then proving.

    Are you familiar with the classic by Hadamard titled, as I recall (I can’t find my copy at the moment) “The Role of Imagination in Mathematics”? Another famous volume (that I’ve given a granddaughter) has the title “Mathematics and the Imagination”. And as I recall, a famous book, around a century ago, on the philosophy of science, was titled “The Philosophy of ‘What If . . .'”

    Most of my guessing in science has started with the question: What if . . . ?
    What if one formulated chemical thermodyamics in terms of ∆S(total) rather than ∆G(system)?
    What if one simply defined ∆S(mech. sys.) = 0 and ∆S(thermal surr.) = ∆E(th. surr.)/T?
    What if one assumes that hybridization accounts for variations in bond lengths, rather than hyperconjugation?
    What if one represented valence-strokes by valence-spheres?
    What if one takes the bumps and hollows of valence-sphere models seriously?
    What if one sought to axiomatize Chemical Periodicity through a natural set of periodic table construction conventions?
    What if one imposed a condition of maximum regularity?
    What if one took helium’s location above beryllium seriously, as a chemist?
    And so forth.

  43. Induction in mathematics has a different meaning than in philosophy of science.
    Polya is of very little relevance too.

    eric scerri

  44. The person who really convinced me, at least temporarily, of the value of the LST was Gary Katz in his clear and concise article in The Chemical Educator whatever I may have said to Henry at some time.

  45. Harking back to Henry’s posting of 3/14/10 (not to mention the initial entry of 3/18/08 by David Bradley’s regarding being bored), where he lists historic steps in the development of the periodic table; “Seaborg announces his “Actinide Hypothesis””, and subsequent discussion concerning Seaborg’s originality and other characteristics, I have some other history concerning Glenn Seaborg and the f-block.

    Some time ago, noticing a published suggestion that an element might be named after him, I called and spoke with him. As he was credited with removal of the f-block from the table, and I was putting it back, I was curious as to how that would sit with him, and he agreed to receive a model of the Alexander Arrangement.

    Far more willing to talk than to put his thoughts on paper, he later told me he was pleased with the “futuristic” model I had sent, and expressed approval of the concept as well.

    Later, in a letter, I was able to secure written agreement from him that the model of the Alexander Arrangement of Elements was “basically correct”, regarding whether its “connections, constructions, and assumptions … in the 3-D table … are correct or not“.

    Sometime later someone from the Associated Press interviewed him, and the photographer asked him if she could photograph him with a periodic table. He chose the AAE, brought it outside in the sunlight, and told her that it was his “favorite”. (Perhaps because I had prematurely put the Sg in place, I admit.)

    The photo came to my attention only after his death, as it accompanied his obituary nearly everywhere in the world, apparently, when a photo was used.

    I have put the letters and photo online for you all to see at (Click on the letters)

    I eagerly look forward to an update by our most prolific author, whenever reprinting his March 16th post, to see:


    Seaborg (1946) was before Alexander (1965),
    and Janet (1928) was before Seaborg,
    and Bohr (1922) was before Janet,

    and Werner (1912) before Bohr,

    And Bassett (1892) before Werner.

  46. Melinda, Yes! I agree with Philip:”A lovely video.”!

    Student-teams executing striking demonstration-experiments safely and explaining them correctly in terms of kinetic-molecular theory for peers, younger students, and the general public?

    It’s a winner for all lives it touches!
    It’s the best game on the block!
    Students love to COMMUNICATE! Witness the use of cell phones, &c.
    And employers love employees who can communicate clearly, with enthusiasm, in speech as well as in writing.
    Chemistry — the most demonstrable of the sciences — becomes a vehicle for acquiring a general education.
    Have fun! I can see you are. That’s great!
    The one thing students prize from teachers above everything else is ENTHUSIASM!

    And periodic tables? First things first.
    First demos to illustrate leading properties of leading members of leading Groups in the Periodic System. Then, perhaps, the exercise sketched on the front cover of the book “New Ideas in Chemistry through Fresh Energy for the Periodic Law,” pictured on some booksellers’ web sites.
    After capturing the left-step-periodic table, students can go easily to the conventional periodic table, and, via the AAE version of the LSPT, to your graphic representation of the Periodic Law.

    Here’s a thought for a video: Four students with the Periodic System’s four blocks, s, p, d, f, arranged fdps, sfdp, and s(f-footnoted)dp. Hey! I wish I were back in a classroom with you!

    I used to roll out “Mendeleev’s Line” on toilet paper on the floor across the front of a lecture hall at the beginning of a period, with generic symbols H, N, A, E for members of the Halogens, Noble Gases, Alkali Metals, and Alkaline Earth Metals; also C and V for the Coinage Metals and the Volatile Metals (Zn, Cd, and Hg). Then I’d tear the line after the HNAE sequences and line them up, vertically. Produced is the LSPT.

    One time a late-arriving student, stepping over the toilet paper, was heard to mutter, “What the s_ _ _ _ is this?”


    Here’s a sketch of a systematic approach to the LSPT and your periodic table, with, for additional perspective, yet another “periodic table” of perfect regularity.

    Plot downward, separately, for values 1 to 8 against values of l, leftward, from 0 to 3, the following three quantities: r + cl for c = 2, 1, and 0;
    i.e., for r + 2l (= n + l), r + l (= n), and r.

    Enter in the diagrams “nl” labels for atomic orbitals.

    The first diagram starts on the rhs with the column 1s – 8s. To its left two steps down is the column 2p – 6p. &c. Lines of constant “n” slope downward to the left. [n + l = l + constant implies (n + l) = l + constant. Lines of constant “n” have a slope of +1.] Lines of constant n + l are horizontal. The diagram might be called JANET’S DIAGRAM. Replacement of columns by the corresponding blocks yields Janet’s LSPT, blocks justified across the bottom.

    The second diagram, a plot of r + l (= n) vs. l, has essentially the same columns, except that after the 1s – 8s column, a 2p – 8p column starts one step down. &c. Lines of constant “n + l” slope downward to the right. [n + l = constant implies that n = – l + constant. Lines of constant n + l have slopes of -1.] Lines of constant “n” are horizontal. The diagram is MADELUNG’S DIAGRAM. Replacement of columns by the corresponding blocks, separated horizontally, with tie-lines, to indicate order of occupancy with increasing Z, yields your periodic table. It has a pleasing two-fold axis of symmetry, but, as for the next table, is not read, for increasing Z, left-to-right, top down.

    The third diagram, a plot of r vs. l, has, again, essentially the same columns as the previous two plots. All columns start at r = 1. Across the top are the labels: 4f 3d 2p 1s. Constant n + l = r + 2l implies that r = – 2l + constant. Lines of constant n + l have slopes of -2. They slope steeply downward to the right.] Replacement of columns by the corresponding blocks yields a construction that may be viewed as the LSPT in which its blocks have been moved upward so as to be justified across the top. The top “r period” (r = 1) contains all first-row elements.

    Moving the LSPT’s blocks upward one step with respect to blocks at their right yields, again, your table. In summary –

    r + 2l vs. l yields “Janet’s Diagram” and Janet’s Table.
    r + l vs. l yields Madelung’s Diagram and your Table.
    r vs. l yields a third plot of “nl” values and a third Table.

    Textbooks that exhibit Madelung’s Diagram and only the traditional, sfdp periodic table tell two truths. Those truths are not, however, related to each other, nor do they tell the whole truth, in that the periodic table that follows from Madelung’s Diagram (with its helium above beryllium) is not the sfdp table.

    If they were logical, textbooks would go from Madelung’s Diagram, which they seem happy to accept, to your periodic table to Janet’s table to the sfdp table to their beloved s(f-footnoted)dp table, which, wrapped on a cylinder and then projected on a plane yields a Janet/Stewart spiral.

    This sketch needs to be fleshed out with figures.
    It’s the kind of exercise students that I had back in the 1950s in an honors section of general chemistry at the University of Minnesota — fresh off farms of central Minnesota and the Dakota prairies; and used to hard work — liked to tackle.

  48. I agree, almost, with what –
    SCHWARZ, W.H.E. says:
    March 18, 2010 at 8:45 am
    Prediction of noble gas(s)es:
    “Two side-remarks . . .
    “Analysing the distribution of atomic-weight differences of adjacent elements shows that a mathematically reasonably educated modern scientist would NOT have predicted the missing noble gas(s)es. The confidence level is definitly too low.”

    The confidence level is, indeed, definitely low, I agree. But not zero!
    The level of confidence among my peers in all of my research of which I am most proud has been
    definitely too low for most of it to have become part of mainstream science, yet.

    There’s something in Bayesian logic to the effect that statements stand chances of being particularly useful if deemed at the outset to be particularly outlandish.

    Einstein (or was it Pauli? or Bohr?) was famous for asking, “Is it crazy enough to be right?”

    I tend to equate “crazy enough to be right” and low confidence level and low probability of being right with a necessary, if not sufficient, condition for a high degree of originality.

    ES’s recent remarks regarding my work paraphrase the last four words of Roald Hoffmann’s Foreword for “New Ideas”.

    As for knowing the difference between induction and deduction, ES, I was publishing scientific articles based on both ways of reasoning before you were born. For most of my life I’ve been a deep admirer of Polya’s volumes on The Role of Induction and Analogy in Mathematics. Speaking of which: Here’s an analogy for you –

    He/Ne Theory : Phlogiston Theory :: the LSPT : the balance. I.e. –
    the LSPT : He/Ne Theory :: the balance : Phlogiston Theory

    The balance, in the hands of Lavoisier, destroyed Phlogiston Theory.
    The LSPT, through regularities it’s suggested searching for, destroys the foundation of He/Ne Theory, some 57 times over.

    Poor He/Ne. It has all the marks of an ARTIFICIAL classification. There’s only route to it! And it’s devoid of implications — other than a false one! It’s a dead end.

    Presented previously is the FATAL FLAW in numerical analysis as it pertains to identification of helium’s natural location in the Periodic System . Suggested was a way, by turning NA on its head, so to speak, to achieve an unexpected, and happy, marriage between NA and PFED. That suggestion has evidently fallen on barren ground.

    [You did write somewhere, before you received “f d p s”, to the effect that chemistry teachers had rightly dismissed the left-step periodic table. And you did write to me, not long after you received “f d p s”, that “You’ve convinced me.” It’s ironic that a self-styled historian of chemistry blatantly distorts the historical record.]

  49. Thank you Melinda: a lovely video. I hope you all know

    Eric: Mendeleev also knew and corrected the Co Ni pair reversal. As to whether he could have found the noble gases, he spent most of the 1870s researching into gases; if he had been open to the idea that there might be more to the atmosphere than the knon gases he might have discovered Ar. I have argued that he could have foreseen a ‘Group Zero’ if he had drawn a spiral instead of a table (‘A century on from Dmitrii Mendeleev: tables and spirals, noble gases and Nobel prizes’, Foundations of Chemistry (2007) 9:235-245 DOI 10.1007/s10698-007-9038-x). Sedgwick envisaged elements with zero valency in 1890, and Crookes should have seen that from his zigzag.

  50. Prediction of noble gas(s)es:
    Two side-remarks
    Statistical laws, standard deviations, reliability levels are often not discussed in chemistry, and even more often in the humanities such as philosophy.
    Analysing the distribution of atomic-weight differences of adjacent elements shows that a mathematically reasonably educated modern scientist would NOT have predicted the missing noble gas(s)es. The confidence level is definitly too low.

  51. Mendeleev stood little chance with the noble gases especially with the placement of the first one to be discovered, argon.

    This is because of a number of contributing factors. He was the only then known gas that was monoatomic, it showed absolutely no reactions and with a weight of 40, if indeed monoatomic, seemed to have no natural place in the periodic system.

    Ar/K happened to also be the only other then significant pair reversal after Te and I which Mendeleev in any case never accepted although he made the reversal.

    Ramsey on the other hand was the person who discovered this and the other noble gases, including terrestrial He as I recall. He was also present at the famous Royal Society meeting on ‘what to do with argon’. See my book for the history.

    Not only is Bent weak in philosophy but also in history of science. His attempts to read into the history what Mendeleev could and should have done at various points are a complete waste of time.

    all the best

  52. Please dont lecture me on philosophy Henry.

    Induction is the opposite of deduction. Go and read up on it instead of just quoting Whewell.

    eric scerri

  53. Actually Henry you first became aware of my interest in the LST when you reviewed a paper which I published in Journal of Chemical Education in 1991, “Chemistry, spectroscopy, and the question of reduction”.

    You were one of the reviewers who pointed out that it was perfectly OK to consider He as a member of the alkaline earths. It is quite clear that you reviewed this paper since you used one of your idiosyncratic phrases, not to say the typically elliptical and bad English in which you delight. Incidentally you also stated that it was a high quality paper that deserved to be published.

    I don’t believe I mentioned the LST in my Scientific American article.

    I will ignore the usual nasty sniping from you.

    eric scerri

  54. CORRECTION [in brackets]: “The He/Ne-created hydrogen-helium GAP in the long-form of the traditional periodic table is UNIQUE. Nowhere else in the Table is there a gap WITHIN PERIODS! ” [that has led to the suggestion of missing elements].


    Philip and Valery,
    For the record, here’s a little history regarding ES and the LSPT.
    He may correct me.
    Around 2001 ES invited me, as I’ve mentioned, to submit a paper on the periodic table for his journal. (I suspect Derek Davenport at Purdue gave him my name.) ES sent me reprints of some of his publications on the periodic table.
    One of them, in Sci. Am.?, contained the remark, as I remember it, regarding the LSPT, to the effect that that table has been properly dismissed by chemistry teachers.
    I submitted a long manuscript with the working title: “f d p s”.
    Several months or so later I received a letter from ES with the remark:
    “You’ve convinced me.”
    Since then, as you’ve noted, he’s evidently changed his mind,
    “without notice or apology”, as one of my colleagues used to say,
    — so perhaps one needn’t apologize for not giving much notice, sometimes, to what he says.
    I’ve tried to construct a model to account for his behavior.
    He’s engaged several of my friends in controversial exchanges.
    I’ve concluded that he’s a seeker of publications, not the truth.
    The truth doesn’t seem to matter. What matters is another publication.
    That may be typical of his field.
    I recall a plenary session at an early Biennial Chemical Education Conference at the University of Wisconsin one summer, devoted to three speeches by historian’s of science, one of them prominent in that field (Stephen Brush). They read their papers, blasted each other (for perceived past sins), but didn’t respond to each other. No dialogue, no discussion. It was strange. Just a game?
    Would it benefit the cause of He/Be, I’ve wondered, to have as a friend an individual who publishes as frequently as ES does? Or not?
    I believe that your invitation to join this blog, Valery, has helped me refine the case for He/Be, perhaps not least of all because of the participation of ES.
    Outrageous remarks spur efforts to set things right.

  56. Dear Stewart and Valery,

    As I tried to explain before I am not so partisan, so hell-Bent on one table or another. I am more interested in discussing the best criteria for selecting an optimal table. If the LST turns out to be more correct then so be it.

    I dont think we know enough about He at present to really settle the issue. Inventing new physical principles, new quantum numbers, tangent sphere models and associating atomic cores with basic substances are all forms of guesswork.

    As I also stated before if one takes all the known properties of he and performs a numerical similarity analysis on He and other elements, the kinship that emerges is with the noble gases.

    We just dont know!

    In my second edition I may just present the case for both the LST and my own triad based table and leave it at that. I have still not decided.

    eric scerri


“I find it absolutely amazing,” writes our philosopher of the Periodic System, “that somebody can claim they are an inductivist while at the same time denying the obvious similarities between He and Ne, Ar, Kr, Xe !!”

    That’s absolutely amazing, coming from an alleged philosopher.
    Induction and classification seem to be virtually conflated.
    Three inductions from a classification illustrate, below, their difference.

    In Mendeleev’s early periodic tables, larger gaps than usual usually appeared in atomic weights in going from the halogens to the alkali metals. They suggest, in retrospect, that, had Mendeleev been more daring, he might have predicted not only the existence and properties of several eka-elements, but, also, the existence and properties of an entire eka-Group! Surely that would have been recognized, in time, by a prize from the Nobel Prize Committee for Chemistry.

    [Mendeleev’s “failure” regarding the Noble Gases, followed by their discovery and location in the Periodic System by Ramsay, for which Ramsay received a Nobel Prize, may have been, in part, what provoked a presumably regretful and disappointed Mendeleev late in his life into something more daring still, based on the shape of his favorite form of the periodic table: a chemical theory of the ether.]

    Lay out elements’ ordinal numbers in the periodic system, Z, and beneath them their atomic weights, A, for the first 14 elements, rounding off for those that are within one-tenth of a unit of an integer, with, beneath them, the differences A – Z (sequenced below, but not properly aligned):
    Z: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
    A: 1 4 7 9 10.8 12 14 16 19 20.2 23 24.3 27 28
    A-Z: 0 2 4 5 6 7 8 10 10 12 14 14

    Query: What’s the simplest model that yields the numbers Z and A?
    Note that for element 1, A = Z. Otherwise, A > Z.

    Suppose that each atom contains a number of identical atom- or particle-characterizing particles equal to Z. Call them “p-particles”.

    Set a p-particle’s mass equal to 1, thereby accounting in the simplest manner for the mass of element 1, and about half the masses of the other cited atoms.

    Suppose that the remainder of an atomic mass, A – Z, arises from the presence of identity neutral “n-particles”. How massive might n-particles be? They could be twice as massive as p-particles, provided A – Z is always an even number. That is not the case for elements 4 and 7.

    p- and n-particles must have approximately the same mass.

    To account for significantly non-integral A-values (elements 5, 10, and 12), assume the existence of atoms that have the same number of p-particles but different numbers of n-particles.

    Latent in Mendeleev’s line-up of the elements according to their atomic weights is the proton-neutron model of atomic nuclei.

    A bit of a stretch? Of course. All inductions are “a bit of a stretch”.

    The Periodic Classification of the Elements, emphasized Mendeleev, is a classification of the elements as “basic substances” that evidently survive the most violent chemical transformations unchanged, as the original elements can be recovered, gram for gram.

    Suppose, after Dalton, that all elements are composed of atoms and nothing else. What part of atoms might pass through matter’s chemical transformations unchanged? An inner part or an outer part?

    Consider one of chemistry’s central doctrines:
    The Collision Theory of Chemical Reactions.
    To react chemically, atomic clusters, called molecules, must collide with each other with bond-breaking violence. Mix and heat.

    In atom-atom collisions, presumably it’s atoms outer parts that collide.
    It’s those parts, presumably, that change in chemical changes.
    Other parts, atoms’ inner parts, evidently do not change.
    Call those unchanging parts, the “basic” stuff, atomic cores.

    Discontinuous changes on entering each block with increasing Z, f to d, d to p, and p to s, might be accounted for by assuming discontinuous changes in atomic cores.

    Discovery of natural classifications, Whewell shows, is a tricky business. How do we form “the idea of likeness”? What properties are significant? If “a few selected characters” [read “boiling point”, e.g., and “inertness”] . . . be made absolute and imperative . . . we form an Artificial System.”

    Once a “natural system” emerges, it’s a new ball game: the system’s explanation in terms of physical models, by means of inductions.

    Inductivist don’t deny, at an earlier stage, “the obvious similarities between He and Ne, Ar, Kr, Xe !!” They merely deny that “the obvious similarities” are of central significance in determining system-determining likenesses that yield a natural system of classification.

    Nature’s deepest similarities, the history of science shows, are usually not her most “obvious” similarities.

    Aristotle’s obvious “state of rest” is not Nature’s most natural mode of being in Newtonian mechanics.
    Earth, air, fire, and water, are not Nature’s most fundamental elements.
    Matter’s seemingly endless divisibility is not its most fundamental characteristic.
    Energy’s fundamental constancy is not one of its obvious properties.

    The word “obvious” in scientific discussions is often a red flag.
    What’s obvious may not be naïve. But what’s naïve is always “obvious”.
    Reference to “the obvious similarities between He and Ne, Ar, Kr, Xe!!”
    signals Beware! Conclusions may be naïve.


    Mendeleev believed that his Classification of the Chemical Elements According to the Periodic Law was a natural classification, not an artificial classification.
    Mendeleev didn’t state, however, with great clarity, a criterion for naturalness, although that had been done by the polymath and brilliant historian and philosopher of science, William Whewell, earlier, in 1867. According to Whewell –


    Both substances are inert gases. Period.
    No other routes to He/Ne exist.

    They include:
    – The Atomic Structure Route
    – The Triads’ First-Element Rule
    – The Group Size Rule
    – The Analogy He:Be::H:Li
    – Extrapolations from the f-block through the d- and p-blocks to the s-block
    – The Ordinal-Number/Quantum-Number Correspondence
    – The Network of Routes consisting of Periodic Tables of Perfect Regularity: Left-Step, Right-Step, and Front-Step, accessed by way of several ramps: Groups’ memberships, maximum oxidation numbers, and first-stage ionization energies
    – The Network of Routes, Vertical and Horizontal, of First-Element Distinctiveness with respect to diverse atomic properties

    Whewell’s definition of a “natural classification” clears up the Helium Issue in a single, beautifully simple, unambiguous stroke.
    Helium-above-beryllium is a slam dunk.

    He/Ne is an artificial classification.
    He/Be is a natural classification.

    He/Be is, accordingly, a highly informative classification.
    He/Ne is not, accordingly, a highly informative classification.

    The sole argument for locating helium above neon — because they are inert gases — is, all things considered, in a bigger picture, a powerful argument against locating helium above neon!

    The He/Ne-created hydrogen-helium GAP in the long-form of the traditional periodic table is UNIQUE. Nowhere else in the Table is there a gap WITHIN PERIODS!

    In his short-form table, Mendeleev — famous eliminator of gaps within periods — left spaces for six elements between H and He.

    Moreover, helium-above-neon may lead students to believe that vertical adjacency in periodic tables always means similarity as simple substances — clearly not the case, however, for B & Al, C & Si, N & P, O & S, F (a “super-halogen”) & Cl, not to mention H & Li!

    There’s nothing at all to say, today, for He/Ne.
    It’s a dead end, a bumpy end, a full stop to thought.

    It might be a significant step forward for scientific thought if a frequent contributor to the literature on periodic tables spoke and wrote in favor of He/Be.
    Promotion of He/Ne — all things considered! — is an astonishing step backwards!

  59. When I read Eric’s book couple of years ago, I was so excited! Given his support for the Left Step Table and for the idea of optimal objective periodic table, I was sure that he was going to embrace Adomah Periodic table. When I first contacted him in February of 2007, I was disappointed. Eric has changed. His views on periodic table have changed to worse. For a moment I thought that it was different Eric Scerri. He was promoting his new, artificially symmetric periodic table at that time. I thought that Eric Scerri who wrote the book and Eric Scerri who I was corresponding with were two different Scerris. No, unfortunately it was transformed Eric Scerri, converted by the establishment back to their well established point of view.

    Come home, Eric! Support the innovation! Be true to your own words that you wrote in own book!

  60. My worries about the Janet table first began to dissipate when I read “such worries are alleviated once one acknowledges that the periodic system is primarily intended to classify the elements as basic substances and not simple substances… It may seem odd to the reader that the suggested periodic trables are ones that appear to rest rather heavily on a reductionist view in favour of the importance of electrronic configurations of atoms. In addition, these considerations, and more specifically the n+l rule… are being placed above current wisdom concerning the chemical nature of helium… My response to such worries is to point out that throughout this book I have sought to examine the limits of reductionism in chemistry and have not been critical of reductionism as a general approach. As mentioned at the outset, reductionism has provided an undeniably successful approach to the acquisition of scientific knowledge.”

    It is not too late for Eric to decide not to swallow his own words, published in 2007 (The Periodic Table, pp. 282-285).


    Science is nothing if not logical, and evidential.

    To say that atomic structure explains the Periodic Classification of the Elements
    and then, immediately, to classify hydrogen, an ns system, with the Halogens, np5 systems, and helium, an ns2 system, with the Noble Gases, np6 systems, is ILLOGICAL. Also –

    To say that the Periodic Classification of the Elements is not a classification of the elements as simple substances and then, almost immediately, to locate helium above neon in periodic tables because the two elements are alike as simple substances in having low boiling points (the lowest and almost the second lowest of all the elements), is, again, ILLOGICAL. And –

    To say that science is empirical and then to ignore the massive body of evidence summarized in the Rule of First-Element Distinctiveness when locating helium in the Periodic Classification of the Elements is UNSCIENTIFIC.

    However one looks at it, He/Ne is, in a word, UNPHILOSOPHICAL.

    One might think that among chemists the old, tired Doctrine of Helium-above-Neon would have been retired by now and that, accordingly, it would not be promoted by well-informed historians and philosophers of chemistry. That that is not the case, in either case, says what about the Old Doctrine (He/Ne), the New Doctrine (He/Be), chemists, and historians and philosophers of science?


    As an historian of the periodic table, Eric, you might resonate to these historical facts:

    Location of helium above neon occurred :
    – before knowledge of atomic structure
    – before knowledge of trends in atoms’ ionization energies
    – before knowledge of trends in atoms’ electronegativities
    – before knowledge of trends in atoms’ refractivities
    – before recognition of the s-block as a distinct block
    – before full knowledge of the lanthanides
    – before knowledge of the actinides beyond uranium
    – before knowledge of the f-block
    – before definitive knowledge regarding hydrogen’s natural location in PTs
    – before knowledge of periodic tables of perfect regularity
    – before recognition of the distinction: primary, secondary, and tertiary kinships
    – before recognition of the distinction between kinship strength and closeness
    – before recognition of a Triad First-Element Rule
    – before recognition of a Group Size Rule
    – before recognition of block-to-block trends in first-element distinctiveness
    – before recognition of a block-to-block trend in l-nobility
    – before recognition of a correspondence between ordinal numbers generated by Chemical Periodicity and quantum numbers generated by atomic spectroscopy
    – Before general recognition that the Periodic Classification of the Elements is a classification of the elements as atoms (specifically, their cores) and not a classification of the elements as simple substances (such as metals, nonmetals, and gases).

    Those are the facts, plain and simple.

    Helium-above-neon in periodic tables was an early and — in light of later knowledge — naïve assignment, based on four facts (two boiling points and chemical inertness) regarding two elements: helium and neon, as simple substances.

    Helium-above-beryllium in periodic tables is a later, more sophisticated assignment based on a LARGE number of facts regarding ALL elements of the Periodic SYSTEM.

    Jump in! (to the ocean of information correlated by helium-above-beryllium).
    The water’s fine!
    It’s not crowded!
    It needs stirring up!
    How can one resist it?


    Philip, you write: “When were the rare earths removed from a super-sized Group III?
    I’m not sure they were ever seen as part of Group III.”

    One can’t be sure, from reading Mazurs and van Spronsen, that the rare earths were ever a part of what we would call a “Group III”. Sometimes van Spronsen seems to use the word “Group” to mean a horizontal series of elements. Below is a brief history of the grouping of the rare earths into a single Group III located at a single site or “node” in the Periodic System.

    Mendeleev introduces a long section in “Principles” on THE ELEMENTS OF THE RARE EARTHS (Vol. II, p107ff) with these remarks:
    “[T]hey [the oxides of Sc, Y, and La] are accompanied in nature by a whole series of other elements . . . which all have so many points in common that they have long been classed under a SPECIAL GROUP [emphasis added] of elements of the rare earths . . .
    the great authority on these elements, Professor B. F. Brauner, of Prague, has at my request written a special description of them for this book . . .”

    At the end of his detailed discussion of the rare earths, Brauner writes:
    “[J]ust as in the eighth group, four elements occupy ONE PLACE in the system [emphasis added], so also the elements of the rare earths form a node or band and occupy the position IV, [series] 8, which was formerly occupied by cerium alone.”

    I recall seeing a 3-dimensional periodic table, planar in all respects except for a projection outward toward the reader from Ce’s position, of a single column of rare earths.
    The closest thing to it in van Spronsen is his Fig. 87, p189.

    In referring to location of the rare earths in the Periodic System, van Spronsen uses, somewhat ambiguously, the phrases “separate Group” and “special group”.

    In their splendid textbook “Chemistry of the Elements”, Greenwood and Earnshaw write that “The lanthanides comprise the largest natural-occurring group in the periodic table.”

    In their classic textbook, “Inorganic Chemistry”, which has had over 100 German editions, Holleman and Wiberg concur. They write:
    “The28 lanthanides and actinides . . . together with all the four related elements Sc, Y, La, and Ac ALL BELONG TO TRANSITION GOUP III [emphasis added], which is thus the largest subgroup in the periodic table, having 32 members and comprising almost 30% of the elements.”

    The custom of locating the rare earths in a single Group was so deeply entrenched in the minds of senior British and European inorganic chemist that when a subset of them on IUPAC’s Inorganic Chemistry Nomenclature Committee introduced new column labels for periodic tables, their 1-18 scheme, they provided no individual labels whatsoever for the f-block’s columns. Rather, they implied, without explanation, that the blocks 28 elements are be associated in some manner with a Group “III”.
    That was the judgment of a group of distinguished inorganic chemists in March, 1986.
    Small wonder that helium remains above neon.

  64. Henry: Bohr can’t claim to have recognized the actinides as he regarded Ac to U as transition elements, placing them under Lu to W, so I still give the credit to Janet, especially as I believe he was tghe first to talk of ‘blocs’.

  65. Not sure that Bill Jensen is following this, Henry, so here goes:


    When were the rare earths removed from a super-sized Group III?
    I’m not sure they were ever seen as part of Group III. Bayley (1882) hedged his bets and put two different sets of lines of affinity between his Period IV (Rb to I) and his Period V (Cs to Th). Thomsen (1895) squeezed the rare earths in between Ce and an unknown element (Hf?), both of which he placed under C, Si, Ti, Zr. The first to put them in what we would call the right place was Alfred Werner – see next answer.

    When did the f-block become a block, rather than two separate “series”?
    I think Werner was the first in his table of 1905. He had only Ac, Th and U to play with and he placed only Th correctly, under Ce, but he allowed 14 places under La to Yb (with a ? mark under Sc and Y).

    In his descriptions of periodic tables, did Seaborg ever use the term “f-block”?
    I’m not interested in Seaborg.

    When did Groups I and II become part of a separate block, rather than part of the same block as the other “Main Groups”? That is to say: When did chemists and physicists begin to use the term “s-block”?
    Janet was the first to make I and II a separate block, and I believe he was the first person to use the term ‘bloc’.

  66. As Philip says, “Nobody denies the similarities between He and Ne, Eric.”


    Distinctions are important in science.
    The Conservation of Energy Principle could not be stated until scientists drew a distinction between what we call today “energy” and “momentum”.
    Modern chemistry is based on the distinction between “element” and “compound”.
    Beginning students often fail to distinguish “heat” from “temperature”.

    The Phenomenon of First-Element Distinctiveness, illustrated by Valery, means that helium, being a “first element”, wherever it is placed, is out of place above neon.

    An important keys to understanding The Periodic System lies in recognizing when characterizing kinships the difference between “closeness” and “strength”.
    Throughout the lower regions of the periodic system, the two characteristics tend to coincide.
    In the upper right hand portion of the left-step periodic table, they do not coincide.

    “Those statements concerning where and in what ways similarities as simple substances do and do not exist among congeners are part of the lore that makes periodic tables useful.” (NI, p118. It’s all there, Eric, for one to read.)


    You’re right, Philip.
    Janet (1928) was before Seaborg (1946).
    And Bohr (1922) was before Janet,
    Werner (1912) before Bohr,
    And Bassett (1892) before Werner.
    (Information from van Spronsen.)

    Werner assigned the lanthanides and actinides 15 members, had Th located correctly beneath Ce, and misplaced, somewhat, U and Ac.
    Bassett assigned the lanthanides and actinides 18 members, had Th located correctly beneath Ce, and located U, correctly, two positions further on.

    Bassett’s table (p150) rotated clockwise 90 degrees is a right-step table, read right-to-left, the mirror image of the left-step table, with the exception of location of the s-block’s elements, and omission of H and the noble gases.
    Bassett’s first four columns are identical to Mendeleev’s first four columns (“Principles”, Vol. I, page xvii).

    (“The first to classify the rare earths as a separate group and also to regard the known actinides as homologues of the rare earths,” writes van Spronsen (p268), “was Bassett.”)

    Seaborg was an interesting individual: tall, with a commanding presence, a dominant figure in a room, yet modest around young people; versatile, in his contributions, on and off campus (as, e.g., a leading member of Berkeley’s Athletic Council and an early (first?) director of the U. S. Atomic Energy Commission); a scientist and an educator (instrumental in enlisting the participation of George Pimentel in the post-Sputnik Chem Study Project); — but, in the view of physical chemistry graduate students at Berkeley around 1950, a light-weight in Berkeley’s chemistry faculty (lead by Kenneth Pitzer, who always seemed to be able to ask the most penetrating questions in departmental seminars of anyone, whatever the seminar topics might be).

    Seaborg and his graduate students usually came down from the “hill” (the location of Berkeley’s cyclotron) for weekly seminars only when a member of their own group was scheduled to speak. He contributed little to the department, as a whole, but mightily to the U.S. war effort during WWII, with his “actinide hypothesis”.

    Seaborg’s team was attempting to separate trans-uranium elements from cyclotron-irradiated atoms, by chromatographic elution methods, without success, as they were assuming that the sought-for elements were congeners of d-block elements. They were searching for the wrong (high) oxidation states. Once they realized, after a seminar for his team by Seaborg, following intense reflection on the issue, that the elements they sought might belong to a second, rare-earth-like “series”, maximum oxidation number +3, their work advanced rapidly.

    It’s been said that credit for an idea should go not to the first person to have the idea (that may be nearly impossible to determine) but, rather, to the first person to show that the idea is EXTREMELY USEFUL, as Darwin did for the idea of “evolution”.

    But useful for whom? Scientists? Humanity?

    Seaborg’s “actinide hypothesis” aided construction of one of the atomic bombs dropped in WWII, which may have shortened the war in the Pacific and diminished loss of life in a continuation of a deadly island-hopping campaign aimed at Japan (I was personally grateful for that), even as it created a huge number of deaths of innocent individuals at Hiroshima and Nagasaki (the ultimate step in a logic that was pursued by both sides in the European theatre, to bomb civilians?).

    [The key to heaven, say Buddhists, is also the key to hell. (Heaven for inorganic chemists is a periodic table. Hell for the Japanese where the plutonium bomb was dropped was chemists’ use of the periodic table to help build the plutonium bomb.)

    [Heaven for a lover of the Phenomenon of First-Element Distinctiveness is helium-above-beryllium. Hell for PFED deniers is evidence in support of PFED.]

    Janet’s recognition of the f-block led to the left-step version of the periodic table, helium above beryllium (A FIRST?), with all the implications pertaining thereunto: including two trans-table trends in first-element distinctiveness, a trans-table trend toward Groups of increasing historical familiarity to chemists, and two across-the-table rules regarding a correspondence between periodicity-generated ordinal numbers and spectroscopy-generated quantum numbers.

    How about calling the f-block, in scientific circles, the BJ block: the Bassett-Janet block?
    Or, more fully, the BWBJ block (the Bassett-Werner-Bohr-Janet block)?

    For whom, then, should the bell toll for the s-, p-, and d-blocks?
    Davy, for the s-block?
    Perhaps Mendeleev, for the p-block?
    And no one in particular for the (biblical) d-block (home of a majority of the metals of antiquity, cited in the bible)?

    The idea of an “f-block” has not yet been deemed to have been demonstrated to be “extremely useful” in the eyes of the old-timers on IUPAC’s Committee for Nomenclature in Inorganic Chemistry and to the authors of at least two leading textbooks in inorganic chemistry, still wedded to the idea of a super-sized Group III (NI, Section 92, p91).

    Absent recognition of an f-block, absent recognition of Periodicity’s intrinsic dyadic character, particularly when the s-block is located on periodic tables’ left-hand-sides (as it almost always is), and absent, accordingly, recognition of regularities in the Periodic System contingent on location of helium above beryllium.

    The chemical history of the periodic table since Mendeleev’s time has been, in significant measure, the history of the f-block. More elements have been added to the f-block since 1869 than to any other block in periodic tables. In the left-step periodic table’s block format, the f-block, points — along with, in order, the d- and p-blocks — in the direction of He/Be (cf. NI, p90).

    The f-block provides one with a long running start along a row of nearly identical elements for leaping upward in three steps of equal height to the top of the table where the Periodic System’s two most distinctive elements — with respect to their congeners — reside: H and He. Conversely, in sledding downward from H and He along increasingly smooth terrain, the f-block provides one with a long, smooth run-out at the bottom.

    Three cheers for the f-block!!!
    Absent the f-block absent correct locations for the rare earths,
    the left-step periodic table,
    the LSPT’s obvious locations for the “problem elements” (H and He, La/Ac and Lu/Lr),
    and a complete Periodic System with new regularities
    (contingent on location of helium above beryllium).

    The f-block and helium in the s-block are synergistic companions in the Periodic System.
    The f-block points, through the d- and p-blocks, to helium in the s-block.
    Helium in the s-block points, through the p- and d-blocks and the Phenomenon of a Block-to-Block Trend in First-Element Distinctiveness with Respect to First-Row Neighbors, to a long block of nearly identical first-row elements, the rare earths.

    The elements that gave Mendeleev in his day the most difficulty in his Classification of the Chemical Elements According to the Periodic Law today complete his Classification in a most satisfying manner.

    In science, if things seem mixed up, just wait.
    Paradoxes tend to vanish in science’s Aristotelian March toward Platonic Ideals.

    For Dulong and Petit and their molar heat capacities, Robert Brown and his Brownian Motion, Mendeleev and his Periodic Law, Clausius and his entropy function, Balmer and his formula for hydrogen’s spectra, and Lewis and his electron-pair, no physical explanations existed at first.

  68. Eric wrote:
    “I find it absolutely amazing that somebody can claim they are an inductivist while at the same time denying the obvious similarities between He and Ne,Ar, Kr, Xe !!”

    You should not be amazed by this, Eric. Nitrogen is a gas and phosphorus is non-metal, but they are in the same group with metallic bismuth! I am as inductivist as the fellow who came up with such “strange” idea.

    By the way, I realized that He has to be next to Be long before I realized that periodic table is tetrahedral by nature.

    Valery Tsimmerman.

  69. Nobody denies the similarities between He and Ne, Eric. We just say that, based on specroscopy etc, there is a deeper kinship between He and Be. The difference (also between H and Li) is fully accounted for by the fact that the K shell is unique in being complete with 2 electrons and that the core is a naked nucleus. The Preriodic System produces many similarities between elements that are not in the same group – diagonal, knight’s move etc.

  70. I find it absolutely amazing that somebody can claim they are an inductivist while at the same time denying the obvious similarities between He and Ne,Ar, Kr, Xe !!

    eric scerri

  71. Thanks Larry- and of course you noticed the consequences for the triadic relationships. We are admirals on the sea of mutual admiration. Perhaps they will name elements for us. Perhaps I will be the first person to walk on Mars. One never knows.

    By the way, I have a new suggestion for trending, though I might have mentioned it somewhere else (with all these blogs who can remember?). We already know about first member anomalies for blocks on the x axis which weakens vertically, and where the biggest anomaly is in the s-block, and it weakens progressively leftwards through the other blocks, and also perhaps more pronounced for more rightward members of each block.

    What about a first member trend on the y axis which weakens horizontally rightwards within a block, and is strongest for the f-block and weakens progressively rightwards between blocks, and is strongest in the lower parts of the LS table.

    That is, we already know that La and Ac ‘jump the gun’ with regard to d-block behavior, Lu remains a ‘lanthanoid’ and Lr with regards to p-block behavior, ‘actinoid’ and perhap poor-metal status (according to Wikipedia). Element 113 may only show a +1 oxidation state (Wiki) as Th tends to due to the ‘inert pair’ effect. 114 may have noble gas character. If 120 is also noble, then already the trend is weakest since it would be at the other side of the block.

    Renormalizing dual height equal to block length would allow us to see the two first member trends as symmetrical, when viewed from the perspective of a diagonal running from upper left to lower right through the system.


    Jess Tauber

  72. These are beautiful words, indeed:
    “Remove the scaffoldings of Aristotelianism after construction of science’s cathedrals, and what remains, from the efforts of good architects and artisans? An approximation to Platonic Ideals.”

    Jess, of course you have similar issues. You looked at The Periodic Table and you have noticed that half of alkaline earths (Be, Ca, Ba, Ubn) have atomic numbers equal to the tetrahedral numbers (4, 20, 56, 120) and the other half (He, Mg, Sr, Ra) have atomic numbers that are their arithmetic means! Have you arranged the elements in such order on purpose? Of course, not. They have been arranged long before you. But you were lucky enough to notice that first. Are you a Platonist? According to professor Bent’s words, you are one of the artisans. Congratulations!

    Easing Acceptance of He/Be?

    A characteristic feature of chemistry is CHANGE.
    Lavoisier called it “PROGRESS”.
    Below is an approximate chronology of progress toward location of helium above beryllium in periodic tables.

    Ancients recognize seven metals: copper, silver, gold, iron, mercury, tin, lead.
    Boyle defines “element”, as the last step of analysis.
    Lavoisier invests Boyle’s definition with significance, through use of the balance.
    Priestley and Scheele prepare oxygen.
    Gravimetric analysis leads to the Law of Constant Proportions.
    Dalton recognizes a Law of Multiple Proportions. Introduces Atomic Theory.
    Davy isolates barium, strontium, calcium, and magnesium.
    Chemists recognize natural families of elements, such as Ca Sr Ba.
    Gay-Lussac discovers the Law of Combining Volumes.
    Avogadro invents the concept “molecule”, to account for Gay-Lussac’s Law.
    Cannizzaro introduces a method for determining rational atomic weights.
    Dobereiner recognizes his first atomic weight triad: Ca Sr Ba.
    Wohler isolates beryllium.
    Lockyer observes helium’s D line in the sun’s chromosphere.

    Newlands and Lothar Meyer arrange the elements in series and families.
    Mendeleev announces the Periodic Law.
    Mendeleev groups Mg with Zn Cd Hg.
    Mendeleev corrects Be’s atomic weight and groups Be with Ca Sr Ba.
    Ramsay and Travers discover Ne, Kr, and Xe.
    Ramsay places the noble gases in a periodic table in a column on its lhs, labeled Group 0.

    Crookes invents the cathode ray tube.
    J. J. Thomson discovers a universal constituent of matter: the “electron”.
    Geiger and Marsden discover backward scattering of alpha particles by gold foils.
    Rutherford introduces his nuclear model of the atom.
    Moseley discovers atomic numbers.
    Bohr and others arrive at an electronic interpretation of periodic tables.
    Group 0 is moved to periodic tables’ rhs.
    The medium long periodic table groups Mg with Ca Sr Ba.
    XeF2 and XeF4 are synthesized.
    Group 0’s label is changed to VIII.
    Seaborg announces his “Actinide Hypothesis”.
    Jensen recognizes a block-to-block trend in first-element distinctiveness.
    Chemical reasons are advanced for locating helium above beryllium in periodic tables.
    Not for the first time in its history the Alkaline Earth Metals Group receives a new member.

    When it’s placed in historical perspective, the (He/Ne)-(s2/p6) anomaly yields unexpected insights into the Periodic System and the minds of chemists and chemistry teachers, historians and philosophers of chemistry, through their reactions to resolutions of that familiar anomaly.
    Anomalies are waves of the future. In surfing them as they iron themselves out, as they tend to do, in their Aristotelian approaches to Platonic Ideals, only every generation or so does one come along that’s as beautiful as the He/Ne wave: easy to catch, satisfying in its significance, and a slam-dunk to ride. No advanced chemistry, physics, or mathematics is required. Even novices can ride it — in their minds — safely to shore. Helium-above-beryllium — all things considered! — is a piece of cake.

    When were the rare earths removed from a super-sized Group III?
    When did the f-block become a block, rather than two separate “series”?
    In his descriptions of periodic tables, did Seaborg ever use the term “f-block”?
    When did Groups I and II become part of a separate block, rather than part of the same block as the other “Main Groups”? That is to say: When did chemists and physicists begin to use the term “s-block”?
    What led to your recognition of a block-to-block trend in first-element distinctiveness?

    Describe false starts in the histories of periodic tables’ Groups.
    Has any Group had a “clean” history: no wrong inclusions or wrong exclusions?
    Identify periodic tables’ distinctive features.
    Which distinctive features have been particularly important?
    What special features of the Periodic System are contingent on location of He above Be?
    How might lovers of He/Ne respond to that last question? By denying existence of (He/Be)-contingent features? Or in some other way(s)? (NI, p1)



    “I am confused,” says Valery. “What if result is Platonic but approach and/or methodology used to come up with the result is not?”

    I’d say you’ve hit the nail on the head.
    Science [i.e., Aristotelianism {i.e., empiricism} (AHD)] is the only route to the “absolute and eternal reality” (AHD) of Plato’s “ideal forms”.

    Remove the scaffoldings of Aristotelianism after construction of science’s cathedrals, and what remains, from the efforts of good architects and artisans? An approximation to Platonic Ideals.

    Plato stated the goal of science. Aristotle described the path to Plato’s goal.
    Science needs both vision and method.
    Vision alone is helpless. Method alone is aimless.
    Jointly, they may yield interesting results.

    My brother, a nuclear physicists, whose experiments would require years to set up, and more years to interpret, said that he sometimes wondered when they were churning out data how their work differed from someone going around a house with a measuring tape and recording distances between various parts of the structure. Absent at the time was a vision of where they might end up.

    The greater the compartmentalism of science, the greater the data-collection and the less “the vision thing”. The coin’s other side is that the greater the compartmentalism, the greater can be contributions of armies of artisans. Needed are only a few architects.

    With some 700 periodic tables, and counting, it sometimes seems, however, that we have rather more architects than artisans. And then, surprise! New tables appear, superior, in some ways, to all the other tables.



    The provocateur’s bag of tricks seems to be inexhaustible.
    To techniques cited previously should be added ARGUMENT THROUGH GUILT BY ASSOCIATION.

    We needn’t pay attention to Bent because of his association with Princeton’s professor Leland Allen, damaged goods because of his ideas about polywater.

    Pauling said that the way to have good ideas is to have many ideas.
    Norbert Wiener said that if you haven’t made mistakes you haven’t pushed yourself as hard as you should have, past your limit.

    [Allen’s mistake illustrates that “Chemistry is an experimental science,” as chemists like to say (in response to physicists’ criticisms of their fact-rich, theory-lean science).
    Experiment’s lead, theory follows — if, at times, distantly: witness the Periodic System and helium.
    Experiments have added hugely to our knowledge of the Periodic System since the time that helium was first placed in a periodic table, by Ramsay, with the other noble gases, on the left-hand-side, in a Group Zero.
    That Group’s location and label have changed since then, but not, yet, its membership.]

    In his reference to Allen, the provocateur told the truth, an irrelevant truth, and a misleading truth — in not being the whole truth. (All in all, a typical ES “truth”?)
    Allen had company.
    I’d toyed with the idea of using Linnett’s Double Quartet Hypothesis to account for polywater, but didn’t publish it. There was no need to. On a bus trip in Italy during a conference, it was mentioned to a seatmate, a famous British chemist, Jack Linnett, who published it. [Woops! “Guilt” by association?]

    Well, whatever. The swipe at LA by ES is the kettle calling the pan black.
    Surely our provocateur remembers the time that he published in a scientific journal a whopper of a mistake that even his students in freshman chemistry would not have made.
    He’d pushed himself past his limits.

    Correcting ES on scientific issues has been like shooting fish in a barrel: not fair game, when what’s in play is a scientific matter, such as the periodic table.

    Not so, says ES, if I understand him correctly.
    The periodic table, today, transcends chemistry.
    Chemists alone should not be deciding what its correct forms are.
    That’s a philosophical issue.

    What does it mean IN PLAIN ENGLISH to say that something is a philosophical issue?
    How do philosophical statements differ from scientific statements?
    Can philosophical statements be proven to be false?
    What are two or three examples of leading philosophical statements, about science?
    About periodic tables?

    Which statement conveys the most information: He/Ne or He/Be?
    He/Ne tells an unsophisticated viewer of the periodic table that helium and neon are alike, as simple substances. Both are inert gases. Period. End of disclosure.
    He/Be can call to mind for sophisticated viewers of periodic tables some 57 regularities, and counting, contingent on He/Be (NI). Here is a new statement of one of them:

    The Group II elements He, Be, Mg, and the “true alkaline earth metals” Ca, Sr, and Ba have the same pattern of electron-removal energies. After two electrons have been removed from their atoms, a huge increase in electron-removal energies occurs: in the case of helium, an infinite increase! It’s a dramatic instance of the phenomenon of first-element distinctiveness. Illustrated, also, are the phenomena of second- and third-element distinctiveness, and the reason for the designation “true [or original] alkaline earth metals”. Below are second- and third-ionization energy differences for Group II(s).

    He infinite
    Be 136
    Mg 65
    Ca 39
    Sr 33
    Ba 27

    An interesting fact emerges.
    First came addition of magnesium.
    Second came beryllium, after Mendeleev corrected its atomic weight.
    Addition of helium is the Group’s third enlargement.
    Along the way the Group suffered a contraction, in its loss of lead.

    Chemists may be surprised by the addition of helium to Group II.
    One might have thought, however, but evidently incorrectly, that that addition would be much less of a surprise to historians of chemistry.

    Many years ago I published a long essay on The Uses of History in Teaching Chemistry.
    A good example would be the use of the history of Group II to pave the way for relocating helium in periodic tables.

    History may be bunk (Henry Ford), for users of periodic tables, but not for modifiers of periodic tables.

    A CORRECTION: The distinctions primary, secondary, and tertiary kinships are professor William Jensen’s inventions.


  76. Valery, I’ve got similar issues- for many years I’ve worked on the issue of sound symbolism (iconicity) in human languages. Plato’s Cratylus is the earliest known discussion of the issues involved. The phonological systems in languages are very matrix-like, and sound symbolism uses the the most geometrically balanced portions of these matrices as motivations for mapping form to meaning (diagrammatical iconicity). In some languages (such as Korean, Japanese, many languages in Africa, etc.) there can be many thousands of these forms, even outweighing in numbers normal words.

    In languages with the largest numbers, however, these forms (called ideophones or expressives) don’t participate fully in the syntax, preferring to remain somewhat (or even largely) aloof. Over many centuries, though, they begin to integrate into normal lexicon with its syntactic priveleges, the inventory shrinking greatly, the iconicity fades as historical sound and structure changes cumulate, meanings alter, etc.

    After studying all this for so long, I have to think that there is some possibility that something similar in flavor happened to the periodic system, that the more perfect underlying matrix-like constructional motivation (diagrammatical) for isolated forms has decayed in favor of changes in behaviors that facilitate the building of larger entities (molecules, bulk metals, etc.) and the creation of higher levels of hierarchy. Compromises and accommodations have been made. It would mean that the universe has properties of a communicative system.

    I see palms being passed over scalps at this point, so I’ll end here….

    Jess Tauber

  77. Henry writes:

    “A Platonist has a hell of the time with “New Ideas”. Its inductions are simply incomprehensible. That’s because a mind shaped by Platonism is a mind that is in poor shape to cope with a book based on the methods of Whewell’s “Inductive Sciences”.

    Hm, that is interesting. I like most ideas in “New Ideas” and they call me a Platonist anyway simply because, by pure coincidence, my periodic table can be folded into perfect tetrahedron, one of the platonic solids.

    I am confused. What if result is Platonic but approach and/or methodology used to come up with the result is not?


    Hydrogen and fluorine are alike in many respects.

    Both elements are low-boiling gases shipped under pressure in sturdy steel tanks.
    Their critical temperatures — above which they cannot be liquefied, however high the pressure — lie well below room temperature.

    Hydrogen and fluorine exist at room temperature as single-bonded diatomic molecules.
    They form with each other diatomic, low-boiling HF.

    H and F atoms both have a single valence-shell vacancy.
    Both atoms accept electrons from active metals, yielding the monovalent anions H- and F- and ionic compounds, such as NaH and NaF, both of which have the rock salt crystal structure and which, on electrolysis, yield at the anodes (the electron-withdrawing electrodes, where chemical oxidation occurs) hydrogen and fluorine.

    Both atoms share electrons with atoms of other nonmetals, yielding covalent compounds with similar molecular formulas, such as CH4 and CF4.
    Both atoms bond to carbon atoms and atoms of other nonmetals by single bonds.
    H and F atoms, when present, reside on the peripheries of molecules.

    Consider the empty array, labeled down at the left and across at the top: (H) (F) (Na).
    Enter in the array: I for “Ionic”; C for “covalent”; and M for “metallic” substance.
    Produced is this array:
    (H) (F) (Na)
    (H) C C I
    (F ) C C I
    (Na) I I M

    The entries for (H) resemble those for (F), not those for (Na).
    For 40 years I believed that H belonged above F in periodic tables, not in a column with Na.

    That was before I learned of Janet’s periodic table, the phenomenon of first-element distinctiveness, the Rules of Triads, Mendeleev’s statement that the Periodic Classification of the Chemical Elements is not a classification of the elements as simple substances, and locations of hydrogen and fluorine in all periodic tables of no irregularities: left-step, right-step, front-step, and step-pyramid.

    I learned that a little learning is a dangerous thing.

    Knowing that helium, like neon, is an inert gas is insufficient information for indentifying helium’s NATURAL location in a complex SYSTEM of over 100 elements.

    For helium’s location in a periodic table to be deemed to be a natural location for it, one must arrive at the location IN MORE THAN ONE WAY.
    NI describes some 57 ways, and counting, for seeing that helium above beryllium is a natural location for helium in all periodic tables.

    Similar ways exist for seeing that hydrogen above lithium, rather than above fluorine, is a natural location for hydrogen.

    Wanting to locate LIGHT elements ADJACENT to each other, owing to SIMILARITIES, as SIMPLE SUBSTANCES, opens a CAN OF WORMS.
    H goes above F and He above Ne. Seemingly o.k., so far. Also –
    Mg, with Be above it, should go above Zn and, similarly, –
    Al, with B above it, should go above Sc (that’s where van Spronsen puts it).
    But one can’t have, simultaneously, both of the last two assignments.
    Also, the pairs La/Ac and Lu/Lr should be, by the similarity/adjacency condition, in the same column as Sc and Y, which, again, is impossible.

    Visual inspection of the left-step periodic table yields correct, natural assignments for all “problem elements”: H and He, La/Ac and Lu/Lr.
    If one is using the traditional periodic table, the Rules of Triads yield correct, natural assignments for the problem elements.
    The phenomenon of first-element distinctiveness yields, independently, correct, natural assignments for the Periodic System’s two lightest problem elements, H and He.

    THE Remaining Problem: How do you make the previous remarks familiar remarks for lovers of He/Ne who do not want to be confused by the facts of the case for He/Be?
    “Everyone knows that helium is an inert gas.” Period. End of discussion.

    In the chemical industry, innovation may be an existential threat.
    “Do you embrace innovation or do you fight it?,” asks Michael Campbell, CEO of Arch Chemicals and 77th recipient of the Society of Chemical Industry’s Medal. “Fighting change is not going to succeed in the long run,” he says. “So you might as well embrace it.”

    In academia, however, the innovation He/Be is not an existential threat.
    It’s fought, or ignored, rather than embraced.



    Scerri is one up on us, Valery.
    With the left-step, fdps periodic table, we go from the conventional, sfdp table of 7 periods to a table of 8 periods.
    With a maximum-number-of-triads table, Scerri can go from 8 periods to 120 periods.

    Responding to ES’s statements calls to mind Popper’s thesis, that theories cannot be proven, only disproven. True, if trite — and not the whole picture. Theories can be supported, and refined. It’s what most scientists spend most of their time doing. It’s what most of the enormous literature of science is about. It’s what NI is about.

    Well, whatever. Provocateurs may play useful roles. When on the receiving end of provocations, it’s useful to be aware, however, of provocateurial strategies, including –

    (1) Use of illogical arguments (as you’ve pointed out, and as Bertrand Russell illustrates with his famous proof — which I can’t recall at the moment — that he and the Pope are one).

    (2) Use of false analogies (e.g., Scerri:Bent::Wallace:Darwin).

    (2) Statement of irrelevant truths (one of our provocateur’s favorite strategies).

    (3) Statement of the truth, but not the whole truth.
    E.g. (I paraphrase): “Yes, I cited your words, without immediate acknowledgment, from some unpublished bound documents,” which, to tell the whole truth, contained a manuscript that I had solicited earlier from you and never published.

    (4) Statements of personal opinion (e.g.: “I don’t think so.”)

    Brought to mind is Dirac’s famous response during a question-and-answer session following a talk he’d given. “I don’t understand,” said a member of the audience, “how you can say such and so.” Silence. Finally the moderator spoke up. “Professor Dirac, are you going to respond to the gentleman’s question?” “That wasn’t a question,” said Dirac. “That was a statement of a fact.”

    The current situation regarding He/Be and block order fdps brings to mind a famous sentence in Eyring, Walter, and Kimball’s preface to their classic textbook on quantum mechanics. “Do not mistake unfamiliarity,” they caution readers, “for inherent difficulty.” After all, even the multiplication table seemed difficult at first.

    I used to recite that remark to my students, until one day a student said to me,
    “But professor Bent, what’s difficulty other than unfamiliarity?”
    How does one respond to that?
    Review. Review. Review.
    Measure progress by how dog-eared your books are.
    My son followed that advice, I knew, from the condition of books in his library.
    This forum serves the same purpose.

    Gertrude Stein says in her book or long essay “America” (that title may be wrong), how she loved to listen to people talk: how they repeat and repeat themselves, with variations.
    That’s what mathematical proofs are: the same things, the premises, repeated again and again, in long proofs, with variations, until finally one arrives at statement of a “theorem”: namely, a particularly interesting way to state a logical implication of the premises.

    The “He/Be” and “fdps” “theorems” are simple, graphical representations of logical implications of a few natural premises regarding Chemical Periodicity and Periodic Table construction.

    A CHALLENGE FOR OUR PROVOCATEUR: State rules of construction and the information beginners need to construct from scratch your favorite periodic table.

    I’d be astonished if he can end up with anything simpler than NI’s Construction Conventions and the information required to take one of three paths from them to fdps, helium-above-beryllium.
    A few added, simple steps take one to a number of popular tables.
    Spirals are the easiest graphical representations of the Periodic Law to construct, up to a crucial point: indication(s) of Groups’ memberships.


    (If you’ve heard enough from Bent, just write “Enough!” HB)

    1. PFED. The Phenomenon of First-Element Distinctiveness refers to the chemical elements’ distinctivess with respect to their congeners and first-row neighboring elements, considered as SIMPLE SUBSTANCES — and also, if one likes, as atoms (Eugen).

    2. MODELS AND PERIODIC TABLES. Periodic tables are models of the Periodic Law. To be useful, they must be, like all models, wrong, in some respects. Otherwise they would be the thing itself, not a model of it. Obviously a ball-and-stick model of a molecule is not the molecule itself.

    The trick in using models is seeing in what ways they are right (i.e., useful) and in what ways they are wrong (not useful). What are their positive and negative analogies?

    Periodic tables are no different than molecular models, in being “right” and “wrong”. What’s the best molecular model? A ball-and-stick model? A Dreiding Model? A conventional space-filling model? An unconventional valence-sphere model (a.k.a. “charge cloud models” and “tangent-sphere models”). As impossible as unnecessary to say. I use all of them, often at the same time, as I do with my favorite models of the Periodic Law.

    3. NATURAL. Are periodic tables’ Groups natural? What’s “natural”? Having something to do with constancy? I like Whewell’s Criterion of Naturalness for a Classification (NI, p15): “The arrangement obtained one way must coincide with the arrangement obtained another way.”

    Have Periodic tables’ Groups been obtained in several ways? Yes, of course. Historians of chemistry know that before chemists had the Periodic Law and Group-generating periodic tables, they had, on chemical grounds, the heavier chalcogens, halogens, alkali metals, and alkaline earth metals. And, of course, a set of “natural” Periodic Table Construction Conventions generates the same arrangements, in two recently described ways: from elements’ maximum oxidation numbers and from atoms’ first-stage ionization energies. Finally, use of Madelung’s Rule in Bohr’s Aufbau Process generates the same Groups.

    FOR THE CHEMICAL ELEMENTS, ARRANGEMENTS OBTAINED FROM FOUR SETS OF DATA OF VARYING DEGREES OF DISTINCT PROVENANCE COINCIDE! Ask our historian: Are there, in the history of human thought, any other, more natural arrangements?

    4. THE PLATONIC IDEAL? What it is? I’ve forgotten. Something to do with shadows and a cave? I’ll check it in a dictionary in a moment. First, here’s something that occurs in science; that may approximate the Platonic Ideal; and that Plato probably never thought of: TRUTH BY DEFINITION. Examples –

    THE CONSERVATION OF ENERGY. Energy, said Rankine, is conserved by definitions framed in strict accordance with Nature’s nature [beginning with Archimedes’ Law of Balanced Fall (his Lever Law), and definition of “potential energy”; then proceeding to Galileo’s Law of Free Fall, and definition of “kinetic energy”, in a manner that guarantees that energy is conserved; continuing with Joule’s Law of Arrested Fall (his paddle wheel experiments), and definition of a change in energy of a thermal reservoir, in the same manner; and concluding, for most chemical purposes, with the Lavoisier/Laplace Law of Free Chemical “Fall” in a calorimeter, and definition of a change in energy of a chemical system, as the opposite of the sum of the changes in energy of its mechanical and thermal surroundings, so that the change in energy of the whole works is, by definitions (framed in strict accordance with Nature’s nature), zero].

    [QUERY: Why, then, are we constantly urged to “conserve energy”?
    By definition, energy is always conserved.
    We can’t help but “conserve energy”.
    What are people really saying when they tell us to “conserve energy”?
    If we spoke more sensibly, might we act more sensibly?]

    THE CALORIE. Joule expressed, in Btu’s and foot-pounds, results of his experiments on friction, disbelieved by everyone except young William Thompson (later Lord Kelvin), who ran with Joule’s’ results. They became, eventually, thanks in large part to Thompson, a central theorem in the field of energetics, referred to as the Mechanical Equivalent of Heat. Finally, so certain became physicists of the truth of Joule’s equivalence, they made it a truth by definition: 1 calorie = 4.184000000 Joules. Illustrated is an initially disbelieved, controversial theory — like helium-above-beryllium — becoming a familiar fact.

    TRIADS. Discovered by Dobereiner decades before Mendeleevev discovered the Periodic Law, triads became for a time a subject of active research by a number of respectable scientists. Today triads have become almost a truth by definition, easily seen to be a “trivial consequence” of Chemical Periodicity’s dyadic character.

    ISOELECTRONIC CORES. For atomic cores, latent in Mendeleev’s concept of “basic substance” and introduced into chemistry by Lewis and Kossel, one recognizes a truth by definition: cores of elements in the same row of the same block of a periodic table are isoelectronic with each other. Periodic tables’ blocks’ rows and columns are about atomic cores and their electron clouds.

    LIGHT’S VELOCITY AND AVOGADRO’S NUMBER. Determinations of “c” and “N-sub-A” were once considered major achievements in the history of physical thought. Today the velocity of light is a defined truth and it appears likely that the same fate, or Platonic destiny(?), awaits Avogadro’s number.

    PLATONISM (American Heritage Dictionary): “The philosophy of Plato, esp. insofar as it asserts ideal forms as an absolute and eternal reality of which the phenomena of the world are an imperfect and transitory reflection.”

    It fits like a glove. Insofar as truths by definition are “absolute and eternal”, they are specific examples of Plato’s “ideal forms”. Would Plato agree?

    In summary: Truths by definition are to Plato’s ideal forms as atomic cores are to Mendeleev’s basic substances: simple aids to thought.

    Adding, however, that “the phenomena of the world are an imperfect and transitory reflection” of “ideal forms” puts the cart (the ideal forms — such as truths by definition, framed in strict accordance with Nature’s nature) before the horse (the phenomena of the world). That’s the naïve, school-room view of science. “Science begins with definition.” That’s where it ends up, when successful. Chemists and alchemists, and before them the Greeks, struggled for a long time to define one word: “element”. Now we have truth by definition. Chlorine, by definition, says our historian, is element number 17.

    Putting the horse (the phenomena) before the cart (ideal forms) makes one an Aristotelian: “A person who tends to be empirical or scientific in his methods or thought” (AHD).

    Looking back on my own career, I’d describe it as a drift from an early, relatively unproductive, immature infatuation with mathematics, thermodynamics, quantum mechanics, and a search for absolute and eternal ideal forms, through deductive reasoning, to, instead, a deeper and deeper love of the phenomena of the chemical world and REASONING BY INDUCTION TO NEW IDEAS.

    That clears up a lot! A Platonist has a hell of the time with “New Ideas”. Its inductions are simply incomprehensible. That’s because a mind shaped by Platonism is a mind that is in poor shape to cope with a book based on the methods of Whewell’s “Inductive Sciences”. Not surprisingly, the book is denounced for being obscure because poorly written and, consequently, publishable only by a “vanity press”. In vain has the book’s author urged its critic to read the book. It might correct all his misconceptions regarding the Periodic System. No thanks! Called to mind is the little boy who asked his mother what a penguin is. “I think it’s an aquatic bird that lives in Antarctica,” she said. But you’d better ask your father. “Oh, no” he said, “I don’t want to know that much.”

    Thank you, ES. It’s been interesting and useful to have the practical consequences of a Platonic mindset exhibited so clearly. Keep up the provocative work.

    To Aristotelians intent on devoting their lives to the methods of the inductive sciences, one may offer an old Chinese proverb: “Fools persisting in their folly find wisdom.”

    For foolish Platonists, what hope is there? Some evidence in my own work, early on, on an application of the theory of vector spaces to the calculation of thermodynamic derivatives, supports the view that persisting with “ideal forms” that, like vector spaces and thermodynamic derivatives, seem destined for “absolute and eternal reality” may yield wisdom, of a sort: if not new knowledge, then at least new routes to previously known knowledge. Mathematicians consider such work, that of Ostwald’s synthesizers, to be as important as the work of Ostwald’s discoverers of new knowledge.

    A Platonic turn of mind may inspire knowledge synthesizers, in emergencies. History suggests, however, that a powerful Aristotelian turn of mind is necessary for discovery of new knowledge.

    Einstein’s life raises a cautionary note for Platonists. Young Einstein was an Aristotelian, in the work, e.g., for which he received his Nobel Prize, and in his work on the anomalous heat capacity of diamond, which persuaded physicists that Planck’s ad hoc quantum theory of black body radiation — the details of which, like PFED for chemists, were unknown to most physicists at the time — might in fact, be significant for physics. Every physicist was familiar with specific heats. And diamond’s unusually low value, at room temperature, was a phenomenon (well-known to chemists) that they could easily accept. Einstein seems to have become a Platonist, however, in his less productive senior years.

    What He/Be Theory needs is a young Einstein, to show people interested in periodic tables that He/Be explains some WELL-KNOWN anomaly.

    What might it be?


  81. More Fibonacci- see

    According to the author, the Fib. number 89 is special in base 10:

    >89 is a particularly special Fibonacci number in base 10 because 1/89 is


    a repeating decimal of 44 digits which is also equal to the sum

    SUM [ Fn / 10n ]

    which is the sum of


    adding all the Fibonacci numbers while shifting each one one place further to the right. The fact that this sum creates a repeating decimal (and furthermore, the reciprocal of a Fibonacci number) seems at first to be non-obvious and surprising.<

    If Z=120 is the end of the PT line, 89Ac is the beginning of the end. so to speak.

    Jess Tauber

  82. Prof. Bent, you have conflated Roy and I into the same group, when our electronic configurations are clearly different! My name has 2 s’, so I’m at least s2.

    Valery, I also am pretty much sold at this point on Bent’s division into primary, secondary, tertiary, and quaternary kinships. Makes life much easier (though the nomenclature after primary suggests a hierarchical relation which I don’t think is the greatest idea, but maybe is unavoidable given the way humans classify).

    I had a Kekule-like reverie last night, in which the tetrahedral model underwent matrix operations along its various axes (4 vertex to opposite base, and 3 edge to opposide, perpendicular edge). My actual models aren’t enough like a Rubik’s Cube to do this, but a computerized version might make it easier.

    I’m still trying to determine if this is of any use- shuffling the spheres out of their comfortable complacancy hypothetically might deliver configurations that more resemble what we actually know about chemical/physical behavior of elements. But who can say at this point whether it was all just a dream……

    Jess Tauber

  83. Hi Henry,

    A few quick points.

    Thank you for conceding that the first member triad rule is indeed your invention.

    Ah yes, Leeland Allen! Was he not the chemist who during the polywater episode insisted that it had to exist because of his own theoretical calculations. He subsequently wrote articles in New Scientist etc. in which he explained how we can learn from our mistakes.

    I agree with much of what you say about chemical education as practiced today. I too dislike the constructivist school of chemical education. You may recall that article I published in J Chem. Ed. which you did your best to suppress. It has been the basis for many interesting subsequent discussions with several more currently in press.

    Memorization is not an issue at UCLA. Even though we teach classes of 350 we provide them with all equations, formulas AND a medium-long form periodic table during exams. Nor do we use multiple choice exams of any form.

    eric scerri

  84. My responses to Eric,

    “Triad first element rule” is obvious. Just look at Jantes LST 1928 version that Eric favors. It is not hard to see that there are no triads that include group first elements in 28 out of 32 groups (if f-block is considered), or in 14 out of 18 groups if only s-, p- and d- are considered.
    On the other hand, in Janets corrected version of the table, where he placed He above Be and H above Li, none of the first group members form triads. Therefore, 1928 version of LST is irregular and Janet’s corrected and final LST version, where non of first group members form triads is perfectly regular. By the way, if Mendeleev was wrong sometimes, Jensen could be wrong too! I’d go with Janet on this one.

    Eric, in your latest writings about changing your mind on few subjects, you openly declared that you have changed your mind in regard to position of He and H not because of some scientific or logical considerations, but because, in your view, majority of chemists would never agree with He over Be favored by Janet and us. Well, even majority of chemists could be wrong too for some time! Question, if in few years we would be able to convince “the majority” to move He to Be, would you change your mind again?

    2) In response to Eric’s question in regard to priority of Z and n+l, I would like to note that in order to come up with any classification that make sense, one have to come up with construction conventions and give priority to some data over the other. Therefore, Henry is absolutely right in his book when he identifies primary, secondary and tertiary kinships, triads, etc. and not mixing them up, as you do. Therefore, identifying such priorities as continuity in accordance with atomic number, then breaking it in accordance with “n+l” levels, followd by the stacking in accordance with “l” to obtain blocks, then shifting blocks in accordance with “n” and finaly, shrinking them in accordance with “ml” and “ms” is the correct and systematic approach to the classification of elements, instead of confusing different traits and treating them equally.



    1. ES says of the Triad First-Element Rule: “This rule is a pure Bent invention.”
    Got to love it! But, in truth, Eric, that’s not exactly the case, as you should know, if you’re read your Whewell, and looked at any periodic table.
    The situation is an example of Whewell’s “Fundamental Antithesis of Science”: “Things and Thoughts” — Man added to Nature. (Now, I know: You’re going to tell me that you know all about that. . . . Well, then, why not have used that knowledge?)
    The “Thing” in this instance is Nature’s nature, as encoded in periodic tables.
    The “Thought” is a verbal statement of what’s seen when one looks at the table:
    Call it “Bent’s [second] Rule”, if you like. I call it “The Triad First-Element Rule”, valid throughout all modern periodic tables, provided helium is located above beryllium.
    Locating helium above neon creates two exceptions to the Rule: at the neon column and at the beryllium column. WIth He/Ne, not He/Be, you’re the odd (or even?) man out: 2 out vs. 30 in.
    TFER has not been stated by others because almost all periodic tables have helium above neon, and nothing above beryllium. For such tables, TFER is not universally valid.
    The Rule is so simple I’ve assigned its capture to beginning students for them to discover for themselves. No problem. As my young grandson said of helium-above-beryllium, “It’s a no brainer.”
    Even the dullest students see almost at a glance that the Triad First-Element Rule is a rule that has been framed in strict accordance with Nature’s nature. It is not, in your words, “a pure Bent invention”. Can we agree on that?

    One should add that the idea of “maximizing [primary] triads” is, however, bizarre, indeed! WHERE DOES IT COME FROM? What’s the justification for it? Theoretically? Empirically? It just seems to arrive out of thin air. It’s a PURE SCERRISM.

    The Triad First-Element Rule is, in Philip’s words, a trivial implication of Periodicity’s dyadic character, expressed most clearly and fully by the left-step periodic table. My grandson had the right words for the Rule. It’s a no-brainer. It not only handles the He problem. It handles as easily the La Ac/Lu Lr problem. That fuss over them in JCE was a tempest in a teapot.

    2. ES writes: “I have done a careful survey of what Mendeleev says on this subject [of “basic substances”] and I don’t think he would agree [with Bent]. Nowhere does he actually identify concretely what he means by element as basic substance. [Correct. Mendeleev struggled with the idea. He used several different phrases to express what he was attempting to get at. In retrospect, we can see why. He sometimes entertained doubts regarding “atoms” and vigorously rejected the idea of subatomic particles. The notion of “atomic core” was something, therefore, that he could not conceive of — but that, by a great leap of the imagination, i.e., by a huge induction, he might have invented. He missed the boat there (albeit no one should fault him for that), as he did with the Noble Gases.] He merely points out that this sense of element is more fundamental [than an element as a simple substance]. But it is a philosophical notion which aims at taking into consideration bonded elements as well as elements as simple substances [which is precisely what the notion “atomic core” does!!! Atomic cores exist in “bonded elements as well as [in] elements as simple substances].” ES’s previous remarks regarding chloride ions suggest, however, that he hasn’t a mental image of what atomic cores are.

    (This blog began as a brief note and grew)

    Roy, You’re right. Your copy of NI from Princeton’s library was annotated by professor Lee Allen. His life and mine have run, partly, along parallel paths: alumni of the U.S. Navy’s Radar Technician Program in WWII; PhD’s in physical chemistry; and academic positions at research universities with, among his many interests, an interest in descriptive inorganic chemistry and periodic tables.

    One of my favorite figures in NI is Figure 44: “Plots of Allen’s electronegativities vs. P(fdps)”, for, among other things, the detailed and dramatic quantitative support it gives to the phenomenon of first-element distinctiveness in the s- and p-blocks, and particularly for its location of helium above beryllium. Nothing like that — and its companion Figure 40 — exists for location of helium above neon. He/Ne Theory is perhaps the most circumscribed theory in the history of science. It “accounts” for one fact: helium as a simple substance is like neon. That’s it. Period. End of story. There’s no book about it waiting to be written.

    Allen tried to get Princeton University Press to publish NI. No go. It publishes books on science, but not on chemistry. Something there is about chemistry that’s off-putting to non-chemists: so much detail; so many partial theories; so many exceptions. Pauli didn’t like chemistry. You have to know so much chemistry to use its theories, he said. Chem101 used to be a popular course, nonetheless, when taught by masters of teaching in the “grand manner” from demonstration-experiments. No more.

    It’s been the misery, for students, of success, for research professors. After WWII contract research WITH OVERHEAD led to university tenure and promotion policies that channeled top talent into research and led to ever narrower PhD programs, in order that graduate students could stay on task as close to 24/7 as possible, cranking out research that supported publications that supported professors’ grant proposals that determined their promotions and tenure. First to go were foreign language requirements, next the minor, then comprehensive examinations in the major. Turned out have been graduates who know more and more about less and less and are poorly prepared to teach in the “grand manner”.

    (It’s never been truer that PhD means “piled higher and deeper”. My late son noticed that when he was a graduate student at Berkeley in the 1980s. The longer his friends were in graduate school, the narrower they became. Brian overcame that phenomenon by following a suggestion passed on to him by his father from a friend of his grandfather’s, E. Bright Wilson of Harvard University: Attend seminars outside your field. To judge by his calendars, Brian did, almost daily!)

    When my father retired after many years as a research chemist, chemistry professor, and graduate dean, including service in Washington, D. C., as the nation’s first administrator of its graduate fellowship program under the NDEA (National Defense Education Act), following Sputnik, he photographed his splendid collection of demonstration apparatus, perhaps the finest collection in the country for teaching general chemistry in the “grand manner”, mounted the photographs in albums, with explanatory captions, and gave copies to the younger faculty involved in teaching general chemistry. Their response? A question: Would you like to do the demos for my class? A few years later, to make room for research programs, they trashed the equipment! It broke my father’s heart. It still makes me angry, merely to think about it.

    Since then things have gone further downhill. The void left by migration of talent to research has been filled by “chemical educators”, more concerned with how students learn than what it is they learn. The animals have, in effect, taken over the zoo. Huge textbooks, costing three times as much as all my fees for a term at the University of Missouri in 1942, have never looked more impressive, to untutored eyes, and never have been more shallow in their science and more naïve in their pedagogy. Chapters end with column after column of mind-numbing numerical exercises to be solved by means of memorized algorithms.

    Chem101 has become a faith-based course permeated by topics — atomic orbitals, molecular orbitals, entropy, the Gibbs energy, &c. — that beginning students can’t possibly understand, step by step, from the ground up, in an intellectually stimulating manner, “How do you get a good grade in Chem101,” I’ve asked honors students. “BY MASSIVE MEMORIZATION.” The result? The winning ACS Student Affiliate Bumper Sticker one year: “Honk if you passed p chem.”

    On the Graduate Record Advanced Chemistry Examination, 150 multiple choice questions to be answered in 3 hours (a terrible exam), the average score used to be about 50 questions answered correctly, 50 incorrectly, and 50 skipped. A monkey would have done nearly as well. “We’re not learning much of anything about the students,” we said. “We’ve got to spread out their scores.” Make the questions easier? Done. Removed were questions usually missed or skipped, replaced by questions from Chem101. You guessed it. Scores dropped! Test takers had largely forgotten what they had never understood when they passed Chem101 by “massive memorization”.

    Enter the periodic table. It’s introduction and non-use in Chem101 is typical of the entire failing enterprise. Students generally see only one table, with twenty-eight (sometimes thirty!) elements in two footnoted series, usually footnoted in such away that it is impossible to determine which element goes beneath yttrium. Students are told that the table is determined by atoms’ electronic structures, which they dutifully learn to write. And then immediately element 2, an s2 element, is located above element 10, a p6 element. And Chemistry is on its way to being a “chemystery”.

    “Oh, chemistry,” said a work-study student checking out books for me. “What’s wrong with chemistry?” I asked. “It all seems so strange,” she said. That’s highly paradoxical. A nonchemist from Mars might think that it would be virtually impossible for “chemical educators” to make a science — whose central doctrine (collision theory) shapes our bodies and civilization — seem “so strange”.

    For to react chemically, molecules must collide physically with bond-breaking violence. That’s why we have legs and feet, hands and arms, eyes, and, for hand-eye coordination, central nervous systems, to collect food; jaws and teeth, stomachs, stomach acid, and other catalysts, to speed digestion of food to transportable particles for transport to our bodies’ organs’ cells; a nose and lungs, to collect oxygen; hemoglobin, blood plasma, arteries, and a pump, to transport oxygen to organs’ cells; and, to maintain our bodies at temperature that ensure that the advancement of the biochemical reactions of life in our cells occurs at life-sustaining rates, clothing and shelter; and to pay for food, clothing and shelter, jobs; and for good jobs, schooling; and to get to those good jobs, cars; and to fuel our cars, oil imports; and to protect sources of imported oil, oil wars; and to execute oil wars, armed forces; and to support our armed forces, taxes; &c., all to enable us to get to work to earn money to pay for food, clothing, and shelter in order to maintain our bodies at temperatures at which the fires of life proceed at life-sustaining rates.

    That’s the story that chemists could tell, with all its beautifully worked out detail at the molecular level involving not only carbon, hydrogen, oxygen, and nitrogen atoms, but, also, for critically important enzymes, metal ions from across the periodic table, all enlivened by striking demonstration-experiments in which — as in research — each demonstration-experiment follows from the previous one and leads to the next one. Seeing that happen right before their eyes in real time, with time for questions, students, teachers, principals, and parents have said of “Van Visits” that featured The Big Four [Flammable Gases, Liquid Nitrogen, Dry Ice, and Chemical Commentary, by chemists! (the work cannot be safely and successfully outsourced to nonchemists)] is the best thing that has happened around here. It’s not the story, however, that’s being told today in that manner by “chemical educators” in campuses’ “killer course” Chem101.

    Thanks for reading,

  87. The “triad first element rule” is simply a statement of the position that the 1s period and the 2s period form a pair. Moving H and He to make a first period of four elements can be argued (if electronic structure is ignored) on the basis that He behaves like a noble gas, but certainly not on the supposition that H is in any respect, other than valency, like a halogen.

    Chemical facts are in any case not enough; on their basis Mendeleev made separate groups of Be, Ca, Sr, Ba and Mg, Zn, Cd, likewise of B, Sc, La and Al, Ga, In, likewise of C, Ti, Z, Ce and Si, Ge, Sn, likewise of N, V, Nb and P, As, Sb, likewise of O, Cr, Mo and S, Se, Te and finally of F, Mn and Cl, Br I (though the last two cases were more to fit in with the structure of his table). His B-Sc rapprochement was particularly successful as it led to the discovery of Sc. Note also that for decades Ac, Th, Pa, U were placed under Sc, Ti, V, Cr on the basis of chemical facts.

  88. Dear ‘gang’,

    The latest issue of the Chemical Information Bulletin, published by the ACS division of the same name (Division of Chemical Information) contains an interview with me on our favorite topic, the PT.

    the interview has its own URL,

    No doubt you will be doubling your efforts to tell me I am wrong on absolutely everything.

    Please also see,

    all the best,

  89. Dear Valery,

    I would be interested in a clarification of your statement,

    “In regard to Ni group argument, Pd and Pt are exceptions, but if one considers elements as “abstract atoms” and realizes that arranging them in accordance with atomic number Z and n+l takes priority over arranging them in accordance with “n” and “l”, those exceptions are not going to look as bad for the overall order.”

    especially the last part, “arranging them in accordance with atomic number Z and n+l takes priority over arranging them in accordance with “n” and “l”, those exceptions are not going to look as bad for the overall order.”


  90. Henry writes,

    “Eric, regarding triads, you’ve never acknowledged, to my knowledge, the Triad First-Element Rule (emphasized in NI). Your triads H F Cl and He Ne Ar violate that Rule. Your response?”

    This rule is a pure Bent invention. First element anomalies are indeed discussed in many textbooks as you correctly stated a few days ago but nobody other than you has ever formulated a rule that bans first elements from belonging to genuine triads.

    Ergo, no need to adopt any position on the matter.


  91. A few thoughts on elements as basic substances.

    Henry uses this notion to justify ignoring the obvious chemical similarity between the properties of He and the noble gases.

    I have done a careful survey of what Mendeleev says on this subject and I don’t think he would agree. Nowhere does he actually identify concretely what he means by element as basic substance. He merely points out that this sense of element is more fundamental. But it is a philosophical notion which aims at taking into consideration bonded elements as well as elements as simple substances.

    Henry wants to identify elements as basic substances with atomic cores. I believe this is incorrect. The only identification one can really make is with Z for each element.

    Mendeleev made a number of predictions as is well known. These concerned the elements as simple substances just as much as their properties when present in compounds. For example he predicted melting and boiling points of elements, their specific gravities and so on.

    If he had predicted He I dont suppose he would have said, oh I cannot possibly predict the properties of this one element as a simple substance because Henry Bent will not like this 140 or so years later. And even today we can only infer the properties of He as a basic substance from its chemical behavior as a simple substance. It does not occur as a bonded element of course.

    But too many of the Platonists here wish to reduce everything to configurations, atomic cores and in one or two cases just numbers. I say it’s a good thing that none of you are chemistry teachers.

    It may just turn out that He has some chemical properties similar to the alkaline earths but until somebody reports this fact (in a reputable publication) we should all stick to the chemical facts.

    eric scerri

  92. I would be interested to know what ” the world’s leading authority on the periodic system, Professor Jensen”, thinks about the LST. But I know the answer. He does not approve of He over Be.

    How could he mistaken over such an important question Henry?

    And just for you Henry, Bill Jensen and I are talking again, very cordially. We had a few exchanges regarding the group 3 debate which appeared in J. Chem. Ed. following Lavelle’s suggestion that group 3 should remain as Sc, Y, La, Ac.

    It seems to me that this is perhaps the one thing that all of us here agree on is that this group should be Sc, Y, Lu, Lr. But I could be wrong of course.

    eric scerri

  93. For the Forum: AN ANALOGY: He/Be and Evolution.

    Evolution: Theory or fact?
    Whewell’s answer: “A Fact is a Familiar Theory.”

    [William Whewell was an English polymath, an Historian and Philosopher of a classic, multivolume account of “The Inductive Sciences”, and a contemporary of (and consultant to) Michael Faraday (on, e.g., electrochemical terminology, widely used to this day.]

    To biologists deeply familiar with many biological facts, evolution is an extremely useful fact, the central dogma of their discipline.
    For individuals familiar with only a few biological facts, evolution is a dubious theory of no use to them whatsoever.

    Likewise for helium-above-beryllium.
    For chemists thoroughly familiar with regularities contingent on He/Be, He/Be is a useful fact, literally one of the leading facts of the Periodic System.
    For individuals not familiar with regularities contingent on He/Be, He/Be is dubious theory of no use to them whatsoever.

    Explained is the famous remark: “DON’T CONFUSE ME WITH THE FACTS.”

    One might have to change one’s mind — reason enough, perhaps, for an advocate of Helium-above-Neon Theory not to study a fact-filled book that describes the usefulness of helium-above-beryllium.


  94. A reply to the statement that “it is not ‘unlawful’ for there to be no 1p subshell to go with 1s, it is certainly singular.”

    Three negatives make a negative?
    It is lawful for there to be no 1p subshell?
    It is not lawful for there to be a 1 p subshell?
    It is unlawful for there to be a 1p subshell?
    I guess I agree. Yes. Yes. Yes. Yes.

    Subshell 1p is “certainly singular” in this sense:
    The principle quantum number n = 1 (of np = 1p), means 1 nodal surface.
    The angular quantum number p means 1 nucleus-containing nodal surface.
    But there’s always a radial nodal surface at infinity.
    Put algebraically, always n = r + l and always r ≥ 1. Substituting n = 1 and l = 1 yields
    1 = r + l. Adding r ≥ 1 yields the “singular” result 1 ≥ 1 + 1 = 2.


  95. Eric, regarding triads, you’ve never acknowledged, to my knowledge, the Triad First-Element Rule (emphasized in NI). Your triads H F Cl and He Ne Ar violate that Rule. Your response?

    Also, in stating that you were maximizing number of triads, meaning number of PRIMARY triads, you didn’t qualify your statement in any manner whatsoever, much less in a precise manner, hence the appropriateness of Valery’s reductio ad absurdum. I suspect it would be exceedingly tedious to qualify your statement in a scientifically satisfactory manner. Perhaps you can prove me wrong. Maximize number of primary triads, subject, precisely, to what conditions? (As you may know from a study of differential equations, it’s boundary conditions that pretty much determine solutions’ shapes.)



    At first glance, H/C in periodic tables might seem to make a lot of sense.
    As pointed out by Marshall Cronin, an organic chemist,
    the elements have half-filled shells and nearly the same electronegativities.

    But as inorganic chemists would point out,
    Mendeleev’s periodic table was first and foremost an oxidation table,
    and the maximum oxidations numbers of H and C are +1 and +4.

    [Cronin might counter by pointing out that from oxygen onward in the p-block
    and from iron onward in the d-block
    Groups’ first elements haven’t the same maximum oxidation numbers as their congeners (those “exceptions” are examples of first-element distinctiveness).
    Mendeleev would say: Nonetheless, the facts of chemistry — meaning, in his day, those chemical facts that led by Cannizzaro’s Method to a system of rational atomic weights — require those assignments for O, N, and F and for Fe, Co, and Ni.]

    Physicists would say that H and C haven’t the same number of outer electrons. Nor are their outer electrons of the same type.

    A lover of the left-step periodic table would say of H above C: “That’s weird! H sticks out like a sore thumb! H-over-C compromises the table’s overall regularity! Lost are all regularities contingent on helium’s location above beryllium!” That was no problem for a non-inorganic chemist (i.e., an organic chemist). [“Minus times minus equals plus/The reasons for this we need not discuss.” (Auden)]. Cronin wasn’t aware of those lost regularities. He later dismissed the simplest ones, such as The Triad First-Element Rule, as “pure numerology”.

    [“Exactly!” Mendeleev might say. Somewhere, as I recall, DM expressed the view that the eventual explanation of Periodicity, unexplained in his day (beyond the fact that it follows from the facts of chemistry), would found in a theory of integers — as, indeed, turned out to be the case, in the form of physicists’ classification of atomic spectra explained in terms of quantum numbers.]

    A philosophical chemist and lover of distinctions would say: “Hydrogen’s kinship with carbon is not a PRIMARY kinship. Vertical arrangement of H and C in periodic tables is, therefore, not appropriate.”

    [The H/C distortion of the periodic table by an organic chemist calls to mind the famous layout of the states of the United States of America by the proverbial parochial New Yorker. Everything west of the Hudson River is compressed into a small region.]

    The world’s leading authority on the Periodic System, professor William Jensen, has said that Cronin’s paper in J. Chem. Educ., on H/C, is the worst paper he’s ever seen.

    Aside from misguided appropriation of hydrogen for the Group containing his beloved carbon, most of what Cronin says about the chemistry of hydrogen and carbon (and silicon) is interesting, from a chemical point of view.

    Every student of organic chemistry should be aware of similarities between carbon and hydrogen. A recently completed personal study of molecular dipole moments begins with the observation that the dipole moment of (CH3)2CH2, in which two CH3 groups have been substituted for two of CH4’s four H atoms, is nearly zero. (The study proceeds from there by way of the Isoelectronic Principle.)

    A time-honored method exists for encoding in periodic tables the information Cronin sought to display. COLOR CODE elements’ locations by their electronegativities, e.g., — or any other property.

    Tabular representations of the Periodic Law have the virtue that colors can be saved for display of non-periodic properties, since color-coding needn’t be used, as it sometimes is with spirals, to make immediately clear to the eye Groups’ memberships. That’s indicated by verticality.

    Periodic TABLES feature verticality. Periodic SPIRALS feature continuity. Betwixt the two “they lick the platter clean.”

  97. Henry,

    thanks for these words:
    “Were wall-decorating with periodic tables my business today, I’d start with Philip’s beautiful “Spiral, Version III” and depict in a step or two how it easily morphs into the left-step table and, thence, to your beautifully symmetrical table”

    Yes! In addition to the symmetry due to quantum number “n” that my table shows in 2D, I would have 3D display with s, p, d and f rectangular blocks placed one behid the other in order to display the symmetry of “ml” values that you discovered first (see NI) and then everyone would realize, and eventually agree upon, that all this PT business is about most simple and beautiful geometric 3D shape: Regular Tetrahedron!

    Then, no one would be surprized that Alkaline Earths metals at the base of the tetrahedron have atomic numbers mathematically connected to Tetrahedral Numbers!

    I wish you would be back in classroom teaching.

  98. Dear Valery and Henry,

    On the question of maximizing atomic number triads. I did not claim that this was the only criterion even if I implied as much while trying to counter Henry’s use of 57 approaches to argue for his table.

    Triads have been historically deceptive. They involve a conjunction of numerical averages and intermediate chemical behavior.

    I do not propose maximizing triads in a hell bent, all over the periodic table, fashion. I propose using them in difficlt cases such as H, He, Lu, Lr, La, Ac.

    Mg for example sits comfortable in the alkaline earths in terms of chemical properties. In any case I have consistently claimed that atomic number triads are a result of the repetition of all period lengths. Moving Mg would be a violation of that.

    It is interestin that you mention Ac. Chemically speaking Lu not Ac should fall in the place that Valery suggest. The confoirmation of this is from Jensens, 1982 paper in chemical terms and from the fact that Y, Lu and Lr form a perfect triad.

    Placing La below Y does not work from the point of view of continuous numbering. Just try it on a long form table.

    A good example of using triads in only a numerical sense and ignoring the chemistry occurred with Lenssen as I discuss in ch 3 of my book.

    Similarly Mike laing disputed my new triad recently in a letter to J. Chem. ed. and proposed a number of other contrived triads made up of rare earths.

    Please see my response to him or ask me for a copy by regular E-mail.

    So triads are about chemistry and numerical aspects. In the case of H and He the chemical similarities are not so clear and that’s what makes this discussion so interesting.

    all the best


  99. Philip- you can make quite nice triads with element 0 (for example, 0,2,4, which puts He above Be!). What the nature of element 0 actually would be I leave up to individual tastes. Mathematically it all fits.

    As for where He belongs, I’m happy to be ambivalent- systemically it goes with the alkaline earths, behaviorally it goes both with first members and the noble elements. SO WHAT?

    Even the last nobles aren’t p6 anymore. These properties travel, and association with particular groups isn’t fixed in stone (or metal….). I think we really need to know the electron configurations and behaviors of all of 6d, 7p, and 8s to see how all this really pans out, and to drive these points home.

    Jess Tauber

  100. Jess: There’s no way element zero could be the naked electron. Atomic number is the number of protons (whether or not associated with neutrons), so element zero must have no protons (hence no electrons); all that is left is the neutron. Matter consisting only of neutrons is thought to make up much of the mass of neutron stars. Whether you follow Antropoff (1926!!) in calling it neutronium is up to you. Antineutronium would be element minus zero, the bridge to a periodic system of anti-matter. On the possibilty of parallel periodic systems see (reference thanks to Mark Leach)

  101. IF one starts with the naked electron (electride ion) as ‘element 0’ (which might help one to create early triads) then we get a relatively consistent general repeated trend of bonding character/metallicity through the entire ‘periodic string’, with increasing emphasis on metallicity.

    Where each repeat sequence starts/ends, though, SHIFTS. For elements 0,1,2 we have maximal quantization, one Z for each type. The more elements are in each period the less crisply quantized the mapping becomes- it gets ‘smeared out’, which is interesting because it correlates with increasing involvement of relativistic effects, which are CONTINUOUS.

    By the time one gets to 7p and 8s, even ‘nobility’ appears to have ‘moved’, and is much, much weaker than what one sees with He.

    Jess Tauber

  102. Eric writes:
    “He is s2 but classified among the noble gases by almost everyone except Bent and Valery.”
    I think that Philip and Jess should also be added to Eric’s list.

    In regard to Ni group argument, Pd and Pt are exceptions, but if one considers elements as “abstract atoms” and realizes that arranging them in accordance with atomic number Z and n+l takes priority over arranging them in accordance with “n” and “l”, those exceptions are not going to look as bad for the overall order.

  103. I quote, “How about La next to Y and Mg next to Zn?”
    These element boxes are in touch at
    Also in the same image, with the convenience of an extra dimension, He (over Ne) gets to be next to H (over Li), but not so close to Be as would please some.
    Do y’all see errors in my statements about kinships in that image?

  104. Eric says:
    “He is s2 but classified among the noble gases by almost everyone exc ept Bent and Valery.
    The Ni group has three elements with different electronic configurations! So possession of a particular configuration is neither necessary nor sufficient for group membership.”

    Right. Right. Wrong.

    Introduction of the phrase “electronic configurations” introduces a straw-man.
    Classification of the chemical elements according to the Periodic Law is not, in its deepest sense, based on “electronic configurations” of ATOMS. Were that so, there’d be no exceptions to the Madelung Rule.

    From an electronic point of view, the Periodic Classification of the Elements is a classification of ATOMIC CORES, by charge, primarily, secondarily by “electron configurations” of the cores themselves.

    CORE CHARGE determines atoms’ NUMBERS of valence-shell electrons, if not their type.
    Cores of Ni, Pd, and Pt all have a charge of +10 (their Group’s number in a systematic and natural Group-labeling scheme). The corresponding atoms all have, accordingly, 10 valence-shell electrons. Same number of outer electrons is necessary for Group membership, if not sufficient.

    The issue of insufficiency arises from the phenomenon of SECONDARY CHEMICAL KINSHIPS. It’s the reason for the existence of some 700 periodic tables — and this blog?

    Regarding He:
    Strip away its outer electrons. What’s left? Its core. Its charge? +2.
    Take Be. Strip away its outer electrons. What’s left? Its core. Its charge? +2.
    Finally, take Ne. Strip away its outer electrons. What’s left? Its core. Its charge? +10!

    Locate He above Be. What have you? All the regularities in the Periodic System contingent on location of helium above beryllium in periodic tables. What are those? Ask a scholar of the periodic table. Ask ES? He’s a PFED denier. And the Triad Rule: has he denied it? No. He hasn’t responded, one way or the other. He just violates it, without comment.

    Is the fact that “He is s2 but classified among the noble gases by almost everyone exc ept Bent and Valery” a necessary and sufficient condition for that classification to be correct?

    At one time almost everyone except Lavoisier believed Phlogiston Theory was correct.
    Helium-above-neon is an excellent candidate for being considered modern chemistry’s phlogiston. Everyone knows that in combustion heat and light are EMITTED, for heaven’s sake.
    And everyone knows that helium, like neon, IS AN INERT GAS, for heaven’s sake.
    And, moreover, every student of chemistry knows that beryllium, unlike helium, is a METAL, for heavens sake.

    Speaking of which:
    Every student of chemistry knows that metallic character increases downward in Groups.
    And every scholar of elements’ metallic character knows that, whereas magnesium, and especially its heavier congeners, Ca, Sr, and Ba, are good metals BERYLLIUM IS A POOR METAL!

    Note the trend: Ba, Sr, Ca: excellent metals; Mg: good metal; Be: poor metal.
    Note, also, the “gap” above Be in traditional periodic tables. Might it be the location of an unrecognized, nonmetallic congener of Be, Mg, and the true “alkaline earth metals”: Ca, Sr, and Ba?

    Lovers of He/Ne like to point out that “Helium is not an alkaline earth metal.” In fact, neither are magnesium and beryllium! Parallel statements hold for hydrogen, lithium, and the alkali metals.

    Modern chemistry’s phlogiston becomes curiouser and curiouser.


  105. Eric: you say ” I am not over-impressed by arguments about H being s1 and halogens being p5 being made by Henry and now Philip.” You can’t say “and now Philip”. I’ve been telling you for two years that I think triads are the trivial consequence of the structure of the system, with pairs of periods of the same length. As to H being a halogen, I have argued in print since 2003, with Cronon, that it behaves most like C, with its general preference for covalent bonding. H with C, together with N and O, account for most of the chemistry of life, while the halogens could be called, in caricature, “the elements of death”.

    Believe me, I really am, trying to stop blogging, but I feel I owe it to Janet to keep going.

  106. OK Jess, one more teeny weeny comment. The diferences between species are discrete jumps. and although it is not ‘unlawful’ for there to be no 1p subshell to go with 1s, it is certainly singular. I think you are forming a false dichotomy between sets like the elements and non-discreet sets.

  107. Eric,

    Isn’t moving He to Ne in order to create He-Ne-Ar triad similar to moving Mg to Zn in order to create Mg-Zn-Cd triad? If He is good next to Ne, why not Mg next to Zn? How about Sc-Y-La triad, just to be consistent?

  108. Valery, regarding maximizing the number of triads:

    Yours is the nicest reductio ad absurdum I’ve seen in a long time!
    How about a rectangle 1×120? 117 triads!

    The proposal to maximize triads expresses the proposer’s scientific and philosophic mindset in a nutshell. However, however nutty a challenge to, in Philip’s felicitious phase, the “LSPTable/spiral, version III” may be, each test it passes with flying colors contributes, however slightly, to its scientific soundness.

    I hope David can derive some small satisfaction from having contributed selflessly to a small yet perhaps significant contribution to the advancement of science — if not, thereby, having obtained relief from his boredom with the standard periodic table on his wall.

    Were wall-decorating with periodic tables my business today, I’d start with Philip’s beautiful “Spiral, Version III” and depict in a step or two how it easily morphs into the left-step table and, thence, to your beautifully symmetrical table, with, along the way, excursions to the long and medium long versions of the “standard” table. Imagine having that modern chemical mural across the front of chemistry buildings’ main lecture halls, or entrance lobbies. Off to the side might be a small stand, shelf, or wall box with brochures containing colored illustrations and explanatory notes, for students and visitors of almost any age and level of sophistication. At N. C. State we had a huge, standard periodic table across the front of our main lecture hall in the chemistry building and built into the lecture demonstration bench an elaborate control box with which to illuminate different portions of the table, by individual element, block, block row, period, &c. With modern technology, I suppose one could do all of that and more, easily (including moving H and He around). The though makes me nostalgic for returning to the classroom.

    Yours for better education in chemistry through better pedagogy through better handling of the Periodic Law,

  109. I agree with Jess Tauber.

    Philosophers of biology have argued for some time that species are not natural kinds since animals evolve. Being a natural kind requires that there be no change. Now of course elements did originally evolve from H and He etc. but given the conditions on earth for example that evolution has ceased.

    In fact philosophers of biology regularly cite elements as a significant remaining natural kind in science.

    Iff Z = 79 then the element is gold. That is to say Z being 79 is both necessary and sufficient for the element to be gold.

    The electronic configuration on the other hand is neither necessary nor sufficient for establishing the identity of elements.
    Or for that matter for the classification of elements as all these arguments here emphasize.

    He is s2 but classified among the noble gases by almost everyone exc ept Bent and Valery.
    The Ni group has three elements with different electronic configurations! So possession of a particular configuration is neither necessary nor sufficient for group membership.

    The motivation for my own book was the question of whether chemistry reduces to QM. I conclude that it does not reduce to electronic configurations at least. This is why I am not over-impressed by arguments about H being s1 and halogens being p5 being made by Henry and now Philip.

    all the best

  110. George Lakoff was one of my instructors at UCB- you are talking about Eleanor Rosch’s (also at UCB) prototype theory. I’m not sure that this particular theory is as good a fit as one might think, given that it deals with features that don’t tend to be ‘lawful’, but more like kluges. When a set of categories has nice crisp boundaries between them, quantized, this type of analysis misses a lot.

    The properties of elements are not wholly the result of a mix of continuously and smoothly shifting variables, as one might see with categorization of colors, or chairs, or dogs. The quantization is more fundamental.

    Jess Tauber

  111. Are Periodic System groups natural kinds? I go with George Lakoff on how the mind forms categories (in Women, Fire and Dangerous Things), chaining out from central representatives to more and more remote outliers. H and He are on the edge of the categories ‘s1’ and ‘s2’ elements, since neither is a metal, just as, for example, the penguin and the ostrich are on the edge of the category bird, neither being able to fly. But we would not put the penguin into the category ‘seal’, nor the ostrich with the tyrannosaur; nor shoud we classify H as a p5 element nor He as a p6 one. Anyway, I’m not for any more blogging; the dead horse has had enough flogging.

  112. Just as an aside- I get my library materials FROM Princeton, and the copy of NI I have has many annotations by someone who knows a LOT more than I. I’m guessing that this copy is the one donated to the library by said theoretical chemist!

    Jess Tauber

  113. I believe that choosing such criterion as “maximization of atomic number triads” over spectroscopically determined quantum numbers and atomic structure can hardly be considered objective approach.

  114. Philip,

    The question is not whether one should follow Plato or Aristotle but whether the question of the placement of certain elements like H and He does or does not have a definitive answer, regardless of whether or not we have arrived at the answer yet. Whether groups in the periodic table represent ‘natural kinds’.

    I believe they do. Your postings imply that you dont.

    Since David has been gracious enough to allow this discussion to continue I think we owe it to him to persist a little further too.


  115. Concerning your ugly accusations Henry,

    I’m glad of the opportunity to clear this up since you have held this against me for several years.

    Yes I was accused of plagiarism which was absolutely ridiculous given that I attributed you at the end of the paper and specifically thanked you for discussion on the first member anomaly business.

    Yes I did cite a string of your words on this question and did not cite your then ‘unpublished handbooks’ at that specific point in my manuscript. This omission was caught at the submission stage and corrected. The accusations of plagiarism went nowhere and I subsequently published many papers in J Chem. Ed. under the watch of the same editor.

    I am actually the only chemical educator in the literal sense in what you call this gang. Each year I teach a total of around 1,500 students. I have been doing so for 10 years at UCLA and several before that at Purdue. I mention the LST as an elegant curiosity which stands little chance of becoming accepted because He as everybody knows behaves as a noble gas.

    It is unfortunate that philosophers of chemistry like Paneth and myself have confused you into running with the idea of ‘elements as basic substances’ which you think allows you to ignore its obvious chemical properties.

    The properties of elements as simple substances cannot be ignored even though they may not be completely fundamental in classification. But hell bent persons can simply ignore simple substances, even in cases when an element doesn’t form any compounds.

    Valery can you please clarify what you mean about triads and La, Mg, Zn etc. ?

    all the best
    eric scerri

  116. For the Forum from Henry:
    It’s been suggested that the huge fuss over helium’s location in periodic tables is a tempest in a teapot.
    On the contrary: Located at the left-step periodic table’s upper right-hand corner, helium is the important starting point, or the concluding anchor point, of two major block-to-block trends (in first-element distinctiveness), both of which make helium the most distinctive — and, arguably, thereby the most important — element in the entire Periodic System!

    It would seem, accordingly, that it might be nearly impossible to be overly confident about helium’s best location in periodic tables. That’s the reason for “New Ideas'” alternative title: “57 Reasons (and counting) for Relocating Helium in Periodic Tables – Repeated Returns to the Helium Question: ‘To Be or Not to Be?'”
    He(nry) Be(nt).
    Of course, that focus on helium-above-beryllium pretty much makes the book impossible reading for helium-above-neon lovers — and PFED deniers.

    Because hydrogen and helium are the only two elements in the Periodic System’s first period, Mendeleev’s method of identifying the positions in his System of “eka-elements” and estimating their properties, by interpolations (his “Atom Analogies”), cannot be applied to hydrogen and helium. One must resort to extrapolations, from the f-block through the d- and p-blocks to the s-block (NI, Table 11, p90).

    Actually, a simple “atom analogy” that involves hydrogen and helium does exist (NI, p10).
    The LSPT’s arrangement –
    H He
    Li Be
    suggests this analogy: H:Li::He:Be.
    Replacement of the “is” of “:” by “/” and the “as” of “::” by “=” yields an alternative expression for the logical relation: H/Li = He/Be.
    (Incidentally, with that simple, familiar notation, one can, after appropriate translations, apply symbolic logic’s formal Rules of Inference — Modus Ponens, Modus Tollens, Hypothetical Syllogism, Disjunctive Syllogism, &c. — by merely using the rules of ordinary algebra.)
    Solving for “He” yields He = Be(H/Li).
    Insertion on the rhs of that expression of the atoms’ first-stage ionization energies (IE) — the periodic table is about atoms — yields –
    IE of He = 9.32 eV (13.6/5.39) = 23.5 ev. Observed: 24.6 eV.
    Not bad. The estimate is almost as good as the best of Mendeleev’s famous eka-element interpolations.

    One may begin to see illustrated, Eric, that NI may be a useful reference book, if not light bedside reading. A noted theoretical chemist at Princeton, known to both of us, has said that it should be required reading for all teachers of general chemistry. Too bad it hasn’t an index. Well, we know whom to blame for that absence.

    With apologies to the rest of the gang for this tooting of one’s own horn. It’s seemed hard to be heard on some days above the din of non-scientific issues.


  117. Eric wrote:
    “Well Henry guess what, I prefer a table with H in the halogens and He in the noble gases. And instead of 57 reasons I give you one. Maximization of atomic number triads.”

    How about La next to Y and Mg next to Zn? I pointed to Eric at another blog that in order to maximize atomic number triads, one has to write atomic numbers in any table of rectangular shape, say 3×40, or 6×20, etc. Just list your atomic number in such tables and you’ll get maximum number of atomic number triads, vertically and horizontally.

    Will such tables be still called periodic? I doubt it.

  118. Scerri writes:
    “Incidentally the story of your rushing into print because I was about to ‘do a Wallace on you’ is rather funny.
    But of course Darwin was wise enough to use a respectable press (John Murray). I am also rather amused to hear that I represented such a threat to you.”

    “do a Wallace on [me]”? Surely you’re joking. Wallace wasn’t picking Darwin’s brains, as you did of Bent’s brains, using a manuscript you’d asked him to submit to you, titled “f d p s”, which you never published.

    The threat you represented to Bent wasn’t amusing, to him, or to a referee, who said of a manuscript you submitted some time later to J. Chem. Ed., that it represented the worst case of plagiarism he’d ever seen. You may recall that you drew on my manuscript, word for word, on a central point, without attribution, for what was it, some 17 words? The referee recommended that it be called to the attention of the chairman of your department. You’re fortunate that recommendation wasn’t followed. More such behavior followed. Hence my apprehension. I mention it now years later to encourage you, as David has encouraged all us, to focus your not inconsiderable talents on scientific and philosophical issues. Your remarks in those domains are almost always interesting to me, because I almost always disagree with them. You probably don’t want to see my copy of your book!


  119. Scerri writes:
    “Well Henry guess what, I prefer a table with H in the halogens and He in the noble gases. And instead of 57 reasons I give you one. Maximization of atomic number triads.”

    Well Eric, guess what: What you have done does not achieve a “maximization of atomic number triads”. It does not change their TOTAL NUMBER!

    What you’ve done merely rearranges the triads, by converting, incorrectly, Periodicity’s two major TERTIARY TRIADS into improper primary triads.

    You’ve managed to MINIMIZE the information latent in location of H and He in the Periodic System!

    What are your answers to the following questions?
    1. Isn’t H an s system, whereas F is a p5 system?
    2. Isn’t He an s2 system, whereas Ne is a p6 system?
    3. What is the angular quantum number of differentiating electrons in your last block on the right?
    4. In your system, in summary, what happens to the electronic interpretation of the periodic table?
    5. What happens to the dyadic character of the left-step table?
    6. What happens to the rule that block width is equal to twice the block’s ordinal number, beginning at zero at the right, plus 1, doubled?
    7. What happens to the rule, true throughout the remainder of your table, that Groups’ first elements are not members of primary (vertical) triads?
    8. What happens to the rule, true throughout the remainder of your periodic table, that a row’s ordinal number within its block is equal to the radial quantum number of its block’s predominant type of differentiating electrons?
    9. What happens to the rule, true throughout the remainder of your table, of first-element distinctiveness for (a) the alkali and alkaline earth metals and (b) the halogens and the noble gases??

    Beware of tampering with a theory that is better than one is?
    No. Keep it up! You’re a fine foil for “New Ideas”!
    You’ve expanded enormously possible additions to Appendix XXI: “A Dialogue Concerning Two Tabular Expressions of the Periodic Law”.
    Don’t worry. I won’t identify you, unless you should like me to.


  120. Eric: I don’t think we should clog up the blog with a discussion about the difference between a theory and its physical representation. The Periodic System is far too complex a set of mathematical relationships for it ever to be possible to represent the whole of it in one image. I think Janet’s LSPTable/spiral, version III is perhaps the most genterally informative one, and I certainly wouldn’t want to spoil it for the sake of a couple of triads.

    Anyway, I hope David will soon give us the chop. Enough has been said.

  121. Scerri writes:
    “The reason why you and Jensen could not agree [about He] is very simple
    As I say in my book he uses first member anomaly to argue that He shoud stay in the noble gases while you think it signals He in group 2. Please clarify.”

    Wrong, “for once again”. Jensen did not use “first member anomaly [sic!] to argue that He should stay in the noble gases”. He views that as HUGE MISTAKE! (at least today he does). He was not comfortable, it’s true, with He/Be. Here’s how NI resolved that issue, in its last paragraph of Appendix XVI: “The Step-Pyramid Table, s-Elements on the Left”. (That SPT is Jensen’s favorite form of the periodic table, particularly for its treatment of H and He, in a monad or block by themselves at the top of the table.)

    “Because of the extraordinary character of H and He, it’s pleasing to see a useful and visually attractive periodic table [a symmetrical step-pyramid table] assign the two elements in a natural manner to an extraordinary location [in the only monad of a table of dyadic character, otherwise]. Similarly, it’s pleasing to see a useful and irregular-free periodic table [the left-step table] assign H and He in a natural manner [from the point of view of the table’s overall regularities] to a non-extraordinary location as an extraordinary instance of the Mendeleev-Jensen Rule [of first-element distinctiveness]. Both views agree on one thing [the most important thing]: Hydrogen and helium are — arguably — the most extraordinary elements in the Periodic System.”

    One can hardly help but arrive at the extraordinary conclusion that there’s scarcely a page in NI that wouldn’t clarify something for a prominent writer on the periodic table, but that for some reason or other he’s hell bent on not reading it.

    Puzzled HB.
    Please clarify.

  122. The remark “[O]ur Hell Bent friend was too busy devising new physics, to eventually be privately published, to bother to follow developments in quantum chemistry” brings to mind a remark by a young girl to her family standing on a portage in the BWCAW (Boundary Water Canoe Area Wilderness). Is that West Bearskin Lake? she asked. Yes. “You see,” she said, turning to her family. “I was right, for once again.”

    ES is wrong “for once again” about Bent’s bothering “to follow developments in quantum chemistry”. Bent should know. He’s followed with interest developments in EDFT (Electron-Density Functional Theory) ever since a friend pointed out to him several years ago that that’s exactly what the Kimball/Bent “Charge Cloud” or “Tangent-Sphere Models of Molecules”, of the 1960s, are about: the central theorem of EDFT!

    It’s turned out that the models were several decades ahead of their time. They are chiefly a Conceptual EDFT (reviewed in Chem. Rev. a few years ago), rather than a computational EDFT (although Frost and several other quantum chemists used the models at the time to make numerical calculations with wave functions based on semi-localized Gaussian valence orbitals). The models may be viewed as a response to a request by C. A. Coulson: “Give me insight, not numbers.”

    Professor Frank Weinhold and coworkers at the University of Wisconsin have supplied numbers for the models in more detail than I’d ever expected in the 1960s would be forthcoming in my lifetime, summarized in his recent definitive monograph with Clark Landis on “Valency and Bonding”. Like the TSM, the book’s emphasis is on “doing quantum mechanics with pictures”. It’s written for those “who wish to learn more about the emerging ab initio density-functional view of molecular and supramolecular interactions”. Featured throughout the book is “Bent’s Rule” (the book even has a picture of Bent) and the inter- and intra-molecular donor-acceptor interactions Bent reviewed in Chem. Rev. in the 1970s — another ahead-of-its-time publication, notes Roald Hoffmann (NI, page vii), if not as much so, it seems likely, as NI.

    If one keeps trying to be ahead of his time, one has to be very unlucky, indeed, not to come up eventually with something (to paraphrase G. P. Thomson) that only a “vanity press” will publish.


  123. Henry wants to draw me into which table I believe to be optimal, while still claiming that there is no such thing.

    Well Henry guess what, I prefer a table with H in the halogens and He in the noble gases. And instead of 57 reasons I give you one. Maximization of atomic number triads.

    And nor am I excessively ‘Hell Bent’ on this particular table. Initially I adopted it just so that you would feel that I had not robbed you of your prized left-step table, which is of course not yours but Janet’s.

    But the more I thought about it the more I like it. Z is the one characteristic of elements as basic substance. This is why a simple relationship among Z’s such as triads is important in my view.

    Incidentally the story of your rushing into print because I was about to ‘do a Wallace on you’ is rather funny.
    But of course Darwin was wise enough to use a respectable press (John Murray). I am also rather amused to hear that I represented such a threat to you.

    all the best.

    all the best.

  124. Philip,

    I did not claim that our theories would ever “completely account for the behavior of the world”. I claim that theories and representations of chemical periodicity progressively converge upon the truth. Asymptotically converge if you like.

    If you accept this of theories then it should also true of representations. A theory is after all a sophisticated ‘representation’ of the world.

    The difference between representation and theory is not grounds for getting off the point. Do you believe that theories converge on the truth as science progresses or not?

    Are you a realist about scientific progress or are you an anti-realist that believes that theories and other scientific ‘entities’,for want of a better word, are merely useful instruments?

    all the best

  125. “Hell Bent”? That’s cute. Henry Bent has been “hell bent” — for He/Be.
    He’d be happy to go down in history for that — and, accordingly, with Dmitri Mendeleev and William Jensen, for trans-table trends, vertical and horizontal, in first-element distinctiveness (The Mendeleev-Jensen-Bent Phenomenon?) and an across-the-table correspondence between ordinal numbers of Chemical Periodicity and quantum numbers of Atomic Physics. ( For whom should that phenomenon be named, ES?)

    Yours truly,
    HAB (Helium Above Beryllium)

  126. Philip,
    At one time I, too, like ES, thought that there was one periodic table — the LSPT — that is best and should be used 24/7 by all chemists and all chemistry teachers on all occasions. After compiling “Desirable Features of Periodic Tables” (NI, Appendix XV), I realized, however, how many-sided the Periodic System is and how naive the view is that one best table exists, since no table possesses all of the “desirable features”.

    Four questions for ES?
    (I) What’s his “best” table?
    (II) Are any of the features cited in Appendix XV not possessed by his “best” table?
    (III) Are any of those features NOT DESIRABLE?
    (IV) If so, which ones?


  127. Further to my response to Eric. I think also that you are confusing system/theory with representation/image. Even at the level of theory, I don’t think we will ever have a theory that completely accounts for the behaviour of the world. Relativity theory and quantum theory explain a lot, but we don’t yet know how to put them together, and even if we do we shan’t have a theory that begins to account for what is represented in human history..

    Anyway, let us respond to David’s request and pour some of HeBe’s nectar into each other’s cups.

  128. David: The following tutorial may be excessively long and/or in other ways inappropriate for your forum on the periodic table. My feelings won’t be hurt if you don’t post it. I’ve posted a small part of it before. It tries to illustrate that once students have seen an electronic interpretation of periodic tables, they have in hand intellectual tools useful for understanding other parts of chemistry. That puts the Periodic Table, with Atomic Theory, front and center in Introductory Chemistry, where it used to be, if for a different reason. (It was an aid in understanding the descriptive inorganic chemistry featured in the demonstration-experiments used in teaching chemistry in the “grand manner”.) I hope that the “tutorial” might be of interest to some of the gang.

    [The Isoelectronic Principle states that chemical systems that have the same number of electrons and the same number of “heavy atoms” (atoms other than hydrogen atoms) may have the same electronic structure. One must say “may” since isomers such as cyclopropane, (CH2)3, and propylene, CH3CH=CH2, exist. (In the case of single atoms, hydrogen atoms should be included, isoelectronic with He+, Li+2, etc.)

    [Isoelectronic species have the same GENERIC BOND DIAGRAMS, meaning bond diagrams that are the same except for numbers of bonds to hydrogen atoms and number of lone-pairs, with their sum, lone-pairs + bonds to hydrogen atoms, the same. The Isoelectronic Principle then states that Isoelectronic species exist. CH4, NH3, and H2O are isoelectronic. All three are 10-electron/1-heavy atom species. Another important isoelectronic family includes HCCH (acetylene), HCN (hydrogen cyanide), and NN (dinitrogen). They are 14-electron/2-heavy atom species, all with a triple bond.

    [A Personal Note: My interest in molecular structure was initiated in 1952 on learning that the bond angles in CH4, NH3, and H2O are nearly the same: 109.5, 107, and 104.5 degrees, respectively. To judge by those angles, bonds to hydrogen and lone-pairs appear to be stereochemically equivalent to each other, nearly, in those molecules.

    [A bond to hydrogen may be viewed as a protonated lone pair. Remove a proton from a C—H bond of CH4 and place it, alchemically, in the carbon nucleus, and the structure — now NH3 — scarcely changes shape! The two molecules are “isoelectronic”. The adjective is a useful, if not exact description of the situation, like bond diagrams: shrewd, if crude — shrewd BECAUSE crude!]

    1. THE ISOELECTRONIC PRINCIPLE AND ATOMIC SPECTRA. In her classic compilation of ATOMIC ENERGY LEVELS, Charlotte Moore summarized her massive collection of data in tables that list downward atomic symbols by increasing atomic number, Z, the ordinate, and, horizontally, degree of ionization, I, the abscissa. The number of electrons, N, for each entry is given by the expression N = Z – I. I.e., Z = I + N. Species on lines of constant N (isoelectronic species) appear along lines of slope 1 (downward and to the right in Moore’s tables). The N = 10 sequence, e.g., begins with Ne(I), N = 10, and ends thirteen species later with V(XIV) (V+13), N (= Z – I) = 23 – 13 = 10.

    2. THE ISOELECTRONIC PRINCIPLE AND THE PERIODIC TABLE. Consider any row of a periodic table that cites ground state electron configurations in the usual manner: bracketed symbols of the noble gases followed by specifications of specific orbital populations. Ignore outer s-electrons (valence electrons in all blocks) and ask:

    What’s the FULLEST ELECTRON CONFIGURATION that carries on across an entire row (of a block of a periodic table)?

    For Sc’s row, it’s [Ar], for Sc through Zn. For Hg’s row, it’s {[Xe] 4f14}. For Tl’s row, it’s {[Xe] 4f14 5d10}. Define –

    Atomic Core = Atomic Nucleus + Its Row’s “Fullest Electron Configuration”

    That definition sidesteps the difficulty that the definition “atomic core = atom – (number of electrons in oxidizable subshells)” encounters with the Zinc Group. (Is Hg’s 5d10 subshell oxidizable?), but yields, otherwise, the same results.

    Atoms’ cores in a given row of periodic tables are, accordingly, by definition, isoelectronic.
    In a given column, subshells occupied by non-core electrons are isoelectronic, at least as to their number of electrons, and usually as to their type.

    If N = number of core electrons, then a core’s charge = Z – N. For Sc, core [Ar], the core’s charge is 21 – 18 = 3. For Zn, core [Ar], the core’s charge is 30 – 18 = 12. In a systematic alphanumeric column-labeling scheme, those core charges are equal to the numbers or numerals in the cores’ columns’ labels: for Sc, IIId; for Zn, XIId.

    3. THE ISOELECTRONIC PRINCIPLE AND CLASSICAL STRUCTURAL THEORY. The simplest, most fundamental example of isoelectronic structures is Classical Structural Theory’s valence-stroke: an electron-pair, IN ALL BOND DIAGRAMS. The next level of complexity recognized, in steps, was the Kekule-Couper(for carbon’s quadrivalence)/CrumBrown(for the valence-stroke)/van’t Hoff(for the tetrahedral carbon atom)/Lewis(for the electron-pair, and the Octet Rule) valence-shell structure about cores of the small-core atoms B, C, N, O, and F, simulated in valence-sphere models of molecules by four close-packed spheres.

    4. THE ISOELECTRONIC PRINCIPLE AND VSEPR THEORY. The concept of isoelectronic valence shells holds for all electron-pair coordination numbers. The tetrahedral arrangement about an atomic core of 4 electron-pair domains becomes for 2 domains a digonal arrangement; for 3, trigonal; for 5, trigonal bipyramidal (usually); and for 6, octahedral. (Sometimes 5 domains are arranged in a square pyramidal arrangement, consistent with the theorem that if a neutral or charged species MX5<-n exist (n may be 0), then MX6<–(n+1) exists.)

    5. THE ISOELECTRONIC PRINCIPLE AND FRONTIER ORBITALS. The most nucleophilic sites of molecules and ions — their HOLMOs (Highest Occupied Localized Molecular Orbitals) — are usually isoelectronic with each other, being exposed lone-pairs. Similarly, usually isoelectronic with each other are molecules’ most electrophilic sites — their LULMOs (Lowest Unoccupied Localized Molecular Orbitals) — being the faces of the tetrahedra of electron-pairs about Octet-Rule-satisfying atomic cores opposite the electron pairs that bond the small cores to “good leaving groups” (which may be atoms bonded to the attacked atom by double bonds, which atoms “leave” in becoming singly bonded substituents).

    6. THE ISOELECTRONIC PRINCIPLE AND REACTION MECHANISMS. In carbon chemistry, SN2 reactions are isoelectronic. Involved are two electron-pairs — a lone-pair (usually), and a bonding pair — and an inversion. The lone-pair of an attacking nucleophile approaches the electrophilic face of the tetrahedron of four electron-pairs about a carbon core opposite the electron-pair that bonds the carbon core to the leaving group. The sum of the number of involved electron-pairs and the number of inversions is 2 + 1 = 3. Many organic reactions are coupled SN2 reactions, in which the departing electron-pair of the first SN2 step serves as the entering-pair in a second SN2 step; &c. For such sequences of coupled SN2 reactions, the sum of the number of involved electron-pairs and the number of inversions is, accordingly, an odd number (n = an integer):

    [2(pairs) + 1(initial inversion)] + n[1(new pair) + 1(additional inversion)]
    3 + 2n = an odd number

    That’s said to be an expression in “purely classical language” of the famous Woodard-Hoffman Rules for allowed pericyclic reactions (A. Rassat, C. R. Seances Acad. Sci., Ser. B, 1972, 274, 730-733. Reference from William Jensen.)

  129. Sorry Eric: we must agree to differ. You are a Platonist; I am an Aristotelian. See my article on musical scales for an example of the compromises imposed on us by the complexity of the world.

  130. If I’m to continue hosting this, I’d like to set some technical ground rules: First, please post your comment once, don’t duplicate it if it doesn’t appear on the site immediately, I don’t let posts go through automatically as I prefer to check for spam first, and I don’t work 24/7 so that means there are sometimes delays. Secondly, please don’t email replies to comments, I get enough email without having to filter those out as well and then email the correspondent to ask them to post it on the site. Thirdly, I don’t want to watch discussions that contain ad hominem attacks or insults, however, gratifying they may feel to the commenter. If you want to have a fist fight do it in the playground among yourselves and post it on Youtube…


  131. Philip,

    Would you say the same about all scientific discoveries. For example the true theory of relativity only exists in a Platonic heaven and that any attempts to capture it here on earth are subjective and depend on who is framing the question.

    But as you know this is not the case. The current theory gets as close to the Platonic theory of relativity as anything that came before.

    Science converges upon the Platonic truth. The choice of theories, models, representations is not unconstrained and allowed to depend on the subjective whims of individuals. Scientific discoveries are constrained by what actually happens in the world. So it is with the periodic table. The evolution of the PT represents an ever closer approach to your Platonic periodic table.

    But if you think otherwise you should perhaps explain why a representation like the PT has a radically different nature from theories and laws of science. Assuming that is that you are a realist about scientific discoveries. If not please explain your brand of scientific anti-realism. How is it that science makes such spectacular progress if not by approaching the Platonic truths more and more closely through the years?

    eric scerri

  132. HeBe, Goddess of Youth, daughter of Zeus and Hera, filled the cups of the gods with nectar. She married Hercules, after he had finished his labours and been received among the gods.

  133. I said it before but I’ll say it again. The ideal representation of the Periodic System is to be found only in Plato’s paradise of pure form. In our world, judgments of what is better or best is subjective and depends on the chooser and his or her criteria of choice. There are people who still prefer Mendeleev’s short form. De gustibus non disputandum!

  134. Our Hell Bent professor disparages the work of LH Thomas, not realizing that Thomas was the person whose calculations convinced Pauli of the importance of electron spin.

    He also disparages the Thomas-Fermi method not knowing that the T-F method has morphed into the density functional method which allows quantum chemistry calculations on vastly larger systems than conventional wavefunction approaches. D-F also operates in ordinary 3-D space rather than 3n dimensions of Hilbert space, where n is the number of atoms.
    The computational advantages of D-F an outgrowth of T-F should be quite obvious.

    But our Hell Bent friend was too busy devising new physics, to eventually be privately published, to bother to follow developments in quantum chemistry.

    all the best!

  135. For an exhaustive list of criteria for selecting an “optimal table”, see NI, Appendix XV: “Desirable Features of Periodic Tables”, pp147-148.

  136. Unlike Professor Hell Bent, I am more interested in the criteria used to arrive at the optimal table than in claiming that I have found that optimal table.


  137. Henry your recent friendliness is very touching.

    I must be as brief as you are long handed.

    The reason why you and Jensen could not agree is very simple
    As I say in my book he uses first member anomaly to argue that He shoud stay in the noble gases while you think it signals He in group 2. Please clarify.

    2. You have now fessed up to being H. Bent on the LST but have not explained why you won’t go full Monty and claim that it is THE optimal table.

    Concluding Remarks Regarding Atomic Cores, Spiral Periodic Tables, Chemical Periodicity for the “Unwashed”, Particles in Boxes, Straying from Familiar Paths, a New Periodic Table for David, and Why the Periodic Table Used to Be Important in Chemical Education.

    1. ATOMIC CORES. Survival of the fittest to survive by their wits has instilled in the witty (Homo Sapiens) a love of regularity. Physicists have their beloved Conservation Laws, based on Nature’s deepest symmetries. Chemists have their Electron-Pair, the Octet Rule, and the Tetrahedral Atom, based on the facts of chemistry. Here’s another stab, in that spirit, at a definition for users of periodic tables of the concept “atomic core”. It side-steps “The Zinc-Group Problem” while agreeing with the definition based on numbers of electrons in chemically oxidizable subshells, and conventional notations for atoms’ electron configurations.

    Consider any row of a periodic table that cites ground state electron configurations in the usual manner: bracketed symbols of the noble gases followed by specifications of specific orbital populations. Ignore outer s-electrons (valence-shell electrons in all blocks) and ask –


    For the Sc row, it’s [Ar]. For the Hg row, it’s {[Xe] 4f14}. For the Tl row, it’s {[Xe] 4f14 5d10}.

    Add that electron configuration to the row’s atoms’ nuclei. Formed are “atomic cores” — atoms’ “hard cores”, if you like (if not absolutely hard, as Eugen has cogently pointed out). By definition, (hard) cores are isoelectronic along a row.

    Let N = number of core electrons. Then core charge = Z – N. For Sc that’s 21 – 18 = 3, for Zn 30 – 18 = 12. In a systematic alphanumeric column-labeling scheme, those core charges are equal to the numbers in their columns’ labels.

    2. SPIRAL PERIODIC TABLES. Tabular periodic tables are like foxes: with all their talk of periods, blocks, and blocks’ rows, block-to-block trends, &c., they may seem to be preoccupied with nitty-gritty details, while spiral periodic table, like badgers, know ONE BIG THING: The Periodic Law. “The elements, if arranged according to their atomic [numbers], exhibit an evident periodicity of properties” (DM). Spiral periodic tables are direct, visual representations of the Law, PRIOR to tabular representations of it.

    3. CHEMICAL PERIODICITY FOR THE “UNWASHED”. Lay out the elements’ symbols in order of their atomic numbers in a SPIRAL. (Many thanks for a copy of your beautiful version, Philip.) Link congeners together with outward radiating lines. (Note that the linkages, however irregular, do not cross each other. That makes possible the second part of a subsequent step.) Next, cut the spiral between Ba and La, Ra and Ac, Ca and Sc, Sr and Y, Mg and Al, and Be and B. Don’t worry, at the moment, about H and He. Unspiral the spiral so that all portions of it are horizontal and radiating lines are vertical. Produced is a major part of the left-step periodic table. Place H above Li. (They have the same maximum oxidation numbers.) What’s missing? An element above Be? What should its atomic number be? 2? Place He above Be. Voila! Created are new regularities in the Periodic System: two trans-table trends, vertical and horizontal, in first-element distinctiveness; a Rule of Triads; a Rule of Groups’ Sizes; a concordance between the table’s ordinal numbers and quantum numbers of atomic physics; &c.

    4. PARTICLES IN BOXES. The P.I.B model is one of the most useful approximations in quantum mechanics, because it’s so simple. Just fit de Broglie wave-lengths into a box. Unfortunately, it’s completely misleading when applied to electrons in chemical systems.

    Whereas the potential energy inside a box is flat and at its edges, and outside, infinite, for an electron and a proton, the potential energy is flat at infinity and dips to minus infinity at the center of the “box”. The statement that electrons in chemical systems (benzene, e.g.) strive (so to speak) to be “delocalized”, thereby lowering their kinetic energies (by being in larger boxes), gets it exactly backwards!

    For coulombic systems, if not boxes, the Virial Theorem holds. It states that E(total), the sum of the kinetic energy T (always positive) and the potential energy V (negative with respect to the parts at infinite separation) is equal to – T! Chemical systems are most stable when their electronic kinetic energy is a maximum (subject to the total energy being a minimum). Think of a hydrogen atom in its compact 1s state, compared to its more “delocalized”, higher energy 2s state.

    [Stabilization of benzene by “resonance” (a superposition of states) arises from the fact that its two spin-sets can be ANTICOINCIDENT: one at any instant in the configuration of one Kekule structure, the other in the configuration of the other Kekule structure — which structures can, thereby, contract, somewhat, owing to nuclear-electron attraction, without as much increase in electron-electron repulsion between electrons of opposite spin as would occur if the two spin-sets were coincident, as in non-aromatic systems. In agreement with the Virial Theorem, the resonance-allowed, electron-crowding, potential-energy-lowering contraction increases T.]

    In node-counting and thinking of connections between nodes and energy, one must be careful when comparing the case of a particle-in-a-box with electrons in atoms.

    5. STRAYING FROM FAMILIAR PATHS. Of course, 99.99 percent of the time, or more, most sensible people don’t stray from familiar paths. And yet, if all of us remained on familiar paths all of the time, noted my wife, the earth would still be flat. No rules to tell us when it may be fruitful to stray from familiar paths, only imagination, based on good judgment, based on experience, based on love of Nature’s nature.

    6. A NEW PERIODIC TABLE FOR DAVID? A suggestion: the “Front-Step” Table in “New Idea” on page 107. For both my inner and outer eyes, it’s a thing of beauty. Each of its ordinary, rectangular coordinates is endowed with deep chemical and physical significance. Try it on your wall? It might engender interesting remarks. What’s that?! Its chief weakness is that visible to the outer eye are symbols for only some sixty percent of the elements — which, however, are far and away the most important elements.

    On the facing page is an exploded view of the version of the “Front-Step” Table pictured on p104. As for the two related tables, it has undesirable gaps in Periodicity’s periods. Perhaps one should try several tables on one’s walls? My choices: a conventional sfdp table, the left-step (fdps) table, Valery’s table, a step-pyramid table, a front-step table, and a modern version of Mendeleev’s “short-form” table.

    7. WHY THE PERIODIC TABLE USED TO BE IMPORTANT IN CHEMICAL EDUCATION. In the “good old days,” introductory chemistry was taught in the “grand manner”, from demonstration-experiments, illustrative, chiefly, of descriptive inorganic chemistry. Titles of textbooks’ chapters were usually the names of the chemical elements, often singly, in the cases of hydrogen and oxygen, and carbon, and otherwise as the two or three leading members of Periodicity’s Groups. Lab work was elemental analysis in the “wet way”, with slippery (soaponifying) sodium hydroxide (for “lithophilic” elements, of the earth’s crust) and stinky hydrogen sulfide (for “chalcophilic” elements, of the earth’s core).

    Polled regarding the most important topics in Chem101, professors sixty years ago listed first Atomic Theory, second the Periodic Table, and last Entropy and the Second Law of Thermodynamics. Chem101 today is a “baby p-chem” course. Entropy has been elevated. And the Periodic Table? It’s mentioned, of course, but little used.

    Goodbye students at Harvard University spilling from Boylston’s Hall’s large, low, first-story windows to escape smoke and fumes from one of A. B. Lamb’s concluding explosions. Hello peering at small, antiseptic, two-dimensional displays of atomic orbitals.

    General chemistry hasn’t gone “downhill”. It’s risen, through the clouds. It’s become a faith-based course, as there is no way in the world that students can understand, proceeding step by step from first principles, what “orbitals” are, as the only route to them is solution of Schrodinger’s equation for the hydrogen atom.

    “Elevate Them Guns Lower,” begged an old-timer, in vain.

    Thanks for reading.
    And apologies for mind-numbing(?) details, today and earlier.
    I’m of an old school that believes that teaching should be like an iceberg: ninety percent beneath the surface supporting the ten percent that shows.

    I’ve enjoyed the gang’s remarks, not least of all impertinent ones directed at me by ES. Now, if someone could just get him to read “New Ideas”. He might find answers to his questions, and new ideas — perhaps useful in Montreal?

    One of my favorite philosophers (cited earlier) asks: What’s the difference between a person who can read but doesn’t and one who can’t read?

    He who can’t read may wish that he could read.
    He who can read may wish that his beliefs that the world is flat and that helium belongs above neon in periodic tables remain intact.


  139. Henry,
    I am impressed by your teaching experience – and envy your exposure to the kids.
    Would you be kind enough provide a look at the original material given to the students and the instructions for achievement of the desired result?
    These are people I hope to help into the periodic table.
    I will look for it online or you can email it to

  140. @David – Please persist.
    The best chapters are yet to come!
    Imagine Cannizaro, Mendeleev, Meyer, de Chancourtois, etc. on a blog.
    Would they quit?
    (Maybe we should adopt their names as nom-de-blogs and continue until we find out we’re all wrong.)

  141. Eric,

    My views regarding “one optimal periodic table” are set forth in a number of places in “New Ideas”, particularly Section 99, “Best Periodic Table?” and in my letter to Roald Hoffmann on p191.

    “Why [am I] devoting so much time and energy and even money in trying to promote one particular periodic table?” Because, in my view, it is an excellent table that has not been properly promoted; it is the first table that beginning students can construct, from scratch, on their own; and it makes obvious, even to beginners, where helium belongs, in all periodic tables. For a short list of additional reasons, see NI’s SHORT ABSTRACT, page xiii.

    Tell me in return: Why don’t you study “New Ideas”? A few sections may seem excessively technical or mathematical. But I don’t believe that could be fairly said of most of it.


  142. Roy,

    You write: “David & I appear to be the only ones concerned with education of the unwashed . . .”

    Speaking for myself, I spent 40 years teaching, with my graduate courses, general chemistry for the “unwashed”. My last three years in academia I directed an outreach program that I’d initiated that presented with chemical commentary striking demonstration-experiments for some 60,000 students and their teachers in the tri-state area of western PA, eastern OH, and northern W Va.

    One reason I like the left-step periodic table is that with a set of simple instructions fifth-graders, starting from scratch, can construct it, in several ways, and easily rearrange it to the form of the conventional periodic table. I’ve never seen that happen before: periodic tables captured by the “unwashed”, starting from scratch. The method works because there’s no need to mention electrons and atomic orbitals. All one needs are the elements’ atomic numbers and either memberships of a few commonly named Groups, elements’ maximum oxidation numbers, or atoms’ first-stage ionization energies.

    The construction becomes a simple game with young students, the results of which may assume deeper and deeper meanings for them as they become older and older. Experience shows, also, that interested and alert fifth graders can cope with the circle/diameter diagrams of atomic orbitals pictured in my book’s Figure 29. That display in FIg. 29 immediately endows their captured left-step periodic table with physical significance.

    Like the 3Rs (Reading, Writing, and Arithmetic), the subject of Chemical Periodicity becomes highly teachable when presented in the manner sketched above. There may be better methods of creating periodic tables, with beginners, but I’ve not seen them. Usually the tables just appear, somehow, from somewhere: before WWII, perhaps from their history; after WWII, perhaps from Madelung’s Rule, but usually not even that, correctly, as it yields not the conventional periodic table but, rather, the left-step periodic table, which, to my knowledge, has never appeared in elementary textbooks, for the “washed” or the “unwashed”, yet in my view, that is the first periodic table that they should see. (Usually, of course, they see only one periodic table, a narrow view of an expansive field.)



    I wish to congratulate and to thank Eric Scerri, again, for his recent description of my book.

    G. P. Thomson said that if you go through life trying promising things, you have to be very unlucky not to hit on one good thing (in his case, co-discovery of the wave-like character of his father’s “corpuscle”, for which they both received Nobel Prizes).

    Similarly, if one continually makes outrageous statements, one must to be very unlucky indeed not to be correct, occasionally.

    Scerri writes that the ideas in “New Ideas” are mine and mine alone. “I should hope so!” said my wife. “That’s why you titled the book ‘New Ideas’”. Where? In chemistry. From what? Fresh energy for the Periodic Law. The full title is a descriptive title, I thought, and correct, I hoped, if regrettably long. Truth over elegance.

    High praise, indeed, then, from our PFED denier — provided, of course, that the mine-and-mine-alone ideas turn out to be right. Actually, as pointed out earlier, praise regarding PFED is too high.

    Bent’s relation to PFED is analogous to Darwin’s relation to evolution. Darwin wasn’t the first person to suggest it. His grandfather espoused the doctrine. But (with Wallace), Darwin was the first person to take it sufficiently seriously to demonstrate its usefulness. Bent’s contribution to FED Theory has been to use it to locate helium in periodic tables and to illustrate the usefulness in chemistry of the left-step periodic table. Jensen has said that I seem to have been the only person to have run with his observation of a block-to-block trend in the magnitude of FED.

    In a sense, therefore, Scerri may be right. Running with PFED was my idea and perhaps my idea alone. The low-hanging fruit along the run wasn’t harvested earlier for several reasons: a frequently footnoted f-block, often considered to be two separate “series”, rather than “block”; a weird block order, from the standpoint of blocks’ sizes, in the conventional periodic table; and two indistinct blocks, owing to the grouping of s-block Groups and p-block Groups together as “Main Groups”, together with location of He above Be, which makes the Ne Group in the p-block the same size as the Be Group in the s-block.

    I wouldn’t have written “New Ideas if I’d though its ideas were old. That wouldn’t have been very exciting: “Old Ideas in Chemistry”, about the Periodic Table? One knowledgeable reviewer of Scherri’s book has said, in effect, however, that that’s in noticeable part what his book is about, except, one should add, where it’s new, where, in my view, it’s not infrequently wrong (or not even wrong, as in the case, e.g., of the author’s triad 50% rule).

    Sherri likes to point out that “New Ideas” was published with a “vanity press”. He’s thrown that in its author’s face many times. Everyone knows, he’s said, that anything published by a vanity press is completely worthless. I wonder if he’s wondered why “New Ideas” was published by a “vanity press”. Evidently he doesn’t realize that he himself is in large measure responsible for that fact.

    Aware of an impending book by Scerri on the periodic table and apprehensive about what it might contain, owing to a history of unpleasant experiences with its author regarding the periodic table, I pressed to get “New Ideas” published on short notice. Hence its absence of an index, for instance, and its publication with a press that, for a fee, can crank out books WITHIN A MONTH, without interfering with their content, however novel (or boring or poorly written) it may be, provided, only, that it’s not libelous.

    I’ve gradually taken it as badge of honor that circumstances involving Scerri, in particular, and the anti-helium-above-beryllium establishment, in general, forced publication of “New Ideas” with a “vanity press”.

    Well, whatever. Congratulations, Eric. And thanks a lot! I believe you’ve hit the nail on the head: creation of the best description “New Ideas” has received.

    While we’re trading intended insults, let me congratulate you, also, for discovering the perfect niche for an astute scam. My hat is off to you for being able to build a career from wrong and not-even-wrong commentary (sometimes wanting appropriate attributions) on a topic that is universally acknowledged to be exceedingly important — the central icon of the central science — and that, nonetheless, and surprisingly, virtually no one in the world knows much of anything about. It’s been a great choice for you!

    A CAVEAT: Previous remarks may be withdrawn without notice or apology if proven to be incorrect.

    Professor William Jensen and I discovered, unexpectedly, in the 1980s, the WORLD WIDE WELL OF IGNORANCE regarding the periodic table, in our work for the American Chemical Society regarding an international column-labeling controversy. I’ve a drawer in a large filing cabinet nearly full of correspondence with chemists and chemistry teachers around the world that reveals immense ignorance regarding virtually all aspects of the periodic table. For a time I kept a growing list of “Misconceptions”, up in the 50s, as I recall, when I stopped. Jensen suggested that we write a book about the entire experience. At the time, however, I was making a move to Pittsburgh, with a host of new responsibilities.

    The most visible evidence of ignorance regarding the periodic table is continued location of helium above neon. One might have thought, naively, that chemists would have immediately scrambled to correct that major flaw in their central icon, once it was pointed out to them, not by physicists, with their spectroscopically derived s2/p6 mantra, but, rather, on chemical grounds, by a fellow chemist, in good standing, at the time (if no longer).

    ADDED NOTE: In my critique of the Thomas-Fermi method, I did not intend to imply that it hasn’t produced noteworthy results, only that it’s a fierce struggle to reach accurate results for atomic systems from its starting point.

    Thanks for reading,

  144. For those interested in continuing a discussion at the T3 site , go to

    You’ll need to sign up for Yahoo Groups to post and access several of the group functions, but you can read the messages and links without it. There should be a link at the top of the group page for signing up.

    I’d like to thank David for allowing us to rant and rave on his blog.

    I keep wondering how the conversations would have gone if the mid-19th century players were here to participate. What would Mendeleev have made of all this?

    Jess Tauber

  145. @Philip I know. It is odd how this blog post has evolved though, it’s not usual for a single post on a blog to take on a life of its own, this kind of extended detailed discussion one would expect to see on a forum. Not that it’s been a problem to have you all discussing the ins and outs of the elements here, it’s just odd that it happened. Most other posts have some activity when they first appear then the chat dies away and rarely re-emerges as it did with this. It’s obviously a hot topic still. Maybe I should write my own book…

  146. I didn’t want to put anybody in his or her place. I just felt that it was time for a conclusion and that the conclusion should be related to the original purpose of the blog. We seem to have exhausted the review of less boring representations of the system. There is more to be said on tetrahedra, but that can be left to Valery, Jess, Demers et al.

  147. @Melinda – I did not intend to denigrate the description of the activity Henry described. Certainly, it is representative of my own, and, it appears to me, that of many others on the blog – except, perhaps, Phillip, who has good things to say about arrangements other than his own.

  148. I would like to welcome Eugene Schwartz to the discussion. It looks like our group is growing. Scientific community has been silent about the issues with traditional depiction of periodic system for too long. I feel that this group can become the beginning of great awakening! David with his post started what, just 3 years ago, was hard for me to imagine. But I sense the he is getting tired of being our host. In this case, I propose to move this discussion to a different forum hosted by Jess Tauber, who I am sure, will never get tired of PT discussions. Jess, if this is OK with David, please provide us with the details of how to sign up to your group. Many of us invested so much time and effort into this discussion and can not afford to stop it now.

    Professor Bent, thanks for your perspective in regard to Mendeleev and regularity.
    Eric, thanks for invitation to Canada. I’d love to go, but I need more of advance notice.
    Philip, once again, thanks for your support. ADOMAH PT gets good reviews from high school students and from college freshmen who like simplified way of deriving electron configurations that it offers.

  149. 1. On inner and outer valence electrons/orbitals and ‘first-elements distinctiveness’:
    The lowest valence AOs of a given angular momentum are special, since they do not ’feel’ the Pauli repulsion of an occupied core shell of the same angular momentum. Pyykkö called them ‘primogenic’. In the second row, 2p AOs are nearly as small as 2s, therefore the strong tendency of 2s-2p hybridization for B,C,N, the tendency being less pronounced for the heavier homologues. 3d is nearly within the 3s3p atomic ‘large core’ of the first-row transition-metals. 3d has less stereochemical activity and less covalence-forming ability than 4d, 5d, 6d. Similarly, 4f of the lanthanoids is an inner ‘spectator’ valence-AO, while 5f of the early actinoids is more covalently active.

    2. On innocent cores:
    I had mentioned the valence-activity of the heavier so-called noble-gas [ns^2 np^6] shells.
    One may add that Eka-Radon and the subsequent superheavy atoms have a very valence-active 7p(3/2) ‘core’. Henry Bent mentioned the valence-active d^10 shells of M(10)^0, M(11)^1+ and even M(12)^2+ (octahedral Zn complexes, recently identified HgF4).
    One may add the valence activity of the ns^2 shell in the main groups, in contrast to the ‘innocence’ of 1s^2 of He, Li, etc.

    3. On the one PT for 24/7:
    Since a graphical TABLE printed on a page is a tool to cut a path through the jungle of nature’s complexity, i.e. since it is a projection of the periodic SYSTEM for the whole ‘chemical space’ onto a finite manifold of facts in a selected subfield of interest, there should not be a single ‘24/7 PT’. One may search for good or better PTs for specific subfields as representations of THE PS of chemistry. Still, it’s not mere convention, it depends on the facts one is interested in.
    An example for the usefulness of several PTs is He that has some relations to Be, and some (more) (chemical) relations to Ne, see above point 1.

    4. On nodes in AOs:
    (a) One may use different conventions, e.g. concerning the special node at ‘large distances’. This has no influence on the consequences of the ‘node theorem’.
    (b) One must take into account that in 1 dimension there is 1 type of nodes, that in 2 or 3 dimensions there are 2 or 3 types of nodes.
    (c) The node theorem, “more nodes -> higher energy”, holds for 1-dimensional problems. You may convince yourself by investigating an electron in a linear and a two-dimensional square box.

    5. On Oxidation States, sorry for the typo on March 4, 2010 at 8:47 pm, it should read:
    “The oxidation state >8< has also been found for Ir and Xe, see a recent review of Kaupp in Coord. Chem. Rev. and a recent communication of Kaupp (et al.) in Angew. Chem.

    eugen schwarz

  150. Thanks for putting me in my place Phil. To be honest, I’ve forgotten what my original point was. I did write the original post almost two years ago…so not really sure why the discussion has persisted so long. I think it is about time for some peace and quiet around here though…maybe once we reach 400 comments we can stop, shouldn’t take more than a day or two at the current rate of chatter.

  151. In the fury of battle over detail, we lost sight of David’s original complaint: that he finds the standard periodic table boring. However he then dismissed “woodworked, spiralled, spherized” representations, which does not leave us many options for making things less boring.

    I am not clear what David wants. If it is another table, I recommend Valery’s Adomah, which combines balance with faithful representation of the electronic structure. I believe that by the end of this century, when all current chemistry teachers are out of action, it will have become the new standard periodic table.

    I personally find tables in general offputting. My memories of school include endless torment by table, with tables of irregular verbs, of declensions, of multiplication, of geological eras, of English kings and queens…. If David is looking for a bit of visual excitement, he should take another looks at those spirals and sculptures. Perhaps he should get Fernando Dufour’s lovely ElemenTree (which as far as I remember nobody has mentioned in this blog). Or he might design his own version, as hundreds of others have done in the last 150 years.

    However, our “excruciating” discussions about the proper place of hydrogen and helium should not be regarded as hair-splitting. They are by far the most singular of all elements, their core a naked nucleus. H’s valence of one and He’s lack of chemical activity do not make them into “fluorine-lite” or “neon-lite”. They account for more than 99% of the matter in the universe (leaving aside dark matter), but most of that is in the form of stellar plasma, so perhaps we must concede that the physicists’ view should take precedence over the chemists’.

  152. One more comment in regard to He/Ne and He/Be:
    If placed above Ne, Helium would be the only element in entire Periodic Table that has both adjacent elements (H and Li) belonging to the same block that is different from the block where the middle element resides. This surely makes He over Ne irregular.

    I think that I read it in NI, but if it is not there, or somewhere else, I would gladly accept the authorship.

    V. T.

  153. Roy,

    Regarding Henry’s statement “…Once one has found one’s way around a small part of the jungle, however inefficiently, through years of hard work, one becomes reluctant to depart from familiar paths.”:

    You say that like it’s a bad thing. I feel that it’s simply a sign of intelligence to use hard-won discoveries as one’s default foundation for further exploration. While I’m sure that it’s a poor scientist who is unwilling to consider new ideas, I think that it’s a worse sin to flit around without any map or home base.

    Perhaps the heart of the problem that this group is facing is not an unwillingness to consider new ideas but the sense that simply because a particular patch of territory is familiar and sensible to one person doesn’t mean that it is the only sensible starting point. Where our paths cross we should explore the connections and expand our maps rather than exhort the other person to come out of the jungle and help expand our tiny domains.

    Although it usually ends up badly when characters in horror movies do it, we might actually do better to split up in order to cover more ground.

  154. Thanks Eric, for kindly including my name among the scientific minds you urge to travel to Canada . I’m afraid my role in Montreal would be mostly concealing my ignorance – unless I were to referee.
    I’ve been lurking on the blog lately and marvel how you all seem to be able to thoroughly, and in excruciating detail, critique element aggregations that I can not even envision – being without Mazurs, van Spronsen, and Bent books and with difficulty picturing Tsimmerman & Tauber’s tables.
    The current discussions and arguments are way over my head (except for the occasional dive), and appear to address more differences than I could ever imagine, and I wonder if any of this should concern the entry-level student or the general public in any way.
    David & I appear to be the only ones concerned with education of the unwashed, and you see how different our approaches are! He has a background of chemistry, however, while I merely shift and twist the IUPAC table so that; 1. it conforms to the Periodic Law, 2. addresses pre-knowledge of even the minimally informed about the dreaded flat table, and 3. recognition of the inevitability of subsequent use of the elements arranged on a flat tabular form.
    Montreal is too far away, and my approach to the arrangement of elements too embarassingly unsophisticated and atechnical to enhance a stratospheric contest between the over-informed.

  155. Any chance, Prof. Bent, that the trend from no diagonal kinships (H, He) to simple diagonals in the later s and upper p, to knight’s moves in d and lower p, be a kind of shifting relationship that might relate perhaps to your factor k, if the latter does utilize successive Fibonacci ratios?

    Thus down zero steps, right one step= 0,1= zero slope, ratio 0.000
    Next down one step, right one step= 1,1= simple diagonal, ratio 1.000
    Next down one step, right two steps=1,2= knight’s move, ratio 0.500
    Next down two steps, right three steps=2,3=?, ratio 0.666

    Could this explain some of the deviations from diagonality in the lower part of the p-block?

    Jess Tauber

  156. Reply to Valery regarding the LSPT and Dmitri Mendeleev:

    I agree. Given Mendeleev’s love of regularity, the LSPT — a table of no irregularities and, within its periods, no gaps (suggestive of missing elements?) — would probably have appealed to him. Notice what he does with his “short form” table (NI, p47).

    To maintain its checkerboard character, bottom up, Mendeleev located B above Sc, C above Ti, N above V, and O above Cr (!) and F above Mn (!).

    Had Mendeleev known about the lanthanides and the actinides, his table of “The Periods of the Chemical Elements” (the first of two periodic tables in “Principles”, Vol. I, page xvii) would have become a right-step table, in which each period is scanned right to left (top down, in his orientation of it), namely the MIRROR IMAGE of the LSPT, with, however, the s-blocks’ congeners not aligned vertically with each other but, rather, located on the left, as the first elements of each period. In other words, it becomes the “long form” of the conventional periodic table with its s-elements moved to the right, adjacent to the first elements of the p-, d-, and f-blocks. Call that a “half-way station”, on the way to moving the s-block completely to the right hand side, as in the LSPT.

    That might be the easiest way to introduce students and chemistry teachers to the LSPT,
    through four or five levels of increasing sophistication. Beginners of almost any age could probably handle the first level below. It would be nice if they could just slide horizontally and vertically at will on computers squares that contain elements’ symbols and atomic numbers. (All tables are to be read for increasing atomic numbers left-to-right, top down.)

    Start with the “long form” of the conventional periodic table.
    Remove, temporarily, H and He (whose locations are controversial).
    Move to the “half-way station” (to eliminate periods’ gaps).
    Move s-elements all the way to the right (to ease scanning membership of the s-elements’ Groups).
    Replace H above Li (as they both have maximum oxidation numbers of +1).
    Note the irregularity at the upper right hand corner. What’s missing?
    Place He in the system, to maximize overall regularity.

    Notice occurrence and locations of Triads (optional).
    Introduce the Phenomenon of Trans-Table Trends in First-Element Distinctiveness (via, e.g., NI’s Figs. 43, 44, and 40).

    Have observers enter ordinal numbers for periods and blocks.
    Have observers generate a row occupancy rule.
    Help observers create the Table’s Equation of Form: P = r + 2l.
    Introduce the “Index of Discontinuity”, n (= r + l), and, accordingly, the expression P = n + l.

    Exhibit orbital diagrams in the format of the LSPT (NI Fig. 29, p61).
    Point out the correlation of orbitals r and l values with the orbitals’ locations in the diagram.

    Start from Mendeleev’s line. Annotate it: HNAE, CV. Then proceed as in Fig. 1 of NI.
    Optional: Repeat with first-stage ionization energies’ major and minor zig-zags standing in for the sequences HNAE and CV.

    Criticisms, corrections, additions, emendations, observations, etc. welcomed!

  157. In other words Henry, please finally resolve where you stand in the philosophical question of whether or not there is one optimal periodic table that should be sought for, or whether it is all a matter of convention.

    And, if as I suspect you support the latter view, why are you devoting so much time and energy and even money in trying to promote one particular periodic table?

    all the best

  158. On atomic cores:
    i) Quantum chemists know that, what ordinary chemists call ‘core’, is more or less flexible and participates more or less in chemical bond formation. The [Xe] core shell must not be assumed as frozen in polar Cs and Ba compounds. And the [Rn] core shell is far from ‘chemically inert’ in polar compounds of the following elements Fr, Ra, Ac, Th, Pa, U. Reliable calculations of U-compounds, for instance, MUST count also U-6s,6p in addition to U-5f,6d,7s,7p among the valence-active shells. For increasing Z, the diffuse spectroscopic high-energy Rydberg orbitals become valence orbital, then valence-active semi-core orbitals (the terminus technicus), finally real core orbitals. These ‘transitions’ are smooth without a sharp border.
    ii) The oxidation state has also been found for Ir and Xe, see a recent review of Kaupp in Coord. Chem. Rev. and a recent communication of Kaupp (et al.) in Angew. Chem.

    On simplicity:
    It is simple, and in many respects sufficient, to talk about “chemists’ atomic small-cores” (the terminus technicus), and about the number of valence electrons.
    But when one decides to talk about states and configurations, and this or that Madelung-rule, then one MUST formulate the details in quite some sophistication. Otherwise the statements and conclusions become afflicted with too many factual and logical errors, as well documented in the chemical literature.

    Regards, eugen schwarz.

  159. A response to –
    Eric Scerri says:
    March 2, 2010 at 8:02 pm
    “On seeking a general solution to the Schrodinger equation.
    “Henry, please see the papers by Sabre and Herschbach which are cited in my book. Moreover the Thomas-Fermi method also provides a universal solution in the sense of a dependence of Energy on Z.”

    I was interested in the authorities cited in your ARGUMENT-BY-AUTHORITY. I respect them highly. Fermi is one of my heros. Herschbach is very bright with a fine sense of humor. (I believe he was one of the instigators of an annual ceremony in Cambridge for awarding Ignoble Prizes for (seemingly) outlandish research. Perhaps I should send him a copy of “New Ideas”?) When Dudley was beginning his career in chemistry, we tried to hire him at Minnesota. Thomas was my most highly regarded colleague at N. C. State University, the first person to go to for definitive answers to questions about theoretical physics. He was a very quiet, completely unassuming person. His P.I. (Publication Index: the ratio of what one publishes to what one knows) was probably about 0.01.

    My problem with the Thomas-Fermi method goes back to experiences as an apprentice glassblower at Berkeley. Your most important step, stressed by mentor, an artful technician of the old German school , is your first step: the initial “get”. No amount of heating and blowing afterwards will fully correct a poor “get”.

    The Thomas-Fermi method’s initial “get” is an electron gas — as far as one can be, physically speaking, from the behavior of electrons in chemical systems. What saves the calculations from complete physical absurdity is electron indistinghishability. Wave functions for electrons must be antisymmetric. That implies a Principle Spatial Exclusion: about an electron is a “fermi hole” into which electrons of opposite spin cannot penetrate. A Thomas-Fermi gas is a gas of fermi holes. In atomic systems electrons’ fermi holes are essentially space-filling. A chemical system’s Thomas-Fermi “gas” is more like a solid. It’s a long haul to there, however, from the initial “get”, sooooooooooooooo unlike what one wants to end up with.

    One class of systems possess fairly accurate and relatively simple atomic IE(Z) functions: isoelectronic systems.

  160. Some remarks from the point of view of a chemist and physicist:

    1) On ‘k’ in (n + kl)

    The structure of the PS is governed by the scheme of atomic orbital energies and radii. The energies depend on Z, n, l, and j (j is a ‘good’ quantum number in physical terms, but s (spin) is not). In the case of neutral atoms, the orbital energies, or energies of ionization without configurational reorganization, are to a high degree of accuracy ε_nlj ≈ Ry / [n – δ(l,j)]^2, where Ry means the Rydberg energy constant, and δ(l,j) is the n-independent, l (and j) dependent so-called quantum-defect parameter. As an ordinary function, δ(l) can be expanded in a power series of l and 1/l . Crude approximations can then be adjusted to the correct δ(l)-function, for example δ(l) ≈a-kl, what yields the term (n+kl)-a.

    2) On the occupation scheme of Sc

    i) The dominant one of a >handful< of reasons, that determine the occupation of d and s AOs in Sc-ions in vacuum, is simply that the orbital energy difference Δε of an electron in the field of a Sc core, i.e. for 3d < 4s (!, energetically and spatially), 0 < Δε = ε(4s) – ε(3d),
    is smaller than the difference ΔR of (a) the large direct+exchange+correlation Coulomb Repulsion energy R(3d-3d) between two electrons in small, compact 3d-orbitals, and (b) the small Coulomb repulsion energy R(4s-4s) between two electrons in diffuse, extended 4s-orbitals, 0 < ΔR = R(3d-3d) – R(4s-4s) .
    That is: since Δε < ΔR for ALL transition metal atoms in vacuum (though not for groups 1 and 2), there holds for the total atomic energies in vacuum: E(Sc^2+(3d)) < E(Sc^2+(4s)), but E(Sc^0(3d14s2)) < E(Sc^0(3d3)).
    By the way, since 4s is higher in molecules and solids than in vacuum, we have for Sc atoms in chemical compounds: ΔR < Δε , and therefore E(Sc^0(3d3)) < E(Sc^0(3d14s2)).
    Note that the total energy is the sum of orbital energies in the core-field PLUS the two-valence-electrons Coulomb-repulsion energies.
    ii) Since all that depends on numerical values, one must compute them or theoretically reconstruct them from measurements. Purely analytical mathematics is not sufficient. Whether that is to be called “good” or “conceptual” depends on how you define “good” and “conceptual”. Anyhow, the explanation holds quite “general”.

    3) On the so-called Madelung rule

    I recall some facts from atomic Vacuum-Physics and from common Compound-Chemistry.
    The original Madelung rule holds in many, i.e. NOT in all cases (Madelung explicitly called his rule an ‘idealized’ one) for these physical things: for the configurations (= approximate orbital occupation schemes), from which the e-e-Coulomb and relativistic-spin-orbit and dynamic-angular-momenta coupled ground states of free atoms in vacuum derive.
    The Madelung rule was originally NOT formulated (and does NOT hold) for the ground configurations of chemically bonded atoms except in groups 1 and 2. I.e. the Madelung rule does not apply in chemistry to ANY transition metal or p-block element atom.

    eugen schwarz.

  161. Suggestion for better title as requested by author,

    57 reasons why the LST is the best option but actually I dont want to claim that it really IS the best option.

    eric scerri

  162. A reply to
    Philip Stewart says:
    March 4, 2010 at 4:15 pm

    Your account of cores and d-electrons in the d-block is highly descriptive and appropriate. It’s one used by inorganic chemists, including myself, even while I place along side it the account I’ve currently given.

    My current account aims at establishing two things:
    (1) A simple connection between column labels and core charges, for, chiefly, purposes of “electron counting”.
    (2) A correspondence between what happens across the d-block with d-electrons and what happens across the p-block with p-electrons.

    A difference between p- and d-electrons is that, in being “outer” electrons, unshared p-electrons are stereochemically active, about, e.g., the cores N+5, O+6, and F+7, whereas, in being “inner” electrons, unshared d-electrons are not stereochemially active.

    Still, your d-subshell “core” electrons in the latter parts of d-blocks’ rows are not chemical “innocent” electrons. They are what make the chemistry of d-block cations different from the chemistry of p-block cations of approximately the same size and charge.

    In, e.g., the famous tetrahedral molecular species Ni(CO)4, Ni’s d10 subshell is actively engaged in bonding with the Ni atom’s carbon monoxide ligands, through “back bonding”, even though most chemists would say that nickel is in its zero oxidation state.

    (Ni, acting as an electron-pair acceptor, forms with each CO a “sigma” type single bond from a C’s lone pair and, acting as an electron-donor, with its d-electrons, forms with each CO a “pi” type bond with a CO’s “antibonding” orbitals, associated with its triple bond.)

    If one says that Ni’s non-oxidizable d-electrons are core electrons, must not one say, correspondingly, that oxygen’s non-oxidizable electrons are core electrons?

    [A valence orbital model of Ni(CO)4 consist, about the Ni nucleus, of a 1s2 pair surrounded by a cubical arrangement of 8 electron domains, four, tetrahedrally arranged, for one spin-set, and 4, tetrahedrally arranged, for the other spin-set (the L shell, 2s2 2p6 electrons), surrounded, in turn, by a larger cube of 8 electron-domains, its two spin-sets as anticoincident as possible with respect to the corresponding inner pair of spin-sets (the M shell, 3s2 3p3 electrons) with, in preparation for bonding to CO, its 5 3d-orbitals doubly occupied, in two sets. Lobes of one set occupy “nooks” at the outer cube’s 6 faces, four in a plane for one of the 3d orbitals, and two on opposite faces for the other 3d orbital. The 6 remaining 3d electrons, in three pairs, occupy slightly less deep “nooks” at the cube’s 12 edges, four, in a square-planar arrangement, for each of the 3 outer pairs, which are the ones involved in back bonding to CO.]

    Your remarks suggest to me that trying to construct a best definition for “atomic core”, to be used 24/7, on all occasions, may be like trying to construct a best periodic table, to be used 24/7, on all occasions. It’s not possible to do. Or necessary? Or desirable?

  163. Roy Alexander says:
    March 4, 2010 at 10:08 am
    “May I quote this on

    I’d feel honored if you do.

  164. Eric Scerri says:
    March 3, 2010 at 7:53 pm
    P.S. And before you cite William Jensen as support just remember that he most definitely does not favor He in the alkaline earths!

    And “he most definitely does not favor He in the” Noble Gases! He considers that a HUGE ERROR.

    The “Jensen Issue” is discussed in NI in Section 99, “Best Periodic Table?” and, more fully, in Appendix XVI, “The Step-Pyramid Table, s-Elements on the Left”, particularly in the paragraph TWO VIEWS OF THE sfdp STEP-PYRAMID’S H-He MONAD, and the Appendix’s concluding paragraph.

    You’re grasping at straws, Eric.

  165. Eric Scerri says:
    March 3, 2010 at 7:52 pm
    “Henry, You speak of First Element Distinctiveness as though it were an agreed upon axiom.
    In reality it is only agreed upon by yourself with yourself as so many of these ‘New ideas from Fresh Energy…’ surely the world’s most awful title for a book.”

    QUESTION: What can one do if the facts don’t fit one’s personal opinions? Two obvious options: (1) Ignore the facts. (2) Deny the facts.

    Scerri is not the first helium-above-neon lover to deny the phenomenon of First-Element Distinctiveness. Other PFED deniers include reviewers for J. Chem. Educ. of early versions of portions of “New Ideas”, who spoke of “Bent’s ALLEGED phenomenon of first-element distinctiveness”. For, of course, once one recognizes that phenomenon, then, logically speaking, helium-above-beryllium becomes highly attractive FROM A CHEMICAL POINT OF VIEW and helium-above-neon becomes, from a chemical point of view, ridiculous (NI, Boxed Statement, Section 37: “An Absolute Prohibition”).

    An alleged scholar of the Periodic System, if not reader of “New Ideas”, should surely know, however, of “Mendeleev’s Rule of Light-Element Distinctiveness” (NI, Section 30) and Jensen’s Extension of it (Section 31).

    Moreover, the Phenomenon of First-Element Distinctiveness is cited, even featured, in all advanced textbooks of inorganic chemistry. It’s one of the leading features of descriptive inorganic chemistry. It honors me far far too much, therefore, to assert that “In reality it is only agreed upon by yourself with yourself.”

    [The phrase “in reality” is a red flag. It often signals that what follows is not “reality”.]

    [Discussed in Section 43 of NI (“Quantification of Chemical Intuition”) is the huge influence first-element distinctiveness has — with, to lesser degrees, second- and third-element distinctiveness — on the organization in textbooks of inorganic chemistry’s massive amount of information.]

    It’s always nice, of course, to move from an author index to a subject index. “Bent’s Phenomenon”? Great! But not deserved, in this instance. (Nor was “Bent’s Rule”, as scholars of the “s-character rule” may know.)

    It’s astonishing that an alleged scholar of the periodic table and historian of chemistry would assign Bent full and exclusive credit for the Phenomenon of First-Element Distinctiveness. The mistake falls, once again, into the “-10” category.

    Bent’s contributions to PFED Theory are three-fold: (1) graphical representations of PFED in its applications to congeners, particularly “Plots of radii of atoms’ cores vs. P(fdps) (NI, p96) and “Plots of Allen’s electonegativities vs. P(fdps) (NI, p97); (2) graphical representation of PFED in its application to first-row neighbors (NI, Fig. 40, “Atom’s first-stage ionization energies of first-row elements in the format of the LSPT”); and (3) use of PFED to support, on chemical grounds, location of helium above beryllium in all periodic tables (many parts of NI, which renders it virtually unreadable for He/Ne lovers, who are an overwhelming majority of readers who might benefit most by reading it. One can bring water to a horse, but if (s)he is not thirsty for new knowledge that questions the validity of dearly held knowledge, (s)he may not drink.)

    Scerri’s remark that PFED “is only agreed upon by yourself with yourself as so many of these “New ideas from Fresh Energy…” seems to be his backhanded way of saying, in Roald Hoffmann’s words (NI, page vii), that “New Ideas . . .” is a “truly original book”. Thanks.

    My wife doesn’t like NI’s long title, either. It honors two of its author’s heros: Alfred Werner, particularly for his classic “New Ideas in Inorganic Chemistry”, and Dmitri Mendeleev, particularly for the inspiration contained in the concluding remarks of his famous Faraday Lecture on the Periodic Law (reproduced in “Principles”, Vol. II, Appendix II), on how the Law “needs not only new applications but also improvements, further development, and plenty of fresh energy.” That bit of chemical history has evidently passed over ES’s head. He’s not alone. NI’s author has, in truth, yet to meet anyone cognizant of the title’s roots.

    Suggestions for a better title welcomed!

  166. Going back to cores again: rather than say that there is a frontier between Cu/Ag/Au and Ga/In/Tl, with Zn/Cd/Hg not clearly on one side or the other, wouldn’t it be better to say that there is a transition from Mn/Tc/Re to Ga/In/Tl, with increasing numbers of d electrons firmly in the core and diminishing numbers of valence electrons. Apart from OsVIII (and a reported RuVIII?) no elements achieve higher oxidation states than VII. This would mean that the constitution of the core is not hard and fast but depends on the chemical/physical environment. In that case it could not be what characterizes an element.

  167. Dear Professor Bent,

    Thanks for these words: “Albert would agree, I believe, were he around, that you’ve made it as simple as possible, and no simpler.”

    I also tend to think that Dmitri would agree too, eventually.

  168. Henry,
    You wrote “Chemistry is a fact-rich science. Owing to the enormous skill of synthetic and analytical chemists, chemistry at any moment is a jungle of facts imperfectly related to each other. Once one has found one’s way around a small part of the jungle, however inefficiently, through years of hard work, one becomes reluctant to depart from familiar paths.”

    May I quote this on

  169. Valery,

    I agree with you 100 percent! You’ve put the case for the LSPT and He/Be as nicely as I’ve seen it put. Albert would agree, I believe, were he around, that you’ve made it as simple as possible, and no simpler. Why do we CONTINUE to make things more complex than they really are?

    Chemistry is a fact-rich science. Owing to the enormous skill of synthetic and analytical chemists, chemistry at any moment is a jungle of facts imperfectly related to each other. Once one has found one’s way around a small part of the jungle, however inefficiently, through years of hard work, one becomes reluctant to depart from familiar paths. Chemists are a conservative bunch, much more so than physicists. Helium-above-neon in their central icon is a monument to that conservatism. It will be interesting to see how much longer it stands on that pedestal. Until most of the present generation has died off, Planck would say. Half a century or so? Hopefully less. I wish I’d known about the LSPT and He/Be fifty years ago. It would have simplified my life in chemistry enormously and have greatly added to its quality.

    “We’re too soon old,” say the Pennsylvania Dutch, “and too late smart.”


  170. Eric Scerri says:
    March 3, 2010 at 3:07 pm
    Concerning Henry Bent’s views on radial nodes which is more fully explained in Bent and Weinhold, J Chem. Ed.

    That’s not fully accurate. Bent’s views on nodal surfaces, radial and angular, are fully explained in “New Ideas”, Section 63, pp52-53. The situation is simultaneously simpler and more complex than Scerri realizes.

    Scerri doesn’t want to count an orbital’s radial nodal surface at infinity as contributing to r. That’s his choice. He’s not alone. Some textbook authors don’t count it. They’re not aware, however, of the two physical interpretations that lie in the wings for r, properly defined (and helium located above beryllium).

    The radial nodal surface at infinity is created by the normalization procedure of quantum mechanics, AN IMPORTANT PROCEDURE.


    Here are two of them: a simple derivation of the important rule l ≤ n – 1 (from n = r + l and r ≥ 1); and the useful rule that ordinal numbers of blocks’ rows are equal to the r-values of the orbitals of their predominant type of differentiating electrons (provided H is located above Li and He above Be), illustrated in NI, Fig. 29, p61. In other words, to make the correspondence between periodic tables’ blocks’ rows and atomic orbitals as simple as possible, one needs r ≥ 1. Physically speaking, there are, in fact, no atomic orbitals with zero radial nodal surfaces.


    Outer contours of orbitals pictured in the scientific literature represent low values of orbitals, approaching zero — or, if one so chooses (as I have in Fig. 29), the nodal surface at infinity brought into view, schematically, from infinity.

    Here’s another virtue of the present definition of r: with that definition and a definition of l (in terms of nodal surfaces) and the rule as to how spectroscopists count (s p d f for 0 1 2 3), elementary school kids can quickly learn to do two things: (1) draw schematic orbital diagrams, given the orbitals’ “nl” names, with n = r + l; and (2) name orbitals, given their schematic diagrams. The exercises can be introduced as a game, preferably, if not necessarily, following the kids’ creation with appropriate apparatus of nodal points and nodal lines.

    With Scerri’s definitions of n and r, one cannot speak of n as the total number of nodal surfaces. In Scerri-speak, one must continually add or subtract 1. One cannot have, simultaneously, P = r + 2l as the Equation of form of the Left-Step Periodic Table and r + 2l = Madelung’s parameter.

    From this ex-GI’s view, it seems like the same old story: Snafu.

  171. Philip asks: “When does {[Kr]4d10} start to be a core? If at In why not at Cd – or even Ag or Pd?”

    {[Kr]4d10} is not completely core-like for Ag and Pd, since they have maximum oxidation numbers of +3 and +4, respectively. That is to say, the d10 subshell is partially oxidized in Ag+3, a d9 species, and in Pd+4, a d6 species.

    Cd is a different story. It’s maximum oxidation number is +2. Cd+2 is a d10 species. It’s d10 subshell has not been oxidized.

    Cd and Zn, and perhaps Hg, are, to my knowledge, the sole exceptions in the Periodic System to the system of core electron configurations I’ve cited. And for them it’s a close call. Their d10 subshells are not far from being oxidizable. As I believe I’ve mentioned, there are at least two reports in the literature of Hg+3, a d9 species, which, however, have been disputed.

    There is a block-to-block trend in oxidizability of filled subshells for first-row elements. The f14 subshell of Yb at the end of the f-block is oxidizable. The d10 subshell of Zn at the end of the d-block is barely not oxidizable. The p6 subshell of Ne at the end of the p-block is far from oxidizable. And the s2 shell of He at the end of the first row of the s-block is the least oxidizable of all (NI, Fig. 38, p84).

  172. Regarding Scerri’s remarks regarding He, Be, and Ne.

    It’s been said that helium’s most important chemical property is that it hasn’t any chemical properties. Actually, that’s not quite correct.

    Elements’ most important properties are their (elective) affinities: for oxygen, e.g. (“lithophilic”); for sulfur (“chalcophilic”); &c. An important affinity for noble gases (small “n”) — He, Ne, Ar, Kr, Xe, and Rn — are their PROTON AFFINITIES. Few affinities in chemistry are more important than proton affinities. Universally used Bronsted Acid-Base Theory is a theory of proton affinities. Proton affinities of the noble gases show that He, the most noble of the noble gases, is not a Noble Gas (“New Ideas”, p28).

    It’s naive in the extreme to locate helium in the Periodic SYSTEM by considering only three elements: He, Be, and Ne. And as simple substances, at that!

    A huge virtue of the Left-Step Arrangement of the elements is this: Imagine all the elements except He arranged in that fashion, including H above Li (owing to maximum oxidation numbers of +1). Now put anyone, a fifth grader, say, in Mendeleev’s position. Ask: Is there an element missing? Where? By extrapolations from the f-, d-, and p-blocks (NI, Table 11, p90), what would you expect its properties to be?


    He-above-Ne in the Left-Step Arrangement of atoms (H above Li) makes hydrogen stand out like a sore thumb.

    “Helium above beryllium,” said a young grandson, “is a no-brainer.”

    A whole book has been written about the chemical and physical implications of He-above-Be. Can one do likewise for the chemical and physical implications of He-above-Ne?
    Are there “57 Reasons” (and counting) for He/Ne?

    Well, for starters, both elements are colorless, inert, low-boiling, low atomic weight, full-shell, high ionization energy, low atomic refractivity, monatomic gases. That’s about it. It doesn’t take one very far into the chemistry and physics of the Periodic Table.

    Helium-above-neon might be called the “elementary school” location of helium in a classification of the elements as simple substances — and, similarly, hydrogen-above-fluorine the “middle school” location for hydrogen. More sophisticated are the classifications H/Li and He/Be.

    It’s noteworthy that the classification He/Ne prevailed prior to development of atomic spectroscopy, the f-block, the Left-Step Periodic Table, and Noble Gas Chemistry.

    He/Ne is an old-fashioned classification, useful in its day, as was, for Mendeleev, classification of thorium with cerium and uranium with tungsten. But it’s long since been passed by by developments in modern chemistry and physics.

    “History is bunk,” said Henry Ford. That may be true for theory-users. It’s not true for theory-modifiers.

    Useful in arriving at a correct periodic table, if not sufficient!, is some knowledge of the history of the periodic table.

    Thanks for challenging He/Be Theory and providing, thereby, opportunities to refine it.

  173. I’ve already mentioned here and elsewhere that in my angled ring tetrahedral model Prof. Bent’s secondary and tertiary kinships have direct mappings.

    Re-reading his book today I realized (though I had to doublecheck against the physical model) that at least one quaternary kinship also maps nicely:

    In the tetrahedron his C, Cr, Sm set (p.76) are in a straight line of contiguous spheres- if W is added, these are all in the same plane, with W at right angles to the other three on a different triangular face.

    Th is on the same ‘bread slice’/ vertical layer of the tetrahedron, on the same triangular face but on the other side of it from Sm. Related by a plane reflection symmetry. I wonder if there are others (for instance from this perspective C and Cr have this relationship with Si and Zr, the latter in a straight line with Th). W is opposite Rf reflectionwise.

    Jess Tauber

  174. Lucas and Fibonacci ‘triads’:

    I noticed this yesterday, and present it here for your minor amusement.

    The Fibonacci sequence: 1,1,2,3,5,8,13,21,34,55,89…
    The Lucas sequence: 2,1,3,4,7,11,18,29,47,76…

    For every four consecutive numbers in the sequence, a ‘triad’ can be constructed which ignores the second member.

    Triads: 1,2,3 2,5,8 3,8,13 5,13,21 8,21,34 13,34,55 21,55,89 and so on.
    2,3,4 1,4,7 3,7,11 7,18,29, 11,29,47 18,47,76 etc.

    As an aside, if one starts from 0 for the Fib. sequence, and then vertically align the sequences, the sum Luc. +Fib. generates 2x Fib.; Luc.-Fib. generates 2x Fib.; product Luc.xFib. generates every other Fib. number.

    Interestingly dividing Luc. numbers by their aligned Fib. numbers converges on the square root of 5 (29/13 is already 2.23…).

    I’ll leave it to you to decide whether any of this means anything.

    Jess Tauber

  175. P.S. And before you cite William Jensen as support just remember that he most definitely does not favor He in the alkaline earths!

    eric scerri

  176. Henry,

    You speak of First Element Distinctiveness as though it were an agreed upon axiom.
    In reality it is only agreed upon by yourself with yourself as so many of these “New ideas from Fresh Energy…”surely the world’s most awful title for a book.

    all the best

  177. As Henry Bent says, “Four types of gaps might occur in periodic tables.
    (1) Gaps within blocks’ rows
    (2) Gaps within blocks’ columns (between congeners)
    (3) Gaps within periods (between blocks)
    (4) Gaps between periods”
    Can anyone call my attention to any of these gaps in the Alexander Arrangement (LU under Y version)?

  178. When does {[Kr]4d10} start to be a core? If at In why not at Cd – or even Ag or Pd?

    Janet started numbering the groups 1 to 32 in 1928.

    I don’t think any of us doubts that He behaves like a noble gas (except that, like He, peeled of its electrons it would be a plasma). But that does not justify its being classified with elements that have a completed shell of 8 electrons.

  179. Regarding “Hints to chemical classification from numerical taxonomy”, from ES.

    Scerri’s concluding remark that “In all cases He invariable falls with the noble gases and nowhere near the alkaline earths” calls to mind the story of the bricklayers’ helper whose job was to load bricks into a bucket and then hoist them by rope and pulley to bricklayers working above him on a building’s roof. One time, as a prank, the bricklayers, instead of emptying the bucket, shoved its previous load into it. Now heavier than the helper, it descended as the helper, still holding onto the rope, rose, collided with the descending bucket and then the building’s cornice as the bucket struck the ground, lost its load, and rose as he fell, collided with it a second time before he struck the ground, let go of the rope, and was struck on the head by the falling bucket. He sued over damages sustained. The judge ruled against him on the grounds of INCOMPETENCE. He held on when he should have let go and let go when he should have held on.

    There’s a FATAL FLAW to attempts to capture the Periodic Classification of the Chemical Elements, fully, by means of “numerical classification”. Owing to the phenomenon of FIRST-ELEMENT DISTINCTIVENESS, and helium’s similarity as a simple substance to neon, “numerical classification” holds on (to helium, as a Noble Gas) when it should let go and lets go (of hydrogen, as the first member of the Alkali Metals Group) when it should hold on.

    It’s IRONIC that an individual who has published again and again and again on the importance of recognizing that the Periodic Classification of the Chemical Elements is NOT A CLASSIFICATION OF THE ELEMENTS AS SIMPLE SUBSTANCES should champion a classification that is strongly influenced by the properties of the chemical elements as simple substances!

    Let me guess: From the standpoint of the Periodic Classification of the Elements, “Numerical Classification” fares poorly for B, C, N, and O.


    And, also, second-element distinctiveness, especially for lithium and beryllium? And, less so, for Al, Si, P, and S? With perhaps some signs of third-element distinctiveness for Na and Mg? And Ga, Ge, As, Se, and Br?

    That should keep the classifiers out of mischief for a while.

  180. The reason why I favor Left Step periodic Table is so simple that some would cosnider it embarassing, but I do not.
    When I see four consequtive integers, I tend to arrange them in uninterrupted order. Given that s,p,d and f blocks of the periodic table correspond to values of quantum number “l” 0,1,2 and 3, arranging them in any other order, except perhaps in opposite order (3,2,1,0), seems very strange at best. That is why traditional depiction of the Periodic System, that arranges blocks in s,f,d,p order, is higly irregular and will always remain as such, despite its popularity.

    Helium is an inert gas, but it belongs in the same group with alkaline earth metals in s-block, simply because it has nothing in its structure that would warrant its placement in p-block.
    Is it too simple? Perhaps, but why make things more complex than they really are?

  181. Valery, about ATOMIC CORES:

    For blocks’ first two rows, atomic core configurations are of the form [X], where X is the symbol for a noble gas: He, Ne, Ar, Kr, or Xe.

    For later block rows, one needs to add additional fully occupied subshells — of which there are none for the s-block.

    Here are core configurations for p-block elements:
    B row: [He]
    Al row: [Ne]
    Ga row: {[Ar] 3d10}
    In row: {[Kr] 4d10}
    Tl row: {[Xe] 4f14 5d10}

    Many periodic tables list those configurations, sans the braces { }.

    Thanks for your question.
    The previous remarks should have appeared in NI’s Section 40 (p35) in connection with Figure 18, “Relative Sizes of Atomic Cores”.


  182. Regarding numerical taxonomy, or phenetics, according to Wikipedia:

    >Phenetic analyses do not distinguish between plesiomorphies – traits that are inherited from an ancestor (and therefore phylogenetically uninformative) – and apomorphies – traits that evolved anew in one or several lineages. Consequently, phenetic analyses are liable to be misled by convergent evolution and adaptive radiation<

    If helium does pattern with the noble gases, this still may be a 'convergent' trait secondary to a deeper patterning- in biology convergences are due to interactions with the larger environment as adaptations, tweaks to the system. How much else of chemistry is similarly motivated?

    Since cladistics has largely replaced phenetics, what would the former have to say about helium?

    By the way, these issues come up in historical linguistics all the time. There are a number of processes that can make languages resemble each other on the surface and so make them seem more genetically relatable than they really are. External borrowing, internal re-innovation, and typological streamlining come to mind.

    Jess Tauber

  183. For the Forum, regarding remarks regarding GAPS IN PERIODIC TABLES

    Four types of gaps might occur in periodic tables.

    (1) Gaps within blocks’ rows
    (2) Gaps within blocks’ columns (between congeners)
    (3) Gaps within periods (between blocks)
    (4) Gaps between periods

    Tabular (table-type) representations of the Periodic Law necessarily have gaps between periods: in sfdp tables, between the p- and s-blocks; in the fdps table, between the s-block and the other blocks. All periodic TABLES have Gaps of Type (4).

    Mendeleev is famous, today, for eliminating several gaps within blocks’ rows. No modern periodic tables have gaps of Type (1), except for a gap between H and He when, as is commonly the case, He is located above Ne.

    The “medium-long” and “long-form” of the conventional periodic table have gaps of Type (3).

    Modern forms of Mendeleev’s “short-form” table have gaps of Types (2) and (3).

    [The terminology “short”, “medium” and “long” is, in a sense, naïve. All modern periodic tables are the same width, in the sense that, for Z through 120, they have 32 columns: 2 s-block, 6 p-block, 10 d-block, and 14 f-block columns. As I recall seeing somewhere, from something from Philip?, Janet so-labeled them, around 1927.]

    The Left-Step Periodic Table is the only period table of perfect regularity (“New Ideas, Table 15, p108) that has no gaps at all — save, of course, for gaps of Type (4).

    The Right-Step Table (NI, Fig. 55) has gaps of Type (2) and (3).

    The Front-Step Table (NI, Fig. 52) — the only three-dimensional periodic table of RECTANGULAR COORDINATES, all three of which have chemical and physical significance — has gaps of Type (3).

    The Step-Pyramid Table, s-elements on the right (NI, p69), has gaps of Type (2) — likely the chief reason step-pyramid tables aren’t more popular with chemistry students and their teachers.

    [Scerri cites the Step-Pyramid Table of perfect regularity in his book, on page 282, pictured in Fig. 10.14, WITHOUT ATTRIBUTION. One should be grateful, perhaps, for small favors: to wit, absence of a false attribution, regarding, e.g., this blooper (note 52, p293): “Relativistic effects, more properly speaking [sic!], arise from the greater nuclear masses of the ‘heavier’ elements.” The middle-member-of-a-pair absurdity is excusable, perhaps, as a slip of the pen? But that whopper? Surely it falls, “properly speaking”, into the “-10” category.]

    Scerri points out in his interesting Chapter 5 on “The Acceptance of Mendeleev’s Periodic System” that what Mendeleev is most famous for today — his prediction of missing elements, and what their properties would be — is not the chief reason his Periodic System was accepted in his day.

    My own feeling, following a remark by Einstein regarding the leading role of textbooks in shaping physical thought (not mentioned by Scerri) is that acceptance of Mendeleev’s Periodic System in his day rested in significant measure on his famous textbook “The Principles of Chemistry”. It went through seven Russian editions in his lifetime. After ending the First Volume, on the descriptive chemistry of the elements, with chapters on the halogens and the alkali metals, Mendeleev opens the Second Volume with his famous Chapter XV on “The Grouping of the Elements and the Periodic Law”. The entire work is a magnificent display of scientific, pedagogical, and philosophical excellence. It’s answer to the question –

    What’s the best textbook ever written in chemistry?

    Scerri’s asks: What’s the best periodic table? A perceptive question? What’s the best table in a Handbook of Chemistry and Physics? Scerri’s answer to his question has been a function of time. Mendeleev’s textbook is timeless. Where it should reside in the personal library of every teacher of general and inorganic chemistry (an excellent English translation exists) there is, today, usually, sad to say, a gap.

    Yours, for closing the gap between hydrogen and helium in conventional periodic tables,

  184. Hints to chemical classification from numerical taxonomy.

    Since the 60s and 70s the methods of numerical taxonomy have been rather successful in the field of biological classification. They were first developed by Sokal and Sneath. The idea is to assume nothing of evolutionary biology but just measure all manner of attributes of living organisms and then do a similarity analysis to reveal kinship. Such studies have revolutionized biological classification and have provided means of assessing the degree of kinship of altogether different species such as humans and bacteria.

    Such methods have now also been applied to chemical classification. Sneath himself published a paper on this issue in the first issue of Foundations of Chemistry. Many studies of this kind have been carried out including by the Colombian school of Villaveces, Restrepo and others. They too have published articles in Foundations of Chemistry.

    In all cases He invariable falls with the noble gases and nowhere near the alkaline earths.

    eric scerri

  185. Sometime ago I suggested that Paneth’s basic substance sense of ‘element’ could be inferred from the properties of the element as a simple substance and also as a combined element.

    This is of course how Mendeleev and others arrived at the periodic table.

    But in the rather unique cases of He and Ne, one cannot consult the properties of the elements in combined form. It follows that all that we know about these elements as basic substances is inferred from their properties as simple substances.

    On this basis He behaves like a noble gas and not like an alkaline earth.

    eric scerri

  186. Concerning Henry Bent’s views on radial nodes which is more fully explained in Bent and Weinhold, J Chem. Ed.

    Bent and Weinhold begin by appealing to the Sturm-
    Liouville theory which applies to a wide class of
    differential equations. This theory essentially holds
    that the solutions to this class of differential equations
    can be placed in order of increasing energy
    according to the number of nodes that they possess.
    This notion appears to be rather promising given
    that orbitals with increasing values of n and are
    indeed known to have an increasing number of
    radial as well as angular nodes with a corresponding
    increase in orbital energy.
    But the promise of simplicity is somewhat shortlived
    once one realizes that the total number of
    nodes in atomic orbitals, as normally defined, fail to
    predict the correct order of increasing energy. The
    4s orbital has 3 radial nodes plus 0 angular nodes,
    making a total of 3 nodes altogether. Meanwhile,
    the 3d orbital has 0 radial nodes and 2 angular
    nodes and thus a total of only 2 nodes. And yet the
    4s orbital with the higher total number of nodes is
    preferentially occupied or has a lower energy than
    the 3d orbital.
    However, the authors soon inform the reader
    that that they are adopting a rather exotic sense of
    the term radial node, as well as treating the angular
    nodes in an unconventional manner. In addition to
    the radial nodes, given by the well-known equation
    of n – l – 1, the authors include an additional
    radial node because of the existence of a node at
    infinity. The result of this change is to produce a
    total of n – l radial nodes.
    Next, instead of counting the normal number of
    angular nodes, or l , the authors consider twice the
    value of l . The net result of both of these changes
    is to give n – l – 2l or a total of n + l. Not

    surprisingly they thereby obtain some consistency
    with the n + l rule, and the number of nodes with
    increasing energy, by using this very specific way
    of counting the nodes in any particular atomic orbital.
    For example, the 4s orbital has 3 radial nodes
    plus 1, plus 0 angular nodes, making a total of 4
    nodes if counted in this particular manner. Meanwhile,
    the 3d orbital has 0 radial nodes plus 1, plus
    2 times 2, giving a total of 5 nodes when counted in
    the same manner.
    As a result of this way of counting nodes the 4s
    orbital has a lower total number of nodes, that is, 4
    when compared with 5 in the case of the 3d orbital.
    Moreover, this order agrees with the experimentally
    observed order whereby 4s has lower energy
    than 3d.10 However, whether this is a satisfactory
    first principles explanation of the n +l rule, which
    meets the Lowdin challenge, is something that
    seems rather unlikely given the ad hoc nature of the
    manner in which nodes have been counted.
    It should also be said that the reason why Bent
    and Weinhold devote such attention to the n
    rule is that, as mentioned earlier, the rule is clearly
    represented on the left-step table, the form of the
    periodic table that they favor.

  187. Valery, concerning “mathematical regularities of the periodic table”:

    I wasn’t aware of many of the regularities that you cite. Thank you for calling my attention to them. They add a distinctive elegance to the Periodic System, one that everyone can responds to. One needn’t be an inorganic chemist, aware of the sense in which the descriptive chemistry of the elements is periodic, or a physicist, aware of the leading features of the electronic structure of atoms, to respond in an aesthetic sense to the beauty of the “mathematical regularities of the periodic table”. Mathematical beauty’s distinctive signature resides in the fact that in order to enjoy it one needn’t know what it could be talking about. Descriptive chemistry? Atomic structure? It doesn’t matter. Early on physicists no less than chemists were intrigued by Periodicity’s “magic numbers”: 2, 8, 18, 32, equal, as is well-known, to twice the integers squared, beginning with 1: 1, 4, 9, 16. I hazard the following remarks:

    2l + 1.

    Perhaps the simplest example of that dependence are the square numbers, cited previously. They are (as Galileo noted, in creation of his famous expression for the distance of free fall from rest, written today s = “one-half g t squared”) the sums of the odd numbers, beginning with unity. (Distances Galileo’s rolling objects moved each successive second were proportional to the odd numbers, beginning at unity.)

    [As I understand it, the Greeks proved the odd-number theorem by a simple geometrical construction. Create from a geometrical picture of a square number, n squared, the next square number by adding to “n squared” n units on one side, n units on an adjacent side, and, to complete (n+1) squared, one unit at the open corner. That is to say: to advance from a square number to the immediately following square number, add an odd number of units. As Algoras (sp?) might have put it: (n squared) + (2n + 1) = [(n+1) squared.]

    The expression (2l + 1) is generated in mathematical solutions of Schrodinger’s equation applied to the hydrogen atom, as the degeneracy of hydrogen atom’s energy levels. Those solutions are characterized by two quantum numbers, r and l, which have a geometrical interpretation. The quantum number r is a solution’s number of radial nodal surfaces. It starts at 1, since there is always (for normalized wave functions) a radial nodal surface at infinity. The quantum number l is the number of angular, nucleus-containing nodal surface. It starts at 0. Of course, the total number of nodal surfaces is r + l. It turns out, fortuitously, some say, that for the hydrogen atom that’s what its different states’ energies depend on: only the sum, r + l, not (as in many electron-atoms), the individual values of r and l. That sum is set equal to a “principle quantum number”, n (= r + l). Consequently, by definition, l = n – r. Since r ≥ 1, l ≤ n – 1, a well-known result cited, without proof, in many elementary textbooks of chemistry and physics.

    In expressing algebraically Periodicity’s Fibonacci character — that an atom’s character depends on the character of the atom that precedes it in Bohr’s Aufbau Process — I started with the terms r and l, in that order, because I wanted to generate, eventually, the Madelung term r + 2l and not, e.g., l + 2r. That is to say, I was allowing Nature to dictate the series’ form. I was proceeding empirically — might one say, “scientifically”?

    It might be interesting, working with a mathematician, to collect all of Periodicity’s mathematical regularities that one can think of, and to check out that, as I’ve asserted, they all follow, in one manner or another, from the odd numbers. Those numbers seem like a solid base to build on. The goal of Whitehead and Russell’s huge effort in “Principia Mathematica”, to reduce all of mathematics to a few logical principles, was aimed, as I recall, at running everything back to the integers.

    [Of course, the integer “2” enters into the picture, owing to the phenomenon of electron spin. Indeed, having tabulated Periodicity’s regularities, and their relation to the odd numbers, and 2, one might introduce into the properties assigned to the electron, a “classially non-describable two-valuedness” (in Pauli’s words), in order to account for Periodicity’s mathematical regularities.]

    Mathematicians are famously thorough in their research. It may well be the case that they’ve already generated a large body of information regarding mathematical regularities related to the odd numbers, and 2. It wouldn’t be surprising to learn that, in fact, that exercise has generated its own small sub-field of mathematics.

    Statements being interrelated as they are in mathematics, it wouldn’t be surprising, either, if a mathematician could start with any particular mathematical regularity of Periodicity and parse it back, step by step, to the odd numbers beginning at unity, and 2.

    A mathematician such as the famous, initially self-tutored Indian mathematician who astonished the mathematical establishment in England with his ability to state mathematical theorems long before anyone was able to create formal proofs of them (his name escapes me at the moment; it begins with S) might look at the left-step periodic table and say, in instant, “That’s odd.”

    Thanks for your perceptive questions,

    P.S. Regarding “the microscopic structure of space-time around atomic nuclei”, I’ve wondered for over fifty years along these lines: if space is a Dirac sea of electrons, with ordinary electrons being those above its fermi level, so to speak (and with positrons being holes in the sea); and if electrons obey a principle of spatial exclusion, in which two electrons of the same spin cannot be at the same place at the same time, there being about each electron a “fermi hole” into which electrons of the same spin cannot penetrate (that picture accounts for Periodicity’s term 2(2l + 1), hence the shapes of periodic tables, and, also, for the validity of valence-sphere models of valence-stroke diagrams of molecules) — if such is the case, then shouldn’t the presence of “ordinary electrons” affect the structure of space in its immediate neighborhood? And likewise for protons? And neutrons?

  188. On seeking a general solution to the Schrodinger equation.

    Henry, please see the papers by Sabre and Herschbach which are cited in my book. Moreover the Thomas-Fermi method also provides a universal solution in the sense of a dependence of Energy on Z.

    Seeking such a universal solution is perfectly natural if one is interested in strict derivations of the PT from quantum mechanics.
    The late Valentin Ostrovsky who was a critic of my work agreed on this point 100%. See his articles in Foundations of Chemistry.

    eric scerri

  189. Professor Bent wrote:
    “Apologies for the length of this communication. I’ve tried [in Einstein’s words] to make it as simple as possible [for myself, and my grandchildren, of high school and college ages, and others], but no simpler.”

    Question for Roy,
    what would your “museum visitors” do if they were given an explanation of Periodic System’s major rule like that of prof. Bent’s?

    I have an idea for professor Bent. What if you, Dr. Bent, come up with the list of atomic core configurations for all known elements as you see them? I think it would be a great contribution to this discussion and to PT theory, if they are agreed upon universally.

  190. For the Forum:


    On page of 58 of his book on the Periodic Table, Scerri writes that “[A]bout 50% of all possible vertical triads, using atomic numbers, are in fact exact.” Of course. In the Left-Step Periodic Table, vertical triads begin with Groups’ 2nd and 4th elements, never with their 1st and 3rd elements (“New Ideas”, Section 25, “Dyads and Triads”).


    Yet, astonishingly, on p181, in order to show that “about 50% of all atomic number triads are exact”, Scerri exhibits a “[s]lightly modified [conventional] LONG-FORM TABLE” (emphasis added), with helium above neon! The “long form” table exhibits, as mentioned, only partial dyadic character. Scerri’s table violates the Triad Rule regarding Groups’ first elements, twice: where He appears, incorrectly, above Ne, making it, its Group’s first element, part of a triad; and where He is missing, making Be, its Group’s first element, although it is a member of a triad. On the facing page, p180, appears this puzzling remark:

    “All one needs to do is to pick a middle element from the first of a repeating pair of periods.”

    What?! “All one needs to do” to do what? Form a triad? By picking “a MIDDLE element from the first of a repeating PAIR of periods”? A pair hasn’t a middle element! Meant, evidently, is this: “All one needs to do [to form a triad] is to pick as its middle element the first element of a repeating pair of periods” — in the conventional periodic table.

    That prescription works for his four exhibited triads, He Ne Ar, Li Na K, S Se Te, and Ru Os Hs. Middle elements Ne, Na, Se, and Os are first elements of “repeating pair[s] of periods”. On the other hand, the middle element in the triad Be Mg Ca, not mentioned by Scerri, is, contrary to his prescription, the SECOND element in a “repeating pair of elements”. Also, the prescription certifies as a triad He Ne Ar, contrary to the author’s figure 10.13 facing page 282. It’s a case of two wrongs — He above Ne; and use of not fully dyadic periodic table, with only 7 periods — making a faulty “right”: agreement with a flawed prescription. Called to mind is the WWII slogan: Snafu. Situation normal, all fouled up.

    It might make an interesting student exercise: unscramble Scerri’s prescription; and create a term or phrase to describe the instruction: pick a “middle element” from a “pair of elements”. Not being a Pauli, I’m at a loss for words. Perhaps the Chinese have the appropriate phrase for Scerri’s philosophy: the sound of the clap of one hand?

    That said, I should say that I’ve enjoyed reading Scerri’s discussion of “Ab Initio Calculations” (pp243-24) and the “Density Functional Approach” (p245-247), although, as with the 50% rule, he ends with a typical Scerriism, when he writes that being able to solve “50 individual Schrodinger equations in order to reproduce the well-known pattern in the periodicities of ionization energies” is “not a GENERAL SOLUTION to the problem of the electronic structure of atoms” (pp244-245, emphasis added).

    There he goes again, with a statement that’s not even wrong. It’s truth by definition. For what does Scerri mean by “a general solution”? He means a “solution” that “is expressed in terms of the variable Z [atomic number]” so that “[o]ne does not need to repeat the calculation separately for each atom . . .” (p246). Just substitute values of Z into the function IE(Z).

    As an alleged expert on the periodic table, surely Scerri should know that Mendeleev would have deemed an effort to find for atoms’ ionization energies a CONTINUOUS FUNCTION OF Z, IE(Z), sheer folly, in as much as, speaking sensibly, in a physical sense, Z can assume only integral values! What’s the physical significance of the numerical value of IE(1.5)? It brings to mind “the middle member of a pair”. When I asked my wife what that might be, she said, “I don’t know. One-and-a-half?”

    My hunch is that an accurate “general solution” would be soooooooooooooooo mathematically complex, being sooooooooooooo removed from reality, that calculating ionization energies by substituting into it 50 different values of Z would require more computer time than it now takes to solve the 50 corresponding “individual Schrodinger equations”.

    Several years ago a theoretician at Princeton told me that quantum mechanicians had conquered the problem of calculating beyond experimental accuracy atoms’ ionization energies from first principles. Scerri challenges that statement, alleging that the calculations “include considerable semiempirical elements at various levels” (p247).

    That would have been o.k. with Berkeley’s renowned chemist Wendell Latimer, who defined physical chemistry as “a method for obtaining correct answers, no holds barred”. The point for chemist is that, in their calculations of ionization energies, the physicists’ “semiempirical elements at various levels”, such as they may be, are not drawn from chemistry.

    In the end, of course, ALL SCIENCE IS EMPIRICAL! Being “semiempirical” sounds like being semi-pregnant. Neither Webster’s unabridged dictionary, the OED, or its 1986 Supplement has an entry “semiempirical”. It’s one of those unphilosophical terms used by some philosophers of science.

    Philosophically significant for chemists interested in the logical foundations of their Periodic System are two facts. (1) Physicists can calculate accurately, one way or another, from physical data, atoms’ first stage ionization energies. (2) From a plot of calculated IEs vs. Z, one can capture the exact form of the chemists’ left-step periodic table, by using a set of Construction Conventions that are isomorphic with those used to capture chemically the LSPT from a generic form of Mendeleev’s line, in which specific symbols for the Halogens, Noble Gases, Alkali Metals, and Alkaline Earth Metals and the Coinage Metals and the Volatile Metals are replaced by the generic symbols H, N, A, E and C, V, which, with cuts in the line, are then aligned, vertically, in a table of no gaps and maximum regularity in lengths of columns and periods.

    The chemists’ HNAE sequences correspond exactly to the physicists’ major zig-zags in their IE/Z plot. The chemists’ CV(III)(IV) sequences [where (III) and (IV) represent elements with maximum oxidation numbers of +3 and +4] correspond exactly to the physicists’ minor zig-zags. Viewing the first zig-zag — formed by the IEs of H He Li Be, and their atomic numbers — as two zags, H He and Li Be, yields maximum overall regularity, with He above Be. The bottom line?


    Thanks for reading,

  191. More more numerology:

    On p.13 of Bent’s NI fig.7 shows the layout of maximum oxidation states laid out over the LSPT.

    If one includes the isolated ‘4’ between blocked off sequences in 4f, an interesting thing happens when considering elements that don’t observe the general trends.

    In the s block there is 1 element, He.
    In the p block there are 5 elements.
    In the d block there are 13 elements.
    In the f block there are 21 elements.

    All odd numbers.

    1,5,13, 21 are the first elements of 1s,2p, 3p, and 3d, another one of those weird coincidences (are there further elements in 6d that would alter the number 13?). 5,13, 21 are triadic, to boot.

    From the Fibonacci perspective 0,1,1,2,3,5,8,13,21,34,55…., note that there are TWO digits (2,3) between the final 1 and 5, ONE digit (8) between 5 and 13, and NO digits between 13 and 21.

    In the s block there is 1 element in the first member set, and 0 elsewhere (1,0 Fib. numbers).
    In the p block there are 3 elements in the first member set, and 2 elsewhere (3,2 Fib. numbers).
    In the d block there are 5 elements in the first member set, and 8 elsewhere (5,8 Fib. numbers).
    The pattern breaks up in the f block, where the first member set has 12 elements (1 short) and there are 9 elsewhere (1 extra), but they are still pretty close to 13,8 (both Fib. numbers). Of the sequence 1,5,13,21, all are prime numbers except for the f block, another failure of f to conform perfectly to the pattern.

    We’d still need to know whether there are more d elements that should be blocked off, which would throw this particular set of coincidences to the winds.

    Jess Tauber

  192. More phi-based numerology. I’ve noted elsewhere that Fibonacci numbers below 120 tended to be significantly relatable periodic table element positions. There is also a patterning where every third number doesn’t quite ‘fit’ this pattern. After 120 this pattern falls apart.

    1,1,2,3,5,8,13,21,34,55,89 where 1, 3, 5, 13, 21, 55, and 89 are the first members of their sub-periods, and 2, 8, 34 are not.

    Note that Al/Sc= 13/21 is close to to inverse phi (is there a relation of triads to phi??), and relate sequential orbital types (3p,3d), but Cs/Ac=55/89 comes at the system from further back, and missing a period (6s,5f).

    Jess Tauber

  193. Valery, Here are some remarks regarding the “well-known exceptions to Madelung Rule among elements of d and f-blocks.”

    Illustrated in passing, Philip, are uses of the definition: atomic core = atom – (all electrons in oxidizable subshells).


    Exceptions to the Madelung (n+l)/l Rule regarding the order of orbital occupancy in Bohr’ Aufbau Process [orbitals with the smallest (n+l) first and, for a given (n+l), largest l first] are frequently said to be major defects in the Rule and compromise seriously, therefore, the scientific soundness of the Rule’s implications, particularly the electronic interpretation of the Left-Step Periodic Table, and its location of helium above beryllium. Those hasty judgments regarding the Madelung exceptions are unphilosophical.


    What is Nature telling us?
    Are there patterns to the exceptions?
    Are the exceptions simple or complicated modifications of expected electron configurations?
    Are the exceptions small, energetically speaking, or large?
    Are the exceptions chemically significant?
    In which parts of the periodic table do the exceptions occur? In which blocks? In which block rows? And in which parts of blocks’ rows?
    And, finally: Are there plausible physical explanations for the exceptions?

    Answers to some of the questions are well-known.
    All exceptions are “single”: i.e., describable by reassignment of a single electron, except in the case of Pd, ground state [Kr] 4d10, rather than, expected from the Madelung Rule, [Kr] 4d8 5s2. But the reassignments are relatively close calls. Energies of Pd’s three lowest electron configurations (in reciprocal centimeters), rounded off from data in Charlotte Moore’s “Atomic Energy levels, are:

    Pd: [Kr] 4d10 0.0000; [Kr] 3d9 5s 8000; [Kr] 4d8 5s2 28000. For comparison, Pd’s first stage ionization energy is 67000.

    Here are the corresponding data for Pd’s congener Ni, “regular”, but only barely:

    Ni: [Ar] 3d8 4s2 0.0000; [Ar] 3d9 4s 700; [Ar] 3d10 15000.

    Ground level for irregular Nb, [Kr] 4d4 5s, lies only 1100 cm-1 below the regular, Madelung configuration [Kr] 4d3 5s2.

    [Personal Note: Some years ago the University of Minnesota invited the late Ronald Nyholm (of the popular Nyholm/Gillespie/Sidwick/Powell Valence Shell Electron-Pair Repulsion Theory) to the University of Minnesota to give the chemistry department’s summer 3M Lectures. Ron arrived at the Twin Cities Airport lugging Charlotte Moore’s three volumes. “Every inorganic chemist should love Charlotte’s Tables,” he explained.]

    “Actually, the center of gravity of [the levels] of [the] 4d3 5s2 [configuration] lies well below the center of gravity of 4d4 5s, so that Nb(I) is not really out of line . . .” writes Cowan (“The Theory of Atomic Structure and Spectra”, p120).

    “[T]he binding energies of 3d and 4s electrons are not greatly different,” adds Cowan, “and in V I, Co I, and Ni I ionization involves not only removal of a 4s electron but also REARRANGEMENT OF THE ION CORE [emphasis added], with the second 4s electron dropping down to the 3d subshell. Similar irregularities [occur] in the other transition elements and the rare earth series.”

    In going, e.g., from V(I) to V(II), the ground state configuration changes from 3d3 4s2 to 3d4. Illustrated is an important phenomenon, mentioned previously.


    That phenomenon gives rise sometimes (as noted previously) to the phenomenon of REORGANIZATION on ionization and, consequently, to the well-known “scandium paradox”. In formation of Sc in Bohr’s Aufbau Process, 3d is the last orbital occupied. However, in ionization of Sc, 4s is the first orbital vacated. Obviously its physically naïve in such situations, when major reorganization occurs, to speak of INDIVIDUAL orbital energies. Which orbital in Sc’s ionization has the higher energy: 3d or 4s? Wrong question. It’s impossible to say.

    (One can say that in the neutral Sc the ground state configuration 3d 4s2 lies below the excited state 3d2 4s, by 11600. Accordingly, 4s is said to lie below 3d. 4s —> 3d is a “promotion”. For Sc+ the ground state configuration 3d 4s lies below the excited state 3d2, by 4900. Again 4s appears to lie below 3d. 4s —> 3d is, again, a “promotion”. On the other hand, 3d2 (singlet D) lies below 4s2, (singlet S) by 11736 – 10944 = 792. Conclusion: As students of atomic spectroscopy well know, descriptions of atoms’ electron clouds adequate to a detailed understanding of their relative energies requires more than two integers: n and l. Creation by the simple Madelung Rule of a table topologically equivalent to chemists’ periodic tables is remarkable, and tells us something about the relative importance of atoms’ various energy terms — another story, one far more complex than the present one. In using Moore’s tables to obtain simple insights into chemistry, it appears that one needs to know where to stop.)

    In most of chemistry, exceptions to the Madelung Orbital Occupancy Rule are UNIMPORTANT, since in elements’ compounds Madelung-exceptional elements generally have an oxidation number of +2 or greater. And irregularities in electron configurations disappear in twofold ionized (hydrogen-like) atoms (except for Sc’s congeners Y and Lu).

    Exceptions to Madelung’s Rule occur in the d- and f-blocks, near, if not actually adjacent to, atoms that have half-filled and filled subshells. Frequently encountered in inorganic chemistry, owing to the dependence of d-orbital sizes on their principle quantum number, is the pattern of the number of Madelung exceptions in the d-block, by row: 4d > 3d > 5d.

    The following explanation of Madelung Rule exceptions is provisional, visual, hence qualitative. (“Give me insight,” said the renowned quantum mechanician C. A. Coulson, “not numbers.”) The explanation stems from Hylleraas’s famous calculations on helium, which evolved in quantum chemistry into the method of DODS: Different Orbitals for [Electrons of] Different Spins, extended to molecular systems by Jack Linnett in his theory of Different Structures for Different Spin Sets. (E.g., for NO’s 5- and 6-membered spin-sets, triple bond and double bond arrangements, respectively, of single electrons of the same spin; for OO’s 5- and 7-membered spin-sets, triple bond and single bond arrangements. The model accounts not only for odd-electron NO’s small tendency to dimerize and dioxygen’s paramagnetism, but also for the previously unexplained fact that 40 percent of the alkali halides haven’t the crystal structures predicted by the Radius Ratio Rules, and why some gaseous alkaline earth dihalides are linear and others are bent.)

    [In speaking of “spin-sets”, I’m visualizing Linnett’s “configurations of maximum probability” for the distribution in space of a spin-set’s “fermi holes”, into which electrons of the same spin do not penetrate. For two parallel spins about an atomic nucleus, that configuration is “digonal”, for three “trigonal”, for four “tetrahedral”, for five usually “trigonal bipyramidal”, for six “octahedral”.]

    Suppose that an atomic core’s two spin-sets are, at any instant, owing to electron-electron coulombic repulsions between electrons of opposite spin, slightly ANTICOINCIDENT, one spin-set slightly more contracted about the nucleus than the other spin-set (as in Hylleraas’s model of the helium atom). Add an additional (valence-shell) electron. To maximize its interaction with the core’s nucleus while avoiding especially, owing to the Principle of Spatial Exclusion for Electrons of the Same Spin, electrons of the same spin, the added electron must have same spin as the spins of the contracted spin-set; and similarly for a second added electron; etc. That’s Hund’s Rule (of Maximum Multiplicity).

    For what type of core is the Hund’s-Rule effect greatest? One with many electrons, presumably. The first exception to Madelung’s Rule occurs for a core that contains 18 electrons, in the d-block (namely, with element 24, Cr).

    Now, just as on the assumption that an anticoincident core influences the character of its valence-shell, so, too, it might be assumed that a core-fitting valence-shell influences, somewhat, the shape of its atomic core, to the extent that, in the d-block, an electron, or electrons, are demoted from an outer s-subshell to a core-shaping d-subshell.

    For what type of d-subshell is its core-shaping effect greatest? Presumably one approaching or immediately past a FULL subshell of occupied spin-orbitals — a so called “half-filled” subshell, in agreement with experiment. The same electron “demotion” might be expected to occur on approaching a second full subshell of spin-orbitals — i.e., at a “full” subshell, again in agreement with experiment.

    In the case of the first element of the f-block, La, Z = 57, orbital 5d (n+l = 7) competes successfully for an electron with orbital 4f (n+l = 7). Contributing to that fact is the fact that La’s 54-electron core is unusually electron-rich, compared to the 36-electron cores of the Y row. A 4f orbital with its 3 nodal surfaces that pass through its atom’s nucleus will tend not to penetrate La’s electron-rich core as successfully as a 5d orbital with only 2 nucleus-containing nodal surfaces. Because of its core’s particularly large screening effect, a modified Madelung Rule prevails for La: for given (n+l), with increasing Z, SMALLEST l first.

    The “smallest-l-first” phenomenon is, as expected, even more pronounced in the f-block’s Ac row, where orbital 6d (n+l = 8) competes successfully, or at par, or in part, with orbital 5f (n+l = 8) from Ac, element 89, through element 93.

    It’s conjectured, by others, that a “super-actinide” series will have complicated ground configurations involving the (n+l) = 9 orbitals 5g, 6f, 7d, and 8p. The bottom line?


    One may wonder: Why don’t exceptions to the Madelung Rule occur among atoms of electron-rich cores of the p-block, like lead? A comparison of lead’s energy levels with those of carbon is instructive.

    Ground states. Pb [Xe] 4f14 5d10 6s2 6p2 J = 0, 1, 2; energy = 0, 7800, 10600.
    C [He] 2s2 2p2 J = 0, 1, 2; energy = 0, 16, 44.

    J’s magnitude indicates the “coupling” between an atom’s spin (angular momentum) and its orbital angular momentum. That coupling for carbon, whose core contains only 2 electrons, is small, compared to the coupling for lead, whose core contains 54 + 14 + 10 = 68 (= 82 – 4) electrons.

    Excited States. Carbon has a 2s 2p3 state at 64,000. (Carbon’s IE is 90878.)
    Listed for lead by Moore are no excited states having less than 2 6s electrons. Lead’s 6s electrons are relatively low-lying, chemically inert electrons, corresponding to the existence in inorganic chemistry of the “inert pair effect” (oxidation state +2, in the case of lead, as in PbO and PbCl2) and, consequently, an atomic core, for lead, that has the electron configuration {[Xe] 4f14 5d10 6s2}.

    (I picture outer s-electrons as good “ligands” for large, instantaneously lumpy atomic cores.)

    Absence of Madelung-like exceptions for lead reflects the fact that its s-orbital is low lying and its 4f and 5d orbitals are fully occupied.

    Apologies for the length of this communication. I’ve tried [in Einstein’s words] to make it as simple as possible [for myself, and my grandchildren, of high school and college ages, and others], but no simpler.


  194. As I understand it from colleagues in the philosophy of physics, the philosophical issues in the foundations of quantum mechanics have no bearing on quantum chemistry and especially the electronic structure of atoms. The only area of overlap is perhaps the long-standing over the Born-Oppenheimer approximation and molecular structure but this does not belong to the area of foundations of quantum mechanics proper.

    Any proposed new physics needs to undergo the peer-review process. Privately published books and Internet sites do not help to establish such new views, although they might serve as a means of airing some ideas.

    So Jess, Valery, Roy and others how about making the trip to Montreal in late March? Where do you all live in any case so that we can start to think about a possible meeting if not in Montreal? I’m guessing that all three of you are on the east coast which would make Montreal a reasonable possibility. It would also provide press coverage on the back of the Concordia talk.

    Another person attending will be Professor Fathi Habashi also from Quebec who has written extensively on the periodic table. He has an article in the next issue of Foundations of Chemistry as does Philip Stewart (on Janet). This will be a special issue devoted to the periodic table. Philip have you been over the pond lately? Any chance of your attending?

    all the best

    eric scerri

  195. I had more time during weekend to think about variable coefficient of “l” proposed by Henry Bent in NI in order to address well-known exceptions to Madelung Rule among elements of d and f-blocks. I have to say that I remain skeptical. I can see where this metod (n+kl, where k is variable) has a flaw. It works fairly well for d-block elements by arriving at approximately equal orbital energies for 3d- and 4s, as well as 4d- and 5s-orbitals. However, it does not work as well in 4f- and 5f-orbitals, because it shows rather big gaps in energies between 4f- and 5d-orbitals, as well as between 5f- and 6d-orbitals.

    Close energies between d- and s-blocks result in “borrowing” s-electrons by d-block elements. However, f-block exceptions occur due to “lending” electrons to d-orbitals within the same LST periods. Variable n+l hypothesis works well for transition between the periods, but it does not work at all within the periods.

    I like Jess’ earlier idea of PT conference. I would love to attend such. I think that meeting and seeing people in person is always more productive than arguing over the Internet.


  196. It should be called the Fibonacci Algorithm rather than the Series. It doesn’t matter what two numbers you start with, you rapidly converge on Phi. For example: -17, 100, 83, 183, 266, 449, 715, 1164, 1879… Already the last two ratios are 1.628 and 1.614. Is this common knowledge? I haven’t seen it stated before.

  197. On March 25th, I will be giving an invited public lecture on the periodic table at the Oscar Peterson Concert Hall, at Concordia University, in Montreal, Canada. This is part of a public lecture series at Concordia going back about 20 years.

    Pierre Demers and Fernando Dufour will be attending.
    It could also provide an opportunity for a conference among some of us as suggested by Jess Tauber a few days ago.

    The expected audience is around 500.

    eric scerri

  198. Henry Bent wrote:

    >“[N]o single value of k is necessary for all parts of periodic tables. Any value greater than zero yields the [essentially hydrogen-like] row-orbital order through element 20, 0.51 the order through element 57, 0.67 the order through element 120. That is to say:


    Regarding Fibonacci character again. What if k directly relates to actual Fibonacci ratios?

    That is, with the sequence 0,1,1,2,3,5,8,13,21……

    0/1= 0, 1/1= 1, giving you your limits for s and p values for elements up to atomic number 20.

    1/2=0.5, 2/3= .66666….., giving the limits for d and f dual through atomic number 56 and 120 respectively.

    Since we can expand the table infinitely (ideally, mathematically), can we then use the following successive ratios in similar fashion for g, h, i, j, k duals, as a test of this hypothesis?

    One can plot the continuous curve for the Golden Ratio from the Fibonacci (and other, such as the Lucas) series, and presumably get from it intermediate noninteger values. It would be interesting to know whether such values might be able to relate to the elements WITHIN blocks and periods, either in terms of skews or offsets from expected behaviors or configurations.

    Jess Tauber

  199. I would like to expand on my question about Fibonacci character of Chemical Periodicity that I ask prof. Bent in previous post:

    Fibonacci sequence is typically shown as 1,1,2,3….. However, somtems it is shown as 0,1,1,2,3. It just does not start from 1 and 1 for no reason. It actually starts from 0.
    In Apendix XIII of “New Ideas” you present following sequence: r, l, r+l, r+2l… It sure looks like begining of Fibonacci series, but it is not, since l=?+r. That is: ?, r, l, r+l, r+2l… That was the reason for my question: Why not ?, l, r, l+r, l+2r? It looks as somebody’s arbitrary decision to begin series with “r” , not with “l” , especially when “l” can have zero (0) value and “r” can not.


  200. Dear Professor Bent,

    thank you very much for your responses. They certainly provide much needed explanations to some very interesting ideas expressed in your book. I enjoyed reading them. I think that you should include them with the next eddition of your book, if such is being planned. I like your explanation of “k” as an attempt to clarify numerical relationship of importance of angular nodal surfaces to those of radial. You define quantum number “n” as r+l, which I agree is a good physical explanation of quantum number “n”. I do understand that you attempt to gage relative “importance” of angular nodal surfaces with the radial, however, the idea of Fibonacci Character of Chemical periodicity based on r, l, r+l, r+2l seem rather contrived. Just try to write it in slightly different order: l, r, l+r, l+2r and it would become nonsensical. One has to give a preference to radial over angular nodal surfaces, for the idea to work. Some one might argue that “l” should follow “r” because it is the order it gets introduced in Aufbau, but we know that Aufbau is rather mental exercise, not the factual process. And also, as you have mentioned, in Appendix XIII of NI, it works only for the first 6 periods. Frankly, I need to look into this matter more deeply. I’d like to see what impact, or perhaps connection, r/l relationship described in your book has with tetrahedral representation of the periodic system presented on my web site, that reflects factual n/l relationship very accurately.

    I would like to draw your attention to Pascal triangle that has direct connection to both, Fibonacci and Tetrahedral numbers, where first diagonal corresponding to zero dimension is 1,1,1,1,1…, the second diagonal corresponding to first dimension is 1,2,3,4,5…, the thrid diagonal corresponding to 2D is 1,3,6,10…, which are also called triangular numbers, and, finally, forth diagonal corresponding to 3D is 1,4,10,20,35,56,84,120…., that is, tetrahedral numbers. Have you noticed that 4, 20, 56, 120 are atomic numbers of Be, Ca, Ba and Ubn? And atomic numbers of He, Mg, Sr, Ra are arithmeitic means of those? (as first noticed by Jess Tauber).

    Fibonacci numbes are also there, however, they are equal to sums of of integers located in skewed diagonals. I find it extremely interesting that all those sequences are directly related to Pascal triangle.

    Also, in your book, you mentioned correspondence of every other Alkaline Earth’s atomic number to Square Pyramidal numbers times four. It turns out that this fact was first noticed by Dr.Pierre Demers of Quebec around 1996. Few months ago I received email from Norwegian mathematician Kurt Mikal Klugland who published few articles in regard of correspondence of square pyramidal numbers and tetrahedral numbers via simple multiplication table. If you present multiplication number as abscissa and ordinate, one diagonal, left top to right bottom are square pyramidal numbers and the opposite diagonal, right top to left bottom represent tetrahedral numbers. I find it all extremely interesting and I am gald that you have been investigating mathematical regularities of the periodic table. I think that all those regularities, along with those described on my web site have something to do with the microscopic structure of space-time around atomic nuclei. All those observations need to be investigated by physicists and chemists, not dismissed.

    Valery Tsimmerman.

  201. Philip, regarding atomic cores: By the definition –

    atomic core = atom – (all electrons in oxidizable subshells)

    the core of Yb, [Xe] 4f14 6s2, maximum oxidation number +3, meaning that its 4f shell is partially oxidizable, is Yb+16, electron configuration [Xe]. (16 is also its Group’s number, in my scheme.)

    The core of Lu, [Xe] 4f14 5d 6s2, maximum oxidation number +3, meaning that its 4f shell is not oxidizable, is Lu+3, electron configuration [Xe] 4f14. In the LSPT it appears in the first column of the d-block, column number 3. People who are still putting it in the f-block are doing so incorrectly. William Jensen made that case definitively in JCE some three decades or so ago, based on then current physical and chemical data, without reference to the LSPT, although, later, he remarked to me that the LSPT does, indeed, place Lu in the Periodic System properly. It places all “problem elements” — La & Ac, Lu & Lr, and H & He — properly. I’ve cited that as one of its leading virtues, at the present time.

    And yes, “only the s and d electrons contribute to the valence of Hf”.

    I’m puzzled by your next statement. What electrons are “in both or neither category” of “core” or “periphery”? In the scheme I’ve described, that would mean that an element’s maximum oxidation number is indeterminant. If not, then the case would seem to be closed. Electrons in oxidizable subshells are not core electrons. Electrons not in oxidizable subshells are core electrons. Those appear to me to be natural and useful definitions, framed in strict accordance with Nature’s nature.

    The issue is significant. If the scheme I’ve described doesn’t hold up, then one probably cannot say, e.g., that a block’s row in block-type periodic tables corresponds to a distinctive set of isoelectronic atomic cores.

    Chemistry should have an unambiguous, useful definition of “atomic core”. Have you an alternative candidate? Or candidates? In most modern periodic tables I’ve seen, atomic cores of the type I’ve described for atoms in blocks’ first and second rows are indicated by the symbols for the Noble Gases, in brackets. For lower rows, one needs to include previously completed d and f subshells.

    Regards, Henry

  202. Philip, regarding wave-particle duality, I try to get my head around it in the following fashion, with the familiar concept of “latency”, expressed in quantum mechanics by the” Superposition Principle”, one of its leading principles.

    A system’s behavior, in quantum physics as in chemistry and everyday life, depends on two things: (1) its intrinsic character — its DNA, in the case of human beings; its electronic structure, in the case of molecules — and (2) its environment or, as it’s called in quantum physics, its Hamiltonian.

    People may be happy or sad, depending on their situation. Water molecules may be proton donors or proton acceptors, depending on the demands of their reaction partners. And electrons may behave as waves, in diffraction experiments, e.g., or as particles, in, e.g., electrolysis; or, as somewhat like both, as “wavecules”, in their occupancy of localized molecular orbitals in molecules; or always as particles, Feynman liked to think, in his original, many-paths formulation of quantum physics.

    I view wave functions and bond diagrams as PERSONALITY FUNCTIONS. If one knew a person’s personality or a system’s wave function perfectly, one could predict exactly the probability that that person or system would behave in such and such a fashion in such and such circumstances. The idea of latency had not entered physics as recently as a century ago, although it had been around for a long time in chemistry, as “elective affinities”.

    Physics is a Johnny-Come-Lately to most of its leading quantum concepts, such as latency, duality, and nameable stationary states of being (the essence of the new mechanics, Bohr said).

    The concept of a plurality of potential behaviors permeates physics, chemistry, and life. It stares us in the face — often the hardest things to see, artists say.

    An historically famous example of latency in chemistry is acetic acid. Reading between the lines, so to speak, of its bond diagram, an experienced decoder can see in its “personality function” many possible chemical reactions.

    G. N. Lewis liked to say that chemists had had a quantum theory from the days of Dalton. Mankind has had a quantum theory from the outset, one might add, in order to survive. It’s just that that knowledge of Nature’s quantum nature is not organized in any systematic fashion, as it is in quantum physics, and chemistry, nor put into mathematical form in the complex affairs of everyday life, since in quantum physics even the three particle problem cannot be solved exactly.

    I try, off and on, to domesticate non-locality. I know enough about it, however, to know that I don’t know enough about it to have any reasonable chance of success. My hunch is that it will be domesticated some day, unexpectedly, and in an unexpected form that will seem, on reflection, nonetheless, as simply a matter of common sense that the man in the street can understand.

    The most remarkable thing about the world, Einstein said, is that it is comprehensible. Evolutionists would say, “Of course. If it weren’t comprehensible a species such as Homo SAPIENS, which lives by its wits, wouldn’t exist.” How do we know, accordingly, that something is truly incomprehensible?
    Chemists have repeatedly said, for instance, that it’s incomprehensible that helium above beryllium in periodic tables could possibly make any chemical sense whatsoever!

    The quantum physicists’ assertion that some features of their discipline are incomprehensible calls to mind a description of the dot in chemists’ early formulations of molecular addition compounds, such as HCl.NH3: “a full stop to thought”.

  203. For the Forum: A Cautionary Principle, suggested by the remark that –

    “If Bent is determined to invent these new physical principles he should be seeking criticism from physicists, not historians, philosophers and periodic table designers.”

    The remark is wrong — surprisingly so, in one (if only one) respect, in coming from an alleged expert on the periodic table and philosopher and historian of chemistry, who should be one of the first individuals to realize that in seeking criticism of “new physical principles” IN CHEMISTRY, physicists are the LAST individuals to consult.

    When Gilbert N. Lewis, in Gilman Hall at UC-Berkeley, proposed his electron-pair theory of classical structural chemistry’s valence-stroke, his physics colleagues across the way in LeConte Hall laughed him out of court. “Everyone knows that electrons repel each other,” they said. “And, if two electrons can share the same region of space [indicated, schematically, by a valence-stroke], then why not three?” Lewis could not say. All he could say was, “The facts of chemistry require it.” Later the physicists discovered the “classically nondescribable two-valuedness of the electron”, called “spin”, and the Exclusion Principle.

    Back in the 1930s a famous physicist at Michigan, Dennison, confessed to a friend of his, my father, that whenever he and his organic chemistry colleagues differed on some point regarding molecular structure, it usually turned out that the organic chemists were right.

    Pauling averred late in his life that he regretted that during his career he had been too deferential toward physicists.

    Most physicists know little chemistry. I know. I’ve worked closely with one, my brother. The periodic table: its history, and theoretical foundation? That’s all pretty much a mystery to most physicists — as, indeed, it is, today, to most chemists, and chemistry teachers. What means the periodic table in the absence of knowledge of descriptive chemistry?

    A chemistry colleague of mine at the University of Minnesota, Z Z. Hugus, served for a time as a chemistry consultant for a team in the physics department. One day he received a call from them. They were trying to make bromine water. But they couldn’t get the bromine to dissolve in their water. “What? You’re kidding! Let me see it,” said Z. Yup. There it was: packing-case vermiculite floating on the surface of water in a beaker.

    Of course, exceptions exist that prove the rule. As a graduate student at Cal Tech, another Minnesota colleague of mine, Doyle Britton, told me that he saw Feynman [of Feynman diagrams] in the chemistry library one day leafing through a book on organic chemistry. Curious, he worked up the courage to ask Feynman why he was doing that. “Looking for ideas,” said Feynman. Information flows between chemistry and physics both ways, as historians of the periodic table well know.

    I’ve reached the point in life where I realize that physicists are, indeed, the last individuals one should consult regarding new ideas in chemistry. The run of the mill among physicists will just say that you are wrong, and not, as Einstein or Pauli might, “Crazy enough to be right?”

    One of the precepts of the Copenhagen School of Quantum Mechanics, for instance, is that quantum phenomena are nonvisualizable. Yet chemists’ bond diagrams are nothing if not visual representations of quantum phenomena: the electronic structures of molecules. What Bohr and company overlooked is the primary role in applications of quantum mechanics to the many electron-systems of chemistry of a NON-QUANTUM MECHANICAL PRINCIPLE: the Pauli/Heisenberg Principle of Spatial Exclusion. All studies of exclusive orbital representations of matter’s electronic structure violate, physicists say, deep quantum mechanical principles. Yet, it’s a fact that the representations fit the facts of chemistry like a glove. They are, in effect, a Mechanics of the Exclusion Principle.

    Thanks for reading,
    Henry Bent


  204. Jess, your question ” What would happen if k VARIED depending upon where you were in the linear sequence?” is precisely a question that occupied much of my attention when I was writing “New Ideas”‘. My conclusions then (2006), which haven’t changed, are summarized in Section 69 (pp58-60): “Generalized Madelung Parameter and the Order of Excited States of Atoms and Ions”. The single sentence in that section that best summarizes it may be this:

    “[N]o single value of k is necessary for all parts of periodic tables. Any value greater than zero yields the [essentially hydrogen-like] row-orbital order through element 20, 0.51 the order through element 57, 0.67 the order through element 120. That is to say:


    That fact led to the statement of a nonexistence theorem. I concluded that “It seems unlikely, therefore, that an analytical proof of the Madelung Rule, based on physical principles [the absence of which Scerri has made a big deal of], will be forthcoming.” Chemically insignificant exceptions to the Madelung Rule in the d- and f-blocks are a further, perhaps more obvious reason for believing in the nonexistence of an analytical proof of the Rule.

    “Is there anything in your formulae which would allow one to do this? [tilt the LSPT]”, you ask. Not that I see, at the moment. On the other hand, there does not seem to be anything in them that does not allow one to do that. The philosophy of periodic tables espoused in “New Ideas” encourages ‘playing around with periodic tables’, inasmuch as “No periodic table has all the desirable features periodic tables might have” (p191). Your remark suggests adding to the list of “Desirable Features of Periodic Tables” in Appendix XV (p147) another feature: The Diagonal Relationship. Thanks a lot.

    Pauling told me that he liked his periodic table of choice because he did not like to see magnesium separated from aluminum. The LSPT also separates Mg from Zn, which William Jensen, following Mendeleev, doesn’t like to see happen. And it separates Be from Al.

    Vertical display of the Diagonal Relationship — is that an oxymoron? — makes primary kinships diagonal relationships and, if made a requirement at the outset of the chemical capture of the LSPT, would require major alterations in the “LSPT’s” Rules of Construction (p3). Once the Table has been captured, however, one of its chief virtues is how easy it is to modify it in order to exhibit one or more of the desirable features that periodic tables might have. The LSPT lies, e.g., directly on a route to the conventional periodic table, Figure 2 (p4). A somewhat more elaborate topological rearrangement of its parts yields a modern version of Mendeleev’s favorite form of the periodic table, in which secondary chemical kinships are indicated by diagonal adjacencies.

    Thanks again for your “k question”. It strikes right to the heart of the physical explanation for the shapes of periodic tables.

    Best regards, Henry

  205. Philip, you write: “Fibonacci! Perhaps . . . though [it is] not clear why neutron numbers might resemble electron screening!”

    Though it is the case that strange things sometimes happen. In combustion “phlogiston lost” (obvious, to the naked body and eye — all that heat and light) became “oxygen gained”. Crookes’ cathode rays, having something to do with the ether, according to European physicists, became, in J. J. Thomson’s more daring hypothesis, universal constituents of matter. JJ’s efforts to use his “corpuscle” to account for Chemical Periodicity’s magic numbers lead in a Christmas roast by his colleagues at the Cavendish laboratory to a toast to the chief that ended “Long live the electron. May it never be of use to anyone!” And, of course, there’s the case of helium, where it’s obvious to the naked eye that it belongs in periodic tables above gaseous neon, not above metallic beryllium, for heavens sake! [Actually, beryllium is a poor metal.]

    [Speaking of “above”. When one goes from a table to a spiral representation of the Periodic Law, something important is gained: continuity of atomic numbers, without those pesky periodic breaks of periodic tables — and controversy regarding where they should occur. But, on the other hand, something useful is lost: the relevance of the adjectives, when speaking of congeners, of “above” and “below”. Conclusion: No periodic table is superior to every other periodic table in every respect.]

    The electron case and the nucleon case are similar to each other in some respects. Like electrons, protons and neutrons are fermions. They have spin 1/2. They obey a Principle of Spatial Exclusion. Two, but no more than two fermions of the same character can not be at the same place at the same time. Two spin-paired electrons at the same place at the same time constitute, according to G. N. Lewis, the valence-stroke of classical structural theory; and a helium atom, Nature’s most stable electron pair. Similarly, two spin-paired protons and two spin-paired neutrons at the same place at the same time constitute an alpha particle, Nature’s most stable atomic nucleus.

    Several “alpha particle” atomic nuclei constitute elements’ principle isotopes: C-12, O-16, Ne-20, Mg-24, Si-28, S-32, and Ca-40. For higher atomic numbers, neutron numbers exceed their alpha-particle numbers, owing to increasing need to “shield” protons from each other, because of proton-proton coulombic repulsion. Also, nuclear physics, too, has a shell model, and “magic numbers”, albeit different ones than Periodicity’s, owing to an absence of a dominant central field of force.

    Neutron numbers must have, somewhat, Fibonnaci character, in that in the build-up of atomic nuclei by addition of protons and neutrons to lighter nuclei, the number of neutrons added per proton depends on the number of protons and neutrons already present. I don’t know enough about nuclear forces to pursue that line of thought very far, although I have convinced myself that models constructed from close-packed spheres do mimic, sometimes, shapes of atomic nuclei and proton and neutron numbers of fragments formed on fission of U-235.

  206. To see the problem of the core at its most acute, go from Tm to Hf. If Tm has 15 ‘valence’ electrons does that mean Yb has 16? And what about Lu? It clearly behaves as if it has only 3, and yet it is so like an f-block element that many people still put it in with them. And surely only the s and d electrons contribute to the valence of Hf. So it doesn’t seem to be a case of either ‘core’ or ‘periphery’; some electrons are in both and neither. Fortunately that doesn’t stop us from drawing images of the Periodic System.

  207. It isn’t Henry’s English that is incomprehensible; it’s the behaviiuor of electrons, as was so clearly put by Richard Feynman, one of the greatest of all physicists. Equations can produce amazinglyexact predictions, but we can’t get our heads round what it means to talk of wave-particle duality or non-locality. We use words like shell and subshell, core and periphery to give us little pictures to imagine, but we don’t really comprehend. I am still struggling over atomic cores.

  208. Valery, I just noticed that the table in my e-mail of Feb. 26, 10:07 pm lost all of its spacings between columns when posted. It’s probably pretty much gibberish, owing to my inexperience with e-mail. Sorry about that. Henry

  209. Valery, the following table probably isn’t anything new, for you. But it shows for the record how LSPT’s Equation of Form P = r + 2l, where –
    P = period ordinal number ≥ 1
    l = block ordinal number ≥ 0
    r = row ordinal number within its block ≥ 1
    yields back, with the Row Occupancy Rule –
    row with the smallest P first and, for a given P, largest l first,
    the LSPT. As usual, s p d f –> l = 0 1 2 3.
    [For later reference, in identifying r and l, and n (= r + l), with quantum numbers, one notes that
    P (= r + 2l = n + l) ≥ 1 –> l ≤ n – 1, and that blocks’ rows’ lengths = 2(2l + l).]

    P (= r + 2l) r l n(= r+l) nl 2(2l+1) ∑2(2l+1)*
    1 1 0 1 1s 2 2 (P=1)
    2 2 0 2 2s 2 2 (P=2)
    3 1 1 2 2p 6 8 (P=3)
    3 0 3 3s 2
    4 2 1 3 3p 6 8 (P=4)
    4 0 4 4s 2
    5 1 2 3 3d 10 18 (P=5)
    3 1 4 4p 6
    5 0 5 5s 2
    6 2 2 4 4d 10 18 (P=6)
    4 1 5 5p 6
    6 0 6 6s 2
    7 1 3 4 4f 14 32 (P=7)
    3 2 5 5d 10
    5 1 6 6p 6
    7 0 7 7s 2
    8 2 3 5 5f 14 32 (P=8)
    4 2 6 6d 10
    6 1 7 7p 6
    8 0 8 8s 2
    * Twice the sum of the odd numbers beginning at unity is twice the square numbers 1 4 9 16.

    Construction of this table, following chemical capture of the LSPT and enunciation of its Equation of Form and the Row Occupancy Rule, makes a nice student exercise. Even beginning students can execute it, with understanding, from the ground up, since there’s been no need along the way to introduce atomic orbitals, the only rigorous route to which requires solution of Schrodinger’s equation, a challenging task for even graduate students. At the same time, the stage is set for introduction, later, of an electronic interpretation of the ordinal numbers r and l and the Order of Orbital Occupancy Rule.

    [Early introduction of orbitals into chemical education leads to faith-based chemistry courses.]

    The electronic interpretation of the periodic table provides a physical model, if not a complete explanation, of the chemical periodic table, which, in turn, captured from chemical data, validates the physical model. The chemical “oxidation table”, becomes, in addition, a physical “spectroscopic table”.

    The spectroscopic table is essential for a physical understanding of the oxidation table. There is no other explanation for it.

    Reciprocally, existence of the oxidation table is essential for the physical significance of the spectroscopic table. That table, alone, without the chemical table, would be like Lewis Carroll’s cat’s grin without the cat. It would have no practical significance.

    One can use the chemical table, as chemists did for many years, without the spectroscopic table, but not, with practical consequences, the latter without the former. In that sense, the chemical table is prior — in both senses of the word (in time and in significance) — to the physical table. But, in time, such a relationship is reversed.

    Science’s characteristic feature, said Lavoisier, is progress. Ideas’ historical roots are forgotten. Pruning occurs. Entire fields become axiomatized. Joule’s famous paddlewheel experiments have passed from disbelief (“He had only hundredths a degree to prove his case by”) to an honored physical theory (“The Mechanical Equivalent of Heat”) to truth by definition (1 cal = 4.18400000 joules).

    And so it is with the periodic table. A recently published advanced treatise on inorganic chemistry has on its cover the Madelung Order of Orbital Occupancy Diagram. Inside, there is no indication of how, historically, that Diagram was captured, or how, by a simple mathematical transformation, it becomes the LSPT, which, by a simple topological transformation, becomes the conventional periodic table. Rather, along side the Madelung Diagram there appears the conventional sfdp periodic table, as if that form of the periodic table follows directly from Madelung’s Diagram, which it does not.

    Called to mind is Bohr’s answer to the question: Why do you place lithium’s third electron in an outer orbit? Bohr’s (honest) answer (near the outset of his work on atomic structure): “The facts of chemistry require it.” (Later Bohr seemed to imply that he did not need to lean on chemistry. He left his colleagues with the impression that he was about to explain Chemical Periodicity’s magic numbers: 2, 8, 18. ) Today we tell students that physical theory requires that lithium’s third electron go into an outer orbital. Electron indistinguishability requires that wave functions be antisymmetric in electrons’ coordinates, spatial and spin, which implies, rigorously, by mathematical deduction (without reference to atomic orbitals), that two electrons of the same spin, either “up” or “down”, cannot be at the same place at the same time. Striking evidence of that fact are the first-stage ionization energies of H 13.6, He 24.6 and Li 5.4 (!) ev, along with G. N. Lewis’s identification of the valence-stroke as two electrons and the rule from classical structural theory of organic chemistry that satisfactory bond diagrams valence-strokes never cross each other. The phenomenon of mutual spatial exclusion of electrons of the same spin plays a central role in theories of molecules’ electronic structure and the periodic table.

    One of the reasons for my personal preference for the LSPT captured chemically, without reference to atomic orbitals, is philosophical. It seems a shame that something as fundamental as the Periodic Law should be given graphic expression by tables that are, in one’s mind, based on a PHYSICAL APPROXIMATION: existence in many-electron systems of individual electron orbitals.

  210. Philip, thanks for that. I wonder if there is any sense that increasing n/p ratio not only converges on phi but also has similar Fibonacci character as it climbs? What would we have to do to show this? Remember also isotopic variation as a monkey wrench to strict adherence here, so just an approximation?

    Professor Bent- What would happen if k VARIED depending upon where you were in the linear sequence? Some time ago I posted the idea of ’tilting’ the LSPT so that lower numbered elements were staggered rightward relative to later ones from the traditional groups. Doing this allowed diagonals to be vertical, and knight’s moves to also be tilted but at the opposite angle from traditional groups.

    Is there anything in you formulae which would allow one to do this?

    Anyway, if k varies by element perhaps the Fibonacci-like character could be made more specifically relatable to the Golden Ratio? The Fib sequence is only one of many like this, so casting a wider net might be of some value?

    Thanks in advance for responses, even if I’m ‘not even wrong’… ;-)

    Jess Tauber

  211. If Bent is determined to invent these new physical principles he should be seeking criticism from physicists, not historians, philosophers and periodic table designers.

    He should also be trying to reach a wider audience by getting published by something other than a Vanity Press.

    But having seen his two recent responses to me, in particular,, this will not be happening very soon in view of his rather incomprehensible and tortured use of the English language.

    eric scerri

  212. Hmm! Fibonacci! Perhaps Jess’s suggestion that n/p converges on the Golden Ratio is not that far out, though not clear why neutron numbers might resemble electron screening!

  213. Valery, I should have indicated clearly and explicitly in “New Ideas”, as I did not, what I was up to with the expression (n + kl). Apologies for that. You ask, accordingly, –

    What is the physics behind “k”? Good question. Answer: A comparison of the order of orbitals generated by the expression (n + kl) for different values of “k” with atoms’ observed levels is an attempt to clarify the physics behind periodic tables. “k”, I should have emphasized, is not a quantum number, or a fractional quantum number.

    “[W]hy not k = 2?” k = 2 yields an incorrect periodic table, namely (largest l first) a left-step periodic table of “triadic”, rather than the observed “dyadic”, character (“New Ideas, Figure 27, p57). So we can say that in the ordering of atomic orbitals by energy, angular nodal surfaces are not 2 + 1 = 3 times more important than radial nodal surfaces. But they are, e.g., for most atoms, more than 1.5 times as important, if not exactly twice as important, as the expression n + l (= r + 2l) might lead one to expect.

    [There’s more regarding (n + l) in section 63, “Node-Counting and Madelung’s Parameter”, and Appendix XIII, “Fibonacci Character of Chemical Periodicity”. As noted there, Periodicity exhibits, not surprisingly, Fibonacci Character, in which terms’ magnitudes depend on the magnitudes of their two previous terms, because, owing to the effects of SCREENING, orbitals’ energies depend on electron densities created by previously added electrons.]

    In summary: Different values of k generate periodic tables of different shapes, which can be compared with the table’s actual shape, yielding, thereby, information regarding the role of orbitals’ nodal surfaces in determining orbitals’ energies, which is fundamental to understanding the Periodic System, from a physical point of view.

    Here’s a route to the Madelung parameter (n + l) for determining the order of orbital occupancy in Bohr’s Aufbau Process. “Proof” may not be the route’s correct label. Perhaps “capture” is a better word. The route is not one I expected to follow, until I began to think about writing my book on the Periodic System, and how to arrange the story’s different parts. It begins with a detour through chemistry. Ontogeny recapitulates phylogeny.

    First, introduce, by induction, a set of Periodic Table Construction Conventions and capture, thereby, the left-step periodic table, in the manner indicated on the cover of “New Ideas” and page 3. The Construction Conventions constitute an AXIOMATIZATION of the Periodic System. Note the absence of any references to electrons and atomic orbitals. The route is one middle school students can navigate, and have. To my knowledge, it’s unique. I’m not aware of any other simple route to periodic tables, starting from memberships of chemistry’s commonly named groups, and atomic numbers.

    Next, note the integers generated by the LSPT (Section 45, p40; also Section 46), in particular the ordinal numbers of its periods, P; its blocks, l; and its blocks’ rows, r. For l = 0, P = r. For l = 1, P = r + 2, &c. P = r + 2l. There’s the form — if not, yet, the substance — of your Madelung Rule for the Order of Orbital Occupancy in Bohr’s Aufbau Process (where r + l = n). The Rule for the Order of Occupancy of Blocks’ Rows with increasing Z is easily read off from the LSPT (a good exercise for bright students), namely: Occupy the row with the smallest P first and, for a given P, largest l first. NO EXCEPTIONS! That’s the beauty of pure phenomenology. It simply states the truth: no more, no less. Of course, one would like to know more. One would like an explanation — i.e., an interpretation in terms of physics. At this point, we’ve gone as far as pure chemistry takes us (unless, by a series of daring — not to say outrageous — inductions, one induces, for fun, in retrospect, “p-particles” (atoms’ identification numbers), “n-particles” (to account for atoms’ masses), and “e-particles” (to account for bond diagrams).

    Finally, by induction (Section 48), identify the “Physical Significance of Periodicity’s Integers r, l, and n.” (The integer “n” is captured in Section 46.)

    With its two sets of inductions, the “proof” sketched above seems to have the right flavor, if one grants that the Madelung/Janet expression (n + l) represented, at the outset, a genuinely new idea.
    For nothing really new, Einstein observed, is ever created by pure deduction alone. New ideas arise from exercise of the imagination.

    Many thanks, Valery, for your perceptive questions. They’re exactly what “New Ideas” needs.

    Best regards,

  214. Philip, your question regarding atomic cores is an excellent one. The definition –

    atomic core = atom – (valence shell electrons)

    is no better than one’s definition of “valence shell electrons”.

    That issue first arose, for me, in the late 1980s, in connection with the international periodic table column-labeling controversy. My views, in 2006 (and today), are summarized in “New Ideas”, Section 94, pp92-95. As you note, there’s no problem in the s- and p-blocks. Mendeleev’s classic column numerals turned out to be equal to not only maximum oxidation numbers but, also, numbers of valence-shell electrons and, accordingly, to charges on atomic cores. New issues emerge (not for the first time) in the d- and f-blocks.

    In the p- and s-blocks, valence electrons are what I called in “New Ideas” “outer” and “outer-outer” electrons. In the d-block they are 2 outer-outer electrons plus “inner” valence shell electrons (in the f-block 2 plus “inner inner” valence shell electrons). Running column numbers (or numerals) on through Mendeleev’s 8 8 8 1 2 to 8 9 10 ll 12, at the end of the d-block, raises the question: What does one mean by “valence-shell electrons” for columns 9 10 11 12, since Groups’ maximum oxidation numbers have never exceeded, so far, 8. Required is a new definition for “valence-shell electrons”, or a broader definition than that which works satisfactorily in the s- and p-blocks.

    In what sense can copper be said to have 11 valence-shell electrons? In this sense: 11 is the total number of electrons in OXIDIZABLE SUBSHELLS for copper, maximum oxidation number 4, which means that its 3d subshell can be oxidized, partially, and that, consequently, its total number of valence-shell electrons is 2 + 9 = 11.

    For Tm, in my Group 15f, its maximum oxidation number of 3 means that its 4f subshell, occupied by 13 electrons, is (partially) oxidizable and, consequently, its “total” number of “valence-shell electrons” is 2 + 13 = 15.

    The “problem” for a set of rational column labels related in some fashion to maximum oxidation numbers arises, already, in the p-block for oxygen and fluorine. On what grounds did Mendeleev place oxygen, maximum oxidation number +2, at the head of the chalcogen Group, S, Se, and Te, maximum oxidation numbers +6?. Well, that’s were its atomic weight puts it. Today we easily rationalize that assignment by noting that oxygen has 6 valence-shell electrons, 4 of which are usually not engaged in bonding, i.e., not oxidizable, but reside, nonetheless, in that atom’s valence-shell as, Lewis suggested, stereochemically active “lone pairs”.

    The Noble Gas Group is a more striking instance of the “oxygen phenomenon”. For a long time after its discovery, its column label was 0. Now its label is 8(p), consistent with existence of XeO4. Yet the maximum oxidation number of its light congener Ne is 0. Ne’s valence-shell has not been oxidized. Nor has that of F. Yet we say that F has 7 valence-shell electrons. They are not oxidizable. But they are not without chemical significance, in, e.g., hydrogen bonding in HF, and in their “mesomeric” or “hyperconjugative” electron-release in organic chemistry (used in a recent unpublished rationalization of molecular electric dipole moments).

    The discussion above leads, in summary, to this definition:

    atomic core = atom – (number of electrons in oxidizable subshells)

    Alternatively, if one uses the column labels 1 2, 3p – 8p, 3d – 12d, and 3f – 16f, one may say that

    atomic core = atom – (the number in its Groups’ alphanumeric column label)

    Does that stretch the meaning of valence beyond its breaking point?

    Required to answer that question is a definition of “valence”. I recently searched through the chemical literature on “valence” for definitions of it. There are many. No generally agreed upon definition of valence exists. Sometimes monographs with the word “Valence” — even only that word — in their titles failed to define the term! My personal definition:

    An atom’s “absolute valence” = the positive charge on the atom’s core.

    It’s absolutely essential to know an atom’s absolute valence in order to draw correct valence-stroke diagrams; i.e., ones that satisfy the Faraday-lines-of-force/Gauss-Law – like rule that the number of valence-stroke terminations at the symbol of an atom is equal to the atom’s core’s charge, provided lone-pairs are represented by “rabbit-ears” (which terminate twice at elements’ symbols). That’s for elements in the p-block. For d-block atoms, unshared valence-shell electrons are generally not indicated in bond diagrams. That would be messy, for d-type electrons.

    With the previous definition(s) of “atomic core”, the core/valence scheme is circular. The definition of “core” uses the word “valence”, whose definition uses the word “core”. Well, that’s the way it is, sometimes, in science, at its “best” — i.e., at its most certain, as, e.g., in classical thermodynamics. “Energy is conserved,” said Rankine, “by definitions framed in strict accord with reality.”

    In the important exercise in chemistry of counting electrons, the alphanumeric column labels cited above are useful in all blocks. So, also, is their relation to atomic cores’ charges, in the p-block and the s-block, if not in the d- and f-blocks, where the concept “atomic core” is not as clear cut as it is in the s- and p-blocks, owing to the inner and inner-inner character of differentiating electrons in the d- and f-blocks.

    One problem: For the zinc Group, column label 12d, the two definitions of “atomic core” are not identical unless one grants the existence of Hg(III), which has been reported several times, but challenged. Even if one does not grant the existence of a +3 oxidation state for the zinc Group, the chemical significance of its d10 subshells is significant. Although Zn+2 and Mg+2 are nearly the same size, Zn+2 is considered by inorganic chemists to be a “soft” cation whereas Mg+2 is a “hard” cation. Zn+2 forms in water Zn(NH3)4+2 whereas Mg+2 does not. (I think of NH3’s H atoms as hydrogen-bonding, weakly, to Zn+2’s 3d electrons.) Similarly, ZnS is insoluble, whereas MgS is not. And the two sulfides have different crystal structures. Well, whatever. William Jensen, whose judgment I esteem, locates the zinc Group in the p-block. Such matters are the reason for Section 90 in “New Ideas”, on “The Zinc-Magnesium Test of the Left-Step Periodic Table and the Concept of l-Nobility”.

    Thanks for your question, Philip. Criticisms of this response would be welcomed! Apologies, Valery, for its length. Fact-rich chemistry is a complicated science.


  215. I am still having diffficulty with atomic cores. It’s easy enough to separate the valence electrons from the core where they are all s or p, but what about, for example, Cu, can the 11 s and d electrons really be described as valence electrons. Still more extreme, does Tm have 15 ‘valence electrons’?! It seems to be stretching the meaning of valence to breaking point.

  216. Response to Scerri, Feb. 24, 2010, 3:06 am. This may be the responder’s final response to S. Life is too short to respond to all of his mistakes — and, in the end, to what end, regarding the advancement of science? Scerri says that –

    “[I]n his book Bent gives 57 reasons why the LST should be preferred and then promptly says that the LST is no better than the traditional table in which He falls above Ne !!”

    That statement is false in three respects. First, Bent mentions on p(ix) “57 Reasons (and counting) for Relocating HELIUM in Periodic Tables”. Second, he does not then “promptly” compare “the LST” with “the traditional table”. He does compare the two tables with each other in detail in Appendix XII, “Positive and Negative Features of sfdp and fdps Periods,” p143, and in additional detail in Appendix XV, “Desirable Features of Periodic Tables”, p147, briefly summarized in a concluding letter to Roald Hoffmann, p191. Third, Bent never says that “the LST is no better than the traditional table in which He falls above Ne”. That’s a huge howler! At last S is consistent — consistently wrong: three statements, three falsehoods.

    Scerri concludes his discussion in his book of the 3d/4s “paradox” with these sentences (p237):

    “The long-standing puzzle, which has exercised the minds of generations of students and their instructors, can be dissolved in a stroke. The question of why 4s fills first but also empties first is an illegitimate question in some respects.”

    Illegitimate in what respects? One is not comparing, in Bohr’s Aufbau Process and ionization, “like with like”, he correctly notes. Fine. But nowhere in his book does one find any recognition at all of the simple physical reason for the unlikeness, namely: THE DEPENDENCE OF THE HYDROGEN-LIKE CHARACTER OF ORBITALS’ ENERGIES FOR MANY-ELECTRON ATOMS ON THE ATOMS’ NET CHARGES AND, CONSEQUENTLY, THE OCCURRENCE ON IONIZATION OF THE PHENOMENON OF REORGANIZATION. That simple physical insight dissolves “in a stroke” the 3d/4s paradox. Perhaps that dissolution will appear in the book’s “2nd edition” (with proper attribution?).

    Regarding atomic cores, Scerri is completely in over his head. Take his remark –

    “Part of the motivation for the concept of element as basic substances is to answer the question of what it is about a simple substance that survives when compounds are formed. When Na and Cl form NaCl the microscopic answer to the question is surely Na+ and Cl- ions.”

    When authors use the word “surely”, it usually means that what follows is not undoubtedly true. Nonetheless, one is tempted to use the word and say: Surely there are no Cl- ions in that pale, green gas called “chlorine”. There are Cl+7 cores, as in NaCl, and valence-shell electrons. Scerri continues –

    “Nor does the notion of atomic cores lend itself to covalent bonding as far as I can see.”

    All right. One can accept that statement, as a statement of fact. Evidently its author has not seen the series of papers in JCE on “Tangent Sphere Models of Molecules”, back in the 1960s, particularly the one on “Ionic Models of Covalent Compounds”. It answers his question –

    “What is it about C atoms that survive when it forms CH4? How can this be addressed via atomic cores?”

    What survives are C atoms’ cores. Draw a valence-stroke diagram for CH4. Apply Lewis’s identification of the valence-stroke, as two electrons. Subtract the 8 electrons represented by CH4’s four valence-strokes. What’s left for the symbols “H” and “C”? The atomic cores H+ and C+4. Repeat the process for diamond, or graphite, and dihydrogen. See what survives in going from carbon and hydrogen to methane? It seems so simple it’s difficult to understand what the questioner’s problem is!

    Just as there is a correspondence between the ordinal numbers generated by the left-step periodic table captured purely from chemical data, and atomic numbers, and the leading quantum numbers of atomic physics, so, too, there’s a correspondence between Pauling’s Rules of Crystal Chemistry and the structures of covalent compounds — on substituting for cations atomic cores and anions electron pairs.

    [Full Disclosure: It should be said that just as chemists have a problem appreciating the regularities introduced into the Periodic System of the Chemical Elements through location of helium above beryllium in periodic tables, so, too, like our questioner, chemists have a problem appreciating the regularities introduced into the theory of the chemical bond through use of an ionic, atomic-core/localized-electron-pair model of chemical bonding.]

    Finally, Scerri asks: “Why does Bent suppose that Paneth did not make the apparently simple association between atomic cores and elements as basic substances?”

    Paneth and other chemists of his day weren’t familiar with ionic models of covalent compounds — and metals.

    Calcium metal, e.g., may be considered a salt, cations Ca+2, anions “electride ions”, e2-2, in the rock salt structure, cations and anions on face-centered cubic lattices, as in cubic close packed spheres. The electride anion is a powerful Bronsted base, easily twice protonated by water molecules, yielding light, colorless, flammable dihydrogen gas and a precipitate of white calcium hydroxide, soluble in hydrochloric acid. (CAUTION: The reaction of the “salt” with water is highly exothermic! A few turnings of calcium metal in a test tube of water may bring the water to its boiling point. Wear goggles, a glove, and a lab coat.

    Have fun, with, also, He/Be and atomic-core/electride-ion models of matter!

    The union of demonstration-experiments with periodic tables, valence-stroke diagrams, and their isomorphic valence-sphere models yields rich visual expressions of chemical information for outer and inner eyes of chemistry students of almost any age, middle school through college and graduate school, and their teachers. It’s impressive to see well-mentored student apprentices highly motivated to learn chemistry in order to execute safely and to explain correctly in terms of kinetic-molecular theory striking demonstration experiments for peers, younger students, and the general public. It’s a winner for all lives it touches, particularly the lives of the student-presenters themselves, provided splendid opportunities to become excellent public speakers, because they have something exciting to speak about. In the process, that “killer course” Chemistry 101 becomes a vehicle for acquiring a liberal education. Sad to say, however, teaching chemistry in the grand manner, from demonstration-experiments, is about as popular with chemistry teachers today as helium above beryllium.


  217. A decent respect for another person’s opinions calls for a — hopefully informative and, consequently, constructive — response, to, in this instance, Scerri’s remark of Feb. 23 that –

    “. . . beginning and ending with ad hominem remarks
    may not be a good way of facilitating free discussion.”

    A profound statement? Then its opposite, Bohr might say, may be a profound statement. With that possibility in mind, here goes: To quote President Reagan, “There you go again.” In what way? With — typically — a remark that, in Pauli’s words, “is not even wrong”.

    It may, indeed, be technically correct to say that, to a particular individual, “ad hominem remarks” feel like precisely that: an attack “on an opponent’s character”. We all identify personally with personal opinions. But to state that obvious truth, AND NOTHING MORE, is completely beside the point; in a word, IRRELEVANT, to the advancement of “free discussion”.

    S doesn’t respond to the argument that it’s incredibly illogical to go from the electron configuration of Sc(III) to a completely outrageous statement regarding Madelung’s Rule. Freely exhibited, it would seem, some might say, is a severe instance of foot-in-mouth disease: namely, as mentioned previously, failure to distinguish two routes to Sc(I).

    Route (1), S’s route, begins with Sc+21. Its 19th step is formation of Sc(III), i.e., Sc+2, electron configuration [Ar]3d. Route (2), the Bohr/Madelulng route, begins with H(I) and adds, alchemically, H(I), 22 times. It’s 19th step forms K(I): [Ar]4s. It’s 20th and 21st steps yield Ca(I), [Ar]4s2, and Sc(I), [Ar]3d4s2. The reason why the last electron added is not the first electron removed, in ionization of Sc(I) to Sc(II), [Ar]3d4s, is easily explained.

    Think of ionization of Sc(I) as occurring in two steps. (In actual fact, the two step occur simultaneously.) The first step, on ionization of the last electron added in Route (2), is formation of Sc(II), [Ar] 4s2 . But positively charged Sc(II) is more hydrogen-like, in the ordering of its energy levels, than is neutral Sc(I). (With increasing net charge, electron-electron repulsion becomes less and less important, compared to nuclear-electron attraction.) In Sc(II), orbital 3d (n = 3) lies — as in hydrogen — lower in energy than 4s (n = 4), contrary to the situation in K(I) and Ca(I). Consequently, during ionization a REORGANIZATION occurs. A 4s electron becomes a 3d electron. The net effect of the two steps is ionization of a 4s electron. Hopefully those remarks may be useful to S in his teaching of freshmen chemistry at UCLA.

    A strategy emerges. Another instance of being N.E.W. in response to criticism is S’s correct but irrelevant observation, in response to Stewart’s contention that he has no grounds for criticizing a book he hasn’t read, that whether or not a book is published by a “vanity press” does not depend on its readership. Touche?

    Additional instances of the use of the not-even-technically-wrong strategy in the advancement of a career involve use of good ideas without attribution, as if they were one’s own ideas, a.k.a. plagiarism. That distorts the history of science, if not science itself. On the contrary, it contributes to the advancement of science, if the ideas are used correctly, as in reliable monographs and textbooks, which, Einstein said, of sophomore physics textbooks, contribute more to the advancement of physics than the work of all Nobel Laureates.

    It’s differences of opinion that contribute to the advancement of blogs. Perhaps S would agree with the famous American philosopher, newspaper reporter, and Mississippi pilot who observed that it’s differences of opinion that make horse racing [and a career in the history and philosophy of science] interesting.


  218. Wow! So much to digest. I do not even know where to start. I’d like to start on reconciliatory note. Eric, I was under impression that prof. Bent was not critical of your understanding of Aufbau, but rather of Eugene Schwartz’s. I am gald that you are talking to each other and this is great!

    In regard to prof. Bent’s (n+kl) formula. Both quantum numbers, “n” and “l” are derived from spectroscopic observations and they happen to be integers. Where fractional “k” comes from? I think that it is rater artificial parameter. So what if k=0.9 gives same result for the first 8 periods? Do we know for sure that element 120 is the last one? What is the physics behind “k”? Where are the observations that point to some fractional quantum number, besides “ms”? What if we decide to apply similar factor to “n” and come up with formula (kn+kl)? why not k=0.883, why not k=2? In the last case, k could replace l all together. Why do we need “l” if we have k? I think that quantum mechanical boundaries should be respected and we should think of quantum number “l” as an integer and we should not be in a business of inventing new parameters. I am not quite ready to give up hope that one day n+l rule will be explained.

    In regard to Aufbau. If we look at spectroscopic signitures of Ca and Sc we would notice the difference. Sc has extra spectral lines that are characteristic only to this element. This is how physicists can detect presence of this element in star dust and elswhere. Those characteristic spectral lines are due to a presence of an extra electron that in its lowest energy state is described as 3d1. Therefore, characteristic electron for Sc is the one that takes 3d1 position in its lowest energy state, corresponding to n+l=5. End of story.

    Each time when charge of atomic nucleus passes one of the modified tetrahedral numbers 2,4,12,20,38,56,88,120… (that are derived by counting spheres in odd rows of bicolor tetrahedral stack only), combined level of electron energy and orbital angular momentum increases by one and thus opens new n+l level where characteristic electrons can reside. It does not matter what particular “n” or “l” are, as lons as their combined value corresponds to the level dictated by the positive charge and as long as atomic number sequence is not violated. n+l level should define period in any natural depiction of the Periodic System.
    Best regards,

  219. Response to Scerri:

    You’re right. I was looking at the number at the top of the page: “69” for, I should have known, Section 69. The page number (at the bottom, obscured by some personal notes) is 59. I hope that helps. The reference is to “Figure 28. Comparison with experiment of orbital orders generated by (n+kl) for different values of k.”

    One may note that a value of k = 0.9 (rather than 1 of the conventional Madelung expression n + l) yields the Madelung order of orbital occupancy through 8s. That result strongly suggests that no analytical proof based on first principles exists for the Madelung Rule — a “stronger” statement than necessary — and that, therefore, it is meaningless to criticize physicists for failing to prove the Madelung Rule, for which, as is well-known, there are a number of exceptions in the d- and f-blocks.
    That’s another reason for believing in the non-existence of a mathematical proof of the Madelung Rule (or, Philip, should it be the Janet Rule?).

    On the other hand, if, instead of referring to order of orbital occupancy in Bohr’s Aufbau Process one refers, purely phenomenologically, without reference to electrons and orbitals, to the order of occupancy with increasing Z of the rows of the blocks of the Left-Step Periodic Table [each row being related, in the electronic interpretation of the Table, to a type of atomic orbital] — if one adopts that point of view, then one can read off immediately from the LSPT the following Row Occupancy Rule FOR WHICH THERE ARE NO EXCEPTIONS: Row with the smallest P first and, for a given P, largest l first, where P = the ordinal number of the row’s period in the LSPT and l = the ordinal number of the row’s block, with, for r = a row’s ordinal number, P = r + 2l (= n + l, if n = r + l). P = r + 2l is the LSPT’s Equation of Form.

    The Correspondence between the purely phenomenological Row Occupancy Rule, stated above in terms of ordinal numbers generated by the LSPT, which can be captured without reference to electrons and orbitals, even to location of He above Be, and Madelung’s Rule, where r, l, and n stand for the radial, angular, and principal quantum numbers of atomic physics is one of the leading — if imperfect — Consiliences in the history of physical thought. The logical rigor of the phenomenological, purely chemical capture of the LSPT is not compromised by the fact that the Consilience is not perfect.

    The situation is analogous, historically, to one in thermodynamics. When Clausius introduced the energy function, and later the entropy function, he did not refer to the atomic hypothesis and kinetic-molecular theory, to which he made fundamental contributions, because he did not want to compromise the logical rigor of what became known as classical thermodynamics, owing to doubts many scientists entertained at the time regarding the existence of atoms.

    Of course, the kinetic-molecular model of matter greatly aids an understanding of classical thermodynamics. Similarly, the electronic structure of atoms greatly facilitates understanding the Periodic System. Each phenomenological system is enriched by atomic theory without being, thereby, replaced by it. One might say, in summary, that the Row Occupancy Rule stands to the Orbital Occupancy Rule as Classical Thermodynamics stands to Statistical Mechanics.

    The organization of the data in Figure 28 on page 59 is an attempt to illustrate the first part of that analogy.

    Apologies for citing the wrong number for the correct page.

    I hope the present remarks will facilitate “free discussion”.

    Criticisms welcomed! The Periodic System is a work in progress.


  220. Response to Bent who claims that
    atomic cores are equivalent to Paneth’s elements as basic substances.

    As I have suggested before I don’t think the concept is amenable to a microscopic understanding.
    When Mendeleev used the term atom he did not mean atoms as microscopic entities. I can provide half a dozen quotations if necessary to show that Mendeleev did not accept atoms although he occasionally used the term in the sense of chemical equivalent.

    In any case back to Bent’s cores. Are they elements as basic substances. I don’t think so.

    Part of the motivation for the concept of element as basic substances is to answer the question of what it is about a simple substance that survives when compounds are formed. When Na and Cl form NaCl the microscopic answer to the question is surely Na+ and Cl- ions.

    For Bent it is the atomic cores of Na and Cl. While the Na core would seem to amount to a Na+ ion, this simply does not work for Cl since the atomic core of Cl contains just 10 electrons. The required 18 electron species is not the atomic core of Cl.

    Nor does the notion of atomic cores lend itself to covalent bonding as far as I can see. What is it about C atoms that survive when it forms CH4? How can this be addressed via atomic cores?

    Why does Bent suppose that Paneth did not make the apparently simple association between atomic cores and elements as basic substances?

    eric scerri

  221. Response to Bent.

    Bent claims that I am referring to an incorrect aufbau. He claims that it should be about adding an electron AND a proton as one moves through the periodic table. I believe that he is limiting the discussion to one sense of the aubfau only, which I’ll call the ‘freshman version’.

    Here is why. A long-standing problem (maybe a pseudo-problem) in chemical education has been the relative occupation and ionization of transition metal elements like scandium. The popular story following the freshman version of aufbau is that Sc involves the preferential occupation of 4s orbitals which have lower energy than 3d.

    The occupation of 4s is supposed to involve the 19th and 20th of the 21 electrons in Sc. The 21st electron is then assumed to go into a 3d orbital to give a configuration of [Ar]4s2, 3d1.

    So far so good. But then it turns out that Sc+ is [Ar]4s13d1. Chemical educators have worried about this apparent paradox. 4s seems to fill first and also empty first!

    Papers have appeared over the years in Journal of Chemical Education among other places by Pilar, Scerri, van Quickenborn et al, Melrose and Scerri and others. These authors have examined the nature of the orbital approximation, and the details of the Hartree-Fock calculations for atoms like Sc.

    These authors have also pointed out that it is inappropriate to assume that one starts with a Ca atom and then just adds the 21st electron into a 3d orbital to obtain the Sc configuration in the way that Bent insists on doing.

    What we should do is to consider the relative energy of the orbitals in Sc itself without assuming that we are just moving on from Ca. In other words we must consider the aufbau for cases where we vary the number of electrons but not the number of protons. Let us call this the sophisticated aufbau.

    However in the course of all these papers these authors seem to have also missed something. They all assumed that 4s does indeed fill before 3d in Sc and other transition metals or implied as much. What is new about Eugen Schwarz’s work is that he went back to the C. Moore tables and just saw that the ordering in Sc is 3d more stable than 4s. The configurations of Sc2+ is 3d1 and that of Sc+ is 3d14s1 and that of Sc is 3d14s2.

    This effectively solves one problem for chemical educators because it gets them out of the former apparent paradox. 4s is preferentially lost for the simple reason that it is less stable than the 3d electron in Sc.

    What it does not explain incidentally is why just one electron enters a 3d orbital rather than the final 3 electrons to enter the Sc atom via the sophisticated aufbau scheme. I don’t think there is a good general conceptual argument for this, but it depends on the details of the Hartree-Fock calculations for any particular atom and the precise nature of the H-F approximation (see Pilar’s paper for a clear account of this in this context).

    Please bear in mind that I did not say I agreed with everything in Schwarz’s recent papers. I believe that the Madelung rule remains valid in the sense of giving the correct resultant configuration. It is only incorrect if taken to indicate the order in which electrons occupy the orbitals in transition metal atoms like Sc.

    The question of the relative occupation of 4s and 3d and similar pairs goes beyond which periodic table one should favor.

    Incidentally, in his book Bent gives 57 reasons why the LST should be preferred and then promptly says that the LST is no better than the traditional table in which He falls above Ne !! This point was well noted by Truman Schwartz (not Eugen Schwarz) who reviewed Bent’s book in J Chem. Ed.

    The elementary point about adding one electron as well as a proton on moving through the periodic table is well known to me and I use the distinction between the two kinds of aufbau precisely to defuse the 4s/3d apparent paradox or pseudo problem on p. 234-237 of my book, although changes will need to be made in the 2nd edition.

    all the best
    eric scerri

  222. Valery- I don’t know about ‘objective’, but I’d go with ‘deeper’ from a derivational perspective.

    Consider the linguistic analogue: phonological systems, consisting of nice columns and rows, sometimes thought of in multiple dimensions, with ‘gaps’, etc. Systems vary by size and by symmetricality as well as by number of relevant matrix dimensions.

    Such phonological systems are very much in the same spirit as the PT. Phonological systems are abstractions from higher level contrasts and parallels in combined forms, yet the features that go into the underlying level have some reality- Acoustic Fourier analysis of spoken forms is analogous to spectrographic analysis of atoms, while it might be more difficult to find analogies to anatomical articulatory position (though not impossible).

    The higher level interactive accommodations and adjustments that phonemes undergo at the phonetic level is similar in spirit to what goes on with chemical units larger than isolated atoms.

    Linguists got over disputes about what is phonological vs. phonetic back in the 1930’s, though one’s transcription of lines of speech may be more one way vs. the other according to taste (as are orthographic systems) and depth of derivation (which makes one or the other more efficient for learners, or experienced readers/writers). Traditional syllabic/alphabetic spelling systems have LOTS of baggage carried over from prelinguistic times, but some are much better than others for the languages they represent.

    I suggest that the issues here about physicist’s vs. chemist’s tables is far more about relatively unexamined received wisdom, tradition-based inertia, and turf than anything else. Multiple levels of representation are alright by me, though, so long as they are labeled for each level and people know what the labels represent hierarchically.

    Jess Tauber

  223. ad ho·mi·nem   [ad hom-uh-nuhm ‐nem, ahd-]
    1. appealing to one’s prejudices, emotions, or special interests rather than to one’s intellect or reason.
    2. attacking an opponent’s character rather than answering his argument.

  224. Frankly, I do not inderstand how can chemists dismiss “fdps” and He/Be periodic tables by calling them “spectroscopic”. Without spectroscopy, puristic chemists would still be speculating if there is an element between H and Li. I personally think that the more periodic table is in line with spectroscopic observations, the more objective it is.

  225. Response to Bent

    Can I suggest that beginning and ending with ad hominem remarks
    may not be a good way of facilitating free discussion.

    May I also suggest that page references might be given more carefully.
    P. 69 is not what he says it is!

    all the best

  226. POSTSCRIPT to my remark of Feb. 23 regarding Eugen Schwarz’s “straw man”.

    Schwarz introduces his straw man, that ““the periodic table of atoms is somewhat irrelevant to chemistry since these are gaseous atoms and uncombined”, because he does not want to see helium located above beryllium in periodic tables, and he knows that atomic helium being an ns2 system, like beryllium, whereas neon is an np6 system, is sufficient reason for most physicists and some chemists to be comfortable with He/Be, rather than He/Ne. It’s also a reason why chemists raised on He/Ne and unfamiliar with He/Be, which, at the moment, is most chemists, are happy to dismiss periodic tables with He/Be as merely “spectroscopic tables”, not genuine “chemical periodic tables”. Therein lies one reason for the significant at the present time in having a purely chemical route — one that makes no reference whatsoever to electrons and atomic orbitals — to the “spectroscopic”, left-step, fdps periodic table, which features He/Be.

    That said, it should be said that the He-Ne kinship is, indeed, one of the strongest kinships in the Periodic System, if not, being a tertiary kinship, one of the closest kinships, whereas the He-Be kinship, although a primary kinship, is, in fact, the Periodic System’s weakest kinship. (Trans-table trends in kinships strengths exist, for the Left-Step Periodic Table.)

    Both He kinships can be given graphic representation through use of tie-lines in a step-pyramid periodic table (a table with centered periods, separated, vertically, by length) that has the s-elements on the left. That table has H and He at the top, by themselves, separated from dyads beneath them — in recognition of their distinctive character, in being the only elements with no inner-shell electrons? Or as a result of recognizing the distinctive character of the s-block, whose differentiating electrons do not become core electrons with increasing Z (the exception that proves the valence/core rule stated previously), by locating, accordingly, the s-block as an almost stand-alone block on the left, so that along periods Groups’ characteristic (maximum) oxidation numbers begin at 1?


  227. Henry Bent wrote:

    ‘H and He are the only atoms whose cores contain no electrons.’

    Given the truth of this, might this not be the basis of some sort of two-step offset for the entire system, i.e. an organizational principle for later derived behaviors?

    Jess Tauber

  228. Janet derived his n+k-1 (=n+l) rule from his table, once he had learnt about the quantum numbers. But he cheated: he thought Bohr et al had got the numbers wrong, so he “corrected” them to fit n+k-1. Of course he needn’t have done, given Valery’s observation of the regular increase of the sum.

  229. Also, wasn’t “n+l” rule derived from spectroscopic observations of real atoms? It is, after all, empirical rule.

  230. Scerri’s remarks of February 23 that –

    “As the tables of Atomic Energy levels by Charlotte Moore reveal, in an atom of scandium for example the 19th electron occupies a 3d orbital not a 4s. The 20th and 21st occupy the 4s orbital. This situation means that the much cited Madelung rule is only correct for the s block elements, not for d or even p plock.”

    calls to mind the story told about Wolfgang Pauli. A colleague who’d given Pauli a copy of a student thesis to read met Pauli in a hallway a few days later and eagerly asked him what he thought of the thesis. Shaking his head sadly, Pauli said, “It’s not even wrong.”

    It’s true that if one builds up a scandium atom, starting with its bare nucleus, charge +21, the 19th electron enters a 3d orbital, not the 4s orbital. But that’s not what Bohr’s Aufbau Process and the Madelung Rule are about! They are about building up atoms starting with hydrogen and adding SIMULTANEOUSLY protons to nuclei and electrons to electron clouds, maintaining ELECTRICAL NEUTRALITY!

    The reason 3d lies lower in energy than 4s for Sc(III), i.e., Sc+2, is that with increasing positive charge, atoms become increasingly hydrogen-like. By the time atom Z has reached a charge of +(Z-1) — i.e., by the time it has become a one-electron species — it is, of course, perfectly hydrogen-like. Most heavy atoms become hydrogen-like long before that, by the time they’ve been stripped down to their atomic cores.

    So, it is not correct to conclude that “the much cited Madelung rule is only correct for the s block elements, not for d or even p plock.” That’s absolutely incorrect. The author has misunderstood the significance of Charlotte Moore’s tables. Evidently he’s not reached in Bent’s book page 69, where much data from CM is displayed, including precisely the case of Sc(III), which is hydrogen-like through its first four excited states, compared to isoelectronic Ca(II) and K(I), which are more Madelung-like, K(I) even more so, so to speak, than Ca(I), which tracks n + l through its 14th excited state.

    Also, Schwarz’s remark that “the periodic table of atoms is somewhat irrelevant to chemistry since these are gaseous atoms and uncombined” is beside the point. Such a table is a straw man. The Periodic Table, as explained above, is about atomic cores — the basic substances that survive from compound to compound — not atoms, since free atoms, as such, do not exist in compounds. For nonlinear molecules, e.g., free atoms’ electronic angular momenta are completely quenched.

    Suggested is a coda to Braque’s warning: “Beware of painting a picture better than you are.” Beware of criticizing a theory better than you are.


  231. Some time ago I responded briefly to the query as to what I meant by the phrase “atomic core”. Here is a fuller response.


    The renowned chemical educator J. Arthur Campbell used to like to ask his students: “What’s periodic about periodic tables?” Nothing, to untutored eyes. Seeing a periodicity of elements’ properties requires a knowledge of elements’ properties.

    One might ask, also: WHAT ARE PERIODIC TABLES ABOUT? The chemical elements? So it might seem. Featured in all periodic tables, whatever their shapes, are the elements’ symbols. And, indeed, a periodic table usually appears on the page, or the page opposite, dictionaries’ entries for the word “element”. The phenomenon of allotropy raises an obvious question, however. What it is, exactly, that the Periodic Classification of the Elements classifies?

    In classifying the elements according to the Periodic Law, what property, or properties, of carbon, e.g., does one take into account? Those of diamond or those of graphite? Similarly for tin. Is its classification based on the properties of grey tin, a metalloid? Or white tin, a metal? Properties of white and red phosphorus are so different Faraday entertained the thought that perhaps the transformation of one into the other was an instance of alchemy.

    The substances of the pairs of substances diamond and graphite, grey and white tin, and red and white phosphorus are alike, chemically, in one respect. Their atoms not only have the same atomic weights. The have, also, the same maximum states of oxidation. As Mendeleev emphasized –

    “[T]he forms of [elements’ highest] oxides [e.g., for C and Pb, CO2 and PbO2] and . . . atomic weights . . . [give] us the means to erect an unarbitrary system as complete as possible” [with C, a nonmetal, and Pb, a metal, in the same Group; cf. N & Bi, O & Te, H & Li, and He & Be].

    Periodic tables were often called, accordingly, “oxidation tables”.

    In the modern electronic interpretation of oxidation numbers, all electrons in a binary oxide are assigned to oxygen (except in oxyfluorides). Stripped of all outer electrons are the atoms of the less electronegative elements, in Mendeleev’s Groups I – VII of the s- and p-blocks. Define: atomic core = atom – (valence-shell electrons). Then one may make the following –


    • Atoms of elements in a block’s row have isoelectronic atomic cores.
    • Atoms of elements in a block’s column have isoelectronic valence-shells — or at least, in the d- and f-blocks, valence-shells that have the same number, if not exactly the same types, of valence-shell electrons — about cores that have isoelectronic outer-shells.
    • Each block row — of which there are 22 for Z through 120 — represents a distinctive type of core.
    • With increasing Z across a block’s rows, valence-shell electrons become increasingly core-like electrons.
    • On exiting a block, the core/valence-shell transformation is complete.
    • Cores are not isoelectronic across periodic tables’ periods. They change from block to block, as well as from row to row within blocks.
    • Sizes of atomic cores provide numbers for creation of numerical indices of elements’ distinctiveness that track closely the manner in which textbooks discuss the chemistries of the elements.
    • The elusive and mysterious “basic substances” that philosophers of the periodic table speak of are nothing more, nor less, than atoms’ cores.
    • Atomic cores’ three most important properties in chemistry are –
    o Charge
    o Size
    o Type(s) of Valence-Shell Electrons
    • The angular quantum number of orbitals of an atom’s predominant type of differentiating electrons is equal to the ordinal number of the atom’s block when blocks are arranged by size, starting at ordinal number 0 for the 2-column block.
    • The radial quantum number of orbitals of differentiating electrons is equal to the ordinal numbers of the rows of the atoms within their blocks.
    • Cores of atoms related by primary kinships have the same charge and the same types of valence-shell electrons. Both conditions rule out grouping H with F and He with Ne.
    • Cores of atoms related by secondary chemical kinships have the same charge but not, predominantly, the same types of valence-shell electrons.
    • Cores of atoms related by tertiary chemical kinships have in their valence-shells the same number of vacancies.
    • Atomic numbers of cores of a Groups’ elements 2, 3, and 4 and 4, 5, and 6 form primary “triads”. Never is a Group’s first element a member of a primary triad.
    • H and He are the only atoms whose cores contain no electrons.
    • In bond diagrams symbols of nonmetallic elements stand for the elements’ atomic cores. That identification was made by G. N. Lewis, in 1916, when he identified the valence-stroke as 2 electrons and introduced, also, the concept of lone-pairs.
    • In chemical species that can be represented satisfactorily by bond diagrams, the atomic cores C+4, N+5, O+6, and F+7 obey an “Octet Rule”. Their valence-shells are occupied by 8 electrons.
    • Valence-shells of cores of congeners of Octet-Rule-satisfying cores may contain 10 and 12 electrons, as in, e.g., PF5, PF6-, SF4 and SF6.
    • Lone-pairs in the valence-shells of large cores of large charge occupy more space about the cores than do bonding pairs and may become, in the presence of “good leaving groups”, “inert pairs”, yielding larger cores of lower charge (by 2 units), as, e.g., in PbCl2 and TlCl.
    • Atomic cores of nonmetals are small cations. The cations M+1, M+2, and M+3 of Groups I, II, and III are large atomic cores.
    • The step-like line that divides metals from nonmetals in periodic tables occurs at core radii equal to approximately 50 pm.

  232. I would like to read his articles, however, from your description, I already sense where he goes wrong.

    If we believe Eugen Schwartz that Madelung rule is distraction that should not be even taught in chemistry, then why do we even care about continuity in regard to atomic number Z in periodic tables? Just forget continuity and go directly to chemical properties. Aufbau, meaning “building up” is about continuity. It is invention of human mind that does not have much to do with the process of synthesis of real atomic nuclei.

    As I tried to emphasize before, the order of orbital filling in any particular atom should not have much to do with the periodic table. What has to be taken in account is final products: abstract atoms. Any classification system deals with abstract objects or subjects. If we classify humans by their shoe size, we know that we are talking about abstract adult humans, or abstract children of certain age. Most shoes are not custom made now days. So why it is so hard to convince chemists that elements are abstract atoms and we are talking about abstract electron shells? But it is perfectly O.K. for classification purposes.

  233. If element 120 turns out to be a ‘noble’ element, and if 120 is the end of the periodic system, then from the perspective of the 2D triangular modification of the Left Step PT, with all the numbers aligned, then this would be a symmetrical arrangement, 120 mirroring Helium, both being in the ‘alkaline earth’ group.

    Jess Tauber

  234. A comment on the recent discussions concerning the alkaline earths and the inert gases.

    Some work by the german theoretician Eugen Schwarz, who regularly attends and speaks at meetings of the International Society for the Philosophy of Chemistry, has emphasized that the s block elements are the only ones for which s genuinely fills before d orbitals.

    Textbooks have propagated a myth that this also takes place in the d block metals but it is not quite correct.

    As the tables of Atomic Energy levels by Charlotte Moore reveal, in an atom of scandium for example the 19th electron occupies a 3d orbital not a 4s. The 20th and 21st occupy the 4s orbital. This situation means that the much cited Madelung rule is only correct for the s block elements, not for d or even p plock.

    For Schwarz the Madelung rule is a distraction that he believes should not be taught in chemistry. He also likes to emphasize that the periodic table of atoms is somewhat irrelevant to chemistry since these are gaseous atoms and uncombined. In the case of combined atoms and ions, the order of filling follows a simple n rule rather than n + l ordering. In other words the madelung rule is largely irrelevant to the real chemistry involving condensed phases and compounds formed by atoms.

    Schwarz has published these views in articles in Foundations of Chemistry and also Angewandte Chemie International Edition.

    I believed they are very important and should be read by anyone wishing to discuss electronic configurations of atoms and their relationship to the periodic table.

    all the best

    eric scerri

  235. I anticipated that you are going to say that and prepared my response:

    Not all periods end with elements that have p-electrons. Four elements do not have p-electrons at all. Therefore, for maximum regularity and in order to assure that all periods end with same kind of elements, speaking in terms of electron configurations, periods have to end with alkaline earths. So the logic of ending the rows with nobel gases does not go far enough in case of tables that do not disregard electron configurations.

  236. This from the English Wikipedia entry on element 120:

    Unbinilium should be highly reactive, according to periodic trends, as this element is a member of alkaline earth metals. It would be much more reactive than any other lighter elements of this group. If group reactivity is followed, this element would react violently in air to form an oxide (UbnO) and in water to form the hydroxide, which would be a strong base and highly explosive in terms of flammability. It is also possible that, due to relativistic effects, the element has noble gas character, as already seen for element 114. A predicted oxidation state is II.

    Does the inert pair effect, or relativistic stabilization with higher s, interact with these trends??

    Jess Tauber

  237. What I find interesting is that the general trend for Aufbau anomalies is that they push towards lower QN l. f contributes to d, which then at least for element 103 contributes to p. Do we have any hints for p>s at the highest atomic numbers?

    s is supposed to be the donor for 6 and 7d blocks, bypassing 4 and 5f. But is this true? Could it be possible that a relay is nearer the truth (that is, s>f>d)? The net effect would be no change for the f blocks, as electrons are themselves indistinguishable. That we don’t find any s>f by itself is perplexing, just purely from a systemic point of view.

    Also, things ain’t as perfect in the p-block as one might think. I grabbed the following from the the English language Wikipedia entry on Element 118:

    Ununoctium is a member of group 18, the zero-valence elements. The members of this group are usually inert to most common chemical reactions (for example, combustion) because the outer valence shell is completely filled with eight electrons. This produces a stable, minimum energy configuration in which the outer electrons are tightly bound.[41] It is thought that similarly, ununoctium has a closed outer valence shell in which its valence electrons are arranged in a 7s2, 7p6 configuration.[1]

    Consequently, some expect ununoctium to have similar physical and chemical properties to other members of its group, most closely resembling the noble gas above it in the periodic table, radon.[42] Following the periodic trend, ununoctium would be expected to be slightly more reactive than radon. However, theoretical calculations have shown that it could be quite reactive, so that it can probably not be considered a noble gas.[5] In addition to being far more reactive than radon, ununoctium may be even more reactive than elements 114 and 112.[1] The reason for the apparent enhancement of the chemical activity of element 118 relative to radon is an energetic destabilization and a radial expansion of the last occupied 7p subshell.[1][43] More precisely, considerable spin-orbit interactions between the 7p electrons with the inert 7s2 electrons, effectively lead to a second valence shell closing at element 114, and a significant decrease in stabilization of the closed shell of element 118.[1] It has also been calculated that ununoctium, unlike other noble gases, binds an electron with release of energy—or in other words, it exhibits positive electron affinity.[44][45][46]

    Ununoctium is expected to have by far the broadest polarizability of all elements before it in the periodic table, and almost twofold of radon.[1] By extrapolating from the other noble gases, it is expected that ununoctium has a boiling point between 320 and 380 K.[1] This is very different from the previously estimated values of 263 K[6] or 247 K.[47] Even given the large uncertainties of the calculations, it seems highly unlikely that element 118 would be a gas under standard conditions.[1][48] And as the liquid range of the other gases is very narrow, between 2 and 9 kelvins, this element should be solid at standard conditions. If ununoctium forms a gas under standard conditions nevertheless, it would be one of the densest gaseous substances at standard conditions (even if it is monatomic like the other noble gases).

    Because of its tremendous polarizability, ununoctium is expected to have an anomalously low ionization energy (similar to that of lead which is 70% of that of radon[49] and significantly smaller than that of element 114[50]) and a standard state condensed phase.[1]

  238. The noble gas configuration of 2s+6p is equally special. It is always followed by two (n+1)s electrons even when (n-1) and (n-2) shells are still incomplete. So there is logic in the practice of ending the rows of a table with these gases.

  239. My response to a previous comment by Philip Stewart.


    you are absolutely right when you say that, because of such elements as Cr, Cu, La and other odd balls that fall out of Afbau order, it is hard to make periodic table absolutely regular by mimicing electron configurations and quantum numbers. However, evey time you get to the alkaline earth metals regularity gets restored! Regularity gets restored even before, in p-block. Electron configurations of alkaline earth metals are PERFECT. Their atomic numbers perfectly match modified terahedral numbers, the numbers that can be arrived at by adding only spheres in odd rows and multiplied by two. I find it interesting that such regularity is violated (sometimes immediately, as in case of La and Ac), as soon as you leave alkaline earth group. That tells me something about special status, or completeness, of alkaline earth atoms.

    Valery Tsimmerman

  240. Perhaps in the environment around or on the surfaces of neutron stars matter makes use of muon and tauon series in addition to normal electron-style stuff? I’d guess this would multiply the periodic possibilities quite a bit (how many possible combinations???).

    Jess Tauber

  241. Which takes us back to neutron stars; perhaps it is only under the intense bombardment of neutrons near the surface of such a star that nuclei heavier than Z=c. 100 could acquire enough of them to be stable for any length of time. Any chance of reproducing such conditions on earth?

  242. More odd mental gymnastics (not quite up to the level of numerology, I expect):

    If one looks at the trends of neutron numbers as one increases atomic number, one finds that the ratio gets to be about 1.5 for n/p, at least around 120 (estimated).

    For uranium 238, the percentage of n vs. total nucleon numbers is 0.6131453, close to the golden ratio number 0.6180339. Using the latter number instead to estimate how many neutrons element 120 ‘should’ have, one gets 314.164, or just over 100 pi.

    Looks like material reality is having a big laugh at our expense?

    Jess Tauber

  243. Chemical behaviour as we know it, and things such as noble gases and alkaline earth metals, exist only in a relatively narrow range of conditions. In a stellar plasma H and He exist as bare nuclei, briefly capturing and then losing electrons and sometimes fusing with other nuclei. Nuclei with more protons manage to hang on to increasing numbers of electrons and exist as ions. And what happens to heavy elements in the immense magnetic fields at the surface of neutron stars? For such ‘extreme’ – but very common – environments, the quantum basis of the periodic system is what connects it with what we see on earth.

  244. Yes, Helium has unusual placement properties simply because the system is just starting to cumulate, and there aren’t any p-block positions yet to backstep 2 moves to.

    Are there any other numerically derivative relationships like this? Knight’s moves? Aufbau anomalies (I know the causal explanations given by chemists, the question is whether there is any more regular, simple equational setup that will give the same results)?

    In linguistics we run into similar issues- where one process has to run its course entirely before we can then make modifications based on finished products (that is, secondary and tertiary effects require a substrate to work on). Sometimes hierarchically lower level productions aren’t entirely completed before they get modified, and this results in unexpected complexity and irregularity- competing motivations, and creation of choice. This is one way languages change.

    It makes me wonder whether the properties of the periodic system are fixed in stone, or may vary. We know that overt element properties can change in different physical regimes of pressure, temperature, and I’d guess also magnetic and electrical fields, etc. What about spacetime itself (which can be stretched or shrunk), or neutrino flux? In such situations, are changes entirely predictable, or can the systems coexist in two or more states, as in quantum superpositions? What determines which dominates? Just local energy, or something more, as in long-distance (how about temporally disjunct as well) entanglements? There may be a lot more negotiation going on than we know about.

    Jess Tauber

  245. Since there was such a tumultuous response to the review of my book, I felt compelled to post another one, for my book on the Philosophy of Chemistry. It features the question of elements as basic substances and simple substances. You can read the review on Sciencebase sibling site

    all the best,
    eric scerri

  246. Jess,

    in regard to placement of He, you observation is correct. It fits with nobel gases since its atomic number 2=(4-2), where 4 is tetrahedral pascal number. However, it perfectly fits with alkaline earths too, if you consider zero (0) as the first tetrahderal number. Therefore, (0+4)/2=2 for Helium. This numerical duality is reflected in ADOMAH PT. Remember our earlier discussion regarding primary and tertiary kinships?

  247. After mapping all the elements to the angled ring system (and I don’t remember whether I’ve posted this before), there is an interesting coincidence.

    Uranium occupies one vertex of the finished tetrahedron. With the tetrahedron basally situated (that is, on the face opposite this vertex), a perpendicular axis goes through the center of the basal face. It turns out that the three spheres that surround the face’s center are Tl, Pb, and Bi.

    I looked at the other three such mappings to the other outermost vertices and faces and can’t see any obvious relations (as with radioactive decay series with the above). But perhaps there is something going on with smaller subtetrahedra. Will have to look closer.

    Jess Tauber

  248. I’m sure someone has mentioned this before somewhere- I was looking at electronic magic numbers:

    2, 10, 18, 36, 54, 86, 118

    The atomic numbers of the ‘noble’ gases (but 118?). All two less than the alkaline earth numbers, of which half are the Pascal numbers, and the others midway between these.

    In such a system He is just fine as a ‘noble’ element, but the numbers are derived relative to the Pascal set. Does this mean that He should be depicted in the same column as the p-group?

    In the angled ring system the p-group nobles form two parallel, rotationally symmetrically placed stacks of three elements each- odd periods on one side of the rotational axis, evens on the other. He doesn’t fit in at all here, as its placement is with the rest of the other 7 alkaline earth element in two 4-member stacks.

    Yet we still have the mathematical fact of 2 as a derived noble number. So perhaps there is a ‘derived’ periodic space? If so, would such a space also be able to accommodate diagonals, knight’s moves, etc., that don’t currently have any easy mapping on the angled ring system?

    Jess Tauber

  249. Just for those interested in predestination, my date of birth contains two of the four Pascal numbers in the alkaline earth group. Unfortunately, the year was not ’56. DRAT! I have no idea what to do with 120….

    Jess Tauber

    [Actual dates removed for security – one should never reveal one’s name and birthday together with other information such as website address on the web]

  250. I am pleased to say that I have just ordered a copy of Henry Bent’s book from Amazon and am looking forward to studying it.

  251. Roy wrote:
    “All the wonderfully detailed and complex periodic tables I have been reading about here (each of which receive little support from others) are for those who have at least been able to make the first step successfully”.

    You can go back and check:
    1) Philip stated that ADOMAH PT is most beautiful tabular depiction of periodic system;
    2) You can go to my web site and see what Henry Bent had to say about ADOMAH PT;
    3) Jess Tauber first came up with tetrahedral concept of PT and is very supportive of ADOMAH;
    4) just yesterday ADOMAH web site was visited by approximately 700 people coming from single blog that posted link entitled “Fascinating Tetrahedral Periodic Table”;
    5) Few month ago I was contacted by movie maker who asked my permition for using materials on my web site;
    6) Text book was written in Spanish that devoted 3 pages on ADOMAH PT and the tetrahedron; Same authors are working on English version of the book.
    7) Few days ago I received beautiful poster “ADOMAH Periodic Table in pictures” as a gift from some one who admires ADOMAH Periodic table;
    8) On this forum I posted link to Pierre Dermes web pages (French) discussing ADOMAH PT in detail;

    Those are most recent developments. I could continue this list on and on.
    So, I do not complain about lack of support for my work on periodic table.

    Valery Tsimmerman

  252. Roy: don’t wait to see Janet’s ‘see-through’ image of his helix. Get down to your library and ask for van Spronsen. You’ll also see most of these other representations we’ve been talking about. And take a look at the weird and wonderful gallery on the Meta-synthesis website (including Steve Jensen’s version which closely resembles yours, found independently). You’ll understand why some of us hedge our bets.

  253. Philip: If, in the AAE, you miss” … the convenience of a flat representation, which can be taken in at a single glance”, then I can’t wait to see what your favorite, “Janet’s helix wound on nested cylinders”, looks like if it must be “made with transparent materials [so] the helix would be visible as a whole”.

    Valery: Yes, the AAE is a simple tool. That’s what it is supposed to be, as I have said, “a stepping stone”. All the wonderfully detailed and complex periodic tables I have been reading about here (each of which receive little support from others) are for those who have at least been able to make the first step successfully. All I have done is what de Chancourtois also did, plug the end of an element period into the beginning of the next. (I have no doubt Mendeleev would be thrilled to see his Law obeyed so gracefully! ;-)

  254. Janet’s helix is in van Spronsen, fig. 73, foldout facing page 174, described p. 320. He calls it ‘a system worthy of special attention. I’d give a lot to have it in perspex.

  255. Philip: I offered to send one to whomever sent me an address and had precious few responses (
    It is not a simple wrap, the s-block descends to line up with the followinf period.
    More relationships than I would have thought existed (before observing this blog) are at
    In the meantime, I have not been able to see what “Janet’s helix wound on nested cylinders” looks like. Does someone have a model that they can photograph and post?
    Likewise, except for your and Valery’s representations I haven’t seen what anyone is talking about that matches the verbal descriptions.

  256. Roy: It’s not that I don’t grasp your 3D representation. In fact I made my own ribbon and wound it several different ways, including yours, but I couldn’t see a good way to show secondary relationships, and I missed the convenience of a flat representation, which can be taken in at a single glance. To me the most satisfying 3D version is Janet’s helix wound on nested cylinders. If it were made, with transparent materials, the helix would be visible as a whole, but that would require great skill with glass or plastic. Meanwhile, I am still playing with the idea of an adaptation of the Minaret of Samarra.

  257. I’ve had a change of heart overnight…there’s really no reason for me to close the comments on this. So, feel free to continue the debate here or otherwise as you see fit.

  258. It is tool. I agree. However, there are simple tools, like those that hit the nail on the head and there are tools such as microscope that let us see what is hidden and helps to make new discoveries.

  259. “Just a tool” defines much (all?) humans have created – physically and intellectually.
    The periodic table tool is a way to remind oneself of the relations between elements – and to learn about them in the first place.
    A given classification of tools, hammers, for instance, has numerous varieties; finished – drop forged then polished or painted, with handles of ordinary polished hardwood, bleached and polished hardwood, or hickory polished handle, of fiber handle with grip or steel tubular handle with grip. All of the above are available as Ball Pein, Claw, Machinist, Upholsterer, Modelmaker, Stoning, Sledge, Rubber, and Wood hammer, a list which is only a good start on the actual variety.
    No surprise that there are different kinds of periodic tables of elements – or hammers – there are different jobs to do.
    Not all periodic tables types are suitable for a person in the position of an outsider to the scientific professions. (What is the percentage of insiders and outsiders?)
    New students and other lay people start out knowing that there are different kinds of things outside and inside themselves and their environments, and that many consist of different materials with varied properties.
    That they can’t drink glass out of a cup made of milk, but vice versa works.
    The submicroscopic world that is chemical is, not surprisingly, invisible to them. They need a stepping stone from this ignorance to a first glimpse into the idea that there are a lot of different forms that material takes when it is REALLY small, and these can mix up to be, in large batches, stuff that some of them can recognize right off.
    The tabular arrangement of the elements can be a tool to help them to see the number, possibilities, and relationships of the astounding number of different small kinds of stuff.
    At this point in the learning process, be it in a classroom, a TV show, or a science museum, a representation of the table that needs no alibis is crucial to permit a clean segue to the further analysis and understanding of chemistry.
    It may be that most of the bloggers here are so far removed from their first step, and bright enough to either have grasped the concept from the standard periodic table the first time they saw one, or trusting enough in the educational process that they could withhold criticality until more information made the first step seem relevant in retrospect.
    As a designer of information representations, however, the first step is always in my mind, and whatever the application of other hammers, I have been reassured by following this blog with great attention until now, that the AAE hits the nail on the head.

  260. Thank Lord Quantum for making electrons obey rules based on the numbers 1, 2, 3, 4… and their squares, as is Pascal’s tetrahedron. And blame Lord Quantum if there is no perfect way of representing this graphically at least in our 3D world.

  261. Well Valery…I never said which filters should be the stock in trade of PTs…but it really is all about patterns and filtering information, there is no ultimate PT that has existed since the Big Bang that we’re simply yet to find.

    Anyway, I’m calling “time” on this post, so any last orders should get in quick…

  262. The table, or any other graphic representation, is just a tool, which can be fashioned according to the interests of its creator, but the periodic system exists independently of us, and every representation should be faithful to some aspect of it, of which quantum mechanics and electronic Aufbau are the most fundamental.

  263. OK, Philip, I suppose near-symmetry (symmetry lite?) will pass for symmetry in most things for most people. So I will defocus my critical statements accordingly
    I will also try to keep from identifying the cause of users’ visual jumps needed while looking at successive elements of every flat periodic table from the end of a period back across (or up) the page to the beginning of the next as a ‘cut’ or “gap”.
    Accordingly, are the IUPAC, tetrahedral, and LSPT supporters going to recognize the error in teaching new students (who are not chemists, physicists, biologists, or mathematicians yet) with a flat table that ALWAYS has internal gaps (or stretches) – no matter if the blocks are flipped, stood on end, shifted left or right, or have elements stuffed into a pyramid?

  264. That is right, David. I can add one more “filter”. Let’s arrange spdf blocks of ADOMAH PT in 3D in such way that the values of quantum number “ml” are also lined up and we would get ADOMAH Tetrahedron. Isn’t that amazing? But what are the quantum numbers and why do they have such interesting geometric relationship?

  265. As I see it, the PT is actually just a tool, it’s not even a model, it’s just a tool for looking at patterns, a filter if you will.

    Like photographic filters one or two are essential (a UV filter, a polariser, and perhaps a neutral density graduated filter for getting your skies right. You can add more and more filters to the front of your camera until image you say goes way beyond the “reality” that’s actually in front of your eyes…

  266. I understand word “element” as abstract atom identified by atomic number “Z” , electrically neutral with electrons in their places and in ground state. Similarly, how would we define “human”? I would define it as abstract biological system with certain type of DNA, with two arms, two legs, ten fingers, ten toes, etc. In real life, do we all have all our limbs intact? No. There are many real humans who miss some body parts, however, thay remain humans, because of DNA and their remaining limbs that they can be dentified by.

    Similraly, if real atom of Ca, for example, has missing electron or two, we know that it is calcium becuase it has nucleus with number of protons Z and remaining electrons, that is core. Experienced detectives can distinguish human bones from animal bones and make a statement that those are human remains. In physics, if we observe bare nucleus, we know what element it is. However, for description and classification purposes we still think of elements as abstract atoms with atomic number Z and their electron clouds intact.

    In regard to LSPT and Step Pyramid table mentioned by prof. Bent. This is how to built LSPT using minimum data:
    1) list maximum n+l values for each element: 11,22,33333333,44444444,555555555555555555,…;
    2) stack groups of numbers shown above on top of each other so all values of quantum number “l” line up vertically.
    That is it. That is LSPT, but it is not complete system yet. There is primary quantum number that needs to be reflected. In order to complete the system one must make one more step:
    3) shift blocks of LSPT so block rows line up in accordance with quantum numer “n”.

    That is complete system, known as ADOMAH PT and it happens to be naturally symmetric! Isn’t it amazing!

    Valery Tsimmerman.

  267. No symmetry in nature?! Most physical laws involve symmetry – action and reaction. The interaction of different factors produces departures from perfect symmetry; there are no perfect spheres, but 99% of the non-dark matter in the universe is in the form of almost spherical stars. Most biological form involves either bilateral or radial symmetry although natural sugars are right-handed and amino acids are left-handed. There is no perfect Platonic symmetry, but the approach to symmetry is everywhere.

    One must distinguish symmetry from regularity. The Periodic System is not one of the places one would expect symmetry, because of the delay in adding the d and f electrons. Nor is it perfectly regular, because of exceptions like Lu and Pd. However these can be shown on a regular background, as in Mazurs’ handsome verion of the LSPT (fold-out at the back of his book).

  268. Jess and Roy,

    Symmetry arguments play a huge role in theoretical chemistry: molecular orbital theory, spectroscopy’s selection rules, xray crystallography, &c. For some 40 years I did not use them in my own work, however, ever since I learned that HOH is not a linear molecule and that nitrous oxide is NNO not NON — until I encountered the problem regarding the location of H and He in periodic tables. If one proceeds as I’ve described in “The Rules of the Game”, with either memberships of commonly named Groups (as described in my book “New Ideas . . . “, beginning with its cover) or with atoms’ first-stage ionization energies, all elements fall into place except H and He, for which there appear, at first sight, to be two locations, above Li and Be or above F and Ne. Regularity — and, actually, not “symmetry” — of the overall pattern locates H and He above Li and Be, WHICH, UNEXPECTEDLY, TURNED OUT TO MAKE A LOT OF SENSE, CHEMICALLY AND PHYSICALLY. Created are a number of new regularities that include, as I’ve mentioned previously: trans-table trends, vertical and horizontal, in first-element distinctiveness; Rules of Triads (the first one being that Groups’ first elements are not members of primary triads); a consilience between ordinal numbers generated by the LSPT and the angular and radial quantum numbers of atomic physics; and regularities (not symmetries) in the dimensions of periodic tables’ blocks. Centering the LSPT’s dyads yields a step-pyramid periodic table whose physical appearance is symmetrical — if not its chemical content! To untutored eyes, it has a pleasing appearance. And it’s useful for exhibiting, by tie-lines, secondary chemical kinships, if not the tertiary kinships H/F and He/Ne, exhibition of which, by tie-lines, requires a less symmetrical table, with the s-elements on the left. Most student-users of a periodic table do not like step-pyramid tables, because congeners do not appear in vertical columns.

    Henry Bent


  269. On the question of elements as “basic substances”.

    This is a subtle question which has been studied a great deal by contemporary philosophers of chemistry. It appears that the term is not amenable to a microscopic interpretation. Paneth as much as states this in his classic paper on the subject which appeared in the British Journal for the Philosophy of Science and reprinted more recently in Foundations of Chemistry. It is significant that this paper should have appeared in philosophy journals. If there were a simple 1:1 association between elements as basic substances and some aspect of the modern atom, there would be no need for philosophical reflection and the subject would become a technical one.

    Mendeleev drew attention to the distinction between element and simple substance but did not explain himself in detail. I believe that Paneth’s version is far more useful.

    Here is my quick attempt to get at the essence of this more philosophical sense of ‘element’. It is what subsumes both element as simple substance and ALSO element as a combined substance. It is what is common to Na the grey stuff and Na+ ions in NaCl. There is a temptation to say that it is nothing but the nucleus with 11 protons but this does not seem to carry much chemical content and so cannot be correct. And yet the identification of element as basic substance with Z which Paneth makes seems to point in that direction.

    I prefer to think of it like this. We can infer the properties of the element as a basic substance from the properties of BOTH the simple substance and the combined element. This then leads to the question of how to combine these two sources of information which is a question that is not easily solved. Perhaps the similarity studies between elements, as those conducted by the Colombian school of Restrepo and Villaveces, as well as many others, have something to tell us.

    eric scerri

  270. I’ve sent David Bradley a fuller account than that posted of what I mean by the phrase “atomic cores”. They’re what periodic tables are about.

  271. Of course that is correct, but aside from orchids, Philip, where is there true symmetry in nature?

    In man’s construct, there may be symmetry in many things, but, Valery, the twist between the blocks of the ADOMAH Periodic Table makes one side different from the other.

    A periodic table built only according to the atomic number Z should do it, however.

  272. I do not believe in imposition of symmetry also. However, symmetry seems to be natural outcome if Periodic Table is built in accordance with quantum numbers “n” and “l” and atomic number Z.

  273. For what it’s worth, I have never seen any science succeed due to the imposition of symmetry (which some seem to feel is a large component of beauty), but have seen the most functional and effective solutions (especially in engineering) to result in one or both.

  274. Another attempt to post prof. Bent’s response:

    Larry (Valery), thanks for posting “Rules of the Game”. Two corrections: (2L + 1) should be 2(2L + 1) and, near the end, 2(2L + 2) should be 2(2L + 1). I’d have posted those corrections myself, but seem unable to have done so, I discovered, when I attempted to reply to Philip Stewart’s request that I clarify the meaning of “atomic core”. Here’s what I tried to say:
    “Atomic Core” or “atomic kernel” is a widely used term in chemistry. It goes back to G. N. Lewis. When Lewis identified the valence-stroke of bond diagrams as 2 (valence-shell) electrons, he simultaneously identified, ACCORDINGLY, the symbols of the elements in bond diagrams as standing for atomic cores (= atoms – valence shell electrons). In his famous 1916 paper he had printers set the symbol “C”, e.g., IN A DISTINCTIVE FONT. Unfortunately, chemists have lost sight of that immensely important distinction. With that loss of sight has come a huge loss of insight into the nature of the chemical bond! With Lewis’ distinction, all of Pauling’s Rules of Crystal chemistry apply, lock, stock, and barrel, to organic chemistry, thereby unifying structural organic and inorganic chemistry, as I attempted to point out in an article some 40 years ago on Ionic Models of Covalent Compounds. The connection between atomic cores and the Periodic System is this:
    Atoms of periodic tables’ blocks’ rows have isoelectronic atomic cores. Atoms of blocks’ columns have isoelectronic valence shells about cores that have isoelectronic outer shells.
    Periodic tables might be viewed, accordingly, as tables of atomic cores. They are the “basic substances” that, for most practical purposes in most of chemistry, are unchanged in chemical transformations of substances.
    (A Caveat: Photoelectron Spectroscopy of inner-shell — core — electrons is an exceedingly important field of pure and applied chemistry. That’s because their energy levels depend, somewhat, on cores’ chemical environments. One of my PhD students has devoted his entire professional career to using that phenomenon as a method of chemical analysis.)
    Best regards, Henry
    P.S. I self-published my ideas regarding Chemical Periodicity because they were too numerous and too novel to be acceptable to either journal editors, their reviewers, or mainline book publishers. Oxford University Press published in the 1960s a book of mine on “The Second Law: An Introduction to Classical and Statistical Thermodynamics” that contained some novelties, but not nearly the number and quality of those in “New Ideas” — which, however, or consequently, was of no interest to OUP. In that regard, “New Ideas” may be in good company. I understand that Mazurs self-published, as did Janet. Insofar as NI’s ideas are correct, they will become, in time, part of conventional wisdom. Meanwhile, one might hope (expect?) true students and philosophers of periodic tables to be familiar with them, in order to criticize them — and, perhaps, thereby, to improve them? Suggestions welcomed!

  275. Please accept my apologies for my two most recent postings.

    This discussion here has been very valuable and cordial and I have lowered the tone.
    I hope we can get back to the subject matter now.

    eric scerri

  276. Philip,

    The term “atomic core” or “kernel” is widely used in chemistry. It goes back to G. N. Lewis. At the same time that he identified the valence-stroke of bond diagrams as 2 electrons, he identified the symbols of the elements in bond diagrams as, ACCORDINGLY, atomic cores (= atoms – valence-shell electrons). To make clear what he meant, Lewis had printers set the symbol “C”, e.g., in his bond diagrams IN A DISTINCTIVE FONT. Unfortunately, Lewis’ important distinction has been lost sight of. With that loss of sight has gone a huge loss of insight, since 1916, regarding the nature of the chemical bond! With Lewis’ distinction, Pauling’s Rules of Crystal CHemistry apply, lock, stock, and barrel, to organic compounds, as I attempted to point out some 40 years ago in an article on Ionic Models of Covalent Compounds.

    The connections between Lewis’ cores and the Periodic System is this: Atoms of blocks’ rows have isoelectronic cores. Atoms of blocks’ columns have isoelectronic valence shells about cores that have isoelectronic outer shells.

    One might argue that periodic tables are atomic core tables. They are the “basic substances” that do not change, significantly, throughout most of chemistry, in going from one substance to another.

    (A Caveat: Photoelectron Spectroscopy of inner-shell electrons is highly significant, in both pure and applied chemistry, inasmuch as energies of inner-shell electrons are somewhat dependent on the chemical environments of atomic cores. One of my PhD students has devoted his entire professional life to that field, in its uses for identifying chemical compounds.)


  277. Let’s not stop the arguing.
    It appears to me that this blog is an example of true science at work, antiauthoritarian, self-correcting, meritocratic and collaborative.
    John Dewey describes science as, “freedom of inquiry, toleration of diverse views, freedom of communication, the distribution of what is found out to every individual”.
    The theoretical physicist, Lee Smolin, says: “Good science comes from the collision of contradictory ideas, from conflict, from people trying to do better than their teachers did”.

    from the NYTimes, 2/12/10, about “The Science of Liberty” by Timothy Ferris

  278. The implication of calling attention to the fact of something being from the vanity press is that it was not good enough for anyone to publish.

    There is a third kind of publication: the publisher takes your copyright, pays you nothing for it, and then offers to sell you, for several thousand dollars, the right to put your own work on the internet. Most science journals fall into this category, including those of Springer Verlag.

    It hardly conduces to rational discussion to imply that someone is a crank who has to pay to get himself into print. Anyway, my objections to the LSPT were first overcome by your own arguments in The Periodic Table. Henry Bent and Valery Tsimmerman just added the icing to the cake.

  279. Sorry Philip but the question of whether a book has or has not been published by a Vanity Press does not depend on whether one or other individual may have read the book.

    There is a natural classification in the world of books into books published by presses where one has to pay to get published (Vanity Press) and books where one gets paid in having the book published (non-Vanity Press).

    In other words Vanity Press books represent a natural kind. The classification does not depend on using colour, shape, typeface etc.

    all the best


  280. I agree with Philip. I do not care who publisher of a book is. I am looking for substance. I think that we all should make an effort to be cordial and professional because I feel that we all benefit from this forum and from each other’s perspective. I would hate to see that our discussion deteriorates to making insults towards each other.

    I agree with Eric’s position that seeking optimal depiction of the Periodic law is legitimate enterprise. I also think that concentrating only on chemical aspect of periodicity is not going to yield desired results. In order to make progress, we should consider spectroscopy more closely. Spectroscopy has already clarified a lot of things. What we know about such things as n, l, ml and n+l rule, Hunds rule and exclusion principle we owe to spectroscopy. As Philip pointed out, Janet was able to come up with his LSPT before QM description of atom was complete. He did it on a basis of spectroscopy. So, LSPT is based strictly on empirical data. It is amazing that Chemistry and Spectroscopy yeilded almost identical results ( except He). Where Chemistry is not clear, we should look for clarification in Spectroscopy.

    ADOMAH added two things to LSPT: 1)blocks shifted to line up block rows with corresponding electron shells (n);
    2) bloks were shrunk to mimic relationship between quantum numbers “ml” and “ms”.
    Result: block perimeters are equal. Conclusion: Periodic System resembles sliced up tetrahedron. Independent check: Alkaline earths that all belong to the last group have mathematical connection with tetrahedral numbers located in forth diagonal of Pascal Triangle.

  281. As long as I have brought up the responsibility of educators of the lay public (especially new chemistry pupils) to avoid “misinformation and misdirection”, I invite all of you to glance through the Questions, Answers, details, and links from the graphic, of the index page of, and let me know how guilty I am… either on the blog or at

    Through attention to this blog (and private communications with fellow bloggers) I have learned that my DeskTopper needed improvement by shifting the f-block to the left, which I’ve taken care of, and that I should address adding an He above Be. Any other change suggestions for the next edition from those who have an AAE?

  282. PS Eric, why call Henry Bent’s book ‘vanity publishing’? You can’t say that of a book you have not read. Philosophers are supposed to listen to those the disagree with. Mazurs had to self-publish until people took notice of him. I agree that Henry’s use of the term ‘atomic core’ is not clear, so ask him to clarify. That’s how philosophy progresses.

    You still use the term ‘optimal’ as if it were independent of the objectives of the person who uses it. As Jess Tauber says, there are many dimensions to the Periodic System; any 2D or 3D representation can take account of only two or three of them (with one or two extra using colour, shape, typeface etc.). What is optimal for one user will be sub-optimal for another.

  283. Valery and Henry clearly mean something different by ‘gaps’. There are no gaps in Janet’s cylindrical helix wound on concentric cylinders; the series runs seamlessly from 1 to 120.

    As regards the element of zero atomic number, it was envisaged by Mendeleev himself (though he thought it would be ‘the ether’) and by various others, including B K Emerson, E I Emerson (no relation, I believe), Janet and von Antropoff, who called it ‘neutronium’, though the neutron and the neutron star had not yet been discovered. Schoolchildren who want to have useful
    adult ‘knowledge’ drilled into them are unlikely to have enough curiosity to be disturbed by the idea of element zero. Those with more imagination will be thrilled at the thought of matter so dense that enough to fill a bottle-top would weigh as much as many battleships.

  284. A depictive representation of the periodic relation may not be able to be idealized given divergent multiple purposes- esp. what you you want to emphasize. However, the NUMBER of total possible internal connections shown by contacts between cells, spheres, etc. can be maximized.

    A tetrahedron of close packed spheres has incredible numbers of mappings of spheres to elements, but maintaining connectivities in keeping with the various subdimensional representations (periodic line, 2D) really cuts down that number to a small handful. And some of these are more geometrically symmetrical than others.

    The angled ring system trades off odd-even period connections for secondary peridicity and registration of right, left, midpoint, etc. parts of blocks. There aren’t any gaps between blocks from the perspective of traditional 2D tables laterally.

    One can recover odd-even connections by rotating the figure 180 degrees around the central axis (s-block). Symmetry has been claimed by some to help pattern the relation (SO(4,2))- rotation in one dimension is only one possibility here. One can also flip the angled ring system and structurally it is identical, or you can invert it inside-out with similar results.

    This makes me think that many currently unknown relations are potentially present in the system via matrix operations that haven’t yet been taken advantage of. For example, if core electrons can end up at significant percentages of lightspeed, could there be some sort of inverse effect, where electrons for lower numbered elements are actually SLOWER than they should be (but we wouldn’t know that because we consider such speeds ‘normal’)?

    Jess Tauber

  285. I disagree with you Philip. Perhaps there is an optimal periodic table, one that best represents the periodic system in the sense of natural kinships between elements. To say that periodic tables are subjective outcomes of our choices is ‘copping out’ in my view.

    I am a realist when it comes to the periodic table. I believe that we / Mendeleev have discovered something about the way that the world really is and not that the periodic table is a result of certain choices.

    I believe that seeking the optimal periodic table is a legitimate activity and the very fact that we have people all over the world arguing about the best way to approach it attests to this view.

    Now to comment briefly on Bent’s last two postings. I say “Bent” since he insists on using my last name only.

    1. Sorry to say so but I do not possess a copy of Bent’s vanity press published book. As a result, being directed to this or that particular section is of no help whatsoever.

    2. The language in the subsequent message is so idiosyncratic as to cause a further block in the transmission of information. Without wishing to state the obvious, language is supposed to convey a message to other readers or listeners. The language that Bent uses guarantees that his publications remain confined to places like vanity presses. In a field that is already crawling with cranks it is surely essential to try to be as clear as possible.

    all the best

    eric scerri

  286. I do not agree with everything that prof. Bent says in regard to gaps. For example, the gaps between the blocks were shown by Janet, the author of LSPT, himself. What you see as gaps between the blocks of ADOMAH PT are “folds” in 3D ADOMAH tetrahedron. Mendeleev’s words “arranged in order of their atomic weights” do not mean “no gaps”. As long as elements are in order and there are no gaps within the blocks, the table is valid. It looks like Mendeleev was concerned with the gaps within what we now call f,d,p,s blocks. He was man of great intuition!

  287. Roy: I am not criticizing your AAE, nor am I trying to make everyone agree with me. I have said over and over again that there cannot be an ideal representation and that all our choices are the subjective outcome of our various objectives. It is wonderful that there is such a huge and varied collection of images.

    That does not take away the fact that there is a pattern in the structure and behaviour of the elements,which is what I called ‘chemcial truth’, and that we should try to represent at least some aspects of it, even though it is not possible to represent all aspects at once.

  288. Philip,
    Your most recent objection was that the AAE was “not a Platonic form”, but now you move to your concern with “the Platonically ideal”. Perhaps the shift is not quite from apples to oranges, but nonetheless, does not follow.
    You repeatedly introduce the aesthetic principle, not I, who confess that appearance was never my goal – I leave “Art for Art’s sake”. You do it to support the effort you made to have the Galaxy a “balance [of] beauty and chemical truth”, and that other PT representations should be judged by those, to me; conflicting, standards.
    The AAE, on the other hand, was developed solely to correct the 2D table’s misrepresentation of Mendeleev’s Law, it’s appearance a result of functionality, with the traditional tabular form made corporeal without losing any of the table’s inherent capabilities or relationships (but adding some), being permissive of displaying any & all element information (text, symbols, numbers, drawings, pictures) on an easy to find and read surface forming an easy to make, hold, and keep model.
    Thanks for recognizing that the AAE is informative. That was my sole goal.
    I will not comment on the aesthetic success of your Galaxy – too subjective – but I fear that the introduction of a mystery element to start off with, the amount of missing data (for elements, blocks, and periods), plus retention of the gaps (stretches?), do not serve the new student well.
    All of us on this blog appear to be doing our best to uphold a conclusion we made some time ago (try as we may to appear objective and respectful), that the world would be a better place if all the others agreed with our view. But those of us who are concerned with the introduction to Chemistry should not be excused from proposing that first steps into the science be knee-deep into misinformation and misdirection.
    All the best,
    P.S. You should enjoy the article; The Final Chemistry Frontier in Science News, the latest support of your early appreciation of the extraordinary drama of elements in space.

  289. Philip,

    thank you for your appreciation of Adomah PT. I would like to add that, Adomah is even more beautiful for the “inner eye”, than for the “outer eye”, as prof. Bent likes to say. I personnaly was impressed when I saw your Chemical Galaxy in Science News magazine. It is thought provoking and extremely beautiful.

    AAE and, so called, Mendeleev’s flower, are good attempt to retain continuity with few interesting side effects. It is only couple steps away from the traditional Depiction. Not as symmetric and beautiful as the real flower though.

    Again, I would like to quote prof. Bent: “the primary goal of the Periodic Table is to demonstrate primary kinships”. I think, if attempt is made to treat elements as simple bodies and to capture all kinships and relationships, the product will not be symmetric and beautiful at all.

  290. Professor Bent is back with another essay (after fighting snow storm, I am sure):

    Rules of the Game
    A game’s rules are the game in a nutshell. No rules, no game. Good rules, good games:
    football, basketball, soccer, cricket, tennis, chess, card games, &c. One might include
    poetry. (Prose, in contrast, said Robert Frost, is like playing tennis with the net down.)
    Languages have rules of grammar, banks regulations, and journals guidelines for authors.
    Arithmetic, algebra, and geometry, quantum mechanics and thermodynamics, crystal
    chemistry, graphic formulas for molecules, and other areas of mathematics and science are
    deemed “mature” when they’ve been axiomatized.
    Societies are deemed “civilized” when they’ve evolved rules of conduct for living together.
    Questions Regarding Graphic Representations of the Periodic Law
    • What are their rules of construction?
    • Are the rules “natural”? Non-arbitrary? Self-evident?
    • Can the representations be fully described simply?
    Answers for the Left-Step Periodic Table
    Cut Mendeleev’s line-up of the elements and translate segments, so that –
    • Congeners appear in vertical columns (the easiest of all arrangements to scan).
    • Columns and rows have no gaps. (Gaps meant to Mendeleev missing elements.)
    • The construction is read for increasing atomic numbers left-to-right, top down.
    • If in doubt regarding an element’s proper location, place it so as to maximize the
    construction’s overall regularity (for a concordance with atomic physics).
    N.B. Side-stepped are references to “electrons” and “orbitals”. A concordance with atomic
    physics is remarkable, but marred by irregularities. The table is “natural” in that it can also
    be generate, independently, without knowledge of chemistry, through use of atoms’ firststage
    ionization energies (and atomic numbers).
    The Left-Step Table may be simply described:
    • Symbols of the elements appear in horizontal, right-justified paired-periods of lengths
    2n2, n = 1 – 4, for Z through 120. (Created are steps or blocks of width 2L + 1 and
    columns of height 8 – 2L, fo Z through 120, where L is the ordinal number of the
    block, beginning at 0 for the 2-column block on the right.)
    • The table has no irregularities in the lengths of its rows and columns.
    The Left-Step Periodic Table is the only tabular representation of the Periodic Law that has
    no irregularities (in lengths of periods and columns) and no gaps.*
    All representations of the Periodic Law are topologically equivalent string-figures. All of them
    can be stretched into Mendeleev’s line and, accordingly, into each other. Because regularities
    are more easily destroyed than created, the Left-Step Table of no irregularities (and no
    gaps) is the representation most easily transformed into other, less regular representations.
    It’s easily turned into a spiral, wrapped on a cylinder, and transformed into a step-pyramid
    table, the conventional periodic table, and a three-dimensional front-step table.
    * Moving H and He from their positions above Li and Be to positions above F and Ne destroys the
    length rules for periods and columns and changes the widths of the last two blocks on the right
    from 2 and 6 [= 2(2L + 2)] to 4 and 4 (of no physical significance in the present context).

  291. Roy, I think you are confusing the beautiful with the Platonically ideal. The Periodic System is not a simple and regular pattern, such as Plato might have regarded as ideal (see his theory that the atoms of the four elements were four of the platonic solids), but that does not mean that a represetation of it cannot be beautiful. Most are not, which is no fault, because their creators sought practical usefulness, not beauty. I tried to balance beauty and chemical truth in my ‘galaxy’, inspired by the lovely mural of the artist Edgar Longman. Among tables, I think Adomah is the most beautiful – not the Samarra Minaret but the profile of the Dubai Tower. Eric Scerri’s halogen-to-oxygen table is beautifully balanced, but only at the cost of losing fidelity to electronic structure and removing the lanthan-actinides from the sequence. Among 3D representations the AAE is informative but I do not find it beautiful. The most artistic is perhaps Crookes’s ‘pretzel’.

  292. I received another email form prof. Bent. Please, see below:

    For my response to Scerri’s first question, see “New Ideas”, Sections 40, 41; for his second question, Sections 61 through 70. Mendeleev’s “basic substances” and Bohr’s Atom Aufbau Process are two different things. Henry

  293. Philip:
    Your complaint that the AAE is not a Platonic form surprised me, as previously you dismissed leaving “…the messy world of everyday bodies and drift[ing] off into Platonic mysticism”.

    Regarding the kinship of the AAE with the “Stedman/Benfey shape”, that is accurate, also to Courtines, Werner, de Chancourtois, and, of course Mendeleev. It is unclear whether Gamov’s work chronologically preceded me in development of an almost identical arrangement, nor have I determined when the author of developed his “Mendeleyev-Chancourtois Flower”, also reminiscent of the AAE both in original approach as well as final product. (His form is aesthetically motivated, and, as you have approved: “A ribbon wound in three dimensions…”)

    While at the time of my invention I was blithely innocent of any periodic table influences beyond Mendeleev’s Law and table, Hubbard’s and Seaborg’s changes, and the authority of Sargent-Welch’s prints, my much later chemistry professor consultants, patent examiners, and Administrative Patent Judges appear to have been equally ignorant.

    My very initial interest was to straighten out, for my own peace of mind, an accidentally observed clear infraction of the Periodic Law by the only table I had ever seen, which was resolved quickly and easily, as any professional educational designer (with no chemistry training at all) might have, unencumbered by knowledge of the intrinsic properties of the elements or the relationships/links between them – other than colors, groups and numbers.

    Never was it my goal to create a thing of beauty.

    In appearance, your effort to create both a Platonic form and a Platonic Form, is like a plan view of your prime example, the Samarra Minaret, with extra spirals. That structure, with interruptions, becomes the Tower of Babel, as does any flat periodic table with its many cuts (or stretches) in Mendeleev’s line, an observation which turned me away from Chemistry at a young age – much as you left, disappointed that your teacher refused to accept “hydrogen belongs with carbon”.

    If achieving elegance, as you put it, requires “stretching the loops”, then it will be done at the expense of the Periodic Law, as do cuts in other 2D versions.

  294. Roy: Whatever you call your AAE, it is not a Platonic form, and its projection on to a plane is the Stedman/Benfey shape with all its bulges. A more elegant 3D shape would be like the Samarra Minaret. To achieve elegance in 2D you have to stretch the loops.

  295. You admit to the gaps, Philip. You use strings to bridge them.
    The gaps are the result of moving from a 3D arrangement to two dimensions.
    Nothing else that exists is only 2D, why should the periodic table be pictured as such?
    De Chancourtois showed Mendeleev the way, but Dmitri drew up his system for a book – hence the flat table.
    What’s Chemistry’s problem today? Dogma?

  296. The gaps are part of the reality. How neat it would be if each electron shell had a fixed number more of electrons than the one below; then we would have a perfect conic spiral. But they don’t. Hence all our stretching and snipping. Plato had similar problems with musical scales, which we gloss over with our logarithmic keyboards. Plato’s god didn’t do maths the way Plato wopuld have wanted.

  297. I was talking about Traditional depiction, not AAE. There is gap between Sr-Yb in long form of traditional PT. AAE is your attempt to get rid of gaps. Chemical Galaxy is another.

  298. I think the reason that we are still looking for the best depiction of the Periodic Table is the fact that traditional PT has literally so many gaps in it: H-He, Be-B, Mg-Al, Sr-Yb…..

  299. Isn’t this year the 150th anniversery of the big conference in Karlsruhe? Perhaps something can be arranged, if not in person (given the economic situation), then an electronic venue a little more formal than a blog?

    Jess Tauber

  300. Not another blog?! People seem to have an endless fascination with the Periodic System. I suspect it has a psychological explanation. We evolved to seek and create patterns in everything, and here is a gigantic pattern that reaches into the hearts of the stars and the cells of our bodies. We just can’t stop worrying at it and trying to express it more perfectly. But there is a law of diminishing returns. Nothing that anyone says now can bring back the excitement that greeted the findings of Mendeleev or Moseley or Bohr or Meitner. Perhaps it’s time to think of something else.

  301. Congratulations to Roy Alexander on having his work featured in an article in the latest issue of Chemistry & Industry in the UK. (Feb 2010 issue).

    eric scerri

  302. I don’t know yet. Perhaps we could let him write in French and then one of us can translate for you.

    It was because I wrote a sentence in French in response to Philip’s joke that he contacted me again to say that he is interested in participating in this debate.

    all the best

  303. Eric,

    This is a good idea, however, I can not read French. How are you going to make him to write in English?

  304. I have had som e private correspondence with Pierre Demers from Quebec, Canada and would like to invite him to make a statement about his preferred periodic system and how it relates to Valery’s in particular.

    all the best

    eric scerri

  305. Philip, you are right- by Jensen’s own definition, of oxidation state of +4 following one of +3. Last night I color-coded all oxidation states from +0 to +8 and used this to create, on paper, the patterning of the maximum oxidation states of the elements on the angled ring tetrahedron.

    The system is irregular, but nonrandom. Pr sits abutting the C-Ti-Ce group, +4, when the next element down in the 2D table is +5, on the other side of the tetrahedron. thus offsetting rotational symmetry described in my last post.

    In addition, there are two other blocks of +4, approximately symmetrically arranged near the two lower vertices of the tetrahedron; Tb, Ni, and Cu on one side, and Pd, Cm, Bk, Cf on the other.

    But even here one sees what looks like hints of fuller underlying, though now distorted, symmetry, as if ideally there were small wedges of contiguous spheres of +4 near each vertex, located and oriented in ‘pinwheel’ fashion, some spheres having been shifted to other numbers.

    Similar issues are seen with the other oxidation numbers, creating the overall impression of an underlyingly 4-way symmetrical object where there was competition between processes or forces, and ‘winning’ states had been negotiated differentially over the whole. By the way, in linguistics this is the domain of ‘Optimality Theory’.

    I do still wonder, though, whether the pattern would change under different environmental conditions, under extreme pressure and temperature, for instance (where everything is supposed to push toward metallic status), or at extreme velocities (for example near light speed), or in extreme gravitational fields (near black holes, with ‘spaghettification’), or in gigantic magnetic fields. IS there even ‘chemistry’ in the latter three environments?

    Could we predict all the shifts in the PT as we alter the external environmental conditions (and include isotopes for completeness)?

    Jess Tauber

  306. In Prof. Bent’s ‘Fresh Energy..’, on page 71 he describes the ‘Jensen Tree’ which connects all the elements that have a maximum +4 oxidation (C, Si, Ti, Ge, Zr, Sn, Ce, Hf. Pb, Th, Rf, 114).

    Turns out that in the angled ring tetrahedral system I’m still investigating, these elements form two coherent flat triangular blocks containing 6 spheres each. The first block:

    Ti Ge
    Ce Hf Pb

    where C and Ce occupy tetrahedral edges, Ti, Hf, and Pb faces, and Ge is body-internal.
    On the other side of the tetraherdron, rotated 180 degrees, are:

    Zr Sn
    Th Rf 114

    where Si and Th occupy tetrahedral edges, Zr, Rf, and 114 faces, and Sn is body-internal.

    I hadn’t realized that oxidation states might form coherent blocks of spheres. I’ll have to look now and see if other numbers associate similarly. I’ll be finished reading the book in a day or two, and will have questions for Prof. Bent, if he is so inclined.

    Jess Tauber

  307. Merci Philipe,

    Pour le moment je n’ai aucunne intention de changer d’idee. Mais on ne sait jamais!

    One might also say, third time lucky!


  308. The Wikipedia article shows Janet’s ‘Essai no. 1’, which he introduced in May 1928 and discarded in November of the same year. Simmons independently reinvented it in 1947 and discarded it in 1948 (JCE). Both authors replaced it by the 8-row LSPT, Janet on grounds of regularity and symmetry, Simmons in order to be faithful to the electronic structure. Perhaps Eric will discard it too; ‘Jamais deux sans trois!’ Someone should replace the Wiki illlustration by Janet’s final version.

    I saw Theo Gray’s luscious book today – a real work of art! I’m not sure I’d learn much chemistry from it, but I need to look at it more closely. I gave up school chemistry at age 15 because it didn’t stimulate my imagination. The lumps of stuff in the little bottles in the lab did not look the least bit exciting. I wanted to know what was on the surface of Venus and in the atmosphere of Jupiter.

  309. Dear Neil,

    Thank you for your input.

    I looked at the Wiki entry for alternative tables. On clicking on the word left-step table I was taken to a rather mysterious table. What indeed is the origin of this table? As Philip Stewart has pointed out Janet published this table before I did and promptly discarded it.

    eric scerri

  310. In addition to which I think this explanation of Bent’s, which appears in Journal of Chemical Education, is erroneous as I have argued in the International Journal of Quantum Chemistry. There and in several other publications I also discuss the question of elements as basic substance and as simple substance in more depth. Incidentally Theo, the terminology is due to Paneth.
    I have just popularized it.

    all the best
    eric scerri

  311. I agree with Theo Grey. The display of elements as simple substances is just as important and as he implies doing so heightens the need for a deeper discussion of how elements persist in compounds. The latter is the central idea in the philosophy of chemistry as I see it.

    I asked David Bradley to withdraw my rather impulsive remark of yesterday. Thanks for doing so David.

    Let me replace it with the following version.

    What exactly does Bent mean when he says elements as basic substances are to be identified with “atomic cores”? And why did he take an entire paper to argue that he and a colleague at U of Wisconsin had explained the n + l rule for the filling of electron shells in atoms and not atomic cores?

    Eric Scerri

  312. The premise of this discussion is alternative 2-D representations; as implied by the word “table,” with the corollary being representations for print media.

    These days, however, we have alternative electronic media, e.g., touch-screen mobile devices, which allow for both 2-D and (virtual) 3-D representations with animated motion. These new media permit alternative actions, e.g., swiveling and drill-down, and are starting to compete with conventional 2-D print media, e.g., e-Readers. All this makes feasible previously cumbersome 2-D and 3-D representations of the PT, e.g., helical, tetrahedral, etc. See for other examples. In this burgeoning electronic milieu, any consideration of “improved” 2-D representations may already be obsolete.

    I also note with interest in the wiki list, a (dead) link to “Janet’s left-step PT.” Does that represent prior art to Scerri?

  313. Your points about presenting science to children are well taken. Education is very important. However, some issues that we are talking about here go beyond just teaching simplified concepts to children. How about better understanding of the peridicity for those who teach?How many chemists understand the difference between primary and secondary or tertiary triads, for example?

  314. I appreciate the importance of communicating the difference between simple and basic substances in Scerri’s terminology, but I must beg to differ with Stewart’s claim that children are not excited by pictures of lumps of metal. And I have experimental evidence to prove it…. My own periodic table poster ( is one of the most popular items for sale in many of the larger science museum gift shops in the US, largely because children like it. This is entirely due to the fact that instead of facts and figures, it consists of nothing but pictures of lumps of metals. Granted, we did go to some effort to select particularly attractive lumps of metal, and took full advantage of the few elements that are not. But nevertheless, it is the pictures alone that sell the poster.
    I must also strongly disagree with the claim that this confuses or diminishes children’s understand of the dual nature of elements as simple vs. basic substances. I think quite the opposite is true. Presented with a conventional periodic table, most students have no point of reference to compare basic vs. simple. They have simply never seen the elements in their simple form. But give them a picture of, say, chlorine as a pale yellow gas, and now you have a starting point from which to discuss the question of how chlorine can be both a toxic yellow gas and part of table salt. Show them that calcium is a shiny metal, and it suddenly becomes considerably more interesting that calcium is also in milk and chalk. Prior to seeing the silvery metal form, most children (and probably not a few adults) assume that calcium is a chalky white element.
    I have received comments from numerous chemistry teachers, mostly at the high school and junior high level, that my poster and other picture-based periodic table products are instrumental in stimulating student interest in chemistry, and serve as a jumping-off point for a discussion of the elements and how they relate to chemistry.
    In the modern world we are awash with facts and figures: No one lacks for access to the electronegativity of scandium, should the need arise, and every classroom already has a conventional numbers-based periodic table. We are overloaded with information about the elements as basic substances. What photos do is tie those abstract facts and figures to the concrete reality that elements are *also* simple substances, things you can actually pick up and drop on your foot, as I like to say.
    P.S. While we’re at it, I might as well include a shameless plug for my new book The Elements, which shamelessly parades the elements in pictures, though unlike my poster, it also includes compounds and applications, and thus arguably represents them as both simple and basic substances. See

  315. It is, Philip, unfortunate that science instructors find it difficult to fit The Dragon’s Egg into the introduction to Chemistry part of their curriculum. Perhaps students would learn the wonders of elements on their own, as pre-teens, if JK Rowling comes up with Harry Potter and the Seconds After the Big Bang (following your outline), to find Nature at least as equally engrossing as the supernatural.
    And we know the depth of insight into matter that freshmen bring to Chem 101, and how instantly enamored and excited they are of the prospect of decoding the chart on the inside cover of their chemistry book – each box just chock full of big and little numbers, some in stacks, some with many to the right of decimal points, with one and two letter mystery codes and many with long and unpronounceable words with a variety of background colors. …Oh, and don’t forget the little circles with few or many dots, and line drawings with few or many sharp corners.

    Effective instruction of the majority of pupils needs to take a more pragmatic route, and count on students’ prior experience of the “accidental effect of the conditions” of the surface of the Earth with its narrow temperature range for them to exist, and when they have seen what they know organized in a way that is new and amazing, the real chemistry teaching with all its complexity and novelty can begin on a firmer foundation.

    “Walk before we run.”

  316. Oops! Revealing slip! I had just been wondering why the six d electrons of Fe and Ru do NOT form a complete eight with the s electrons; not ‘outer’ enough I suppose (but there is OsVIII. What would Hs be like?).

  317. Whether an element as simple substance is a gas, liquid or solid, monatomic, diatomic, crystalline or amorphous is the accidental effect of the conditions under which it is observed. It is remarkable that so much about chemical behaviour on earth’s surface can be explained by the more abstract character of the ‘basic’ substances.

    I don’t think children are excited by pictures of lumps of metal (most of which look very similar). It is more stimulating to the imagination to know that the elements we see on earth are created in the heart of a supernova, blown into space to condense into suns and planets, dissoved in seas of liquid nitrogen, crushed to vast densities in a neuron star… I would want every thirteen-year- old to read, for example, TheDragon’s Egg by Robert Forward. And for adults Life Beyond Earth by Feinberg and Shapiro…

    I think the peculiar behaviour of He can be explained in terms of the remarkable completeness of an octave of outer electrons (which Newlands anticipated, but on a wrong basis). Helium is the only element with a full s shell that cannot be complemented by six d electrons.

  318. I like Jess Tauber’s remark that “one might be able to create an algorithm that takes one on a well-motivated journey through the various lower dimensional projections.” For students, I like the “journey” fdps —> a step-pyramid table (for exhibiting with tie-lines non-primary kinships) —> sfdp —> s(f-footnoted)dp (the conventional table, currently) —> a modern version of Mendeleev’s “short form” table (for exhibition of secondary kinships by adjacency).

    I like Philip Stewart’s remark about periodic tables not being about simple substances [such as inert gases, which locates helium above neon] but, rather, about ‘basic substances’ [which I take to be atomic cores (not atoms, as Scerri says I have)], as Mendeleev astutely realized, and emphasized (followed by Paneth and others).


  319. Valery asked, in reference to “.. .you have reinvented the Alexander Arrangement…” –
    “Is that when I sarcastically suggested to wrap continuous lines around Traditional Periodic table in order to connect right side of it with the left?”

    Yes, Valery, the p-block down-slant connects the end of one period (“the right side”) with the beginning of the next (“the left”), and, with the inclusion of the looped d- block, rids the arrangement of the familiar cuts in the top center of the ordinary flat table, and the f-block loop re-integrates the La/Ac block Seaborg shunted away.
    Probably too easy a solution for real thinkers, but perhaps a gentle enough approach for the new student to segue into a table described by yourself and Jess Tauber.
    And for those seeking kinships, there are nine (count ’em) nine shown at, and they are only ones mentioned in your emails and on this blog sofar. Can you see more, now that you have a DeskTopper?

  320. To give an idea of the angled ring system, see page 5, number D in the illustrations. This is what one triangular face of my T3 tetrahedron looks like, though I turn it upside down comparted to the illustration for the two upper faces, while the two lower triangular faces look like the illustration without any change, which you would see if one rotated the tetrahedron a quarter turn CW or CCW..

    In the close-packed sphere system, the smallest triangle represents 3 of 4 s elements (the first two periods at one end at the top), and 3 of 4 s block elements in periods 7 and 8 down below. The next V outward is 7 spheres in 2 and 3p on the upper side, and the same for 6 and 7 p for the lower. The next larger V is 11 spheres for 3 and 4d up top, and 5 and 6d below, and finally the outermost V represents 15 spheres for 4 and 5f, the same for both upper and lower ends.

    Because the V’s link at their ends, doubled V’s give the angled rings of 2x these numbers minus 2 spheres: 4 for s, 12 for p, 20 for d, and 28 for f. The tetrahedron internally contains hidden s and p rings (a total of 20 spheres, representing 1 more p ring for 12, and 2 more s rings of 4 each).

    Jess Tauber

  321. Roy wrote,

    “.. .you have reinvented Alexandr Arrangement…”.

    Is that when I sarcastically suggested to wrap continuous lines around Traditional Periodic table in order to connect right side of it with the left?

  322. Jess,

    Roy is right. You can not keep describing something that exists in your mind only. At one point your have to introduce some images so people could better understand what you are talking about.

  323. Perhaps someone can post a URL here for an image and details of several periodic arrangements repeatedly referenced, such as Jess Tauber’s angled ring system, Henry Bent’s three helices, and Melinda Green’s organic fractal.

  324. Pure logic Valery, you have just re-invented the Alexander Arrangement (less the looping to avoid cuts and the down-slant in the p-block).
    Not really new since de Chancourtois.

  325. I think, if we try to reflect quantum mechanical features of the elements we should look at how many variables we are dealing with and take similar approach to that of mathematicians.

    Shrodinger equation has three quantum variables: n, l and ml. If we take only two “n” and “l”, as in Madelung diagram, they shoud be presented as abscissa and and ordinate. That is how mathematicians present it. That should be the basis for two dimensional representation. If we want to expand it to 3rd dimension, third axis should be added “ml”. In this case, as I mentioned before, Madelung rule diagram becomes tetrahedral.

    Now, you will probably say: “here he goes again, mentions his tetrahedron”. But this is neither my choice, nor my goal to fit the PT into tetrahedron. This happens NATURALLY! Don’t you see? Do I like it? Yes. Do I like Chemical Galaxy? Yes, also. Do I like Roy Alexandr’s pen holder and Melinda’s fractals? Yes. But this is not a matter of preference. This is what it is, the tetrahedron is natural representation of n+l rule in 3D! And “n+l” rule is first out of 3 rules that constitute the Periodic Law.

  326. After reading more of Bent’s book and thinking again about possible relations between unusual kinships, I’ve got something that might be of use, if not in its current form. In his graphic depiction of highest oxidation state anomalies, Bent tries to demonstrate that He is the (sole? but Be too perhaps) major anomaly for the s block, then the upper/right members of the p block, similar types of anomalies in d and f. The numbers of actual elements involved grow horizontally with increasing l.

    But there seems also to be the beginnings of a pattern when it comes to diagonals (only involving s and p transitions), diagonals (only involving d and p transitions), etc.
    There is no mismatch when only considering H, He, Li, Be.

    So is the pattern somewhat dyadic in nature? 0 steps to the right around periods 1 and 2 in s, 1 step to the right around periods 3, 4 in s (diagonals), then shifting 2 steps to the right around periods 5 and 6 in s (knight’s moves, though only easily seen in d and p blocks), and hypothetically and ideally (numerologically) 3 moves to the right around periods 7 and 8 in s.

    There might be interferences for the f block that prevent the 3 moves to the right from showing up fully for period 7.

    As for multidimensionality, I’ve been thinking in terms of all-spatial dimensions, but this may be a mistake. The real world is 3 spatial and 1 temporal (plus other hidden dimensions that may add up to 16 in total, with 4 timelike and 12 spacelike, of which normal spacetime might only be a quarter of the total).

    If a fourth dimension for the periodic system is timelike, then perhaps it is also quantized. Could this explain numbers of steps to the right with increasing dyadic number? And as relativistic effects accumulate on electrons for higher elements, relativity being more of a continuous thing and somewhat at cross-purposes to quantization, could this be a possible source of interference preventing a 3-step from fully showing up?

    Could these effects (including aufbau anomalies) all be linked through distortions of TIME?

    Now, if there is some sort of tension between quantization on the one hand, and continuous variation on the other, might we see it in the increasing gentleness of changes of properties with increasing n, l, etc.? In my angled ring system, the s block is a mostly vertical axis running 4 rings deep through the tetrahdron from the center of one edge through to its perpendicular mate on the other side, but as one goes out to the f-ring numbers of rings in the stack decrease from 4 in s, to 3 in p, to 2 in d, and just 1 for f. Does this number change iconically describe smoothness of property changes as numbers of m sub l states increases?

    How do these facts pattern in TIME is considered? Does it take time for electrons to exchange (since they aren’t fixed into particular slots)? Remember that if energy and mass can interchange according to Einstein, the space and time must be able to as well (time-dilation, foreshortening, but also some sort of weird rotation I recently read about).

    Would the addition of a time dimension also smooth out some of the angularity of the tetrahedral system (at least mine anyway)? Things to think about.

    Jess Tauber

  327. If the choice of an ‘optimal’ periodic chart is subjective, we should not expect agreement. What each prefers will be a matter of personal taste, interest and priorities. All we can hope for is a better understanding of why people prefer what they do. For me, Janet’s helix on nested cylinders is the most perfect alliance of the beauty and truth of the system. And of course I ike my ‘galaxy’.

  328. Well, if you like continuity, I can suggest another PT formulation here:
    Let’s take traditional periodic table and wrap it with continuois lines just to preserve continuity between its left and right sides. Have I just invented new formulation of the Periodic Law?


  329. New students already “think in terms of simple substances”, therefore, providing recognizable elements in a rational arrangement while introducing a concept of organization and relationships (without misrepresentation) can be a welcome less abrupt step to absorbtion of more technical data on a flattened chart, which has traditionally been a major psychological hurdle.

  330. If the possibility exists, as Jess suggests, that “the periodic system is capturable in its entirety only in multiple dimensions”, the problem may not be that a 3DPT will be able to “get everything”, but whether the professionals will be able to conclude just what constitutes “everything”.
    You all don’t seem to be getting any closer to agreement.

  331. I don’t go with Henry Bent’s statement that helical/spiral representations ‘do not exhibit integers that indicate period’s ordinal numbers’. There is nothing to stop such numbers being inserted, as well as any other information that is desired. The structure of increasingly long pairs of loops is clearly visible even without numbers. There is a problem in any graphic representation that overcharging with detail will detract from the overall picture.

    The current fashion is for tables that have a little picture to illustrate each element – often a photo for elements that are solid or liquid at standard temperature and pressure. I think this is a mistake, because it encourages people to think in terms of simple substances rather than the abstract ‘basic substances’ to which Scerri has rightly drawn our attention.

    Janet presented two diagrams of the n+l rule. Both use a spiral line. It seems to me to be a good way to indicate the continuity in an x/y graph.

  332. Well, IF it turns out that the periodic system is capturable in its entirety only in multiple dimensions, then there aren’t any 2 or 3D representations that will get everything- one will have to choose what goes in, and what stays out. However, one might be able to create an algorithm that takes one on a well-motivated journey through the various lower dimensional projections.

    Jess Tauber

  333. This is what Henry Bent has to say in regard to tabular and non-tabular depictions:
    (received on 02-01-10)

    Periodic Table’s Periods

    Artifacts of periodic tables or fundamental features of the Periodic System? And if so, where should they end? Or start?

    Graphical, Two-DIMENSIONAL representations of the Periodic Law are of two types: tabular and non-tabular.

    Non-tabular representations with their continuous race-course formats or small and large intestinal loops generally do not exhibit integers that indicate periods’ ordinal numbers.

    On the other hand, Periodic Tables, qua tables [orderly arrangements of data, esp. ones in which the data are arranged in columns and rows in essentially rectangular forms (The American Heritage Dictionary)] feature periods, of two kinds: sfdp and fdps.

    In s(f)dp periodic tables, often referred to originally as “oxidation tables”, periods start with elements of a Group of elements whose maximum oxidation number is +1. (After discovery of the noble gases and before discovery of the di- and tetra-fluorides of xenon, the first group was often the Noble Gas Group, Group number 0.)

    In fdps periodic tables, periods end with the Alkaline Earth Metals Group. That arrangement can be captured, purely chemically, as in the case of early “oxidation tables”, without reference to electrons and orbitals, by cutting a line-up of the elements by atomic number annotated with generic symbols for elements of the commonly named Groups (Halogens, Noble Gases, Alkali Metals, Alkaline Earth Metals, Coinage Metals, and Volatile Metals) so as to line up vertically elements in the same Group in a table that is read for increasing atomic numbers in the usual manner, left-to-right top down, and that has no gaps in its columns and periods. One such table exists: the fdps, “Left-Step Periodic Table”.

    Both sfdp and fdps periods have a quantum mechanical interpretation: sfdp periods start when the differentiating electrons in Bohr’s Aufbau Process adopt a new value for the principal quantum number n; fdps periods start when the Madelulng Parameter n + l for the order of occupancy of orbitals in Bohr’s Aufbau Process adopts a new value.

    The periods, sfdp and fdps, exhibit, jointly, two different trans-table trends.

    Along sfdp periods nonmetallic character and the acidity of elements’ highest oxides generally increase, left to right. Along first rows of blocks arranged as in fdps periods elements’ distinctiveness with respect to their congeners and first-row neighbors increases left-to-right (provided helium is located above beryllium).


    Periods are a fundamental feature of the Periodic System.
    There are two natural kinds of periods. Both kinds –
    Can be captured solely from chemical data.
    Have quantum mechanical indices that describe where they start.
    Have associated with them an important trans-table trend.
    Elimination of periods would greatly impoverish the Periodic System.
    Periods give the Periodic System in its tabular expressions it periodic character.
    The continuity of atomic numbers featured by non-tabular graphic representations of the Periodic Law is expressed in tabular representations by the well-known convention that periodic tables are to be read for increasing atomic numbers left-to-right top down.

    Henry A. Bent

    Philip, in your article about Janet you have Janet’s n+l diagram that is very close to contemporary depiction of Madelung rule. The difference is continuous line that connect left side of the diagram with the right side. Do you consider that a spiral representation of n+l rule? Those lines are nice , but hardly necessary features.

    I tend to agree with Dr. Bent that tabular depictions of the periodic system better reflect important information in regard to quantum mechanical features of the elements than continuous representations.


  334. It is years since I saw a good science programme on TV. It’s all had to be dumbed down in the interests of ratings. The world is ruled by corporations and their accountants. The exploding of the hydrogen-filled soap bubbles was a lovely moment though.

    Optimality is a value judgment and therefore inevitably subjective. For me the optimal representation of the Periodic System cannot be a table but should be some form of 2-D spiral or 3-D helix.

  335. I have to agree Eric, the BBC program hosted by Jim Al-Khalili is typical of the format for TV documentaries these days. Content is repeated throughout the program (presumably to sustain the attention of American viewers faced with ad constant breaks) so no real depth is ever achieved and one has to dangle from only the simplest of intellectual threads in each episode. I’m sure historians and others in various fields have the same complaints about “their” documentaries, particularly those where a US producer is a collaborator/backer.

    Jim is gettng good at the presenting lark, he comes across as knowledgeable and awed at the same time. His previous series about Arab/Islamic science and maths was very good. But, if the content isn’t strong…

  336. People in this group may be interested to see a TV series from the BBC in the UK on the elements and the periodic table.

    They can be downloaded with some difficulty or much easier just go to youtube and search for

    Chemistry A Volatile History.

    Episodes 1 and 2 are available and there is one more, 3, to be aired in the UK on thursday. If you use youtube you will need to view six parts for each episode. These are not always presented in order on the youtube website.

    The visual quality is excellent but the academic content leaves a lot to be desired. I worked as a consultant for this series and managed to talk them out of quite a lot of mistakes but not all. The program is presented by a theoretical physicist, with the consequence that the periodic table is made to look like it is fully explained by quantum mechanics.

    Incidentally, the recent discussion on whether there is an objectively best periodic table or not is rather interesting. I will try to find time to comment. My own brief thoughts on the subject are that yes there exists one optimal objective form. I am not necessarily implying that my H in the halogens table is it. I am more interested in discussions on the criteria for an optimal table than in desperately defending one particular table.

    all the best
    eric scerri

  337. In Henry Bent’s New Ideas…Fresh Energy, on p.xv in the Short Abstract Amplified section, he defines n, the Orbital’s Principle Quantum Number, as n=r+l, where r=orbital’s radial quantum numbers. He also defines n+l to be the Madelung parameter r+2l.

    If n=r+l, then n-l= r.

    So my (n-l) has physical meaning, and isn’t just numerology? In the angled ring system, the two upper tetrahedral faces map (n+l) where upper is defined by where H is, and the lower two faces map (n-l), near element 120. Each face pair is symmetrical around one edge, and these two edges are oriented perpendicularly to each other. Does this have physical meaning, relating (n+l) at right angles to (n-l)? Magnetic fields are perpendicular to electrical ones.

    Jess Tauber

  338. The idea of a “block [being] a parallelogram instead of a rectangle” is evident in de Chancourtois’ and the Alexander Arrangement. It surprised me at the time that this feature (it needs only the p-block slanted to align periods and hold to an unbroken Mendeleev’s Line throughout the whole table) was available for patent in the early ‘70s – but no longer appears a wonder when one sees how doggedly the professionals cling to flat tables. It is clear that it takes an “amateur” as Philip Stewart refers to Charles Janet, who “derived his table from a helix arrangement “, to provide forward motion, and provide a fresh view of element relationships.
    As to the “knight’s moves” to which Melinda Green and Jess Tauber refer, the knight’s agility is multiplied when one jumps around a corner to another plane completing a tertiary kinship ( impossible in the flat table. As an amateur myself, I cannot be aware of all the “knight’s moves” (or new bishop’s moves) which, as Melinda says “could lead to ideas for discovering some hidden features of atoms and their interactions”.

  339. Valery- in the angled ring system secondary periodicity can be read directly as vertical apposition- the odd period orbitals are atop the other odd ones in sequence, and the even ones other evens.

    The rings register with each other laterally- so that (going outward from the central axis) the first members of s, p, d, and f connect in lines of spheres, on one side of an edge, and the last ones on the other side.

    Jess Tauber

  340. Actually if we ever do see element 120 anywhere, given the need for extra neutrons, we might have to conclude that it got there through the agency of intelligence, if only an ordered and highly unlikely set of circumstances were necessary to produce it. According to the rest of the movie, there are a few hundred thousand tons of it underneath San Francisco Bay, which is why cellphone service there is so bad, since it ‘aggressively’ broadcasts its own frequency spectrum! When one hits it with a rock hammer it violently breaks with a strong flash of light, and has a static electric attraction to itself, which is why the incoming meteors head directly to SF, because of the previous fall.

    What other interesting properties might the writers have missed?

    Jess Tauber

  341. Element 120 was first included in a periodic table/spiral by Janet, so it would have to be called janetium, not that we are likely ever to give it enough neutrons to have a half-life more than a nanosecond. Such stuff might exist near the surface of a neutron star though.

  342. In regard to “n-l” in ADOMAH PT, it stands for row number for each particular block. If n-l=1, for example, it means all elements in 1st rows of s,p,d and f blocks. It can also be presented as n=l+1. Then, it shows electron shell number for each 1st row in s,p,d and f blocks. It is presented by ADOMAH especially well. In tetrahedral stack of spheres “n-l” menas consecutive layers of spheres.

  343. In the Syfy channel’s movie ‘Meteor Storm’, which is playing now even as I write this, San Francisco is bombarded by waves of bullet-size meteorites which pack an overly large wallop. Aside from the mishmash of science-slaw including obvious inanities as people out in the city lights of SF to watch the shower (including folks with telescopes- I guess the light is better under street lamps), the most interesting aspect was the identification of the mystery substance of the space rocks as ‘the ever elusive element 120). They even correctly named the ‘placeholder’ specification, though some of the predicted properties don’t seem right. Someone has been paying attention, maybe one of Eric’s students who writes for movies?.

    Jess Tauber

  344. I have not checked ADOMAH for n-l paterns. It is something I need to check. Meanwhile, I made few observations in regard to secondary and tertiary kinships. The primary kinships, reflected by LSPT and ADOMAH are arrived at by adding atomic numbers one at a a time until next Alkaline Earth metal is reached. After it is reached, you start new period and add atomic numbers until the nex alkaline earth and so on, thus folding Mendeleev’s line after each alkaline earth. Same thing can be achived by counting down one atomic number at a time. If you start, for example at 120, keep subtracting atomic numbers until alkaline earth with atomic number of Ra(88) is reached and put it next to 120 and so on.

    Secondary kinships occur when you make mistake while adding atomic numbers. For example, if you counting from Ca and place next element Sc (21) next to Al (13) instead of advacing 10 points back. Another example, if you count from Ba and place La next to Y, instead of advancing 14 points back.

    Tertiary kinships happen, if mistake is made while counting down. For example, if you count down starting at Be (4) and instead of stopping at Li and placing He under Be, you miss this target and place He next to Ne. Samething happens if you counting down from Ca and instead of returning Mg next to Ca you miss the target again and continue by placing Mg next to Zn. This is how Secondary and Tertiary kinships and triads occur. Some chemists do not realize this and put all triads and kinships in the same category and it becomes very confusing. In reality, not all kinships and triads are equal. As I demonstrated here, there are at least three categories: primary, secondary and tertiary. There are also other relationships.
    You have to have LSPT or ADOMAH in front of you in order to appreciate this.


  345. I don’t remember whether I’ve written this already, but if one takes the LSTP, as a system of linked rectangular blocks, and shifts the upper edges to the right so that what were vertical relations now engage the element below and next right (so each block is now a parallelogram instead of a rectangle), then one at least geometrically motivates some of the nontraditional kinships.

    In this slanted format periods are unaltered, while normal groups now go from lower left to upper right, diagonals are now vertical, and knight’s moves go from upper right to lower left.

    Has anyone thought of this already?

    Jess Tauber

  346. Well, I noted here as well as elsewhere that in an angled ring system (at least- what about ADOMAH?) (n-1) is just as valid as (n+1). Both terms give ordered, coherent patterns, patterns that are perfectly complementary.

    Could other interactions between quantum numbers motivate some of the unusual kinships? Or aufbau anomalies? Has anyone ever looked? We already see in secondary periodicity some sort of preference for even-even or odd-odd period connection. Is there any similar kind of thing going on for groups?

    I’ve started considering whether the packed-sphere tetrahedron’s own internal structure acts as a kind of ‘computer’, of neural network type. Each sphere would count as a ‘node’, with a minimum of 3 connections, for vertices, then 6 for edge members, 9 for faces, and maximally 12 for sphere in the central subtetrahedron. Could property skews from expectations pattern based on some give and take between the spheres both locally and globally?

    Jess Tauber

  347. Charles Janet discovered the n+l rule in 1930, soon after he had read the work of Bohr and Stoner. It was the final vindication of his LSPT, which he had constructed without knowing quantum theory – an amazing feat for an amateur in his late seventies, whose main work had been in biology

  348. I agree with Philip, however I think it should also be noted that electron “addresses” within atoms include not only electron energy levels (“shells”), that are quantized by quantum number “n”, but also orbital angular momentum that is quantized by “l”. If you follow either “n” or “l”, the “irregularities” mentioned by Philip indeed happen. But no irregularities happen if “n” and “l” are combined and n+l is followed. While no one observed actual “shells” in atoms, n+l rule is strictly empirical and it is the real thing. It was discovered via spectroscopy.


  349. We live in a world on the metre scale, and our idea of the picometre world inevitably sees it in the terms familiar to us. So we imagine concentric shells of electrons, with outer shells and inner shells, and we see new electrons being added to particular ‘shells’, although other experiments tell us than an electron is not an ‘object’ that is ‘in’ a ‘place’.

    Some of our problems with the Periodic System result from these visualizations. For example, the division into ‘blocks’ reflects the notion that new electrons are added systematically into particular ‘shells’. As there are 14 f electrons, there should be 14 elements in the f ‘block’, and pesky La doesn’t have one, although it should be the first, since Ce has two, Pr three etc. So people put La in the d ‘block’, which seems to make Lu an f ‘block’ element, although Yb be has already recieved the 14th f electron, and the lanthanoid contraction makes Lu much more akin than La to Hf, Ta etc. There are a couple of dozen elements that do not fit into the neat progression; our regular representations translate the complexity into terms we think we understand.

  350. Re objectivity of natural laws- the quantum reality shows that observer choice is a component at every level, but the higher the level more choices tend to average out- like hands on a Ouija board, or the operation of nerve cells in a brain, or voters in booths.

    The lower you go the more it seems that state superposition shows that matter acts, on its own, like deer caught in the headlights, Presidents told their nations are under attack, or folks with approach/avoidance issues. Do I stay or do I go. Do I choose door number one, two, or three.

    Ultimately it comes down to larger context. Atoms don’t react identically in different external magnetic fields, or gravitational fields, or pressures. Just as with abstract feature-based phonemes in linguistics, statement of the context makes a big difference. Similarly the meaning of entire utterances changes with context.

    So Aufbau anomalies, as others have written, aren’t absolutes but results, in the context of the experiments that measure them, of state superpositions. One has to believe that, in other circumstances, the configurations would be different. Probably true also of the elements with mathematically expected configurations.

    So Helium can’t be robbed of an electron by any other element (except, perhaps, another helium ion)? Not that hard to knock electrons off by other means. What would happen if a carbon ion floated in a sea of helium atoms- no attachments of any kind?

    All the interesting secondary, tertiary, and other unusual linkages, kinships, etc. in the periodic relation show there is context involved, since these links are NOT across the board, but deal only with particular single interactions or sets of interactions.

    From the linguist’s perspective, analogous connections appear ready-made to help larger combinations of forms hang together more optimally and so help create the next hierarchical structural level. Anthropic implications? Given the crazy fundamental particle rest masses it seems that such shifts don’t even start at the level of the periodic relation. We live in slightly twisted or tweaked reality. Is the tweak lawful? Analytically transparent? Time will tell (though perhaps it has been told to keep its fat mouth shut….).

    Jess Tauber

  351. Yes, David. Because we are also part of the physical world we do affect it. In order for us to “see” a small particle we need to probe it with another particle. In the quantum world particles are so small that this simple act of probing changes their behavior. However, even if our physical act of seeing affects a photon that chooses which slit to pass through, the photon still exists and follows certain rules even when we are not there to observe it. We would not affect the behavior of a photon by thinking about physical laws that govern its motion. It happens only during our physical process of sight. You do not have to see tetrahedral PT on your wall in order to observe its connection with tetrahedral numbers. Have you tried to affect a law of physics just by thinking about it?

    As I have mentioned before, few people have noticed tetrahedral patterns in the Periodic Table completely independently. I have yet to see independent analogies of Roy’s and Melinda’s depictions of the Periodic System.


  352. @David: It is true that our perception affects what we perceive, but the point of science is to compare what is perceived in many different experiments in the hope of converging on an agreed model. I think that is a distinct question from our comprehension; we seem quite incapable of comprehending what happens at quantum level or inside black holes, but the mathematics seems to work notwithstanding. It would be astonishing if talking apes could comprehend everything.

  353. @Valery I have to pitch in with a more general philosophical comment…you say that the physical world follows physical laws irrespective of our perception. The more we find out about nature from the cosmological to the quantum the less that seems to hold. Sure, apples fall to the ground from trees but our perception very much affects the rules we apply to the universe inside black holes and beyond the Big Bang or when a photon “chooses” which slit to pass through in the classic quantum wavicle experiment.

  354. Melinda,

    I believe that your belief that tetrahedral arrangement of the periodic table is not objective is certainly subjective. It has been established long ago that physical world follows certain rules, that are called physical laws, irregardless of our perception. Why would people like you exclude the Periodic System from this is beyond my understanding.

    Perhaps you could come up with alternative explanation why atomic numbers of Be, Ca, Ba correspond to every other tetrahedral number and Mg, Sr and Ra correspond to arithmetic means of those tetrahedral numbers? Also, why n+l diagram extended into 3rd dimension to show quantum number “ml” becomes tetrahedron?

    ADOMAH PT goes beyond putting elements in boxes and drawing pretty pictures. It provides simplified algorithm for deriving electron configurations, that makes it naturally symmetric by the way. Can you become objective for a moment and admit this simple fact?

  355. Melinda: The representations have evolved in human brains and eyes and hands, but the Periodic System is a mathematical abstraction from the behaviour of real atoms and would be the same in any advanced culture on any planet. Given the symmetry of matter and anti-matter, it would probably be an identical or almost identical mathematical object in an anti-matter world.

    Representations have grown to resemble each other more and more as experimental knowledge of matter has evolved, and it should be possible to agree on a family of optimal representations. The argument over H and He is between more physics-inclined people who see the structure of atoms as primary, and chemistry-inclined people who are more interested in chemical behaviour. Eric Scerri’s latest table has been invented and dismissed twice before by Janet, 1928, and Simmonds, 1948, so perhaps Eric too will dismiss in in the end. Triads seem too superficial a feature to dictate such a deviation from mathematical regularity.

  356. @ Valery: I believe that a tetrahedral layout is just as subjective as any other, including the standard PT. None of these inventions are god-given. Some are simply more or less useful for various needs of ours. I wouldn’t be surprised if intelligent beings on other planets come up with some of the same diagrams that we do, but that wouldn’t indicate anything special about the universe, but rather something common about the goals of beings similar to ourselves. But rather than say that they’re all subjective, I’d prefer to say that none of them are objective.

    @ Jess: Regarding the 4D equivalent of the tetrahedron, it has five 3D hyper-faces, not projections. It’s best not to call this a 4D tetrahedron because there’s nothing “tetra” about it. You could call it a pentachoron but better is probably just “4-simplex”. (The tetrahedron is a 3-simplex, and the triangle is a 2-simplex). My main point is that there’s nothing particularly dimensional about elemental relationships. The relationship graphs that I talked about simply describe the connections between pairs of elements, and elements are related to each other in a lot of ways, not just two. Steps along a row or column of the standard PT describe one kind of relationship but there are more. Knight’s moves describe more graph connections, etc.

    The game that I think we’re playing on this blog involves two steps: First, choose a graph of elemental relations that we think are the most fundamentally important to our needs, and second, to find the most symmetric presentation of that graph. Arguments about how He connects to other elements involve the first step whereas arguments about the best diagrams involve the second step.

    The cubic and other lattices in various spatial dimensions that you talk about, really just describe some particularly symmetric graph layouts. I won’t say that it’s folly to try to map a popular elemental graph onto one of these regular graphs. If you do find a good mapping, then it could lead to ideas for discovering some hidden features of atoms and their interactions. The tetrahedral sphere packing model that you and others advocate is intriguing because of it’s high symmetry but chemistry is not my field so I just have no idea whether it means anything. It sure is a fun game though!


  357. Valery,
    You mention that “We have another person who has come up with similar idea in 1996. Isn’t it an indication that this tetrahedron layout is not subjective at all?”
    Acceptance doesn’t necessarily follow, it appears.
    A 3D table was the first true table, that of deChancourtois, and, more recently, I found and reported here that George Gamow (a well respected theoretical physicist and cosmologist who discovered alpha decay via quantum tunneling and worked on radioactive decay of the atomic nucleus, star formation, stellar nucleosynthesis, big bang nucleosynthesis, Cosmic Microwave Background Radiation, nucleocosmogenesis and genetics besides writing numerous books on science) developed an almost Identical 3D periodic table to the Alexander Arrangement (patent drawings compared at in the sixties, and no other on the blog responded to my offer of a gratis example of an AAE – despite being so enamored of extra dimensions that the dialogue easily drifts towards multiple dimensions.
    Two dimensions seem to be sufficient for most, but considering three may be too ordinary when the lure of double digit dimensions beckon. Few take pity on the new student.

    (How long did it take Gell-Mann to obtain acceptance?)

  358. Response to Melinda

    From what I’ve read online, a 4D hypertetrahedron has 5 TETRAHEDRAL 3D projections. I’m no mathematician, just plodding along. But since one tends to lose information from higher dimensions when projecting to lower ones, I’ve thought that one might utilize this possiblity for the unusual linkages in the PT, such as knight’s moves.

    In a regular triangular slice made up of close-packed spheres (using Pascal diagonals for count) there are maximally three different rows of spheres (maximally because for ex. the vertices only have access to two). In the traditional rectangular box depiction you only have two linear sequences- rows and columns. But because the blocks are of different heights and widths connectivities are a bit freaky- there are a good number of ways to stack or align/justify which account for part of the unusual connectivities PT workers are familiar with.

    In a tetrahedron of close-packed spheres there are, for body-internal spheres, a maximum of 12 linear sphere sequences passing through the sphere- the minimum, again for vertices, is 3.

    Unless I’m wrong, a 4D tetrahedron (or other solid) will have even more connectivity. Vertices will have at least 4 (2 for triangle slice, 3 for tetrahedron so 4 for hypertetrahedron?). Internally things are even more interesting: 3 for triangular slice, 12 for tetrahedron- anybody know what the number will be for the hypertetrahedron?

    My tetrahedral model already connects, in linear fashion, many of the unusual PT memberships that don’t fit this way in the traditional 2D tables, but not all. With an extra dimension maybe these others fit too.

    Jess Tauber

  359. I received reply from Dr. Henry Bent. Here it is, with personal details removed:

    Dear Valery

    Apologies for not replying sooner to your email requesting input regarding the triad issue.

    The modified fdps table is not new. It appeared in JCE some sixty years ago. What I gather is new are crackpot reasons for locating H above F and He above Ne.

    For many years I, like a number of other chemists, located H above F. In the fdps table, both atoms lie the same distance from the right ends of their blocks, and, accordingly, have, according to the electronic interpretation of the periodic table, the same number of valence-shell vacancies and, accordingly, are alike, in two ways. From metals, H and F accept electrons, forming the monovalent anions H- and F-, not widely different in size, and hence, crystallographically, often equivalent to each other. And with nonmetals they share electrons, in single covalent bonds and lie, consequently, on molecules’ peripheries, with comparable van der Waals radii.

    But to suppose, for such reasons, that H and F are related to each other in the Periodic Classification of the Elements by a primary kinship and, consequently, by verticality in periodic tables, is to make the same mistake Mendeleev made when he located magnesium above zinc, as both metals form solely in solution bivalent cations of about the same size, with, hence, comparable crystallographic properties. Similarly, owing to their oxidation state of +1, Mendeleev often placed the coinage metals along side the alkali metals in his short form periodic table.

    Before Mendeleev, chemists made a string of such mistakes: e.g., classification of Tl, because of Tl+, with the alkali metals; Pb, because of Pb+2, with the alkaline earth metals; Cr, because of Cr+3, with Al. Al, because of Al+3, with Sc; Ti, because of TiO2, with Si of SiO2; and V, because of VO4-3, with P of PO4-3.

    In the evolution of the Periodic System, mistaking non-primary kinships for primary kinships had a long history. It’s ironic, therefore, that a self-proclaimed historian of chemistry would make the same mistake today, if for different — and logically groundless — reasons. For today no greater sin exists, regarding periodic tables, than misattribution of chemical kinships, since that is the primary purpose of periodic tables: display of primary chemical kinships (usually by verticality) in the context of the Periodic Law, in two ways: (1) by a table-reading convention, that, for increasing atomic numbers, tables are read left-to-right top down; and (2) by race-track – like strings of elements. Of course –
    Lost when H & He are located above F & Ne are regularities in the
    Periodic System contingent on location of H & He above Li & Be.
    With H & He above F & Ne:-
    LOST is one the leading consiliences in the history of human thought: a correspondence between ordinal numbers of the Periodic System’s blocks (ordered by size) and blocks’ rows and the leading quantum numbers of atomic physics (New Ideas, Section 48).
    LOST is one of two trans-table trends: a block-to-block trend in first-elements’ distinctiveness (NI, p154) with respect to their congeners (NI, Fig. 44, p97) and with respect to their first-row neighbors (NI, Fig. 40, p87).
    The other trans-table trend is the well-known trend in sfdp periodic tables in the metal/nonmetal character of the elements and the acid/base character of their oxides.
    LOST is a simple Periodic Table Construction Rule: lay out the integers 1 – 120 in horizontal paired periods, justified at the right, of lengths 2n2, n = 1 – 4.
    LOST is a rule regarding occurrence of tertiary kinships — between atoms the same distances from the right ends of their blocks.
    LOST are trans-table rules regarding the occurrence of triads.
    Groups’ first elements are not members of primary triads (NI, Sect. 25).
    LOST are the Left-Step Periodic Table’s numerical regularities in periods’ and columns’ lengths (NI, Sect. 27). Consequently –
    LOST is the leading property of the Left-Step Table, its most important property, Einstein and Dirac might say: beauty, for the inner and the outer eye.

    To inner and outer eyes, the modified Left-Step Table is ugly.
    The losses cited above stem from failure to recognize existence of primary, secondary, and tertiary chemical kinships, and their corresponding triads (NI, Sections 80, 81, and 84).
    The H F Cl and He Ne Ar triads are tertiary, not primary, triads!
    NOT LOST with location of H and He above Li and Be are the Periodic System’s first two, leading tertiary triads: H F Cl and He Ne Ar. It’s just that they are not displayed vertically, as that would mean that all members of each triad belonged to the same Group. A similar statement holds for secondary triads, such as B Al Sc and Sc Y La. (The First Rule of Triads properly locates in periodic tables the “problem elements”: H, He, La, and Ac.)
    Advice for the Miscreant: Read cited sections in New Ideas. That exercise might terminate public exhibitions of shooting oneself in the foot.
    It’s silly — today, all things considered — to locate H above F and He above Ne.

    Called to mind is the professor who returned a student paper with the grade “-10, for an unnecessary display of ignorance.”

    I hope the previous remarks are helpful.


    Henry A. Bent

  360. -ium was a mistake. In Latin all metals ended in -um: aurum, argentum, cuprum, ferrum, hydrargyrum, plumbum, stannum… It all started to go wrong in 1755 with magnesium. So the Americans are right for once with aluminum!

  361. The names are a problem for poets – all those -iums! But come to think of it, fans of the LSPT can find comfort in the fact that helium rhymes with the alkaline earths and not with the noble gases.

  362. @Philip There’s a thought…you say Random, but I wonder whether there’s actually some hidden pattern in Lehrer’s lyrics, it’s worthy of an undergraduate project to find out surely? ;-)

  363. Jess Tauber writes:
    > In the angled ring tetrahedron both (n+1) and (n-1) appear to be meaningful, and pattern in complementary fashion on the rings and subtetrahedral faces. This makes me think that perhaps ml and ms might have a similar relationship, though ms, as ±1/2, seems hard to integrate. If ms was an integer (or if the other numbers were made into halves) things might fall into place better.
    > As for continuity and dimensionality, everyone seems to avoid 4 dimensions, which have enough linkage capacity to cover all known relations. Although a static, single representation in 4D is hard to imagine, I’ve seen dynamic hypertetrahedral depictions, but not using spheres (or hyperspheres?), nor linkages between these. A hypertetrahedron has 5 conventional 3D projections. My guess (which I’m finding hard to visualize) is that such a set (along with the inter-projection transformations) would carry all the things we argue about, and perhaps more nobody has noticed yet.
    > Jess Tauber

    I didn’t follow your first paragraph, but regarding the second, I don’t see what 4 dimensions has to do with any of this unless you’re talking about some 4 special dimensions of atomic qualities such as atomic number, atomic weight, etc. That’s because graphs don’t have any particular dimension. You can always flatten any graph onto a 2D plane, or into any other dimension for that matter. I.E. all dimensions have the same linkage capacity.

    We are looking for good or even ideal visualizations of the elemental relations graph, so in that regard you might find a highly symmetric embedding of that graph into 4 dimensions. There are lots of ways to visualize a 4-space, so you shouldn’t have to worry about that. It’s enough to just find a good embedding.

    Also I have no idea what you mean when you say that “A hypertetrahedron has 5 conventional 3D projections.” There are any number of ways to project any 4D object into 3-space.


  364. I find any rectangular layout difficult to remember: ‘Is it 3rd or 4th row down?’, ‘Is it 13th or 14th column from the left?’ Much easier with lines at different angles and curves with different radii! Rhythmic chanting helps too: a pity the Lehrer song is in random order!

  365. Something out of linguistics here- while the LSPT may be better at keeping relations between elements clearer than the traditional table, as a memory aid the traditional type may be better.

    It has been found, counterintuitively, that all the complicated sandhi rules in languages, that add little nitpicking rules about phoneme interactions of forms abutting one another, actually aid in learning these systems. Putting blocks in the wrong place is like that- they become ‘marked’ semantically in the minds of learners. The more iconic (transparent) a visual depiction becomes the easier it is to interpret, but it is harder to learn as a system. Something to think about?

    Jess Tauber

  366. Periodic table plays major role in chemical education. There is an image of it in almost every school in the world. Thousands of teachers use it daily for teaching students about the elements. However, when it comes to teaching how to write electron configurations, one thing becomes clear. IT IS DEFECTIVE !

    Yes, that is right. It has major defect, just as all other alternative depictions of the Periodic Law, including LSPT. They do not have sufficient information for writing electron configurations. That is why it requires other image to be used: Madelung Rule Diagram.

    Teachers have to do a little dance moving from PT to Madelung Rule diagram in order to explain electron configurations to confused students.

    Only ADOMAH Periodic Table merges classification system with the Madelung rule diagram and eliminates the need for teacher’s dancing. At the same time it retains all groups intact, displayed in the same order as Traditional PT.

    Best Regards,

  367. Good to be reminded of Melinda’s wonderfully organic fractal – a bit like yeast seen under the microscope! Men and dogs have quarrelled over rigidly regular representations of the Periodic System, but the universe has been going its own way, more like women and cats.

  368. @philip: I *love* the idea of a Snakes & Ladders game based on the PT! (Chutes & Ladders we call it in the US.) I’d often thought that my periodic fractal spiral version (click my name link to see) would make for a great game but didn’t know how to proceed. I think you’ve found the key. Spin the dial and move your piece along the ribbon and then roll the dice to determine probabilistically whether your new element splits or fuses, and if so, sends you to the appropriate new element. First one to Uranium wins!

    The spiral could be lofted into 3D similar to your minaret but the cylinders need not be nested. Rather you’d go twice around one cylinder, and then twice more around that one plus a second one next to the first, then twice more around those plus a third. See the diagram for that to make sense. Two things appear to be “periodic”: The main one is the “always twice around” part (probably the 2x part of Janet’s equation). The larger (fractal-like) one is in the regular way the bifurcations happen which is what my diagram emphasizes.

    I don’t think that the 3rd dimension is really needed, but if desired, I like the approach used by the folks that came up with the periodic T-shirt of the elements. ( Very clever to use molecular modeling software to relax the logical graph into a physical model! The resulting relaxed shape is very much like you’d expect from my “lofting” description above.

  369. In the angled ring tetrahedron both (n+1) and (n-1) appear to be meaningful, and pattern in complementary fashion on the rings and subtetrahedral faces. This makes me think that perhaps ml and ms might have a similar relationship, though ms, as +/-1/2, seems hard to integrate. If ms was an integer (or if the other numbers were made into halves) things might fall into place better.

    As for continuity and dimensionality, everyone seems to avoid 4 dimensions, which have enough linkage capacity to cover all known relations. Although a static, single representation in 4D is hard to imagine, I’ve seen dynamic hypertetrahedral depictions, but not using spheres (or hyperspheres?), nor linkages between these. A hypertetrahedron has 5 conventional 3D projections. My guess (which I’m finding hard to visualize) is that such a set (along with the inter-projection transformations) would carry all the things we argue about, and perhaps more nobody has noticed yet.

    Jess Tauber

  370. Well, I anticipated such responses. They are based on solid science of today. I do not expect that you will agree with all “fringe” ideas introduced here. However, saying that my (and Jess’) ideas are totally subjective and detached from reality, is going too far either.

    We agreed here that n+l is important rule for the Periodic Law. Well, n+l values are also descrete, that is “quantum”. It does appear in the radial function of solution of Shrodinger equation. Two dimensional Madelung rule diagram, tha is n+l diagram, if extended into third dimension to show quantum number “ml” does become a tetrahedron as shown at ( Too bad that no one has done it before me.
    Facts are facts.


  371. Oops! the delivery man came with my wife’s new TV, just as I was about tow write [as Eric agrees] ‘is fundamental’

    Incidentally, the continuous sequence is a construction of the human mind. The sequence of the creation of the elements in the stars was a much messier affair, more like snakes and ladders (hey, chemical snakes and ladders – any ideas for a creation-of-the-elements board game?!)

  372. The stepped pyramid is a nice physical demonstration of Janet’s sequence 2x(1^2+1^2+2^2+2^2+3^2+3^2+4^2+4^2), but it loses the continuity of the sequence, which, as Eric agrees. I would prefer something inspired by the great Minaret of Samarra,

    The tetrahedron of coloured glass spheres would be a wonderful tool to inspire and teach, but can someone make it in a form that allows it to be taken apart and put together without the balls getting muddled or lost?!

    I would not say that the punctuation of the sequence into periods is arbitrary or irrelevant, though, only that the word ‘period has been used in several different ways, so that it has lost any unambiguous meaning. Mendeleev called them ‘rows’, which is safer. Valery’s maximum N+l series shows clearly that Janet’s way of carving the sequence into rows has a firm foundation in quantum theory. And don’t forget that Janet derived his table from a helix wound on four nested cylinders; he never lost sight of the continuity.

  373. Response to Valery’s comment of Jan 21, 10.43pm,

    No I do not believe that n + l is another quantum number. Quantum numbers represent ways of labeling solutions to the Schrodinger equation for the H atom. n + l has no such significance whereas separate n and l do.

    I support Philip Stewart’s idea that the periodic system is continuous and so the question of where periods end is somewhat irrelevant. They don’t end, as such, there is just one continuous sequence within which repetitions occur. So I don’t think there is anything fundamental in supposing that periods end at the noble gases, the alkaline earths or any other group.

    The question of which group marks the end of a period is an artifact of representing the periodic system in a 2-D rectangular form.

    If one uses a circular or elliptical form there is no ‘last group’.

    I think you are attached to your version of the LST and are trying to find theoretical justifications for regarding the alkaline earths as the place where periods end.

    Why else would you be reaching for these invented new quantum numbers from the likes of Henry Bent.
    His own listing of 50 reasons why the LST is the optimal form is something of an over-kill in my view.

    One could also argue that the standard, medium long form table is theoretically founded because reading from left to right the order of filling is correctly captured, ie, s, d and then p,

    or the long form in which the order is s, f, d, p from left to right.

    It could be objected that for all its elegance the LST lists the blocks of the periodic table in terms of distance of orbitals from the nucleus, namely f, d, p, s. But order of filling is surely more fundamental than distance from nucleus.

    So you see ‘theoretical arguments’ of this kind or rather pseudo theoretical arguments are not decisive.

    all the best

    eric scerri

  374. I think we reached some common ground. I do not view our discussion as hairsplitting. We are just trying to get to the bottom. I would like to understand Eric’s position further.

    Looking at two quantum numbers “n” ,that quantizes energy, and “l” that quantizes orbital momentum, going along the line of elements in the order of atomic numbers, one can observe that those two numbers go up and down and change their values rather abruptly. On the other hand, n+l value increases in a step like manner gradually. Henry Bent suggeted that n+l, that also corresponds to period numbers in LSPT, is another quantum number. I tend to agree with him. It seems that n+l serves to regulate relationship between energy and momentum. The higher energy level, the lower momentum and vice versa. I would go as far as to suggest that n+l is even more “primary” than primary quantum number “n”. What is your opinion in that regard?

    Everybody are welcome to comment.

  375. Well, then a tetrahedron is ideal- it has symmetry, hierarchical structure, a texture, heft (you can hold it in your hand, and throw it at the teacher!). You can take it apart and put it back together. One can fashion it into jewelry, or candy with something else in the center. Makes a great paperweight. Lots of possibilities.

    Jess Tauber

  376. Bravo Philip!

    “To stimulate a child learning chemistry, we need something that appeals more to the eye and stimulates the imagination – better still a three-dimensional representation (perhaps more robust than folded paper) that can be handled and played with.”

  377. This conversation is in danger of descending into theological hair-splitting. We evolved to swing about in trees, judging the safeness of branches and the ripeness of fruit. Our brains are not adapted to seeing atomic particles. As Feynman said, nobody understands quantum mechanics. We dimly perceive the periodic pattern that emerges as protons (and neutrons) are notionally added one by one to atoms, and we grope after good ways to represent this in images that our eyes can seize. What constitutes good depends what our object is. For a chemist in a lab, some form of table – it doesn’t matter much exactly which form – is useful. To stimulate a child learning chemistry, we need something that appeals more to the eye and stimulates the imagination – better still a three-dimensional representation (perhaps more robust than folded paper) that can be handled and played with. To search for The Ideal Periodic Representation is to take leave of the messy world of everyday bodies and drift off into Platonic mysticism. Let us think of the rich variety of images that have been proposed in the last 150 years as something more like an art exhibition than a competition to achieve perfection.

  378. I agree with the first part of what you say. In my previous posting I was reporting Schwarz’s work, not necessarily agreeing with it and its consequences for the PT. Regardless of the order of filling what distinguishes the Ca atom from the Sc atom is indeed a differentiating 3d electron for which n + l = 5.

    The second statement by Valery is more problematic. Yes the usual thinking is that the periodic table is about neutral atoms but going back to the discussion about elements as basic substances, combined substances and simple substances this now raises the question of what their microscopic counter parts might be.

    According to Schwarz neutral atoms are analogous to elements as simple substances, whereas combined atoms are analogous to basic substances. This is why he places more emphasis on combined atoms and ions and considers their n rule to be more fundamental that the n + l rule for atoms.

    Again I disagree with Schwarz and have discussed this issue in a paper in International Journal of Quantum Chemistry.

    To me combined atoms are not the equivalent of basic substances. Incidentally Henry Bent holds the more incorrect view that neutral atoms represent elements as basic substances.

    This is a round about way of saying that I agree fully with Valery on the continued importance of the n + l rule but now, following Schwarz’s work, for identifying the differentiating electron rather than the order of filling.

    I hope this is not too confusing.

    eric scerri

  379. Eric says: “contrary to what textbooks state, for transition metals 4s does not in fact fill before 3d. This is confirmed by examining the Charlotte Moore tables of atomic energy levels.”

    When I talk about “n+l” I mean (and often state) the maximum value of n+l achieved by electrons in neutral atoms in groud state. That is, maximum value of n+l for Ca is 4 and maximum value of n+l for transition metals of 5th period in LSPT is 5. It does not matter in what order filling of orbitals occur in any particular atom, the maximum n+l value achived in the neutral atom is what counts. That is, Ca is the last element that corresponds to maximum n+l=4. Next element, Sc corresponds to max(n+l)=5. Jump has occured.

    As presented on my web site, list of maximum n+l values for the elements listed in order of atomic numbers:

    The jumps in max. n+l value denoted by the comas above occur always after alkaline earths. That should be enough make them special.

    I always thought that PT is meant to list abstract neutral atoms, not ions or bonded atoms.

  380. Helium is obviously not an alkaline earth metal, but if we talked about the He-Be group there would be no problem. Similarly H is not an alkali metal, whatever people say about ‘metallic hydrogen’ in the heart of Jupiter. A metal consists of cations in a sea of electrons, but naked protons in a sea of electrons would be a plasma. Again, if we talked about the H-Li group there would be no problem. We already accept that Li and Be are not typical of their groups, so putting H and He above them is just pushing the trend still further. Incidentally, astatine is hardly a halogen, and element 118 if we could ever have any of it, might hardly be a noble gas. And on a planet with too high a temperature for liquid mercury, perhaps monatomic Hg gas would be considered ‘noble’.

  381. Sorry to say this but the validity and scope of the Madelung Rule is an issue that I will also be taking up in the 2nd edition.

    There are at least 2 issues about this. The Madelung Rule applies to neutral gas phase atoms. Ions and bonded atoms generally follow a simpler n rule for order of filling. If one believers that the PT primarily summarizes bonded atoms rather than isolated atoms then the Madelung Rule ceases to ‘rule’.

    This has been pointed out in a number of articles by Eugen Schwarz who also has a paper coming out soon in J Chem. Ed.

    And, contrary to what textbooks state, for transition metals 4s does not in fact fill before 3d. This is confirmed by examining the Charlotte Moore tables of atomic energy levels.
    It turns out that the n + l rule only applies to s block even in the case of neutral gas phase atoms.

    eric scerri

  382. The every-other-tetrahedral-number fact, when related to a tetrahedral modeling of the system, seems to relate to which particular ways the model can be cut up into periods, etc.

    In a face-based tetrahedron of close-packed spheres, each layer’s sphere count conforms exactly to the Pascal triangular numbers, the sums of which give the Pascal tetrahedral numbers.

    Relevant triangular numbers are: (0),1, 3, 6, 10, 15, 21,28, 36. Note that intervals between each triangular numbers are the integers, which are the next earlier Pascal diagonals. The triangular numbers pair in odd-odd (1,3), (15,21) alternating with even-even (6,10),(28,36).

    IF one wanted to cut up the tetrahedron to be a model of periodic relations, one could simply use the known face-based triangular-number layering. But this would force each period to be different in sum from every other- no repetitions as found in the ‘real’ periodic relation. So period 1 would be H only (1), and then period 2 would contain He,Li,Be (2,3,4) to sum at that point to 4=sq2. Period 3 would contain B,C,N,O,F,Ne, and miss the 3s set, while period 4 would contain both 3s and 4s. And so on.

    The above is the periodic system one would get if it were forced to use every tetrahedral number.

    However, there ARE other ways to cut the tetrahedron. The nuclear folks appear in many cases to be just fine with the double tetrahedral notion, where two virtual close-packed sphere tetrahedra actually intersect, which means that the total sum is NOT the sum of two independent tetrahedra, thus taking into account the weird fact that the number of neutrons doesn’t start to outstrip the number of protons until after Ca.

    In the angled ring model I’m still developing, the rings sum to period doublets, like taco shells- that is, triangular faces that share an edge, so their sum is that of two triangular faces minus an edge. Very similar in spirit to the double tetrahedron idea for the nucleus, but pushed down to lower dimensionality.

    Another way of looking at the ‘taco shell’ double triangular face is that it is mathematically identical to adding sequential triangular layers from the face-based tetrahedron together along one edge. But now the two triangles are identical and symmetrically oriented along the shared edge. Robbing Peter to pay Paul. Two equal triangular faces together in this fashion means that the odd tetrahedral numbers are ‘out’, and forces us to use two equal intervals between the even tetrahedral numbers.

    Jess Tauber

  383. One more thing. Irregardless of how periodic table is presented, the n+l rule remains very important part of the Periodic Law. I do not think that Dr. Scerri in 2nd edition of his book will go as far as to deny its importance. Therefore, my argument that Alkaline group of elements is special among all other groups because n+l value changes only between the alkaline earths and the elements of the first groups of spdf blocks remain valid and irrefutable.

    Also, the fact that atomic number of every other alkaline earth element corresponds to every second tetrahedral number and the atomic numbers of intermediate alkaline earths are arithmetic means of those tetrahedral numbers is very interesting and is telling us that Periodic Law somehow is related to tetrahedral stack of spheres. I think that significance of this fact needs to be discussed and looked into, instead of being flatly rejected.


  384. Didn’t someone write (Prof. Scerri?) that the electrons in He were unpaired in some way, or might have a tendency towards this? If so, would this count as a kind of behavior similar to Aufbau anomalies? Somebody remind me. Thanks.

    Jess Tauber

  385. Interesting. Dr Scerri says that he abandoned his support for LSPT because of one element He, since he can not accept that He is an alkaline earth metal. He says that he wants to make changes in his book in that regard. Does it make my argument invalid then?

    On the other hand, Philip Stewart went opposite way and supports moving He to alkaline earths. Also, Henry Bent, who made huge contributions in Chemistry and chemical education serving as a chair of the American Chemical Society’s Division of Chemical Education and was on Ad Hoc Committee on Column Labels in Periodic Table states in his book that all his life he argued that He has to be next to Ne until certain moment in his carrier when he realized that He has to be above Be. He also gives fifty some reasons why He has to belong in the same group with alkaline earths.

    So, poor me! Who do I have to listen? Well, I don’t . I believe that periodic table, that is built strictly in accordance iwth electron configurations, n+l rule and quantum numbers also predicts all primary chemical kinships correctly, except He. It is too bad that chemical behavior of helium in this climate and its label “inert gas” is not what He is, that is element with both electrons in s-block. My periodic table is based on n+l rule, electron configurations and quantum numbers and I am not changing my mind because of one element.

    Perhaps, at some point of time, everybody will stop changing their minds and agree with me. Then, the “bomb” will explode and everybody will see the light. I do not care how much time it will take.

    Valery Tsimmerman

  386. It all seems to boil down to a difference of opinion about what the periodic System is. One view is that Mendeleev et al. discovered, by consideration of chemical behaviour, a fundamental pattern in the electronic structure of atoms. The other view is that they discovered a fundamental pattern of chemical behaviour. Whether or not you you choose the LSPT depends on whether you thing electronic structure or chemical behaviour is more important. I suppose that as long as professions are divided into physics and chemistry, this disagreement will persist.

    Henry Bent offers a way out with his generalization of the ‘first element’ effect into gradients of eccentricity running down the LSPT and from right to left – or out from the centre of a periodic spiral and from the main groups through the transition elements to the lanthan-actinoids, pp. 17 and 29 of New Ideas in Chemistry. The peculiarity of H and He is then simply the most extreme of the first-element eccentricities.

    As regards H, I gave up school chemistry largely because of a bitter disagreement with my teacher over it. She said H must be either a halogen or an alkali metal. I developed more and more adolescent ferocity in my insistence that it was neither. I remember writing hundreds of times in blank spaces in my exercise books “hydrogen belongs with carbon”. Our other disagreement was over the “rare earths”; I thought she was hiding something from us by refusing to talk about them.

  387. I would like to say a little more about why I no longer believe that the left-step table is the optimal form of the PT and consequently also the ADOMAH variation of the LST.

    The main worry is that chemically He is not an alkaline earth.

    In my book I overcame this issue by suggesting that Mendeleev and others regard the periodic table to classify elements as basic substances not as simple substances. I recommended ignoring the chemical properties of He because those are the properties of the element as a simple or isolated substance and not those of the element as the more fundamental “basic substance”.

    I argued that the only property of elements as basic substances is atomic number or weight in the time of Mendeleev.

    This too may be a little extreme. The properties or nature of the element as an abstract basic substance are arrived at inductively from the properties of the combined element and the element as a simple substance. To completely ignore the chemical inertness of He is therefore too extreme as I know believe.

    The arguments I gave in my book were in the form of “why not” place He in the alkaline earths since its apparent properties should not be an objection. I now think one requires a “why yes” argument, a positive argument in other words for [placing elements like H and He into particular groups of the PT.

    And as I have argued in American Scientists and J. Chem. Ed. that more positive criterion may well be the maximization of atomic atomic number triads which would leave He in the noble gases and would mean moving H into the halogens.

    eric scerri

  388. Valery Tsimmerman says:
    January 18, 2010 at 11:01 pm

    besides”platonic argument” that you have latched on I have made few of non arbitrary scientific arguments for ending periods with alkaline earths that went unnoticed by you.

    Once more I am quoting Eric Scerri’s book “Periodic Table, Its story and its Significance”:
    page 285. “It is suggested that an optimal classification can be obtained by identifying the deepest and most general principals that govern the atoms of the elements, such as the n+l rule, and by basing the representation of the elements on such principles.” Did Eric Scerri say that?

    (meanwhile, the time bomb keeps ticking)

    Dear Valery,

    Maybe I have not explained before, I have now abandoned my support for the left-step table as described in the final chapter of my book on the periodic table. Changes will be made in the second edition in due course. I now support my own table, apparently first discovered by Janet also, in which H falls in the halogens. This is published in American Scientist and J. Chem. Ed.

    Nor do I think that an optimal table necessarily needs to reflect the Madelung rule.
    In the next issue of Foundations of Chemistry I have a new paper in which I argue that the use of triads can be motivated by arguing that nuclear structure governs electronic structure but that in difficult cases, nuclear structure as embodied in Z and relations between Z’s such as atomic number triads, are decisive. So yes reduction to physics may hold the key but merely claiming allegiance to quantum mechanics or the Madelung rule is just not persuasive enough for adopting a particular new form of the PT. The new special issue also contains papers by Philip Stewart on Janet’s work which should be of great interest to folks here.

    all the best
    eric scerri

    P.S. I will think further about the notion of ending periods with alkaline earths. You are of course technically correct to say that most of the noble gas atoms do not have full shells but they do have full octets and that is what is more chemically relevant and the reason why traditional tables end their periods there.

  389. In a tetrahedral arrangement of close-packed spheres, any sphere has a minimum of three points of contact (vertices) and a maximum of twelve inside the body of the figure. This leads to many different possible interesting configurations that might exhibit unusual element to element linkages.

    With the angled ring configuration, half-tetrahedral cuts are special in this regard. With one cut on one side we have 1s1, 2p1, 3d1, and 4f1 all in-line, and together on one outer triangular face of the tetrhahedron. At the other end of the block 1s2, 2p6, 3d10, and 4f14 are in-line, on a different triangular outer face. Along the same cut, but in the other side of it, are 2s1, 3p1, 4d1, 5f1 on the same face as the last set, and finally 2s2, 3p6, 4d10, 5f14 in line back on the same triangular outer face as the first set above. Similar alignments take place body-internally and on the other two outer triangular faces.

    This arrangement also may predict connectivities that wouldn’t occur to most people, something I’m still looking into.

    Jess Tauber

  390. I just read new posts and realized that some of my comments apear twice. This is because I had a trouble yesterday with posting on this blog. That was not intentional.

    Also I have to make a correction: only He and Ne have shells completed. Zn and Yb do not. My apologies.


  391. Bill Jensen has argued that the Be/Mg group bifurcates, with Ca/Sr as one branch and Zn/Cd as the other. Note also that Mendeleev predicted the properties of Sc on the basis of those of B. And one could say that the lanthan/actinoids represent a “multifurcation” of the B/Al group (hence the quarrel over whether La or Lu belong with Y), with Eu and Yb showing resemblances to Ba. Such secondary relationships are most easily shown by a colour scheme, as pioneered by John D Clark.

    Incidentally, I have given up using numbers for the groups. The IUPAC compromise is not really an improvement on the old Roman-numeral systems, it loses the link with highest oxidation states, and it does not work for the LSPT. It is simpler just to name each group by the element(s) at its head.

  392. Correction:
    only He and Ne have all shells full. (Zn has shell 4 started but not complete and Yb has shells 5 and 6 started, but not complete). All other inert gases have open shells: Ar has shell 3p complete, but 3d is not even started, that is incomplete; Kr has 4s and 4p complete, but 4d and 4f are not even started, etc.

    My appologies,

  393. I sent email to Dr. Bent telling him that we desperately need his input. Hopefully, he will respond.

    besides”platonic argument” that you have latched on I think I have made few of non arbitrary scientific arguments for ending periods with alkaline earths that went unnoticed by you.

    I am quoting Eric Scerri’s book “Periodic Table, Its story and its Significance” again:
    page 285. “It is suggested that an optimal classification can be obtained by identifying the deepest and most general principles that govern the atoms of the elements, such as the n+l rule, and by basing the representation of the elements on such principles.”

    Alkaline earth metal group (that includes also He because of two s-electrons) is special because n+l changes its value only and always between elements of that group and the elements of the first groups of s,p,d,f blocks. Those are the only locations where value of n+l changes.

    That is why, per your own words, LSPT and it’s modern version ADOMAH PT, which are based strictly on n+l rule (especially ADOMA that closely resmble well known n+l diagram by having diagonal tie lines connecting adjacent subshells), constitute the most “optimal classification that can be obtained”, because those two tables reflect one of “the deepest and most general principles that govern the atoms of the elements, such as the n+l rule”. Is that arbitrary or not?


  394. Eric wrote asked “But if we put our attention on the filling of shells does this not bring us back to ending the periods with the noble gases?”

    No, because only He, Ne, Zn and Yb have completed shells. Ar, Kr and all other noble gases do not have full shells.


  395. Jess, Eric, Valery,
    Another vantage point for looking at the ongoing discussion might be helpful in resolving differences; departure to three-dimensions from the flat table where the noble gases are period termini, as Jess says, instead of adjacent to the databox of first element of the next period, an n+l (a necessity, according to Valery), and which may have something to do with Janet moving to another level of his helix, according to Philip.
    If anyone contributing to the blog, or lurking, wishes to have an Alexander Arrangement, just email your address to me at roy@allperiodictables with your request. You may discover new relationships of which I am unaware.
    For instance, Valery mentioned in passing a wish that he would like to place Mg next to Zn and Sr next to Yb. I have no idea why this would be desirable, but looking at my AAE model I am surprised to see that those wishes are realized. I find that these element data boxes have a point of corner to corner contact on another plane of the model.
    This is the sort of thing I have hoped for, of previously impossible real relationships becoming realized, and imagined scientists using my new tool to see beyond the familiar.

  396. Eric,
    besides”platonic argument” that you have latched on I have made few of non arbitrary scientific arguments for ending periods with alkaline earths that went unnoticed by you.

    Once more I am quoting Eric Scerri’s book “Periodic Table, Its story and its Significance”:
    page 285. “It is suggested that an optimal classification can be obtained by identifying the deepest and most general principals that govern the atoms of the elements, such as the n+l rule, and by basing the representation of the elements on such principles.” Did Eric Scerri say that?

    Alkaline earth metal group (that includes also He) is special because n+l changes its value only and always between elements of that group and the elements of the first groups of s,p,d,f blocks. That is the only locations where value of n+l changes.

    That is why, per your own words, LSPT and it’s modern version ADOMAH PT, which are based strictly on n+l rule, constitute the most “optimal classification that can be obtained”, because those two tables reflect one of “the deepest and most general principals that govern the atoms of the elements, such as the n+l rule”. Is that considered to be non arbitrary scientific argument or platonic argument?

    Also, if we put our attention to filling of shells we would not end periods with noble gases, because all noble gases, except Ne, have incomplete shells.

    (meanwhile, the time bomb keeps ticking)


  397. Rydberg’s sequence was for the noble gases and therefore missed out the first 1 squared. Janet saw that applying the sequence to the alkaline earths including helium, the series became perfectly regular.

    The closing of the p subshell (and s1) does bring a form of chemical closure, though this breaks down increasingly with atomic weight/radius, starting with krypton. But from calcium onwards, after np and (n+1)s have been completed, shell filling has to go back to the nd and later the (n-1)f electrons. With Valery’s version of the LSPT, the rows/columns represent successive shells.

  398. Actually, given secondary periodicity, couldn’t an argument be made that double periods might be better depicted as repeated (n+1) sequences rather than stacking them one over the other?



    This is the way things work with my angled ring tetrahedral model. Just a thought…

    Jess Tauber

  399. OK, let me suspend my skepticism for a moment and ask for further clarification on the idea of ending periods with the alkaline earths.

    Philip Stewart mentions Janet’s apparently non-arbitrary approach to ending periods and the sequence 1^2 + 2^2 + 3^2 as previously noted by Rydberg.

    He then immediately adds that this is an anticipation of QM and the filling of shells if I understand him correctly. But if we put our attention on the filling of shells does this not bring us back to ending the periods with the noble gases?

    The non arbitrary scientific argument for ending periods with alkaline earths is not yet clear to me. I say scientific because I dont believe that a Platonic argument based on their having nice atomic numbers (actually half of them) is enough to constitute Valery’s “time bomb”.

    all the best,

    P.S. Can anybody persuade Henry Bent to enter this conversation?

  400. You are correct. I meant Meyer’s first 1864 version. You must mean that he stopped at alkaline earths. Whatever reason it was, it sure looks like “p” and “s” blocks of LSPT, without inert gases, of course. In that version he did not include transition metals either.

  401. You must mean 1864. He stopped at the alkali metals because of difficulties in classifying metals with a valency of more than two. Crookes had a similar idea of going from the highest negative valencies to the highest positive ones, putting the noble gases in the middle. It is not the left step; just yet another way of parsing the sequence.

  402. I have noticed some time ago that first 1884 version of Lothar Meyer’s periodic table is in fact incomplete version of LSPT with all alkaline earths lined up in the right column. Wow! LSPT is at least 5 years older than 1st Mendeleev table.

  403. Tables have not always ended the rows with the noble gases. Mendeleev placed themse elements at the beginning; with a highest oxidation state of zero they logically formed group zero to the left of the alkali metals. Eric Scerri in a recent proposal made the rows run from the halogens on the left to the oxygen-sulphur group on the right; Periods thus seemed to be a matter of taste.

    Janet found a non-arbitrary way for ending the periods; after the alkaline earth metals he always moved to another level of his helix. He also noted, by modifying an observation of Rydberg’s, that the atomic numbers of these elements are successive expansions of the series 1 squared+1 squared+2 squared+2 squared+3 squared… multiplied by 2. This is not mere numerology because it relates to the quantum numbers of electron shells, though Janet did not know this at the time he made his arrangement.

  404. In fact one cannot bisect (without cutting through spheres) any close-packed sphere tetrahedron of 1, 3, 5, 7 layers (having tetrahedral numbers 1,10, 35, 84) with a plane, just because each edge has an odd number of balls. Maybe in another universe?

    Jess Tauber

  405. The alkaline earths DO seem to be special in the LSPT- the ‘end of the line’ for reworked periods with ascending block subperiod numbers relating to (n+l):


    Perhaps too much emphasis goes with the noble gases due to their former suppressed reactivity as period termini?

    Between Valery and I on the T3 list I think it was clear that the even reworked LSPT periods had the tetrahedral numbers, and that the odd ones lay equidistant between these (starting for convenience at 0, often left out of the discussion).

    The (LSPT) periodic system is built on doubled periods of equal length, while utilizing all the tetrahedral numbers would(?) demand periods of unequal length. At least in my own angled ring model of the system, unequal periods would destroy utterly any symmetry, given that there is a plane bisecting the nested tetrahedra and the rings marking the beginning of one period and the end of its equal length partner, and another that marks that halfway point between these, where each orbital type has (ideally) a single occupying electron.

    It might be interesting to try to build a model using all the tetrahedral numbers, and see what it would look like. I would imagine it would be a mess not corresponding to what we know.

    Jess Tauber

  406. That is right, Eric. Alkaline earths are just one group, but it is very special group! It is unlike all other groups. If you take any other group of elements and add one (+1) to their atomic numbers, you will get atomic numbers of the elements that belong to next group of elements. For example: take halogens and add one to their atomic numbers. You will get inert gases.

    Now, try to do this with alkaline earths. Will you get elements that belong to the same group? No. You will get Li, B, Al, Sc, Y, La, Ac. Those elements do not belong to the same group. This is the reason for huge gaps in traditional PT that are not present in LSPT, that ends with Alkaline earths. (You can find more on this in Bent’s book).

    Similarly, Atomic numbers of all other elements can be arrived at by subtracting natural numbers from alkaline earths until next lower Alkaline earth is reached. All groups and primary triads will be retained in process.

    And finally, as I noted before on this forum, if you look at Mendeleev’s line in terms of maximum n+l values you will notice that maxim values of n+l change always after the alkaline earths. You stated in your own book that objective formulation can be achieved only if it is based on such deep and basic principals as n+l rule.

    Here you go. Alkaline earths are the elements that whole Periodic System is based on.



  407. The alkaline earths are just one group of 18 or 32 groups.
    Just this serves to diffuse any time bomb.

    And even then only half the alkaline earths.
    why is one particular diagonal on Pascal’s triangle so ‘explosive’?
    Where is the sensation?

    Eric scerri

  408. Gentlemen,

    It is the matter of fact that these alkaline earth metals: Be, Ca, Ba (and Ubn, still waiting to be discovered) have atomic numbers: 4, 20, 56 and 120. Those numbers are known to mathematicians as Tetrahedral Numbers. They can be found on 4th diagonal of Pascal Triangle that denotes third dimension.

    Rest of the alkaline earth metals, Mg, Sr and Ra have atomic numbers: 12,38 and 88, which are arithmetic means of the tetrahedral numbers. This fact was recently observed by Jess Tauber form here

    It seems that all of you think that this is irrelevant. But I view this fact as time bomb (alluding to Philip’s analogy to recent act of war).

    The time bomb is ticking and it is only matter of time when it is going to “blow up” and bring down all construction of the past.

    By the way, it can not be defused.
    Valery Tsimmerman :-)


  409. sorry I meant to say, elements as basic substances are not synonymous with atoms.

    My critique of Bent’s views are published in an article in International Journal of Quantum Chemistry for 2009

    E. Scerri The Dual Sense of the Term “Element, Attempts to Derive the Madelung Rule and the Optimal Form of the Periodic Table, if any, International Journal of Quantum Chemistry, 2009; volume 109.

    and in my 2007 book on the Periodic Table.
    The Periodic Table , Its Story and Its Significance, OUP, New York and Oxford, 2007

    Also see, E. Scerri Critique of Hendry on The Elements, On the Continuity of Reference of the Elements,
    Studies in History & Philosophy of Science, 2006; (37): 308-321.

    eric scerri

  410. Valery writes,

    “I am not alone in believing that Mendeleev would approve reduction to QM. I share Henry Bent’s view on this. Mendeleev liked to emphasize that he talked about Periodic System in terms of Atoms, not simple bodies.”

    Sorry to disagree with you again but Mendeleev was not a believer in atoms. Yes he did not put the emphasis on elements as simple bodies but instead on elements as basic substances. Simple substances are not synonymous with atoms. I know that Henry Bent holds your view or vice versa but there is absolutely no textual evidence for claiming that Mendeleev supported the notion of atoms. In fact he frequently criticized the atomic theory and the belief that atoms exist.

    I published an article in Studies in History and Philosophy of Science which contains half a dozen or so quotes from Mendeleev which confirm that he was not a supporter of the atomic theory.

    I would also mention the work of a Belgian PhD student Pieter Thyssen who has written on the rare earth elements. His research confirms that Mendeleev was certainly not a believer in atoms.

    When Mendeleev talked of atomic weights he sometimes substituted the term element weight.

    eric scerri

    P.S. Nice to see Philip Stewart giving his views on this forum.

  411. Mendeleev took highest oxidation state as his chief criterion, hence his group VIII for the problematic Fe Co Ni groups. That is why he was not bothered by the fact of metals and non-metals being in the same group and why melting points did not seem important for his classification. Since highest oxidation states are related to quantum numbers, he was in effect anticipating quantum states. As regards spirals, he wrote “…in reality, the series of elements is uninterrupted and corresponds, to a certain degree, to a spiral function.” (Mendeleev on the Periodic Law, edited by W B Jensen, p. 56.)

    The problem with the spiral is that the coils increase in length, so they cannot be regularly spaced on a cylinder, and they come in pairs, so they cannot be regularly spaced on a cone. A good form would be like the famous Minaret of Samarra (damaged in the Iraq War because the Americans used it and invited a bomb), but that does not work if one wants the groups to line up.

    The drawback of any representation which puts the transition elements and lanthan/actinoids separate from the main groups, (whether as extra columns on the side as in Janer’s left-step table, or in bulges like Benfey’s and Alexander’s, or in an annexe), is that you lose the information about highest oxidation state that is responsible for similarities between, for example perchlorates and permangnates, which is conserved in Mendeleev’s short form. The best solution, I believe, is to use colour to indicate these connections, as in Clark’s chart in Life Magazine, May 1949, and in my Chemical Galaxy (where I have used Mike Laing’s ideas to introduce some colour into the lanthan/actinoids).

    As regards triads, I see them as simple arithmetic consequences of the structure of the Periodic System, and I do not believe they can be used to dictate that structure. Janet decided in 1928 that it was less shocking to place H and He over Li and Be than to break the perfect regularity of four pairs of rows (or rather coils, since he derived his table from a helix inscribed on four nested cylinders). After years of resisting the idea, I now believe he was right.

  412. I am not alone in believing that Mendeleev would approve reduction to QM. I share Henry Bent’s view on this. Mendeleev liked to emphasise that he talked about Periodic System in terms of Atoms, not simple bodies. You are right. He was not receptive to the new reductionist ideas, but when evidence would become overwhelming, and those ides would become main stream, he would be tempted to look into Periodic Law in terms of QM. I think. I can only speculate, of course.

    To re-write Mendeleev’s Periodic Law in modern terms I would use Atomic Numbers instead of atomic weight (this change has already occurred anyway) and I would change word “properties” to “quantum attributes of atoms” (I believe that this change will come sooner or later).

    Best Regards,


  413. Hi Valery,

    I have one question arising from your last posting.

    What makes you think that Mendeleev would approve of reduction to QM?

    In many ways he was anti-reduction. For example he was opposed to Prout’s hypothesis that all elements were composites of H. He was suspicious of radioactivity and wrote a book in which he tried to argue against it. He was against the idea of fundamental particles. This does not sound like somebody who would be drawn to QM were he still living 30 years after he in fact died.

    Mendeleev was rather classical in thinking of atoms as immutable, and in fact there is much evidence to suggest that he did not believe in atoms in the physical sense. I can provide quotations if necessary. He believed rather that elements were strictly individual. He even disliked Lothar Meyer’s idea of drawing a smooth curve through the properties of the elements since he believed there was no such continuity.

    In my book I argue that he was a reductionist in one rather specific sense, namely putting atomic weight above all other criteria when classifying the elements. But as you say atomic weight alone does not allow one to go from Mendeleev’s line to a 2D or 3D table.

    all the best
    eric scerri

  414. Good questions. Classification of the elements can be done many different ways. In our three dimensional world you can choose only between three major types:
    one dimensional, that is simple list of atomic numbers like 1,2,3,4….118,119,120…, also called Mendeleev’s line; two dimensional, such as LSPT and traditional PT; and three dimensional.

    In order to go from first dimension to second you either need to “cut” Mendeleev’s line and put pieces back together, one on top of the other to form the groups, or you can make a spiral and adjust it in such way that elements lined up radially, like in Stewart’s Chemical Galaxy and other spiral representations. Even though spiral representations are technically continuous, the elements are not equally spaced along the spiral in order to form the groups and blocks. The elements along the spiral are shifted to make that happen, therefore in spiral “tables” the shifts replace the “cuts”.

    In order to decide where to make such “cuts” or “shifts”, one can use chemical properties of the elements, physical properties, or structural features of the atoms that are known to us, thanks to the spectroscopy and other methods of probing the atoms. From Mendeleev’s numerous writings and speeches I tend to believe that he would prefer to base his classification on something more substantial than chemical and physical properties, such as melting points, weights and volumes. It is quite obvious, that he would prefer to use quantum attributes of the atoms as a basis for his periodic table.

    In regard to the cuts. You are right. The cuts are numerous, but they are always done at the similar points along the Mendeleev’s line, that is why I use word “cut”. In traditional depiction, the cuts are always done between inert gases and alkali metals. In Left Step Table and in its new version ADOMAH PT cuts are done where maximum n+l value changes, that is after each alkaline earth metal.

    In regard to your depiction, you claim that it is continuous, but in order to make it you had to cut things, right? That what I meant by “cut”

    Best Regards,

    Valery Tsimmerman.

  415. Valery, on your website; , you have done really well pointing out the technical errors in the standard IUPAC PT formulation of the periodic table.
    There is much that I, however, a museum exhibit designer and not a scientist, cannot grasp, and I assume would be difficult for other laymen and new students.
    You quote from Dmitri Mendeleev’s article “The Relations Between the Properties of Elements and Their Atomic Weights”: “…every system, however, that is based upon exactly observed numbers is to be preferred, of course, to other systems not based upon numbers because then only little margin is left to arbitrariness… Properties, such as the optical and even the electrical or magnetic ones, cannot serve as basis for the system naturally, since one and the same body, according to the state in which it happens to be at the moment, may show enormous differences in this regard.”
    You then write that “This is exactly what is wrong with the traditional periodic table that ‘cuts’ the sequence of the elements in periods primarily on the basis of metallic/nonmetallic/inert properties.” I assume your objection is to the last sentence, but I can only understand the first, and in there, assume it is the dozen+ breaks at the right, left, and center of the standard chart – ‘cuts’ – that were the sole reason for me to come up with an alternative.
    You ask “what could be the ‘exactly observed numbers’ that Mendeleev alluded to?”, and note that “One of such numbers would obviously be the Atomic Number Z.” That leaves me up a tree again, probably due to my lack of a proper education.
    But then you claim that “if only this number is used, the Periodic Table would take a form of a continuous line or a column.” Now I’m back in the game! I don’t understand the first part of the quote, but for the “continuous line” of elements is exactly where the Alexander Arrangement (AAE) excels – without the ‘cuts’ mentioned earlier, and describes precisely how I approached my design. I included, in the term ‘cuts’, those breaks requiring a jump from the end of a period to the beginning of another as well as those between sequentially numbered element data boxes.
    However, the (non-tetrahedral) table on your homepage (a left step long form reversed & on end?), it seems to me, has many cuts; the top or top/left two elements of every block. For the scientist, there may be reasons, but is this form more useful for the introduction to chemistry than a spiral with all elements, groups, and blocks contiguous such as in the AAE?

  416. Dear Roy,

    Thanks for your responses. I am often asked why my periodic table has H and He shown in two places. Eric Scerri was the first one who asked me that about three years ago when I emailed him my first version of ADOMAH Table. Philip Stewart even asked me to make up my mind and to choose one of the two locations, when he was preparing his article about Janet for publication in Foundations of Chemistry. I would like to give you some background, so you can see where I am coming from.

    Charles Janet was struggling with this question for some time. You can see that his version II periodic table ( had H and He above F and Ne respectively. However, his Version III periodic table has H and He above Li and Be. He realized that it would be controversial, but he insisted that this is the right position for those two problem elements.

    Eric Scerri writes in his book that he believes that only one particular representation reflects chemical periodicity as an objective fact. I happened to believe the same, except I would use word “periodicity”, instead of two words “chemical periodicity”.

    Mendeleev’s 1869 Periodic Law states: “The elements, if arranged to their atomic weights, exhibit an evident periodicity of properties.” The term “atomic weights” are now replaced by atomic numbers, but meaning of words “periodicity of properties” are not quite understood because, I argue, word “properties” are mistranslated.

    I say that because Russian is my first language. Russian word “svoistva” and English “properties” is not quite the same thing. For example, Russian-English Dictionary by A.M. Taube et al, Moscow Russian Language Publishers, 1978, that I happen to have on my book shelf gives following translation for word “Svoistvo”: characteristic, quality, property. Do you see the difference? I would also add to that list word “attributes”. Therefore, when Mendeleev states “All that I am going to say [about the Periodic Law] must be understood as relating to atoms … not to simple bodies” and Periodic Law “expresses the svoistva of real elements and not of what may be termed their manifestations visually known to us” I understand exactly what he was trying to say. He actually meant that periodicity had to be understood in terms of attributes of the atoms.

    I believe, as mathematicians do, in describing things with minimum possible terms. That is, if I can come up with equation that describes some natural process with only two terms, I would not consider optimal equations that describe same thing with three or more terms. On my home page I demonstrated that, based only on Atomic numbers and maximum n+l values, the periodic system, as it is known today can be replicated almost completely, with exception of one problem element, He.

    According to Dr. Scerri, elements are defined by their atomic numbers only. He also states in his book that “.. an optimal classification can be obtained by identifying the deepest and most general principles that govern the atoms of the elements, such as n+l rule and by basing representation of the elements on such principles.”

    Based on aforesaid I agree with Henry Bent’s statement that “dualistic classifications, such as metal-nonmetal, are not based on any natural law … Because elements, as simple substances, have many properties, they can be classified artificially, in many ways, according, e.g., to density, volatility, hardness, abundance, toxicity, metallic character…”, etc. “Useful though such classifications are in particular instances, they do not lead beyond themselves, to broad generalizations. Consequently, they do not lead to a unique, natural classification.”

    In regard to ADOMAH Periodic Table, I have shown one location of H and He, that I consider artificial, in dashed lines and the other location, that I consider natural, in solid lines. I admit that this was done before I reached current understanding of the Periodic Law. Later I decided to keep it this way, just to illustrate, why that common misconception exists. Similarly, I could place Mg in dashed lines next to Zn and Sr next to Yb.

    Therefore, per the quote above, your periodic table, useful though in some respects, does not lead to a “unique, natural classification”. And the unique and natural classification I strive to achieve.


    Valery Tsimmerman

  417. I see, Valery, on your Perfect table, that H & He have been repeated.
    How do you like the 3D solution on my small table (at )?
    One more dimension in a periodic table permits placement of H in multiple conjunctions, as the “Hydrogen Crown” loops (or starts) from the Noble Gases, traverses the Non-Metals, and then touches down to both F and He, all adjacencies for H which have been under scrutiny, and all proposed individually or in tandem by various experts – but only in the 3D AAE are realized simultaneously.
    You have studied this aspect extensively, it seems, and I wonder if you think the material I have copied from here and there for the edification of students at holds water, is to complex, or is sufficient for the new student.

  418. Yes, Valery, as Gell-Mann said “certain negative principles get embedded in science sometimes”, and the objectivity of minds open to improvements are necessary for science.
    De Beguyer placed elements in sequence, just as Mendeleev later stated they should be in what became “The Periodic Law”. Also no slave to precedent, Courtine preceded my similar construct by at least 40 years.
    Having no knowledge of these previous 3D models, it was the surprising conflict between the Sargent-Welch flattened table and the “Law” that I, with the instincts and objectivity of a museum exhibit designer to provide clarity, went about placing related element data boxes contiguous both vertically and horizontally, avoiding the dozen or so breaks that are unnecessary in a 3D model.

  419. I have no doubt that Dr. Eric Scerri arrived at LSPT (1928) layout independently. I did not mean to question his integrity. I learned a lot from his book “The Periodic Table, Its Story and Its Significance”. In fact, it happened to me also, when I thought that I discovered it in early 2006. It was quite a disappointment when, after extensive search on Internet, I found it here: I know at least two more people who came up with the same layout long after Janet. Here is one from 2002: I am little surprised that Journal of Chemical Education did not find those sites while reviewing the article.

    I find it fascinating that many different people keep coming up with the same layout again and again. Doesn’t it say something about its objectiveness?

    Valery Tsimmerman.

  420. Dr. Philip Stewart in his article “Charles Janet: Unrecognized Genius of the Periodic System” ( January 2009, Foundations of Chemistry) points out that the periodic table layout presented by Eric Scerri in Journal of Chemical Education (PDF 2008, 85, 585-589) is, in fact, Charles Janet’s Version II left step periodic table, which was first published in 1928.

    For those who are interested in the Left Step Periodic Table (LSPT), I recommend you visit where its new version, known as the ADOMAH Periodic Table, or Tetrahedral Periodic Table, is presented. This Periodic Table, also mentioned by Dr. Stewart in the above referenced article, combines LSPT with the Madelung Rule mnemonic diagram. Such changes resulted in a new, more user friendly, procedure for writing electron configurations.

    Also, for those who are interested in the mathematical regularities of the Periodic System, I recommend you go to, or to which are specifically dedicated to that topic. Just for a teaser, did you know that every other alkaline earth metal’s atomic number corresponds to a tetrahedral number?

  421. Doesn’t saying it is “a bit of both” imply that mathematics might be there if even if we aren’t? I.e. that it exists outside human awareness and was something we discovered rather than invented? What do you mean by there being infinitely many truths?


  422. People have also argued intently about how many angels can dance on the head of a pin. Sometimes very smart people just make mistakes.

    Invention or discovery? Mathematics is a bit of both. We invent mathematical systems that we think will be interesting, and then we explore them to discover interesting results that they give. The important point things to remember are

    1) there’s not just one perfectly valid, perfectly complete and self-consistent mathematical system, and
    2) within the interesting ones, there are infinitely many truths, nearly all of which are totally uninteresting.

    In both cases we are deeply involved. We only spend time inventing and examining the interesting systems, and we only look to discover interesting truths in them and ignore everything else that is uninteresting *to us*.

  423. I agree, yes, the universe cannot “know” anything in the sense that we do, and yes mathematics seems like a human invention used to organise the patterns we see. However, aren’t there those who have argued that we didn’t invent mathematics, we discovered it?


  424. David, you say that atomic number is somehow a special quality of atoms beyond what is useful to beings like ourselves. That it’s intrinsically special to the universe itself. It’s just not so. Your reasoning is that this property is mathematically simple, and that makes it special. But what’s so special about our mathematics other than the fact that it’s useful to us? Nature doesn’t really prefer forms because of their ability to be described by elegant mathematics. It’s more that we tend to study those physical and mathematical systems that we find to be elegant and useful for our needs. It should therefore be no surprise that those physical and mathematical systems complement each other nicely because what they really have in common is us. You even hinted at the key truth with your last line in which you said that if not even mathematics is intrinsic to the universe, then everything is subjective. Now *that* is the real truth.

    Maybe I should try to demystify that last statement a little by replacing the word “everything” with “every thing”. “Everything” mostly means the universe itself which I believe is not subjective. I.E. it will continue to exist whether or not any living things are here to perceive it. “Every thing”, on the other hand, refers to all “things”, and things are things only within minds that decide so. We might agree that there are two clouds in the sky but that’s just an agr