At Last, A Definitive Periodic Table?

  • DOI: 10.1002/chemv.201000107
  • Author: David Bradley
  • Published Date: 20 July 2011
  • Source / Publisher:
  • Copyright: WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
thumbnail image: At Last, A Definitive Periodic Table?

Discussion Spawned Development in the Field

A recent Research Highlight on on the nature of the Periodic Table of the Elements attracted a lot of readers and has stimulated an ongoing debate among those arguing as to whether or not there is a definitive format for this iconic tool. Intriguingly, however, the article and ensuing discussion has also spawned a development in this field courtesy of UCLA chemistry professor Eric Scerri.

"One of the most positive outcomes of the very popular 'Periodic Debate' discussion has been that the relative virtues of the so-called 'Stowe' and the 'left-step' periodic table, in various formats, have been vigorously discussed," Scerri says. "In the course of this debate I have come up with a compromise table which includes the best features of both types of systems."

Stowe Table

The Stowe table is named for Tim Stowe who published his system on a website several years ago but has, apparently, published nothing since. Chemists have attempted to track him down, but he seems to have vanished from the community without a trace, leaving behind an interesting periodic legacy. "Many people interested in the periodic table have tried to track him down," says Scerri, "but nobody has yet succeeded."

Stowe’s system is four dimensional in the following sense: the x and y axes depict values of the m and s quantum numbers. In the case of the s or spin quantum number values are either positive or negative, while the values of the m quantum number can range from -l, through 0 up to +l in integer steps. The z-axis is taken as the n or main quantum number representing the main shell. The fourth dimension, which obviously cannot be depicted spatially, is shown by the use of different colors each of which denotes a different value of the l quantum number. In this way, the Stowe table seeks to depict the four quantum numbers of the electron that differentiates each atom from the previous one in the sequence of increasing atomic numbers.

However, the Stowe representation has several drawbacks, which is where Scerri's new approach comes to the fore. The left-step table has received a great deal of attention in recent years. It was originally designed by the French engineer and polymath Charles Janet in the 1920s. However, with the advent of quantum mechanics and the quantum mechanical account of the periodic system it was realized that his system displays the elements in order of increasing n + l values of the differentiating electron. Many authors have claimed that this is a more natural system since electron filling accords with this criterion rather than increasing values of n.

New Modifications by Scerri

Scerri has now modified the left-step table by combining it with Stowe’s idea of using the quantum numbers explicitly to represent the elements in the periodic system. "The notion that n + l is more fundamental than n alone is key," says Scerri. "The format I have now constructed depicts the arrangement of the elements in this fashion for elements 1 to 65 inclusive and can be easily extended up to 118 the currently heaviest atom and indeed beyond to elements that will in all probability be
synthesized soon." In what he now calls the Stowe-Janet-Scerri periodic system each level represents a particular value of n + l which take the form of horizontal periods in the case of the original Janet table.

Following Scerri's introduction of this new layout in the comments of the ChemistryViews item, commenter Valery Tsimmerman, pointed out that Scerri's efforts in re-working the Stowe table is bringing us closer to the realization of the numerical and geometrical regularities of the Periodic System. Tsimmerman also claims to have devised the perfect Periodic Table based on the concept of tetrahedral sphere packing.

Tsimmerman's Concept of Tetrahedral Sphere Packing

Tsimmerman points out that chemists such as Henry Bent mentioned that every other alkaline earth atomic number equals to four times the pyramidal number, while Wolfgang Pauli noticed that length of periods are double square numbers: 2x(1, 4, 9, 16). This latter point is, Tsimmerman says, not surprising because square numbers are the sums of odd numbers 1, 1+3, 1+3+5, 1+3+5+7 ... We know the meaning of odd numbers in the periodic system. They are the lengths of s, p, d and f blocks. Adding the number of elements in block rows results in the lengths of the periods. Adding square numbers results in pyramidal numbers: 1, 1+4=5, 1+4+9=14, 1+4+9+16=30. Multiply them by four and you will get every other tetrahedral number 4, 20, 56, 120 ... Those are the atomic numbers of Be, Ca, Ba and Ubn. "Great scientists like Pauli, Niels Bohr and others were marveling at numerical relationships found in periodic system," says Tsimmerman. He suggests that Scerri's latest periodic table is not quite the final version and suggests that any further reworking of Stowe's table will take us closer to a definitive 3D table.

"I hope that this system will not be just another periodic table to add to the depository of tables that people dream up every so often but may represent a definitive step forward in the quest for improved periodic tables," Scerri told us.

  • Periodic Debate, David Bradley
    Mendeleev's Periodic Table is, for many, the symbol of chemistry but is the current layout the best one?
    including discussion mentioned in article

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Jess Tauber wrote:

Bagge pants?

I just learned, while researching literature on tabletop nuclear reactions (see, that the nuclear double triangular/tetrahedral number relations (which feed into the (semi)magic numbers, had been noticed at least as far back as 1948, from one E. Bagge, Naturwissenschaften 35, 376. Has anyone ever seen this? Boy that wheel just keeps getting reinvented (how many times did the Janet table get rediscovered by the proud new owners?). Jess Tauber

Thu Jul 21 10:36:08 UTC 2011

Jess Tauber wrote:


The odd numbered periods do not produce in-column triads, but the even-numbered ones do. However, interestingly, the odd triads' means are the half-filled orbital positions for 2p,3d,4f respectively. Perhaps this is not just a mathematical curiosity but has some hidden meaning or function. In any case this does go back to the fact that only every other tetrahedral number corresponds to an alkaline earth atomic number. Intermediate numbers differ by monotonically increasing amounts: Alkaline earth-tetrahedral numbers, 2-1=1; 12-10=2; 38-35=3; and 88-84=4.... Valery commented on this a long while ago on the T3 List ( Jess Tauber

Thu Jul 21 10:17:49 UTC 2011

Philip Stewart wrote:


I said 46 elements not in triads; that should read 54 - nearly half of 120!

Thu Jul 21 09:48:28 UTC 2011

Philip Stewart wrote:

Plato where art thou?!

This is all getting too Platonic for me. Juggling around with four small quantum numbers you are bound to get lots of regularities, but I think the irregularities are more interesting. As for Z triads, there are 46 elements in the Janet table that do no belong to any triad, so how can that be fundamental? Leave the definitive table for Plato's Heaven!

Thu Jul 21 06:57:49 UTC 2011

Jess Tauber wrote:

By the numbers

Remember that tetrahedral numbers are themselves sums of all odd or all even squares, since 4x any square is also a square. This also means that the electronic period lengths are simultaneously double AND half squares. Thus 2 is 2x1 and 4/2, 8 is 2x4 and 16/2 and so on. The original mapping of every other alkaline earth number to every other tetrahedral number was my discovery- connection to the pyramidal numbers was Valery's finding. I found that leftward movement by triangular number amounts from the alkaline earth positions (within periods only) landed on midpoint positions within idealized half orbital rows- Valery pointed out that these were positions where quantum number ml=0. Jess Tauber

Thu Jul 21 03:28:36 UTC 2011

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