At Last, A Definitive Periodic Table?

  • DOI: 10.1002/chemv.201000107
  • Author: David Bradley
  • Published Date: 20 July 2011
  • Source / Publisher: ChemistryViews.org
  • 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 ChemistryViews.org 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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5 Comments

J Gregory Moxness wrote:

An interactive 4D visualization of the Stowe-Janet-Scerri Periodic Table

Please see

http://theoryofeverything.org/MyToE/?p=1099

For full interactivity, you will need the free Wolfram CDF Mathematica player.

Wed May 01 13:23:31 UTC 2013

Eric Scerri wrote:

new periodic table blog

http://blogs.nature.com/soapbox_science/2011/12/07/the-periodic-table-matter-matters ericscerri.com/

Wed Dec 07 18:23:12 UTC 2011

Jess Tauber wrote:

Fiblike Silver Ratio-related sequences

Well, I worked out the first few number series whose contiguous members give Silver Ratio values. So at least these do exist. This makes me wonder whether Pascal Triangle-like figures exist for the Silver Ratio (1+squareroot2) also. If so, then are there diagonals? Anything relevant to the Periodic System?

Fri Oct 28 17:06:17 UTC 2011

Jess Tauber wrote:

Pascal and Metal Means

I've found a relation between Pascal triangle analogues and the so-called 'metal means'. What this portends for our understanding of the periodic relation remains to be explored. At least my muse hasn't left me entirely. Sometime I worry, esp. in dry periods. The monsoons are returning at last. See: http://en.wikipedia.org/wiki/Silver_ratio and the discussion page whose link you can click at the top of the main page- my addition appears at the very bottom of the discussion page.

Thu Oct 13 11:43:31 UTC 2011

Jess Tauber wrote:

More on Pascal analogues

After weeks of exploration I can now conclude that all Pascal Triangle analogues (where the numbers down the side aren't just 1's) are interconvertible variants of each other. In all cases the dimensionality of the diagonals remains unchanged, or so it seems so far. In addition, no matter what side numbers you start out with, these numbers provide 'seeds' for Fibonacci-like sequences when you sample across diagonals and then sum. My convention for listing side numbers is (X,Y), where X is the left side number, and Y the right. The seed for the left side Fib-like series is X,Y, and the seed for the right is Y,X. So for a 2,1 system, on the left we have the Lucas sequence: 2,1,3,4,7...., and on the right we have 1,2, for the Fibonacci sequence proper but starting one move ahead of the sequence using 1,1. This also means that very many different Pascal analogues generate upstream-started Fib, Lucas, and other series. For example an 8,13 Pascal. I don't know how this might yet be relevant for the PT, but I bet it will be.

Fri Sep 30 04:33:04 UTC 2011

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