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

Eric Scerri wrote:

First Member Rule

Valery throws out the "first member rule" as though it were a well founded principle of science. We would need a far more detailed account of this "rule" The rule also makes it rather too easy to justify any placement whatsoever as far as first members are concerned. For example, somebody like Valery places He at the top of the alkaline earths and a chemist objects on the basis that the properties or lack of properties of He make this improbable. Valery can then reach for this first member rule to argue that any placement, however improbable, can be justified by claiming that the first member is completely anomalous. Perhaps Valery would be prepared to go through a few examples of just how anomalous first members actually are otherwise this will not impress chemists very much. Nor is it very convincing to claim that the periodic table is now completely out of the hands of chemists and that crude reductionism according to the number of outer electrons in an atom is all that matters.

Fri Jul 22 09:21:57 UTC 2011

Valery Tsimmerman wrote:

First member rule

The first member rule is based on observation of all groups of the periodic system. It suggests that LSPT format is the most regular, since all group first members in LSPT follow the rule. The first member rule is consistent with recurrence of the lengths of the periods._____ The existence of triads is based on the fact that the lengths of periods recur. It is simply inconsistent to deny recurrence of the first period in order to justify two extra triads and, at the same time, to base the explanation of triads on a basis of such recurrence of the rest of the periods.

Thu Jul 21 22:27:05 UTC 2011

Eric Scerri wrote:

first member rule

I don't see why it matters if first members are or are not members of perfect triads. Can you explain to us why a first member rule should be an additional criterion. Can you also explain what do you mean by first member rule? eric

Thu Jul 21 20:56:20 UTC 2011

Valery Tsimmerman wrote:

Response to Eric

I was referring to H/F LST table, not to your new table, which is more consistent with my views regarding position of H and He. The two more groups that I referred to, that violate the optimization (not maximization) of triads are 1st and 17th. By that I mean that, if H is moved to halogens, first members of halogen and alkali groups will become parts of the triads, unlike groups 3 through 16, where first members are not members of triads. In Janet's LSPT all 32 groups follow first member rule without exclusion.

Thu Jul 21 17:31:25 UTC 2011

Eric Scerri wrote:

2nd response to Valery

Valery writes, "Eric's proposition of maximization of triads would increase the number of such exclusions from the rule by another 2 groups. It sure looks like a move in wrong direction." Please explain how my table does that. Which are the 2 more groups that violate maximization of triads. I hope you are not confusing the new suggestion Janet-Stowe-Scerri with my previous H in halogens table. They are 2 separate and conflicting proposals as I tried to explain.

Thu Jul 21 17:22:36 UTC 2011

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