At Last, A Definitive Periodic Table?

  • ChemPubSoc Europe Logo
  • 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

Jess Tauber wrote:

Unlocking the Universe

I discovered quite by accident today a new series of 3 one-hour episodes, on the Science Channel here in the eastern US, called 'Unlocking the Universe', which details the history of chemistry. Only into the first few minutes of it, but it looks quite good. These series tend to repeat on these cable channels, so you should be able to catch it either tonight or in the next days/weeks. Jess Tauber

Tue Jul 26 03:30:55 UTC 2011

Eric Scerri wrote:

Thanks Valery

OK I will. Here is my revised point. Consider a short form table, by which I mean an eight column table which excludes both d and f block as footnotes. ________________________ Now He and Ne are similar and so are all the other noble gases in having full shells. So I mean full shell in the sense of full s and p orbitals. After all most of the noble gases do not have strictly full shells, only He and Ne in fact do. ____________________The fact remains that they are chemically very similar. So structurally, in the sense of having full s and p orbitals He and Ne ARE SIMILAR. Why is this similarity any less relevant in the sense of electronic configuration, than the similarity between both He and Be having as s2 configuration. And to turn your argument back onto you, so do most of the transition metal atoms have an s2 outer shell. _______________Surely you don't propose placing He together with Be and most of the transition metals just because of an s2 outer shell? There is more to the periodic table than a purely reductive view. ______________The interest in the table and its lasting value lies in the fact that it crosses levels and remains relevant at multiple levels from the macroscopic to the microscopic and in between. Your highly reductive approach, apparently shared by Philip, is counter-productive in my view.

Tue Jul 26 01:12:32 UTC 2011

Valery Tsimmerman wrote:

On a side note

Eric, when you do your survey of full-shells I suggest you to use ADOMAH PT. I think it is especially convenient for such purposes. You will find that elements He, Ne, Zn and Yb, that mark completion of 1st, 2nd, 3rd and 4th shells, are located in left bottom corners of s, p, d and f blocks respectively. Valery.

Mon Jul 25 17:03:46 UTC 2011

Eric Scerri wrote:

Responses to Philip and Valery

Philip. Your point about all gaps being artificial is of course valid, but some gaps are more artificial than others. For example the gap between H and He in the conventional or medium-long form. One can ask the question about gaps within a 2-D representation in order to weigh up the pros and cons of the medium-long form and some of the other alternative 2-D forms that have been discussed here. Valery, your points about full shells of various kinds are interesting. I need to make a more systematic survey of full-shells of all kinds. Thanks for moving the discussion forward over this question.

Sun Jul 24 18:24:38 UTC 2011

Jess Tauber wrote:

Gaps

Except that one kinked uninterrupted sequence, my Mendeleev's Line model, folds neatly into a tetrahedron. It takes two mirror-image T3 models, bisects them at equivalent positions, and then recombines them so that each new model has one half from one, and the other from the other mirror-image model. It retains certain symmetries, for instance all the s-block elements flank an equatorial bisection. Because of difficulties I have in visualizing hidden elements (in this case both literally and figuratively), it is taking a long time to see if other features of the model conform to known anomalies in 2D tables. The line starts just offset from the center of the figure. Because filling within periods involves switchback folding of subperiods, and then period blocks fold in a different way (analogous to beta sheet versus alpha helix in protein structures), one cannot consider this model to be any kind of single helix or spiral stucture. Jess Tauber

Sun Jul 24 08:58:53 UTC 2011

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