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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Eric Scerri wrote:

A few comments

Yes I agree the Janet-Stowe-Scerri is not definitive. And yes in a sense I have returned to my 2007 position as presented in my The Periodic Table, Its Story and Its Significance (2007). But I now have two conflicting proposals on the table, excuse the pun. I am presenting the H in the halogens proposal my Very Short Introduction to the Periodic Table book which is due out soon. I received the proofs from the publisher just today. These discussions have helped enormously to sharpen my views and I will be making small changes to the concluding chapter on alternative tables as a result of our conversations. ______Incidentally, while looking for something on my computer I accidentally came across a very nice version of the Timothy Stowe table (one m not 2 here). It appeared in the well-known, in the US at least, calendar that was issued by the I2R company each year for many years. They have become something of a collectors item. That's I squared R. The Stowe table is shown along with an explanation of what it's about. Could this be the original source, in which case it is conceivable that somebody connected with these calendars might know the origin of the Stowe table. All the best, eric. I would be happy to send copies of this Stowe table via E-mail on request.

Wed Jul 27 12:14:31 UTC 2011

Philip Stewart wrote:

Not definitive

Can't we just agree that 'Janet-Stowe-Scerri' is not definitive? We should note that it places H and He under Li and Be, so Eric, you seem to have come back to your 2007 view.

Wed Jul 27 09:28:19 UTC 2011

Valery Tsimmerman wrote:

Structural similarity.

He and Ne as structurally similar, as Zn and Yb are, not as Zn and Cd though._____If we were able to look at the atoms in detail, we would be able to recognize that structural similarity between He and Be is much stronger than that between He and Ne.

Tue Jul 26 16:05:46 UTC 2011

Philip Stewart wrote:


I'm not a reductionist. Ecology is the most irreducible of the sciences. But the great progress of the 1860s was the move from classifying elements by their behaviour to classifying them by numerical values, RAM and valence. Once Z had replaced RAM and quantum numbers had been discovered, it became possible to represent the elements on that basis alone. The electronic structure explains much behaviour (not all; relativistic effects appear in heavy elements), but it is inconsistent to misrepresent the position of just two elements on the basis of behaviour. Valery's table is unique in showing clearly both the completion of periods and the completion of shells. There remains the mystery of why Ar behaves like a noble gas with an incomplete M shell, when Kr and Xe can react with F. There is no mystery with He, since He++ would be a naked alpha particle.

Tue Jul 26 06:46:22 UTC 2011

Eric Scerri wrote:

TV series

Yes this is a repackaging of a series first shown on UK TV called Chemistry A volatile History. The quality is mostly very good. I was a consultant on the original series and am mentioned in the credits of one or two of the episodes directly connected with the periodic table and Bohr's model of the atom. The narrator is the British-Iraqi physicist called Jim Al-Khalili. As a result the material is viewed a little too much from the physics point of view. You can also view the whole thing on youtube by searching for "Chemistry a Volatile History". Also see,

Tue Jul 26 03:41:54 UTC 2011

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