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:

1st Response to Valery

Valery says "Maximization of number of Z-triads seems to work well for confirming placement of He next to Ne. However, I think that majority of chemists would argue that it does not work as well with placing H next F. Traditional periodic system is the testimony of that." If we are to be guided by the traditional periodic system this would also argue against moving He to group 2 surely, as you seem to favor. If we are trying to find a better or optimal periodic table the argument that it might go against the traditional one is rather puzzling!

Thu Jul 21 17:16:04 UTC 2011

Eric Scerri wrote:

Responding To Philip

OK, call it trivial if you like but it implies that H is in the wrong place in the conventional table. It should be in the halogens. That's the only difference my proposal makes, apart from confirming that group 3 should be Sc, Y, Lu, Lr. But a movement of H is as momentous as moving He to group 2 as in the left-step table.

Thu Jul 21 17:12:19 UTC 2011

Philip Stewart wrote:

Trivial triads

Eric: You say '1/2 of all possible triads', but there are no other possible triads (unless you prolong the sequence to element 170 to get 32 more), And you say it 'follows from the fact that period lengths repeat', but this sounds like what I've said all along: that triads are the trivial consequence of the structure of the periodic system.

Thu Jul 21 17:04:18 UTC 2011

Valery Tsimmerman wrote:

On triads

I think that significance of atomic number triads, or Z-triads, as Eric calls them, has yet to be completely realized. I do not agree with Eric's position that maximization of number of triads will somehow address the problems of the periodic system. Maximization of number of Z-triads seems to work well for confirming placement of He next to Ne. However, I think that majority of chemists would argue that it does not work as well with placing H next F. Traditional periodic system is the testimony of that. I believe that instead of maximization we should look deeper for basic reasons of double periodicity and, therefore, triads. As Eric noted, the apparent reason for the triads is the fact the lengths of periods recur. Why, then, he attempts to brake this basic regularity by turning first two periods of Janet's LST into one?___ Perhaps, instead of maximization we should look for optimization of number of triads. Take, for example, long form of traditional periodic system, which has first period that does not recur, as the early a version of LST promoted by Eric. It can be observed that first group members of all but two groups do not belong to triads. Out of 32 groups only 2 groups, 2nd and 18th, are exceptions to this rule. Those two groups are the odd balls. 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. Optimization calls for decrease in number of triads by placing He next to Be. Optimization calls for identical first two periods, just as in Janet's LSPT. ____ Some time ago Jess made interesting observation that every other alkaline earth element, beginning with second element Be matches every other tetrahedral number and all remaining alkaline earths are exact arithmetic means of those numbers. Even Helium, if counted among the alkaline earths, fits this rule if atomic number zero, that Philip calls for in his Chemical Galaxy, is considered. I believe that Eric is correct when he talks about looking at the elements in terms of Z, but it is simplistic to look at triads without regard to the relationship of atomic numbers to the tetrahedral numbers. ____After Jess' mentioned above discovery, I modified Pascal triangle by suppressing all even numbers and using zeros instead of even numbers in one of the two second diagonals (see images at yahoo T3 group). The result was that numbers in fourth diagonal of modified Pascal triangle corresponding to three dimensional space exactly match halves of Z numbers of EVERY alkaline earth element. This type of numerical regularity is much more interesting than triads. Triads are simply outcome of this regularity on a higher level. Therefore, I choose optimization over maximization of triads, since this has much more interesting math at the foundation and remarkably fits the structure, as well as behavior of the elements.

Thu Jul 21 16:24:48 UTC 2011

Eric Scerri wrote:

Z triads

Yes Philip you are correct. As I have often written, about half of all possible Z triads are valid. This follows from the fact that period lengths repeat and is no indictment on triads themselves. The idea is not to maximize triads period, otherwise I would arrange them in a linear sequence and would have even more of them. The idea is to combine the natural phenomenon of property repetition with an approach that will correct some of the irregularities in the medium-long form table. I proposed an analogy to the change from atomic weight ordering to atomic number ordering although I do not imply that Z triads are as fundamental as Z itself. Perhaps I should be more modest about the claim. I am using Z triads to correct small trouble areas in the periodic table. None of the other criteria are completely replaced. Eric

Thu Jul 21 12:10:07 UTC 2011

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