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

Philip Stewart wrote:

anomalies

Mendeleev tinkered with atomic weights to get rid of anomalies, Janet idealized shell structures to get rid of them, and the standard table does not show them at all except in the hesitation over La, Lu, Ac and Lr. We should just accept that there are things that physics cannot yet explain, but that does not mean that they are not explicable in principle.

Fri Jul 29 09:28:13 UTC 2011

Bernard Schaeffer wrote:

A definitive periodic table

The official IUPAC periodic table is 97% in accord with quantum mechanics. Indeed, only three elements (He, Lu and Lr) are at the wrong place in the official table according to rigorous mathematical quantum mechanics (Schrödinger equation of the hydrogen atom combined with the Pauli exclusion principle without taking into account the electron anomalies) as shown in the table de described here http://bernardschaeffer.canalblog.com/archives/2008/09/23/4934243.html

Fri Jul 29 08:50:40 UTC 2011

Jess Tauber wrote:

Primary anomalies cont'd

We often discuss n+l values here and on other online lists. But the anomalies/first-member deviations discussed in the first post below seem to be more about n-l instead, where the values are fixed at 1 (for odd periods) or 2 (for even). It has always puzzled me, in a universe filled with symmetry, why only n+l would be important. Might both n+l and n-l be? Could there also be some mathematical function linking them and thus forcing the mappings in a motivated fashion?

Fri Jul 29 04:57:26 UTC 2011

Jess Tauber wrote:

Primary anomalies?

I took another look at the system of elements with ground state anomalies, and now wonder whether some are more 'primary' or prototypical than others. In the f block we have positions where we would expect f1 and f8, while in the d block instead d4 and d9. It turns out that if one maps just these to the T3 model an interesting pattern emerges. They are distributed in a radially symmetrical manner about the rotational axis of the tetrahedron. I usually orient the T3 so that H, He, Li, Be are at the very top. Remember that tetrahedra have 4 faces. The dual periods, when T3 and its subtetrahedra are oriented H-top, build up the tetrahedral structure as bent up (skew) rhombi from below, that is, the two lower tetrahedral faces. But the primary anomalies (and near neighbor anomalies) mostly occupy the UPPER two faces of the tetrahedron. Exceptions are few, unless one counts spin-orbit distortions from Janet period 8, which are on the lower two faces of a 120-sphere tetrahedron. If we also include the first-member issues from the first (1 or 2) periods containing s and p blocks, the picture is fuller. The s, p first member sets are 'outer' electronic structures, whose activated electronic configurations (for bonding?) may be odd (as in hybridization, or the covalent character when ionic is expected). The d, f are more internal, and their anomalous behavior is more in the ground state instead (but what about the addition of 2 s electrons here?). I'm curious what the s, p spin-orbit period 8 elements are like in this regard.

Fri Jul 29 04:41:38 UTC 2011

Eric Scerri wrote:

Talk in London

I will be giving a talk on my forthcoming book, "A tale of seven elements" at University College, London on the evening of August 18th, to a history of chemistry reading group organized by Professor Hasok Chang of Cambridge. I assume the meeting is open to all comers. I dont know the location but please get in touch by E-mail if you are interested in attending. eric

Thu Jul 28 10:59:43 UTC 2011

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