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

Bernard Schaeffer wrote:

Electron filling of the shells

Let us begin with hydrogen. It has only one electron usually in the fundamental level. Excited levels are normally not used but they may contain electrons. Each of these excited levels may be filled progressively with electrons. Each time an electron is added, a proton (and eventually neutrons) must also be added. The fundamental level of hydrogen may contain two electrons but it is unstable. It becomes stable if a proton (and neutrons) are added to the nucleus, giving a helium nucleus with two protons and one to ten neutrons, depending on the isotope. To obtain a He atom, two electrons have to be added around the nucleus. ___________ Each level (letter n, constant on a horizontal line for atoms lighter than Ca) contains a maximum of 0, 6, 10 or 14 electrons given by 2(2l+1) (the l should be in italics, not possible here). ______________________________________________________See figure (http://storage.canalblog.com/94/49/292736/67010620.jpg) Each sublevel contains a maximum of 2 or 4 electrons, from m = 0 to m =±l. Number l appears as a letter spdf, corresponding to 0, 1, 2, 3. It is constant in a column. _______ It is not possible to put more than two electrons in the fundamental level of hydrogen and in sublevels. This is described by the Pauli exclusion principle.____________ The fundamental level has n=1 with no sublevel: l =0. This can be seen on the figure where the elements are paired according to the Pauli exclusion principle (I am probably the first to do that)._____________ Now let us add one proton, some neutrons and one electron to obtain Li. This electron has to be at a higher level n = 2 and l =0. In this level we can put one electron more, giving Be. Then we have l =1 where we can put two more electrons. The toal number of electrons is now of 6 and so on… until Ca. Then the regularity is broken and the Schrödinger model fails as it can be seen on the figure where on the right of Ca there are two values of n, 3 and 4. The 3d subshell is lower than the 3p. In the last line, one may see, right of Ra, 3 levels 5, 6 and 7. This may be described by empirical principles or rules but it has no effect on the table which is what it is. The many presentations are probably all more or less equivalent except for the He, Lu, Lw case.__________________________________________________ All this seems somewhat complicated but it may be intuitive by observing the spherical drawings of the vibration modes of a sphere, called spherical harmonics, angular solution of the Schrödinger equation. I hope to have no mistake…

Mon Aug 01 14:38:40 UTC 2011

Valery Tsimmerman wrote:

Sorry for assaulting the French

Sorry for Assaulting the French Chemists, but their position would assault Charles Janet. One day they will regret that, I am sure. There is no question that Janet's LSPT is superior to IUPAC traditional table, simply because no satisfactory definition of a period can be provided on a basis of traditional PT.___ Eric, you are absolutely correct, QM does not explain the basis of the Periodic Table, that is n+l rule. ____ Sorry, but Chemists will have to deal with the math, because it is obvious, for at least some of us, that mathematics rules the Periodic System. It was even obvious to Mendeleev, who believed that one day there would be a mathematical theory that would explain the intricacies of the Periodic Table. IUPAC table is dead, despite the fact that so many fail to recognize it. It was first introduced in 1905 and rejected by most of the chemists then, it was revived in 1960's, after half of century. It might take long time, but that clumsy structure will be rejected again. No doubt about that. Valery Tsimmerman.

Mon Aug 01 13:06:59 UTC 2011

Eric Scerri wrote:

To Bernard

Please explain how QM augmented with Pauli's Principle can explain the order of electron filling, in other words the n + l or Madelung rule? If there is any explanation it needs to assume the n + l rule rather than deriving it and that is not quite good enough. eric scerri

Sun Jul 31 23:59:18 UTC 2011

Bernard Schaeffer wrote:

Response about

I think that similarities is somewhat subjective. A mathematical theory is not if it is experimentally verified. This is the case for the Schrödinger theory of the hydrogen atom completed by the Pauli exclusion principle. It explains rigourously the periodic table for atomic numbers less then 20 (Ca). For heavier atoms it may be seen only when the atomic levels and the electron numbers are considered. It has no incidence on the shape of the official periodic table. For elements heavier than Ca, the atomic levels are interpenetrating but it is not very important for the periodic table. This is why the IUPAC official table should be only slightly modified. The french Academy said that it is totally absurd to place He above Be and that I assaulted chemistry… The Definitive Problem of the Periodic Table seems to be now restricted to the problems of Lu, Lr, He and some exotic elements about whose very little is known. The elements 103, 104, 112, 118 are produced by a nuclear reaction. I am not sure that they may exist as atoms.

Sun Jul 31 19:47:34 UTC 2011

Jess Tauber wrote:

Re: Ignobility

See http://en.wikipedia.org/wiki/Relativistic_quantum_chemistry All of a piece, with different instantiations depending on where we are in the table, including inert pair/knight's move effect. Combine contractions with shielding, hold your breath for two moves, rinse, repeat. How many periodic properties depend on atomic size, or ionic, etc.? What about element 112? That *should* be like Hg- is it? Are there any unusual properties seen between 104 til then? I haven't found any references to such, but have enough experiments been done on the handful of atoms often produced? What about spectra- are the data completely consistent with normal d configurations? No anomalies other than Lr at 103?

Sun Jul 31 00:21:41 UTC 2011

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