The Pyriodic Table of the Elements

A More Elegant Element Arrangement?


"The Evolution of the Periodic System" [Scerri, 1998] presents a pyramidal table of the chemical elements. That table, based on [Jensen, 1989], is reproduced here without the lines connecting related elements: Element Period Pyramid (old)

From an esthetic point of view, two aspects of the arrangement are less than optimally elegant. First, the top layer has only one row, H and He, whereas all other layers have two rows. Second, the logical groupings within each row feature 2, 6, 10, and 14 elements. This suggests an orderly arithmetic progression. Yet the groupings of 2 are on the far left while the groupings of larger size decrease in size from left to right. Thus the groupings by row from left to right are:

2   6
2   6
2   10   6
2   10   6
2   14   10   6
2   14   10   6

Thus, because the groupings of size 2 are on the left end of each row, the groupings are not in numerical sequence. Esthetics suggest placing the groupings of size 2 on the far right. But is this just wishful thinking, or can it somehow be achieved without disrupting other requirements of element arrangement?

The following minor modifications to the arrangement satisfy both esthetic criticisms, yet preserve the sequencing of elements by atomic number and the layering. First, we move Li and Be up to form a second row for the first layer. We then take the two leftmost elements from each subsequent row and move them up to the right end of each preceding row, beginning with Na and Mg. The result is a new version of the pyramidal table: Element Period Pyramid (new).

Now that the top layer has two rows, all layers have two rows. The sequence of logical groupings within each row is now in numerical progression from right to left:

  6 2
  6 2
  10   6 2
  10   6 2
  14   10   6   2
  14   10   6   2

Relationships in the original pyramidal table diagram used in the Scerri article, denoted by heavy solid, light solid, and dashed lines, are preserved. The only problem introduced is the (apparent) distancing of helium from the rest of the inert gases.

Of course, most people are more familiar with the standard periodic table of the elements: Element Periods (old). Does the new arrangement have any effect on that? Aligning each row in the new pyramidal table along its right edge instead of centering it produces: Element Periods (new).

We can see that a very different look arises. A long-standing, glaringly inelegant aspect of the traditional table disappears --- the placement of the Lanthanides and Actinides. The traditional approach is to stick them in as if they were a footnote, at the bottom of the chart and not where they belong in the sequence of elements. This problem is caused by there not being room to place them where they belong, because they are blocked by the two columns on the left end of the traditional table.

Just such a new arrangement has actually been suggested before by Janet [Janet, 1927] and Neubert [Neubert, 1970]; see also The Double-Shell Periodic System of Elements. This new arrangement seems more parsimonious and elegant, and therefore possibly more "accurate." The issue of helium's distance from the other inert gases might be resolved by invoking a connection outside the plane of the diagram or at least a dotted line of some kind. Perhaps a three- or higher-dimensional version of the diagram is more faithful to the "actual" arrangement. There may be something to be said for a spiral arrangement such as the one on p.80 of [Scerri, 1998] or the 3D arrangement on pp.78-79.

Is there any underlying rationale besides esthetics that might motivate this new arrangement? If we look at the grouping of electron subshells, we can see how the new arrangement follows naturally. The traditional periodic table is organized on the basis of electron shells. The new organization is based on electron subshells.

The shells are in sequence by increasing energy: Shell 1, Shell 2, Shell 3, and so on, have increasing energy. But, their constituent subshells do not line up by energy when we list them by shell. Listing the subshells by shell we have 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s, 5p, 5d, 5f, 6s, 6p, 6d, 7s, 7p, 8s. But listing them by increasing energy we get instead 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s.

The subshells form pyramids, based on the number of electrons per subshell. Each subshell is composed of orbitals, with up to two electrons per orbital. Electron Subshell Pyramids distills the subshell pyramid information presented in the Carnegie Mellon University chemistry website element diagram CMU Periodic Table with Electron Subshell Energy Progression. Please note: if you are prompted about security when clicking the CMU link, choose the option to not block the activity.

Flattening the subshell pyramids gives the more horizontal arrangement Flattened Electron Subshell Pyramids. It is a simple step from this diagram to the new periodic table, or Pyriodic Table of the Elements, named in honor of the subshell pyramids. We show the new table, complete with electron subshell information, in Element Subshells (new). Here one can see the orderly progression through the rows of the table (traditionally called "periods") of the electron subshell pyramids. Contrast this with a similar chart for the traditional table: Element Subshells (old).

The traditional table rows correspond to electron shells being filled: Electron Shell Filling. The new table's rows correspond to electron subshell pyramids being filled: Electron Subshell Pyramid Filling.


Charles Janet
La structure du noyau de l'atome, considérée dans la classification périodique des éléments chimique
Beauvais November, 1927, p. 15.

William B. Jensen
Classification, Symmetry and the Periodic Table
Computing and Mathematics with Applications, vol. 12B, nos. 1-2, pages 487-510, 1989.

Karl-Dietrich Neubert
Double Shell Structure of the Periodic System of the Elements
Zeitschrift für Naturforschung B (Chemical sciences), 25a (1970), p. 210.

Eric R. Scerri
The Evolution of the Periodic System
Scientific American, September 1998, pages 78-83.

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