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Introduction to the Double-Shell PSE
Prolog The Aufbau (Build-up) principle of the conventional periodic system of the elements is based on the consecutive filling of the states of the hydrogen atom. However, as widely discussed in the literature, there are many exceptions to that rule. One might raise the question, if it is not possible to find a simplified system, which conserves the chemical families of the conventional periodic system, but is characterized by a less complicated formulation of the Aufbau principle.

Here a periodic system is introduced, which is of a high symmetry and is decribed by a very simple Aufbau principle, which does not require exceptions. We call it the Double-Shell Periodic System (PSE).
of the

Essential Features of the Double Shell Periodic System

Some essential features of this system are:
  1. Up to element 120, the PSE consists of four shells.For a view on the new system, see
    Double-Shell PSE: - Table of elements (HTML) with special columns highlighted
    Each shell of the PSE is a double-shell with twice as many electrons per shell as in the conventional periodic system.

  2. By the Aufbau principle for the double-shell periodic system, the filling of a new shell starts with states of highest angular momentum of the shell and then continues with decreasing l. After filling of the lower half of a double-shell, this process is repeated for the upper half. Due to the magnetic quantum number m, there are 2l + 1 states for each l. In addition to the spin quantum number s = ±1/2, which for fixed l results in a doubling of states according to spin up and spin down electrons, a newly introduced topical quantum number c = ±1/2 results in a further doubling of states according to electrons in the lower and upper halves of the double-shells. In addition, the system is drawn such, that it is imaging in a natural way a potential well's state filling. See the diagram
    Occupied states of elements: Table elucidating elements' electronic structure (HTML) for the example of the element Z = 32, Germanium.

    Here we have to mention the well known Madelung rule. By this rule, not states with n = nr + l + 1, but states with N = nr + 2l + 1 are of the same energy. This rule is intimately connected to the structure of double-shell periodic system and may be viewed to be a natural consequence.

  3. With regard to latest experimental findings, the PSE correctly places the metallic form of Hydrogen. For high atomic number Z, it correctly places the transuranium elements.

  4. Diatomic compounds with ionic bonding are centered around the group 18 elements, those with predominantly covalent bonding are centered around the group 14 elements.

  5. A hypothesis:
    For high Z, the modification of the central Coulomb potential due to the interaction of the shell electrons is not to be questioned and has been "predicted" already by the Madelung rule. But what effect produces the fourfold degeneracy at small Z? As a hypothesis, the following model is offered:
    By elementary geometry, three electrons define a plane. Since the plane may have any orientation in space, it cannot define an isotropic three-dimensional space. Thus, disregarding the nucleus, it takes four electrons to define an isotropic three dimensional space. In full symmetry, the four electrons form a tetrahedron: each two of the four electrons at the corners may be viewed as having opposite spin and sitting on one of the two orthogonal edges. The spin axis of the electrons of one edge are orthogonal to the spin axis of the electrons of the other edge. These spin properties are not effected, if the charges of the electrons are considered to be smeared out. In in this highly symmetric static model, each of the electrons may occupy a spherical triangle on the surface of the a tetrahedral sphere, as shown in In essence, the spatial arrangement of the interacting shell electrons - rather than the hydrogen spectrum - dominates the structure of the PSE. We expect the fourfold degeneracy of states to extrapolate consistently from the lowest shell to higher shells.

  6. The element Beryllium, having four electrons, has a remarkable combination of extreme properties. Even though very light, it is a very stable metal. Its elasticity is larger than that of steel, its strength four times that of aluminum. The melting point at nearly 1600 K is very high. In the gaseous phase, it is mono-atomic. How do these properties relate to an atomic shell with four electrons arranged according to the tetrahedral sphere?

  7. It remains to solve the mystery of the hidden symmetry by unifying the related arguments available in the literature to obtain a consistent theory on the double-shell structure of the PSE.
See also


  • M. Schaedel, J. V. Kratz, Chemie des Seaborgium, Chromatografie mit einzelnen Atomen, Phys. Bl. 53 (1997), p. 865
  • Edward G. Mazur, Graphic Representations of the Periodic System during One Hundred Years, The University of Alabama Press, Alabama 1974
  • Niels Bohr, Z. Physik, 9 (1922), p.1
  • E. Madelung, Die mathematischen Hilfsmittel des Physikers, 3rd ed., Springer Verlag, Berlin, 1936
  • Charles Janet, La structure du noyau de l'atome, considérée dans la classification périodique des éléments chimique, Beauvais: novembre, 1927, p.15
  • D. Neubert, Double Shell Structure of the Periodic System of the Elements, Z. Naturforschung, 25a (1970), p. 210
  • A. O. Barut, Group Structure of the Periodic System, in Wybourne, Ed., The Structure of Matter (Rutherford Centennial Symposium, Christchurch 1971), University of Canterbury Press, Christchurch 1972, p. 126.
  • M. Kibler, The Periodic System of the Elements: Old and new Developments, Journal of Molecular Structure (Theochem), 187 (1989), p. 83
  • Hanno Essén, Periodic Table of the Elements and the Thomas-Fermi Atom, Int. Journal of Quantum Chemistry, 21 (1982), p. 717
  • Christian K. Jørgensen, The Periodic Table and Induction as a Basis of Chemistry, Journal de Chemie Physique, 76 (1979), p. 630
  • S. T. Weir, A. C. Mitchell, and W. J. Nellis, Metallization of Fluid Molecular Hydrogen at 140 GPa, Phys. Rev. Letters, 76 (1996), p. 1860
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