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).
Essential Features of the Double Shell
Some essential features of this system are:
- Up to element 120, the PSE consists of four shells.For
a view on the new system, see
- Table of elements (HTML) with special columns
Each shell of the PSE is a double-shell with twice as
many electrons per shell as in the conventional periodic
- 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
This rule is intimately connected to the structure of
double-shell periodic system and may be viewed to be a
- 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.
- Diatomic compounds with ionic bonding are centered
around the group 18 elements, those with predominantly covalent
bonding are centered around the group 14 elements.
- 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.
- 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
- 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.
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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
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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
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The Structure of Matter (Rutherford Centennial Symposium, Christchurch 1971),
University of Canterbury Press,
Christchurch 1972, p. 126.
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Journal of Molecular Structure (Theochem), 187 (1989), p. 83
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Int. Journal of Quantum Chemistry, 21 (1982), p. 717
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Journal de Chemie Physique, 76 (1979), p. 630
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Phys. Rev. Letters, 76 (1996), p. 1860