Electron distribution in completed shells

Atoms and ions with noble-gaS electron configurations have usually been described as having spherical symmetiy. For some considerations this description is satisfactory for others, however, it is advantageous to consider the atoms or ions to have a shape other than spherical—the helium atom can be described as deformed to a prolate ellipsoid of revolution, and the neon atom and other noble-gas atoms as deformed to a shape with cubic symmetry. 

If the structure of the helium atom were exactly described by the symbol la9 and that of neon by 1 a22a 2p these atoms would have spherically symmetrical electron distributions.24 However, the mutual repulsion of the two electrons in the atom causes them to avoid one another the wave function for the atom corresponds to a larger probability for the two electrons to be on opposite sides of the nucleus than on the same side (for the same values of the distances of the two electrons from the nucleus, there is greater probability that the angle described at the nucleus by the vectors to the electrons is greater than 90° than that it is less than 90°). This effect, which is called correla- 

The electron distribution of the helium atom in field-free space is, of course, spherically symmetric. The atom has, however, a large polarizability in a quadrupole electric field, which we may ascribe to the partial orientation of the prolate ellipsoid. 

A consequence of the Pauli exclusion principle is that electrons with parallel spins tend to avoid one another it is said that about an electron there is a Fermi hole which other electrons tend to avoid. In consequence, four electrons with parallel spins occupying the four sp% orbitals of an atom tend to assume relative positions corresponding to the corners of a tetrahedron about the nucleus.16 Hence the carbon atom in the state s22s2pz S may be described as tetrahedral. The effect of correlation is to increase the tetrahedral character by the assumption by the orbitals of some d, f, character, which concentrates them about the tetrahedral directions. 

It has been assumed16 27 that the neon atom and other atoms with an s2p outer shell also may be described as tetrahedral. However, the four spa electrons with positive spin are independent of the four with negaiive spin, and the two corresponding tetrahedra are free to assume arbitrary relative orientation.28 Correlation requires that the most stable relative orientation be the inverse one hence the neon atom and the other s2p6 atoms can be described as cubic. Their polarizability in a cubic multipole electric field is large and that in a tetrahedral field small.29 

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