LXXIV. The spatial correlation of electrons in atoms and molecules IV: The correlation of electrons on a spherical surface

Abstract

Summary The aim of this paper is to compare the effects of the exclusion principle and the interelectronic repulsion on the correlation of electrons when they are restricted to move on a spherical surface. The two examples considered are four electrons of the same spin and eight paired electrons, four of each spin. These are analogous to the 5S state of carbon and the neon closed shell respectively. Lennard- Jones(1952), using a single determinant wave function has shown that the correlation of electrons in these systems is such that particles with the same spin tend to arrange themselves in a tetrahedral configuration relative to one another, but that in the closed shell there is no correlation between the two tetrahedra. In this paper a more accurate wave function is used, making some allowance for the correlation of electrons due to electrostatic repulsion. It is found that the probability of electrons of the same spin having a tetrahedral distribution is increased while at the same time there is a ten...