Hund's basic potential from direct summation

Abstract

The Coulomb potential at points inside NaCl and CsCl structures was calculated previously by a method of direct summation. This method consists, simply, of adding all the Coulomb potentials, at the point of consideration, due to the point charges of the ions in a piece of the crystal. The shape of the piece of crystal should be determined correctly. Although this method succeeded when applied to NaCl and CsCl structures, it failed when applied to ZnS, CaF2, and Cu2O structures; the reason is that the last three structures lack a certain type of symmetry. However, a hypothetical structure H was constructed such that this method succeeded when applied to it. Moreover, Hund's basic potential can be expressed in terms of the potentials of H and CsCl by a simple relation derived from Hund's identity. Thus, Hund's basic potential was computed at a grid of points of intervals a/16 and tabulated. The potential inside all structures having the cubic Bravais lattices as components can, therefore, be computed easily from this table.