Continuous charge distribution models of ions in polar media. Part 6.—Reltationship between quantum and classical charge distributions

Abstract

A formal relationship between the classical phenomenological charge distribution representations of ions and the quantum mechanical treatment is presented. This relationship is established by means of an expansion of the molecular electronic quantal charge density in terms of a complete set of orthonormal functions. Such an expansion is similar in form to a classical multipole expansion for an arbitrary charge distribution. The analysis reported provides a rigorous mathematical and an enhanced physical interpretation of the “effective Bohr radial” quantities introduced with the earlier phenomenological models.