Gaussian multipole functions for describing molecular charge distributions

Abstract

Differentiating spherical Gaussians produces a set of Gaussian multipole functions that behave asymptotically in the same way as point multipoles but are more useful for describing molecular charge densities as they also include charge overlap effects at short range. Coulomb matrix elements between Gaussian multipoles are readily evaluated, including the anisotropy. A simple general equation for interactions between point multipoles is also derived.