Statistical Mechanics of Non‐Spherical Molecules: Spherical Harmonic Expansions on Non‐Spherical Surfaces

Simple pseudo‐spherical harmonic expansions over non‐spherical surfaces are proposed for two body functions such as pair potentials and pair correlation functions of anisotropic fluids. It is shown that the thermodynamics of fluids with Gaussian overlap potential with constant well depth (GOCE fluids) can be calculated from only the leading terms in the expansions over equipotential surfaces. Resummation of the individual terms in the expansions of pair correlation functions over equipotential surfaces give molecular correlations for specific orientations which agreed very well with the same functions calculated directly during the simulations. These functions are used to bring out some significant differences in the structures of GOCE fluids and equivalent site‐site fluids. Support for this work by a grant from the Chemistry Division of the National Science Foundation is gratefully acknowledged.