New and proper integral equations for site-site equilibrium correlations in molecular fluids

Abstract

We show that the often used site-site direct correlation function cannot be defined in terms of a sum over a subset of the diagrams in the interaction site cluster series for the equilibrium pair correlation functions of a molecular fluid. However, from an exact topological reduction, we arrive at a new class of site-site direct correct correlation functions that are properly defined in the diagrammatic sense. The class is composed of four topologically distinct functions which are related to each other and the pair correlation function through four coupled Ornstein-Zernike-like equations. These new integral equations are exact and provide a rigorous foundation for integral equation theories of molecular fluids. The formal solutions to the equations are constructed, and the utility of the formulation is illustrated by discussing one example of an approximate closure to the integral equations.