Symmetry based approach to triplet correlation functions

Abstract

Two related approaches to the theory of inhomogeneous classical systems are introduced, both yielding analytic forms for triplet and higher-order direct correlation functions in the homogeneous limit. The present theories lead to results that exactly obey the known sum rule relating the triplet direct correlation function to the derivative of the Ornstein-Zernike function. The resulting triplet direct correlation functions are then found to be simple products in both reciprocal and real space. Agreement with simulation results for the triplet direct correlation function in the hard sphere fluid is generally found to be very good; even the simpler version of the theory agrees well with the results of the more computationally intensive weighted density approximation.