Free-energy model for the inhomogeneous hard-sphere fluid mixture: Triplet and higher-order direct correlation functions in dense fluids

Extensive Monte Carlo simulation results for the pair and triplet direct correlation functions of the one-component, hard-sphere system near freezing are presented. These results are in good agreement with the analytic predictions of a recently derived free energy density functional for the inhomogeneous hard-sphere fluid. This free energy model is based on the fundamental geometric measures of the particles. It provides the first unified derivation of the analytic description of the hard-sphere thermodynamics and pair structure as given by the scaled-particle and Percus–Yevick theories, and yields simple explicit expressions for the high order direct correlation functions of the uniform fluid.