High-order direct correlation functions of uniform fluids and their application to the high-order perturbative density functional theory

Abstract

Simple analytical expressions for the direct correlation functions of uniform fluids of all orders are derived based on a simple weighted density approximation. The equation thus obtained for the third-order direct correlation function is in satisfactory agreement with simulation data for uniform hard sphere fluids. The obtained expressions are employed to derive two general equations for the perturbative density functional theory of all orders. One of them concerns the direct correlation functions, while the other concerns the direct correlation functions weighted with the present weighting function. The general equations have been used to determine the equilibrium structure about a test molecule immersed in a bulk fluid of the same species. The calculations indicated that both equations with expansions truncated at the fifth order provided for bulk fluids improvements with respect to the second-order perturbative density functional theory (corresponding to the hypernetted-chain closure). The second equation with the bulk density considered as an adjustable parameter, determined by equating the ``virial pressure'' calculated for a bulk fluid to the Carnahan-Starling pressure, provided the best agreement with simulation data. The second equation with an adjusted bulk density was also used to determine the density profile of a hard sphere fluid in a spherical cavity; good agreement with simulation data was obtained.