Density-functional approach to the structure of classical uniform fluids

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Abstract
An underlying connection between the structure of a uniform fluid and that of its nonuniform counterpart provides a means of testing various approximations used in density-functional theories of nonuniform fluids. This paper proposes a density-functional approach to the structure of classical uniform fluids that is based on a simple version of the weighted-density approximation for the one-particle direct correlation function of the corresponding nonuniform fluid. In the context of the integral-equation method, this approach provides a closure to the Ornstein-Zernike relation that implicitly includes correlations to all orders. To demonstrate and test the accuracy of the approach, it is applied, at the first level of iteration, to the hard-sphere fluid. Results for three important structure-related functions, namely the radial distribution function, the cavity function, and the bridge function, are all shown to be in generally good agreement with simulation. In contrast, corresponding results from an alternative approach, based on a truncated-expansion approximation for the one-particle direct correlation function, are in significantly poorer agreement with simulation at higher densities.