The pair and direct correlation functions of an inhomogeneous fluid

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Abstract
Functional expansions are given relating the pair and direct correlation functions of an inhomogeneous fluid to the many body direct correlation functions of a homogeneous fluid. The exact expression for the pair correlation function to second order in density gradients contains a coupling between particle correlation and density inhomogeneity. In contrast to several local density correlation models, typical of those used recently in the theory of fluid interfaces, the exact theory predicts such coupling even for particles lying in the plane perpendicular to the direction of the density gradient. This means that an interface can never be viewed strictly as a stack of thin homogeneous phases. In the low density limit, the three local density approximations considered agree with the exact theory to first order in density gradients but not to second order.