Integral equation approximations for inhomogeneous fluids: functional optimization

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Abstract
Following a systematic approximation to the Kirkwood—Green entropy expansion, within the grand canonical ensemble, functional optimization of the grand potential is used to derive closed sets of integral equations which approximate the structure and thermodynamics of both homogeneous and inhomogeneous fluids. Connections are made with existing approximations in the literature, and compact derivations are presented. Selected new equation sets are presented. The central role of the ‘ring’ term in the entropy expansion is emphasized.