On the equilibrium structure of dense fluids

A factorization ansatz for the triplet direction correlation function c(3) is combined with the exact relation between c(3) and the derivative of the pair function c(2) with respect to density to derive a simple and tractable approximation for c(3) in dense, classical fluids. The predictions of this approximation are found to be in good agreement with the results of 'exact' molecular dynamics simulations for the 'soft sphere' model near freezing. The approximate c(3) is then used to derive an improved integral equation for the pair correlation function which is found to yield satisfactory results. In another application, the third order term in the density functional theory of freezing is systematically evaluated for the first time and is found to lead to significant improvement over the usual second order theory, particularly for soft interatomic repulsions.