Abstract
An exact equation for the pair correlation function of fluids is derived by density functional methods. Comparing this result with the hypernetted chain (HNC) equation we propose a weighted density approximation for the so-called bridge function that improves the ordinary HNC theory. For a hard sphere fluid this method leads to thermodynamically more consistent results than the HNC, Percus-Yevick (PY) and Rogers-Young (RY) approximations. Adding an attractive potential to the hard sphere repulsion we obtain better correlation functions than can be found with the HNC and the reference HNC (RHNC) approximation.
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