Modified weighted-density-functional theory of nonuniform classical liquids

A new formulation of the weighted-density approximation (WDA), as currently applied in the theory of nonuniform classical liquids, is presented. This modified weighted-density approximation retains a key feature of the original approximation by including correlations, at least approximately, to all orders in the functional expansion of the excess free energy. It continues to require as input only the two-particle direct correlation function of the uniform liquid. In contrast to the original WDA, however, practical implementation of the modified WDA demands considerably less computational effort. When applied to the freezing of the hard-sphere liquid, the results obtained previously with the original WDA, already in good agreement with simulation, are reproduced quite accurately. It is concluded that in its new formulation the WDA is now just as simple to implement as the widely used Ramakrishnan-Yussouff theory. But as with the original WDA the new formulation more accurately describes the freezing of hard spheres and is more soundly based in the sense of including correlations to all orders.