Generating function density functional theory: free-energy functionals anddirect correlation functions for hard-spheres

A recent density functional theory for the inhomogeneous hard-sphere fluid expresses the free-energy in terms of a set of derivatives, with respect to the particle radius, of a simple generating function. In the present paper this generating function approach (GFA) is reformulated in terms of genera l conditions on the coefficients of the differential operator involved in t he theory. This gives more flexibility to the theory and allows for ready d erivation of new functionals that are tested in the calculation of density profiles of hard spheres near a hard wall. Comparison with the results of t he previous formulation of the GFA shows a better performance of the new fu nctionals and also gives a much deeper understanding of the structure of th e theory and its connections with the fundamental measures theory of Rosenf eld. A simple modification of the GFA pair direct correlation functions yie lds explicit analytic expressions with very good agreement with simulation results. (C) 2001 Elsevier Science B.V. All rights reserved.