Density functional theory of charged, hard-sphere fluids

An approximate electrostatic (ES) excess free energy functional for charged, hard sphere fluids is presented. This functional is designed for systems with large density variations, but may also be applied to systems without such variations. Based on the Rosenfeld method of perturbation about a bulk (homogeneous) reference fluid [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)], the new ES functional replaces the reference fluid densities with a functional of the particle densities, called the RFD functional. The first-order direct correlation function (DCF) in the particle densities is computed using as input the first- and second-order DCFs in {(rho) over bar (i)(x)}, the inhomogeneous densities defined by the RFD functional. Because this formulation imposes no a priori constraints on the form of the RFD functional-it is valid for any choice of {(rho) over bar (i)(x)}-the RFD functional may be chosen (1) so that the input DCFs (that is, DCFs in {(rho) over bar (i)(x)}) may be approximated and (2) so the combination of {(rho) over bar (i)(x)} and input DCFs yields a good estimate of the first-order DCF in the particle densities. In this way, the general problem of finding the excess free energy functional has been replaced by the specific problem of choosing a RFD functional. We present a particular RFD functional that, together with bulk formulations for the input DCFs, accurately reproduces the results of Monte Carlo simulations.