Some calculations of the density profile of inhomogeneous hard spheres using the Fischer-Methfessel approximation

Abstract

The Fischer-Methfessel approximation consists of approximating a pair correlation function of an inhomogeneous fluid by the corresponding homogeneous (bulk) correlation function evaluated with a locally averaged density. The averaging is done over a sphere of molecular dimensions. Using both the Born-Green and the Lovett-Mou-Buff-Wertheim equations to relate pair functions and the singlet density profile, we find that this approximation gives reasonably good density profiles for inhomogeneous hard spheres but that the averaging should be make over a larger sphere than that suggested by Fischer and Methfessel. Also, in our calculations at least, the version of the Lovett-Mou-Buff-Wertheim equation involving the direct correlation function seems preferable to both the Born-Green equation and the other version of the Lovett-Mou-Buff-Wertheim equation. © 1990 American Chemical Society.