Integral-equation perturbation theory for the radial distribution function of simple fluids

Abstract

The radial distribution function (RDF) for a fluid whose molecules interact according to the Lennard-Jones potential is calculated by means of statistical-mechanical perturbation theory using the Percus-Yevick (PY) and hyper-netted-chain (HNC) theories to approximate the perturbation corrections. In both cases the infinite perturbation series can be summed in closed form. The contribution of the attractive part of the pair potential to the RDF is treated as a perturbation to a reference system whose molecules interact according to the repulsive part of the potential. The RDF of the reference system is expanded about RDF for a fluid of hard spheres of diameter d. Five criteria for the determination of d are presented and tested. Excellent agreement between the calculated RDF and computer simulations are obtained over a wide range of densities from the HNC perturbation treatment for the attractive intermolecular forces and the PY perturbation expansion for the repulsive forces with the hard-sphere diameter d given by a PY compressibility criterion which is proposed here.