Correlation functions of classical fluids. IV. Perturbation theory on correlation functions and the scaling properties of the Lennard-Jones system

Abstract

A perturbation equation is derived from the formalism of inhomogeneous systems of Percus for the calculation of the radial distribution function (rdf). Two special aspects of this development are noted: (1) The derivation is via a mixture system; (2) the direct evaluation of the inhomogeneous direct correlation function C2(1,2/U) is circumvented by the application of a previous result (Ref. 19) on the Percus–Yevick (PY) approximation. The equation arrived at is quite simple and is amenable to numerical solution. As a test, we propose an ’’internal’’ perturbation, or ’’scaling’’ theory, on the Lennard–Jones (LJ) system. Tests on the temperature scaling and the density scaling were carried out with respect to the correlation functions and the thermodynamic properties. The results were compared with the molecular dynamics data. Remarkable improvement was found as compared with the corresponding PY results, especially at high densities and low temperatures. A ratio function w (r) is introduced, which is found to be essential in determining the performance of the perturbative equation. This w function is unity for the PY case and can be viewed as a correction to the regular PY theory. Its functional form is closely related to the direct correlation function and its behavior was determined for several cases.