Perturbation approach

Abstract

Perturbation theories became a powerful technique in the theory of liquids in the early 1970s. The main idea of a perturbation approach in general terms reduces to the following. The system under consideration is decomposed into a reference model, characterized by some reference interaction potential and the same density and temperature as the original system, and a perturbation which, strictly speaking, must be small.¹ Properties of the reference model are assumed to be known to appreciable accuracy. The thermodynamics of the full system is obtained by appropriate averaging of the perturbation over the reference model. It is important to bear in mind that the perturbation is in the interaction potential (and not in density). The peculiar thing about application of this approach to liquids is that the reference model must be nonideal. In most cases it is a hard-sphere system with an appropriately chosen effective diameter. Hard spheres are a starting point in the theory of liquids, as an ideal gas is in the theory of gases and a harmonic solid in solid-state physics. Nowadays a lot of data is available from computer simulations of hard spheres and from integral theories of correlation functions. The reason for the success of perturbation theories is that the structure of a liquid is determined primarily by the repulsive (hard-core) part of the interaction, while the attractive part provides a uniform background potential in which the molecules move. This is the main concept of the perturbation approach. Throughout this chapter we assume a pairwise additive interaction energy with spherical potentials.