Variants of the optimised random phase approximation: from one direct correlation function to many different radial distribution functions

Abstract

It is shown that there are an infinite number of radial distribution functions (RDFs), corresponding to only one direct correlation function (DCF) of the optimised random phase approximation (ORPA). This observation in the thermodynamic perturbation theory is in sharp contrast to that of integral equation theories in which they uniquely correspond. By devising a new method we will be able to introduce various perturbation theories of simple liquids all coming from one DCF. Among all, we will only present analytically seven variants of the ORPA in the thermodynamic perturbation theory of liquids. The DCF of hard-core potential for all variants is assumed to be the same as the ORPA. However, interestingly enough the resulted expressions for the Helmholtz free energies and the RDF are obtained very differently. Furthermore, the resulted thermodynamic properties come out somehow the same, whereas the structural functions of some variants are found to behave much better than the standard ORPA.