Perturbation theory of the structure factor and the Helmholtz free energy of a classical fluid: II. Thermodynamic consistency

Abstract

For part I see ibid., vol.20, p.2483, (1987). A perturbation theory of the structure factor of a classical fluid is developed. It is emphasised that the combination of the fluctuation-dissipation theorem and the Henderson-Ashcroft expansion of the two-particle distribution function of the reference system yields a thermodynamically consistent formalism of the structure factor and the free energy. The ring diagram approximation is employed here, so that the compressibility equation of state becomes identical with the energy equation of state calculated from the so-called random-phase approximation (RPA) free energy. The author's approximation to the structure factor, however, goes far beyond the RPA for the same quantity and can be considered as an extension of the mean-density approximation to higher order. The two formalisms developed here and in paper I of this series are complementary to each other, and the emphasis in this paper is on the description of the long-wavelength density response.