Hypervertex approximations for fluids. I. General formalism and the linear hypervertex approximation for symmetric fluids

A method for generating Dyson equations for two-particle fluid correlation functions is applied to the case of ionic and polar fluids to systematically yield a sequence of approximations that go beyond the lowest-order gamma-ordered approximation. The first two such approximations are given here. For the simplest class of such fluid models—those having hard-core potentials and a high degree of symmetry (e.g., the restricted primitive model, dipolar spheres)—the first of these approximations, the linear hypervertex approximation, is used to derive explicit expressions for thermodynamic quantities and the dielectric constant in terms of the hypervertex function, the hard-sphere reference correlation function, the perturbing pair potential, and the state of the fluid (e.g., the temperature and density of species).