Perturbation theory and the thermodynamic properties of fluids. I. General theory

This paper is the first of three articles describing a new approach to the perturbation theory of liquids and dense gases. The thermodynamic properties are calculated from an expansion about a hard sphere fluid reference system, in which the hard sphere diameter is chosen by a variational principle. The method differs from that of other investigators in the description of the intermolecular forces and in the calculation of corrections to first order theory. The energy of a fluid molecule is defined by a function which depends upon the local configuration of its neighbors. All terms in the expansion are given by averages of this quantity instead of the pair potential. A modified form of the λ expansion is used to derive new expressions for corrections to first order theory, and approximations for these corrections are derived using concepts from macroscopic fluctuation theory. Using these formulas, the expansion can be computed to all orders in the perturbation. The theory is developed in terms of a general set of variables and the corresponding distribution functions which describe the short range structure of fluids.