The dielectric constant and related equilibrium properties of molecular fluids: Interaction site cluster theory analysis

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Abstract
The interaction site formalism for molecular fluids is used to develop a microscopic theory for the dielectric constant ε. A rigorous correlation function expression for ε is obtained from an elementary application of linear response theory. The formula is applicable to mixtures and fluids composed of polarizable and deformable molecules. The derivation shows that the correlation functions which determine ε are short ranged so that ε can be expected to be independent of sample shape or any other macroscopic boundary conditions. The theories for ε developed by Nienhuis and Deutch and by Ho/ye and Stell are shown to be special cases of the formalism given herein. A cluster diagramatic analysis is presented to examine the origin and significance of the large distance behavior of the correlations between neutral polar molecules. The diagramatic analysis is also used to show that the large distance form for the potential of mean force between two microscopic ions at infinite dilution in a dielectric liquid solvent is zAzA′/εr where zA and zA′ are the charges of the two ions. This asymptotic form is independent of the short‐ranged interactions between the ions and solvent molecules.