Theory of polar fluids. II

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Abstract
Previous work on fluids of polar polarizable molecules is extended. Simplification is obtained by eliminating the direct correlation function c(12) in favour of a translationally invariant function w(12) defined previously, and by consolidating equations in matrix form. Two closely related problems are the asymptotic form of the pair correlation function h(12), and the calculation of microscopic expressions for the dielectric constant in a form which manifestly exhibits the required independence of the shape of the system. The solution is obtained by a procedure which formally exactly parallels the case of rigid polar molecules, with matrices replacing numbers. The connection between the chemical potential and the renormalization of the dipole moment and the polarizability is pointed out and utilized to obtain an expression for the excess Helmholtz free energy ΔA due to dipolar forces. The SSC approximation is examined; it is found that ΔA can be calculated directly from the solution of the SSC equation at a single density and temperature without explicit integration over a coupling parameter. Similar results for the pressure and internal energy are given.