A statistical formulation is presented for the reaction and cavity-field response functions of an isotropic nonpolar substance. It is shown that the reaction-field approach can be made consistent to a good approximation with statistically calculated fields by a reasonable choice of the cavity radius a. The cavity radius is a complicated function of density, temperature, and molecular parameters and, in first approximation, is given by expression a−3= ∫ 0∞3r−4ρ(r)dr,where ρ(r) is the radial distribution function. The value of a3 computed for liquid Xe from x-ray scattering data according to the latter formula is found to be equal to ½σ3, where σ is the Lennard-Jones collision diameter; this value is in very good agreement with the Böttcher—Onsager value for a3 calculated on the basis of the macroscopic dielectric constant and polarizability of the free molecule. The dielectric and statistical reaction and cavity-field functions are compared and discussed.

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The many-body aspects of intermolecular forces are examined for the model based on a fluctuating reaction field. This is accomplished by expanding the reaction field in a series involving optical and translational parameters, and an expression is obtained for the cohesive free energy in terms of frequency-dependent polarizabilities and dipole-coupling tensors. When applied to a system of fixed translational parameters a series expansion is obtained for the configurational total potential energy, the leading term of which arises from pair interactions, the next higher term from triple interactions, etc. It is shown that the pair and triple potentials reduce to forms identical with the ones obtained by ordinary quantum-mechanical second- and third-order perturbation theory. The significance of the results is discussed.

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