Quantum theory of polarization in liquids: Exact solution of the mean spherical and related approximations

The mean spherical approximation and related integral equations theories (such as the linearized hypernetted chain equation) are studied for a fluid composed of atoms or spherical molecules with quantum mechanical fluctuating internal dipoles. We derive the solutions of these equations for the case in which the intramolecular restoring force for a fluctuating dipole is harmonic (i.e., a quantum Drude model). In the limit of low oscillator frequencies, the solutions reduce to those deduced by Pratt on the basis of classical theory. We discuss the frequency dependence of the fluid renormalizations of atomic polarizabilities, and show that for the zero frequency applications discussed by Pratt, the classical theory is correct. We find, however, that the finite frequency quantum effects play a dominant role for many experimentally relevant properties. Generalizations of the quantum theory to include features such as charge overlap and hyperpolarizabilities are also discussed. The relationship between low order quantum mechanical perturbation theory and the integral equation theories is described.