Force constants of solvent polarization fluctuations: Softening at intermediate wave vectors

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Abstract
A microscopic calculation of the wave vector (k) dependent force constant [K(k)] of solvent polarization fluctuations in a dipolar liquid is presented. We find that the force constant of the pure liquid undergoes a pronounced softening at intermediate wave vectors (kσ≂2π, where σ is the solvent molecular diameter). An analysis of the modification of the solvent polarization force constant because of the presence of a polar solute molecule is also presented. In agreement with the calculation of Carter and Hynes, we find that this modificaton is a nonlinear effect. In the present density-functional theory, the contribution of the solute enters through the space- and orientation-dependent triplet direct correlation function. We use the convolution approximation of the triplet direct correlation function to derive an analytic expression for the solute-induced contribution to both free energy and force constant. A preliminary numerical calculation shows that the long-wavelength (k→0) force constant increases because of the presence of the solute, which is in agreement with Carter and Hynes and also with Kakitani and Mataga. The significance of these results in charge transfer processes in a dipolar liquid is discussed.