SOLVATION FREE-ENERGIES AND SOLVENT FORCE-CONSTANTS

A theoretical formulation for the solvent force constant k(q), which gauges electrical potential fluctuations for an ion in solution and whose charge dependence is a measure of nonlinear aspects of solvation, is presented in terms of the solute charge (q) variation of the solvation free energy. This formulation allows the calculation of k(q) via integral equation theories. This is illustrated by a series of calculations for ionic solutes in model dipolar-quadrupolar solvents via the reference hypernetted chain (RHNC) integral equation approach. It is found that the q variation of k(q) can be comprehended in terms of the cooperative (or competing) contributions of the solvent dipole and quadrupole to the acceleration of the solvation free energy. By contrast, traditional notions of dielectric saturation prove to be of much less direct relevance, due in part to the importance of competing electrostriction effects. The formalism is also applied to available simulation and integral equation solvation free energy studies of aqueous ionic solvation to infer the behavior of k(q). The extensions for the formalism to more complex solutes (e.g., ion pairs), to higher order fluctuations (e.g., electric field), and to the solvent frequency and effective mass are briefly indicated.