Ion solvation dynamics in an interaction-site model solvent

The molecular theory of the frequency-dependent and wavevector-dependent longitudinal dielectric function ε{lunate}L(k, ω) is derived for fluids comprising interaction-site model molecules in which point charges are located on the interaction sites. We find that ε{lunate}L(k, ω) is a simple functional of a particular charge susceptibility χμφ{symbol}0 (k, ω), which in turn is related to a collective charge-charge equilibrium time correlation function. The electrostatic part FBorn (t) of the time-dependent free energy of solvation of a solute that instantaneously changes its charge state is, on the other hand, determined by a charge susceptibility χμφ{symbol}0(1) (k, kt́, ω) of the solvent in the presence of the solute molecule in its initial charge state. Using an approximate relation between χμφ{symbol}0(1) and χμφ{symbol}0 we express F Born(t) in terms of χμφ{symbol}0. The resulting theory is applied to calculate the solvation time correlation function of the solute immersed in a dipolar hard sphere (DS) and in dipolar dumbbell (DD) model solvent; the mean spherical approximation and an extended mean spherical approximation are used to compute the structure of the DS and DD solvent models, respectively. With parameters chosen so that the two models have the same molecular volume and the same electric dipole moment, it is found that they have very nearly the same ε{lunate}L(k, ω) except at large wavevector, but significantly different solvation time correlation functions.