A simple power-law approximation for the solvation time correlation function

In previous work we developed a new class of molecular theories of solvation, the "surrogate Hamiltonian" (SH) theories, to elucidate the structural, energetic, and dynamical aspects of the solvation process relevant to ultrafast time-domain spectroscopy and charge transfer reactions in solution. In these theories we represent both the solute and the solvent molecules by interaction site models of the sort already used in many computer simulation studies of solutions. Of special interest to the characterization of the nonequilibrium solvation process is the solvation time correlation function Z(t), that can be obtained in time-dependent fluorescence Stokes shift experiments. The experimental and theoretical studies of Z(t) in polar solvents have revealed an important dependence of the solvation time correlation function on the nature of the solute, especially with respect to the multipolar order of the charge jump. Here we investigate a simplified version of our theory of solvation dynamics, which is based on the straightforward application of a method previously developed by our group, the reference frequency modulation approximation (RFMA). In the earlier paper we showed that when applied to the solvation tcf, the RFMA leads to a simple interpretation of the power law equation for Z(t) found empirically by Maroncelli and coworkers. Here we propose a new power-law approximation to the solvation time correlation function that retains the dependence of Z(t) on the features of the solute. More specifically, the new application of the RFMA discussed here enables us to express the solvation tcf Z_Y(t) of solute Y in terms of the solvation tcf Z_R(t) of another solute R in the same solvent. The solutes R and Y may differ in size, shape, and charge distribution. The consistency of Z(t) calculated with more accurate methods and the simpler RFMA theory is quite satisfactory.