Response theory in the multipole reaction field model for equilibrium and nonequilibrium solvation: Exact theory and the second order polarization propagator approximation

Exact response functions are derived for a multipole solvent reaction field model of equilibrium and nonequilibrium solvation using the generalized Ehrenfest theorem and assuming a spherical cavity surrounding the solute. The starting point is the Schrödinger equation and we shortly review how the reaction field is introduced into the Schrödinger equation in order to clearly identify the limitations of describing solute–solvent interactions with a reaction field model. The solvent is described as an isotropic homogeneous linear dielectric medium characterized by a static and an optical dielectric constant. From the exact response functions we derive linear response functions within the higher random phase and the second order polarization propagator approximation. Excitation energies, oscillator strengths, and polarizabilities are then calculated for solvated H2S and furan using the augmented correlation consistent triple-ζ (aug-cc-pVTZ) and double-ζ (aug-cc-pVDZ) basis sets for H2S and furan, respectively. We have also calculated excitation energies and oscillator strengths for H2S with standard (vacuum) ab initio methods using a variety of basis set, as there has been no previously reported values of these quantities calculated with the second order polarization propagator approximation. The second order polarization propagator approximation gives excitation energies and oscillator strengths close to values obtained by coupled cluster methods for a solvated H2S molecule, whereas the higher random phase approximation tends to overestimate the value of these quantities. The solvent effect of the excitation energies follow the same trends for all of the reaction field ab initio methods used in the present study, but some oscillator strengths show different solvent effects whether they are calculated with correlated or with noncorrelated ab initio methods. The calculated polarizabilities show the same solvent effect independent of any inclusion of dynamical electron correlation. It is also shown that the equilibrium solvation model is not appropriate for high-frequency perturbations.