Surrogate Hamiltonian description of solvation dynamics. Site number density and polarization charge density formulations

We explore a recently developed theory of solvation dynamics that analyzes the molecular response of the solvent to a sudden change of the charge distribution of a solute particle immersed in it. We derive an approximate nonequilibrium distribution function f_∑^h(Γ, t) for a "surrogate" Hamiltonian description of the solvation dynamics process. The surrogate Hamiltonian is expressed in terms of renormalized solute-solvent interactions, a feature that allows us to introduce a simple reduction scheme in the many-body dynamics problem without losing essential solute-solvent static correlations that rule the equilibrium solvation. With f_∑^h(Γ, t) in hand we calculate the solvation time correlation function in two ways. The first one, previously reported, is basically a "dielectric formulation" in which the local polarization charge density of the solvent is the primary dynamical variable that couples to the field of the solute. In the new development reported here, the "site number density formulation," the primary dynamical variables comprise the set of local solvent site number densities. We find that the dielectric formulation is embedded in the solvent site number density formulation as shown, for example, by comparing the respective time correlation functions of the solvation dynamics. An important feature of our approach is that at every stage the coupling between the solute and solvent is formulated in terms of the solute-solvent intermolecular interactions, rather than some sort of cavity construction. Furthermore, both the solute and the solvent molecules are represented by interaction site models. Applications of the dielectric theory are illustrated with calculations of the solvation dynamics of a cation in water and an exploration of the effect of the details of the charge distribution on the solvation dynamics of a benzenelike solute in acetonitrile.