Surrogate Hamiltonian description of solvation dynamics. Resolution of global responses into spatial profiles

Abstract

We present a more formal development of our recent theory of solvation dynamics, allowing a more detailed examination of the mechanism of solvent response to the sudden change of the charge distribution of an immersed solute. A distinctive feature of the theory is that both the solute and the solvent molecules are described in terms of relatively realistic interaction site models. Furthermore, in the theory the solute-solvent coupling is formulated in terms of the solute-solvent site-site interactions, rather than by appealing to some sort of cavity construction. Appling the general formulation of nonequilibrium statistical mechanics we derive an approximate nonequilibrium distribution function f Σ h(Γ, t) for a “surrogate” Hamiltonian description of solvation dynamics. 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 dynamic problem, without losing the important solute-solvent static correlations that are important for the equilibrium solvation. With f Σ h(Γ, t) we can calculate not only the solvation time correlation function but also other observables of interest such as the evolution of the solvent polarization charge density around the solute. We also consider the spatial resolution of some of the measures of the solvent response to the sudden transition, namely the reaction potential and the electrostatic energy gap. Applications of the theory are illustrated with calculations of the solvation dynamics of a cation in acetonitrile and the solvation dynamics of formaldehyde in water.