Equilibrium and nonequilibrium solvation and solute electronic structure. I. Formulation

Abstract

A theoretical formulation is developed to describe the electronic structure of an immersed solute, electrostatically coupled to a polar and polarizable solvent. The solvent is characterized, in the dielectric continuum approximation, by electronic and orientational polarizations. Starting from a general free-energy expression for the quantum solute–solvent system, a time-independent nonlinear Schrödinger equation is derived. The nonlinearity arises from the assumed equilibration of the solvent electronic polarization Peqe, to the solute electronic wave function Ψ and the solvent orientational polarization Por. When Por is arbitrary, there is nonequilibrium solvation. When Por is equilibrated to Peqe and Ψ, equilibrium solvation obtains. The theory is illustrated for a model symmetric electron donor–acceptor solute system in a two state basis set description. Solution of the nonlinear Schrödinger equation in the presence of arbitrary Por yields nonequilibrium solvation stationary states (NSS) for the solute–solvent system, including the solvent-dependent solute electronic structure, and the associated free energies. When Por=Peqor, the corresponding equilibrium solvation states (ESS) and their characteristics are obtained. The NSS are classified into three distinct regimes, according to the relative strengths of the electronic coupling, which tends to delocalize the solute electronic distribution, and the solvent polarization, which tends to localize it. The ESS stability characteristics are also important in this classification. Two of the regimes correspond to activated electron transfer processes, and differ according to whether there is or is not a continuous free-energy path leading from localized reactants to localized products. The third regime, in which the electronic coupling dominates the solvent polarization, corresponds to stable delocalized states between which spectroscopic transitions are of interest. Finally, the inclusion of electronic exchange in the theory leads to the necessity of more than one solvent coordinate in order to describe the free-energy surface for the solute–solvent system.