Equilibrium and nonequilibrium solvation and solute electronic structure. III. Quantum theory

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Abstract
The electronic structure of a solute in a polar and polarizable solvent depends on the nonequilibrium (or equilibrium) state of the solvent. Here we present a theory for this phenomenon, at the level of a dielectric continuum description of the solvent, characterized by an orientational polarization Por and an electronic polarization Pel. The entire range of electronic coupling between solute electronic states is considered. The present theory supersedes, in important respects, our earlier work [H. J. Kim and J. T. Hynes, J. Phys. Chem. 94, 2737 (1990); J. Chem. Phys. 93, 5194 (1990); 93, 5211 (1990)] by including a full quantization of Pel; this is a feature recently shown in a model study for weak electronic coupling [J. N. Gehlen, D. Chandler, H. J. Kim, and J. T. Hynes, J. Phys. Chem. (to be published)] to be necessary for, e.g., a correct description of electron transfer activation free energies and transition states. The quantization of Pel is effected via a coherent state formulation, coupled with a multiconfiguration self-consistent representation of the solute-Pel wave function. Nonequilibrium free energies and solute electronic structure are found and depend explicitly on the comparative time scales of a transferring electron in the solute and of Pel. The corresponding equilibrium relations are also found. For activated electron transfer, the current theory recovers (and generalizes) the conventional expression for the activation free energy, in both the electronically nonadiabatic and adiabatic regimes, for small electronic coupling. For larger electronic coupling—but still within the regime of activated electron transfer—the theory predicts an increased activation free energy compared to conventional results, associated with the (partial) solvation by the electronic polarization of delocalized solute electronic structure of the transition state. This trend is the same as that previously reported by us, but is smaller in magnitude due to the finite time scale of the transferring electron. The same is true for even stronger electronic coupling, characteristic of delocalized complexes, SN1, SN2, and proton transfers. Our previous predictions of novel spectroscopic aspects for delocalized complexes are confirmed.