Dispersion solute-solvent coupling in electron transfer reactions. I. Effective potential

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Abstract
Theories of electron transfer (ET) reactions and optical spectra in condensed phases consider electronic transitions between instantaneous Born-Oppenheimer energies of the intramolecular electronic states which depend on the system nuclear configuration. With the aim of constructing a molecular description of the solvent effect on these phenomena, we consider in the present paper a system composed of a polar polarizable solute immersed in a solvent of polar polarizable molecules. The instantaneous free energies are defined in terms of partial partition functions obtained by averaging over the electronic degrees of freedom of the solute and the solvent. Electronic polarizabilities of the solvent molecules are modelled as quantum Drude oscillators. For the solute, two models are considered: (i) the Drude oscillator and (ii) the two-state solute. The former enables us to derive the solute-solvent dispersion potential with account for the effects of nonlocal polarizability coupling in the solvent and the many-body solute-solvent dispersion contributions. These effects are analyzed using equilibrium theories of nonpolar liquids. The two-state description of the solute involves redistribution of the electron density between the two localized sites. The instantaneous adiabatic (in contrast to diabatic in the Drude oscillator model) free energy can be derived in this case under the only restriction of the quantum character of the solvent electronic excitations. It leads to the ET matrix element renormalized from its vacuum value due to the equilibrium field of the electronic solvent polarization and the instantaneous field of the permanent solvent dipoles. The theory predicts some useful relations which can be applied to treating the solvent effect on transition moments of optical spectra. The equilibrium ET matrix element is found to depend on the orientation of the solute diabatic transition dipole in the solute molecular frame and the spectral shift due to solvation by permanent and induced dipoles. This offers an interesting phenomenon of self-localization of the transferred electron (zero ET matrix element). Finally, the comparison of two derivations performed enables us to write down the diabatic instantaneous free energies which can be used for a molecular formulation of the effect of the solvent and the solute energy gap on ET rates.