Spontaneous emission and nonadiabatic electron transfer rates in condensed phases

In this paper we explore the non-Condon effect of fluctuations of the tunneling matrix element caused by a condensed medium on the rates of nonadiabatic electron transfer (ET) and spontaneous emission from an excited electronic state. For a charge-transfer complex immersed in a polar polarizable liquid, the solvent effect renormalizes the ET matrix element due to (i) the instantaneous field of the solvent nuclear polarization and (ii) equilibrium solvation by the electronic solvent polarization. Fluctuations of the classical electric field of the solvent affect the form of the preexponential factor in the ET rate constant. In the new expression for the rate preexponent the vacuum ET matrix element is multiplied by the factor theta forming an effective ET matrix element in condensed phases. The parameter theta is controlled by the magnitude and orientation (relative to the differential solute dipole) of the diabatic transition dipole of the charge-transfer complex. The theory predicts a possibility of localization of the transferred electron when theta becomes equal to zero. The same treatment is applied to the rate of spontaneous radiative electronic transitions. We find that the product of the transition frequency and the adiabatic transition dipole is invariant in all solvents when (i) the diabatic transition dipole is collinear to the differential solute dipole moment and (ii) the spectral shift due to dispersion solvation is small. Under the same conditions, the adiabatic transition dipole in condensed phases and the effective ET matrix element are related by the Mulliken-Hush equation that becomes exact in our treatment.