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 e xcited electronic state. For a charge-transfer complex immersed in a p olar polarizable liquid, the solvent effect renormalizes the ET matrix element due to (i) the instantaneous field of the solvent nuclear pol arization and (ii) equilibrium solvation by the electronic solvent pol arization. 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 e lement is multiplied by the factor theta forming an effective ET matri x element in condensed phases. The parameter theta is controlled by th e magnitude and orientation (relative to the differential solute dipol e) of the diabatic transition dipole of the charge-transfer complex. T he theory predicts a possibility of localization of the transferred el ectron 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 transit ion dipole is invariant in all solvents when (i) the diabatic transiti on dipole is collinear to the differential solute dipole moment and (i i) the spectral shift due to dispersion solvation is small. Under the same conditions, the adiabatic transition dipole in condensed phases a nd the effective ET matrix element are related by the Mulliken-Hush eq uation that becomes exact in our treatment.