Vibrational Relaxations and Dephasing in Electron-Transfer Reactions.

The rates of nonadiabatic electron-transfer reactions depend on four main factors: the probability of finding the system in a conformation in which the reactant and product states have the same energy, the electronic coupling that drives oscillations between the two diabatic states, the dephasing that damps these oscillations, and the vibrational or electronic relaxations that trap the product state by transferring energy to the surroundings. This paper develops a simple expression that combines these factors in a relatively realistic manner. Values for all the parameters in the expression can be obtained from microscopic quantum-mechanical/molecular-mechanical simulations. The theory is tested by calculations of the rates of electron transfer from excited indole rings to a variety of acceptors in peptides and indole-acrylamide compounds. For the systems that are studied, the theory gives considerably better agreement with experiment than expressions that do not consider the rates of vibrational relaxations and dephasing.