On the quantum theory of electron transfer: effect of potential surfaces of the reactants and products

In this study the electron transfer theory for the high frequency intramolecular mode and low frequency medium mode has been rederived using different methods. For a single-mode case when the reactant surface is not in a thermal equilibrium but in a thermocoherent state the authors have derived the rate and discussed about the quantum features of the rate. In the limit of very low and very high temperatures the expressions are derived analytically and compared with the case of thermal distribution. Secondly, a Franck-Condon factor for a multimode displaced, distorted, and Duschinsky rotated adiabatic potential surfaces has been derived to obtain the rate. Lastly, a systematic investigation is made to show the temperature dependence on the rate due to displacement, distortion, and Duschinsky rotation of the harmonic potential energy surfaces of the reactant and product manifold.