The effect of intramolecular quantum modes on free energy relationships for electron transfer reactions

A general quantum mechanical description of exothermic electron transfer reactions is formulated by treating such reactions as the nonradiative decay of a "supermolecule" consisting of the electron donor, the electron acceptor, and the polar solvent. In particular, the role of the high-frequency intramolecular degrees of feedom on the free energy relationship for series of closely related reactions was investigated for various model systems involving displacement of potential energy surfaces, frequency shift, and anharmonicity effects. The free energy plots are generally found to pass through a maximum and to be asymmetric with a slower decrease in the transition probability with increasing energy of reaction. For high-frequency intramolecular modes this provides a rationalization of the experimental observation of "activationless" regions. Isotope effects are discussed as also are the oscillatory free energy relationships, predicted for low temperatures and high frequencies, and which are analogous to the vibrational structure in optical transitions.