SELF-CONSISTENT ENVIRONMENTAL FLUCTUATION EFFECTS ON THE ELECTRONIC TUNNEL FACTOR AND THE ACTIVATION GIBBS ENERGY IN LONG-RANGE ELECTRON-TRANSFER

Electronic-vibrational interaction including the solvent environment in long-range electron transfer is disregarded in most applications of electron transfer theory and the electron tunnel factor associated with a constant electron density. We provide here a formalism for self-consistent variational calculation of both the electron tunnel factor and the polarization configuration at the crossing of the reactants' and products' potential Gibbs energy surfaces for diabatic processes. The scheme applies to arbitrary localized electronic wave function forms and leads in general to modulation of the electronic wave functions by the environment, to non-Condon effects, and to lower activation Gibbs energy compared with the Condon limit of constant electron density. We show specifically how the formalism can be combined with a set of LCAO MOs. We also show that single-exponential wave functions lead to significantly larger tunnel factors which reach asymptotic limiting values at long electron transfer distances where the orbital exponent has dropped to 60-75% of its value at polarization equilibrium.