Temperature- and pressure-dependence of the outer-sphere reorganization free energy for electron transfer reactions: a continuum approach.

The outer-sphere reorganization free energy for electron-transfer reactions in polar solvents and its variations with temperature and pressure are studied in the dielectric continuum framework by extending the recent fluctuating cavity description [J. Chem. Phys. 2005, 123, 014504]. The diabatic free energies are obtained as a function of three variables, i.e., radii of two spherical cavities for the donor and acceptor moieties of an electron-transfer complex and a solvent coordinate that gauges an arbitrary configuration of solvent orientational polarization. Equilibrium cavities relevant to the reactant and product states are determined via the variational principle. This incorporates cavity size readjustment accompanying electron transfer and related electrostrictive effects. Another important consequence of the variational determination of equilibrium cavities is that their size depends on thermodynamic conditions. The application of the theoretical formulation presented here to electron self-exchange shows that in contrast to the prediction of the standard Marcus theory, the solvent reorganization free energy decreases with temperature. This is in excellent accord with a recent experiment on a mixed valence dinuclear iron complex in acetonitrile [J. Phys. Chem. A 1999, 103, 7888]. It is also found that electrostriction makes a significant contribution to outer-sphere reorganization. Model calculations for the dinuclear iron complex system show that about 25-30% of the total solvent reorganization free energy arises from cavity size changes, while solvent repolarization is responsible for the rest.