Investigation of the free energy functions for electron transfer reactions

The free energy functions for electron transfer reactions in solution are explored using a previously developed microscopic simulation approach that provides a clear definition of these functions and the variable (the reaction coordinate) used as their argument. The issue of whether the curvatures of the two functions (which correspond to states with nonpolar and polar solutes) are different is given special attention. It is found, in contrast to some previous suggestions, that the curvatures of the two functions are quite similar, even when one would expect differences due to dielectric saturation effects, and that Marcus’ approximation (and, in fact, the linear response theory inherent in this approximation) provides a valid description of the solvent’s role in electron transfer reactions over a wide range of conditions. The present study demonstrates that direct simulations of the reactant and product states do not provide the data needed for determination of the free energy functions in high energy regions. On the other hand, a free energy perturbation approach developed in our early studies does allow one to obtain statistically significant data for these regions of high free energy. Inclusion of the solvent electronic polarizabilities in the potential results in a marked lowering of the solvent reorganization energy, but does not change the ratio of the curvatures of the free energy functions for the nonpolar and polar states. Finally, the effect of solvent tunneling is evaluated with the dispersed polaron method and shown to be rather small, and it is argued that the observed deviations from the classical Marcus theory in the inverted region are due to quantum mechanical tunneling associated with the solute vibrations, rather than to differences in the curvatures of the solvent free energy functions.