Reaction coordinates for electron transfer reactions.

The polarization fluctuation and energy gap formulations of the reaction coordinate for outer sphere electron transfer are linearly related to the constant energy constraint Lagrangian multiplier m in Marcus' theory of electron transfer. The quadratic dependence of the free energies of the reactant and product intermediates on m and m+1, respectively, leads to similar dependence of the free energies on the reaction coordinates and to the same dependence of the activation energy on the reorganization energy and the standard reaction free energy. Within the approximations of a continuum model of the solvent and linear response of the longitudinal polarization to the electric field in Marcus' theory, both formulations of the reaction coordinate are expected to lead to the same results.