Reorganization free energies and quantum corrections for a model electron self-exchange reaction: comparison of polarizable and non-polarizable solvent models

The solvent contribution to the reorganization free energy for electron self-exchange in aqueous Ru(II)-Ru(III) is computed for two recently developed polarizable water models, AMOEBA [J. Phys. Chem. B 107, 5933 (2003)] and SWM4-NDP [Chem. Phys. Lett. 418, 241 (2005)], and for the earlier POL3 model [J. Phys. Chem. 99, 6208 (1995)], and compared with the reorganization free energy of non-polarizable water models. The 'solute', defined as the two ions and their first hydration shells, is treated as non-polarizable. We find that the solvent ('outer sphere') reorganization free energy is reduced by 22% for SWM4-NDP and by 11% for POL3 relative to the non-polarizable TIP3P water, but increased by 5% for AMOEBA water. This is less than the 38% reduction suggested by standard continuum theory and confirms the view that continuum theory predicts a stronger dependence of solvent reorganization on the optical dielectric constant than what is obtained from atomistic simulation. The varying degree of reduction in reorganization free energy for polarizable water models is the consequence of two opposing effects: (i) reduction in reorganization free energy due to decreased electronic response; and (ii) increase in reorganization free energy due to increased nuclear response. The first effect gives a consistent decrease of about 30%, while the second effect strongly depends on the polarizable water model used and is largest for AMOEBA water. Rate enhancements due to quantum corrections are computed in the harmonic bath approximation and range between 3.8 and 10.9, in good agreement with the estimate obtained from experimental dispersion data of liquid water, 7.7. The rigid non-polarizable water models overestimate the quantum correction in the libration modes, which effectively compensates for the neglect of quantum corrections in the absent stretching modes. About 85% of the solvent reorganization is due to the second and third solvation shell of the ion pair. Size effects caused by the finite number of solvent molecules are minor and much smaller than for oxidation of a single ion.