Quantum correction for electron transfer rates. Comparison of polarizable versus nonpolarizable descriptions of solvent

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Abstract
The electron transfer rate constant is treated using the spin‐boson Hamiltonian model. The spectral density is related to the experimentally accessible data on the dielectricdispersion of the solvent, using a dielectric continuum approximation. On this basis the quantum correction for the ferrous–ferric electron transfer rate is found to be a factor 9.6. This value is smaller than the corresponding result (36) of Chandler and co‐workers in their pioneering quantum simulation using a molecular model of the system [J. S. Bader, R. A. Kuharski, and D. Chandler, J. Chem. Phys. 93, 230 (1990)]. The likely reason for the difference lies in use of a rigid water molecular model in the simulation, since we find that other models for water in the literature which neglect the electronic and vibrational polarizability also give a large quantum effect. Such models are shown to overestimate the dielectricdispersion in one part of the quantum mechanically important region and to underestimate it in another part. It will be useful to explore a polarizable molecular model which reproduces the experimental dielectric response over the relevant part of the frequency spectrum.