Dynamical effects in the calculation of quantum rates for electron transfer reactions

Abstract

This paper presents results of path-integral quantum dynamics simulations of electron transfer rates in a simple class of model Hamiltonians for symmetric and asymmetric electron transfer systems. Our study is aimed at testing the practical usefulness of a centroid factorization of the electron transfer rate constant in the deep tunneling regime. To circumvent the sign problem in quantum Monte Carlo simulations of the electron flux, local filtering techniques have been employed. The simulations show that due to dynamical effects, the reactive flux far outside the transition state region also plays an important role in determining the rate. These results suggest that while the centroid formulation of the equilibrium (imaginary-time) quantum transition state theory (QTST) applied to the electron path is accurate for nonadiabatic electron transfer reactions, dynamical (real-time) effects can produce significant corrections to the QTST estimate for the rate outside this region. For model parameters characteristic for a chemical electron transfer system, we found that the rate is enhanced by a factor Ze≊4. The origin of these dynamical corrections can be understood within a perturbation theory in the number of kinks on the imaginary-time electron quantum path.