Calculation of Electron Transfer Rates Using Mixed Quantum Classical Approaches: Nonadiabatic Limit and Beyond

We investigate the applicability of the Ehrenfest and surface hopping methods to calculate electron transfer rates using the spin-boson model with different parameters. Rate constants are obtained from short time dynamics performed in both the diabatic and adiabatic basis sets. Numerical results and theoretical analysis show that these two methods can be reasonably accurate in the nonadiabatic limit, by staying close to an approximate Fermi's golden rule. Beyond the nonadiabatic limit, the calculated mixed quantum classical rates are compared with numerical exact results, and similar accuracy was found as in the nonadiabatic limit. The relation between the current finding and recent studies using the surface hopping method based on long time dynamics is also discussed. It is found that the short time dynamics could be more accurate in calculating rate constants using the mixed quantum classical methods.