A comparative study of different methods for calculating electronic transition rates

We present a comprehensive comparison of the following mixed quantum-classical methods for calculating electronic transition rates: (1) nonequilibrium Fermi's golden rule, (2) mixed quantum-classical Liouville method, (3) mean-field (Ehrenfest) mixed quantum-classical method, and (4) fewest switches surface-hopping method (in diabatic and adiabatic representations). The comparison is performed on the Garg-Onuchic-Ambegaokar benchmark charge-transfer model, over a broad range of temperatures and electronic coupling strengths, with different nonequilibrium initial states, in the normal and inverted regimes. Under weak to moderate electronic coupling, the nonequilibrium Fermi's golden rule rates are found to be in good agreement with the rates obtained via the mixed quantum-classical Liouville method that coincides with the fully quantum-mechanically exact results for the model system under study. Our results suggest that the nonequilibrium Fermi's golden rule can serve as an inexpensive yet accurate alternative to Ehrenfest and the fewest switches surface-hopping methods.