Theoretical study of electron transfer rates in the inverted region

We apply the hierarchical equations of motion (HEOM) approach to study the electron transfer (ET) rates in the inverted region. The relation of ET rates with electron coupling strength and the solvent relaxation time is investigated. It is found that with the increase of the electronic coupling, the ET rate first increases then decreases. The ET rate also increases with the decrease of the solvent relaxation time. Comparison to the approximate theories based on Fermi's golden rule and Landau-Zener theory shows that: the FGR based on first order perturbation is only valid at small couplings, and the Landau-Zener theory is also not valid at large electronic coupling due to the assumption of ballistic motion of the reaction coordinate.