Modeling of ultrafast electron-transfer dynamics: Multi-level Redfield theory and validity of approximations

The short-time electron-transfer (ET) dynamics following short-pulse optical excitation is investigated for representative models by numerical reduced density-matrix calculations. The multi-level Redfield-theory equations are solved for two-site models with up to three strongly coupled reaction modes, which are weakly coupled to a dissipative environment. The so-called normal and inverted regimes of ET and stationary as well as nonstationary initial-state preparation are considered. The simulations illustrate the importance of electronic backflow in the case of strong electronic coupling and the effect of coherent vibrational wave-packet motion on the ET process. Three approximations, which have widely been used in ET modeling, are tested against the Redfield-theory results: The golden rule (GR) formula for nonadiabatic electron transfer, the secular approximation to the Redfield tensor and the diabatic-damping approximation (DDA) (neglect of the electronic interstate coupling in the construction of the Redfield tensor). The results illustrate the breakdown of the GR formula with increasing electronic coupling strength and the failure of the secular approximation for coherently driven ET. It is found that the DDA can provide a surprisingly accurate description of ultrafast ET processes when the zero-order vibrational levels are nearly in resonance. It is demonstrated by a benchmark calculation for a three-mode ET model that the near-resonance condition is generally fulfilled for multimode models in the inverted regime.