Application of a multilevel Redfield theory to electron transfer in condensed phases

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Abstract
A quantum mechanical theory of photoinduced electron transfer, based on the Redfield theory of relaxation, is developed and applied to the standard two state–one mode system interacting with a thermal bath. Quantum mechanical treatment of the reaction coordinate allows incorporation of both finite vibrational dephasing and energy flow rates into the description of electron transferdynamics. The field–matter interaction is treated explicitly to properly incorporate the total energy and magnitude of the vibrational coherence present in the initially prepared state. Calculation of the reduced density matrix of the system is carried out in a vibronic basis that diagonalizes the electron exchange coupling so that the method is valid for arbitrarily large coupling strength. For weak electronic coupling, we demonstrate the equivalence between the results from Redfield theory and those obtained from the standard perturbative expression (golden rule) for nonadiabaticelectron transfer. We then discuss quantitatively the breakdown of the Fermi golden rule with increasing electronic coupling strength. The failure of the golden rule is seen to result from either slow energy equilibration in the reactant or product well or from quantum interference effects resulting from finite dephasing rates. For cases where the reorganization energy is large compared to the frequency of reactive motion, such that we may ignore nuclear tunneling, results from the theory show good agreement with those from the semiclassical Landau–Zener theory when motion of the reaction coordinate through the surface crossing region can be considered to be ballistic. Finally results are shown in the weak damping (coherent) limit that demonstrate interference effects between phase coherences involving states in both wells.