Electron Transfer Theory Revisit: Motional Narrowing Induced Non-Markovian Rate Processes

While the exact theory of chemical reaction rate processes is always non-Markovian, experimental rates do often show practically Markovian that supports kinetics rate constant description. In this work, we propose to use the Kubo's motional narrowing line shape function to characterize the Markovian character of the simplest two-state electron transfer reaction system. On the basis of analytical results, we demonstrate the related Markovianicity parameter as an interplay between the °uctuating solvent environment and the coherent transfer coupling. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast solvent modulation regime, where the resonant tunneling enhancement plays the important role. The e?ect of quantum solvation on electron transfer, which is dominant in the fast modulation regime, will also be highlighted.