Non-Condon nature of fluctuating bridges on nonadiabatic electron transfer: Analytical interpretation

Rigorous expressions for the calculation of nonadiabatic electron transfer rates are presented in closed forms for donor-acceptor systems incorporated fluctuating bridges and their non-Condon electronic couplings. In high temperature limit, they show a similar property to the Marcus formula. However, the Marcus parabolic with respect to the driving force is shifted for the exponential coupling while it becomes an overlap of several Gaussian functions for the linear coupling. Furthermore, the effective couplings are exponentially and linearly dependent on temperature and the squared frequencies of bridge modes for the exponential and linear couplings, respectively.