Electron transfer through fluctuating bridges: On the validity of the superexchange mechanism and time-dependent tunneling matrix elements

The superexchange mechanism of electron-transfer reactions is studied for time-dependent donor–bridge–acceptor systems. It is shown that superexchange may not be a relevant mechanism in a situation where donor and acceptor states are off-resonant to the bridge with an energy gap much greater than $K_B\mathrm{T.}$ The competing mechanism in this case involves coherent through-bridge transfer. Methods for estimating its contribution to the electron-transfer probability are presented. It is also shown that the superexchange component of the electron-transfer probability can generally be described by a time-dependent two-state effective Hamiltonian. The off-diagonal element of this Hamiltonian is a generalized superexchange matrix element applicable to time-dependent donor–bridge–acceptor systems. It is nonperturbative and should be used to compute time-dependent superexchange pathways. The derivation of the effective Hamiltonian also applies to time-dependent superexchange systems with multiple donor (acceptor) states. All calculations are carried out on azurin and they involve molecular dynamics simulations coupled to electronic-structure/dynamics calculations using the complete neglect of differential overlap method.