Protein dynamics and electron transfer: Electronic decoherence and non-Condon effects

We compute the autocorrelation function of the donor-acceptor tunneling matrix element (T-DA(t)T-DA(0)) for six Ru-azurin derivatives. Comparison of this decay time to the decay time of the time-dependent Franck-Condon factor (computed by Rossky and coworkers [Lockwood, D. M., Cheng, YA. W Rossky, P. J. (2001) Chem. Phys. Lett. 345, 159-1651) reveals the extent to which non-Condon effects influence the electron-transfer rate. (T-DA(t)T-DA(0) is studied as a function of donor-acceptor distance, tunneling pathway structure, tunneling energy, and temperature to explore the structural and dynamical origins of non-Condon effects. For azurin, the correlation function is remarkably insensitive to tunneling pathway structure. The decay time is only slightly shorter than it is for solvent-mediated electron transfer in small organic molecules and originates, largely, from fluctuations of valence angles rather than bond lengths.