Protein Dynamics and Electron Transfer: Electronic Decoherence and Non-Condon Effects

We compute the autocorrelation function of the donor-acceptor tunneling matrix element$\langle T_{DA}(t)T_{DA}(0)\rangle $for six Ru-azurin derivatives. Comparison of this decay time to the decay time of the time-dependent Franck-Condon factor {computed by Rossky and coworkers [Lockwood, D. M., Cheng, Y.-K. & Rossky, P.J. (2001) Chem. Phys. Lett. 345, 159-165]} reveals the extent to which non-Condon effects influence the electron-transfer rate.$\langle T_{DA}(t)T_{DA}(0)\rangle $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.