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

<jats:p> We compute the autocorrelation function of the donor-acceptor tunneling matrix element ⟨ <jats:italic> T <jats:sub>DA</jats:sub> </jats:italic> ( <jats:italic>t</jats:italic> ) <jats:italic> T <jats:sub>DA</jats:sub> </jats:italic> (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, Y.-K. & Rossky, P. J. (2001) <jats:italic>Chem. Phys. Lett.</jats:italic> 345, 159-165]} reveals the extent to which non-Condon effects influence the electron-transfer rate. ⟨ <jats:italic> T <jats:sub>DA</jats:sub> </jats:italic> ( <jats:italic>t</jats:italic> ) <jats:italic> T <jats:sub>DA</jats:sub> </jats:italic> (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. </jats:p>