Multidimensional configuration-space models of the electronic factor in electron transfer by superexchange: Implications for models of biological electron transfer

We employ multidimensional configuration-space models to investigate the el ectronic factor that appears in theories of electron transfer. Of particula r interest is the electronic factor in models of long-range biological elec tron transfer (ET), which is thought to occur via a bridge-mediated superex change mechanism. The configuration-space electron tunneling fluxes that we calculate give explicit information on the relative importance of many-ele ctron effects such as correlation and hole vs particle transfer. The result s from our models lead to a nonintuitive indication that simple state-space perturbation theory expressions for the electronic factor can lead to inco rrect interpretations of electron-transfer processes. In particular, we fin d that the exclusion of lower-energy bridge bound states may misrepresent t he bridge attractive potential and may result in significant errors in the electronic factor contribution to the electron-transfer rate. The importanc e of the lower energy bridge levels in describing the tunneling state does not, however, imply that hole transfer is important. We find that through-b ond electron tunneling interactions a:re more reliably viewed in terms of t he tunneling barrier (using WKB theory) than in terms of the energy gaps be tween the tunneling electron and the respective bridge bound and virtual st ates (i.e., a second-order perturbation theory perspective). In the present superexchange models we find no instance in which hole transfer dominates the ET mechanism; however, as the energy level of a bridge eigenstate appro aches that of the donor-acceptor, we find that multiple transfer pathways a re simultaneously possible. Finally, results from these models suggest that the effects of electron-electron repulsion are small and relatively unimpo rtant.