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 electronic factor that appears in theories of electron transfer. Of particular interest is the electronic factor in models of long-range biological electron transfer (ET), which is thought to occur via a bridge-mediated superexchange mechanism. The configuration-space electron tunneling fluxes that we calculate give explicit information on the relative importance of many-electron effects such as correlation and hole vs particle transfer. The results from our models lead to a nonintuitive indication that simple state-space perturbation theory expressions for the electronic factor can lead to incorrect interpretations of electron-transfer processes. In particular, we find that the exclusion of lower-energy bridge bound states may misrepresent the bridge attractive potential and may result in significant errors in the electronic factor contribution to the electron-transfer rate. The importance of the lower energy bridge levels in describing the tunneling state does not, however, imply that hole transfer is important. We find that through-bond electron tunneling interactions are more reliably viewed in terms of the tunneling barrier (using WKB theory) than in terms of the energy gaps between the tunneling electron and the respective bridge bound and virtual states (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 approaches that of the donor−acceptor, we find that multiple transfer pathways are simultaneously possible. Finally, results from these models suggest that the effects of electron−electron repulsion are small and relatively unimportant.