Tunneling matrix element, electron-transfer effects

Effects of nuclear dynamics on electron tunneling in redox proteins have been an important question for the biological electron transfer community. While it has been understood how nuclear dynamics controls the Pranck-Condon factor, little was known until now about how the dynamics affects the tunneling matrix element. Our results show that, when tunneling is dominated by a single pathway tube, dynamical effects are small and Pathways level calculations provide reasonable results. The situation changes when several pathway tub are important and destructive interference exists among them. In this case dynamic amplification becomes important,... 

Electron tunneling was first analyzed by Bardeen [12] and Cohen et al. [13] using the perturbative transfer Hamiltonian (TH) approach and more recently by many other authors [14-16]. Although the TH gives, in many cases, a good description of the observed effects, it lacks a firm first principles theoretical basis and does not account properly for many-body effects [17]. An improved form of TH [18] that involved energy dependent transfer matrix elements was used to incorporate many-body effects. However, this model does not describe the electron-phonon interaction properly [19]. 

This has grown to form a considerable area of chemistryIt includes such varied topics as the ab initio calculation of electronic matrix elements/ the effect of bridging groups,electron tunneling theories,selection rules for electron transfer, and the distance dependence of electron transfer rates/ ... 

To be more precise, we assume that there is no coupling in the sense that the matrix element of the perturbation between states of the two systems is very small compared with current bond energies. Then, in addition to the polarization effect just illustrated, and provided that element is not exactly zero, an effect associated with the possibility of electron tunneling can take place charge transfer. 

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