Dynamical theory of electron transfer: Inclusion of inner-shell reorganization

The dynamical formulation of electron transfer rate theory, including inner sphere and outer sphere reorganization terms, electronic structure polarization, and an ab initio treatment of the electrons on donor, acceptor, and bridge molecules, is presented and applied to electron transfer betwen benzene/anion radical and pyridine. The formulation involves the use of mean field (Ehrenfest) relations to obtain the time evolution of electron and vibration operators. This formulation yields an effective density matrix for the time evolution of the electronic system; the elements of this density matrix depend on averages over electronic and vibrational motions. For the electron transfer system actually studied, the rates are strongly dependent upon relative geometry of donor and acceptor, and maximize sharply at geometries such that electronic levels on donor and acceptor become degenerate - the so-called "coincidence event" geometry.