Electron transfer via bridges

In this paper we explore the energetic control of sequential and superexchange electron transfer (ET) mechanisms on the basis of quantum-mechanical simulations and calculations for long-range ET in DBA systems, where the donor (D) and the acceptor (A) are separated by a bridge (B). We studied ET dynamics in a Franck-Condon (FC) system characterized by three multi-dimensional displaced harmonic potential surfaces, where an initial single vibronic doorway state \alpha>) (with energy E-alpha) in the DBA (=D) electronic state is coupled to the mediating {\beta]} vibronic quasicontinuum of the D(+)B(-)A (=B) electronic state, which in rum is coupled to the final {\gamma>} vibronic quasicontinuum of the D(+)BA(-)(=A) electronic state. The level structure was described by the vibrational frequencies (for a four-mode harmonic system) and the energy gaps Delta G(DB) and Delta G(DA) between the origins of the corresponding electronic states (with n(alpha) = 1 - 50, n(beta) = 1000 - 2000, and n(gamma) = 1000 - 2000 states in the {\alpha>}, {\beta>}, and {\gamma>} manifolds, respectively), while the couplings were characterized by the spectral densities and by the pair correlations (specified in terms of correlation parameters eta(alpha alpha') and eta(beta beta')) between states belonging to the same manifold. The correlation parameters eta(alpha alpha')(alpha, alpha' = 1 - 40) for the doorway-quasicontinuum coupling and eta(beta beta') (beta, beta' = 150 - 190) for the interquasicontinuum coupling are considerably lower than unity (\eta(alpha alpha')\ less than or equal to 0.4 and \eta(beta beta')\ less than or equal to 0.3), obeying propensity rules with the highest values of \eta(alpha alpha')\ and \eta(beta beta') which correspond to a single vibrational quantum difference, while for multimode changes between alpha and alpha' or between beta and beta' very low values of \eta(alpha alpha')\ or \eta(beta beta')\ are exhibited, Radiationless transitions theory was applied for quantum-mechanical simulations based on the dynamcis of wave packets of molecular eigenstates for resonance (Delta G(DB) < E-alpha) and for off-resonance (Delta G(DB) > E-alpha) coupling. Resonance \alpha> - {\beta>} - {\gamma>} coupling results in two-step sequential ET kinetics for all doorway states \alpha>, manifesting phase erosion due to weakly correlated intercontinuum coupling, without the need of intermediate state phonon induced thermalization. Off-resonance \alpha> - {\beta>} coupling in conjunction with {\beta>} - {\gamma>} resonance interactions results in unistep superexchange ET kinetics. The simulated sequential ET rates and the superexchange rate are in good agreement with the calculated quantum-mechanical rates obtained using the electronic couplings and FC densities. The energy-gap (Delta G(DB)) dependence of the simulated and the calculated ET rates from a single doorway state reveal a ''transition'' from sequential to superexchange ET with increasing Delta G(DB). For a finite-temperature system, characterized by a fixed Delta G(DB) (> 0) small energy gap, the thermally averaged rate from a canonical ensemble of doorway states will result in the superposition of both superexchange and sequential mechanisms. (C) 1997 American Institute of Physics.