Nonadiabatic bridge-assisted electron transfer ͑ET͒ is described by a set of kinetic equations which simultaneously account for the sequential ͑hopping͒ as well as the superexchange mechanism. The analysis is based on the introduction of a certain reduced density operator describing a particular set of electron-vibrational levels of the molecular units ͑sites͒ involved in the transfer act. For the limiting case of intrasite relaxations proceeding fast compared to intersite transitions a set of rate equations is obtained. This set describes the time evolution of the electronic site populations and is valid for bridges with an arbitrary number of units. If the rate constants for the transition from the bridge to the donor as well as to the acceptor exceed those for the reverse transitions the ET reduces to a single-exponential process with an effective forward and backward transfer rate. These effective rates contain a contribution from the sequential and a contribution from the superexchange mechanisms. A detailed analysis of both mechanisms is given showing their temperature dependence, their dependence on the number of bridge units, and the influence of the energy gap and the driving force. It is demonstrated that for integral bridge populations less than 10 Ϫ3 the complicated bridge-mediated ET reduces to a donor-acceptor ET with an effective overall transfer rate. This transfer rate contains contributions from the sequential as well as the superexchange mechanisms, and thus can be used for a quantitative analysis of the efficiency of different electron pathways. For room-temperature conditions and even at a very small bridge population of 10 Ϫ4-10 Ϫ10 the superexchange mechanism is superimposed by the sequential one if the number of bridge units exceeds 4 or 5.
The voltage and the temperature behavior of inelastic interelectrode current mediated by a short molecular wire is analyzed within a nonlinear kinetic approach that accounts for strong Coulomb repulsion between transferring electrons. When the coupling to the heat bath occurs via high-frequency vibration modes we predict a generally nonlinear current-voltage characteristics (an Ohmic behavior at small voltage, rising towards saturation and being followed by an abrupt decrease at large voltage) and a bell-shaped current response vs temperature at not too large temperatures.
To describe nonadiabatic bridge-assisted donor-acceptor (D-A) electron transfer (ET) kinetic equations for the electronic site, populations are presented that simultaneously account for the sequential as well as the superexchange transfer mechanism. The derivation of the kinetic equations is based on the precondition of fast intrasite vibrational relaxation, which is used to introduce a coarse-grained kinetic description. If the electron hopping across the bridge units is fast compared to the overall D-A ET, the number of kinetic equations can be reduced additionally. A set remains that covers only the donor, acceptor, and the integral bridge populations, independently on the number of bridging units. The case of a small bridge population is studied in detail. In such a situation, the D-A ET process can be described by single-exponential kinetics with a transfer rate that is the sum of the overall sequential and superexchange rate. The ratio of these overall rates is analyzed in the framework of the Song and Marcus model for the vibrational spectral function. If the reorganization energy of the D-A ET amounts to about 1 eV the sequential mechanism can dominate the superexchange ET, even though the population of the bridge by the transferred electron is of the order of 10 -4 to 10 -10 . The dominance of the sequential ET mechanism increases not only with increasing bridge length but also with increasing frequency of the ET reaction coordinate. Finally, the whole approach is applied to earlier experiments on D-A ET through a peptide bridge formed by proline oligomers of varying length. 39 The measured fast decrease of the overall transfer rate with an increase of the bridge length for short oligomers (trimers and tetramers) followed by a much weaker decrease for larger oligomers can be completely reproduced.
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