A Unified Description of Superexchange and Sequential Donor−Acceptor Electron Transfer Mediated by a Molecular Bridge

Abstract

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.