Nonadiabatic electron-transfer rates in intramolecular situations involving bridged structures intervening between donor and acceptor will generally be quite small in magnitude and will depend on the energetics of the transfer process, the chemical identity and nature of the donor, acceptor, and bridge species, the environment, and the temperature. We develop a self-contained perturbative method for the calculation of the electron-transfer matrix elements corresponding to intramolecular long-range electron transfer. This scheme is based on the Lippmann-Schwinger equation for the effective scattering matrix. Iteration of this perturbation equation easily yields such well-known results as the McConnell formula for long-range superexchange interactions, the competition of through-bond and through-space coupling in bridge structures, the identification of superexchange, the relationship of superexchange process to exponential decay at long distance, and so forth. The scheme also permits direct calculation of the very small matrix elements involved in weak intramolecular electron-transfer coupling, even in situations with many competing bridges. The resulting perturbation theory formula for the effective matrix element is easily visualized, easily calculated even in extremely weak coupling situations, directly suggests the dominant pathway for electron transfer, and is within the realm of computational practicality even for large molecules.
ASJC Scopus subject areas
- Physical and Theoretical Chemistry