Nonadiabatic two-electron transfer mediated by an irregular bridge

Nonadiabatic two-electron transfer (TET) mediated by a linear molecular bridge is studied theoretically. Special attention is put on the case of a irregular distribution of bridge site energies as well as on the inter-site Coulomb interaction. Based on the unified description of electron transfer reactions [J. Chem. Phys. 115 (2001) 7107] a closed set of kinetic equations describing the TET process is derived. A reduction of this set to a single exponential donor–acceptor (D–A) TET is performed together with a derivation of an overall D–A TET rate. The latter contains a contribution of the stepwise as well as of the concerted route of D–A TET. The stepwise contribution is determined by two single-electron steps each of them associated with a sequential and a superexchange pathway. A two-electron unistep superexchange transition between the D and A forms the concerted contribution to the overall rate. Both contributions are analyzed in their dependency on the bridge length. The irregular distribution of the bridge site energies as well as the influence of the Coulomb interaction facilitates the D–A TET via a modification of the stepwise and the concerted part of the overall rate. At low temperatures and for short bridges with a single or two units the concerted contribution exceeds the stepwise contribution. If the bridge contains more than two units, the stepwise contribution dominates the overall rate.