  We develop a mathematically rigorous theory for the quantum transfer
processes in degenerate donor-acceptor dimers in contact with a thermal
environment. We calculate explicitly the transfer rates and the acceptor
population efficiency. The latter depends critically on the initial donor
state. We show that quantum coherence in the initial state enhances the
transfer process. If the electron is initially shared coherently by the donor
levels then the efficiency can reach values close to 100%, while an incoherent
initial donor state will significantly suppress the efficiency. The results are
useful for a better understanding of the quantum electron transport in many
chemical, solid state, and biological systems with complex degenerate and
quasi-degenerate energy landscapes.
