Higher-order processes of excitation energy transfer in supramolecular complexes: Liouville space analysis of bridge molecule mediated transfer and direct photon exchange

Long-range electronic excitation energy transfer is studied in the framework of a generalized master equation approach, which offers a systematic account for higher-order processes. Bridge molecule mediated transfer is confronted with the direct excitation energy exchange via photon emission and absorption. It is the central aim of this paper to present a systematic study of fourth-order rates, which describe both types of transfer processes characterized by the presence of intermediate states. While such a Liouville space formulation of rates is known from bridge mediated transfer, it is new for the case of photon mediated processes. In the former case, however, a novel approach to account for intermediate state relaxation is introduced. Finally and for illustration, some estimates are offered for the length dependence of the various discussed transfer rates.