Semiclassical Modified Redfield and Generalized Förster Theories of Exciton Relaxation/Transfer in Light-Harvesting Complexes: The Quest for the Principle of Detailed Balance

A conceptual problem of transfer theories that use a semiclassical description of the electron-vibrational coupling is the neglect of the correlation between momenta and coordinates of nuclei. In the Redfield theory of exciton relaxation, this neglect leads to a violation of the principle of detailed balance; equal "uphill" and "downhill" transfer rate constants are obtained. Here, we investigate how this result depends on nuclear reorganization effects, neglected in Redfield but taken into account in the modified Redfield theory. These reorganization effects, resulting from a partial localization of excited states, are found to promote a preferential "downhill" relaxation of excitation energy. However, for realistic spectral densities of light-harvesting antennae in photosynthesis, the reorganization effects are too small to compensate for the missing coordinate-momentum uncertainty. For weaker excitonic couplings as they occur between domains of strongly coupled pigments, we find the principle of detailed balance to be fulfilled in a semiclassical variant of the generalized Förster theory. A qualitatively correct description of the transfer is obtained with this theory at a significantly lower computational cost as with the quantum generalized Förster theory. Larger deviations between the two theories are expected for large energy gaps as they occur in complexes with chemically different pigments.