Semiclassical Modified Redfield and Generalized Forster 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 Forster theory. A qualitatively correct description of the transfer is obtained with this theory at a significantly lower computational cost as with the quantum generalized Forster theory. Larger deviations between the two theories are expected for large energy gaps as they occur in complexes with chemically different pigments.

Automated summary

A conceptual issue in transfer theories using semiclassical descriptions of electron-vibrational coupling is the neglect of correlation between nuclear momenta and coordinates, leading to violations of detailed balance principles and equal transfer rate constants obtained uphill and downhill. Reorganization effects due to partial localization of excited states promote preferential downhill relaxation of excitation energy, but are too small to compensate for missing coordinate-momentum uncertainty in realistic spectral densities of light-harvesting antennae. Semiclassical variants of generalized Forster theory fulfill detailed balance principles in weakly coupled pigment domains, providing qualitatively correct transfer descriptions at lower computational costs compared to quantum counterparts.