Non-perturbative exciton transfer rate analysis of the Fenna-Matthews-Olson photosynthetic complex under reducing and oxidizing conditions

Two-dimensional optical spectroscopy experiments have examined photoprotective mechanisms in the Fenna-Matthews-Olson (FMO) photosynthetic complex, showing that exciton transfer pathways change significantly depending on the environmental redox conditions. Higgins et al. [Proc. Natl. Acad. Sci. U. S. A. 118(11), e2018240118 (2021)] have theoretically linked these observations to changes in a quantum vibronic coupling, whereby onsite energies are altered under oxidizing conditions such that exciton energy gaps are detuned from a specific vibrational motion of the bacteriochlorophyll a. These arguments rely on an analysis of exciton transfer rates within Redfield theory, which is known to provide an inaccurate description of the influence of the vibrational environment on the exciton dynamics in the FMO complex. Here, we use a memory kernel formulation of the hierarchical equations of motion to obtain non-perturbative estimations of exciton transfer rates, which yield a modified physical picture. Our findings indicate that onsite energy shifts alone do not reproduce the reported rate changes in the oxidative environment. We systematically examine a model that includes combined changes in both site energies and the frequency of a local vibration in the oxidized complex while maintaining consistency with absorption spectra and achieving qualitative, but not quantitative, agreement with the measured changes in transfer rates. Our analysis points to potential limitations of the FMO electronic Hamiltonian, which was originally derived by fitting spectra to perturbative theories. Overall, our work suggests that further experimental and theoretical analyses may be needed to understand the variations of exciton dynamics under different redox conditions.