Why Quantum Coherence Is Not Important in the Fenna-Matthews-Olsen Complex

We develop and present an improvement to the conventional technique for solving the Hierarchical Equations of Motion (HEOM), which can reduce the memory cost by up to 75% while retaining the same (or even better) convergence rate and accuracy. This allows for a full calculation of the population dynamics of the 24-site FMO trimer for long time scales with very little effort, and we present the first fully converged, exact results for the 7-site subsystem of the monomer, and for the full 24-site trimer. We then show where our exact 7-site results deviate from the approximation of Ishizaki and Fleming [A. Ishizaki and G. R. Fleming, Proc. Natl. Acad. Sci. U.S.A., 2009, 106, 17255]. Our exact results are then compared to calculations using the incoherent Förster theory, and it is found that the time scale of energy transfer is roughly the same, regardless of whether or not coherence is considered. This means that coherence is not likely to improve the efficiency of the transfer. In fact, the incoherent theory often tends to overpredict the rates of energy transfer, suggesting that, in some cases, quantum coherence may actually slow the photosynthetic process.