Excitation energy transfer rates: comparison of approximate methods to the exact solution

Abstract

We have evaluated excitation energy transfer rates in photosyntetic complexes using the exact HEOM method and various approximate methods frequently used in the literature, namely, the F\"orster method, the Redfield method, the modified Redfield method and the variational master equation. The rates are evaluated for the case of a simple dimer and a trimer photosynthetic complex, with vibrational environment characterized by the Drude-Lorentz spectral density. Comparing approximate rates to the exact ones, we have confirmed the validity of approximate methods within appropriate limits, however these limits are often well outside parameter ranges that are relevant for the dynamics in real photosynthetic complexes.