Accuracy of approximate methods for the calculation of fluorescence-type linear spectra with a complex system-bath coupling

Abstract

Much can be learned about molecular aggregates by modeling their fluorescence-type spectra. In this study, we systematically describe the accuracy of various methods for simulating fluorescence-type linear spectra in a dimer system with a complex system–environment interaction, which serves as a model for various molecular aggregates, including most photosynthetic light-harvesting complexes (LHCs). We consider the approximate full cumulant expansion (FCE), complex time-dependent Redfield (ctR), time-independent Redfield, and modified Redfield methods and calculate their accuracy as a function of the site energy gap and coupling, excitonic energy gap, and dipole factor (i.e., type of spectrum). We find that the FCE method is the most accurate method for couplings smaller than 300 cm−1 at 300 K, but this method fails for very strong couplings or low temperatures due to inaccurate modeling of the equilibrium initial state. The ctR method performs well for the calculation of fluorescence and linear anisotropy spectra but poorer for circularly polarized fluorescence spectra or for all spectra when the coupling is strong ⁠. The Redfield and modified Redfield methods generally perform much more poorly than the ctR and FCE methods—especially for small excitonic energy gaps and strong couplings. We show that accurate modeling of the Stokes shift is crucial and present a version of the ctR method that treats both the Stokes shift and initial state correctly for the parameter ranges in plant LHCs. Apart from the application to LHCs, our results will be useful for the spectral characterization and design of organic molecular aggregates.