Linear and Nonlinear Spectra in Photosynthetic Light Harvesting Complexes: Benchmark Tests of Modi ed Red eld Method

We employ the numerically exact hierarchical equations of motion (HEOM) method to perform benchmark tests for the popular modified Redfield method in calculating linear and nonlinear spectroscopic signals of molecular aggregates in photosynthetic light harvesting complexes. It is currently well known that the perturbative and Markovian approximations involved in the modified Redfield equation may give inappropriate description of the excitation energy transfer processes in the intermediate coupling regime. An interesting topic is thus to test the validity of the modified Redfield method in calculating various types of spectroscopic signals. By using model dimers with different sets of parameters and a model of the Fenna-Matthews-Olson complex, we calculate and compare the absorption, emission, and 2D spectra using the modified Redfield and HEOM methods. It is found that results from the modified Redfield method agree well with the HEOM ones in a wide range of parameter regimes. The comparison also helps to understand the quantum beating signals in the 2D spectra of the photosynthetic light harvesting complexes.