A time domain two-particle approximation to calculate the absorption and circular dichroism line shapes of molecular aggregates.

The hierarchical equations of motion (HEOM) method has recently emerged as an effective approach to simulate linear and nonlinear spectroscopic signals of molecular aggregates in the intermediate coupling regime. However, its application to large systems is still limited when there are a large number of molecules in the molecular aggregate. In this work, we propose a time domain two-particle approximation (TPA) in combination with the HEOM method to calculate the absorption and circular dichroism line shapes of molecular aggregates. The new method is shown to reduce the number of auxiliary density operators (ADOs) significantly for large systems, and a further truncation of the two-bath-set excited terms based on geometric considerations can lead to a linear increase of the number of ADOs with the system size. The validity of the HEOM-TPA method is first tested on one-dimensional model systems. The new method is then applied to calculate the absorption and circular dichroism line shapes of the Photosystem I core complex, as well as the population evolution of the Fenna-Matthews-Olson complex to demonstrate its effectiveness.