Modeling of excitation dynamics in large-size molecular systems: Hierarchical equations with compartmentalization

We describe the new method that can be useful for calculation of the excitation dynamics in large molecular arrays that can be split into compartments with weak exciton coupling between them. In this method, the dynamics within each compartment is evaluated nonperturbatively using hierarchical equations of motion (HEOM), whereas transfers between the exciton states belonging to different compartments are treated by the generalized Förster (gF) theory. In a combined HEOM-gF approach, the number of equations increases linearly when adding new compartments as opposed to pure HEOM, where a depth of hierarchy exhibits strong non-linear grows when scaling the total number of molecules. Comparing the combined HEOM-gF method with an exact HEOM solution enabled us to estimate the parameters corresponding to a validity range of the proposed theory. The possibility of using the method for modeling of energy transfers in photosynthetic antenna supercomplexes is discussed.