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

The article presents a hybrid computational method combining hierarchical equations of motion (HEOM) and generalized Förster (gF) theory to model excitation dynamics in large molecular systems partitioned into weakly coupled compartments. Within each compartment, excitation dynamics are treated nonperturbatively using HEOM, while energy transfers between compartments are described perturbatively via gF theory, which assumes weak inter-compartment exciton coupling and equilibrated phonon baths. Numerical comparisons with exact HEOM solutions reveal that the HEOM-gF approach accurately reproduces excitation transfer kinetics when inter-compartment couplings are small and phonon bath relaxation is fast, but deviations arise at larger electron–phonon coupling strengths due to differences in reorganization energy shifts between the two formalisms. The method offers computational efficiency by scaling linearly with the number of compartments and is particularly relevant for modeling energy transfer in photosynthetic antenna supercomplexes, though its accuracy depends on system-specific parameters such as coupling strengths, phonon dynamics, and energetic disorder.