Quantum master equations for multisite exciton dynamics based on an extended perturbative approach: Redfield–Förster limits and application to the FMO complex

We extend an approximate method for excitation energy transfer, previously developed for two-pigment systems, to multisite systems. An iterative Givens-rotation algorithm is introduced to identify a basis that reduces the thermal average of the squared off-diagonal Hamiltonian elements, and the uniqueness of the converged solution is examined by varying the rotation order. For three-site models, the method approaches the Redfield and Förster limits in the corresponding parameter regimes and incorporates features of both limits in a mixed regime, reproducing the main qualitative characteristics of hierarchical-equations-of-motion dynamics. However, in an intermediate-coupling regime nonunique converged solutions with comparable perturbation measures yield different dynamics, indicating that the perturbation measure alone does not guarantee a reliable basis. Calculations for a standard seven-site FMO model demonstrate the numerical feasibility of the proposed approach for a biologically relevant multisite Hamiltonian. These results establish the potential utility of the method for multisite excitation-energy-transfer dynamics while identifying nonuniqueness of the optimized basis as an important practical limitation.