Extended perturbative approach including Redfield and Förster limits for qualitative analysis of exciton dynamics in any photosynthetic light harvesting and reaction center

According to many reports, the various structures of photosynthetic light-harvesting/reaction-center complexes and their molecular-dynamics simulations necessitate a numerically efficient and quality-conserved theory of excitation energy transfer and exciton relaxation in large pigment systems. Although exciton dynamics depend on various parameters, such as exciton coupling strength, exciton-phonon coupling, site energy values for each pigment, and temperature, classifying the transition mechanism for any Hamiltonian into perturbatively delocalized or localized theories is challenging. In this study, perturbative quantum master equations of a reduced density matrix for any orthogonal transformation similar to the coherent modified Redfield theory are derived. Our approach qualitatively conserves the dynamics of relevant perturbative approximations in each limiting case. As an application, any orthogonal transformation of a relevant system is optimized using the average of the square of interactions between orthogonal state transitions. The numerical results for two pigment systems are compared with the limiting formalisms of the modified Redfield and Förster theory.