Extended perturbative approach for quantitative calculation of the coherence excitation energy transfer in photosynthetic light harvesting complex

There are non-negligible exciton couplings and coherent oscillations in the excitation energy transfer within the light-harvesting complex and the exciton dynamics. In addition, the exciton dynamics depends on a variety of system parameters, such as electron coupling, electron-phonon coupling, and the site energy of each chromophore. In order to investigate the detailed interaction process, we propose an extended perturbation theory approach and derive the coherent dynamics of reduced density matrices under arbitrary orthogonal transformations. Our method quantitatively presents the dependence of system parameters on exciton state dynamics and the mathematical analysis of coherent dynamics, expands the application boundary of standard Förster and modified Redfield theories, and provides a mathematical description in the general case with an arbitrary basis. In the two-level dimer system, our model provides an excellent correspondence with the calculation of numerically exact hierarchical equations of motion. As an application, we quantitatively describe the long-lived vibronic coherence within recombinant allophycocyanin and the electron coherence process between chromophores within cryptophyte phycocyanin 645.