The Relationship between the Spatial Arrangement of Pigments and Exciton Transition Moments in Photosynthetic Light-Harvesting Complexes

Considering bacteriochlorophyll molecules embedded in the protein matrix of the light-harvesting complexes of purple bacteria (known as LH2 and LH1-RC) as examples of systems of interacting pigment molecules, we investigated the relationship between the spatial arrangement of the pigments and their exciton transition moments. Based on the recently reported crystal structures of LH2 and LH1-RC and the outcomes of previous theoretical studies, as well as adopting the Frenkel exciton Hamiltonian for two-level molecules, we performed visualizations of the LH2 and LH1 exciton transition moments. To make the electron transition moments in the exciton representation invariant with respect to the position of the system in space, a system of pigments must be translated to the center of mass before starting the calculations. As a result, the visualization of the transition moments for LH2 provided the following pattern: two strong transitions were outside of LH2 and the other two were perpendicular and at the center of LH2. The antenna of LH1-RC was characterized as having the same location of the strongest moments in the center of the complex, exactly as in the B850 ring, which actually coincides with the RC. Considering LH2 and LH1 as supermolecules, each of which has excitation energies and corresponding transition moments, we propose that the outer transitions of LH2 can be important for inter-complex energy exchange, while the inner transitions keep the energy in the complex; moreover, in the case of LH1, the inner transitions increased the rate of antenna-to-RC energy transfer.