Exciton dynamics in ring-like photosynthetic light-harvesting complexes: a hopping model

Excitation localization and dynamics in circular molecular aggregates is considered. It is shown that the Anderson localization of the excitons is taking place even in the finite size of the ring-type systems containing tens of pigments in the case of comparable values of the spectral inhomogeneity and of the intermolecular resonance interaction. The second type of localization comes from the dynamical disorder caused by exciton interactions with environment fluctuations. Because of these two reasons the hopping type migration of the small-size excitons is postulated to be responsible for the excitation dynamics in this kind of systems. This process is considered for the ensemble of independent rings and for the array of the interacting rings by means of Monte Carlo simulations. The intra-ring and inter-ring energy disorder with possible correlations is accepted in simulations performed for the cases of high and low temperatures. It is shown that for the typical parameters of the peripheral light-harvesting pigment-protein complexes LH2 of photosynthetic bacteria the excitation population reaches equilibrium within 1 ps in the case of the disconnected rings at nonselective excitation conditions, while equilibration on longer time scale is taking place in the system of connected rings. This nonexponential relaxation kinetics is observed at room temperature and is more pronounced by lowering the temperature. In the case of selective excitation the equilibration process is wavelength dependent for the disconnected rings at room temperature and becomes more pronounced by lowering the temperature. The wavelength dependence is resulted from the interplay between exciton population redistribution among pigments and the population, which stucks in the most red pigments.