The availability of atomic scale structural information on several light-harvesting pigment protein complexes triggered a host of experimental and theoretical investigations directed towards the understanding of the structure-function relationship in these systems. The current status of knowledge about optical properties of the individual chlorophyll molecules and their spatial arrangement in the antennae has to be contrasted with the rather crude insight into the influence of their natural environment. This includes in particular the coupling of singlet exciton motion to vibrational modes belonging, for instance, to the protein scaffold, which is crucial for the function of the antenna. In this contribution we review the present understanding of exciton-vibrational interaction using a density matrix approach which allows for a description of exciton relaxation and dephasing in terms of spectral densities of vibrational modes. Different models of exciton-vibrational coupling are introduced and critically discussed in the context of antenna systems. First, we consider weak coupling of exciton motion to a heat bath comprising all vibrational modes of the complex. This model lends itself to the description of energy dissipation, essential for the trapping at the reaction center. Then, theoretical efforts to account for strong exciton-vibrational interaction are presented. This includes incoherent Förster transfer but also quasi-coherent exciton-vibrational dynamics involving the damped motion of effective vibrational modes. The density matrix theory is set in relation to spectroscopic observables which enable to draw conclusions about the details of exciton-vibrational coupling. Thereby we consider results from frequency-domain a.s well as ultrafast time domain experimental setups. Special emphasis is put on the discussion of recent subpicosecond pump-probe experiments on the peripheral antenna of photosynthetic purple bacteria as well as the antenna complex associated with photosystem II of green plants.
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