The process of energy transduction in the membranes of photosynthetic bacteria begins with the absorption of visible light by light harvesting antennas which then funnel the energy into the reaction center. The light harvesting complexes are molecular aggregates composed of several units that contain peptides, chlorophyll molecules and carotenoids. These building blocks are organized in symmetric structures that assume the shape of a ring. The first light harvesting complex (LH1) immediately surrounds the reaction center, while a second type of light harvesting complex (LH2) channels energy to the reaction center through LH1. The basic unit of LH2 is a heterodimer consisting of two small protein subunits. The heterodimers bind three bacteriochlorophyll (BChl) molecules, two of which are in close contact. These dimers form a ring which absorbs around 850 nm. The third BChl of the structural unit is located about 19 Angstroms away on an outer ring whose absorption maximum lies at 800 nm. Carotenoid molecules in close proximity to the outer BChl ring harvest light in a different spectral range and also prevent photooxidation of the chlorophylls. The LH2of the above species is composed of eight or nine such units.
We employed a simple model for the electronic excitations and the exciton-vibration coupling characterizing the B850 ring of the light harvesting complex in photosynthetic bacteria to investigate the possibility of coherence in the energy transfer within the system. The structure of the equilibrium density matrix was studied using the path integral formulation of quantum statistical mechanics. The calculated mean coherence length was computed from the average root-mean-square deviation of closed imaginary time paths which are sampled via a Monte Carlo procedure. This procedure allows simultaneous examination of the effects of thermal averaging, dynamic and static disorder in a single calculation. The mean coherence length was found to be of the order of two to three chlorophyll monomers at room temperature. The principal factor responsible for this localization is thermal averaging, although static and dynamic disorder further destabilize extended states. At low temperatures the circular arrangement of the pigments favors coherence with respect to the situation in a linear aggregate. Visual inspection of typical paths offers an intuitive picture of the extent of coherent energy delocalization in biological antenna systems.