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Efficient energy transfer in light-harvesting systems, III: The influence of the eighth bacteriochlorophyll on the dynamics and efficiency in FMO

The most recent crystal structure of the Fenna-Matthews-Olson (FMO) protein complex indicates that each subunit contains an additional eighth chromophore. It has been proposed that this extra site functions as a link between the chlorosome antenna complex and the remaining seven chromophores in FMO [Schmidt am Busch et al, J. Phys. Chem. Lett., {\bf 2}, 93 (2011)]. Here, we investigate the implications of this scenario through numerical calculations with the generalized Bloch-Redfield (GBR) equation and the non-interacting blip approximation (NIBA). Three key insights into the population dynamics and energy transfer efficiency in FMO are provided. First, it is shown that the oscillations that are often observed in the population relaxation of the dimer composed of sites one and two may be completely suppressed in the eight site model. The presence of the coherent oscillations is shown to depend upon the particular initial preparation of the dimer state. Secondly it is demonstrated that while the presence of the eighth chromophore does not cause a dramatic change in the energy transfer efficiency, it does however lead to a dominant energy transfer pathway which can be characterized by an effective three site system arranged in an equally spaced downhill configuration. Such a configuration leads to an optimal value of the site energy of the eighth chromophore which is shown to be near to its suggested value. Finally we confirm that the energy transfer process in the eight site FMO complex remains efficient and robust. The optimal values of the bath parameters are computed and shown to be closer to the experimentally fitted values than those calculated previously for the seven site system.