We simulate the long-range inter-complex electronic energy transfer inPhotosystem II -- from the antenna complex, via a core complex, to the reactioncenter -- using a non-Markovian (ZOFE) quantum master equation description thatallows us to quantify the electronic coherence involved in the energy transfer.We identify the pathways of the energy transfer in the network of coupledchromophores, using a description based on excitation probability currents. Weinvestigate how the energy transfer depends on the initial excitation --localized, coherent initial excitation versus delocalized, incoherent initialexcitation -- and find that the energy transfer is remarkably robust withrespect to such strong variations of the initial condition. To explore theimportance of vibrationally enhanced transfer and to address the question ofoptimization in the system parameters, we vary the strength of the couplingbetween the electronic and the vibrational degrees of freedom. We find that theoriginal parameters lie in a (broad) region that enables optimal transferefficiency, and that the energy transfer appears to be very robust with respectto variations in the vibronic coupling. Nevertheless, vibrationally enhancedtransfer appears to be crucial to obtain a high transfer efficiency. We compareour quantum simulation to a "classical" rate equation based on amodified-Redfield/generalized-F\"orster description that was previously used tosimulate energy transfer dynamics in the entire Photosystem II complex, andfind very good agreement between quantum and rate-equation simulation of theoverall energy transfer dynamics.
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