  We simulate the long-range inter-complex electronic energy transfer in
Photosystem II -- from the antenna complex, via a core complex, to the reaction
center -- using a non-Markovian (ZOFE) quantum master equation description that
allows us to quantify the electronic coherence involved in the energy transfer.
We identify the pathways of the energy transfer in the network of coupled
chromophores, using a description based on excitation probability currents. We
investigate how the energy transfer depends on the initial excitation --
localized, coherent initial excitation versus delocalized, incoherent initial
excitation -- and find that the energy transfer is remarkably robust with
respect to such strong variations of the initial condition. To explore the
importance of vibrationally enhanced transfer and to address the question of
optimization in the system parameters, we vary the strength of the coupling
between the electronic and the vibrational degrees of freedom. We find that the
original parameters lie in a (broad) region that enables optimal transfer
efficiency, and that the energy transfer appears to be very robust with respect
to variations in the vibronic coupling. Nevertheless, vibrationally enhanced
transfer appears to be crucial to obtain a high transfer efficiency. We compare
our quantum simulation to a "classical" rate equation based on a
modified-Redfield/generalized-F\"orster description that was previously used to
simulate energy transfer dynamics in the entire Photosystem II complex, and
find very good agreement between quantum and rate-equation simulation of the
overall energy transfer dynamics.
