  Following the observation of coherent oscillations in non-linear spectra of
photosynthetic pigment protein complexes, particularly phycobilliprotein such
as PC645, coherent vibronic transport has been suggested as a design principle
for novel light harvesting materials operating at room temperature. Vibronic
transport between energetically remote pigments is coherent when the presence
of a resonant vibration supports transient delocalization between the pair of
electronic excited states. Here, we establish the mechanism of vibronic
transport for a model heterodimer across a wide range of molecular parameter
values. The resulting mechanistic map demonstrates that the molecular
parameters of phycobiliproteins in fact support incoherent vibronic transport.
This result points to an important design principle: incoherent vibronic
transport is more efficient than a coherent mechanism when energetic disorder
exceeds the coupling between the donor and vibrationally excited acceptor
states. Finally, our results suggest that the role of coherent vibronic
transport in pigment protein complexes should be reevaluated.
