Nuclear quantum effects slow down the energy transfer in biological light-harvesting complexes

We assess how quantum-mechanical effects associated with high-frequency
chromophore vibrations influence excitation energy transfer in biological
light-harvesting complexes. After defining a classical nuclear limit that
is consistent with the quantum-classical equilibrium, we include nuclear
quantum effects through a variational polaron transformation of the
high-frequency vibrational modes. This approach is validated by comparison
with fully quantum-mechanical benchmark calculations and applied to three
prototypical light-harvesting complexes. For light-harvesting complex 2 of
purple bacteria, the inter-ring transfer is 1.5 times slower in the
quantum treatment than the classical. For the Fenna-Matthews-Olson
complex, the transfer rate is the same in both cases, whereas for
light-harvesting complex II of spinach, transfer is 1.7 times slower in
the quantum treatment. The effect is most pronounced for systems with
large excitonic energy gaps and strong vibronic coupling to high-frequency
modes. In all cases, nuclear quantum effects are found to be unimportant
for the directionality of energy transfer.