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.