Vibrational Relaxation Completes the Excitation Energy Transfer and Localization of Vibronic Excitons in Allophycocyanin α₈₄-β₈₄

Phycobilisomes are light-harvesting complexes that play a key role in photosynthesis in cyanobacteria, which generate more than 40% of the world's oxygen. The near-unity excitation energy transfer efficiency from phycobilisomes to photosystems highlights its importance in understanding efficient energy transfer processes. Spectroscopic studies have shown that the 280 fs rapid excitonic downhill energy transfer within the α₈₄-β₈₄ chromophore dimer in allophycocyanin (APC), a subunit of phycobilisomes, is crucial to this efficiency. However, the role of strong chromophore-protein interactions and vibrational relaxation requires further exploration to fully explain this efficient downhill energy transfer. A theory is required that adequately describes exciton dynamics in an intermediate region while also incorporating vibrational relaxation mediated by protein bath modes. In this work, we incorporate vibrational relaxation into modified Redfield theory by introducing coupling fluctuation. We holistically simulate the rapid excitation energy transfer process of the α₈₄-β₈₄ chromophore dimer in APC and successfully model the recently observed rapid energy capture. We find that vibrational relaxation dictates capture of excitons by the localized state of the β₈₄ chromophore. The calculated rate shows excellent agreement with previous ultrafast spectroscopic experiments. Our results show that the inclusion of vibrational relaxation is essential for systems that utilize vibronic coupling to enhance energy transfer and capture. Consequently, incorporating vibrational relaxation into Modified Redfield theory shows promise for accurately describing the excitation energy transfer process in other photosynthetic systems.