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In 2D electronic spectroscopy studies, long-lived quantum beats have recentlybeen observed in photosynthetic systems, and it has been suggested that thebeats are produced by quantum mechanically mixed electronic and vibrationalstates. Concerning the electronic-vibrational quantum mixtures, the impact ofprotein-induced fluctuations was examined by calculating the 2D electronicspectra of a weakly coupled dimer with vibrational modes in the resonantcondition [J. Chem. Phys. 142, 212403 (2015)]. This analysis demonstrated thatquantum mixtures of the vibronic resonance are rather robust under theinfluence of the fluctuations at cryogenic temperatures, whereas the mixturesare eradicated by the fluctuations at physiological temperatures. However, thisconclusion cannot be generalized because the magnitude of the coupling inducingthe quantum mixtures is proportional to the inter-pigment coupling. In thisstudy, we explore the impact of the fluctuations on electronic-vibrationalquantum mixtures in a strongly coupled dimer. with an off-resonant vibrationalmode. Toward this end, we calculate electronic energy transfer (EET) dynamicsand 2D electronic spectra of a dimer that corresponds to the most stronglycoupled bacteriochlorophyll molecules in the Fenna-Matthews-Olson complex in anumerically accurate manner. The quantum mixtures are found to be robust underthe exposure of protein-induced fluctuations at cryogenic temperatures,irrespective of the resonance. At 300 K, however, the quantum mixing isdisturbed more strongly by the fluctuations, and therefore, the beats in the 2Dspectra become obscure even in a strongly coupled dimer with a resonantvibrational mode. Further, the overall behaviors of the EET dynamics aredemonstrated to be dominated by the environment and coupling between the 0-0vibronic transitions as long as the Huang-Rhys factor of the vibrational modeis small.

Influences of quantum mechanically mixed electronic and vibrational  pigment states in 2D electronic spectra of photosynthetic systems: Strong  electronic coupling cases