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