  Recently, nuclear vibrational contribution signatures in 2D electronic
spectroscopy have attracted considerable interest, in particular as regards
interpretation of the oscillatory transients observed in light-harvesting
complexes. These transients have dephasing times that persist for much longer
than theoretically predicted electronic coherence lifetime. As a plausible
explanation for this long-lived spectral beating in 2D electronic spectra,
quantum-mechanically mixed electronic and vibrational states (vibronic
excitons) were proposed by Christensson et al. [J. Phys. Chem. B 116, 7449
(2012)] and have since been explored. In this work, we address a dimer which
produces little beating of electronic origin in the absence of vibronic
contributions, and examine the impact of protein-induced fluctuations upon
electronic-vibrational quantum mixtures by calculating the electronic energy
transfer dynamics and 2D electronic spectra in a numerically accurate manner.
It is found that, at cryogenic temperatures, the electronic-vibrational quantum
mixtures are rather robust, even under the influence of the fluctuations and
despite the small Huang-Rhys factors of the Franck-Condon active vibrational
modes. This results in long-lasting beating behavior of vibrational origin in
the 2D electronic spectra. At physiological temper- atures, however, the
fluctuations eradicate the mixing and, hence, the beating in the 2D spectra
disappears. Further, it is demonstrated that such electronic-vibrational
quantum mixtures do not necessarily play a significant role in electronic
energy trans- fer dynamics, despite contributing to the enhancement of
long-lived quantum beating in 2D electronic spectra, contrary to speculations
in recent publications.
