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Excitation of Low-Frequency Modes and the Effects of Protein Dynamics on Spectral Densities of Bacteriochlorophyll Molecules

In the theory of open quantum systems, spectral densities are key quantities for modeling the dynamics and spectroscopic properties of the system under investigation. In the case of light-harvesting complexes, they encode the frequency-dependent coupling of electronic excitations in pigment molecules to their environment, reflecting contributions from both intrinsic vibrational modes and the protein surrounding. In particular, the low-frequency components of the spectral densities are crucial for exciton transfer between pigment molecules. Apparently, slow internal modes of bacteriocholophyll molecules in the gas phase are less well represented by common force fields based on classical molecular dynamics (MD) simulations. Here, we demonstrate that Born-Oppenheimer molecular dynamics (BOMD) based on the numerically efficient density functional-based tight-binding approach can accurately recover these low-frequency features, whereas normal mode analysis captures them only partially. In contrasting approaches for determining spectral densities, the low-frequency region of the spectral densities obtained is only associated with protein fluctuations; the usage of BOMD, however, also captures the low-frequency contributions arising from slow intramolecular vibrations of the pigment molecules themselves. Notably, this behavior is consistently observed for both the flexible B800 and the more rigid B850 rings in light-harvesting 2 (LH2) complexes of purple bacteria, as well as in the Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria. Interestingly, we also find that the spectral densities of the pigments in the B850 ring of LH2 are not influenced by the environment, i.e., the gaps between ground and first excited state are not changed significantly by the fluctuations of the protein environment.