Empirical Asymmetric Phonon Sideband Due to Phonons in the Protein Matrix Present in Photosynthetic Complexes: Time-domain Response Theory

The phonon spectral density plays a key role in probing the dynamical and spectral behavior of molecular aggregates. One may utilize the intimate connection between the one-phonon profile and the phonon spectral density to extract a plausible form of the spectral density of media with rich structure using advanced optical spectroscopy. The excitonic transition is normally accompanied by a broad, asymmetric phonon-side band due to the coupling to the phonons in the surrounding protein matrix present in photosynthetic complexes. The asymmetry in the one-phonon profile of a homogeneous absorption spectrum and other experiments performed on photosynthetic bacterial reaction centers (BRCs) led the Small group to employ a half-Gaussian distribution function on the red side and half-Lorentzian distribution function on the blue side of the absorption lineshape to account for the one-phonon profile asymmetrical shape and relaxation effects contributing to spectroscopy and dynamics of BRCs at hand. Different research groups successfully employed the theory of Small to simulate their photosynthetic spectral data so they could calculate the homogeneous absorption and hole-burned spectra of photosynthetic complexes. Although this report does not directly use the formulae of homogeneous absorption, hole-burning, and fluorescence line-narrowed spectra of BRCs, and photosynthetic complexes, developed by Hayes-Small, it builds on their idea of the phonon sideband asymmetric shape in deriving an accurate and computationally efficient linear electronic transition dipole moment time correlation function. Besides the compelling tractability and efficiency of this correlation function, it accounts for excitonic coupling and eliminates all the inconsistencies arising in the Hayes-Small theory.