The primary steps of photosynthesis generate, transport and trap delocalised electronic excitations (excitons) in pigment-protein complexes (PPCs). Generically, PPCs possess highly structured vibrational spectra with a large number of discrete intra- and quasi-continuous inter-pigment modes while exhibiting electron-vibrational (vibronic) couplings that are comparable to electronic inter-pigment coupling. Consequently, establishing a quantitative connection between spectroscopic data and underlying microscopic models of PPC dynamics remains an outstanding challenge. We address this challenge with two numerically exact simulation methods that support an analytical theory of multimode vibronic effects. Vibronic coupling across the entire vibrational spectrum, including high-frequency modes, needs to be accounted for to ensure quantitatively correct description of optical spectra, where dynamic localization effects modulate the intensity of vibrational sidebands and multimode mixing shifts the absorption peaks. Furthermore, we show that high-frequency modes can support long-lived oscillations in multidimensional nonlinear spectra, which are not obtained in a coarse-grained description of the electron-vibrational coupling.
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