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The primary steps of photosynthesis rely on the generation, transport, andtrapping of excitons in pigment-protein complexes (PPCs). Generically, PPCspossess highly structured vibrational spectra, combining many discreteintra-pigment modes and a quasi-continuous of protein modes, with vibrationaland electronic couplings of comparable strength. The intricacy of the resultingvibronic dynamics poses significant challenges in establishing a quantitativeconnection between spectroscopic data and underlying microscopic models. Herewe show how to address this challenge using numerically exact simulationmethods by considering two model systems, namely the water-solublechlorophyll-binding protein of cauliflower and the special pair of bacterialreaction centers. We demonstrate that the inclusion of the full multi-modevibronic dynamics in numerical calculations of linear spectra leads tosystematic and quantitatively significant corrections to electronic parameterestimation. These multi-mode vibronic effects are shown to be relevant in thelongstanding discussion regarding the origin of long-lived oscillations inmultidimensional nonlinear spectra.

Exact Simulation of Pigment-Protein Complexes Unveils Vibronic Renormalization of Electronic Parameters in Ultrafast Spectroscopy