  The primary steps of photosynthesis rely on the generation, transport, and
trapping of excitons in pigment-protein complexes (PPCs). Generically, PPCs
possess highly structured vibrational spectra, combining many discrete
intra-pigment modes and a quasi-continuous of protein modes, with vibrational
and electronic couplings of comparable strength. The intricacy of the resulting
vibronic dynamics poses significant challenges in establishing a quantitative
connection between spectroscopic data and underlying microscopic models. Here
we show how to address this challenge using numerically exact simulation
methods by considering two model systems, namely the water-soluble
chlorophyll-binding protein of cauliflower and the special pair of bacterial
reaction centers. We demonstrate that the inclusion of the full multi-mode
vibronic dynamics in numerical calculations of linear spectra leads to
systematic and quantitatively significant corrections to electronic parameter
estimation. These multi-mode vibronic effects are shown to be relevant in the
longstanding discussion regarding the origin of long-lived oscillations in
multidimensional nonlinear spectra.
