The conceptual formalism to understand the properties and function of chlorophylls in the gas and solution phases as well as in protein matrices is reviewed. This formalism is then applied to interpret modern high-resolution spectroscopic data, resulting from methods such as differential fluorescence line-narrowing spectroscopy and selective fluorescence excitation spectroscopy, which resolve individual vibrational transitions within the inhomogeneously broadened emission and absorption spectra of chlorophyll-a, bacteriochlorophyll-a, and pheophytin-a. Density functional theory and ab initio quantum chemical calculations are applied to interpret this data and fill in missing information needed to understand photosynthetic processes. The focus is placed on recognizing environmental and thermal effects, as well as the roles of Duschinsky rotation and non-adiabatic coupling in controlling the spectra. A critical feature of chlorophyll spectroscopy is determined to be absorption-emission asymmetry. Its ramifications for chlorophyll's function in photosystems are expected to be significant, as most current models for understanding their function assume that absorption and emission are symmetric, i.e. in the absence of relaxation processes, molecules coherently re-emit the light that they absorbed to enact exciton transport. The effect of the Duschinsky rotation is that after vibrational excitation during the electronic transition chlorophylls mostly emit light at different energies to what they absorb, while the effect of non-adiabatic coupling is that the polarization of the light is changed.
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