Evaluation of approximate lineshape theories for photosynthetic light-harvesting antennae

Modeling optical spectra of pigment-protein complexes requires accurate treatment of both excitonic and vibronic interactions. While nonperturbative approaches, such as the hierarchical equations of motion, are, in principle, numerically exact, they are computationally demanding, making the use of approximate lineshape theories appealing. However, the biases introduced by these perturbative treatments still need assessment. Here, we systematically compare methods based on cumulant expansion and successive approximations against exact calculations. Using chlorophyll dimers in the water-soluble chlorophyll-binding protein and the CP29 light-harvesting complex as test systems, we analyze absorption spectra under varying coupling strengths. Our results show that vibronic renormalization of excitonic coupling can be captured by the partially Markovian complex Redfield (cR) theory, whereas fully non-Markovian approaches are essential for reproducing the intensities of vibronic sidebands. A model that treats electronic transitions involving high-frequency vibrational modes as localized recovers many of the non-Markov and non-secular effects. We extend our analysis to fluorescence spectra, which pose more difficulties because excitonic and vibrational states are entangled before emission. While non-Markovian methods still perform better for fluorescence, their performance in reproducing vibronic sidebands is less than satisfactory. Our results allow quantifying the errors made by approximate theories and define a reliability range for spectroscopic simulations.