Focusing on the spectral shape, we note that the pure third order cumulant approach predicts a much more pronounced vibronic fine structure than the second order cumulant approach. Additionally, while in the second order cumulant approximation and in the experimental spectrum, the second vibronic peak has the highest intensity, the third order cumulant approach erroneously predicts the first vibronic peak to be more bright. The dampened third order cumulant method produces a spectrum with a more resolved vibronic fine-structure and improved peak separation compared to the second order cumulant approach, but still predicts a high intensity for the second vibronic peak. In general, the dampened spectrum is in good agreement with the experimental spectrum, with only a minor overestimation of the first vibronic peak. The origin of remaining discrepancy with the experimental spectrum is unclear, but can potentially be ascribed to inaccuracies in the (TD)DFT description of the system Hamiltonian, rather than the truncation of the cumulant expansion.