To examine the usefulness of the dampening factor Φ(µ (3) , µ (4) ) in realistic systems, we first demonstrate that typical condensed phase systems sampled from MD fall into the statistical range of non-Gaussian energy gap fluctuations sampled by the randomly parameterized GBOMs used in this work. Such an analysis is provided for nine selected molecules in SI Sec. VII. Both isolated molecules in vacuum and chromophores in condensed phase environments are included in the data set. For all nine molecules, it is found that the non-Gaussian features of the energy fluctuations, µ (3) and µ (4) , fall into the region sampled by the GBOMs. Additionally, they all fall into a region where the optimized third order cumulant approximation is predicted to outperform the second order cumulant approximation, thus indicating that the dampening factor Φ can likely be used to improve spectral lineshapes in these realistic systems. Here, we focus on a single selected system in more detail, namely coumarin-135 in toluene, due to the fact that vibronic peaks are well resolved in the lineshape, and an experimental spectrum is readily available. We emphasize that to produce what one may define as a sufficiently accurate spectrum for a molecule in the condensed phase using the MD-based cumulant method involves additional challenges when compared to the study of simple model systems where the exact spectrum can be readily computed. Vibronic lineshapes are often found to differ considerably depending on the level of theory used for modeling the ground-and excited state potential energy surfaces with TDDFT. Thus, any discrepancies with respect to the experimental spectrum cannot be easily ascribed to errors introduced in the low order cumulant expansion alone. For this reason, we more broadly focus on observed changes in the vibronic fine structure under the different cumulant approximations, rather than direct a quantitative comparison to the experimental lineshape.