However, unlike for the first transition, there are visible differences between the spectra where the environment is described by PE or PDE. In particular, in the low-intensity regions where the spectrum exhibits broader and less well-defined transition bands when the environment is modeled using PE. This difference can be understood by considering the underlying density of states, as shown in figure . The lowest-lying excitations (from 2.5-4.5 eV) are similar in both cases and relatively well-separated. When moving towards higher excitation energies, however, the spectrum based on the PE model becomes plagued by a much higher density of (partially unphysical) states. As a result, the state distribution, when using the PE model, shows a less well-defined structure. Moreover, to reach the same energetic range (i.e., converging the spectrum up to 6 eV) when using the PE model requires the solution of a larger number of states (40) than when using the PDE model (20), which can be seen from the number of color alternations along the y-axis of the histograms in figure . Overall, the PE and PDE models show almost identical performance for the low-energy, bright excitation in Nile Red, and also yield quite similar one-photon spectra for higher energies, although the underlying physical description is clearly less satisfactory when using PE to model the environment.