To test the validity of the prefactor mapping on molecular systems which contain strongly anharmonic modes, we construct model systems under the scheme outlined in Appendix A 2, where the chromophore is approximated through a set of harmonic modes described as a GBOM and a single anharmonic mode described as a Morse oscillator. The results of pure and dampened cumulant approximations are once again assessed against the exact spectrum. The results for a specific model parameterization can be found in Fig. , with the exact model parameters specified in Appendix A 5 c.