To illustrate the points made in Sec. II B 2, we demonstrate the effect of truncating the cumulant expansion at low order on a simple 2-mode harmonic model system described by the GBOM Hamiltonian (see Appendix A 1 and Appendix A 5 a for model parameters). For this Hamiltonian, the second order cumulant expansion is no longer exact, as the ground-and excited state PESs can have different curvatures and individual modes can be coupled. The resulting spectra for a specific model parameterization can be found in Fig. .