Here, D is the well depth of the potential, k is the displacement between the ground and excited potential minima, and α g and α e are the anharmonicity parameters for the ground-and excited state. Analytical expressions for the Morse oscillator wavefunctions exist, such that the exact response function for this Hamiltonian can be constructed directly through Eqn. 5. Additionally, cumulants based on the exact quantum correlation function can also be constructed numerically. The exact analytical expressions for the Morse oscillator wavefunctions are numerically unstable, meaning that the parameters this model have to be chosen somewhat carefully to guarantee well-defined results. As such, it less apt for the high-throughput screening of parameter space desired in this study. Instead, we construct a few selected Morse oscillator parameterizations inspired by realistic molecular systems to test whether the conclusions obtained for the GBOM Hamiltonian can be carried over to the anharmonic case. In these model calculations, we combine the Morse oscillator with a GBOM to model a chromophore with a few harmonic and a single anharmonic mode. The anharmonic mode is taken to be decoupled from the harmonic ones, such that the total response function can be written as: