We have shown that the functional form of Φ(µ (3) , µ (4) ) can be parameterized by stochastically sampling model parameters of the GBOM, a harmonic model Hamiltonian that is widely applied to the prediction optical spectra of semi-rigid molecules. By constructing Φ for a model system where the exact spectrum cam be computed analytically, we were able to parameterize an ideal dampening factor as a function of the non-Gaussian fluctuations only, rather than the parameters of the underlying system Hamiltonian. With this predictive plot in place, we were able to find optimal dampening factors Φ in MD-type simulations of molecular systems in the condensed phase.