tween 0 and 1, and finding the minimum of the resulting convex function κ(Φ), as outlined in Fig. . Additionally, the degree of non-Gaussian behavior in the energy gap fluctuations is evaluated by determining skew and excess kurtosis via Eqn. 22, thus obtaining a single point of the function Φ(µ (3) , µ (4) ) in statistical space. Repeating this process across a large number of unique GBOMs with randomly sampled parameters, we then construct a continuous function Φ(µ (3) , µ (4) ) by fitting an analytic function to the sampled data. This allows us to predict the ideal dampening factor Φ for arbitrary systems from the measures µ (3) and µ (4) of the underlying non-Gaussian energy gap fluctuations alone, with the aim of improving the lineshape in realistic systems sampled from MD. Thus regardless of the model system or realistic condensed phase molecule that generated an energy gap fluctuation distribution, the degree of dampening which would occur from the inclusion of higher order cumulants is now being inferred from quantifiable properties of the underlying distribution. In Sec. IV, we rigorously test the performance of the Φ(µ (3) , µ (4) ) derived from the GBOM sampling on a range of model systems and real molecules in the condensed phase.