Evaluation of the performance of the prefactoroptimized third order cumulant approach versus the second order cumulant approach with an analogous relative metric κ rel (see Fig. ) reveals a substantial expansion in statistical space where the third order cumulant approximation may be applied to good effect. Specifically, introducing the dampening factor Φ significantly improves the performance for systems with a positive skewness value in the energy gap fluctuations. As is demonstrated in Sec. IV C, this expansion of the third order cumulant method to positive skew, low kurtosis energy gap fluctuations is key for obtaining reliable corrections to the lineshape in real molecular systems in the condensed phase sampled with MD.