with ω = ω + ω ′ . Substituting the Fourier representation of Eqns. 14 and 15 into Eqn. 12 and Eqn. 13, approximate expressions for g 2 (t) and g 3 (t) may be obtained that can be computed directly from energy gap fluctuations sampled along MD trajectories. To the best of our knowledge, there are no generally applicable correction factor analogs for higher order correlation functions. Thus the MD-type construction of the cumulant response is limited to the third order, and the implication of such truncation of the cumulant expansion will be explored in detail in this work.