for FEP are shown in Table . All NEQ raw data are available in Tables estimate based on the negative NNP→MM ∆U values shows a negative error (hp21 is an outlier to this general trend). This is expected behavior: the free energy estimate based on the MM→NNP process tends to overestimate, while the estimate based on the NNP→MM process tends to underestimate the free energy. The bidirectional equilibrium free energy perturbation estimate (using Bennett's acceptance ratio estimator) is accurate within ±1 k B T for the majority of the systems, with only two of them (hp5 and hp13) exhibiting an error greater than 2 k B T . The MM→NNP/NNP→MM ∆U distributions for all systems are shown on the left-hand side of Figures . One immediately sees that for most systems, there is either limited (hp2, hp3, hp4, hp7, hp8, hp12, hp15, hp16, hp17, hp18, hp20, hp21) or no overlap (hp5, hp9, hp10, hp13, hp14, hp19), see also Table . Despite this, the BAR estimator can estimate the correct free energy estimate in most instances. In the limit of no overlap, the BAR estimate converges to the average of the unidirectional free energies. This approach yields favorable results for most systems, but it remains an unjustified assumption that can be readily violated, leading to sporadic failures.