In Eq. 11, λ is a coupling parameter controlling the linear interpolation between the physical ensemble, characterized by potential energy function (U ), and the ensemble of the Einstein crystal, described by harmonic potential energy function ( k 2 ∥r -r 0 ∥ 2 ), where r 0 can be any static configuration of the system with center of mass shifted to zero, and k is the scalar spring constant. We set r 0 to the initial configuration, with the center of mass removed. The spring constant was fixed to 6 × 10 3 kJ(mol) -1 (nm) -2 so that the Gaussian distributions associated with the harmonic potential have negligible periodic images along the smallest box length (0.6358nm). The ground truth FE of a given supercell (f ECM crys ) is then estimated as: (12) where µ i = ( N j=1 m j ) -1 m i are normalised masses m i of the atoms in the system. In this work, n λ = 20 separate simulations were ran with λ parameters λ 1 , ..., λ 20 taking on values 0, ..., 1, respectively. The intermediate values, arranged in ascending order between zero and one, are reported in SI Figure . The same set of lambda values were used in all systems. Since the λ 1 = 1 simulation samples the translationally invariant ensemble of the unperturbed system of interest, all other simulations were initialized from r 0 with CMMotionRemover functionality of openMM being active. This removes the average momentum of the center of mass during the simulations. Additionally, every 50 timesteps during these simulations, the center of mass was actively removed from the positions (r) to make sure that all systems remained on the same 3(N -1) dimensional subspace. In Eq. 12, ∆f i was calculated n λ -1 = 19 times using BAR functionality of pymbar. This was done several times during the simulations to show how the FE estimates converge as a function of more data becoming available for the BAR calculations (SI Figure ). The set of ground truth FEs reported in this paper utilized all of the available data. The standard error of f ECM crys was estimated by summing the n λ -1 intermediate standard errors provided by pymbar. This approach provides a lowerbound estimate of the uncertainty on f ECM crys , because this error estimate assumes complete decorrelation between the samples used to compute free energy differences between neighboring replicas. While underestimating the uncertainty of the ground-truth method, this approach is fast (i.e., does not require bootstrapping) and provides a relatively more ambitious target with which to compare the PGM-based methods. Finally, f 0 appearing in Eq. 12 is defined as: