In particular, Ref. 30 demonstrated that building a normalising flow model with this representation allows for efficiently learning an accurate approximation of the Boltzmann distribution over DOFs belonging to atoms that are not covalently bonded and thus obtaining FE estimates of ice XI crystal supercells modelled with rigid molecules. Motivated by the approach proposed in Ref. , we compare the quaternions-based representation with a direct Cartesian representation (Fig. ). In particular, we compare two different PGM architectures that differ only in how the two hydrogen atoms in each water molecule are represented. The first representation is based directly on their Cartesian coordinates (model C), while the second relies on unit-quaternions (model H), as illustrated in Figure , and discussed in sections II A and II B respectively. To assess their accuracy, efficiency, and ability to deal with an increasing number of DOFs, we extended our comparison to three system sizes and two temperatures. To maintain consistency in comparing free energy differences computed from the two models and the ground truth, we established the following ground rules: