Here, we use flow-based PGMs to compute the Helmholtz FE differences between crystal supercells using two ice polymorphs (Ic and XI) as simple but representative examples of systems requiring the explicit representation of all nine DOFs for all Cartesian blocks. For such systems, it is important to consider the most cost-effective way of representing a Cartesian block inside the PGM. In this regard, we highlight Ref. , which has contributed a powerful method of representing the Cartesian block based on a unit-quaternion to describe the rotational state of a given molecule. In particular, they have demonstrated that building a normalizing flow model with this representation allows 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 modeled with rigid water molecules. In the following, we compare two PGM architectures, respectively implementing a quaternionsbased representation inspired by Ref. and a direct Cartesian representation. These two models only differ in how the hydrogen atoms in each water molecule are represented.