degrees of freedom. We would therefore expect many of the 156 lower-frequency Y$_2$W$_3$O$_{12}$ phonons to correspond to rigid W–O and Y–O rod motions. shows that this is largely the case. Much of the *ab inito* phonon spectrum in the 0–12 THz range is a strong match for rigid W–O/Y–O flexibility model modes. However, this motion is not confined to specific phonons in the spectrum but, instead, there is a high degree of eigenvector mixing and the flexibility of the model is spread over multiple phonons in the real material. This mixing follows from the relatively low symmetry and the complexity of the dispersion curves. Despite the high degree of eigenvector mixing present, it is still possible to observe general trends within the phonon spectrum. Specifically, phonons in the 0–5 THz (approximately 64 modes) and 9–10 THz (approximately 28 modes) ranges have the strongest match for rigid W–O and Y–O motions. These differences correspond well with the separation of PTE and NTE phonons in the Y$_2$W$_3$O$_{12}$ spectrum as seen in . NTE phonons have the strongest match with the flexibility model (corresponding to negligible W–O and Y–O bond stretching) while PTE phonons have the weakest match (corresponding to small, but non-trivial, 