to this; in the 9–10 THz range the match between this model and the *ab initio* phonons *increases* slightly and is slightly stronger than that for the rigid WO$_4$ tetrahedra/Y–O rod model, which is consistent with the identification of the frequency region above 9 THz corresponding to WO$_4$ bond-bending modes. At frequencies above 10 THz the match values decrease once again.

This all suggests that the full phonon spectrum of Y$_2$W$_3$O$_{12}$ involves some degree of O–Y–O bond angle bending. The amount of bending is least in two NTE regions of the phonon spectrum: the strongest NTE phonons in the 0–5 THz frequency band and the weak NTE phonons in the 9–10 THz frequency band. The latter is also a region where significant O–W–O bond angle bending can been seen. Otherwise, the general trend observed is for the degree of O–Y–O bond angle bending to increase as a function of increasing frequency.

The analysis of \[maxwell\_counting\] shows that the addition of the Y…W distance constraint leads to the flexibility model having more constraints than degrees of freedom. This result is confirmed by the corresponding data plotted in , which show a negligible match between the flexibility model and the *ab initio* 