be seen that the lower overall flexibility manifests itself in the lightening of the greyscale, indicating a weaker overall match with the *ab inito* phonons. This lightening is not uniform; match values are still relatively strong in the 0–5 THz region and approach a perfect match for the lowest frequency phonons. Above 5 THz the match between this model and the *ab initio* phonons decreases with increasing frequency. The largest reduction in the match with the flexibility model is in the 9–11.5 THz region. We can identify this region with the modes involving significant bending of the bonds within the WO$_4$ tetrahedra. The analysis of \[maxwell\_counting\] shows that the number of WO$_4$ bond-bending modes is 60, which is exactly the number of modes in the 9–11.5 THz region.

The phonons in the 0–5 THz range also correspond to the strongest NTE-driving phonons. This, together with the above observations, suggests that these lowest frequency NTE modes correspond to motion of near-rigid WO$_4$ tetrahedra and rigid Y–O rods.

The addition the Y…W distance constraint leads to a very weak match between the flexibility model phonons and those of the *ab initio* calculation. This can be seen in the considerable lightening of the 