mode – shows a softening with decreasing temperature, a step discontinuity at the transition temperature $T_{OO}$, followed by an increase of the velocity of sound for further decreasing temperature. The second paper [@Pytte73] includes the coupling of the degenerate orbitals to the optical phonon modes and finds a “central peak” in the dynamical structure factor $S\left(q,\omega\right)$. Central peaks have been reported to often co-occur with soft modes and had first been identified in $\mathrm{SrTiO_3}$ [@Riste71] and $\mathrm{Nb_3Sb}$ [@Shirane71; @Axe73]. They are also discussed theoretically in Refs. .

The theory developed by Pytte predicts temperature dependent changes to the TA2 phonons (with velocity proportional to $C_{11}-C_{12}$) and this is the same mode which displays anomalies in [[$\textrm{Mg}\textrm{V}_2\textrm{O}_4$]{}]{} over intermediate wavevectors. However, there are several important differences which make the relevance of this theory to the case here questionable. The theoretical prediction is in the context of a two-fold orbital degeneracy associated with the partial occupancy of the $e_{g}$ orbitals. As outlined above, this is not the case for S=1 V$^{3+}$ where two electrons occupy the $t_{2g}$ orbitals resulting in a three-fold orbital degeneracy. Pytte [@Pytte71] also predict a true soft mode whose energy reaches zero at the phase transition for momenta 