  I study dynamical instabilities in Ta$_2$NiSe$_5$ using density functional
theory based calculations. The calculated phonon dispersions show two unstable
optical branches. All the acoustic branches are stable, which shows that an
elastic instability is not the primary cause of the experimentally observed
orthorhombic-to-monoclinic structural transition in this material. The largest
instability of the optical branches occurs at the zone center, consistent with
the experimental observation that the size of the unit cell does not multiply
across the phase transition. The unstable modes have the irreps $B_{1g}$ and
$B_{2g}$. Full structural relaxations minimizing both the forces and stresses
find that the monoclinic $C2/c$ structure corresponding to the $B_{2g}$
instability has the lowest energy. Electronic structure calculations show that
this low-symmetry structure has a sizable band gap. This suggest that a
$B_{2g}$ zone-center optical phonon instability is the primary cause of the
phase transition. An observation of a softening of a $B_{2g}$ zone-center
phonon mode as the transition is approached from above would confirm the
mechanism proposed here. If none of the $B_{2g}$ modes present in the material
soften, this would imply that the transition is caused by electronic or elastic
instability.
