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I study dynamical instabilities in Ta$_2$NiSe$_5$ using density functionaltheory based calculations. The calculated phonon dispersions show two unstableoptical branches. All the acoustic branches are stable, which shows that anelastic instability is not the primary cause of the experimentally observedorthorhombic-to-monoclinic structural transition in this material. The largestinstability of the optical branches occurs at the zone center, consistent withthe experimental observation that the size of the unit cell does not multiplyacross the phase transition. The unstable modes have the irreps $B_{1g}$ and$B_{2g}$. Full structural relaxations minimizing both the forces and stressesfind that the monoclinic $C2/c$ structure corresponding to the $B_{2g}$instability has the lowest energy. Electronic structure calculations show thatthis low-symmetry structure has a sizable band gap. This suggest that a$B_{2g}$ zone-center optical phonon instability is the primary cause of thephase transition. An observation of a softening of a $B_{2g}$ zone-centerphonon mode as the transition is approached from above would confirm themechanism proposed here. If none of the $B_{2g}$ modes present in the materialsoften, this would imply that the transition is caused by electronic or elasticinstability.

Orthorhombic-to-monoclinic transition in Ta$_2$NiSe$_5$ due to a zone-center optical phonon instability