Symmetry breaking in vanadium trihalides

In the light of new experimental evidence we study the insulating ground state of the $3d^2$-transition metal trihalides VX${}_3$ (X=Cl, I). Based on Density Functional Theory with the Hubbard correction (DFT$+U$) we systematically show how these systems host multiple metastable states characterized by different orbital ordering and electronic behaviour. Our calculations reveal the importance of imposing a precondition in the on site $d$ density matrix and of considering a symmetry broken unit cell to correctly take into account the correlation effects in a mean field framework. Furthermore we ultimately found a ground state with the $a_{1g}$ orbital occupied in a distorted VX${}_6$ octahedra driven by an optical phonon mode.