Mott-to-Goodenough insulator-insulator transition in LiVO$_2$

I critically examine Goodenough's explanation for the experimentally observed phase transition in LiVO$_2$ using microscopic calculations based on density functional and dynamical mean field theories. The high-temperature rhombohedral phase exhibits both magnetic and dynamical instabilities. Allowing a magnetic solution for the rhombohedral structure does not open an insulating gap, and an explicit treatment of the on-site Coulomb $U$ interaction is needed to stabilize an insulating rhombohedral phase. The non-spin-polarized phonon dispersions of the rhombohedral phase show two unstable phonon modes at the wave vector $(\frac{1}{3},-\frac{1}{3},0)$ that corresponds to the experimentally observed trimer forming instability. A full relaxation of the supercell corresponding to this instability yields a nonmagnetic state containing V$_3$ trimers. These results are consistent with Goodenough's suggestion that the high-temperature phase is in the localized-electron regime and the transition to the low-temperature phase in the itinerant-electron regime is driven by V-V covalency.