  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.
