Orbital Occupation, Local Spin, and Exchange Interactions in $V_2{O}_3$

A local-density-approximation (LDA) and $\mathrm{LDA}+U$ band structure study of various phases of ${\mathrm{V}}_2{\mathrm{O}}_3$ shows that the most prominent (spin- $\frac{1}{2}$) models used to describe the semiconductor-metal transition are not valid. We find that the large on-site Coulomb and exchange interactions result in a total spin of 1 rather than $\frac{1}{2}$ and especially an orbital occupation which largely removes the orbital degeneracy. The calculated magnetic structure is consistent with experiment, again without the need for orbital ordering. These results strongly suggest that the phase transition in ${\mathrm{V}}_2{\mathrm{O}}_3$ which is so often quoted as the example of a spin- $\frac{1}{2}$ Mott-Hubbard system have a different origin.