Electronic excitations in Vanadium Dioxide (VO$_2$)

Vanadium dioxide has a metal-insulator transition at T$_C$ = 340 K. The role of correlation in this first-order transition has been debated for a long time: is VO$_2$ a Peierls or a Mott-Hubbard insulator? Despite a good agreement with experimental lattice parameters, DFT-LDA yields a negative gap in the insulating phase and hence is not able to give a good answer to this question. This seeming failure of LDA is discussed and different possible approaches to solve this problem are reviewed: from standard perturbative G$_0$W$_0$ to self-consistent GW. Also results concerning other kinds of electronic excitations (in particular: electron energy loss spectra) are presented.