  During the last decade, ab initio methods to calculate electronic structure
of materials based on hybrid functionals are increasingly becoming widely
popular. In this Letter, we show that, in the case of small gap transition
metal oxides, such as VO2, with rather subtle physics in the vicinity of the
Fermi-surface, such hybrid functional schemes without the inclusion of
"expensive" fully self-consistent GW corrections fail to yield this physics and
incorrectly describe the features of the wave function of states near the
Fermi-surface. While a fully self-consistent GW on top of hybrid functional
approach does correct these wave functions as expected, and is found to be in
general agreement with the results of a fully self-consistent GW approach based
on semilocal functionals, it is much more computationally demanding as compared
to the latter approach for the benefit of essentially the same results.
