Limitations of the hybrid functional approach to electronic structure of transition metal oxides

During the past decade, ab initio methods to calculate the electronic structure of materials based on hybrid functionals have increasingly become widely popular. Here 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 a 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.