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 VO${}_2$, with rather subtle physics in the vicinity of the Fermi surface, such hybrid functional schemes without the inclusion of “expensive” fully self-consistent $\mathit{GW}$ 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 $\mathit{GW}$ 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 $\mathit{GW}$ 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.

Figure 1

The photoemission data taken from Ref. 36 is compared with the density of states (DOS) of the occupied states as calculated within sc $\mathit{GW}$ on top of different HSE functionals. The calculated data was smoothed using an exponentially weighted moving average with a smoothing factor of 0.25. We averaged each data point with its seven neighbors by using a decreasing weight ${(1-\alpha )}^n$, where $n$ is the number of points to the central point.

Figure 2

The partial density of states (PDOS) near the Fermi level projected onto the spherical harmonics around one of the unique vanadium atoms (V1) in the $M_1$ phase of VO${}_2$, for a variety of functionals. The $\vec{x}$ axis is parallel to the $M_1$ “$a$” axis, $\vec{y}$ is parallel to the $M_1$ “$b$” axis (Ref. 18), and $\vec{z}$ is perpendicular to those, using a right-hand rule.