Understanding the origin of bandgap problem in transition and post-transition metal oxides

Improving electronic structure calculations for practical and technologically-important materials has been a never-ending pursue. This is especially true for transition and post-transition metal oxides for which the current first-principles approaches still suffer various drawbacks. Here we present a hierarchical-hybrid functional approach built on the use of pseudopotentials. The key is to introduce a discontinuity in the exchange functional between core and valence electrons. It allows for treating the localization errors of sp and d electrons differently, which have been known to be an important source of error for the band gap. Using ZnO as a prototype, we show the approach is successful in simultaneously reproducing the band gap and d-band position. Remarkably, the same approach, without having to change the hybrid mixing parameters from those of Zn, works reasonably well for other binary 3d transition and post-transition metal oxides across board. Our findings point to a new direction of systematically improving the exchange functional in first-principles calculations.