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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 different amounts of exact exchange to core and valence electrons. It allows for treating the delocalization errors of sp and d electrons differently, which have been known to be an important source of error for the band structure. Using wurtzite ZnO as a prototype, we show that the approach is successful in simultaneously reproducing the bandgap and d-band position. Importantly, 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 thus point out a new direction of systematically improving the exchange functional in first-principles calculations.