  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.
