  We formulate the on-site occupation dependent exchange correlation energy and
effective potential of hybrid functionals for localized states and connect them
to the on-site correction term of the DFT+U method. Our derivation provides a
theoretical justification for adding a DFT+U-like onsite potential in hybrid
DFT calculations to resolve issues caused by overscreening of localized states.
The resulting scheme, hybrid- DFT+Vw, is tested for chromium impurity in
wurtzite AlN and vanadium impurity in 4H-SiC, which are paradigm examples of
systems with different degree of localization between host and impurity
orbitals.
