We report a series of electronic structure calculations for CrN using different exchange correlation potentials: PBE, LDA+$U$, the Tran-Blaha modified Becke-Johnson, and hybrid functionals. In every case, our calculations show that the onset of magnetism in CrN should be accompanied by a gap opening. The experimentally found antiferromagnetic order always leads to an insulating behavior. Our results give further evidence that the Tran-Blaha functional is very useful for treating the electronic structure of correlated semiconductors allowing a parameter free description of the system. Hybrid functionals are also well capable of describing the electronic structure of CrN. The analysis of the system is complemented with our calculations of the thermopower that are in agreement with the experimental data.
