  The bandstructure of the zinc-blende phase of AlN, GaN, InN is calculated
employing the exact-exchange (EXX) Kohn-Sham density-functional theory and a
pseudopotential plane-wave approach. The cation semicore d electrons are
treated both as valence and as core states. The EXX bandgaps of AlN and GaN
(obtained with the Ga 3d electrons included as core states) are in excellent
agreement with previous EXX results, GW calculations and experiment. Inclusion
of the semicore d electrons as valence states leads to a large reduction in the
EXX bandgaps of GaN and InN. Contrary to common belief, the removal of the
self-interaction, by the EXX approach, does not account for the large
disagreement for the position of the semicore d electrons between the LDA
results and experiment.
