  We use fully self-consistent GW calculations on diamond and silicon carbide
to reparametrize the Heyd-Scuseria-Ernzerhof exact exchange density functional
for use in band structure calculations of semiconductors and insulators. We
show that the thus modified functional is able to calculate the band structure
of bulk Si, Ge, GaAs, and CdTe with good quantitative accuracy at a
significantly reduced computational cost as compared to GW methods. We discuss
the limitations of this functional in low-dimensions by calculating the band
structures of single-layer hexagonal BN and MoS$_{2}$, and by demonstrating
that the diameter scaling of curvature induced band gaps in single-walled
carbon nanotubes is still physically incorrect using our functional; we
consider possible remedies to this problem.
