  Recent theoretical work has provided evidence that hybrid functionals, which
include a fraction of exact (Hartree Fock) exchange in the density functional
theory (DFT) exchange and correlation terms, significantly improve the
description of band gaps of semiconductors compared with local and semilocal
approximations. Based on a recently developed order-$N$ method for calculating
the exact exchange in extended insulating systems, we have implemented an
efficient scheme to determine the hybrid functional band gap. We use this
scheme to study the band gap and other electronic properties of the ternary
compound In$_{1-x}$Ga$_{x}$N using a 64-atom supercell model.
