We have applied a virtual crystal approximation to the linear combination of atomic orbitals method to calculate critical point energies of unstrainedSi1−x−yGexCyalloys spanning the composition parameter space. Additionally, we have calculated the band structure across the Brillouin zone for a series of alloy compositions. We found the band energies had significant bowing departures from linearity throughout the system. In some cases, the energy band gap was not monotonically dependent on composition. Our theoretical results are compared with recent experimental results, and good agreement was found overall. ©1997 American Institute of Physics.