  We perform hybrid functional and quasi-particle band structure calculations
with spin-orbit interaction to investigate the band structures of Mg2Si, Mg2Ge,
and Mg2Sn. For all Mg2X materials, where X = Si, Ge, and Sn, the
characteristics of band edge states, i.e., band and valley degeneracies, and
orbital characters, are found to be conserved, independent of the computational
schemes such as density functional generalized gradient approximation, hybrid
functionals, or quasi-particle calculations. However, the magnitude of the
calculated band gap varies significantly with the computational schemes. Within
density-functional calculations, the one-particle band gaps of Mg2Si, Mg2Ge,
and Mg2Sn are 0.191, 0.090, and -0.346 eV, respectively, and thus severely
underestimated compared to the experimental gaps, due to the band gap error in
the density functional theory and the significant relativistic effect on the
low-energy band structures. By employing hybrid-functional calculations with a
35% fraction of the exact Hartree-Fock exchange energy (HSE-35%), we overcame
the negative band gap issue in Mg2Sn. Finally, in quasi-particle calculations
on top of the HSE-35% Hamiltonians, we obtained band gaps of 0.835, 0.759, and
0.244 eV for Mg2Si, Mg2Ge, and Mg2Sn, respectively, consistent with the
experimental band gaps of 0.77, 0.74, and 0.36 eV, respectively.
