Quasiparticle self-consistent $GW$ band structures of Mg-IV-N${}_2$ compounds: the role of semicore $d$ states

We present improved band structure calculations of the Mg-IV-N${}_2$ compounds in the quasiparticle self-consistent $GW$ approximation. Compared to previous calculations (Phys. Rev. B 94, 125201 (2016)) we here include the effects of the Ge-3$d$ and Sn-4$d$ semicore states and find that these tend to reduce the band gap significantly. This places the band gap of MgSnN${}_2$ in the difficult to reach green region of the visible spectrum. The stability of the materials with respect to competing binary compounds is also evaluated and details of the valence band maximum manifold splitting and effective masses are provided.