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

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