Variable-cell-shape-based structural optimization applied to calcium nitrides

Symmetry corrections are added to a structural optimization at constant pressure in order to preserve the symmetry during the numerical relaxation of a structure. The enthalpy is minimized as a function of the electronic structure, the metric $g_{\mathrm{ij}}$, and the atomic positions. For the antiperovskite structures ${\mathrm{AsNCa}}_3,$ ${\mathrm{PNCa}}_3,$ and ${\mathrm{BiNCa}}_3$ the structural parameters and the band structure are calculated. The results are in good agreement with the available experimental data. For ${\mathrm{AsNCa}}_3$ the pressure dependence of the structural parameters and of the band-gap energy is also discussed. A possible transition from the orthorhombic phase to an eightfold-coordinated cubic phase (SC15) is found at 59 GPa.