The force constants required for phonon calculations were calculated using DFT from finite displacements of atoms in a supercell. A 2×2×1 supercell was used for all orthorhombic anti-perovskites, and a 2 × 2 × 2 supercell was used for all cubic anti-perovskites. The cubic unit cell was used for all spinel structures. These dimensions were chosen to ensure that the dimensions of all supercell structures are at least 8 Å. In these calculations, a 2×2×2 k-point grid was used for all anti-perovskite structures, except for Ca 3 NBi, for which a 3 × 3 × 3 grid was used, and for Mg 3 NAs and Mg 3 NBi, for which 4 × 4 × 4 grids were used. In order to ensure high accuracy of the calculated force constants, an additional support grid was used to evaluate the augmentation charges (i.e. by specifying ADDGRID = True), and an electronic convergence criterion of 10 -8 eV was used. Force constants were symmetrized to ensure translational and permutational symmetry.