All calculations were carried out using the Vienna Ab initio Simulation Package (VASP). For all ground-state calculations to optimize the atomic geometries and study the total energies E of the polymorphs, we employed the AM05 exchange-correlation functional, which is known to provide excellent values for the lattice constants of group-III nitrides and ox-ides. The all-electron projector-augmented wave (PAW) method was used to describe the single-particle wave functions and pseudopotentials. Spin-orbit coupling (SOC) effects were not considered, as test calculations indicated negligible differences in energy band structures and a calculation time ranging from 2 to 5 times higher (see Supplementary Information Figs. and). The better performance of the AM05 functional has also been demonstrated in the Supporting Information (SI) in Figs. S1-S6. Shallow Ga 3d and In 4d core electrons were included among the valence electrons. A plane-wave cutoff of 500 eV was chosen for the expansion of wave functions, and this value was applied for total energy, force, and electronic structure calculations. Monkhorst-Pack meshes were used for standard k-point sampling of the Brillouin zone (BZ). Specifically, we employed meshes of 5×5×5 (5×5×2, 5×5×5) for monoclinic and rhombohedral (orthorhombic, cubic) polymorphs. For band structure calculations, denser Γ-centered meshes of 10×10×10 (10×10×5, 10×10×10) were applied.