All of the DFT calculations were performed within the VASP code , using the PBEsol generalized gradient approximation exchange-correlation functional . Projector augmented-wave pseudopotentials were used to model the ion cores , while treating the N 2s and 2p, and the Li 1s and 2s electrons as valence electrons. The electronic wave functions were expanded in a planewave basis with a kinetic-energy cutoff of 950 eV. We used 4 × 4 × 4 and 8 × 8 × 4 Monkhorst-Pack k-point meshes to sample the Brillouin zone for the αand the β-phases, respectively . k-point mesh sizes were reduced for relevant supercell calculations to preserve net k-point density. Geometry optimisations were performed using a quasi-Newton algorithm with a convergence setting of 0.005 eV/ Å for the atomic forces. The resulting optimised structures of α-Li 3 N and β-Li 3 N are shown in Figure . The calculated lattice parameters for these DFToptimised structures compare well with previous computational and experimental data (full details are given in Table of the Supplementary Information).