Total energies were calculated with Density Functional Theory (DFT) approximated by the Perdew-Burke-Ernzerhof (PBE) functional. The Projector Augmented Wave (PAW) pseudopotentials were used for describing electron-ion interactions: Li sv 23Jan2001, P 17Jan2003, O s 07Sep2000, and N s 07Sep2000. A plane-wave cuto↵ energy of 340 eV was used for all the calculations. Initial structures were taken from the Inorganic Crystal Structure Database (ICSD): Li 2 O (ICSD#057411), Li 3 N (ICSD#34675) , Li 3 P (ICSD#240861), and Li 3 PO 4 (ICSD#10257). First, the primitive cells were fully relaxed with -centered k-point grids automatically generated with a length parameter of 10. Next, supercells were constructed from the relaxed primitive cells. Supercells containing 96 atoms (Li 2 O), 108 atoms (Li 3 N), 144 atoms (Li 3 P), and 128 atoms (Li 3 PO 4 ) were used. The atomic positions in the defect supercells were relaxed while keeping the volume and cell shape fixed. Defect supercell relaxations were performed with a -centered 2⇥2⇥2 Monkhorst pack kpoint grid for Li 3 P and a 4⇥4⇥4 grid for the others with fewer atoms in the supercells.