To address the underestimation of band gaps by DFT, individual valence and conduction band edge shifts (relative to the DFT-computed band edges) were determined from GW quasi-particle energy calculations using a methodology detailed in Ref. . We used dense k-point grids to sample the band edges in GW calculations. Speficially, we used -centered 12⇥12⇥12 k-point grid for Li 2 O, 12⇥12⇥10 for Li 3 N, 10⇥10⇥10 for Li 3 P, and 6⇥6⇥8 for Li 3 PO 4 . The calculations were set up, managed, and analyzed with the pylada-defects software package. The electronic conductivity ( e ) is estimated in the framework of the Drude theory of Eq. 3