First-principles calculations were performed with the Vienna ab initio simulation package (VASP) to predict the density of states (DOS) of Co-doped LLZO. Core-valence electron interactions were treated with the projector-augmented wave method. The semi-local generalized gradient approximation of Perdew-Burke-Ernzerhof 56 was used for ionic relaxations and the Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) with a screening parameter of 0.11 bohr -1 was used for DOS calculations. The electronic convergence was set to 10-4 eV and an energy cutoff of 400 eV was used. All atom positions were relaxed until the forces were less than 0.05 eV/Å. Spin polarized electronic occupancies were determined using Gaussian smearing with an energy-broadening of 0.1 eV and a Gamma-only k-point mesh.