Quasiparticle self-consistent band structure and excitons of V₂O₅and LiV₂O₅

V₂O₅ is a layered material of interest as Li battery cathode. Recent cathodoluminescence measurements by Walker et al. [J. Mater. Chem 8, 11800 (2020)] show effects as function of Li content which are not yet understood, in particular in view of the recent finding that exitonic effects are huge in V₂O₅ [Gorelov et al. npj Comput. Mater. 8, 94 (2022)]. We present calculations of the band structure and optical properties of V₂O₅ and LiV₂O₅ in the α and γ-structures. The self-energy is calculated using the quasiparticle self-consistent QSGW method with W calculated either with or without ladder diagrams as recently implemented in the Questaal-code [Cunning- ham et al. arXiv:2106.05759]. The quasiparticle gap is found to be much higher than the optical gap and is only slightly reduced by including ladder diagrams, while exciton binding energies exceed 1.5 eV. The gap and exciton binding energies are further enhanced in monolayer V₂O₅. In both α and γ-LiV₂O₅ we find an antiferromagnetic ordering of the magnetic moments along the zig-zag chain direction, induced by half-filling of the V-d_xy-splitoff band. We investigate the effects of this Li induced band filling on the quasiparticle band structure and excitons.