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Cobalt based perovskites have great potential for numerous applications. Contrary to a generally assumed hexagonal space group (SG P63/mmc) model as the ground state of BaCoO3 (BCO), our hybrid DFT calculations with B1WC density functional and the symmetry group-subgroup derived crystal structure model support the ground state of BCO to be indeed monoclinic, in agreement with recent experimental predictions [Chin et al., Phys. Rev. B, 2019, 100, 205139]. We found for the monoclinic BCO that the C-type anti-ferromagnetic low-spin (AFM L
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