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In addition to structure, we directly examine the density matrix of the 3$d$ orbitals produced by the DFT calculations. calculations and magnetization per Co atom (see Table~\ref{tbl:bacoso}).  The $U-J$ term penalizes non-integer occupancies. We can rationalize this behavior by [need to look at the data here — maybe it has to do with the local ligand environment of the Co atom, and maybe we won’t be able to rationalize it.]