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\label{sec:bacoso}  % Illustrates The material BaCoS$_2$ is a layered antiferromagnetic Mott insulator which transitions into a metal under pressure concommitant with  the need for Ran’s reshuffling.  % Illustrates suppression of  the need for U.  % Outcome, a material that was magnetic ordering temperature. Many novel superconductors are  found slightly earlier experimentally. in the region of phase diagram where magnetism is suppressed. However, it's not always the case that if (a) we have a magnetic layered magnetic compound, and (b) we suppress ordering, then (c) we necessarily get superconductivity. There are other, less-understood factors at play, and BaCoS$_2$ is an example.  \emph{Electronic structure} -- The material BaCoS$_2$ is a layered antiferromagnetic Mott insulator which transitions into Motivated by these ideas and the observation of  a metal under pressure-tuned metal-insulator transition, there was an experimental effort to apply chemical  pressure concommitant with the suppression via substitution  of the magnetic ordering temperature. Many novel superconductors are found large sulfur ion by the smaller oxygen ion  in BaCoS$_2$ to form BaCoSO. The fully-substituted end member BaCoO$_2$ was already known. In this work, we attempted to predict  the region structure  of phase diagram where magnetism is suppressed. However, it's not always the case that if (a) we have a magnetic layered magnetic compound, and (b) we suppress ordering, then (c) we necessarily get superconductivity. There are other, ill-understood factors at play, and BaCoS$_2$ is an example. BaCoSO without input from experiment.  Motivated by these ideas and the observation \emph{Electronic structure} -- We have performed DFT calculations for BaCoSO. The orbitally-resolved densities  of state are plotted in Fig.~\ref{fig:bacoso-dos}. From DFT, we find  a pressure-tuned metal-insulator transition, there was an experimental effort to apply chemical pressure via substitution $d$-metal where the density at the Fermi level is composed mainly  of the large sulfur ion by Co $3d$ states. As expected, these states hybridize moderately with  thesmaller  oxygen ion in BaCoS$_2$ to form BaCoSO. The fully-substituted end member BaCoO$_2$ was already known. and sulfur $p$ states, which are located XXXeV below the Fermi level.  We have performed both DFT and DFT+DMFT calculations for BaCoSO. The orbitally-resolved densities of state are plotted in Fig.~\ref{fig:bacoso-dos}. From DFT, we find a $d$-metal where the density at the Fermi level is composed mainly of the Co $3d$ states. As expected, these states hybridize moderately with the oxygen and sulfur $p$ states, which are located XXXeV below the Fermi level.  With a more realistic treatment of correlations, we find that BaCoSO is an insulator of the Mott-Hubbard type, since the gap is between the upper and lower Hubbard bands originating form the Co $d$ states. [Discuss crystal field levels arising from tetrahedral geometry] [Also give precise parameters for U, J, double-counting, temperature, etc. etc.] \emph{Structure prediction} -- It has been commonly assumed that LDA/GGA is sufficient for structure prediction [citation?]. prediction.  Whereas comparisons between compounds with differing compositions certainly require the corrections detailed above, it is has been  assumed that the systematic errors in LDA/GGA energies should cancel for differing structures of a *single* given composition. We argue this is not the case. In fact, correlations are important for comparison of energetics among structures for a single composition. We use USPEX to sample the local minima in the energy landscape of the Ba-Co-S-O system with the elements in a 1:1:1:1 ratio. We allow two formula units in a unit cell. We use VASP as our DFT engine. We use spin-polarized LDA/GGA and do not include U corrections. Around 300 k-points are used, with convergence criteria EDIFF=1e-6, NELM=40.  To capture the relevant local minima, we retain all candidate structures produced in any of the USPEX generations that lie within 0.5eV/(unit cell) of the final lowest energy structure. We group together similar structure using the criterion that their symmetry groups are identical and their computed energies are less than 3meV apart. As a result, of the original set of 152 structures we keep 58 distinct ones. The energies of this set of structures are then examined as a function of $U$, which we plot in Fig.~\ref{fig:reordering}. We do not structurally relax kept  the structures. structures fixed as tuned $U$, i.e. no structural relaxation.