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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. 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. 2. We do not structurally relax the structures. We find that the inclusion of even a very small $U-J \approx 1eV$ causes a clear separation of a single structure from the remaining minima, which we term the "ground state". The energy gap between the next-best structure and the ground state widens significantly as U-J increases. This ground state, as it turns out, is indeed the experimentally observed structure.