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It goes without saying that our theory has nothing to say about the stability of a (Formula presented) phase with respect to competing, structurally different phases, possibly at different coverages, a point that can be addressed only by a full ab initio calculation
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We observe that, in principle, nondiagonal terms, i.e., terms that cannot be recast in the form of a density-density interaction, should be included. However, the magnitude of such terms—which involve overlap integrals between Wannier orbitals at different adatoms—can be estimated to be quite smaller than the diagonal terms we keep
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