deletions | additions       diff --git a/While_we_did_not_perform__.tex b/While_we_did_not_perform__.tex  index 0541d71..b1858c2 100644  --- a/While_we_did_not_perform__.tex  +++ b/While_we_did_not_perform__.tex 
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\emph{Reexamination} -- In the intervening years, the maturation of materials databases allowed us to revisit the question of global stability. Various databases have computed and tabulated the convex hulls of binary, ternary and some quaternary systems, and provided tools for researchers to apply their framework to novel chemical systems. In the following, we describe our new understanding of the global stability of La$_2$CuO$_2$S$_2$ and La$_2$CuO$_3$S$_S$ against all known competing phases in the La-Cu-S-O chemical system. Since the Cu site contains significant correlations, we must address the effect of $U$ on the energies provided by density functional theory.  Corrections to LDA/GGA energies for convex hull construction have been systematically investigated for transition metal oxides \cite{Wang_2006,Jain_2011}. \cite{Wang_2006, Jain_2011}.  The corrections arise from two sources: (a) the GGA overbinding of the anion (most commonly the $O_2$ molecule) and (b) correlations. The GGA overbinding differs based on the anion, and the corrections are tabulated in the Materials Project. The correlation corrections are further divided into two components: (1) a contribution due to the U for atomic-like orbitals, treated by LDA+U, and (2) a correction in the energies required when comparing correlated (modeled using LDA+U) and uncorrelated (modeled using LDA) compounds. This is often the case in construction phase diagrams containing transition metal ions as their behavior can be considered “correlated” or “uncorrelated” depending on their valence and chemical environment.