deletions | additions       diff --git a/tuning.tex b/tuning.tex  index b1fb2d6..d8e0c11 100644  --- a/tuning.tex  +++ b/tuning.tex 
...
Work by Zanaan, Sawatzsky and Allan showed that the relative alignment of the oxygen 2$p$ and copper 3$d$ orbital levels combined with the magnitude of the onsite repulsion $U$ controls the charge transfer energy. Dynamical mean-field calculations corroborated this picture by showing how the spectral charge transfer energy varies with the underline parameters of the hamiltonian. Additionally, density functional theory showed that the distance of the apical oxygen from the CuO$_2$ plane there is a charge transfer energy. Since we wanted to reduce the charge transfer energy to produce higher Tc's, we replaced the apical oxygen with sulfur, reasoning that its more extended 3$p$ orbitals would screen and reduce the strength of the in plane correlations.  \emph{Structure prediction} -- Local checks. In plane rotations. No global structural optimization. We chose the $T$-type layered perovskite La$_2$CuO$_4$ as the starting point. Our intuition led us to propose the site substitution of the apical oxygen with sulfur. Due to the larger ionic radius of sulfur as compared to oxygen, we expect that the LaS charge reservoir layer to be crowded. To compensate, we explored the effect of substituting the large La ion with smaller trivalent ions, selected from the lanthanide-like elements.  c) Check While we did not perform global structural prediction, we performed local checks for stability, which we acknowledged were by no means exhaustive. Using a $2\times2\times1$ unit cell, we performed full structural relaxation to check if the structure would be unstable towards distortion to the $T'$-type layered perovskite, knowing that substitution of the large La ion for the smaller Pr and Nd led to a rearrangement of the charge reservoir layer into the fluorite structure. We found that the $T$-type structure was indeed stable and there was no out-of-plane buckling, although the CuO$_6$ octahedra favored axial rotations ($a^0a^0c_p^-$ in Glazer notation).  \emph{Global stability} -- We checked the thermodynamic stability of the proposed compounds against competing phases by selecting commonly known reactants and computing the formation enthalpies of the synthesis pathways.   to check for the dynamic stability,Check  some slices using reactions. More work shows that that slices give a different picture.  BirdOutcome : do any of these materials exist ?  \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 [PRB 73, 195107 (2006), PRB 84, 045115 (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. 
...
With modern materials databases, we are able to reanalyze the entire La-Cu-S-O system to construct the convex hull (plotted in Fig. 1) and globally investigate stability. Notice that La2CuS2O2 and La2CuSO3 are not among the stable compounds on the hull.  Using the convex hull, we can assess the stability of the reactants and products reported in experiment. In Fig. 2, we plot the energies relative to the convex hull for all reported compounds. Negative values are stability energies against decomposition. We find that La2CuS2O2 and La2CuSO3 are highly unstable at nearly 500meV/atom above the hull. Additionally, LaCuSO is marginally unstable at 23meV/atom above the hull, but this is indistinguishable from zero given the error bars of the current method. In hindsight, we could have predicted that the proposed compounds would not have formed and instead have decomposed into:  La2CuS2O2 => La2SO2 \begin{equation}  \text{La}_2\text{CuS}_2\text{O}_2 \rightarrow \text{La}_2\text{SO}_2  + CuS \text{CuS}  \end{equation}  4 La2CuSO3 => 3 La2SO2 + 4 Cu + La2SO6  We also investigate the sensitivity of the stability energies to the LDA+U