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superconductivity and roughly constrains the in-plane lattice constant. The  remaining layers must tune the chemical potential of the CuO$_2$ layer without  rumpling the plane or introducing disorder, and isolate each CuO$_2$ plane to  create a 2D system.In the Hg-cuprates, the HgO$_\delta$ layer harbors dopant atoms which tune the  chemical potential. The BaO layers immediately adjacent to the CuO$_2$ plane  spatially separate the superconducting electrons from the detrimental effects  of the disordered dopant layer. Additionally, the highly ionic nature of the  BaO layer means they do not capture dopant electrons intended for the CuO$_2$  plane. The preference of Hg to be dumbbell coordinated bonds the entire  structure together without introducing structural distortions. Finally, the  highly ionic O-Hg-O dumbbells minimize $c$-axis hopping to maintain  2-dimensionality.  Due to their spatial proximity, the adjacent BaO layers tune the hoppings and  interaction strengths of the in-plane Hamiltonian. Designing compounds with  novel adjacent layers provides a mechanism for controlling superconductivity  by, e.g., reducing the charge-transfer energy. We quickly realized the most  stringent constraint is structural stability, so we focused first on isolating  stable candidates, then subsequently investigating their electronic properties.  To maximize the likelihood that a proposed composition is stable, we note that  the layers adjacent to the CuO$_2$ plane form a rock salt structure. Using  materials databases, we selected all naturally occurring rock salt compounds  AX, composed of an cation A and an anion X. The phase space is large and the  rate limiting step is structural prediction, so we quickly pre-screen  candidates by discarding compositions with (1) large lattice mismatches  relative to the in-plane Cu-Cu distance, which we took to be 3.82~\AA, and (2)  anions less electronegative than Cu, as these anions would capture dopants  intended for the superconducting plane, producing additional Fermi surfaces.  With the hindsight of   Revisisted with a and b done very well.  Outcome : proposed compound with more confidence.  Jury is out.  Discuss the notion of confidence.  Accuracy of LDA. Metastable structures do exist. One cuprates are above the hull.