Inspecting $\sim$700 A$_{2}$BX$_{4}$ compounds for energy applications: sorting their $\sim$40 crystal structures by diagramatic orbital radii maps without energy minimization*

The A$_{2}$BX$_{4}$ family of compounds covers $\sim$44 different crystal structure types and manifest a wide range of physical properties, including ferromagnetism, ferroelectricity, transparent conductivity, as well as superconductivity. We describe here a diagrammatic separation of the different crystal structures of $\sim$688 A$_{2}$BX$_{4}$ compounds by plotting a $R_{A}=R_{s}(A)+R_{p}(A)$ \textit{vs} $R_{B}=R_{s}(B)+R_{p}(B)$ map, where $R_{s}$ and $R_{p}$ are the $s$ and $p$ ``orbital radii'' of the neutral, free atoms, previously determined from first-principles pseudopotential theory. We find a 98\% successful separation of 688 A$_{2}$BX$_{4}$ compounds into 44 structure types. Applying this approach to separate Normal from Inverse spinel structures, we find a 96\% successful separation for 230 spinels known. These success rate using first-principles orbital radii uniformly exceed the success rates using classic radii (e.g Shannon's crystal radii; Pauling's covalent radii) or Pettifor's numbers. Once the separation maps was constructed, the crystal structure of a new chemical compound can be predicted by placing its $R_{A}$ and $R_{B}$ values in the map.