Ions in crystals: The topology of the electron density in ionic materials.II. The cubic alkali halide perovskites

We present here the topological (Bader) analysis of the electronic structure for 120 cubic perovskites ${\mathrm{AMX}}_3$ (A denotes Li, Na, K, Rb, Cs; M denotes Be, Mg, Ca, Sr, Ba, Zn; X denotes F, Cl, Br, I). The perovskite being perhaps the simplest and most abundant structure for ternary compounds, we have found up to seven different topological schemes for the electronic density. Those schemes can be simply arranged and explained in terms of ratios of topologically defined ionic radii. However, no set of empirical radii, even of best-fitted radii, can accomplish the same objective. All crystals do present M-X and A-X bonds, many have X-X too, and only ${\mathrm{CsSrF}}_3$ and ${\mathrm{CsBaF}}_3$ have A-A bonds. The topology and geometry of the electronic density has been further analyzed by depicting the shape of the attraction basins of the ions. Basins have polyhedral shapes and can be simply predicted, in most cases, after the knowledge of the bonds that the ion forms. ${\mathrm{M}}^{2+}$ basins do present, however, bizarre nearly bidimensional wings on those topological schemes lacking X-X bonds. Lattice energy has been found to be dominated by Coulombic interactions and determined by the crystal size more than by the electronic topological scheme, although the influence of the electronic density at the M-X bond critical point is also observed. The stability of the perovskite structure with respect to the decomposition into ${\mathrm{MX}}_2$+AX has been found to be mostly governed by the ${\mathrm{M}}^{2+}$ cation, the crystals having small ${\mathrm{M}}^{2+}$ and large ${\mathrm{A}}^{+}$ ions being the most stable ones. There is also a clear tendency for the crystals lacking X-X bonds, and having bizarre ${\mathrm{M}}^{2+}$ shapes, to decompose.