Nuclei act as the attractors in the electronic density gradient fields. Since the topological structure and stability are determined as a result of the balance between the attractors of the system, we should anticipate a significant degree of similarity in the topological properties of the AMX3 perovskites. The rich variety of topological schemes found is, in this regard, an interesting surprise. Our study has shown that the organizing principle behind that variety is the ratio between topological ionic radii along the main bond paths or, in other words, the competition between atomic basins to achieve a kind of preferred size.
Ionic radii along the bond paths follow systematic trends in passing from one crystal to another, even though the ionic radius of an ion in a crystal do strongly depend on the direction being considered.
Ionic basins have, essentially, a polyhedral shape, even though faces and edges present very large curvatures in some cases. The type and number of CP's in the unit cell is limited by the Morse relations. The type and number of CP's in the surface of an ionic basin is limited by the Euler relation. Both, together with the space group symmetry, posse strict requirements on the shape of the ionic basins. This point of view helps to explain some of the bizarre features exhibited by the basins in some cases, particularly the nearly bidimensional wings of the M(+2) basins in the C8, R9 and B10 topological schemes.
We have found a suggestive connection between the topological properties of the electronic density and the chemical stability of the perovskites. In particular, we have found that the crystal tends to be more stable, with respect to the decomposition into MX2 and AX, when there are X-X bonds and the attraction basins of the ions are free of strange features like wings and spikes. This view is in agreement with previous work (Martín Pendás et al. 1995) relating the phase stability of the B1 and B2 alkali halides to the ratios of ionic radii obtained through topological arguments.
As a final remark, the Atoms in Molecules theory may be used to give a rigorous foundation to important historical concepts like ionicity, index of coordination, coordination polyhedron or volume of an atom or an ion in a solid. Several interesting mappings between atoms and polyhedra can be built, some of which have been examined and exploited in this work. We think that there is room in solid state thinking for the new tools and concepts emerged from AIM, and that a judicious use of them, will give new ways to correlate chemical behavior and chemical structure in solids.