The hypothesis of the molecular structure, i.e. that a molecule is a collection of atoms linked together by a network of bonds, was developed at the end of the nineteenth century. Despite its role as the backbone of our modern chemical wisdom, the hypothesis appears unrelated to the postulates of Quantum Mechanics, and it has been considered by many to be beyond theoretical definition.

The theory of Atoms In Molecules (AIM), developed by R.F.W. Bader and collaborators (Bader et al 1981, Bader 1990, Bader 1995), has provided, however, a rigorous quantum mechanical foundation to the molecular structure concepts. By means of the analysis of the multi electron molecular wavefunction, AIM theory gives unambiguous answers to questions such as which bonds do exist, what is the shape or the charge of an atom in the molecule. The AIM theory does not rely on any approximation and the quality of the derived properties only depends on the quality of the wave function analyzed.

We present in this work the results of an extension of the AIM theory to the realm of crystalline systems, particularly ionic crystals. Our aim is threefold.

In the first place we will briefly revise the main facts emerging from the AIM theory in molecular systems. When applied to periodic systems, a collection of new topological concepts do arise. These new concepts (primary bundles, atomic or repulsion polyhedra) are inmediately related with many ill-defined geometrical entities (ionic radii, atomic volume, coordination polyhedra) that dominate the empirical discourse of the crystalline structure. As the AIM recipe is able to give unambiguous values for all those concept, the theory can, in principle, transform the art of relating geometry to energetics and thermodynamics into a contrastable discipline.

Secondly, we will present the actual topological analysis of
representative ionic compounds. Most of our discussion will refer
to the 120 alkali halide perovskites, AMX3 (A: Li, Na, K, Rb, Cs;
M: Be, Mg, Zn, Ca, Sr, Ba; X: F, Cl, Br, I), with some considerations
of the alkali halides (AX) and the alkaline earth halides (MX2).
This work is part of an ongoing effort to determine and analyze the
structural and chemical stability of the *AmMnXo* compounds.
Consequently, one of our motivations in using AIM theory
was to determine the connections
between stability and electronic density topology.

Finally, our last aim is to show that the visualization of the three-dimensional objects of the AIM theory is essential to condense the vast amount of information contained in actual calculations. Modern modelization and rendering techniques may be used to get maximal information images that, besides its scientific content, transmit the intrinsic beauty of Nature's electronic geometry.

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