Topology of the Electron Density in Ionic Crystals.

Víctor Luaña, Aurora Costales, and A. Martín Pendás

Departamento de Química Física y Analítica
Universidad de Oviedo, 33006-Oviedo, Spain
email: victor@hobbit.quimica.uniovi.es
We present in this work the results of an extension of the theory of Atoms in Molecules (AIM) of Prof. R.F.W. Bader [1] and collaborators to the realm of crystalline systems, particularly ionic crystals. Our aim is three-fold.

In the first place we will briefly revise the main facts emerging from the AIM theory in molecular systems. Then we will show how its use in periodic systems is the source of a whole new set of topological concepts. These new objects (primary bundles, atomic or repulsion polyhedra) are immediately related with many ill-defined geometrical entities (ionic radii, atomic volume, coordination polyhedra) that sustained the first predictive theories in the development of solid state physics and chemistry. As the AIM recipe is able to give unambiguous values for all these "observables", the theory transforms the art of relating geometry to energetics and thermodynamics into a contrastable discipline.

In the second place, we will present the actual topological analysis of a whole family of ionic compounds: the 120 alkali halide perovskites, AMX3 ( A: Li, Na, K, Rb, Cs; M: Be, Mg, Ca, Sr, Ba, Zn; X: F, Cl, Br, I). The electron densities feeding the topological study [2] have been obtained through ab initio Perturbed Ion Calculations [3] at the theoretical static equilibrium geometries. We will show how to extract meaningful information from our data, and how to connect topological trends with chemical knwoledge, particularly with thermodynamical stability.

Finally, our last aim is to show that, due to the intrinsically geometrical nature of the topological studies of the electron density, the appropriate visualization of the three-dimensional objects of the AIM theory is essential to condense the vast amount of information contained in actual calculations. Powerful modern visualization techniques, like ray-tracing, may be used to obtain maximum information images. These images, besides its scientific value, hold another property: beauty.

Citations

  1. [1] R. F. W. Bader, Atoms in Molecules. (Oxford U. P., 1990).
  2. [2] A. Martín Pendás, The critic program, 1995.
  3. [3] V. Luaña, A. Martín Pendás, J. M.(Recio, E. Francisco, and M. Bermejo, Comput. Phys. Commun. 77 (1993) 107.