5. Results

5.6 The shape of ions

The classical image of ions in crystals is that of spheres, maybe slightly deformed, touching each other. We have seen previously that the topological partition of the crystal must fill completely the space and the actual shape of ions corresponds to polyhedra with curved faces and edges. We can, however, recover the spheres picture by examining the surfaces of constant electron density.

We have represented in Fig. 5.6 several isodensity surfaces of KMgF3. The electron density exhibits relative maxima at the nuclear positions, and decays more or less exponentially as we move out of them. In the case of KMgF3, the density at the nuclei is 4.539e3 (K+), 1.091e3 (Mg++), and 4.469e2 (F-), and the density at the bond critical points is 3.661e-2 (Mg-F), 1.177e-2 (K-F), and 9.913e-3 (F-F). If we chose a density value of 0.040 a.u., or higher, the isodensity surfaces appear as spheres centered on the nuclei. As we approach to the value of density on the bonds, the ionic spheres develop small spikes in the direction of the bond lines (See, for instance the image for 0.0366 in KMgF3). The spikes of two ions contact when the isodensity surface corresponds exactly to the electron density at the bond critical point. If we continue to examine surfaces of even lower density, the spikes of two bonded ions will form, approximately, a cylinder.

Fig. 5.6 Surfaces of constant electron density in KMgF3. The details are better appreciated on the larger pictures that you can get by clicking on each image. From left to right the value of the electron density is: 0.060, 0.0366, 0.020, and 0.010 a.u. The surfaces are clipped by the basin surfaces, and portions of the surface are colored according to the basins that contains them. The isodensity surfaces have been determined with Tessel 1.3 from critic calculations and have been rendered with POV-Ray 2.2.

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Copyright © 1996 Víctor Luaña, Aurora Costales and Angel Martín Pendás.