Simple arguments and quantum mechanical calculations are used to analyze the occurrence of non-nuclear maxima (NNMs) in the electron density of crystals and molecules. The recent controversy concerning the experimental detection of NNMs in Be and Si is thus clarified, and NNMs are shown to be a normal step in the evolution of chemical bonding of homonuclear groups as internuclear distances decrease.

An application of the atoms in molecules theory to the partitioning of static thermodynamic properties in condensed systems is presented. Attention is focused on the definition and the behavior of atomic compressibilities. Inverses of bulk moduli are found to be simple weighted averages of atomic compressibilities. Two kinds of systems are investigated as examples: four related oxide spinels and the alkali halide family. Our analyses show that the puzzling constancy of the bulk moduli of these spinels is a consequence of the value of the compressibility of an oxide ion. A functional dependence between ionic bulk moduli and ionic volume is also proposed.

The results of a theoretical study on the point defects of monoclinic $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ are reported here. The point defects considered here are vacancies, interstitials together with dopant ions such as Be, Mg, In, Cr, Si, Ge, Sn, and Zr. Since the low symmetry of the monoclinic lattice does not provide an unambiguous location of interstitial sites and migration paths, we propose a unique way for their identification in terms of the electron density topology. Special attention has also been given to the preference among the lattice and interstitial sites for the impurity defects, and its explanation in terms of structural, electrostatic, and electron density arguments. The calculated results find the most prominent features in the lattice to be the existence of (i) empty channels along the $\mathbf{b}$ direction, and (ii) atomic layers perpendicular to them. Their interplay governs the stability and mobility of the point defects in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$. The anionic Frenkel pair consisting of the oxygen vacancy and oxygen interstitial is predicted to dominate the defect structure in the lattice. The dopants considered here are likely to be stabilized at the octahedral gallium sites, except for ${\mathrm{Be}}^{+2}$, which prefers a tetrahedral gallium site in the lattice. Some of the possible migration paths have been determined, and the pseudoactivation energies for the intrinsic, oxygen-rich, and oxygen-deficient conditions are computed as a function of temperature. It is suggested that tuning the concentration of oxygen can lead to a change in the anisotropy of the ionic conductivity in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$.

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.