The structural and thermodynamic properties of MgF2 have been investigated in a wide range of pressures (0−80 GPa) and temperatures (0−850 K) by coupling quantum-mechanical ab initio perturbed ion calculations with a quasi-harmonic Debye model. The room temperature, zero-pressure structural parameters and lattice energy are computed with errors smaller than 2% when correlation energy corrections are incorporated in the calculation. Our computed equation of state is compatible with direct measurements of the bulk modulus and obeys universal p−V relations. We have simulated the rutile-to-fluorite phase transition during the loading process and have found lower (≃4 GPa) and upper (≃45 GPa) bounds for the transition pressure by means of thermodynamic and mechanical criteria for phase stability. Bonding properties and their change with pressure have been derived through a topological analysis of the electron density using Bader's theory of atoms in molecules. This analysis reveals that MgF2 is a highly ionic compound. Its ionicity decreases linearly with increasing pressure and, as in other ionic compounds, the crystal shows anion−anion bonds.

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In this paper we study the chemical bonding of the small (monomer, triatomic, and dimer) neutral clusters of AlN, GaN, and InN presented earlier in paper 1. It includes the analysis of the topology of the electron density and its Laplacian, together with relevant atomic properties, in light of the theory of atoms in molecules. The most prominent feature of the bonding here, the existence of strong N-N bonds, is seen to diminish with an increase in the number of metal atoms and the degree of ionicity. The Al-N bond shows a large transfer of charge, but also a significant deformation of the Al electron shells, so it can be understood as a highly polar shared interaction. On the other hand, Ga-N and In-N bonds are nonshared interactions, with smaller charge transfers and polarizations. In all cases, the existence of a N-N bond weakens the metalnitrogen bond. The bonding picture that emerges depends only on the reliability of the electron densities, and it is consistent with the conclusions of our previous work in paper 1.

We present the application of Bader's topological analysis of the electron density to geometric properties in ionic materials. Particular attention is paid to the concept of ionic radius, in relation to the shapes of ions in crystals, and to the various correlations among atomic properties, i.e., electronegativities, deformabilities, etc., that it induces. Using a simple model to fit our results to a theoretical frame, we show that ionic bonds display properties in complete parallelism to those known in covalent bonds. This allows us to define unambiguosly the strength of an ionic bond, which is found to correspond to Pauling's bond valence.

We present here the topological ͑Bader͒ analysis of the electronic structure for 120 cubic perovskites AM X 3 (A denotes Li, Na, K, Rb, Cs; M denotes Be, Mg, Ca, Sr, Ba, Zn; X denotes F, Cl, Br, I͒. 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 CsSrF 3 and 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. M 2ϩ 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 M X 2 ϩAX has been found to be mostly governed by the M 2ϩ cation, the crystals having small M 2ϩ and large A ϩ ions being the most stable ones. There is also a clear tendency for the crystals lacking X-X bonds, and having bizarre M 2ϩ shapes, to decompose. ͓S0163-1829͑97͒09204-7͔