The approach of Pauling (1960 ; small cations lodged in the voids of close-packed arrays of bulky anions) has been the paradigm for describing crystal structures during the last century. Although commonly accepted, it has not offered a satisfactory explanation of crystal structures, most of which remain misunderstood.

The phase transitions and the structures of both Ca and CaO are represented in Fig. 1 . Elemental Ca is fcc (a = 5.58 Å) at ambient conditions. At 723 K it transforms to bcc (a = 4.38 Å). However, under pressure it undergoes the transition sequence fcc → bcc (body-centred cubic) → sc (single cubic, α-Po structure) at 19.5 and 32 GPa (Olyjnik & Holzapfel, 1984 ). The unit-cell parameters of these high-pressure phases are a = 3.56 and 2.62 Å. Olyjnik & Holzapfel (1984 ) found that the two bcc phases, observed at 723 K and at 19.5 GPa, are identical and can be correlated by a common equation-of-state (EOS).

The density-functional theory (DFT) calculations (Hohenberg & Kohn, 1964 ; Kohn & Sham, 1965 ) were carried out for sc-, fcc- and bcc-Ca using the Perdew–Burke–Ernzerhof (PBE; Perdew et al., 1996 ) approximation for the exchange-correlation function, and the pseudo-potential plane-wave method within the quantum-ESPRESSO software package (Giannozzi et al., 2009 ). Specifically, the core-valence interactions have been described through the Vanderbilt ultrasoft pseudo­potentials (Vanderbilt, 1990 ), including nonlinear core correction and treating the Ca semicore s and p states as valence electrons (i.e. Ca [Ne] 3s ²3p ⁶4s ²). The electronic wavefunctions and the charge density have been expanded by using plane-wave basis sets defined by energy cutoffs of 70 and 700 Ry, respectively. The Brillouin-zone integration has been performed employing the Gaussian-broadening technique and using a converged reciprocal space k-point meshing. A smearing parameter of 0.002 Ry has been employed. The set of parameters used for these calculations allowed the computation of the equation-of-states for both sc and fcc phases that are in good agreement with the available experimental data (Yabuuchi et al., 2005 ; Brandes & Brook, 1992 ). In addition, the bcc–sc transition pressure has been calculated to be around 39 GPa, a value that compares well with the experimental transition at 32 GPa (Olyjnik & Holzapfel, 1984 ) and ab initio calculations 40.4–41.2 GPa (Jona & Marcus, 2006 ).

We will begin our discussion by considering the second question posed above, that is why does CaO adopt the B1 structure and why should fcc-Ca shrink when O atoms are inserted. It should be emphasized here that such questions were (if ever) rarely formulated and therefore no clear explanations have been provided.

At high pressure, BaSn undergoes the CrB → CsCl transition (Beck & Lederer, 1993 ). The isomorphism of both the perovskite BaSnO₃ and the high-pressure phase of the BaSn (B2) (Martínez-Cruz et al., 1994 ) suggests that an ELF calculation for B2 BaSn, should show localization at regions coincident with the oxygen positions in BaSnO₃. A similar isomorphism was reported for the LnAl alloys and the perovskites LnAlO₃ (Ramos-Gallardo & Vegas, 1997 ). This hypothesis is consistent with a Zintl phase approach to BaSn, when the transfer of Ba valence electrons converts Sn atoms into pseudo-Te atoms (Ψ-Te). Accordingly, the Sn-substructure is similar to the high pressure of Te (γ-Te), which is a rhombohedrally distorted simple cubic structure (a = 2.95 Å, α = 102.6°; Po-type). In this structure, the Te atoms have six nearest neighbours which should be bonded by two-centre, two-electron bonds. The O atoms, in BaSnO₃, are located at the middle of these bonds. Recall the similarity of the γ-Te structure with that of TeO₃ (FeF₃- or AlF₃-type) and how, at high temperature, the FeF₃ (AlF₃) structure transforms to a cubic ReO₃-type structure.

The computation of the ELF for different phases of calcium (fcc, bcc and sc) discloses crucial aspects of these crystal structures which have been hidden for almost a century. Our results give strong support to the intuitive hypothesis that considered the metallic subnets in compounds as metastable structures of the parent metal. This hypothesis, formulated on the basis of the analogies existing between the cation arrays and high-pressure phases of the alloys, has been expressed as follows: ‘If high pressure gives rise to a redistribution of the electrons and hence to a phase transition, similar results could be obtained if electrons are redistributed by the presence of foreign atoms’. This term was first coined to denote unlike atoms added to a parent metal structure when forming a compound. Later, it was seen that these ‘foreign atoms’ can act like pressure and/or temperature, provoking phase transitions in the parent metal structures (Vegas & Martínez-Cruz, 1995 ; Vegas, 2000 ).