Properties of atoms under pressure: bonded interactions of the atoms in three perovskites

The crystal structures for the three perovskites, CaSnO(3), YAlO(3), and LaAlO(3), were geometry optimized at the density functional theory level for a wide range of simulated isotropic pressures up to 80 GPa. The connections between the geometry optimized bond lengths, R(M-O), the values of the electron density, ρ(r(c)), the local kinetic, G(r(c)), potential, V(r(c)), energy densities, H(r(c)), and the Laplacian, ∇(2)(r(c)), at the bond critical points, r(c), for the M-O nonequivalent bonded interactions were examined. With increasing pressure, ρ(r(c)) increases along four distinct trends when plotted in terms of the Al-O, Ca-O, Sn-O, Y-O, and La-O bond lengths, but when the bond lengths were plotted in terms of ρ(r(c))/r where r is the periodic table row number of the M atoms, the data scatter along a single trend modeled by the power law regression expression R(M-O) = 1.41(ρ(r(c))/r)(-0.21), an expression that is comparable with that obtained for the bonded interactions for a large number of silicate and oxides crystals, R(M-O) = 1.46(ρ(r(c))/r)(-0.19) and that obtained for a relatively large number of hydroxyacid molecules R(M-O) = 1.39(s/r)(-0.22) where s is the Pauling bond strength of a bonded interaction. The similarity of the expressions determined for the perovskites, silicate and oxides crystals, and hydroxyacid molecules suggest that the bonded interactions in molecules and crystal are not only similar and comparable. The close correspondence of the expressions for the perovskites, the silicate and oxide crystals, and the molecules indicates that Pauling bond strength and ρ(r(c)) are comparable measures of the bonded interactions, the larger the accumulation of the electron density between the bonded atoms the larger the value of s, the shorter the bond lengths. It also indicates that the bonded interactions that govern the bond length variations behave as if largely short ranged. Like ρ(r(c))/r, the values of G(r(c))/r, V(r(c))/r, ∇(2)(r(c))/r likewise correlate in terms of R(M-O) in a single trend. With increasing pressure, the value of V(r(c)) decreases at a faster rate than G(r(c)) increases consistent with the observation that ρ(r(c)) increases with increasing pressure thereby stabilizing the structures at high pressures. As evinced by the well-developed power law trends between R(M-O) and the bond critical point properties, the bulk of the bonded interactions for the perovskites are concluded to change progressively from closed-shell to i