Bonded interactions and the crystal chemistry of minerals: A review

Connections established during last century between bond length, radii, bond strength, bond valence and crystal and molecular chemistry are briefly reviewed followed by a survey of the physical properties of the electron density distributions for a variety of minerals and representative molecules, recently generated with first-principles local energy density quantum mechanical methods. The structures for several minerals, geometry-optimized at zero pressure and at a variety of pressures were found to agree with the experimental structures within a few percent. The experimental Si-O bond lengths and the Si-O-Si angle, the Si-O bond energy and the bond critical point properties for crystal quartz are comparable with those calculated for the H₆Si₂O ₇ disilicic acid molecule, an indication that the bonded interactions in silica are largely short ranged and local in nature. The topology of model experimental electron density distributions for first and second row metal M atoms bonded to O, determined with high resolution and high energy synchrotron single crystal X-ray diffraction data are compared with the topology of theoretical distributions calculated with first principles methods. As the electron density is progressively accumulated between pairs of bonded atoms, the distributions show that the nuclei are progressively shielded as the bond lengths and the bonded radii of the atoms decrease. Concomitant with the decrease in the M-O bond lengths, the local kinetic energy, G(r_c), the local potential energy, V(r_c), and the electronic energy density, H(r_c) = G(r_c) + V(r_c), evaluated at the bond critical points, r_c, each increases in magnitude with the local potential energy dominating the kinetic energy density in the internuclear region for intermediate and shared interactions. The shorter the bonds, the more negative the local electronic energy density, the greater the stabilization and the greater the shared character of the intermediate and shared bonded interactions. In contrast, the local kinetic energy density increases with decreasing bond length for closed shell interactions with G(r_c) dominating V(r_c) in the internuclear region, typical of an ionic bond. Notwithstanding its origin in Pauling's electrostatic bond strength rule, the Brown-Shannon bond valence for Si-O bonded interactions agrees with the value of the electron density, ρ(r_c), on a one-to-one basis, indicating that the Pauling bond strength is a direct measure of ρ(r _c), the greater the bond strength, the more shared the interaction. Mappings of the Laplacian, the deformation electron density distribution and the electron localization function for several silicates are reviewed. The maps display hemispherical domains ascribed to bond pair electrons along the bond vectors and larger kidney-shaped domains ascribed to lone pair electrons on the reflex sides of the Si-O-Si angles. In the case of the nonbridging Si-O bonded interactions, the O atoms are capped by mushroom shaped domains. With few exceptions, the domains agree in number and location with those embodied in the VSEPR model for closed-shell molecules, defining reactive sites of potential electrophilic attack and centers of protonation. The electrophilicity of the O atoms comprising the Si-O-Si bonded interactions in coesite is indicated to increase with decreasing angle, providing a basis for understanding the protonization of the structure. The shapes and arrangements of the bond and lone pair features displayed by the bridging O atoms in quartz and and the nonbridging O atoms in forsterite are transferable on an one-to-one basis to sheet and chain magnesiosilicates that possess both bridging and nonbridging O atoms. The G(r_c)/ρ(r_c) ratio increases for each of the M-O bonds along separate trends with decreasing bond length and the coordination number of the M atom, suggesting that the ratio is a measure of bond character. An examination of the interactions in terms of the \V(r _c)\/G(r_c) ratio indicates that the Li-O, Na-O and Mg-O bonds are closed shell ionic interactions, that the C-O bond and one of the S-O bonds is shared covalent and that the Be-O, A1-O, Si-O, B-O, P-O and S-O bonds are intermediate in character. It is noteworthy that the classification closely parallels Pauling's classification based on the electronegativity differences between the M and O atoms. Bond critical point properties calculated for Ni bearing sulfides and high and low spin Fe bearing sulfides are discussed. The properties correlate linearly, as observed for the M-O bonds, with the experimental bond lengths, the shorter the bond lengths, the greater the ρ(r_c) and ∇²ρ(r_c) values. The high and low spin Fe-S data scatter along parallel but separate trends with the values of ρ(r_c) and ∇²ρ(r_c) for a given low spin Fe-S bond length being larger than those calculated for a given comparable high spin Fe-S bond length. The properties of the Ni-Ni bonded interactions calculated and observed for the Ni sulfides are virtually the same as those calculated for bulk Ni metal. No bond paths were found between the Fe atoms of the face sharing octahedra of troilite. The experimental bond critical point properties for the Ni sulfide heazlewoodite, Ni₃S2, are in close agreement with those calculated. The |V(r_c)|/G(r_c) ratio indicates that the Fe-S, Ni-S and Ni-Ni bonded interactions are intermediate in character. The successful reproduction of the bond lengths and angles for several silicates, the comparable properties of the electron density distributions and the location of sites of potential chemical reactivity recounted in the review bodes well for the exploitation of the properties of minerals and the deciphering of crystal chemical problems, using first principles computational quantum chemical strategies.