CONNECTIONS BETWEEN THE PROPERTIES OF ELECTRON DENSITY AND BOND CHARACTER FOR M-O BONDED INTERACTIONS FOR FIRST AND SECOND ROW M ATOMS IN MINERALS

The value of electron density, r(r_c), and the Laplacian, ∇ ² ρ(r_c), at the bond critical points, r_c, for M-O bonded interactions increase as the experimental bond lengths decrease with the shared character of the interactions increasing with increasing r(r_c) and ∇ ²ρ(r_c). The interactions are classified (1) as closed shell ionic when the local electron energy density,  H(r_c) = G(r_c) + V(r_c) > 0 where G(r_c) is the positive definite local kinetic energy density and V(r_c) is the always negative local potential energy density  and (2) as shared covalent when ∇ ²ρ(r_c) < 0. With these constraints, Espinosa et al. (2002, J. Chem. Phys) showed that when the ratio |V(r_c)|/G(r_c) > 2, a bonded interaction classifies as shared covalent, when |V(r_c)|/G(r_c) < 1, it classifies as closed shell ionic and when |V(r_c)|/G(r_c) is between 1 and 2, it classifies as intermediate. On the basis of the ratio, the Li-O, Na-O, Mg-O bonded interactions classify as closed shell ionic, the Be-O, Al-O, Si-O, B-O, P-O and S-O interactions classify as intermediate with the shared character increasing in the order of the bonds listed and one of the S-O bond and the C-O bonds in the carbonates classifying as shared covalent. If |V(r_c)| is greater than G(r_c), then it indicates that the accumulation of the electron density in the internuclear region is stabilizing. In contrast, if  G(r_c) is larger than |V(r_c)|, then it indicates that the accumulation is destabilizing, typical of a nonbonded situation (i.e., where there is no component of covalent bonding).

The properties of model electron density distributions, r(r), recorded with high energy synchrotron single crystal X-ray diffraction data for stishovite, forsterite , fayalite,  tephoite and Co₂SiO₄ olivine and for the high resolution single crystal data collected for coesite, valentinite and heazlewoodite are comparable with those calculated with first principles quantum mechanical methods almost quantitatively. On the other hand, those collected with low energy single crystal diffraction data usually depart by as much as 30% in some cases from the calculated values. The close agreement of the synchrotron and the first principle values bodes well for using these calculations for studies of the bonded interactions and the crystal chemistry of minerals.