The SiO bond and electron density distributions

Abstract

Electron density distributions, ϱ(r), have been calculated for the partially and fully geometry optimized molecules Si I O, Si II O2, H2Si III O3, H4Si IV O4, H6SIV2O7, H8Si VI O6, H10SiVI2O10 and H12Si VIII O8, using SCF Hartree-Fock wavefunctions calculated with a 6-311++G** basis set (the Roman numeral superscripts denote the coordination number of Si). The value of the electron density distribution, ϱ(r c), evaluated at (3,−1) critical (stationary) points, r c, along the SiO bonds of these molecules increases linearly with decreasing SiO bond length, R(SiO), from ϱ(r c)=0.50e/A3 for R(Si VIII O)=1.96A to ϱ(r c)=1.36e/A3 for R(Si II O)= 1.48A. A mapping of the Laplacian of the distribution, ∇2 ϱ(r), together with a determination of the bonded radii, rb(O), calculated for the oxide ions indicate that the fractional ionic character of the bond increases with increasing coordination number from ∼0.40 for an Si II O bond to ∼0.50 for an Si IV O bond to ∼0.60 for an Si VI O bond to ∼0.75 for a Si VIII O bond. Unlike the ionic and crystal radii of the oxide ion, rb(O) is not constant for a given coordination number but increases linearly with R(SiO) from rb(O)=0.86A for R(SiO)=1.48A to rb(O)= 1.20A for R(SiO)=1.96A. Concomitant with this increase in the size of the oxide ion, the atomic charge on the O atom increases as the volume of its basin expands and the fractional ionic character, ƒi(SiO), of the SiO bond increases. As ƒi(SiO) increases, not only is there a decrease in the value of ϱ(r) at r c, but also the sharpness (curvature) of the maximum in ϱ(r) radiating perpendicular to the bond and the sharpness of the minimum in ϱ(r) along the bond are both diminished. Electron density distribution calculations for five H6Si2O7 molecules with geometries fixed to match those observed for the nonequivalent `Si2O7 dimers' in coesite show that the value of ϱ(r c) for the bridging SiO bond increases as the SiOSi angle widens and R(SiO) shortens. The properties of ϱ(r) for the SiO bonds of the molecules are similar to those measured for coesite demonstrating that ϱ(r) is similar in both systems. The ellipticity of the electron density of the SiO bond decreases slightly as the angle widens with the cross-section of the bond becoming circular at 180°. Such an effect is consistent with the formation of weak π-bonds where the π-system perpendicular to the SiOSi plane becomes more dominant as the SiOSi angle narrows. Relief and level line contour −∇2 ϱ(r) maps calculated through the OSiO planes in H4SiO4 and H8SiO6 show that the electron density of the valence shell concentration of the oxide ion is enhanced in the directions of the Si atoms with the enhancement being greater for the Si IV O than for the Si VI O bond in conformity with the greater ionic character of the latter. Maps calculated for H12SiO8 show little dissipation of the valence shell of the oxide ion and little or no enhancement in the direction of the Si atom in agreement with the larger fractional ionic character of the Si VIII O bond and a nearly spherical distribution of the valence shell enhancement of ϱ(r) for the oxide ion.