An Exploration of Theoretical and Experimental Electron Density Distributions and SiO Bonded Interactions for the Silica Polymorph Coesite

Abstract

A multipole representation of the experimental electron density distribution for the high-pressure silicapolymorph coesite, using Hirshfeld-type radial functions, has been generated with single-crystal X-raydiffraction data recorded to a sin θmax/λ value of 1.21 Å⁻¹ at 100 K. Unlike an earlier modeling of thedistribution, where a more limited data set was analyzed, deformation electron density maps display bananashapedisosurfaces in the lone-pair regions of each of the oxide anions involved in the bent SiOSi angles aswell as teardrop-shaped ones along each of the SiO bond vectors. They also display a ring torus isosurfaceabout O1, the oxide anion involved in the straight angle. Laplacian -▽²p maps display belt-shaped isosurfaces,centered near the apexes of the bent angles, that wrap about halfway around the oxide anions, with a ringtorus-shaped isosurface surrounding O1. An analysis of -▽²p revealed that the (3,-3) critical point associatedwith the anions involved in the bent angles are associated in general with larger maxima than that associatedwith the straight angle, evidence that the electron density is more locally concentrated on the oxide anionsinvolved in the bent angles. As such, these anions are asserted to be more susceptible to electrophilic attackby hydrogen, a feature that provides an experimental basis for why hydrogen in H- and Al-bearing coesiteavoids O1 and is observed to dock in the vicinity of the oxide anions involved in the bent angles. The bondcritical point properties of the experimental multipole representation of the electron density distribution forcoesite together with those for the very high-pressure silica polymorph, stishovite, conform with those calculatedfor the SiO bonded interactions for a relatively large number of silicate crystals. Not only are they similar invalue with the theoretical properties, but together they correlate with the observed SiO bond lengths as predictedby the calculations. The observed SiO bonds display a relatively wide range of ▽²p(r[c]) values between ~10e Å⁻⁵ for stishovite and ~20 e ��⁻⁵ for coesite. The larger ▽²p(r[c]) values recorded for coesite, consideredtypical of first row closed-shell ionically bonded atoms, may not be typical for a closed-shell bonded interactioninvolving second row atoms such as the four-coordinate Si in coesite. The maxima along the bond vectorsand in the lone-pair regions displayed by the experimental △p and -▽²p maps are indicative of shared covalentbonded interactions. The evidence suggests that the value of the electron density at the bond critical point fora given bonded interaction is a reliable measure of bond type: the larger the value p(r[c]), the greater theshared covalent interaction.