SiO and GeO bonded interactions as inferred from the bond critical point properties of electron density distributions

The topological properties of the electron density distributions for more than 20 hydroxyacid, geometry optimized molecules with SiO and GeO bonds with 3-, 4-, 6- and 8-coordinate Si and Ge cations were calculated. Electronegativities calculated with the bond critical point (bcp) properties of the distributions indicate, for a given coordination number, that the electronegativity of Ge (∼1.85) is slightly larger than that of Si (∼1.80) with the electronegativities of both atoms increasing with decreasing bond length. With an increase in the electron density, the curvatures and the Laplacian of the electron density at the critical point of each bond increase with decreasing bond length. The covalent character of the bonds are assessed, using bond critical point properties and electronegativity values calculated from the electron density distributions. A mapping of the (3, −3) critical points of the valence shell concentrations of the oxide anions for bridging SiOSi and GeOGe dimers reveals a location and disposition of localized nonbonding electron pairs that is consistent with the bridging angles observed for silicates and germanates. The bcp properties of electron density distributions of the SiO bonds calculated for representative molecular models of the coesite structure agree with average values obtained in X-ray diffraction studies of coesite and danburite to within ∼5%. Received: 18 August 1997 / Revised, accepted: 19 February 1998     

A study of the bonded interactions in nitride molecules in terms of bond critical point properties and relative electronegativities

Bond critical point properties calculated for the MN bonds in a number of geometry optimized nitride molecules containing first- and second-row M cations are compared with those calculated for a number of oxide molecules. As reported for the oxides, the value of the electron density, ρ(r _c ), at the bond critical points, r _c , increases with decreasing bond length while for the more electronegative cations, the local energy density, H(r _c ) decreases nonlinearly in value as the relative electronegativities of the M-cations, χ _M , tend to increase. In the majority of cases, χ_M, |λ₁|/λ₃ and ∇²ρ(r _c ) increase with decreasing minimum energy bond lengths. The bond lengths adopted by the molecules are indicated to be an important determinant of the critical point properties of the electron density distributions. The relative electronegativities derived from the electron density distributions of the nitrides agree with those derived for the oxides and Pauling’s electronegativities to within ∼5%, on average. Received: 3 February 1997 / Revised, accepted: 11 July 1997     

Experimental and theoretical bond critical point properties for model electron density distributions for earth materials

Generalized X-ray scattering factor model experimental electron density distributions and bond critical point, bcp, properties generated in recent studies for the earth materials stishovite, forsterite, fayalite and cuprite with high energy single crystal synchrotron X-ray diffraction data and those generated with high resolution diffraction data for coesite and senarmonite were found to be adequate and in relatively good agreement, ~5% on average, with those calculated with quantum chemical methods with relatively robust basis sets. High resolution low energy single crystal diffraction data, recorded for the molecular sieve AlPO₄-15, were also found to yield model electron density distribution values at the bcp points for the AlO and PO bonded interactions that are in relatively good to moderately good agreement with the theoretical values, but the Laplacian values of the distribution at the points for the two bonded interactions were found to be in relatively poor agreement. In several cases, experimental bcp properties, generated with conventional low energy X-ray diffraction data for several rock forming minerals, were found overall to be in poorer agreement with the theoretical properties. The overall agreement between theoretical bcp properties generated with computational quantum methods and experimental properties generated with synchrotron high energy radiation not only provides a basis for using computational strategies for studying and modeling structures and their electron density distributions, but it also provides a basis for improving our understanding of the crystal chemistry and bonded interactions for earth materials. Theoretical bond critical point properties generated with computational quantum methods are believed to rival the accuracy of those determined experimentally. As such the calculations provide a powerful and efficient method for evaluating electron density distributions and the bonded interactions for a wide range of earth materials.Dedicated to Professor Robert F. Stewart of Carnegie Mellon University on his retirement for his brilliant and original work modeling electron density distributions.     

A crystal chemical study of protoanthophyllite: orthoamphiboles with the protoamphibole structure

Two new protoamphibole-type amphiboles with space group type Pnmn, have been found in nature: protoferro-anthophyllite (Fe_0.80Mn_0.20)₂ (Fe_0.98Mg_0.02)₅ (Si₄O₁₁)₂(OH)₂, and protomangano-ferro-anthophyllite, (Mn_0.70Fe_0.30)₂ (Fe_0.82Mg_0.18)₅ (Si₄O₁₁)₂(OH)₂. Protoferro-anthophyllite (PFA) occurs in pegmatites at both Gifu Prefecture, Japan and at Cheyenne Mountain, El Paso County, Colorado, USA. Protomangano-ferro-anthophyllite, (PMFA) occurs in pegmatites at Fukushima Prefecture and in a Mn mine at Tochigi Prefecture, Japan. Structure determinations of the two amphiboles show that both are isostructural with the synthetic fluorian-amphibole, protoamphibole (= protofluorian-lithian-anthophyllite). A calculation of the procrystal electron density distributions, the bond paths and the bond critical point properties of PFA, PMFA, grunerite and protoamphibole indicates that the M4 cation in these amphiboles is 4-coordinated. A calculation of the electron density distributions at the Becke3LYP/6-311G(2d,p) level for model silicate tetrahedra for these amphiboles and anthophyllite reveals that the value of the electron density at the bond critical points, ρ(r _c ), for the SiO(nbr) bonds is larger, on average (0.93 e/ų), than that for the SiO(br) bonds (0.90 e/ų). The observed SiO bond lengths decrease linearly with increasing ρ(r _c ) while the magnitudes of the curvatures of ρ(r _c ) both perpendicular and parallel to the bonds and the Laplacian of ρ(r _c ) each increases. These trends are associated with an increase in the electronegativity of the Si cation, a possible increase in the covalent character of the SiO bond and a tendency for SiO(nbr) bonds to be involved in wider OSiO angles than SiO(br) bonds. It is possible, if not likely, that protoanthophyllite has often been misidentified as anthophyllite.     

Critical point properties of electron density distributions for oxide molecules containing first and second row cations

 Minimum energy geometries and electron density distributions, ϱ(r), for ∼40 polyatomic oxide molecules containing first and second row M-cations have been calculated at the Hartree-Fock level with a 6-311++G** basis set. The nature of the bonded interactions in these molecules is examined in terms of the relative electronegativities, χ _M , of the M-cations and the properties of the electron density distribution, ϱ(r _c ), evaluated at the bond critical points, r _c , along each MO bond. As ϱ(r _c ) and the Laplacian of ϱ(r _c ) increase, χ _M increases indicating an increase in the covalent character of the bonded interactions between M and O. The ratios of the curvatures of ϱ(r _c ) indicate that the NO bond is predominantly covalent, that the CO and SO bonds are of intermediate type and that the remaining MO bonds are indicated to be predominantly ionic in character. A comparison of the critical point properties of ϱ(r _c ) and χ _M indicates that the minimum energy MO bond length is an important determinate of the properties of ϱ(r _c ) and the character of the MO bonds. On the other hand, values of the local energy density, H(r _c ), indicate that the LiO, BeO, NaO, MgO and AlO bonds are predominantly ionic and that the BO, CO, NO, SiO, PO and SO bonds are predominantly covalent in character. The χ _M -values provided by the properties of ϱ(r _c ) indicate that the covalent component of a bond increases with decreasing bond length, coordination number and increasing bond strength. Each MO bond seems to represent a unique entity and to possess a distinct set of ϱ(r _c ) properties, the distinction being greater for the more electronegative cations. The bonded radius of the oxide ion, r _b (O), and the χ _M -values determined from ϱ(r _c ) correlate with values determined from promolecule electron density distributions. In addition, r _b (O) and χ _M -values determined from experimental electron density distributions for crystals correlate with values determined from procrystal electron density distributions. The number of critical points and bond paths are modeled rather faithfully by procrystal and promolecule electron density distributions, despite the neglect of the binding forces in their constructions. Received: October 15, 1996/Revised, accepted: February 10, 1997     

A mapping of the electron localization function for earth materials

The electron localization function, ELF, generated for a number of geometry-optimized earth materials, provides a graphical representation of the spatial localization of the probability electron density distribution as embodied in domains ascribed to localized bond and lone pair electrons. The lone pair domains, displayed by the silica polymorphs quartz, coesite and cristobalite, are typically banana-shaped and oriented perpendicular to the plane of the SiOSi angle at ~0.60 Å from the O atom on the reflex side of the angle. With decreasing angle, the domains increase in magnitude, indicating an increase in the nucleophilic character of the O atom, rendering it more susceptible to potential electrophilic attack. The Laplacian isosurface maps of the experimental and theoretical electron density distribution for coesite substantiates the increase in the size of the domain with decreasing angle. Bond pair domains are displayed along each of the SiO bond vectors as discrete concave hemispherically-shaped domains at ~0.70 Å from the O atom. For more closed-shell ionic bonded interactions, the bond and lone pair domains are often coalesced, resulting in concave hemispherical toroidal-shaped domains with local maxima centered along the bond vectors. As the shared covalent character of the bonded interactions increases, the bond and lone pair domains are better developed as discrete domains. ELF isosurface maps generated for the earth materials tremolite, diopside, talc and dickite display banana-shaped lone pair domains associated with the bridging O atoms of SiOSi angles and concave hemispherical toroidal bond pair domains associated with the nonbridging ones. The lone pair domains in dickite and talc provide a basis for understanding the bonded interactions between the adjacent neutral layers. Maps were also generated for beryl, cordierite, quartz, low albite, forsterite, wadeite, åkermanite, pectolite, periclase, hurlbutite, thortveitite and vanthoffite. Strategies are reviewed for finding potential H docking sites in the silica polymorphs and related materials. As observed in an earlier study, the ELF is capable of generating bond and lone pair domains that are similar in number and arrangement to those provided by Laplacian and deformation electron density distributions. The formation of the bond and lone pair domains in the silica polymorphs and the progressive decrease in the SiO length as the value of the electron density at the bond critical point increases indicates that the SiO bonded interaction has a substantial component of covalent character.     

Bond length variation in hydronitride molecules and nitride crystals

Bond lengths calculated for the coordination polyhedra in hydronitride molecules match average values observed for XN bonds involving main group X-cations in nitride crystals to within 0.04 Å. As suggested for oxide and sulfide molecules and crystals, the forces that determine the average bond lengths recorded for coordinated polyhedra in hydronitride molecules and nitride crystals appear to be governed in large part by the atoms that comprise the polyhedra and those that induce local charge balance. The forces exerted on the coordinated polyhedra by other parts of the structure seem to play a small if not an insignificant role in governing bond length variations. Bonded radii for the nitride ion obtained from theoretical electron density maps calculated for the molecules increase linearly with bond length as observed for nitride crystals with the rock salt structure. Promolecule radii calculated for the molecules correlate with bonded and ionic radii, indicating that the electron density distributions in hydronitride molecules possess a significant atomic component, despite bond type.     

Electron density distributions and bonded interactions for the fibrous zeolites natrolite, mesolite and scolecite and related materials

 For the fibrous zeolites natrolite, Na₂[Al₂Si₃O₁₀]·2H₂O, mesolite, Na₂Ca₂[Al₂Si₃O₁₀]₃·8H₂O, and scolecite, Ca[Al₂Si₃O₁₀]·3H₂O, with topologically identical aluminosilicate framework structures, accurate single-crystal X-ray diffraction data have been analyzed by least-squares refinements using generalized scattering factor (GSF) models. The final agreement indices were R(F ) = 0.0061, 0.0165, and 0.0073, respectively. Ensuing calculations of static deformation [Δρ(r)], and total, [ρ(r)], model electron density distributions served to study chemical bonding, in particular by topological electron density analyses yielding bond critical point (bcp) properties and in situ cation electronegativities. The results for 32 SiO, 24 AlO, 14 CaO, and 12 NaO unique bonds are compiled and analyzed in terms of both mean values and correlations between bond lengths, bonded oxygen radii, bcp densities, curvatures at the bcps, and electronegativities. Comparison with recent literature data obtained from both experimental electron density studies on minerals and model calculations for geometry-optimized molecules shows that the majority of the present findings conforms well with chemical expectation and with the trends observed from molecular modeling. For the SiO bond, the shared interaction is indicated to increase with decreasing bond length, whereas the AlO bond is of distinctly more polar nature, as is the NaO bond compared to CaO. Also, the observed ranges of the Si and Al in situ electronegativities and their mean electronegativities agree well with both Pauling's values and model calculation results, and statistically significant correlations are obtained which are consistent with trends described for oxide and nitride molecules. Received: 10 May 1999 / Revised, accepted: 14 September 1999     

Power law relationships between bond length, bond strength and electron density distributions

The strength of a bond, defined as p=s/r, where s is the Pauling bond strength and r is the row number of an M cation bonded to an oxide anion, is related to a build-up of electron density along the MO bonds in a relatively large number of oxide and hydroxyacid molecules, three oxide minerals and three molecular crystals. As p increases, the value of the electron density is observed to increase at the bond critical points with the lengths of the bonds shortening and the electronegativities of the M cations bonded to the oxide anion increasing. The assertion that the covalency of a bond is intrinsically connected to its bond strength is supported by the electron density distribution and its bond critical point properties. A connection also exists between the properties of the electron density distributions and the connectivity of the bond strength network formed by the bonded atoms of a structure. Received: 20 August 1997 / Revised, accepted: 3 November 1997     

Electron density distribution and bond critical point properties for forsterite, Mg2 SiO4, determined with synchrotron single crystal X-ray diffraction data

A generalized X-ray scattering factor model experimental electron density distribution has been generated for the orthosilicate forsterite, using an essentially extinction and absorption free set of single crystal diffraction data recorded with intense, high energy synchrotron X-ray radiation (E=100.6 keV). A refinement of the model converged with an R(F)=0.0061. An evaluation of the bond critical point, bcp, properties of the distribution at the (3, –1) stationary points for the SiO and MgO bonded interactions, yielded values that agree typically within ~5%, on average, with theoretical values generated with quantum chemical computational strategies, using relatively robust basis sets. On the basis of this result, the modeling of the experimental distribution is considered to be adequate. As the bcp properties increase in magnitude, the MgO and SiO bonds decrease in length as calculated for a number of rock forming silicates. As asserted by Coppens (X-ray charge densities and chemical bonding. Oxford University Press, Oxford, 1997), large negative ²(r_c) values, characteristic of shared interactions involving first row atoms, may not be characteristic of closed shell covalent bonded interactions involving second row Si, P and S atoms bonded to O. This study adds new evidence to the overall relatively good agreement between theoretical bcp properties generated with computational quantum strategies, on the one hand, and experimental properties generated with single crystal high energy synchrotron diffraction data on the other. The similarity of results not only provides a basis for using computational strategies for studying and modeling structures, defects and the reactivity of representative structures, but it also provides a basis for improving our understanding of the crystal chemistry of earth materials and the character of the SiO bonded interaction.     

A comparison of procrystal and ab initio model representations of the electron-density distributions of minerals

 The procrystal calculation of the electron density is a very rapid procedure that offers a quick way to analyze various bonding properties of a crystal. This study explores the extent to which the positions, number, and properties of bond-critical points determined from the procrystal representations of the electron density for minerals are similar to those of first-principles ab initio model distributions. The purpose of the study is to determine the limits imposed upon interpretation of the procrystal electron density. Procrystal calculations of the electron density for more than 300 MO bonds in crystals were compared with those previously calculated using CRYSTAL98 and TOPOND software. For every bond-critical point found in the ab initio calculations, an equivalent one was also found in the procrystal model, with similar magnitudes of electron density, and at similar positions along the bonds. The curvatures of the electron densities obtained from the ab initio and the procrystal distributions are highly correlated. It is concluded that the procrystal distributions are capable of providing good estimates of the bonded radii of the atoms and the properties of the electron-density distributions at the bond-critical points. Because the procrystal model is so fast to compute, it is especially useful in addressing the question as to whether a pair of atoms is bonded or not. If the Bader criteria for bonding are accepted, then the successful generation of the bond-critical points by the procrystal model demonstrates that bonding is an atomic feature. The main difference between the critical-point properties of the procrystal and the ab initio model is that the curvature in the electron density perpendicular to the bond path of the ab initio model is sharper than for the procrystal model. This is interpreted as indicating that the electrons that migrate into a bond originate from its sides, and not from the regions closer to the nuclei. This observation also suggests that ab initio optimization routines could see an improvement in speed if the parameters relating to the angular components of atomic wave functions were to vary before the radial components. Received: 6 August 2001 / Accepted: 21 November 2001     

Bond length and radii variations in fluoride and oxide molecules and crystals

Molecular orbital calculations completed on fluoride molecules containing first and second row cations have generated bond lengths, R, that match those observed for coordinated polyhedra in crystals to within ～0.04 Å, on average. The calculated bond lengths and those observed for fluoride crystals can be ranked with the expression R=Kp ^?0.22, where p=s/r, s is the Pauling strength of the bond, r is the row number of the cation and K=1.34. The exponent -0.22 (≈ -2/9) is the same as that observed for oxide, nitride and sulfide molecules and crystals. Bonded radii for the fluoride anion, obtained from theoretical electron density maps, increase linearly with bond length. Those calculated for the cations as well as for the fluoride anion match calculated promolecule radii to within ～0.03 Å, on average, suggesting that the electron density distributions in the vicinity of the minima along the bond paths possess a significant atomic component despite bond type. Bonded radii for Si and O ions provided by experimental electron density maps measured for the oxides coesite, danburite and stishovite match those calculated for a series of monosilicic acid molecules. The resulting radii increase with bond length and coordination number with the radius of the oxide ion increasing at a faster rate than that of the Si cation. The oxide ion within danburite exhibits several distinct radii, ranging between 0.9 and 1.2 Å, rather than a single radius with each exhibiting a different radius along each of the nonequivalent bonds with B, Si and Ca. Promolecule radii calculated for the coordinated polyhedra in danburite match procrystal radii obtained in a structure analysis to within 0.002 Å. The close agreement between these two sets of radii and experimentally determined bonded radii lends credence to Slater's statement that the difference between the electron density distribution observed for a crystal and that calculated for a procrystal (IAM) model of the crystal “would be small and subtle, and very hard to determine by examination of the total charge density.”     

Ab initio calculated geometries and charge distributions for H4SiO4 and H6Si2O7 compared with experimental values for silicates and siloxanes

Ab initio STO-3G molecular orbital theory has been used to calculate energy-optimized Si-O bond lengths and angles for molecular orthosilicic and pyrosilicic acids. The resulting bond length for orthosilicic acid and the nonbridging bonds for pyrosilicic acid compare well with Si-OH bonds observed for a number of hydrated silicate minerals. Minimum energy Si-O bond lengths to the bridging oxygen of the pyrosilicic molecule show a close correspondence with bridging bond length data observed for the silica polymorphs and for gas phase and molecular crystal siloxanes when plotted against the SiOSi angle. In addition, the calculations show that the mean Si-O bond length of a silicate tetrahedron increases slightly as the SiOSi angle narrows. The close correspondence between the Si-O bond length and angle variations calculated for pyrosilicic acid and those observed for the silica polymorphs and siloxanes substantiates the suggestion that local bonding forces in solids are not very different from those in molecules and clusters consisting of the same atoms with the same coordination numbers. An extended basis calculation for H₄SiO₄ implies that there are about 0.6 electrons in the 3d-orbitals on Si. An analysis of bond overlap populations obtained from STO-3G* calculations for H₆Si₂O₇ indicates that Si-O bond length and SiOSi angle correlations may be ascribed to changes in the hybridization state of the bridging oxygen and (d – p) π-bonding involving all five of the 3d AO's of Si and the lone-pair AO's of the oxygen. Theoretical density difference maps calculated for H₆Si₂O₇ show a build-up of charge density between Si and O, with the peak-height charge densities of the nonbridging bonds exceeding those of the bridging bonds by about 0.05 e Å^?3. In addition, atomic charges (+1.3 and ?0.65) calculated for Si and O in a SiO₂ moiety of the low quartz structure conform reasonably well with the electroneutrality postulate and with experimental charges obtained from monopole and radial refinements of diffraction data recorded for low quartz and coesite.     

Thioarsenides: a case for long-range Lewis acid–base-directed van der Waals interactions

Electron density distributions, bond paths, Laplacian and local-energy density properties have been calculated for a number of As₄S _n (n = 3, 4 and 5) thioarsenide molecular crystals. On the basis of the distributions, the intramolecular As–S and As–As interactions classify as shared bonded interactions, and the intermolecular As–S, As–As and S–S interactions classify as closed-shell van der Waals (vdW) bonded interactions. The bulk of the intermolecular As–S bond paths link regions of locally concentrated electron density (Lewis-base regions) with aligned regions of locally depleted electron density (Lewis-acid regions) on adjacent molecules. The paths are comparable with intermolecular paths reported for several other molecular crystals that link aligned Lewis base and acid regions in a key–lock fashion, interactions that classified as long-range Lewis acid–base-directed vdW interactions. As the bulk of the intermolecular As–S bond paths (~70%) link Lewis acid–base regions on adjacent molecules, it appears that molecules adopt an arrangement that maximizes the number of As–S Lewis acid–base intermolecular bonded interactions. The maximization of the number of Lewis acid–base interactions appears to be connected with the close-packed array adopted by molecules: distorted cubic close-packed arrays are adopted for alacránite, pararealgar, uzonite, realgar and β-AsS and the distorted hexagonal close-packed arrays adopted by α- and β-dimorphite. A growth mechanism is proposed for thioarsenide molecular crystals from aqueous species that maximizes the number of long-range Lewis acid–base vdW As–S bonded interactions with the resulting directed bond paths structuralizing the molecules as a molecular crystal.     

A molecular orbital study of bonding in sulfate molecules: Implications for sulfate crystal structures

Molecular orbital calculations have been completed on sulfate monomers and a dimer in a determination of minimum-energy geometries and electron density distributions. SO bond lengths calculated for the monomer and dimer correlate linearly with the fractional s-characters of the bonds, as observed for sulfate groups in crystals. With increasing coordination number of S, the bonded radii of S and O, as determined from electron density maps, increase at the same rate. This is at variance with the assumption that the radius of the oxide ion is nearly constant and that bond length variations arise primarily from changes in cation radii. The dimer shows a relatively large change in energy as its SOS angle is deformed from its minimum-energy value (125.6°) to 180°, in conformity with the small variation among observed angles. This is in contrast to the wide variation of bridging angles observed for silicate and phosphate dimers in crystals and molecules, and may imply that significant differences should be expected in the behavior of sulfates with respect to polymorphism and glass formation. The reaction energy of SO₃ + H₂O → H₂SO₄, calculated with second-order Møller-Plesset perturbation theory, agrees with the experimental value. Other properties of H₂SO₄ are also calculated and compared with experimental observations and previous calculations.     

Atomic and ionic radii: a comparison with radii derived from electron density distributions

 The bonded radii of anions obtained in topological analyses of theoretical and experimental electron density distributions differ from atomic, ionic and crystal radii in that oxide-, fluoride-, nitride- and sulfide-anion radii are not constant for a given coordination number. They vary in a regular way with bond length and the electronegativity of the cation to which they are bonded, exhibiting radii close to atomic radii when bonded to a highly electronegative cation and radii close to ionic radii when bonded to a highly electropositive cation. The electron density distributions show that anions are not spherical but exhibit several different radii in different bonded directions. The bonded radii of cations correlate with ionic and atomic radii. But unlike ionic radii, the bonded radius of a cation shows a relatively small increase in value with an increase in coordination number. In contrast to atomic and ionic radii, the bonded radius of an ion in a crystal or molecule can be used as a reliable and well-defined estimate of its radius in the direction of its bonds. Received April 16, 1996 / Revised, accepted August 6, 1996     

Experimental multipole-refined and theoretical charge density study of LiGaSi<Subscript>2</Subscript>O<Subscript>6</Subscript> clinopyroxene at ambient conditions

The synthetic LiGaSi₂O₆ clinopyroxene is monoclinic C2/c at room-T. Its experimental electron density, ρ(r), has been derived starting from accurate room-T single-crystal diffraction data. Topological analysis confirms an intermediate ionic-covalent character for Si–O bonding, as found by previous electron-density studies on other silicates such as diopside, coesite and stishovite. The non-bridging Si–O bonds have more covalent character than the bridging ones. The Ga–O bonds have different bonding characters, the Ga–O2 bond being more covalent than the two Ga–O1 bonds. Li–O bonds are classified as pure closed-shell ionic interactions. Similar to spodumene (LiAlSi₂O₆), Li has sixfold coordination, but the bond critical points associated to the two longest bonds are characterized by very low electron density values. Similar to what previously found in spodumene and diopside, O···O interactions were detected from the topological analysis of ρ(r), and indicate a cooperative interaction among the lone pairs of neighbouring oxygen atoms. In particular, this kind of interaction has been obtained for the O1···O1 edge shared between two Ga octahedra. Integration over the atomic basins gives net charges of −1.39(10), 2.82(10), 1.91(10) and 0.82(8) e for O (averaged), Si, Ga and Li atoms, respectively. Periodic Hartree–Fock and DFT calculations confirm the results obtained by multipole refinement of the experimental data. Moreover, the theoretical topological properties of the electron density distribution on the Si₂O₆ group are very similar to those calculated for spodumene. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Exploration of structure and bonding in stishovite with fourier and pseudoatom refinement methods using single crystal and powder X-ray diffraction data

The structure and bonding in stishovite, SiO₂, is explored with Fourier summation and pseudoatom refinement of merged x-ray single crystal and powder diffraction data. Replacement of the 25 lowest-angle, highly extinction-affected, single crystal reflections with structure factors obtained from low-extinction powder diffraction data has resulted in a significant improvement in the analysis compared with earlier studies. The deformation electron density, total electrostatic potential and total and valence electron densities are mapped. Accumulations of electron density are observed in both SiO bonds, together with non-bonding features displayed about the oxygen on both sides of a plane formed by three bonds with Si. Deficits of electron density between O atoms across the shared-edges are rationalized in terms of the Pauli exclusion principle. There is no evidence for strong repulsion of Si atoms across the same ring. The total electrostatic potential has a continuous low value for the vacant channels in the structure along c with localized minima between O atoms on opposite sides of the channel. The sizes of Si and O are related to the electron density and to the electrostatic potential.