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.     

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     

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.     

Crystal chemical characteristics of α-CaSi2O5, a new high pressure calcium silicate with five-coordinated silicon synthesized at 1500°C and 10 GPa

The crystal structure of α-CaSi₂O₅ synthesized at conditions of 1500°C and 10 GPa, has been solved and refined in centrosymmetric space group P , using single crystal X-ray diffraction data. The composition (Z=4) and unit cell are Ca_1.02Si_1.99O₅ by EPMA analysis and a=7.243(2) Å, b=7.546(4) Å, c=6.501(4) Å, α=81.43(5)°, β=84.82(4)°, γ=69.60(3)°, V=329.5(3) ų, yielding the density value, 3.55 g/cm³. The structure is closely related to that of titanite, CaTiSiO₅ and features the square-pyramid five-fold coordination of silicon by oxygen. The ionic radius for five-coordinated Si calculated from the bond distances is 0.33 Å. The substantial deviation of valence sum for Ca indicates the existence of local strain and the instability of α-CaSi₂O₅ at room pressure.     

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     

Structural characterisation of the high-pressure phase CaAl4Si2O11

Single crystals of CaAl₄Si₂O₁₁ were synthesised at 1,500?°C and 14 GPa in a multi-anvil press, and the structure of the phase determined by single-crystal X-ray diffraction at room conditions. The structure-type is that of the “hexagonal barium ferrites”. The space group of the average structure is P6 ₃ /mmc and the cell parameters are a?=?5.4223(4) Å, c?=?12.7041(6) Å, V?=?323.28(5) ų, with Z?=?2, and its density is 3.905?g?cm^?3, which is reasonable for a high-pressure alumino-silicate phase. The 22 oxygen and two calcium atoms within the unit-cell form an approximate hexagonal-close-packed array. Ten of the twelve octahedral interstices within this array that have only oxygen atoms for apices are filled with Si and/or Al. M1 octahedra share edges to form a spinel-like sheet of octahedra. The average bond length ?=?1.833 Å suggests mixed occupancy by Si and Al. The M1 octahedral sheets are linked by shared corners to pairs of face-sharing M2 octahedra containing Al, with ?= 1.918 Å. The remaining two cations of the unit-cell contents statistically occupy four tetrahedrally-coordinated interstices, which occur as face-sharing pairs. The average bond length for these sites (1.742 Å) suggests that they are occupied by Al, although Si occupancy cannot be excluded by the data. It is proposed that only one interstice of each pair is locally occupied, with the possibility of some short-range ordering of such occupancies. Complete long-range order leading to the acentric space group P6 ₃ mc is excluded by the data, as is the possibility of the average structure being comprised of merohedral (0?0?0?1) twins of P6 ₃ mc symmetry.     

SiO bonded interactions in coesite: a comparison of crystalline, molecular and experimental electron density distributions

Bond critical point properties of electron density distributions calculated for representative Si₅O₁₆ moieties of the structure of coesite are compared with those observed and calculated for the bulk crystal. The values calculated for the moieties agree with those observed to within ∼5%, on average, whereas those calculated for the crystal agree to within ∼10%. As the SiOSi angles increase and the SiO bonds shorten, there is a progressive build-up in the calculated electron density along the bonds. This is accompanied by an increase in both the curvatures of the electron density, both perpendicular and parallel to each bond, and the Laplacian of the electron density distribution at the bond critical points. The cross sections of the bonds at the critical points become more circular as the angle approaches 180o. Also, the bonded radius of the oxide anion decreases about twice as much as that of the Si cation as the SiO bond length decreases and the fraction of s-character of the bond is indicated to increase. A knowledge of electron density distributions is central to our understanding of the forces that govern the structure, properties, solid state reactions, surface reactions and phase transformations of minerals. The software (CRYSTAL95 and TOPOND) used in this study to calculate the bond critical properties of the electron density and Laplacian distributions is bound to promote a deeper understanding of crystal chemistry and properties. Received: 23 February 1998 / Revised, accepted: 16 July 1998     

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.     

OH groups in nominally anhydrous framework structures: An infrared spectroscopic investigation of danburite and labradorite

The pleochroic behaviour of two nominally anhydrous structurally similar minerals, danburite and An59 labradorite, was investigated in the region of the OH stretching frequencies. Danburite shows a sharp absorption band at 3540 cm^?1, labradorite shows a broad band with an absorption maximum at 3230 cm^?1. On the basis of the pleochroic scheme of theinfrared (IR) absorption spectra it is proposed that the OH dipoles in danburite are located within the symmetry plane showing a distinct orientation parallel to [010]; the OH groups in labradorite are oriented approximately perpendicular to (001). The proposed models are in accordance with bond valence calculations showing that in both framework structures the most deficient oxygens, O5 in danburite and O _C m in labradorite, are partially replaced by OH.     

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     

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.     

Application of infrared spectroscopy to studies of silicate glass structure: Examples from the melilite glasses and the systems Na2O-SiO2 and Na2O-Al2O3-SiO2

Infrared (IR) and Raman spectroscopic methods are important complementary techniques in structural studies of aluminosilicate glasses. Both techniques are sensitive to small-scale (<15 Å) structural features that amount to units of several SiO₄ tetrahedra. Application of IR spectroscopy has, however, been limited by the more complex nature of the IR spectrum compared with the Raman spectrum, particularly at higher frequencies (1200–800 cm^?1) where strong antisymmetric Si-O and Si-O-Si absorptions predominate in the former. At lower frequencies, IR spectra contain bands that have substantial contributions from ‘cage-like’ motions of cations in their oxygen co-ordination polyhedra. In aluminosilicates these bands can provide information on the structural environment of Al that is not obtainable directly from Raman studies. A middle frequency envelope centred near 700 cm^?1 is indicative of network-substituted AlO₄ polyhedra in glasses with Al/(Al+Si)>0·25 and a band at 520–620cm^?1 is shown to be associated with AlO₆ polyhedra in both crystals and glasses. The IR spectra of melilite and melilite-analogue glasses and crystals show various degrees of band localization that correlate with the extent of Al, Si tetrahedral site ordering. An important conclusion is that differences in Al, Si ordering may lead to very different vibrational spectra in crystals and glasses of otherwise gross chemical similarity.     

High-pressure single-crystal X-ray diffraction study of jadeite and kosmochlor

The crystal structures of natural jadeite, NaAlSi₂O₆, and synthetic kosmochlor, NaCrSi₂O₆, were studied at room temperature, under hydrostatic conditions, up to pressures of 30.4 (1) and 40.2 (1) GPa, respectively, using single-crystal synchrotron X-ray diffraction. Pressure–volume data have been fit to a third-order Birch–Murnaghan equation of state yielding V ₀ = 402.5 (4) Å³, K ₀ = 136 (3) GPa, and K ₀ ^′  = 3.3 (2) for jadeite and V ₀ = 420.0 (3) Å³, K ₀ = 123 (2) GPa and K ₀ ^′  = 3.61 (9) for kosmochlor. Both phases exhibit anisotropic compression with unit-strain axial ratios of 1.00:1.95:2.09 for jadeite at 30.4 (1) GPa and 1:00:2.15:2.43 for kosmochlor at 40.2 (1) GPa. Analysis of procrystal electron density distribution shows that the coordination of Na changes from 6 to 8 between 9.28 (Origlieri et al. in Am Mineral 88:1025–1032, 2003) and 18.5 (1) GPa in kosmochlor, which is also marked by a decrease in unit-strain anisotropy. Na in jadeite remains six-coordinated at 21.5 (1) GPa. Structure refinements indicate a change in the compression mechanism of kosmochlor at about 31 GPa in both the kinking of SiO₄ tetrahedral chains and rate of tetrahedral compression. Below 31 GPa, the O3–O3–O3 chain extension angle and Si tetrahedral volume in kosmochlor decrease linearly with pressure, whereas above 31 GPa the kinking ceases and the rate of Si tetrahedral compression increases by greater than a factor of two. No evidence of phase transitions was observed over the studied pressure ranges.     

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     

Resonance bond numbers: A graph-theoretic study of bond length variations in silicate crystals

The resonance bond number n, as defined in this paper, is designed to describe the strength of an XO bond as a function of the kinds of atoms present and which atoms are bonded. The calculation of n is made on a fragment extracted from the crystal encompassing the XO bond. If this fragment consists of only the X atom and its coordinating O atoms, then n is numerically equal to the Pauling bond strength, s. In this study a graph-theoretic algorithm is developed permitting the calculation of n using fragments including up to 50 atoms. This algorithm was used to calculate n for all of the bonds in ten silicate crystals. Since bond strength is be inversely related to bond length, we examined the relationship between these two variables and found that n can be used to explain over 70 percent of the variation of XO bond lengths from their average values in the crystals. A fit of the parameter n/r, where r is the row number in the periodic table of the metal atom X, to the observed bond lengths in these crystals yielded the equation R(XO)=1.39(n/r)^?0.22 which explains over 95.5 percent of the variation of bond lengths in the crystals. The fact that the same formula with s replacing n was found in an earlier study to be a good estimator of average bond lengths in crystals shows that n relates to individual variations in bond lengths in crystals in the same way that s relates to average bond lengths in crystals. Using minimum energy SiO, AlO and MgO bond lengths and harmonic force constant data calculated for these bonds in hydroxyacid molecules, theoretical equations similar to those used by Pauling to explain bond length variations in hydrocarbons are derived. Bond lengths calculated with these equations for the 10 crystals shows that 95 percent of the variation of the observed bond lengths in these crystals can be explained in terms of n by this purely theoretical model.     

Kulkeite,a new metamorphic phyllosilicate mineral: Ordered 1∶1 chlorite/talc mixed-layer

Kulkeite occurs as platy, colorless, porphyroblastic, single crystals up to 2 mm in size in a low-grade dolomite rock associated with a Triassic meta-evaporite series at Derrag, Tell Atlas, Algeria, It is associated with sodian aluminian talc, unusual chlorite polytypes, and both K and Na phlogopite. Kulkeite is optically biaxial, negative, n _x=1.552, n _y=1.5605, n _z=1.5610, 2V_z=24° (obs.). Based on microprobe analysis the empirical formula is (Na_0.38K_0.01Ca_0.01)(Mg_8.02Al_0.99)[Al_1.43Si_6.57O₂₀](OH)₁₀ with some variation in Na, Si, and tetrahedral Al. The crystals are monoclinic with a=5.319(1), b=9.195(2), c=23.897(10) Å, β=97° 1(3)′; Z=2; the calculated density is 2.70 g cm^?3. The four strongest lines in the X-ray powder pattern are (d, I, hkl): 7.90, 100, 003; 1.533, 100, 060; 7.42, 80, 002; 3.38, 80, 007; the 001 reflection with 23.7 Å has intensity 10. Transmission electron microscopy confirms the nature of a regular 1∶1 mixed-layer, which consists of 14 Å chlorite (clinochlore) sheets alternating with sheets of one-layer (9.5 Å) talc characterized by the lattice substitution NaAl→Si just as in the talc occurring as a discrete mineral co-existing with kulkeite. Kulkeite is intergrown with lamellae of clinochlore that represent two-layer and five-layer (70 Å) polytypes with optical birefringence exceeding the normal value for clinochlore by a factor of 3. The origin of kulkeite is due to low-grade metamorphism with temperatures probably not exceeding 400° C. As the clinochlore lamellae and sodian aluminian talc are found in mutual contact, kulkeite seems to represent a metastable mineral at least during the latest phase of metamorphism. However, at an earlier stage, prior to clinochlore formation, kulkeite might have been stable, and the incorporation of Na and Al into its talc component could indeed be the decisive factor for the formation of the mixed-layer.     

Thermal expansion of hydrated six-coordinate silicon in thaumasite,Ca<Subscript>3</Subscript>Si(OH)<Subscript>6</Subscript>(CO<Subscript>3</Subscript>)(SO<Subscript>4</Subscript>)·12H<Subscript>2</Subscript>O

Thaumasite, Ca₃Si(OH)₆(CO₃)(SO₄)12H₂O, occurs as a low-temperature secondary alteration phase in mafic igneous and metamorphic rocks, and is recognized as a product and indicator of sulfate attack in Portland cement. It is also the only mineral known to contain silicon in six-coordination with hydroxyl (OH)^? that is stable at ambient P–T conditions. Thermal expansion of the various components of this unusual structure has been determined from single-crystal X-ray structure refinements of natural thaumasite at 130 and 298 K. No phase transitions were observed over this temperature range. Cell parameters at room temperature are: a= 11.0538(6) Å, c=10.4111(8) Å and V=1101.67(10) ų, and were measured at intervals of about 50 K between 130 and 298 K, resulting in mean axial and volumetric coefficients of thermal expansion (×10^?5K^?1); α _a =1.7(1), α _c =2.1(2), and α _V =5.6(2). Although the unit cell and ^VIIICaO₈ polyhedra show significant positive thermal expansion over this temperature range, the silicate octahedron, sulfate tetrahedron, and carbonate group show zero or negative thermal expansion, with α _V (^VISiO₆) = ?0.6 ± 1.1, α _V (^IVSO₄)=?5.8 ± 1.4, and α _R (C–O)= 0.0 ± 1.8 (×10^?5 K^?1). Most of the thermal expansion is accommodated by lengthening of the R(O...O) hydrogen bond distances by on average 5σ, although the hydrogen bonds involving hydroxyl sites on ^VISi expand twice as much as those on molecular water, causing the [Ca₃Si(OH)₆(H₂O)₁₂]⁴⁺ columns to expand in diameter more than they move apart over this temperature range. The average Si–OH bond length of the six-coordinated Si atom 〈R(^VISi–OH)〉 in thaumasite is 1.783(1) Å, being about 0.02 Å (?20σ) shorter than ^VISi–OH in the dense hydrous magnesium silicate, phase D, MgSi₂H₂O₆.     

Pauling bond strength, bond length and electron density distribution

The power law regression equation, <R(M–O)> = 1.46(<ρ(r _c)>/r)^?0.19, relating the average experimental bond lengths, <R(M–O)>, to the average accumulation of the electron density at the bond critical point, <ρ(r _c)>, between bonded pairs of metal and oxygen atoms (r is the row number of the M atom), determined at ambient conditions for oxide crystals, is similar to the regression equation R(M–O) = 1.41(ρ(r _c)/r)^?0.21 determined for three perovskite crystals at pressures as high as 80 GPa. The pair are also comparable with the equation <R(M–O)> = 1.43(<s>/r)^?0.21 determined for oxide crystals at ambient conditions and <R(M–O)> = 1.39(<s>/r)^?0.22 determined for geometry-optimized hydroxyacid molecules that relate the geometry-optimized bond lengths to the average Pauling bond strength, <s>, for the M–O bonded interactions. On the basis of the correspondence between the equations relating <ρ(r _c)> and <s> with bond length, it seems plausible that the Pauling bond strength might serve a rough estimate of the accumulation of the electron density between M–O bonded pairs of atoms. Similar expressions, relating bond length and bond strength hold for fluoride, nitride and sulfide molecules and crystals. The similarity of the expressions for the crystals and molecules is compelling evidence that molecular and crystalline M–O bonded interactions are intrinsically related. The value of <ρ(r _c)> = r[(1.41)/<R(M–O)>]^4.76 determined for the average bond length for a given coordination polyhedron closely matches the Pauling’s electrostatic bond strength reaching each the coordinating anions of the coordinated polyhedron. Despite the relative simplicity of the expression, it appears to be more general in its application in that it holds for the bulk of the M–O bonded pairs of atoms of the periodic table.     

Crystal structure refinement and electron density distribution in diaspore

Diaspore from Dilln, Hungary, AlOOH, is orthorhombic with space group Pbnm, a=4.4007(6), b=9.4253(13), c=2.8452(3) Å, and Z=4. The crystal structure and electron distribution have been refined from 791 graphite-monochromatized MoKα data (maximum 2θ=130°) to R=0.035 (R _w =0.029). Difference maps show substantial electron density ascribed to covalent bonding in the hydroxyl group, O(2)-H, but no residual density is observed along the Al-O(1,2) bonds. An analysis of the charge distribution implies net charges of +1.47(26), ?1.08(16), ?0.59(13) and +0.20(5) for Al, O(1), O(2) and H respectively. Semi-empirical molecular orbital calculations of the Hückel type agree with the experimentally determined atomic charge distribution and also allow a rationalization of the observed bond length variations.