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  • 1
    Electronic Resource
    Electronic Resource
    Resonance bond numbers: A graph-theoretic study of bond length variations in silicate crystals (1988)
    Springer
    Physics and chemistry of minerals 15 (1988), S. 409-415 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00311046
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  • 2
    Electronic Resource
    Electronic Resource
    SiO and GeO bonded interactions as inferred from the bond critical point properties of electron density distributions (1998)
    Springer
    Physics and chemistry of minerals 25 (1998), S. 574-584 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract  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%.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002690050150
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  • 3
    Electronic Resource
    Electronic Resource
    SiO bonded interactions in coesite: a comparison of crystalline, molecular and experimental electron density distributions (1999)
    Springer
    Physics and chemistry of minerals 26 (1999), S. 264-272 
    Details
    ISSN: 1432-2021
    Keywords: Key words Coesite ; Electron density ; Critical point properties ; Laplacian ; SiO bond
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract  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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002690050186
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  • 4
    Electronic Resource
    Electronic Resource
    Framework silica structures generated using simulated annealing with a potential energy function based on an H6Si2O7 molecule (1994)
    Springer
    Physics and chemistry of minerals 21 (1994), S. 269-284 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract A simulated annealing technique was used to search for global and local minimum energy structures of a potential energy model for silica. The model is based on ab initio SCF MO calculations on the disilicic acid molecule, H6Si2O7. Starting with 4 SiO2 units, with the atoms randomly distributed in the unit cell, 23 distinct silica tetrahedral framework structures were found, with a variety of space group symmetries and cell dimensions. Despite the assumption of P 1 space group symmetry for the starting structure, only 7 of the local minimum energy structures were found to possess triclinic symmetry with the remainder exhibiting symmetries ranging from P c to $$I\bar 42d$$ to within 0.001 Å. Although the interaction potential for the disilicic acid molecule has a single minimum energy SiO bond length and SiOSi angle, the local minimum energy structures exhibit angles that range between 105° and 180° and bond lengths that range between 1.55 and 1.68 Å. The correlation observed for coesite and the other silica polymorphs between SiO bond length and fs(O) is reproduced. The generated structures show a wide variety of coordination sequences, ring sizes and framework densities, the later ranging from 19.8 to 35.5 Si/1000 Å3. The energies of these structures correlate with their framework densities, particularly for higher energy structures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00202091
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  • 5
    Electronic Resource
    Electronic Resource
    Molecular mimicry of the bond length-bond strength variations in oxide crystals (1987)
    Springer
    Physics and chemistry of minerals 14 (1987), S. 327-331 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract Minimum energy theoretical bond lengths R t obtained with robust split-basis molecular orbital calculations for 27 hydroxyacid molecules containing first- and second-row cations X n+ reproduce XO bond lengths in crystals. Plots of ln(R t ) vs. ln(s), where s is the Pauling bond strength, define two different but essentially parallel trends (for first- and second-row cations, respectively) as observed for crystals. A new bond strength parameter p=s/r is defined where r=1 for first- and r=2 for second-row main-group cations. When a ln(R t ) vs. ln(p) plot is prepared with these theoretical bond lengths, a single trend is obtained. A regression analysis of this data set shows that more than 99 percent of the variation of ln(R t can be explained in terms of a linear dependence on ln(p), yielding R=1.39 p −0.22 as an estimator of the bond lengths. A comparison of 153 mean XO bond lengths compiled by Shannon (1976) for main-group closed-shell X-cations from all 6 rows of the periodic table with those estimated with this formula for r=1, 2, ..., 6, respectively, shows that these bond lengths are estimated within 0.05 Å on average with nearly 85 percent estimated within 0.10 Å of the observed value. More than 97 percent of the variation of these observed bond lengths can be ranked in terms of a linear dependence on the estimated bond lengths. The success of these calculations is further evidence that the forces that govern bond length variations in oxide crystals behave as if they are short-ranged.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00309805
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  • 6
    Electronic Resource
    Electronic Resource
    Bond length variation in hydronitride molecules and nitride crystals (1992)
    Springer
    Physics and chemistry of minerals 19 (1992), S. 127-132 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00198610
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  • 7
    Electronic Resource
    Electronic Resource
    Bond length and radii variations in fluoride and oxide molecules and crystals (1994)
    Springer
    Physics and chemistry of minerals 20 (1994), S. 617-624 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract 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.”
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00211857
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  • 8
    Electronic Resource
    Electronic Resource
    Power law relationships between bond length, bond strength and electron density distributions (1998)
    Springer
    Physics and chemistry of minerals 25 (1998), S. 585-590 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract  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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002690050151
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  • 9
    Electronic Resource
    Electronic Resource
    A method for calculating fractional s-character for bonds of tetrahedral oxyanions in crystals (1987)
    Springer
    Physics and chemistry of minerals 14 (1987), S. 373-376 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract A method for calculating fractional s-character, f s , for TO bonds has been devised to apply to TO4 tetrahedral oxyanions in crystals. These f s -values rank bond lengths with the better correlations obtained for T atoms associated with larger bond strengths and larger electronegativities. As a simple formula, it is found that 2cot2〈ϑ〉3 does a good job of estimating f s where 〈ϑ〉3 is the triple angle average of the three angles common to a given bond.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00309813
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  • 10
    Electronic Resource
    Electronic Resource
    A modeling of the structure and compressibility of quartz with a molecular potential and its transferability to cristobalite and coesite (1993)
    Springer
    Physics and chemistry of minerals 20 (1993), S. 123-135 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract Several computer models of quartz were developed and tested. A simple model based on a potential energy function, derived in large part from quantum mechanical calculations on the molecule H6Si2O7, was found to reproduce the compressibility curve for quartz up to pressures of 8 GPa. The potential includes quadratic expressions for the SiO bond lengths, the OSiO angles and a parameter spanning the SiOSi angle together with an exponential OO repulsion term for non co-dimer O atoms. The variations in the cell edges and in the SiOSi angle, as a function of pressure, parallel observed trends when the bond lengths and angles calculated for the molecule are used as rgressor values. Poisson ratios calculated using the model match those observed. Two configurations for quartz related by the Dauphiné twin law are generated as minimum energy structures of the model with about equal frequencies as observed in nature. It is shown that the model, devised for quartz, can also be applied to the silica polymorph cristobalite, giving reasonable estimates of its compressibility curve, structural parameters and its negative Poisson ratio. When the observed bond lengths and angles are used as regressor values, the model generates the absolute coordinates of the atoms and the cell dimensions for quartz to within 0.005 Å and those of cristobalite to within 0.001 Å, on average, both at zero pressure. When applied to coesite, the model yields a zero pressure structure that is close to that observed but which is significantly softer than observed. The resulting SiO bond lengths are linearly correlated with f s (O), as observed for coesite, despite the use of a single bond length and a single SiOSi angle as regressor values in the calculation. When the structures are optimized assuming P1 space group symmetry and triclinic cell dimensions, the resulting frameworks of silicate tetrahedra exhibit the translational, rotational and reflection symmetries observed for quartz, cristobalite and coesite. The fact that the resulting frameworks exhibit observed space group symmetries is evidence that the symmetry adopted by the silica polymorphs can be explained by short ranged forces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00207206
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