M. B. Boisen

Framework silica structures generated using simulated annealing with a potential energy function based on an H6Si2O7 molecule

AbstractA 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

Laplacian and bond critical point properties of the electron density distributions of sulfide bonds; a comparison with oxide bonds

I\bar 42d

Derivation of the normalizers of the space groups

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.

An application of graph theory to the estimation of bond numbers in 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 Slaters 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.”

MATOP: an interactive FORTRAN 77 program for solving problems in geometrical crystallography

Abstract Topological and bond critical point properties of electron density distributions, ρ(r), were calculated for a series of sulfide molecules, containing first- and second-row main group M-cations. Laplacian maps of the distributions, ∇2ρ(r), show that the valence shell charge concentration (VSCC) of the sulfide anion is highly polarized and extended into the internuclear region of the M-S bonds, coalescing with the VSCCs of the more electronegative first-row cations. On the other hand, maps for a corresponding set of oxide molecules show that the oxide anion tends to be less polarized and more locally concentrated in the vicinity of its valence shell, particularly when bonded to second-row M-cations. A search for extrema in the ∇2ρ(r) distributions reveals maxima in the VSCCs that can be ascribed to bonded and nonbonded electron pairs. The different and distinctive properties of sulfides and oxides are examined in terms of the number and the positions of the electron pairs and the topographic features of the Laplacian maps. The evidence provided by the electron density distributions and its topological properties indicates that the bonded interactions in sulfides are more directional, for a given M-cation, than in oxides. The value of the electron density distribution at the bond critical point and the length of a given M-S bond are reliable measures of a bonded interaction, the greater the accumulation of the electron density and the shorter the bond, the greater its shared (covalent) interaction.

Interactive software for calculating and displaying X-ray or neutron powder diffractometer patterns of crystalline materials

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.

Variations of bond lengths and volumes of silicate tetrahedra with temperature

A method for the derivation of the affine normalizers of the space groups using matrix methods is presented. Published lists of normalizers have been verified, using matrix methods, both by hand and by computer. Generating matrices for the affine normalizers of triclinic and monoclinic space groups are listed.

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

Abstract An application of graph theory to the study of the nature of bonding in crystals is discussed. The limiting factor to this application is the intensity of the computer calculations that are required. An algorithm is described that permits the solution of the problem in some relatively small cases. However, even these small cases have yielded interesting results in describing bond lengths in crystals. More efficient algorithms, that may be developed in the future, could provide new and valuable insights into the field of crystal chemistry.