Molecular structure does not easily identify the intricate noncovalent interactions that govern many areas of biology and chemistry, including design of new materials and drugs. We develop an approach to detect noncovalent interactions in real space, based on the electron density and its derivatives. Our approach reveals the underlying chemistry that compliments the covalent structure. It provides a rich representation of van der Waals interactions, hydrogen bonds, and steric repulsion in small molecules, molecular complexes, and solids. Most importantly, the method, requiring only knowledge of the atomic coordinates, is efficient and applicable to large systems, such as proteins or DNA. Across these applications, a view of nonbonded interactions emerges as continuous surfaces rather than close contacts between atom pairs, offering rich insight into the design of new and improved ligands.

/pdf/revealing-noncovalent-interactions-1oqknfvmfi.pdf

Revealing noncovalent interactions.

The thermodynamic properties of 154 mineral end-members, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set. The use of a temperature-dependent thermal expansion and bulk modulus, and the use of high-pressure equations of state for solids and fluids, allows calculation of mineral–fluid equilibria to 100 kbar pressure or higher. A pressure-dependent Landau model for order–disorder permits extension of disordering transitions to high pressures, and, in particular, allows the alpha–beta quartz transition to be handled more satisfactorily. Several melt end-members have been included to enable calculation of simple phase equilibria and as a first stage in developing melt mixing models in NCKFMASH. The simple aqueous species density model has been extended to enable speciation calculations and mineral solubility determination involving minerals and aqueous species at high temperatures and pressures. The data set has also been improved by incorporation of many new phase equilibrium constraints, calorimetric studies and new measurements of molar volume, thermal expansion and compressibility. This has led to a significant improvement in the level of agreement with the available experimental phase equilibria, and to greater flexibility in calculation of complex mineral equilibria. It is also shown that there is very good agreement between the data set and the most recent available calorimetric data.

An internally consistent thermodynamic data set for phases of petrological interest

The tetragonal to orthorhombic ferroelastic phase transition between rutile- and ${\text{CaCl}}_{2}$-type ${\text{SiO}}_{2}$ at high pressures is studied using first-principles calculations and the Landau free-energy expansion. The phase transition is systematically investigated in terms of characteristic phonon modes with ${\text{B}}_{1g}$ and ${\text{A}}_{g}$ symmetries, shear moduli, transverse-acoustic mode, rotation angle of the ${\text{SiO}}_{6}$ octahedra, spontaneous symmetry-breaking and volume strains, and enthalpy. The results show that these physical behaviors at the transition are well described using the Landau free-energy expansion parametrized by the first-principles calculations.

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First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures

A cross-platform program, VESTA, has been developed to visualize both structural and volumetric data in multiple windows with tabs. VESTA represents crystal structures by ball-and-stick, space-filling, polyhedral, wireframe, stick, dot-surface and thermal-ellipsoid models. A variety of crystal-chemical information is extractable from fractional coordinates, occupancies and oxidation states of sites. Volumetric data such as electron and nuclear densities, Patterson functions, and wavefunctions are displayed as isosurfaces, bird's-eye views and two-dimensional maps. Isosurfaces can be colored according to other physical quantities. Translucent isosurfaces and/or slices can be overlapped with a structural model. Collaboration with external programs enables the user to locate bonds and bond angles in the `graphics area', simulate powder diffraction patterns, and calculate site potentials and Madelung energies. Electron densities determined experimentally are convertible into their Laplacians and electronic energy densities.

VESTA: a three-dimensional visualization system for electronic and structural analysis

Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrachedral corrdination complexes, both of which show variations in bond length and bond angle. The quadratic elongation is dimensionless, giving a quantitative measure of polyhedral disortion which is independent of the effective size of the polyhedron.

https://science.sciencemag.org/content/sci/172/3983/567.full.pdf

Quadratic elongation: a quantitative measure of distortion in coordination polyhedra.

Systematic trends in the geometry of 149 oxide and 80 sulfide binary and ternary spinels have been examined from the standpoint of ionic radius and electronegativity. The mean ionic radii of the octahedral and tetrahedral cations, taken together, account for 96.9 and 90.5% of the variation in the unit cell parameter, a, of the oxides and sulfides, respectively, with the octahedral cation exerting by far the dominant influence in sulfides. The mean electronegativity of the octahedral cation exerts an additional, but small, influence on the cell edge of the sulfides. The equation a=(8/3√d)d
tet+(8/3)d
oct, where d
tet and d
oct are the tetrahedral and octahedral bond lengths obained from the sum of the ionic radii, accounts for 96.7 and 83.2% of the variation in a in the oxides and sulfides, respectively, again testifying to the applicability of the hard-sphere ionic model in the case of the spinel structure. Comparison of observed and calculated u values for 94 spinels indicates that up to 40% of the experimentally measured anion coordinates may be significantly in error. In addition to these compounds, u values are given for 52 spinels for which no data have previously been determined. Diagrams are presented for the rapid interpretation of the internal consistency of published data and the prediction of the structural parameters of hypothetical or partially studied spinels.

Systematics of the spinel structure type

Refined structures of eight natural garnets [Cr-pyrope, almandine, spessartine, Mngrossular, grossular, uvarovite, goldmanite, and andradite] are compared with that of synthetic pyrope to determine the effects of the substituent cations on polyhedral interactions,bond lengths, and angles. The Si-O bonds in these garnets constitute two populations whichcan be related to (r!X!), the mean radius of the X dodecahedra] cation. If (r{X}) is lessthan 1.0 A, then Si-O= 1.635 :1:0.005A, but if (r!X\) exceeds 1.0 A, then Si-O = 1.650 to.005 A. However, the X-O and Y-O bond lengths and the O-X-O, O-Y-O, and O-Si-O anglesare linearly dependent on (r{X!) and on (r[Y]) (where (r[Y])= the mean radius of the Y octahedral cation). A multiple linear regression analysis indicates the positional parameters of these garnets to be related to (1'{X} ) and (1'[ V]) using Shannon and Prewitt's effectiveradii as follows: x = 0.006 + 0.022(r{X} > + 0.014(r[Y]) y = 0.051 - 0.023(r{X}) + 0.037(r[Y]) z = 0.643 - 0.009(r{X}) + 0.034(r[Y]). The positional parameters of Fe-pyrope calculated with these equations [x=0.0336; y =0.0491; z=0.6530] are in statistical agreement with the observed [x=0.0339(5); y =0.0491(6);z=0.6535(6)] (Euler and Bruce, 1965). Furthermore, using a cell edge calculated from an equation obtained by regression analysis of 56 well characterized silicate garnets [a=9.04+1.61(r{XD+1.89(r[YJ)], the predicted positional parameters give bond lengthsand angles that are statistically identical with those observed. These equations were used to predict the structural details of over 200 hypothetical cubic silicate garnet compounds by assigning (r{XI) values between 0.80 and 1.50 A and (r[Y]) values between 0.50 and 1.15 A (at 0.05 A intervals). Using criteria based on reasonable 0-0, Si-O, X-O, and Y-O distances, a diagram was prepared in which the structural "stability" field of silicate garnets is delineated as a function of (r{X}) and (r[Y]).

Gerald V. Gibbs

Papers

Quadratic elongation: a quantitative measure of distortion in coordination polyhedra.

Systematics of the spinel structure type

The crystal chemistry of the silicate garnets

Molecules as models for bonding in silicates

Silica : physical behavior, geochemistry and materials applications