How big are atoms in crystals?

Atoms and bonds are central concepts in structural chemistry, but neither are concepts that arise naturally from the physics of condensed phases. It is ironic that the internuclear distances in crystals that are readily measured depend on the sizes of atoms, but since atoms in crystals can be defined in many different ways, all of them arbitrary and often incompatible, there is no natural way to express atomic size. I propose a simple coherent picture of Atoms-in-Crystals which combines properties selected from three different physically sound definitions of atoms and bonds. The charge density of the free atom that is used to construct the procrystal is represented by a sphere of constant charge density having the quantum theory of atoms in molecules (QTAIM) bonded radius. The sum of these radii is equal to the bond length that correlates with the bond flux (bond valence) in the flux theory of the bond. The use of this model is illustrated by answering the question: How big are atoms in crystals? The QTAIM bonded radii are shown to be simple functions of two properties, the number of quantum shells in the atomic core and the flux of the bond that links neighbouring atoms. Various radii can be defined. The univalent bonded radius measures the intrinsic size of the atom and is the same for all cations in a given row of the periodic table, but the observed bonded radius depends also on the bond flux that reflects the chemical environment.     

Congested molecules. Where is the steric repulsion? An analysis of the electron density by the method of interacting quantum atoms

The computed electron density of several congested saturated hydrocarbons and halogenated derivatives has been analyzed by the method of interacting quantum atoms (IQA). For all the molecules studied, the calculations show the existence of a bond path between the congested atoms and which, according to the Quantum Theory of Atoms in Molecules, indicates that there is a stabilizing interaction between these atoms. The bond path is found to exist up to interatomic distances well‐beyond the sum of the van der Waals radii. The IQA results indicate that steric hindrance is not a repulsive force between the congested atoms but that is the result of an increase in the intra‐atomic or self‐energy of the congested atoms. This increase in self‐energy is caused by the deformation of the atomic basin of the congested atoms. © 2013 Wiley Periodicals, Inc.     

Combining X-ray scattering and exafs experiments for studying amorphous alloys of 3d transition metals with zirconium

The atomic structure of the amorphous alloys of several transition metals (Fe, Co, Ni, and Cu) with zirconium is studied in terms of partial paired correlation functions. The short-range order parameters, namely, the shortest interatomic distances, coordination numbers, and the form of distribution functions, are compared and a correlation between the atomic structure and the interaction between atoms of different sorts is established. The study offers the possibility to model the spatial distribution of atoms and the physical properties of the analyzed alloys and predict the properties of new systems. Translated fromZhurnal Struktumoi Khimii, Vol. 39, No. 6, pp. 1025–1030, November–December, 1998.     

Metallocages for Metal Anions: Highly Charged [Co@Ge9]5− and [Ru@Sn9]6− Clusters Featuring Spherically Encapsulated Co1− and Ru2− Anions

Endohedral clusters count as molecular models for intermetallic compounds—a class of compounds in which bonding principles are scarcely understood. Herein we report soluble cluster anions with the highest charges on a single cluster to date. The clusters reflect the close analogy between intermetalloid clusters and corresponding coordination polyhedra in intermetallic compounds. We now establish Raman spectroscopy as a reliable probe to assign for the first time the presence of discrete, endohedrally filled clusters in intermetallic phases. The ternary precursor alloys with nominal compositions “K₅Co_1.2Ge₉” and “K₄Ru₃Sn₇” exhibit characteristic bonding modes originating from metal atoms in the center of polyhedral clusters, thus revealing that filled clusters are present in these alloys. We report also on the structural characterization of [Co@Ge₉]^5? ( 1a ) and [Ru@Sn₉]^6? ( 2a ) obtained from solutions of the respective alloys.     

Correlation between intramolecular bond lengths and K-shell σ-shape resonances in gas-phase molecules

Analysis of K-shell excitation spectra of gas-phase molecules containing at least two atoms of either B, C. N. O or F reveals the existence of a striking correlation between the bond length of the atomic pair. the sum of their atomic numbers and the associated α-shape resonance energy. Empirical rules are established which allow the derivation of intramolecular distances with accuracies reliably better than ± 0.05 A from the K-.shell absorption spectrum of one of the atoms in the Molecule.     

Coordination polyhedra LnFn (Ln = La-Lu) in crystal structures

Voronoi-Dirichlet (VD) polyhedra and the intersecting spheres method are used to study stereochemical features of lanthanides (Ln) surrounded by fluorine atoms in the structures of 118 compounds. The coordination numbers of Ln atoms range from 6 to 12. Nine types of coordination polyhedra LnF_n are found; depending on the CN of Ln, the Ln-F bond length can change by 0.2–0.7 Å. Despite the considerable differences in bond lengths, the volume of the VD polyhedra of Ln atoms depends only on their nature and oxidation state. The change in the radii of the spherical domains whose volume is equal to that of the VD polyhedra of Ln atoms shows the tetrad effect.     

Ein Beitrag zur Stereochemie des Arsens in As(III)—Sauerstoffverbindungen

The oxygen coordination sphere around As(III) consists of the three primary oxygen atoms (average As–O distance 1.78₅ Å) and secondary oxygen atoms between 2.70 and 3.37 Å (3.37 Å is the assumed sum of theVan der Waals radii). Reasons are discussed why neither the number (0–3) nor the length of the secondary As–O distances exert an influence on the geometry of the [AsO₃]-group and its As–O distances.

     

A new method of determination of radii of ions with arbitrary effective charges

An equation for calculation of the radii of ions with an arbitrary effective charge has been derived. The ionic radii of halogens, chalcogens, and other atoms with different charges have been calculated. Under the assumption of pure ionic bond character, these values have been used for calculating the R ₁₂ distances for a large group of different molecules—halogens, interhalides, oxygen, chalcogens, and nitrogen and their compounds—by the previously derived equation for the a priori determination of internuclear distances. The error of calculation of the internuclear distance for halogens and interhalides is no more than 0.07 Å (3–4%). The internuclear distance in dihalogen cations Hal ₂ ⁺ and binary ionic molecules of p elements and their oxides and sulfides have been calculated. It has been demonstrated that the coordination (environment) of atoms should be taken into account and that there is a possibility of estimating the bond multiplicity and the character of bonding electron pairs in a molecule.     

Bond orders and electron delocalization indices for S–N,S–C and S–S bonds in 1,2,3-dithiazole systems

A parametric QTAIM-based (topological) model of bond orders and a modification of the Pauling bond order model are proposed for N,S-containing heterocycles, in particular, for 1,2,3-dithiazoles and 1,2,3-dithiazolium systems, which are prone to the formation of stable radicals and therefore are promising compounds in photovoltaics. These models have been parameterized for covalent S–N, S–C and S–S bonds using the electron delocalization indices. A modified Pauling’s bond order model uses turning radii, that is, the distances within which the potential acting on an electron in a system still tends to return that electron to the atomic basin, and avoids the need to choose the hybridization state of bound atoms arbitrarily.     

Geometry and orientation of molecules in a graphite fluoride matrix

Polarization dependences of the EXAFS and XANES spectra of graphite fluoride intercalation compounds C₂F_x·yA (x ≈ 1, A=Br₂, Fe(AA)₃, FeCl₃, SnCl₄; AA=acetylacetonate) synthesized by diffusion from solution were measured. The measurements were carried out in the FeK-, BrK-, and SnK-edge of absorption spectral regions using synchrotron radiation of the VEPP-3 storage ring (Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences). The polarization dependences of effective coordination numbers and edge σ-resonance intensity are analyzed, and parameters of the local surroundings of atoms (coordination numbers, interatomic distances, Debye-Waller factors σ²) are determined. For the Br₂ intercalates, the orientation angle with respect to the matrix layers is 64±1.5°, and the interatomic distances are close to those in the gas phase. The FeCl₃ molecule forms dimers in the matrix as it does in the gas phase, and the iron atoms have tetrahedral surroundings. For the Fe(AA)₃ molecules intercalated into the matrix, the iron atoms have significantly distorted octahedral environments. For the SnCl₄ intercalates, the lowering of temperature does not cause additional coordination of Sn atoms, and structural disorder of SnCl₄ makes the major contribution to σ². Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 6, pp. 1081–1088, November–December, 1996 Translated by L. Smolina     

Lanthanoid Antimonides Ln2Sb5 (Ln = Sm,Gd, Tb,Dy) and Rationalization of Chemical Bonding within the Antimony Polyanion by Combining the Zintl‐Klemm Concept with Bond‐Length Bond‐Strength Relationships

The title compounds are formed by peritectic reactions. Single crystals could be isolated from samples with high antimony content. Their structure was determined for Dy₂Sb₅ from four‐circle X‐ray diffractometer data: P2₁/m, a = 1306.6(1) pm, b = 416.27(4) pm, c = 1458.4(1) pm, β = 102.213(8)°, Z = 4, R = 0.061 for 2980 structure factors and 86 variable parameters. All dysprosium atoms have nine antimony neighbors forming tricapped trigonal prisms with Dy–Sb distances varying between 308 and 338 pm. The antimony atoms occupy ten different sites with greatly varying coordination. One extreme case is an antimony atom surrounded only by dysprosium atoms in trigonal prismatic arrangement, the other one is an antimony atom in distorted octahedral antimony coordination. The various antimony‐antimony interactions (with Sb–Sb distances varying between 284 and 338 pm) are rationalized by combining the Zintl‐Klemm concept with bond‐length bond‐strength considerations.     

Molecular polarizability of organic compounds and their complexes: LIX. Molar volumes, intrinsic atomic solvation radii, and spatial structures of certain conformationally flexible compounds in solutions

The molar volumes and structures in individual liquids and solutions of a series of conformationally flexible compounds, such as alkanes and diaryl-substituted systems with sp ³-hybridized bridging atoms, were analyzed in terms of intrinsic solvation radii of atoms constituting the molecule. Intrinsic solvation atomic radii were determined for various molecules to show that they are larger than the van der Waals radii of the same atoms. An approach to parametrization of the intrinsic solvation radii of atoms constituting a molecule, using appropriate model compounds, was proposed. From the resulting values of intrinsic atomic solvation radii, the possible conformations of a series of diphenylmethanes, diphenylsilanes, diphenyl sulfides, diphenyl sulfoxides, and diphenyl sulfones in solutions were assessed.     

Topology of the structure of metal sublattices in inorganic compounds

The Voronoi-Dirichlet polyhedron (VDP) method is used to study the topology of atomic metal sublattices in the structures of 350 inorganic compounds. For the sample under consideration, it is confirmed that the rule of twelve and fourteen neighbors is valid. It is found for 26 compounds that the environment of metal atoms in the cationic framework possesses noncrystallographic features. The advantages of using the VDP method for determination of coordination numbers of atoms are shown on several examples. The local and global homogeneity of the structures of the compounds is discussed. Samara State University. Translated fromZhurnal Struktumoi Khimii, Vol. 37, No. 1, pp. 116–122, January–February, 1996. Translated by L. Smolina     

Monoclinic superstructure of SrMgF4 with perovskite‐type slabs

Crystals of Ce‐doped SrMgF₄, strontium magnesium tetrafluoride, have been found to have a monoclinic P2₁ structure with doubled a and tripled c cell lengths compared with the orthorhombic Cmcm structure previously reported in the literature. The perovskite‐type slabs, composed of corner‐sharing MgF₆ octahedra and Sr atoms, are stacked along the b axis. The six crystallographically independent MgF₆ octahedra are rotated so as to provide long periodicities along a and c . The coordination numbers and bond distances around the six crystallographically independent Sr atoms are slightly different in each case. In the superstructure, the Sr atoms lie on local mirror planes which are thought to originate at the high‐temperature phase transition.     

HETEROCYCLIC CATIONS WITH DELOCALISED PI-SYSTEMS AND SHORT INTRAMOLECULAR SULFUR… SULFUR CONTACTS: THE STRUCTURES OF TWO DERIVATIVES OF THE 2-(1,3-DITHIOL-2-YLIDENEMETHYL)-1,3-DITHIOLIUM CATION

Abstract

The effective size of bonded divalent sulfur in S…S contacts is a function of the orientation of the groups, with the shortest contacts occurring when the groups are coplanar. A lower limit for the loner is indicated by the structures of the 2-(1,3-benzodithiol-2-ylidenemethyl)-1,3-benzodithiolium and 2-(1,3-dithiolan-2-ylidenemethyl)-1,3-dithiolanium cations, 2 and 3. These show almost mm symmetry with all four sulfur atoms involved in stabilisation of the positive charge. Short intramolecular sulfur… sulfur contact distances, 0.5–0.7 Å within the sum of traditional van der Waals radii, and maximised by in-plane angular distortions, indicate a lower limit to the effective size of the bonded divalent sulfur atom of ca. 1.45 Å.     

On the Volume Chemistry of Solid Compounds: the Legacy of Wilhelm Biltz

For the calculation of the atomic or ionic volumes the Quantum Theory of Atoms In Molecules method was applied. The regions (basins) around the nuclei confined by the zero‐flux surfaces in the electron density gradient are called QTAIM atoms. They are non‐overlapping and completely fill the space. The volume of the basins gives volumes of atoms or ions. The integration of the electron density within the volumina yields effective charges, defining neutral or ionic character of the given QTAIM species. Present investigations refer to metal hydrides, metal nitrides and to intermetallic compounds of the system Al‐Pt. A linear relation between the ionic volumina of hydrogen or nitrogen established according to QTAIM and after Biltz has been found with (homodesmic) binary metal hydrides and binary metal nitrides, but has been observed merely as a trend with stronger deviations for heterodesmic compounds, such as ternary hydrido‐ and nitridometallates A_a[M_mX_x] (A – alkali or alkaline earth metal, M – transition metal and X – H or N). The deviation from linearity for heterodesmic compounds is caused by the different kinds of chemical bonds being present within the [M_mX_x] anions on the one hand and between the anions and the cations on the other hand reflected by the calculated volumes and the QTAIM charges of M and X components. Concerning the intermetallic compounds of the system Al‐Pt, the quantum chemical calculations reveal negative charges for the platinum atoms and positive ones for the aluminium atoms in accordance with their electronegativities. Introducing the variation of the atomic volume with the composition extends the Vegard's approach and gives a non‐linear slope for the concentration dependence of mean atomic volume which explains qualitatively the experimental results.     

Theoretical electron density distributions for Fe- and Cu-sulfide earth materials: a connection between bond length, bond critical point properties, local energy densities, and bonded interactions

Bond critical point and local energy density properties together with net atomic charges were calculated for theoretical electron density distributions, rho(r), generated for a variety of Fe and Cu metal-sulfide materials with high- and low-spin Fe atoms in octahedral coordination and high-spin Fe atoms in tetrahedral coordination. The electron density, rho(rc), the Laplacian, triangle down2rho(rc), the local kinetic energy, G(rc), and the oxidation state of Fe increase as the local potential energy density, V(rc), the Fe-S bond lengths, and the coordination numbers of the Fe atoms decrease. The properties of the bonded interactions for the octahedrally coordinated low-spin Fe atoms for pyrite and marcasite are distinct from those for high-spin Fe atoms for troilite, smythite, and greigite. The Fe-S bond lengths are shorter and the values of rho(rc) and triangle down2rho(rc) are larger for pyrite and marcasite, indicating that the accumulation and local concentration of rho(r) in the internuclear region are greater than those involving the longer, high-spin Fe-S bonded interactions. The net atomic charges and the bonded radii calculated for the Fe and S atoms in pyrite and marcasite are also smaller than those for sulfides with high-spin octahedrally coordinated Fe atoms. Collectively, the Fe-S interactions are indicated to be intermediate in character with the low-spin Fe-S interactions having greater shared character than the high-spin interactions. The bond lengths observed for chalcopyrite together with the calculated bond critical point properties are consistent with the formula Cu+Fe3+S2. The bond length is shorter and the rho(rc) value is larger for the FeS4 tetrahedron displayed by metastable greigite than those displayed by chalcopyrite and cubanite, consistent with a proposal that the Fe atom in greigite is tetravalent. S-S bond paths exist between each of the surface S atoms of adjacent slabs of FeS6 octahedra comprising the layer sulfide smythite, suggesting that the neutral Fe3S4 slabs are linked together and stabilized by the pathways of electron density comprising S-S bonded interactions. Such interactions not only exist between the S atoms for adjacent S8 rings in native sulfur, but their bond critical point properties are similar to those displayed by the metal sulfides.     

Verfeinerung der Kristallstrukturen von KN3, RbN3, CsN3 und TIN3

Crystal structure refinements of KN₃, RbN₃, CsN₃, and TIN₃ The crystal structures of the isostructural compounds KN₃, RbN₃, CsN₃ and TIN₃ were refined by the method of least-squares using new X-ray diffraction data. The substances crystallize in a tetragonal variety of the CsCl type (space group I4/mcm) with four formula units per unit cell. The metal ions are surrounded by eight closest N atoms in a distorted quadratic antiprismatic arrangement at distances which correspond to the sum of the ionic radii. The azide ions are strictly linear and symmetrical with N — N bond lengths of 1.16 to 1,18 Å.