Multi-Reagent Autonomous Kinetic Invariants of Chemical Reactions

Kinetics and Catalysis - New exact multi-reagent autonomous kinetic invariants for chemical reactions occurring in a gradientless isothermal reactor have been established. Invariants are...     

The rich stereochemistry of eight-vertex polyhedra: a continuous shape measures study

A stereochemical study of polyhedral eight-vertex structures is presented, based on continuous shape measures (CShM). Reference polyhedra, shape maps, and minimal-distortion interconversion paths are presented for eight-vertex polyhedral and polygonal structures within the CShM framework. The application of these stereochemical tools is analyzed for several families of experimental structures: 1) coordination polyhedra of molecular transition-metal coordination compounds, classified by electron configuration and ligands; 2) edge-bonded polyhedra, including cubane structures, realgar, and metal clusters; 3) octanuclear transition-metal supramolecular architectures; and 4) coordination polyhedra in extended structures in inorganic solids. Structural classification is shown to be greatly facilitated by these tools, and the detection of less common structures, such as the gyrobifastigium, is straightforward.     

Ytterbium Coordination Polymer with Four Different Coordination Numbers：The First Structural Characterization of Lanthanide Phthalate Complex

The novel ytterbium coordination polymer is a t4wo-dimensional framework in which the central metal ions have four different coordination numbers and form four kinds of coordination poly-hedra,The four kinds of coordination polyhedra connect into infinite chains by sharing oxygen atoms.     

The Coordination Polyhedra BC<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> in Crystal Structures

The method of intersecting spheres and Voronoi–Dirichlet polyhedra are used for crystal chemical analysis of 3817 structures comprising 4533 crystallographically nonequivalent sorts of boron atoms contained in BC_n coordination polyhedra. In these coordination polyhedra, boron has coordination numbers (CNs) from 2 to 6, the CN 4 being most typical. With increasing boron CN, the average B–C interatomic distances of the BC_n polyhedra increase by 0.01–0.13 Å, while the average radii of the spheres whose volumes are equal to the volumes of the Voronoi–Dirichlet polyhedra of boron atoms virtually do not vary within the determination error. The characteristic features of intermolecular contacts in the structures of two crystalline hydrates, Fe[B(CN)₄]₂ · 2H₂O and Fe[B(CN)₄]₃ · 6H₂O, are considered according to the method of Voronoi–Dirichlet molecular polyhedra.     

Permutation representations in molecular symmetry

The reducible representations of the point groups are generally studied because of their relevance to molecular orbital and vibration theory. Triple correlations within the polyhedra are described by group-theoretical invariants that are related to the permutation representations and termed polyhedral isoscalar factors. These invariants are applied in theorems on matrix elements referring to the symmetry-adapted bases at different centres. Further invariants or geometrical weight factors inter-relate different types of reduced matrix elements of irreducible tensors (generalization of the Wigner-Eckart theorem to the polycentric case). As a demonstration a complete tabulation is given for the point group C ₄.     

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.     

Tetrahedral Fulleroids

Fulleroids are cubic convex polyhedra with faces of size 5 or greater. They are suitable models of carbon molecules. In this paper sufficient and necessary conditions for existence of fulleroids of tetrahedral symmetry types and with pentagonal and n-gonal faces only depending on number n are presented. Either infinite series of examples are found to prove existence or nonexistence is proved using symmetry invariants.     

Stereochemistry of vanadium in oxygen-containing compounds

Using Voronoi-Dirichlet (VD) polyhedra and the method of overlapping spheres, we analyze the coordination of 714 crystallographically different vanadium atoms in the structure of compounds containing VO _n polyhedra. Vanadium atoms are found to be bonded to 4, 5, 6, or 7 oxygen atoms. The effect of the valence state and coordination number of vanadium atoms on the main parameters of their VD polyhedra is considered. A unified linear dependence between the solid angles of VD polyhedron faces corresponding to V-O bonds and the respective interatomic distances varying in a range of 1.55 Å to 2.79 Å is stated to exist. It is shown that the parameters of VD polyhedra can be used to determine the valence state of vanadium atoms.     

Modes of coordination and stereochemistry of nitrate groups in organic and organometallic nitrates

Stereochemical features of nitrate groups in the structures of 3856 organic and organometallic compounds are generalized with use of the TOPOS program package designed for geometrical and topological analysis. Nitrate groups are classified according to coordination modes using Voronoi-Dirichlet polyhedra and a method of intersecting spheres. The main coordination mode is shown to be terminal bidentate (42% from the test dataset of nitrate groups). The occurrence of the bridging mode is much lower compared with inorganic nitrates (3.2%). The essential part of nitrate groups are not coordinated to complexing atoms, being linked to their environment through hydrogen and ionic bonds (41%). The relationship that exists between structural and crystallochemical features of nitrate groups is elucidated, including the involvement in coordination to complexing atoms of different nature.     

Version of zones and zigzag structure in icosahedral fullerenes and icosadeltahedra

A circuit of faces in a polyhedron is called a zone if each face is attached to its two neighbors by opposite edges. (For odd-sized faces, each edge has a left and a right opposite partner.) Zones are called alternating if, when odd faces (if any) are encountered, left and right opposite edges are chosen alternately. Zigzag (Petrie) circuits in cubic (= trivalent) polyhedra correspond to alternating zones in their deltahedral duals. With these definitions, a full analysis of the zone and zigzag structure is made for icosahedral centrosymmetric fullerenes and their duals. The zone structure provides hypercube embeddings of these classes of polyhedra which preserve all graph distances (subject to a scale factor of 2) up to a limit that depends on the vertex count. These embeddings may have applications in nomenclature, atom/vertex numbering schemes, and in calculation of distance invariants for this subclass of highly symmetric fullerenes and their deltahedral duals.     

Coordination polyhedra LnOn (Ln = Er, Tm, Yb, Lu) in crystal structures

The Voronoi-Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to analyze crystal structures of 728 compounds containing 976 crystallographically non-equivalent sorts of LnO_n polyhedra (Ln = Er, Tm, Yb, Lu). The Ln C.N. vary from 3 to 10, and 14 sorts of coordination polyhedra are present in the structures. Despite the great diversity of C.N., the volume of the VDP was found to depend only on the nature of the Ln atom and its valence state.     

Crystallochemical Analysis of Rare-Earth Halogen-Containing π-Complexes

Ninety-six halogen-containing -complexes of rare-earth elements were studied to reveal how the volume of the area of action of the Ln atom in coordination polyhedra LnC _n X _m (X = F, Cl, Br) depends on its nature, coordination and oxidation numbers, and on the number of Ln–X bonds. A method was proposed for estimating the ligand sizes in the coordination sphere by making use of the molecular Voronoi–Dirichlet polyhedra. The effect of the ligand sizes on the stability of -complexes and formation of aghostic contacts in their structures was analyzed.     

次级键与晶体中锑(III)螯合物配位多面体研究

考虑立体活性孤对电子附近次级键配位原子的贡献, 对文献报道的三十个氨基多羧酸锑(III)螯合物的晶体结构中配位多面体描述进行了全面的修正. 配位多面体的几何构型指定采用了单位球内截多面体的两面角判据及其相关的ANVPDA程序. 所有配位多面体几何构型的修正均得到了键价计算的有力支持.     

次级键与晶体中锑(III)螯合物配位多面体研究

考虑立体活性孤对电子附近次级键配位原子的贡献,对文献报道的三十个氨基多羧酸锑(III)螯合物的晶体结构中配位多面体描述进行了全面的修正.配位多面体的几何构型指定采用了单位球内截多面体的两面角判据及其相关的ANVPDA程序.所有配位多面体几何构型的修正均得到了键价计算的有力支持.     

La4.27Mg2.89Zn30, a new structure type with strong positional disorder

Ternary tetralanthanum trimagnesium tricontazinc, La_4.27Mg_2.89Zn₃₀, crystallizes as a new structure type. It belongs to the structural family that may be derived from the hexagonal CaCu₅ and Th₂Ni₁₇ structure types by combination of internal deformation and multiple substitution. The triangular 3₆ and hexagonal 6₃ nets are alternately stacked with Kagomé 3636 nets. The atoms with the largest radius (La) are enclosed in 18‐vertex polyhedra (distorted pseudo‐Frank–Kasper polyhedra). The coordination polyhedra of the two Mg atoms are bicapped and monocapped hexagonal antiprisms, with coordination numbers of 14 and 13, respectively. For all the Zn atoms, the typical icosahedral coordination is observed. In the direction of the six‐ and threefold axes, strong positional disorder is observed as a result of partial substitutions of La atoms by pairs of Mg atoms.     

Structure of the products of TiCl4 chemisorption on the surface of porous silica in the process of vapor-phase hydrolysis

Changes in coordination environment of titanium atoms in the composition of the titanium oxychloride groups chemisorbed on the surface of porous silica after the vapor-phase hydrolysis are considered. It is shown that after the substitution of chlorine atoms by the OH groups, additional coordination bonds between the titanium-containing group and neighboring hydroxo groups are formed, that leads to an increase to 6 in the coordination number of titanium in the composition of the surface polyhedra.     

The coordination polyhedra GaS<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> in crystal structures

Voronoi-Dirichlet polyhedra (VDP) and the intersecting sphere method were used to perform coordination analysis of 204 crystallographically different gallium atoms in the structures of all known compounds containing GaS _n polyhedra. The Ga(III) atoms in crystal structures were found to be linked to 6, 4, or three sulfur atoms to form coordination octahedra, tetrahedra, and triangles, respectively, whereas Ga(II) atoms are bound only to three sulfur atoms and a gallium atom. The effect of the valence state and the coordination number of gallium atoms on the key parameters of the VDP is considered. A common linear dependence of the solid angles of the VDP faces corresponding to the Ga-S bonds on the corresponding interatomic distances, which vary from 2.09 to 2.53 Å, was established to exist.     

Distribution of spatial polyhedra on coordination spheres in a b.c.c. lattice

In this paper we suggest a convenient algorithm of practical crystallography to correlate the index of a coordination sphere to the set of the filling polyhedra for simple cubic (s.c.) and body-centered cubic (b.c.c.) lattices. Any coordination sphere may be represented as a combination of seven polyhedra. We introduce here the notion of coordination spheres with, zero filling and derive a rule for going from the sphere numbering obtained in this way to the traditional one.Altai Polytechnical Institute. Translated fromZhurnal Struktornoi Khimii, Vol. 34, No. 4, pp. 107–111, July–August, 1993.Translated by T. Yudanova     

极性晶体结晶习性的形成机理

将负离子配位多面体生长基元模型应用于对极性晶体结晶习性的研究。从结晶化学角度探讨了晶体中负离子配位多面体的结晶方位与晶体各族晶面显露规律，提出负离子配位多面体在晶体各族晶面上联结的稳定性决定了晶面的生长速率。在不同的生长温度和溶液碱浓度下，负离子配住多面体相互联结构成不同维度的生长基元，而不同维度的生长基元往晶体各族晶面上叠合的速率比例是在变化的，这是导致晶体结晶形态多变性的主要原因。同时提出：如果把PBC模型中的化学键链设定为配位多面体相联结的键链，使得极性晶体结晶习性中难以解释的问题就会迎刃而解，从而使PBC理论模型的应用会得到更进一步的拓宽。