Structural polyhedra

In anion-deficient structures, polyhedra may share comers, edges, or faces. 

Bulak, E., Sarper, O., Dogan, A., Lissner, F., Schleid, T. and Kaim, W. (2006) Dichlorogold(III) complexes of bis(l-methyl-2-imidazolyl)ketone and related ligands Geometrical and electronic structures. Polyhedron, 25, 2577. 

At the same time, there are two aspects of this synthesis which require special discussion. These are the creation of complex compounds with definite manner of localization of the coordination bond (regioselective synthesis) and programmed structure (polyhedron-programmed synthesis). 

Fig. 4. Three zeolites with the same structural polyhedron, cubo-octahedrons. (a) Type A, Na12[(Al02)12(Si02)12] 27H20 (b) sodalite [1302-90-5, (c) faujasite (Type X, Y), where X = Na86[(.-yO2)86(SiO2)106] 264H,O Y = Na56[(.A102)Kl i02)13(S]-250H20...

Morita Y, Nishida S, Fukui K, Hatanaka K, Ohba T, Sato K, Shiomi D, Takui T, Yamamoto G, Nakasuji K (2005) 2-Aryl substituted 3-oxophenalenoxyl radicals Jt-spin structures and properties evaluated by dimer structure. Polyhedron 24 2194—2199... 

Moffat, J.B. Cation-anion effects in heteropoly compounds with Keggin structures. Polyhedron 1986, 5, 261-269. 

WebLab Viewer gives a very-high-quality display suitable for publication and presentation. Molecules can be displayed as lines, sticks, ball and stick, CPK, and polyhedrons. In addition, different atoms within the same structure may be displayed in different ways. Text can be added to the display as well as labeling parts of the structure in a variety of ways. The user has control over colors, radii, and display quality. The program can also replicate a unit cell to display a crystal structure. Several types of molecular surfaces can be displayed. 

Structures of heteropolytungstate and isopolytungstate compounds have been determined by x-ray diffraction. The anion stmctures are represented by polyhedra that share corners and edges with one another. Each W is at the center of an octahedron, and an O atom is located in each vertex of the octahedron. The central atom is similarly located at the center of an XO tetrahedron or XO octahedron. Each such polyhedron containing the central atom is generally surrounded by octahedra, which share corners, edges, or both with it and with one another. Thus, the correct total number of... 

The symmetry of the structure we are looking for is imposed on the field 0(r) by building up the field inside a unit cubic cell of a smaller polyhedron, replicating it by reflections, translations, and rotations. Such a procedure not only guarantees that the field has the required symmetry but also enables substantial reduction of independent variables 0/ the function F (f)ij k )- For example, structures having the symmetry of the simple cubic phase are built of quadrirectangular tetrahedron replicated by reflection. The faces of the tetrahedron lie in the planes of mirror symmetry. The volume of the tetrahedron is 1 /48 of the unit cell volume. 

P. F. Kelly and J. D. Woollins, The Preparation and Structure of Complexes Containing Simple Inorganic Sulfur-Nitrogen Ligands, Polyhedron, 5, 607 (1986). 

W. P. WF-BERandC. W. GOKEL, Phase Transfer Catalysis in Organic Synthesis, Vol. 4 of Reactivity and Structure, Springer-Verlag, 1977, 250 pp. C. M. Starks and C. Uotta, Phase Transfer Catalysis, Academic Press, New York, 1978, 365 pp. F. MontanaRI, D. Landini and F. Rolla, Topics in Current Chemistry 101, 149-201 (1982). E. V. Dehmlow and S. S. Dehmlow, Phase Transfer Catalysis (2nd edn.), VCH Publishers. London 1983, 386 pp. T. G. Southern, Polyhedron 8. 407-13 (1989). 

Oxygen chelates such as those of edta and polyphosphates are of importance in analytical chemistry and in removing Ca ions from hard water. There is no unique. sequence of stabilities since these depend sensitively on a variety of factors where geometrical considerations are not important the smaller ions tend to form the stronger complexes but in polydentate macrocycles steric factors can be crucial. Thus dicyclohexyl-18-crown-6 (p. 96) forms much stronger complexes with Sr and Ba than with Ca (or the alkali metals) as shown in Fig. 5.6. Structural data are also available and an example of a solvated 8-coordinate Ca complex [(benzo-l5-crown-5)-Ca(NCS)2-MeOH] is shown in Fig. 5.7. The coordination polyhedron is not regular Ca lies above the mean plane of the 5 ether oxygens... 

Figure 6.1 The icosahedron and some of its symmetry elements, (a) An icosahedron has 12 vertices and 20 triangular faces defined by 30 edges, (b) The preferred pentagonal pyramidal coordination polyhedron for 6-coordinate boron in icosahedral structures as it is not possible to generate an infinite three-dimensional lattice on the basis of fivefold symmetry, various distortions, translations and voids occur in the actual crystal structures, (c) The distortion angle 0, which varies from 0° to 25°, for various boron atoms in crystalline boron and metal borides.

Figure Three represernarions of the structure of Cm- (a) normal ball-and-stick model (b) the polyhedron derived by truncating the 12 vertices of an icosahedron to form 12 symmetrically separated pentagonal faces (c) a conventional bonding model.

The ratio between the anionic and cationic radii leads to coordination numbers, the lowest of which is 6, which correspond to a octahedral polyhedron of anions around a central cation [135]. In this case, the compound structure type depends on the ratio of total number of anions and cations. The total number of anions (X) is calculated by summing up the number of oxygen (O) ions and of fluorine (F) ions X=0+F, while the total number of cations (Me) is the number of tantalum ions, niobium ions and other similar cations. 

Fig. 24. The structure of coordination polyhedrons of Ta and K in K TaF7. Reproduced from [144], C. C. Torardi, L. H. Brixner, J. Solid State Chem. 67 (1987) 21, Copyright 1987, with permission of Elsevier.

Fig. 25. Structure of the NbOF63, polyhedron in NasNbOFs (after Stomberg [58]).

The structure of KNbF6 consists of potassium ions and isolated NbF6 complex ions that were shown by Bode and Dohren to occur in the lattice in a configuration similar to that of a-CsCl [165]. The complex anion Nb(Ta)F6 has a configuration of a distorted bi-pyramid (four fluorine atoms are shifted in pairs from their positions in the basic plane, towards the vertexes). The structure of KNb(Ta)F6 compounds and of the Nb(Ta)F6 polyhedron are shown in Fig. 26. Nb/Ta-F distances are equal to 2.13 and 2.15 A, respectively, and F-F distances are 2.61, 3.03, 3.22 and 3.55 A. Each potassium atom is surrounded by 12 fluorine atoms that are at unequal distances from each other 8 of them are 2.50 A apart and four others are 2.94 A apart. 

Fig. 26. Structure of Nb(Ta)F6 polyhedron and of KNb(Ta)F6. Reproduced from [165], H. Bode, H. Dohren, Acta Cryst. 11 (1958) 80, Copyright 1958, with permission of Blackwell Publishing.

According to crystal analysis performed by Stomberg [173], Na2NbOF5 is made up of sodium ions and isolated NbOF52 complex ions and is similar in structure to FeWC>6. NbOFs2" polyhedrons comprise slightly distorted octahedrons that are located in one of two equivalent positions. The niobium atom is shifted 0.234 A from the equatorial plane towards the oxygen atom. 

The polyhedron NbF72 is more similar to a pentagonal bi-pyramid but is distorted due to a strong shift of F6 towards F3 (F6F3 and FiF distances are 2.39 and 3.08 A, respectively). This distortion renders the polyhedron structure closer to an Archimedes antiprism with a truncated comer, as shown in Fig. 31. 

Fig. 31 Crystal structure of Rb sNb30Ft8. Projection on the plane (001). Numbers in brackets are the atom coordinates on the z-axis in percents of c parameter. Structure of NbOFj chains and NbFf polyhedron. Reproduced from [209], A. I. Agulyansky, V. E. Zavodnik, V. Y. Kuznetzov et al. Neorgan. Mater. 27 (1991) 380, Copyright 1991, with permission of Nauka (Russian Academy of Sciences) publishing.

The compounds of the MMe205F type, where Me = Nb or Ta M = Rb, Cs, Tl, crystallize in cubic symmetry and correspond to a pyrochlore-type structure [235-237]. This structure can be obtained from a fluorite structure by replacing half of the calcium-containing cubic polyhedrons with oxyfluoride octahedrons. 

The lowest coordination number of tantalum or niobium permitted by crystal chemistry formalism is 6, which corresponds to an octahedral configuration. X Me ratios that equal 3, 2 or 1 can, therefore, be obtained by corresponding substitutions in the cationic sub-lattice. A condition for such substitution is no doubt steric similarity between the second cation and the tantalum or niobium ion so as to enable its replacement in the octahedral polyhedron. In such cases, the structure of the compound consists of oxyfluoride octahedrons that are linked by their vertexes, sides or faces, according to the compound type, MeX3, MeX2 or MeX respectively. Table 37 lists compounds that have a coordination-type structure [259-261]. 

In order to construct an MeX-type compound (X Me = 1) using only octahedral elements, the octahedrons must be linked via their faces i.e. by sharing of three angles. This arrangement of the octahedral polyhedrons yields a rock-salt type structure (NaCl type structure). 

S Tantalum and niobium are present in the crystal structure in the form of complex ions. The lowest coordination number, 6, corresponds to the formation of slightly distorted octahedrons. The linking and packaging of the octahedrons depends on the X Me ratio, where X is the total number of oxygen and fluorine atoms, and Me is the total number of tantalum or niobium ions as well as other metals that can replace tantalum or niobium in the octahedral polyhedron. The crystal structure type can be defined based on the X Me ratio, as follows ... 

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