Polyhedra connected

The polyhedral connectivity generates large Mo8Cu2P40i2C4 rings of 14 polyhedra connects within the layers. The water molecules of crystallization occupy these intralamellar cavities. The bpy ligands project from the surfaces of the... 

As alluded to at the begiiming of Section 3.3, probably the most challenging task is predicting, a priori, the extended structure - not only the coordination preferences of all the atoms or ions, but the polyhedra connectivity as well. In this area, Tulsky and Long have taken a major step forward by formalizing the application of dimensional reduction to treat the formation of ternary phases from binary solids (Tulsky and Long, 2001) ... 

Solids with octahedral, tetrahedral, square planar, and linear metal coordination geometries, including many different types of polyhedra connectivity modes, are amenable to dimensional reduction. Tulsky and Long compiled an enormous database of over 300 different allowed combinations of M and X and over 10,000 combinations of A, M, and X. The formalism may be extendable to quaternary phases as well. However, frameworks containing anion-anion linkages, anions other than halides, oxide, or chalcogenides, nonstoichiometric phases, and mixed-valence compounds were excluded from their initial study. 

This results in the formation of the i[U20io] chains with SBU consisting of UO7 and an UOe polyhedra connected through one oxygen (Fig. 12). These chains run along the a and b directions and are connected through VO4 tetrahedra. As in Li2(U02)3(V04)20, the UOe octahedra and VO4 tetrahedra form autunite anion-topology sheets parallel to (001) (Fig. 13a), but with an inverted occupation of the squares by the UOe octahedra and the V(2)04 tetrahedra. The V(l)04 tetrahedra are attached above and below the empty squares to form the [(U02)2(V04)3] double sheets (named D) Fig. 13b. 

Fig. 5. Distorted G 2 polyhedra, connected through cl face-sharing, in the Mo3S7C16 clusters of the M03S7CI4 framework (projection in an arbitrary direction)...

Y-S for polyhedra connected by vertices or edges S denotes the number of common vertices or edges. Y= —H iox polyhedra containing common faces, where H is the number of hidden edges. 

Extended structures crystal structures with polyhedra connected to a one-, two-, or three-dimensional arrangement... 

Sr-3 The doping sites are similar to those of 2Sr-l. However, in this configuration two Sr(l)0 polyhedra connect via edge to edge bond. These polyhedra are connected with one Ca(l)0 polyhedron and three Ca(2)0 polyhedra. 

The addition of thermal energy causes a pair of atoms to acquire a larger mean interatomic separation (based on residence time) because of the asymmetric potential well about each atom. In network systems, such as glasses, the variation in polyhedra-connecting bond angles provides yet another mechanism for expansion. Thus, although fused silica is structurally similar to j8-cristobahte, the two have widely different thermal expansion. 

In equation (4), v, is the number of vertices of degree i (i.e. having i edges meeting at the vertex). This relationship arises from the fact that each edge of the polyhedron connects exactly two vertices. Since no vertex of a polyhedron can have a degree less than three, the following inequality must hold in all cases ... 

Sr-4 The doping sites are similar to those of 2Sr-2. However, this configuration is obtained by replacing calcium atoms with strontium atoms at neighboring Ca(l) and Ca(2) sites of a P-C2S crystal. In this configuration, the Sr(l)0 polyhedron connects to the Sr(2) polyhedron via face to face bond. Sr(l)0 and Sr(2) polyhedra are connected with two CaO polyhedra. 

Figure C2.12.6. Framework topology of ZSM-5. The 5-ring polyhedron is connected into chains which fonn the ZSM-5 stmcture with the 10-membered openings of the linear channels.

Carbon tends to adopt the position of lowest coordination number on the polyhedron and to keep as far from other C atoms as possible (i.e. the most stable isomer has the greatest number of B-C connections). 

Fig. 16.1 S elected polyhedral representations showing connectivity of mixed MO Clm n+m<6) (shaded polyhedron) and M 04 (open) units observed in the examples given in this report.

The coordination polyhedron results when the centers of mutually adjacent coordinated atoms are connected with one another. For every coordination number typical coordination polyhedra exist (Fig. 2.2). In some cases, several coordination polyhedra for a given coordination number differ only slightly, even though this may not be obvious at first glance by minor displacements of atoms one polyhedron may be converted into another. For example, a trigonal bipyramid can be converted into a tetragonal pyramid by displacements of four of the coordinated atoms (Fig. 8.2, p. 71). 

This mode of calculation has been called the EAN rule (effective atomic number rule). It is valid for arbitrary metal clusters (closo and others) if the number of electrons is sufficient to assign one electron pair for every M-M connecting line between adjacent atoms, and if the octet rule or the 18-electron rule is fulfilled for main group elements or for transition group elements, respectively. The number of bonds b calculated in this way is a limiting value the number of polyhedron edges in the cluster can be greater than or equal to b, but never smaller. If it is equal, the cluster is electron precise. 

A conglomerate of three hexagons contains one central atom and 12 atoms around it. A conglomerate of seven hexahedrons comprises 12 external and 12 internal (common) atoms. In these two cases geometric centers of hybridized molecular orbitals of each hexahedron are equidistant from such nearest centers of a conglomerate. This, apparently, explains the experimental fact that polyhedrons of carbon clusters represent an icosahedron - 12-apex crystalline structure each apex of which is connected with five other apexes. 

A cluster may be considered, in a sense, the antithesis of a complex even if there are many similarities between the two groups of compounds due to common symmetry properties. In both cases a set of atoms defines the vertices of a polyhedron in the complex, however, these atoms may be considered as bound to another, central, atom and not to each other. In the cluster, on the other hand, there is not necessarily a central atom and the atoms at the vertices can be described as directly connected to each other. 

The engineering of zinc-binding sites in a-helical peptides, where metal binding stabilizes protein tertiary structure, has been reported by Handel and DeGrado (1990). In these experiments zinc-binding sites are incorporated into a dimeric helix-loop—helix peptide (H3 2) and a protein composed of four helices connected by three short loop sequences (H3 4). a model of one subunit of the H3 2 dimer is found in Fig. 47. In addition to metal complexation by two histidine residues at positions n and n+4 of one a helix, the metal is coordinated by a third histidine residue of an adjacent a helix. The composition of the zinc coordination polyhedron is like that of carbonic anhydrase (i.e., Hiss), and spectroscopic results suggest that all three histidine residues are involved in zinc complexation. This work sets an important foundation... 

The structure of p-CsBeFs is usually described as consisting of chains of corner-connected Bep4 tetrahedra, with Cs atoms/ions interposed between them so that the Cs atoms are 8-coordinated by fluorine, but in a very irregular way. Figure 5 shows that, in fact, this Cs-centred coordination polyhedron is a rather irregular trigonal prism with two lopsided caps. 

Although the connected coordination polyhedron approach is useful in crystal chemistry, it has certain implicit rigidity which makes it difficult to extend to less regular and more complex structures. Several alternative approaches to the description... 

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