Vertex-sharing Octahedra

Fig. 29.1. The ReOj-type host framework MOj octahedra vertex-share to create a three-dimensional network of voids interconnected by square windows defined by oxygen atoms. In hydrogen bronzes derived from hosts of this type the H-atoms are present attached to the oxygen atoms (as hydroxyl groups lying in the windows) .

Fig. 29.2. Two views of the hexagonal WOjfh-WOj) host framework WO octahedra vertex share to produce an open structure with hexagonal and triangular tunnels in the c direction. These tunnels are interconnected by square windows akin to those in the ReOs-type host oxides. In h-H WOj, the H is present in hydroxyl groups (exact location to be determined).

In the families of heptanuclear clusters, two geometries are found the capped octahedron that is typical for 98-valence electrons, and the vertex-sharing open tetrahedral (butterfly) stmctures typical for 106-valence electrons. An example of the former is Osy(CO)22 (51) an example of the latter is [H2AuOsg(CO)2Q] (52). In the AuOs cluster anion, the gold atom is at the vertex-sharing position. 

MX4 layer of vertex-sharing octahedra, and the packing of such layers in the K2NiF4 type. The packing in SnF4 is obtained by leaving out the K+ ions and shifting the layers towards each other in such a way that every octahedron apex of one layer comes to be between four apexes of the next layer... 

Some forms of rings and chains of vertex-sharing tetrahedra in silicates. How the chain conformations adapt to the size of the cation octahedra is shown for two chains (the octahedron chain is a section of a layer)... 

A combination of two square-pyramids of [Ln5((jt4-OH)( X3-OH)4] with one hollow octahedron of [Ln6([X3-OH)8] by vertex-sharing leads to the assembly of esthetically pleasing tetradecanuclear complexes with a rod-like cluster core (Figure 6.16). Complexes characterized by such a core have been successfully prepared using aryloxide [34, 35], P-diketonate [87], and amino acid ligands [104],... 

Fig. 8 Orbital ordering in pseudo-cubic perovskite KCUF3 with vertex-sharing octahedrons [CuFe]. Type a is layer-antiferrodistortive and Type d is layer-ferrodistortive pattern. (After Kugel and Khomskii [19], Reinen and Friebel [16], and Binggeli and Altarelli [20])...

It should be emphasized that the validity of conclusion (iii) rests on our assumptions (a) that the distance of closest approach of X atoms of different vertex-sharing octahedra (x in Fig. 5.3(c)) may not be less than the distance X-X within an octahedron, and (b) that the octahedra are regular. Structures in which three octahedra share a common vertex but no edges or faces contravene (a) and/or (b). 

FIG. 15.11. Layer formed from vertex-sharing [Mg(H20)6l and [CUH ) ] groups in MgCl2.12 H2O (diagrammatic). The squares represent [Mg(H20)6 and the rhombuses [C1(H20)61 groups. Two (unshared) vertices of each octahedron are not shown. 

There exist a number of tetradecanuclear lanthanide hydroxide complexes whose core can be viewed as formally constructed by combining two square pyramids of [Ln5(/44-OH)(/i3-OH)4] with one hollow octahedron of [Ln<5(/43-OH)8] by vertex sharing. The structural relationship between the penta-, hexa-, nona-, and tetradecanuclear species... 

Probably, the most common structural unit in the solid state is the octahedron. We start at the most simple one-dimensional class and first look at vertex-shared examples v/ith a ML4X formula unit, 15.55. Here, L is atwo electron a donor and the bridging atom, X, contains s and p AOs. The band structure for this polymer is easy... 

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... 

A further decrease in the X Me ratio, to 4, leads to linkage of the octahedral units by sharing more than one ligand so as to achieve coordination saturation. Sharing of two vertexes (two comers of the each octahedron) leads to the formation of compounds with layered-type structures. 

The compounds characterized by X Me = 3.5 have a common formula of M2Me205F2 and crystallize either in a pyrochlore [192] or a veberite [229] type structure. According to X-ray powder diffraction patterns, the structure of Na2Nb205F2 can be regarded as a super-structure of pyrochlore, which is made up of octahedrons connected in layers and arranged in the (111) direction. The layers are linked via octahedrons so that each octahedron in one layer shares three vertexes with an octahedron in the adjacent layer. 

Take pairs of face-sharing coordination octahedra and join them by common vertices to form a chain, with every octahedron taking part in one common vertex not belonging to the shared face. What is the composition of the resulting chain ... 

If six equilateral triangles share a common vertex, the sum of the angles around the vertex is 6 x 60 = 360°. The array is planar and cannot form part of a regular polyhedron. It is clear that the three possibilities listed give rise to the tetrahedron, the octahedron, and the icosahedron, as shown in Table 3.2. 

Only the second one is possible and we should have n — p. If j = 3, then G is Octahedron. At every vertex of Octahedron, we have two ways to put 2-gons. Those possibilities are indexed by a pair of 3-gons sharing only an edge. Since we have 6 vertices, this makes 64 possibilities and, up to isomorphism, 7 possibilities. Clearly, every 3-gon should belong to at least one pair. This restricts us to three possibilities. The first possibility is shown below with the number associated to each vertex ... 

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