Cluster octahedron

Such clusters of FeOe octahedra also exist in other inorganic compounds. For instance they exist in ilvaite (CaFe TFe 2Si20700H) where silicate layers replace phosphate anions and FeOs octahedra form ribbons. It is interesting to note that such a material is active and selective for the reaction although to a lesser extent than the previous hydroxyphosphates [24]. The lower catalytic behaviour may be due to the presence of Ca " cations in the structure and/or to the silicate counter anion whose basicity in the sense of Pearson is different from that of the phosphate anion and/or the infinite size of Fe06 octahedra clusters. 

Fig. 4. Electron exchange between iron cations in (Fe06)n octahedra clusters calculated by extended Huckel molecular orbital theory (from [21] and [22].

Figure 2 The (a) mass- and (b) surface-averaged distribution of atoms on the (111) and (100) crystal faces and on the edges and corner sites of a cubo-octahedral cluster model. (From Ref. 4.) Mass-averaged and surface-averaged distributions are based on calculations using cubo-octahedron cluster model and represent number of different crystallographic planes divided by the (a) mass or (b) the surface area of the cluster (at the corresponding particle size). Hence (e- -c) in (a) represents edge and kink positions and (100) (111) the normal cubic crystal planes.

Figure 3 A plot of variation of ratio of the number of sites with different coordination number with total surface atoms, and overall coordination number (A"cubo-octahedron) as a function of particle size. The calculations are based on algorithms developed previously by Benfield (Ref. 35) based on cubo-octahedron cluster model. Therefore, N enex/Ng represents the ratio of the number of sites at the vertex position in the cluster to the total number of surface sites. The other ratios based on different cluster positions [such as Kink sites, (100) and (111)] are similarly marked.

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. 

Ooso (structure I) has a regular octahedral cluster of 6 B atoms surrounded by a larger octahedron of 6 radially... 

Figure 25.11 Metal frameworks of some high-nuclearity binary carbonyl and carbonylate clusters of osmium (a) Os5(CO)i6 (trigonal bipyramid) (b) Os6(CO)ig (bicapped tetrahedron, or capped trigonal bipyramid) (c) [Os6(CO)ig] (octahedron) (d) Os7(CO)2i (capped octahedron) (e) [Osg(CO)22] (bicapped octahedron) (f) [Osi7(CO)36] (3 shaded atoms cap an Osu trigonal bipyramid).

K3Ta40gF7 [225] too has a layered structure and contains clusters of the Ta3X,5 type. Each cluster is composed of three TaX6 type octahedrons that are linked to one another via their vertexes. 

The Mg clusters with 6N + 14 (N = 0-2) valence electrons assume regular octahedrons, whereas those with the other numbers of valence electrons do not. 

The octahedron is classified into the c/o o-structure by Wade [3,4]. Closo-structures with n skeletal atoms are stable when they have 4n-i- 2 valence electrons. Wade s rules predict that the 26 (= 4 x 6 + 2) valence electrons could stabilize the regular octahedrons since n is 6 for the octahedron. This prediction is contained in our 6N + 14 (N= 2) valence electron rule. Our rule also predicts the stability of octahedral metal clusters with the other numbers (14 and 20) of valence electrons. 

Solid-state cluster chemistry is dominated by octahedral (M 5L8)L6 and (MsLi2)L units which are the focus of this paper. These two cluster types are different in the way the metal octahedral core is surrounded by the ligands. In (MsLg)L6-type clusters (Fig. 6.1a), typical for molybdenum and rhenium halides, chalcogenides, and chalcohalides, eight innei hgands (L ) cap the octahedron faces and six outer ligands (L ) are located in the apical positions [9]. For metals with a smaller number of valence electrons, the (M6L i2)L -type clusters... 

Fig. 6.1 The fundamental structural unit found in the Chevrel phases (cluster MoeXg full circles Mo atoms) displayed in three ways to emphasize different views of the connectivity. In (a) an octahedron of molybdenums (Mo-Mo = 2.7 A) is encased in a cube of chalcogens (Mo-S 2.45 or Mo-Se 2.6 A). Scheme (b) exhibits the same cluster as consisting of an octahedron with its triangular faces capped by chalcogenides. In (c), the cluster has been reoriented so that a threefold axis is vertical. (Reproduced from [10])...

Calculations on the basis of density functional theory have been used to check the structure of Rh clusters supported on zeolite X the results indicate a slightly twisted prism, nearly matching the octahedron inferred on the basis of the EXAFS data [28,29]. (These clusters were inferred not to be bare but to have hydride ligands, as described later). 

Mo6 octahedron) the cluster is electron-precise, the valence band is fully occupied and the compounds are semiconductors, as, for example, (Mo4Ru2)Se8 (it has two Mo atoms substituted by Ru atoms in the cluster). In PbMo6Sg there are only 22 electrons per cluster the electron holes facilitate a better electrical conductivity below 14 K it becomes a superconductor. By incorporating other elements in the cluster and by the choice of the electron-donating element A, the number of electrons in the cluster can be varied within certain limits (19 to 24 electrons for the octahedral skeleton). With the lower electron numbers the weakened cluster bonds show up in trigonally elongated octahedra. 

However, certain polyhedra allow the inclusion of another electron pair without cleavage of any bond. This applies especially to octahedral clusters which should have 84 valence electrons according to equation (13.12), but they frequently have 86 electrons. The additional electron pair assumes a bonding action as a six-center bond inside the octahedron. An octahedral cluster with 86 valence electrons fulfills the Wade rule discussed below. 

---