Clusters skeletal electron pairs theory

The geometries of metal carbonyl and metallocarborane cluster compounds have been systematized recently by a set of simple rules described collectively as the polyhedral skeletal electron pair theory (153, 218, 232). This approach originated from a perceptive analogy between isostructural metal carbonyl and borane polyhedral cluster molecules (232), and its applications have been widely discussed and reviewed (147, 153, 210, 218, 233, 234, 235, 240). In this review,... 

Polyhedral carboranes (continued) seven-vertex carboranes, 3, 58 six-vertex carboranes, 3, 56 small carborane syntheses, 3, 54 subicosahedral carborane geometrical patterns, 3, 50 subicosahedral and icosahedral, 3, 51 supraicosahedral, characteristics, 3, 96 ten-vertex carboranes, 3, 60 thirteen-vertex carboranes, 3, 100 tricarbaborane synthesis, 3, 54 twelve-vertex carboranes, 3, 98 Polyhedral skeletal electron pair theory, Ru and Os tetranuclear clusters, 6, 874-875 Poly(iV-heterocyclic carbene) ligands... 

Ru3(CO)12 with Pt(PBu )2 at room temperature affords 92 as the main product, whereas reaction in refluxing hexane affords small amounts of octanuclear cluster 93 and tetranuclear 94. The capped-pentagonal bipyr-amidal 93 contains 104 cluster electrons, or six fewer than predicted by the Polyhedral Skeletal Electron Pair Theory. Solutions of 93 slowly decompose to give a small amount of 93, together with Pt3(CO)3(PBu3)3. No platinum homologue of 91 has yet been isolated.63... 

A particularly useful tool is the Polyhedral Skeletal Electron Pair Theory (PSEPT),3 originated by K. Wade, elaborated by D. M. P. Mingos and others, and known colloquially as Wade s Rules. This approach and its applications to carbocations, metal clusters, and other non-boron species, are described in numerous books and reviews. Here we simply outline the basic rules. 

A theory which shows greater applicability to bonding in cluster compounds is the Polyhedral Skeletal Electron Pair Theory (PSEPT) which allows the probable structure to be deduced from the total number of skeletal bond pairs (400). Molecular orbital calculations show that a closed polyhedron with n vertex atoms is held together by a total of (n + 1) skeletal bond pairs. A nido polyhedron, with one vertex vacant, is held together by (n + 2) skeletal bond pairs, and an arachno polyhedron, with two vacant vertices, by (n + 3) skeletal bond pairs. Further, more open structures are obtainable by adding additional pairs of electrons. This discussion of these polyhedral shapes is normally confined to metal atoms, but it is possible to consider an alkyne, RC=CR, either as an external ligand or as a source of two skeletal CR units. So that, for example, the cluster skeleton in the complex Co4(CO)10(RCCR), shown in Fig. 16, may be considered as a nido trigonal bipyramid (a butterfly cluster) with a coordinated alkyne or as a closo octahedron with two carbon atoms in the core. 

The polyhedral structures adopted by most metallacarbab-orane compounds can usually be rationalized using polyhedral skeletal electron pair theory (PSEPT) (see Electronic Structure of Clusters). This approach is summarized as follows ... 

The hexanuclear cluster [Os6(CO)ig] (69) and the corresponding dianion [69] are notable since the structural change from the bicapped tetrahedron of 69 (170) to the octahedron of osmium atoms in [69f (171) is exactly that predicted by polyhedral skeletal electron-pair theory (172). 

Development of the concept of the chemical bond from hydrogen to cluster compounds Limitations of the polyhedral skeletal electron pair theory in organometallic cluster chemistry examples in tri- and tetrametallic systems Electron-count versus structural arrangement in clusters based on a cubic transition metal core with bridging main group elements... 

Density-functional theory of spin polarisation and spin coupling in iron-sulfur clusters Stereochemical aspects of organometallic clusters. A view of the polyhedral skeletal electron pair theory... 

Keywords Aluminum Capping principle Closed-shell principle Clusters Condensed clusters Copper Electron-counting rules Gallium Gold Jellium model Nanoclusters Palladium Polyhedral skeletal electron pair theory Silver Tensor surface harmonic... 

It became necessary to develop new approaches for predicting electron closed-shell structures, and ideas came from Williams, Wade, Mingos, and Rudolph, which now make up the polyhedral skeletal electron pair theory (PSEPT). The bonding in clusters can sometimes be described in terms of edge-localized, two-center two-electron bonds. Thus, through the formation of element-element bonds, the atoms of a polyhedron can acquire an effective inert gas configuration (8 valence electrons for a main group element and 18 for a transition metal atom). 

Transition Metal Clusters. For the application of the skeletal electron pair theory deduced from the structural properties of boranes and carboranes to transitions metal clusters, it is necessary to establish some assumptions ... 

Platinum clusters generally do not agree with the electronic requirements of transitions metal clusters established by the polyhedral Skeletal Electron Pair Theory. These clusters generally possess fewer electrons than expected from this theory. 

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