Polyhedral Skeletal Electron Pair Theory

The polyhedral skeletal electron pair approach retains the condition that each metal atom uses its nine valence atomic orbitals. However it does not consider all the electron in the system but only those involved in the metal network. This approach is fundamentally grounded on the analogy existing between metal clusters and boron hydrides and carboranes. 

Bonding in Boranes and Carboranes. Although in Chapter 4 some aspects of the boron cluster chemistry will be considered, it is convenient to discuss here some structure and bonding features characteristic for boron clusters. 

Boron hydrides and carboranes adopt structures in which their skeletal boron and/or carbon atoms form complete or nearly complete deltahedra, i.e. regular polyhedra with triangular faces. 

Compound Polyhedron Distances Type of Ligands Number Ref. 

5 Ciani G, D Alfonso G, Freni M, Romiti P, Sironi A, Albinati A (1977) J. Organomet. Chem. 136.C49 

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Polyhedral Skeletal Electron Pair Theory The Wade-Mingos Rules... 

The following optimum electron numbers have been defined on the basis of the so-called Polyhedral Skeletal Electron-Pair Theory (PSEPT) . 

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. 

H2OEP = Octaethylporphyrin PPN = Bis(triphenylphos-phino)immium(l+) PSEPT = Polyhedral skeletal electron pair theory TMEDA = Af,Af,A, A -Tetramethylethylene-diamine nbd = Norbomadiene cod = 1,5-Cyclooctadiene. 

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 ... 

DFT = Density Functional Theory DSD = Diamond-Square-Diamond HOMO = Highest Occupied Molecular Orbital IR = Irreducible Representation LCAO = Linear Combination of Atomic Orbitals Ph = Phenyl PSEPT = Polyhedral Skeletal Electron Pair Theory SCF = Self-Consistent-Field SDDS = Square-Diamond, Diamond-Square TSH = Tensor Surface Harmonic. 

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... 

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