PSEPT

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

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. 

Each of these n-vertex carboranes has the same cage geometry as its B H counterpart, except that C2B3H5 has no known B5H " analogue. Application of the PSEPT rules (see p 145) is straightforward, with contributions of 3 electrons from... 

Metallacarborane structures are mostly consistent with the PSEPT approach. It is impossible to convey the richness of this field in a short chapter, but a few representative examples of the many hundreds of structurally characterized species are shown in Fig. 5-18. 

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 ... 

Examples are as follows in each case, PSEPT predicts the skeletal geometry but not the particular isomer(s) that is (are) adopted in practice. 

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. 

Worked example 23.3 Application of Wade s rules (PSEPT)... 

Within the remit of Wade s rules (PSEPT), the addition of one or more capping units to a deltahedral cage requires no additional bonding electrons a capping unit is a cluster fragment placed over the triangular face of a central cage. 

The OS7 core of Os7(CO)2i is a capped octahedron. Show that this is consistent with the PSEPT capping principle. 

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