Clusters, metal closo-, nido-, arachno

Atoms in Cluster Vertices in Parent Polyhedron Framework Electron Pairs Valence Electrons (Boranes) Closo Nido Arachno Examples Valence Electrons (Transitlon-Metal Clusters) Closo Nido Arachno Examples ... 

Wade expanded the 1971 hypothesis to incorporate metal hydrocarbon 7T complexes, electron-rich aromatic ring systems, and aspects of transition metal cluster compounds [a parallel that had previously been noted by Corbett 19) for cationic bismuth clusters]. Rudolph and Pretzer chose to emphasize the redox nature of the closo, nido, and arachno interconversions within a given size framework, and based the attendant opening of the deltahedron after reduction (diagonally downward from left to right in Fig. 1) on first- and second-order Jahn-Teller distortions 115, 123). Rudolph and Pretzer have also successfully utilized the author s approach to predict the most stable configuration of SB9H9 (1-25) 115) and other thiaboranes. 

Let us now ask how we could predict the correct total electron count, as just defined, for a stable cluster of known structure (i.e., closo, nido, or arachno). To do this for metal carbonyl clusters, it is postulated that in addition to the electrons necessary for skeletal bonding each metal atom will also have 12 nonskeletal electrons. The basis for this assumption is that in the pyramidal M(CO)3 unit each M—CO bond will comprise two formally carbon tr electrons that are donated to the metal atom and two formally metal it electrons that backbond, at least partially, to the CO ligand. Thus, in predicting the total electron count for a closo polyhedral cluster of n vertices, the result would be 12n + 2 n + 1). Similarly, for nido and arachno clusters that are derived from an n-vertex polyhedron (their parent polyhedron) by removal of one or two vertices, respectively, there will be 12 and 24 fewer total electrons, respectively. 

Closo, nido, and arachno Borane and Transition Metal Clusters... 

Examples of closo, nido, and arachno borane and transition metal clusters are given in Table 15-12. Transition metal clusters formally containing seven metal-metal framework bonding pairs are among the most common examples illustrating the structural diversity of these clusters are given in Table 15-13 and Figure 15-20. 

To underline the structural and bonding relationship between these mixed metal-carbon cluster species and carboranes, we list the formulae of representative examples in Table 4.1, classified according to the numbers of skeletal bonding electrons they contain and thus according to their structural type (closo, nido, or arachno ). 

Table 2. Closo, nido and arachno transition metal clusters (based on deltahedra with more than 6 skeletal atoms) possessing interstitial main group atoms...

The mechanistic implications of these facile formal cluster oxidations arachno nido closo by nett loss of Hp at moderate temperatures are considerable. The processes are accompanied by, and presumably assisted by a flexibility of coordination geometry about the Ir atom and also by its ready oxidation. The metal atom can be seen as a potential source of electrons for cluster bonding either by involving its lone pairs of electrons or by switching between Ir-H-B bridging and Ir-H terminal bonding... 

There are a number of other important boron cage compounds as well as structurally similar metal atom cluster molecules that are not closed polyhedra. Generally, these may be regarded as derived from closed polyhedra by removal of one or two vertices. The diagram below illustrates how removal of one or two vertices generates the so-called nido and arachno relatives of a closo octahedral structure. 

A transition element has 5 additional valence orbitals, the 5d orbitals, and therefore 10 additional electrons are required per atom to fill the valence shell of each metal atom. A closo cluster consisting only of transition metal atoms should have a total of 14/i + 2 valence electrons. A capped cluster should have 14n, a nido cluster 14/i + 4, and an arachno cluster 14n+6. The combined formula 4/i+2 + 10m would represent the total electron count for a closo cluster, A mMm, of n atoms that contains m transition metal atoms and n -m main group atoms.Table 8.2 summarizes the main rules, and the following examples show how the total electron counting scheme is applied. 

For polyhedral clusters (sometimes called deltahedral, because the faces are all triangles resembling the Greek letter delta) the ancestor of all electron counting schemes is the correlation proposed by Wade between borane (or carborane) cages and metal carbonyl cages. Wade first drew attention to the similarity of a M(CO)3 unit and a BH (or CH) unit, a relationship that we would now call isolobality (Section 1-6). He then proposed that the 2n + 2 rule for closo boranes (Chapter 5) would also apply to closo metal cluster species such as [Os CO) ]2, and that 2n + 4 and 2n + 6 electron counts would, similarly, be appropriate for stable M clusters with nido and arachno structures. Hydrogen atoms are assumed to contribute one electron each, an interstitial carbon atom four electrons, and so on. 

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. 

Lauher, subsequently, performed Extended Hiickel calculations on a wide range of n-atom closo transition metal clusters and confirmed the presence of (2n - 1) high-lying inaccessible antibonding orbitals, leaving a total of (9n - (2n - 1) = (7n + 1) occupied cluster valence MO s and an electron count of (14 n + 2)85. Lauher s calculations were made on bare metal clusters and the introduction of ligands was considered to constitute only a small perturbation. Calculations on nido and arachno transition metal clusters showed them to be characterised by (14 n + 4) and (14 n + 6) valence electrons... 

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