Structure-electron counting correlations

Fig. 1.32. Production mass spectrum obtained after reaction of a mass-selected Ni4 cluster with approximately 3 x 10 mbar of CO. The geometric structure of the saturated carbonyl cluster proposed on the basis of simple electron count-structure correlations is also displayed [31]...

The polyhedral electron count usually correlates with the structure in the case of metalloboranes and metallocarboranes, as well as for the parent compounds. 

Table 2.11. Correlation between metal polyhedron geometry and cluster valence electron counting. Structural properties of selected rhenium clusters...

Of the clusters with more than six metal atoms, the structures [75] of Os2(CO)2j (757, 284) and Rh2(CO)igj2 (79) can be rationalized in terms of skeletal electron-pair counting. For the clusters with six 38), nine (57), and eleven (59) gold atoms the rules have to be modified in order to agree with the observed structures, the main assumption being that one orbital per gold atom remains empty (55). For clusters of 8 to 15 metal atoms there is no correlation between structures and electron counts yet. 

A classical example of correlation of structure with valence electron count of transition-metal clusters is shown in Fig. 19.4.2. There the structures of a series of osmium clusters are systematized by applying the capping and decapping procedures. 

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. 

Table 16-2 Examples of Correlating Structures with Total Electron Count on a Wade s Rules Basis...

The theoretical models which have been used to describe the bonding in cluster compounds of the main group and transition metal elements are reviewed. The historical development of these models is outlined and special emphasis is placed on those studies which have led to the elucidation of structure-electron count correlations. Theoretical treatments of cluster bonding are based on localised, delocalised (molecular orbital) or free electron methods derived from the solution of the Schrodinger equation for a particle on a sphere. A detailed analysis of the Tensor Surface Harmonic method, as an example of a free electron model, is presented. Group theoretical consequences of the model are also presented. 

Fig. 8. Correlation of structure with valence electron count for transition metal cluster, utilising the Capping and Debor principles...

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