Electron counting cluster hydrides

Williams [1] has given an excellent review on Early Carboranes and Their Structural Legacy and he defines carboranes as follows Carboranes are mixed hydrides of carbon and boron in which atoms of both elements feature in the electron-deficient polyhedral molecular skeleton . According to the electron counting rules [2] for closo- (2n + 2 SE), nido- (2n + 4 SE) and arachno-clusters (2n + 6 SE SE = skeletal electrons, n = number of framework atoms) and the An + 2 n electron Hiickel rule, small compounds with skeletal carbon and boron atoms may have an electron count for carboranes and for aromatics (see Chapters 1.1.2 and 1.1.3). 

Wade electron counting rules borane-like cluster nomenclature. On initially studying compounds such as boranes (boron hydrides) and carboranes (or carbaboranes boron—carbon hydrides), Wade (1976) proposed a number of rules which have then been extended to several compounds and which relate the number of skeletal electrons with the structure of deltahedral clusters. A polyhedron which has only A-shaped, that is triangular, faces is also called a deltahedron. 

The electron-counting scheme which allows to understand this situation and which also works for the simpler clusters was developed from the MO theory for boron hydride polyhedra 389-393). It rests on the fact that a regular triangular faced polyhedron of n boron atoms in the molecule requires n + 1 bonding... 

Addition of protons to anionic clusters to generate hydrides leaves the cluster electron count unaffected, yet the process is sometimes accompanied by structural changes. For example, both [Os6(CO)i8] (87) and [Os6(CO)igH] (88) have octahedral arrangements of metal atoms as predicted by Wade s rules. In the dihydride Osg(CO)i8H2, however, the metal atoms describe a capped square-based pyramid (87). 

Flgure 2 Schematic metal framework of rhenium carbonyl hydride clusters, electron counts, and selected examples... 

The TEC model developed by Teo also has been successfully applied to rationalize the geometries of a large number of cluster compounds. The TEC model combines Lauher s rule with Euler s theorem and adds an adjustable parameter This parameter X is equal to the number of electron pairs present in excess of that predicted by the 18-electron rule. " X has also been interpreted in terms of the number of missing antibonding orbitals. Given a value for X, determined by the shape of the cluster, an equation predicts the electron count for a cluster. Theoretical justification of the parameter X is based largely upon the classical molecular orbital calculations performed by Hoffmann and Lipscomb via the extended Hiickel method on the corresponding polyhedral boron hydride clusters The values... 

The remaining hydride remains coordinated to the cluster, bridging two of the framework osmium atoms. In terms of the electron count, this electron-precise cluster has 45 cluster valence electrons from the Os3(CO)ioH fragment, and thus three are contributed, as required, by the stannyne group. Notable features of the structure are (i) the appreciable lengthening of the Os Os distance bridged by the... 

These and related methods of structure prediction depend upon the allocation of specific electron counts to different framework geometries and these applications have been very successful in assigning structures to cluster carbonyls and their derivatives. However, for the higher polynuclear carbonyls as the molecularity of the compounds increases the predictive power of the theories becomes less decisive in differentiating between alternative structures. In essence the Wade-Mingos approach assumes that the frontier orbitals of the complex primarily involve metal orbitals so that any variation in the electron occupation will be reffected in a structural change in the metal framework. The Wade theory also requires that the structure of the complexes are based on triangulated polyhedra as found for the boron hydrides. 

The stability of cluster hydrides seems to follow a similar pattern. Bridging seems to be the predominant structural form, but fluxional behavior, presumably involving intermediate terminal hydride spedes, is common. Norton has discussed binuclear elimination as an important cluster-forming decomposition pathway for metal hydrides (see Section 19.5.3). Structural rules due to Wade, Mingoes, Hoffmann, Lauher and Teo have been proposed to account for the structures of the higher nuclearity clusters. It is quite possible that clusters of several different electron counts will be accessible for any given polyhedron of metals, especially for the larger clusters. The relative usefulness of the different systems is still under discussion. 

The number of cluster valence electrons (CVE) expected for a linear M3 array is 50 (110), however the formulation from the X-ray and magnetic susceptibility data suggests a 48 CVE count for the [Fe3(CO)u]2- moiety. It is possible that the Fe3(CO)u unit is electron deficient, but another explanation is that it is a 50-electron system with two hydride ligands. No evidence for an M—H bond is present in the H-NMR spectrum. Similarly, the disposition of the carbonyl ligands on the terminal iron atoms does not suggest the presence of hydrogen ligands. 

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