The Ligand Polyhedron

2 Electronic Structures of Metal Clusters and Cluster Compounds 

Since organometallic clusters are well defined molecular objects of finite size (although perhaps a bit large), standard molecular quantum mechanical methods like ab initio or density functional techniques are the ideal tools for the description of their electronic structures. Unfortunately, the dimensions of these molecules , combined with the fact that they contain transition metal atoms, places this class of compounds well beyond the range of practical ab initio calculations. Only recently, due to improvements in quantum mechanical computer codes and to the extremely rapid increase in computing power, has it become posable to successfully tackle the electronic structure problem of ligated dusters on a quantitative or semiquantitative basis. So far, most of the theoretical analyses have been based on approximate computational schemes, topological considerations, or even simple empirical rules. 

The effective atomic number rule is an extension of the 18 electron rule for transition metal complexes. [222] One assumes that each CO ligand contributes two electrons and that the polyhedral edges represent two-electron/two-center bonds. 

According to this rule, [Os5(CO)it] [223] has an electron count of [(S x 8) + (16 X 2)] = 72 electrons, yet in order for all five Os atoms to attain a noble gas configuration, 90 (i.e. 5 x 18) electrons are required. The formation of nine metal-metal bonds in the trigonal bipyramidal structure of [Oss(CO)i6] thus accounts for the misang nine electron pairs. Many exceptions to this ride are known. For instance, [Nis(CO)t2] [224] has an electron count of 76 valence electrons, but nevertheless has the same structure as [Oss(CO)i6]- 

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Exchange mechanisms can be postulated for these clusters involving the types of mechanisms reported for the binuclear complexes. However, it is more informative to consider the shape of the ligand polyhedron, as well as that of the circumscribed metal skeleton (71). For... 

It is useful to start the description of the electronic structure of a ligated metal cluster by separately considering the bare metal atom duster, with the exact same geometry as the metal core in the ligated duster, and the ligand polyhedron, as an empty spherical cavity, and then finally allowing the two parts to interact (Fig. M6). 

The ambient temperature solution NMR spectra of the tris(dithiocarbamate) complexes, including those of Al (see above), show the complexes to be fluxional on the NMR chemical shift time scale. The stereodynamics can be quite complex with several different processes possible, namely, (1) a metal-centered rearrangement of the ligand polyhedron, (2) reversible ligand dissociation, (3) restricted rotation about the single N—C bonds of (bulky) N substituents. 

P. F. Kelly and J. D. Woollins, The Preparation and Structure of Complexes Containing Simple Inorganic Sulfur-Nitrogen Ligands, Polyhedron, 5, 607 (1986). 

If there are different kinds of ligands, those which have the smaller influence according to the spectrochemical series prefer the positions with the stretched bonds. For example, in the [CuC14(OH2)2]2 ion two of the Cl atoms take the positions in the vertices of the elongated axis of the coordination polyhedron. 

The electrons supplied by the ligands and the valence electrons of the n metal atoms of an M cluster are added to a total electron number g. The number of M-M bonds (polyhedron edges) then is ... 

For mixed lanthanide-transition metal clusters, Yukawa et al. have synthesized an octahedral [SmNi6] cluster by the reaction of Sm3+ and [Ni(pro)2] in nonaque-ous medium [66-68]. The six [Ni(pro)2] ligands use 12 carboxylate oxygen atoms to coordinate to the Sm3+ ion, which is located at the center of an octahedral cage formed by six nickel atoms. The coordination polyhedron of the central Sm3+ ion may be best described as an icosahedron. The [SmNir, core is stable in solution but the crystal is unstable in air. The cyclic voltammogram shows one reduction step from Sm3+ to Sm2+ and six oxidation steps due to the Ni2+ ions. Later, similar [LaNis] and CjdNif> clusters were also prepared. 

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