Cluster chemistry symmetry

The boron hydrides, including the polyhedral boranes, heteroboranes, and their metaUa derivatives, encompass an amazingly diverse area of chemistry. This class contains the most extensive array of structurally characterized cluster compounds known. Included here are many novel clusters possessing idealized molecular geometries ranging over every point group symmetry from identity (C[) to icosahedral (I[). Because boron hydride clusters may be considered in some respects to be progenitorial models of metal clusters, their development has provided a framework for the development of cluster chemistry in... 

The complexities of structures such as those of etemenfary boron are better appreciated after studies of symmetry theory and cluster chemistry, and so are not elaborated in this text. 

The degree of symmetry that the point group represents is given by the order, h, whieh is simply the sum of the number of symmetry elements that the point group possesses. For Cav /i = 4 for h = 7A and for Oh / = 48. The highest (non-infinite) symmetry group encountered in chemistry is the icosahedron, 4 (order h = 120), which describes a polyhedron sometimes encountered in cluster chemistry, e.g. and... 

With metal clusters it is even harder than in other fields of inorganic chemistry to substantiate theoretical results by energy measurements. Only two such measurements have come to the attention of the author — the photoelectron spectrum of [CpFe(C0)]4 370) andbond energy determinations in 03(00)9CX-compounds 187). However, a considerable number of papers deal with metal-metal bonding in, and the symmetry properties of, clusters as related to their stoichiometry and their electron count. These studies have confirmed the wide apphcability of the simple 18-electron rule in predicting metal-metal bonds and structures, but they have also led to an understanding of the limits of this rule for clusters with more than four metal atoms. 

E. Brandas, Complex Symmetry, Jordan Blocks and Microscopic Selforganization An Examination of the Limits of Quantum Theory Based on Nonself-adjoint Extensions with Illustrations from Chemistry and Physics, in N. Russo, V. Ya. Antonchenko, E. Kryachko (Eds.), Self-Organization of Molecular Systems From Molecules and Clusters to Nanotubes and Proteins, NATO Science for Peace and Security Series A Chemistry and Biology, Springer Science+Business Media B.V., Dordrecht, 2009, p. 49. 

Substitution at one or more metal sites will generally break the symmetry of the cluster core, and can greatly influence its electronic properties and reactivity. Consider, for example, the possible substitutions of a metal M into an octahedral core of composition MfiX v (x = 8, 12). The first substitution will afford an MsM X core, for which the symmetry has been lowered to C4v. A second substitution generates an M4M 2Xx core with two possible isomers One in which the M atoms are positioned at trans vertices (D4/,) and another where they are positioned at cis vertices (C2v). With a third substitution to give an M3M 3Xx core, fac and mer isomers become possible, while further substitutions simply repeat the pattern with M and M interchanged. Here again, the substitutions can be anticipated to alter the basic electronic properties of the cluster. Moreover, the outer-ligand substitution chemistry could potentially be quite different... 

The replacement of main-group atoms in clusters by transition-metal atoms generates a richer structural chemistry superimposed on the cluster basics illustrated by the p-block systems. A logical question arises here. What would a one-dimensional material containing a transition metal look like Well, the d AOs will generate bands in a similar manner as the s and p orbitals. The major novelty will be the introduction of orbitals of 8 symmetry. Let s look at a hypothetical chain composed of equidistant Ni atoms (d = 2.5 A). The computed band structure, DOS and COOP are illustrated in Figure 6.14. The COs at k = 0 and ir/d arc drawn below. As a review of the previous section, we will reconstruct it starting from the Bloch functions associated with the nine Ni AOs. 

Coordination Organometalhc Chemistry Principles Electronic Structure of Main-group Compounds Electronic Structure of OrganometaUic Compounds Electronic Structure of Clusters Ligand Field Theory Spectra Molecular Orbital Theory Symmetry Point Groups. 

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