Topological theory boranes

More elaborate electron-counting procedures have been established, and these are usually more appropriate for the rationalisation of high-nuclearity clusters. An approach which was originally applied to complex boranes has been extended to carbonyl clusters and a number of topological theories have been described. Although there is some way to... 

Until now we considered the topology of various organic molecules. In inorganic chemistry the topological methods are not so popular. Therefore, in this chapter we shall confine ourselves to only two topics, the topological theory of borane structure and the discussion of the interrelationship between topology, symmetry, and electronic structure of coordination compounds. 

Lipscomb s topological theorem. In 1954 W. Lipscomb with coworkers suggested a so-called topological theory of boranes which he continues to improve even now. On the basis of that theory it became possible to predict,... 

From the Lipscomb theory one can get the topological graphs for any borane of assigned composition and thus predict new structures. Certain limitations should be imposed, though, on the quantities appearing in the balance equations (31)-(34), for example,... 

In 1977 we reported a method based on graph theory for study of the skeletal bonding topology in polyhedral boranes, carboranes, and metal clusters Q). Subsequent work has shown this method to be very effective In relating electron count to cluster shape for diverse metal clusters using a minimum of computation. Discrete metal clusters treated effectively by this method Include post-transition metal clusters (, ) > osmium carbonyl clusters (O, gold clusters, platinum carbonyl clusters (J., 7 ) > and... 

The rearrangement of boranes has been studied by theoretical methods. The popular diamond-square-diamond (DSD) process has been studied by the tensor surface harmonic theory [37], and by topological [38, 39] and orbital symmetry analyses [39, 40]. Advances in the NMR technique as applied to boranes were reported [41] methods to predict B NMR... 

Another approach for studying the electronic structure of boranes uses the localized three-center bonds arising from the Lipscomb topological models (section II.A) as the basis set for Huckel-type MO computations. Kettle and Tomlinson showed that this method leads to the same pattern of MO energy levels as the LCAO methods of Lipscomb. Subsequent work showed that this method is a topologically correct extension of Hiickel theory to three dimensions. 

In recent years the fundamental ideas of Huckel molecular orbital theory, the Huckel rule, and other aspects of aromaticity have been extended to polyhedral three-dimensional inorganic structures regarded as aromatic like the two-dimensional aromatic hydrocarbons. Such an extension of Huckel molecular orbital theory requires recognition of its topological foundations so that they can be applied to three-dimensional structures as well as two-dimensional structures. In this connection graph theoretical methods can be used to demonstrate the close analogy between the delocalized bonding in two-dimensional planar aromatic systems such as benzene and that in three-dimensional deltahedral boranes, and carboranes. Related ideas can be shown to be applicable for metal carbonyl clusters, bare post-transition metal clusters, and polyoxometallates. ... 

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