Theoretical investigations of polyhedral inorganic molecules
This Thesis describes some theoretical studies on cluster compounds of the main group and transition metal elements. Chapter 1 presents a review of the theoretical aspects of cluster chemistry. Three major theoretical approaches are identified, namely the localised, delocalised and free electron models and their historical development is described. The research described in this Thesis is based on extensions of Stone's Tensor Surface Harmonic (TSH) methodology, supported by Extended Huckel molecular orbital calculations. In Chapter 2, the TSH approach is used to describe the skeletal bonding in 3- and 4-connected polyhedral clusters. Like the deltahedral clusters, 4-connected molecules are generally characterised by (n+1) Skeletal Electron Pairs (SEP's). 3- connected clusters, however, possess 3n/2 SEP's. This difference is attributed to the occurrence of additional non-bonding orbitals in the 3-connected case. In Chapter 3, the bonding in a novel class of deltahedral metallaborane clusters is discussed. These hyper-closo or iso-closo species are studied from a fragment orbital viewpoint, regarding the structures as metal-capped fragments of a borane icosahedron. In this way, the problem of whether these clusters possess n or (n+1) SEP's is studied for n=9, 10 and 11. Although most deltahedral clusters conform to the (n+1) SEP rule, there are a significant number which do not. In Chapter 4, these deviations are rationalised from a group theoretical/topological viewpoint. A group theoretical paradigm is developed which simplifies the derivation of the frontier orbitals for these molecules. Chapter 5 extends the TSH methodology to clusters with bispherical topologies. To discuss these clusters, the TSH wavefunctions are modified to include radial, as well as angular nodes. The methodology is also applied to clusters with toroidal topologies, where the capping atoms form a ring around the equator of the inner cluster sphere. The bonding in π-donor- and π-acceptor-bridged clusters of the transition metals are compared in Chapter 6. Although the symmetry aspects are identical and lead to similar bonding patterns, the ir-donor clusters are characterised by a number of unoccupied dδ-based orbitals. The bonding in a series of closo, nido and arachno π-donor clusters, based on edge- and face-bridged octahedral molecules is considered and a relationship between the cluster electron count and the number of unavailable dδ-based orbitals is identified.