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This Thesis describes some theoretical studies on ligated and bare clusters. Chapter 1 gives a review of the two theoretical models, Tensor Surface Harmonic Theory (TSH) and Jellium Model, accounting for the electronic structures of ligated and bare clusters. The Polyhedral Skeletal Electron Pair Theory (PSEPT), which correlates the structures and electron counts (total number of valence electrons) of main group and transition metal ligated clusters, is briefly described. A structural jellium model is developed in Chapter 2 which accounts for the electronic structures of clusters using a crystal-field perturbation. The zero-order potential we derive is of central-field form, depends on the geometry of the cluster, and has a well-defined relationship to the full nuclear-electron potential. Qualitative arguments suggest that this potential produces different energy level orderings for clusters with a nucleus with large positive charge at the centre of the cluster, enabling the spherical jellium model to be applied to alkali metal clusters seeded with magnesium and zinc. Analysis of the effects of the non-spherical perturbation on the spherical jellium shell structures leads to the conclusion that for a cluster with a closed shell electronic structure a high symmetry arrangement which is approximately or precisely close packed will be preferred. It also provides a basis for rationalising those structures, which have been predicted using ab initio calculations, of clusters with incomplete shell electronic configurations In Chapter 3, the geometric conclusions derived in the structural jellium model are developed in more detail. Alkali metal clusters with closed shell electronic configurations according to the jellium model adopt geometries of high symmetry and based on the T_d , O_h and I_h point groups. For high nuclearity clusters alternative high symmetry structures can occur and those which are either the most close packed or spherical are predicted to be the most stable. When the jellium closed shell "magic numbers" coincides with one of these high symmetry structures then the cluster will be particularly stable. The group theoretical consequences of the Tensor Surface Harmonic Theory are developed in Chapter 4 for[ML₂]_n, [ML₄]_n and [ML₅]_n clusters where either the xz and yz or x²-y² and xy components to L^π_d and L^δ_d do not contribute equally to the bonding. The closed shell requirements for such clusters are defined and the orbital symmetry constraints pertaining to the interconversion of conformers of these clusters are described. In Chapter 5 Stone's Tensor Surface Harmonic methodology is applied to high nuclearity transition metal carbonyl cluster compounds with 13-44 metal atoms. Two limiting bonding situations are identified and represented in terms of general electron counting rules. If the radial bonding effects predominate the clusters are characterised by 12n_s+Δ_i valence electrons, where Δ_i is the characteristic electron count of the interstitial moiety. If radial and tangential bonding effects are important then the total number of valence electrons is 12n_s+2(s_s+s_i-l), where s_s and s_i are the number of skeletal bonding molecular orbitals associated with surface (s_s) and interstitial (s_i) moieties. Chapter 6 develops a new theoretical framework to account for the bonding in the high nuclearity ligated clusters with columnar topologies. The wave functions of columnar metal clusters can be expressed as an expansion based on the particle on the cylinder problem. This bonding analysis is applied to clusters containing columns of triangles and squares. In Chapter 7 the origin of non-bonding orbitals in molecular compounds is reviewed and analysed using general quantum mechanical considerations. A combination of the pairing theorem and a group theoretical analysis leads to a definition of the number of the non-bonding molecular orbitals in co-ordination, polyene and cluster compounds. The non-bonding molecular orbitals have been generated by defining the nodal characteristics of the relevant orbitals and evaluating the solutions under the appropriate boundary conditions. The stereochemical role of nonbonding molecular orbitals in co-ordination compounds is also discussed.

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 d^δ-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 d^δ-based orbitals is identified.

2 v. : ill. ; 26 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--Dept. of Physical and Inorganic Chemistry, University of Adelaide, 1974

vii, 165 [14] leaves : ill. ; 26 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physical and Inorganic Chemistry, 1973

Thesis (Ph.D.)--McMaster University (Canada), 1995. / Source: Dissertation Abstracts International, Volume: 56-12, Section: B, page: 6741. Adviser: C. J. L. Lock.

Thesis (Ph.D.) -- Dept. of Physical and Inorganic Chemistry, University of Adelaide, 1974.

Thesis (Ph.D.) -- University of Adelaide, Dept. of Physical and Inorganic Chemistry, 1973.

Thesis (M.S.)--South Dakota School of Mines and Technology, Rapid City, 1976. / Vita. Includes abstract. Includes bibliographical references (leaf 29). Also issued in print.