An Investigation of the Diels-Alder Reaction of 2,4-Hexadiene with Sulfur Dioxide and a Novel Procedure for Non-Orthogonal Localisation of Molecular Orbitals.

This thesis is divided into four parts, which reflect the various components of the research covered. The introductory section covers the essential, basic quantum chemistry necessary for any fruitful study in the subject; a review of necessary tools is given which ranges in topic from the presentation of Schrödinger 's equation for many-body theory to density functional theory versus perturbation theory. After a clear exposition of these topics, their practical implementation to characterise the
Diels-Alder reaction of 2,4-hexadiene with sulfur dioxide is described. This theoretical study is rooted in the experiments on the same reaction; additionally, a previous – albeit, more elementary – theoretical study was also completed by another group. The work herein is distinct in two ways: first, all possible isomers of the diene were
investigated; secondly, the reactions were studied with greater accuracy and results were compared using different methods. Additionally, the molecular orbitals of the
reaction were localised using standard techniques in the literature. The third section of the thesis is devoted to clearly covering a series of numerical methods which can be
used to solve common problems encountered in quantum chemistry. A discussion of the strengths and weaknesses of each method is also given. Although, it is true that
many of these methods are implemented in stable quantum chemistry packages, these methods were primarily discussed in light of their potential application for solving
the, yet unresolved, issue of constructing highly localised non-orthogonal molecular orbitals. To date, localised molecular orbitals are constructed as linear combinations
of atomic orbitals with the restriction that the molecular orbitals form an orthonormal set; while mathematically convenient, the constraint that the set be orthogonal
is unrealistic and its removal should allow for constructing non-orthogonal LMOs. Presented is an original solution to Boys' functional for optimising the construction
of non-orthogonal molecular orbitals.