The thesis is broadly arranged into three sections:

Electronic structure methods are introduced and details of Quantum Monte Carlo methods are given in chapters 2 - 4. In chapter 2, density functional and several quantum chemical methods are reviewed and their advantages and disadvantages presented. Chapter 3 introduces the two most important QMC methods: variational and fixed-node diffusion Monte Carlo. Several key results are derived. The computational realisation of the methods is described in chapter 4.

In chapters 5 and 6, two QMC techniques are developed and their utility verified. In chapter 5, many techniques for optimising many-body wavefunctions are tested and an efficient optimisation procedure proposed. The treatment of finite size effects, due to the supercell approximation used for periodic systems, is examined in chapter 6. A modified form of Coulomb interaction is shown to significantly reduce finite size effects.

Finally, two specific applications of QMC are presented: In chapter 7, the one-body density matrix of the valence electrons of bulk silicon is computed using a correlated wavefunction. The band structure of silicon is also determined using an extension of Koopmans' theorem. In chapter 8, the energetic (zero temperature) stability of small carbon clusters, including fullerenes, are examined. QMC calculations are used to identify the smallest energetically stable fullerene and analyse the performance of currently popular density functionals.

In chapter 9, the results obtained are summarised and an outline given for future work in the field.