List of Figures

• Flow chart illustrating the VMC algorithm.
• Flow chart illustrating the parallel VMC algorithm.
• Flow chart illustrating the DMC algorithm.
• Illustration of different supercell sizes.
• Conventional unit cell of the diamond structure.
• Primitive unit cell of the FCC Bravais Lattice
• Convergence of the total energy with simulation cell size for different -point sampling schemes
• Schematic representation of the two components of the Ewald charge density.
• Schematic representation of the electron-ion interaction.
• Difference in the energy of VMC and DMC results for 2x2x2 bulk germanium in the diamond structure.
• Schematic representation of the reduction in the energy and variance of the energy during the optimisation process.
• Charge density along the Ge-Ge bond for different functions.
• Results of optimising the function.
• Dependence of on the angle between and
• Reduction of vectors into the Wigner-Seitz cell.
• Comparison of spin-parallel u functions for the HEG at .
• Comparison of QMC and LDA density for the germanium pseudo-atom.
• Variance minimisation on a parallel machine using the ``master-slave'' programming model.
• Total energy per atom calculated using VMC as a function of system size.
• Total energy per atom calculated using LDA as a function of system size.
• Total energy per atom calculated using HF, as a function of system size.
• Exchange-Correlation hole in diamond-structure silicon.
• VMC Charge density calculated for 3x3x3 diamond structure silicon plotted in the (110) plane through the centre of a silicon-silicon covalent bond.
• VMC results corrected using finite size errors from LDA calculations.
• VMC results using the new electron-electron potential.
• An illustration of the new interaction for a rhombohedral simulation cell.
• The energy per atom in diamond-structure silicon as a function of simulation cell size, from VMC calculations using the Ewald electron-electron interaction and the new interaction.
• The energy per atom of diamond-structure silicon as a function of simulation cell size, from HF calculations using the Ewald electron-electron interaction and the new interaction.
• Addition of a single electron to the simulation cell
• Possible excitations in 2x2x2 Silicon
• Calculation of the Band Width
• Excited states via Band Folding