In chapter , the two QMC methods used for the calculations in the rest of this thesis, the Variational quantum Monte Carlo (VMC) and Diffusion quantum Monte Carlo (DMC) method are introduced. Details of the algorithms used to implement these methods on serial and parallel computers are given.
In chapter , the specific details of how to perform a QMC calculation on a solid using the supercell technique are given. The choice of wavefunction and evaluation of Coulomb interactions are discussed.
Chapter describes our application of the variance minimisation, optimisation technique to the problem of producing trial/guiding wavefunctions for use in QMC calculations of solids. Again details are given of the algorithm used and how to implement it on both serial and parallel computers. New functional forms of wavefunction are introduced, that yield comparable if not improved accuracy over traditional functional forms, are more suitable for optimisation and are considerably faster to evaluate within a QMC code.
Chapter describes new forms of electron-electron interaction that are designed to dramatically reduce the troublesome Coulomb finite size effects present in QMC supercell calculations.
The technical advances made to the QMC technique described in chapters and are brought together in chapter to enable us to attempt a new application of QMC - the calculation of excitation energies. Two separate methods of evaluating excitation energies within QMC are, (i) the addition and subtraction of electrons and (ii) the promotion of electrons. Both these techniques require energies to be evaluated to at least an order of magnitude higher accuracy than previous QMC calculations. The results obtained from the two techniques are compared both with each other and with the results of more established electronic structure techniques.
Finally, in chapter , some conclusions on the work are drawn.