This thesis is concerned with the development and application of <i>quantum Monte Carlo </i>(QMC) methods for calculating the energies of atoms, molecules and solids from first principles. Several modifications to the variational and diffusion Monte Carlo (VMC and DMC) methods are investigated. It is shown that biases due to the use of finite time steps largely cancel when the ionisation energy of neon is calculated. A new form of trial wave function, which is more flexible and computationally efficient than existing forms, is proposed for use in QMC simulations. Results obtained with the new trial wave function are analysed and discussed. The results of an investigation into some aspects of a class of QMC methods in which the computer time is proportional to the square of the number of particles simulated are given. It is found that the least biased method of truncating localised orbitals is to cut them off abruptly. The results of applying QMC methods to two different electronic systems are presented: (i) An accurate calculation of the density at which a three-dimensional uniform gas of electrons will crystallise at zero temperature is described. The DMC energy of the crystalline phase is evaluated at different densities, and the point at which the energy curve crosses that of the fluid phase is located. (Accurate energy data for the fluid phase are already available). The transition density is found to be <i>r<sub>s</sub></i> = 106 ± 1 a.u. (ii) DMC calculations of the <i>optical gaps </i>of various nanometre-sized diamond molecules are reported. It is found that molecules which are smaller than about 1 nm have larger optical gaps than bulk diamond. These <i>quantum-confinement </i>effects are not found to be present in molecules with diameters in excess of 1 nm. The electron affinity of C<sub>29</sub>H<sub>36</sub> is found to be negative.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:598657 |
| Date | January 2004 |
| Creators | Drummond, N. D. |
| Publisher | University of Cambridge |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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