Improved wave functions for quantum Monte Carlo

Quantum Monte Carlo (QMC) methods can yield highly accurate energies for correlated quantum systems. QMC calculations based on many-body wave functions are considerably more accurate than density functional theory methods, and their accuracy rivals that of the most sophisticated quantum chemistry methods. This thesis is concerned with the development of improved wave function forms and their use in performing highly-accurate quantum Monte Carlo calculations. All-electron variational and diffusion Monte Carlo (VMC and DMC) calculations are performed for the first-row atoms and singly-positive ions. Over 98% of the correlation energy is retrieved at the VMC level and over 99% at the DMC level for all the atoms and ions. Their first ionization potentials are calculated within chemical accuracy. Scalar relativistic corrections to the energies, mass-polarization terms, and one- and two-electron expectation values are also evaluated. A form for the electron and intracule densities is presented and fits to this form are performed. Typical Jastrow factors used in quantum Monte Carlo calculations comprise electron-electron, electron-nucleus and electron-electron-nucleus terms. A general Jastrow factor capable of correlating an arbitrary of number of electrons and nuclei, and including anisotropy is outlined. Terms that depend on the relative orientation of electrons are also introduced and applied. This Jastrow factor is applied to electron gases, atoms and molecules and is found to give significant improvement at both VMC and DMC levels. Similar generalizations to backflow transformations will allow useful additional variational freedom in the wave function. In particular, the use of different backflow functions for different orbitals is expected to be important in systems where the orbitals are qualitatively different. The modifications to the code necessary to accommodate orbital-dependent backflow functions are described and some systems in which they are expected to be important are suggested