Enormous advances in computing power in recent decades have made it possible to perform accurate numerical simulations of a wide range of systems in condensed matter physics. At the forefront of this progress has been density functional theory (DFT), a very popular approach to tackling the complexity of quantum-mechanical systems that very often strikes a good balance between accuracy and tractability in light of the finite computational resources available to researchers.

This thesis describes work utilising DFT methods to tackle two distinct problems. Firstly, the theoretical prediction of stable and metastable periodic structures under specified conditions using the ab initio random structure searching (AIRSS) method, which involves a large scale exploration of the Born-Oppenheimer energy surface, and secondly the use of a vibrational self-consistent field (VSCF) approach to investigate the effects of nuclear motion and anharmonicity in crystal systems, which involves a local exploration of the Born-Oppenheimer energy surface.

The AIRSS crystal structure prediction method is here applied to a study of defect structures in graphene. It is also applied to a study of the xenon-oxygen binary system under a range of geological pressures (83–200 GPa). Novel xenon oxide structures are predicted and characterised theoretically. This work was carried out in collaboration with an experimental study of the system at the lower end of the pressure range.

The VSCF approach to investigating anharmonicity is here applied to the study of tin selenide (SnSe), a material that has recently been shown to demonstrate consider- able promise as a thermoelectric material. In this thesis, the effects of the anharmonic nuclear motion on the vibrational and electronic properties of SnSe are investigated quantitatively.