Over the past few decades, advances in computing power and the continued development of efficient modelling techniques, capable of providing chemical accuracy, have made in silico crystal structure prediction (CSP) a reality. Armed with this powerful technique, it is now possible to explore the energy landscapes of unknown systems and predict stable phases with confidence. Having determined the structure of a material, many useful material properties, such as hardness, ionic conductivity and optical absorption spectra can then be calculated in a routine fashion. In this thesis, the ab initio random structure searching (AIRSS) approach is coupled with density-functional theory to study a variety of different, technologically relevant materials.

Firstly, the stable phases in two binary systems, MgS and NaGe, with promising battery chemistries were investigated. For MgS, the stability of S-rich polysulphide compounds observed during charge-discharge cycles was probed. As well as this, the stability of the hypothetical MgS₂ structure, predicted in a previous study, was investigated thoroughly with respect to choice of exchange-correlation functional, external pressure and temperature. A similar CSP study, motivated by the use of Ge as an anode in Na-ion batteries, was performed on the relatively unexplored NaGe binary system. A number of new phases are predicted to be stable at both 0 and 10 GPa leading to an increase in the theoretical capacity of the Ge anode. A neural network potential (NNP) was trained, tested and then used to expedite the searches performed on NaGe.

Following this, the Wyckoff Aligned Molecules (WAM) technique for generating symmetric trial structures using extended building units such as molecules or fragments was developed. This approach utilises the point group symmetry of these units to place them on compatible, high symmetry Wyckoff sites; the use of both general and special Wyckoff sites is crucial in providing complete coverage of search space. The WAM approach was coupled with AIRSS to perform CSP on a selection of metal-organic frameworks (MOFs) and high pressure phases of molecular methane. This work on MOFs is thought to be the first example of true ab initio structure prediction of a MOF, where no prior assumptions were made on the topology or coordination. The searches for methane recovered all stable phases predicted in previous work, after which a full structural model for methane B, based on the experimentally known carbon-substructure, was constructed. This model was then added to the predicted pressure-temperature phase diagram of CH₄.

Finally, the way in which symmetry constraints are applied during CSP is discussed, with a particular focus on the AIRSS method. The normalizers of space groups are used to show equivalence between various allocations of atoms across Wyckoff sites whilst group-subgroup relations are employed to illustrate the relation between such allocations within different space groups. These considerations highlight how some methods for applying symmetry constraints can lead to unwanted bias and suggestions are made as to how this may be alleviated.