Crystal structure prediction based on density functional theory

The atomic arrangements in solids fundamentally govern the physical properties of a material. In solid state physics, resolving the crystal structure is therefore one of the key approaches when investigating novel materials. However, experimental methods to determine the crystal structure can be very difficult, expensive, or even impossible, depending on the problem and external conditions applied to the material. Examples are high pressure experiments, where accessible pressures are limited to roughly 400 GPa, or investigations of materials with constituents that cannot be detected in X-ray diffraction experiments. Furthermore, investigating crystal structures is not only fundamental in material science, but also in chemistry, biology and pharmacy. Therefore, efficient computational methods for predicting crystal structures based solely on the system's composition would provide a powerful tool with wide scientific applications.
In 1994, Angelo Gavezzotti published an article titled ``Are Crystal Structures Predictable?'', providing simultanously the simple answer: ``no''. Meanwhile, with increasing computational resources, the situation has changed and prediction of crystal structures from first principle calculations has become feasible, while still remaining a demanding task. In 2004, the minima hopping method was developed and has there-since been successfully applied to predict structures in a wide range of non-periodic systems. In this thesis, we present an extended version of the minima hopping method for crystal structure prediction by generalizing the efficient search algorithm for finding the most stable structures within any periodic system. As applications of this approach, we investigated binary Lennard-Jones benchmark mixtures, silicon crystals, high pressure phases of carbon resulting from cold compressed graphite, superconduction phases in disilane and low energy structures in the hydrogen storage material LiAlH4.