The thesis is arranged as follows. Chapter 2 describes the technique of ab initio molecular dynamics used to calculate the properties of two complex structures of carbon, silicon and germanium in Chapter 3. It is found that ab initio methods are too compute intensive for a full free energy calculation and therefore empirical methods are used to calculate the full pressure-temperature phase diagram of these complex structures. One of these structures, BC8, is found to have several natural (001) cleavage planes. Several possible reconstructions of these surfaces are considered for silicon in Chapter 5. Since it is short range correlations that govern the properties of amorphous materials, the local bonding topologies found in point defects within the diamond structure are also likely to be found in the amorphous structure. Several point defects are therefore investigated by both ab initio and empirical molecular dynamics in Chapter 6. Finally, in Chapter 7, relaxed structures of randomly packed silicon and carbon atoms are examined in order to make a comparison between the complex crystals and their amorphous counterparts.