This thesis describes the dimer method, which is an algorithm that can be used to find state transitions in an atomistic system, and the application of this method to two different atomistic diffusion problems. The dimer method is an algorithm that locates the saddle points of a potential field of arbitrary dimensionality. These saddle points correspond to the points of transition between metastable states of an atomistic system. A number of improvements to the algorithm of the dimer method have been described and implemented in this work. The first atomistic problem to be described is the diffusion of Au adatoms on a face-centred cubic Au(100) surface. By applying the dimer method to this system, a number of state transitions involving varying numbers of atoms are discovered, from the initial configuration of a single adatom on the surface and from configurations of two adatoms close together.
