Ab initio modelling of low-dimensional systems

In this thesis, theoretical electronic structure methods have been used to study systems of interest to materials science and engineering. The many-body problem of quantum mechanics has been reviewed, and it has been explained that the density functional theory (DFT) of Hohenberg, Kohn and Sham is a very practical approach to solving it. The core details of DFT have been explicitly laid out. Having then demonstrated an awareness of the many different powers and varied capabilities of DFT in predicting material properties, systems laying at the current frontiers in nanoelectronics (chapters 3 and 5) and theoretical surface science (chapter 4) have then been focused on. In chapter 3, the behaviour of metal adatoms on graphene substrates has been predicted using DFT. From adatom binding energy and migration energy calculations, it has been theoretically suggested that single Cr, Au and Al adatoms diffuse randomly on graphene at room temperature until they collide with edge sites or defects, where they form stable bonds. This prediction has been used to explain experimental electron microscopy data which shows that metal adatoms evaporated onto graphene by chemical vapour deposition (CVD) have only ever been observed at edge sites and defects, and never on the pristine regions. In chapter 4, a new methodology has been developed for predicting the energies of step defects on crystalline solid surfaces, and it has been applied to steps on the (110) surface of TiO2 rutile. The limitations of currently published methods of calculating step energies have been explained in detail, and it has been demonstrated that this new method is much more reliable. The method has been used to predict the shape of a terrace island on the (110) surface of TiO2 rutile, and the prediction has been found to compare well with published experimental electron microscopy data. In chapter 5, current progress on an ongoing project has been summarised which investigates whether there is an energetic advantage to multiple substitutional nitrogen dopants in graphene occupying the same sublattice. The results are inconclusive so far, although it has been shown so far that magnetic effects are unlikely to be playing a role. In chapter 6, the accomplishments of this thesis have been summarised and future directions suggested.