This thesis deals with theoretical investigations of the electronic structure of conjugated carbon based materials. Novel materials like the C60 fullerene and the carbon nanotubes, but also the more well known, but closely related, graphite phase of carbon were studied. In addition, low dimensional structures like conjugated polymers and DNA, containing other atoms besides carbon, were investigated.

The recently discovered fullerene phase of carbon, especially the C60 molecule  has obtained a lot of attention among researchers. It has been observed that C60 under certain conditions can form linear polymeric chains, as well as two-dimensional polymeric structures. In the work presented in this thesis, Hückel model parameters have been developed for describing the intermolecular bonds within single bonded C60 polymers. These parameters were used in simulations to establish a simple rule explaining the phase diagram of the observed single bonded C6o polymer structures, namely that each electron added to a C60 monomer stimulates the creation of one single bond to a neighbouring C60 anion. A similar study on graphite was also performed, yielding Hückel parameters which describe the complicated bonding structure

surrounding an atomic vacancy in the graphite. From calculations on large graphitic sheets containing several vacancies, insight was gained of the electronic properties associated with such defects, leading to a better understanding of Scanning Tunnelling Microscopy images of defected graphite.

In one-dimensional materials, disorder is known to have an immense effect on electron localisation, seriously affecting the transport properties of these materials. Conjugated polymers and carbon nanotubes are not perfectly one-dimensional, but are often referred to as quasi one-dimensional. In this thesis, work is presented that deal with electron localisation in disordered quasi one-dimensional materials, studied at the Hückel level. To do this, a new method was developed for obtaining the transfer matrix, from which the localisation length of the electronic wave function can be deduced. This was applied to some conjugated polymers and carbon nanotubes using various kinds of disorder. It was shown that it is meaningful to speak about different dimensionalities for quasi one-dimensional systems, and that this is an important concept for understanding localisation in these materials. Furthermore, disorder induced localisation in metallic carbon nanotubes was shown to be independent on tube chirality. By treating functionalisation of nanotubes as a disorder, it was also concluded that such a process may significantly lower the conductance of the tubes. This effect may be utilised in chemical sensors based on carbon nanotubes.

The charge migration process in DNA is subject to a lively debate among researchers at the moment. The possibility to use DNA in molecular electronics has triggered an extensive study of the subject, but contradicting experimental findings exist in literature. In the work presented in this thesis the Landauer formula, combined with a pseudo potential method was used for calculating the current through the synthetic poly(G)-poly(C) form of DNA. These calculations substantiate a recent report which indicates band like conduction for this particular form of DNA. The conductivity results from overlap of the 1r-orbitals along the DNA base stacks. It was also demonstrated that the observed increase of the threshold voltage with temperature in poly(G)-poly(C) DNA is the result of electron localisation due to the structural fluctuations associated with temperature.