This chapter has described the theoretical framework for the calculations performed in this thesis. Sections and outlined the conceptual problem and an approach to its solution, namely Density Functional Theory. Sections though described a series of approximations made so that the calculations may be performed in a reasonable time with good accuracy. These approximations may be summarised as follows:
The implementation of this method for finding the ground state energy and charge density was discussed in Sections and . Once these quantities have been found, the ionic forces may be calculated and used as explained in Section . Finally, a post-hoc correction to the results obtained for charged systems was detailed in Section .
The methods described in this chapter have been implemented in the CASTEP  code for serial and vector computers and the CETEP  code on parallel machines. These codes have been used for all of the calculations described in this thesis.