Summary

 

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:

• LDA or GGA to exchange-correlation potential (Section )
• choice of a converged plane-wave basis set (Section )
• imposition of periodic boundary conditions (Section )
• discrete k-point sampling within the Brillouin zone (Section )
• pseudopotential approximation (Section )

These approximations differ from those made in non-first principles approaches in that they depend on general physical and chemical principles and not on the specific interactions within the system to be investigated. Section described a correction to the conventional pseudopotential approximation that gives greater accuracy when considering spin dependent potentials.

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 [5] code for serial and vector computers and the CETEP [42] code on parallel machines. These codes have been used for all of the calculations described in this thesis.