Summary

The five approximations discussed: LDA, GGA, MGGA, hybrid and WDA, represent the main functionals that have been proposed. Since the aim of this thesis is to improve the current status of functional development, it is first necessary to ascertain what the best type of functional is to develop. To help make this decision, a summary of the five types is given in Table 2.1, which compares the main features of each functional, with specific reference to principle exact conditions. The last column entitled ``Exact'' refers to the exact functional (2.9) given by the adiabatic connection method.

Table 2.1: Summary of the main characteristics of the different exchange-correlation functionals and which exact properties are obeyed. The last column refers to the exact functional defined by (2.9).

It is clear from this table that the WDA seems the logical choice for functional development since it obeys the most exact conditions. Another factor is that a fully self-consistent version of the WDA is implementable within a plane-wave code, which is difficult for the MGGA and hybrid functionals. As a consequence, the WDA will form a major part of this thesis. However before the WDA is investigated, a highly flexible GGA containing $15$ fitted parameters is studies in the next chapter to assess whether the GGA form has actually reached the limits of its accuracy.