| In the first part of this thesis, the modified weighted density approximation of classical density functional theory is extended to higher order and is shown to be an example of a more general approach, which introduces considerable functional freedom. This is shown to arise from the introduction of scaling functions which can be set by imposing known physical limits on the generally unknown excess free energy functional. Results are presented for the melting of classical hard spheres using functionals accurate to a third-order functional Taylor series in the homogeneous limit. A uniform improvement in the solid phase free energies, pressures and melting parameters is found when a third-order theory is used and further improvement results when these functionals are also optimized using the close packing limit. Required input into the third order theories are the triplet direct correlation functions (DCFs) of the uniform phase. In this thesis several related approaches are introduced that lead to simple and in some cases analytic calculation of triplet DCFs which obey exactly the known sum rule relating them to the derivative of the Ornstein-Zernike function.; The second part of this thesis is concerned with topics in the area of electronic structure calculations (also inhomogeneous systems in general). An efficient method is presented for finding ghost states in separable non-local pseudopotentials with an arbitrary number of projector functions. These solutions, which arise in the application of iterative diagonalization methods, can ruin a calculation if gone undetected. Finally, we use the all-electron linearized augmented plane wave (LAPW) method, to calculate the effect of including gradient corrections to the exchange correlation functional on the structural properties of the simple metal Al, transition metals Ta, W, Pt, and noble metals Cu, Ag, Au. The generalized gradient functional introduced by Perdew and Wang (PW91) yields corrections that are in the right direction (larger bond-lengths and smaller bulk moduli than given by the local density approximation), but it frequently over compensates. |
