Enabling More Accurate Calculation Of Thermoelectric Properties From Density Functional Perturbation Theory.

Significant progress has been made over recent years in improving the accuracy of density functional approximations for electronic structure simulations. The advent of the so called ``meta generalised gradient approximations'' (meta-GGAs) has significantly improved the chemical accuracy possible using density functional theory methods, with minor additional computational cost. However, the introduction of meta-GGAs poses additional challenges that need to be overcome. Much work has been done to develop the formalism of density functional perturbation theory as an accurate and efficient method to calculate material properties; however, the formalism must be extended to enable such calculations using meta-GGA functionals. In addition to this, following the development of the first successful meta-GGAs, it was quickly observed that many meta-GGA functionals suffer from severe numerical instability, which can have significant effects on the physical properties predicted by electronic structure simulations. This thesis gives details of the necessary steps to extend the framework of density functional perturbation theory calculations of material properties with meta-GGA functionals, as well as approaches to quantify and address the numerical instability present in calculations using meta-GGAs. This is then applied to the calculation of commonly calculated material response functions, phonon modes and elastic constants tensors. The developed methods are verified against finite difference calculations.