Implementation and application of advanced density functionals
Density functional theory (DFT) is a method of effectively solving the many-electron Schrödinger equation, enabling the properties of condensed matter systems to be calculated from first principles. With the commonly used local density approximation (LDA), and generalised gradient approximations (GGAs), to the exchange correlation functional, it is currently possible to perform calculations on systems containing several hundred atoms. The accuracy of such calculations depends on the system under study and on which particular properties one wishes to calculate. The use of more advanced functionals has the potential to improve accuracy, at the expense of greater computational demand. In this work we use the LDA to calculate certain properties of GaN, such as geometry, band structure, and surface properties, including the reconstruction of GaN surfaces under the presence of hydrogen. We then describe our computational implementation of advanced density functionals, including screened exchange (sX-LDA), Hartree-Fock (HF), and exact exchange (EXX), within an efficient, fully parallel, plane wave code. The implementation of sX-LDA and HF is used to calculate band structure properties of Si, GaN, and other simple semiconductors, and it is found that sX-LDA can improve results significantly beyond the LDA. We also derive and implement the theory that allows one to calculate directly the contribution to the stress tensor from exchange and correlation when using these functionals, and demonstrate this with some simple test cases. Finally, we introduce some new theoretical ideas that may pave the way for yet more accurate density functionals in the future.