| Density functional theory (DFT) has become the workhorse of computational chemistry and physics in the past two decades. The continuous developments of high-quality exchange-correlation functionals (xcFs) have enabled chemists and physicists to study complex as well as large systems with high accuracy at low-to-moderate computational expense. Although a wide range of normal systems have been well understood by DFT, there are still complex ones presenting particular challenges where most commonly used xcFs have failed due to the complex nature of the system, lack of or difficulty to obtain reliable reference data, or the practical limitations of the Kohn-Sham DFT (KS-DFT) formulation.;This thesis presents studies with various exchange-correlation functionals on a wide selection of complex systems in chemistry and solid-state physics, including large organic molecules, adsorption on metallic surfaces, transition states, as well as transition metal atoms, ions, and compounds, to (i) draw conclusions upon recommendations of xcFs for important practical applications; (ii) understand the root of errors to help design better xcFs or propose new theoretical schemes of DFT; (iii) explore the utility of noncollinear spin orbitals in KS-DFT for better description of multi-reference systems. |
