| Computational simulation has become an important tool in material science, for both understanding experiment results and predicting unknown material properties. In this thesis, we focus on two basic problems: how to perform fast quantum mechanics simulations for large scale features in materials and how to apply highly-accurate quantum mechanics methods to materials while keeping the computational cost affordable.;For the first problem, we work on the orbital-free density functional theory (OF-DFT). Unlike any other orbital-based methods, in OF-DFT the total energy is formulated solely based on electron density, which makes OF-DFT a promising linear-scaling method for material simulations. The most challenging part in OF-DFT is to construct a good approximation to the Kohn-Sham kinetic energy density functional (KEDF). A second challenge is to accurately describe the electron-nuclear interaction. In this thesis, we introduce a new KEDF for semiconductors, based on the low-q limit of the response function in semiconductors. We also discuss attempts to formulate KEDFs for treating transition metals and phase changes in semiconductors. We also describe an efficient means of constructing accurate local electron-ion pseudopotentials.;To tackle the second problem, we work on the density-based embedding theory, in which the material is divided into a local region of interest (a cluster) and the rest of the material (the environment). The cluster is treated with highly-accurate quantum mechanics methods, and the environment is replaced with an embedding potential. We first introduce a constraint to remove the non-uniqueness in conventional embedding potentials and show how one can eliminate use of approximate KEDF potentials that were employed in previous density-based embedding theories. Then we propose a unified potential-functional embedding theory which couples the cluster and its environment in a seamless and self-consistent way. Studies on large systems, in which detailed electronic structures of local region are required, are made possible with this novel embedding theory, for example, the excitation and polarization of molecules on surfaces which is related to photocatalysis.;Lastly, we introduce an efficient direct minimization method for calculating an optimized effective potential (OEP). An OEP is required for solving the KS equations when orbital-dependent exchange-correlation functionals (ODXCFs) are employed. Compared with other widely-used electron-density-based XCFs, ODXCFs have many striking advantages, such as being free of self-interaction error and reproducing the discontinuity of XC potential during charge transfer. However, the traditional integral equations for calculating an OEP are cumbersome to solve. With our efficient direct minimization method, it is now possible to apply KS-DFT-ODXCFs calculations to many important problems, such as spin canting in molecules, local torque on spins in spin devices, electric response in molecules, etc. |
