Computer simulations of crystal structures using density functional theory

During past several decades, first principles pseudopotential methods based on density functional theory have provided the basis for the majority of first-principles calculations of the ground state electronic properties of a wide variety of condensed matter systems. However, as the numerical accuracy of these calculations has improved, it has become apparent that there are some sizable discrepancies between the calculations and the experimental measurements of the ground state properties of many of these materials. Part of the difficulty comes in determining the form of the exchange-correlation interaction, the local-density approximation (LDA) and generalized-gradient approximation (GGA) being the most common forms. It is important to explore the limits of density-functional theory and of the LDA and GGA forms of the exchange-correlation functional. Another difficulty lies in determining the accuracy of the frozen core approximation which is the basis of first-principles pseudopotential methods. In this context, simulations of the transition metal material FeS{dollar}sb2{dollar} and of the SiC (100) surface are very important.; This thesis describes an effort to simulate the ground state properties of materials using density functional theory (DFT) with focus on investigation of the exchange-correlation functional and the frozen-core approximation. Comparison of the calculations with experiments for FeS{dollar}sb2{dollar} and for the SiC (100) surface using first-principles pseudopotential and the all-electron linearized-augmented-plane-wave (LAPW) methods are analyzed. Advantages of using the recently developed new projector-augmented-wave (PAW) ideas, which reduce the gap between the all-electron LAPW and first-principles pseudopotential methods are discussed. Test results for bulk materials silicon, diamond, and SiC are presented.; Analysis of the reliability of the frozen-core approximation and of the pseudopotential theory for the cohesive energy indicates that for materials containing the transition metal Fe, the core effects, especially the treatment of Fe 3p semicore states, are important for optimizing the structures. All-electron calculations using an extension of the LAPW method with additional local orbitals improves the accuracy of the simulated FeS{dollar}sb2{dollar} geometry in comparison with the pseudopotential results. In contrast to the low-energy-electron-diffraction (LEED) experiments and some empirical methods, our calculation results for the SiC (100) surface using the first principles pseudopotential method show that there is virtually no reconstruction for the Si-terminated surface. All-electron LAPW calculations for this surface confirmed the results calculated from the pseudopotential method. For the C-terminated surface there are very stable carbon dimers.; Simulation of the bulk materials of silicon, diamond and SiC based on our new version of the PAW method shows that the accuracy of the PAW method is comparable with the all-electron LAPW method. The simplicity of the PAW method is comparable to that of the pseudopotential method, and it may be incorporated into the Car-Parrinello algorithm to become one of the most accurate and efficient computer simulation methods for materials.