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We present a new all-electron, augmented-wave implementation of the GW approximation using eigenfunctions generated by a recent variant of the full-potential LMTO method. The dynamically screened Coulomb interaction W is expanded in a mixed basis set which consists of two contributions, local atom-centered functions confined to muffin-tin spheres, and plane waves with the overlap to the local functions projected out. The former can include any of the core states; thus the core and valence states can be treated on an equal footing. Systematic studies of semiconductors and insulators show that the GW fundamental bandgaps consistently fall low in comparison to experiment, and also the quasiparticle levels differ significantly from other, approximate methods, in particular those that approximate the core with a pseudopotential.

We present a new all-electron, augmented-wave implementation of the GW approximation using eigenfunctions generated by a recent variant of the full-potential LMTO method. The dynamically screened Coulomb interaction W is expanded in a mixed basis set which consists of two contributions, local atom-centered functions confined to muffin-tin spheres, and plane waves with the overlap to the local functions projected out. The former can include any of the core states; thus the core and valence states can be treated on an equal footing. Systematic studies of semiconductors and insulators show that the GW fundamental bandgaps consistently fall low in comparison to experiment, and also the quasiparticle levels differ significantly from other, approximate methods, in particular those that approximate the core with a pseudopotential.

Progress in a long-standing objective in computational materials science, the calculation of alloy phase diagrams from first-principles, has been paced by the associated problems of accurate yet efficient total-energy calculations and statistical approximations of the alloy partition function. The former is well understood, and the evolution of Density-Functional Theory (DFT) to computationally suitable methods using the Local-Density Approximation (LDA) is a renowned (though, arguably, a qualified) success. The high precision required of the total-energy band-structure methods for phase-equilibrium calculations is attainable for most chemical systems. The connection between the total-energy calculations and a general solution to the Ising problem is provided by a cluster expansion in a series of multi-atom interaction energies. This rigorous expansion my be inverted to calculate the total energy of any lattice configuration using the multi-atom interactions. Two main aspects of the cluster expansion method remain unresolved: the convergence of the expansion and the effect of strain energy on the convergence. These two issues are central to this thesis, and a major portion of this study is devoted toward a resolution.

We present a new full-potential method to solve the one-body problem, for example, in the local density approximation. The method uses the augmented plane waves (APWs) and the generalized muffin-tin orbitals (MTOs) together as basis sets to represent the eigenfunctions. Since the MTOs can efficiently describe localized orbitals, e.g, transition metal 3$d$ orbitals, the total energy convergence with basis size is drastically improved in comparison with the linearized APW method. Required parameters to specify MTOs are given by atomic calculations in advance. Thus the robustness, reliability, easy-of-use, and efficiency at this method can be superior to the linearized APW and MTO methods. We show how it works in typical examples, Cu, Fe, Li, SrTiO$_3$, and GaAs.

The structural and electronic properties of cubic GaN are studied within the local density approximation by the full-potential linear muffin-tin orbitals method. The Ga $3d$ electrons are treated as band states, and no shape approximation is made to the potential and charge density. The influence of $d$ electrons on the band structure, charge density, and bonding properties is analyzed. It is found that due to the energy resonance of the Ga 3$d$ states with nitrogen 2$s$ states, the cation $d$ bands are not inert, and features unusual for a III-V compound are found in the lower part of the valence band and in the valence charge density and density of states. To clarify the influence of the Ga $d$ states on the cohesive properties, additional full and frozen--overlapped-core calculations were performed for GaN, cubic ZnS, GaAs, and Si. The results show, in addition to the known importance of non-linear core-valence exchange-correlation corrections, that an explicit description of closed-shell repulsion effects is necessary to obtain accurate results for GaN and similar systems. In summary, GaN appears to be somewhat exceptional among the III-V compounds and reminiscent of II-VI materials, in that its band structure and cohesive properties are sensitive to a proper treatment of the cation $d$ bands, as a result of the presence of the latter in the valence band range.

The structural and electronic properties of cubic GaN are studied within the local density approximation by the full-potential linear muffin-tin orbitals method. The Ga $3d$ electrons are treated as band states, and no shape approximation is made to the potential and charge density. The influence of $d$ electrons on the band structure, charge density, and bonding properties is analyzed. It is found that due to the energy resonance of the Ga 3$d$ states with nitrogen 2$s$ states, the cation $d$ bands are not inert, and features unusual for a III-V compound are found in the lower part of the valence band and in the valence charge density and density of states. To clarify the influence of the Ga $d$ states on the cohesive properties, additional full and frozen--overlapped-core calculations were performed for GaN, cubic ZnS, GaAs, and Si. The results show, in addition to the known importance of non-linear core-valence exchange-correlation corrections, that an explicit description of closed-shell repulsion effects is necessary to obtain accurate results for GaN and similar systems. In summary, GaN appears to be somewhat exceptional among the III-V compounds and reminiscent of II-VI materials, in that its band structure and cohesive properties are sensitive to a proper treatment of the cation $d$ bands, as a result of the presence of the latter in the valence band range.