Structure of icosahedral quasicrystals and density-matrix functional theory for correlation effects

In the first part of this work, the atomic and electronic structure as well as the energetics of the icosahedral TiZrNi quasicrystal and the 1/1 approximant W-TiZrNi were determined. An atomic decoration model for the quasicrystal was developed invoking similarities to the structure of the 1/1 approximant. The structure of the quasicrystal was refined using a combined approach of diffraction refinement and ab initio calculations. The ternary ground state phase diagram was calculated using density-functional calculations. It was found that the TiZrNi quasicrystal is lower in energy than the competing phases indicating that it is a ground state quasicrystal. The electronic density of states of the quasicrystals shows a pseudogap. The hydrogen site energy distribution of the approximant was calculated and it was shown that a determination of the distribution by chemical potential measurements is impossible due to its complexity and the strong temperature and concentration dependent hydrogen-hydrogen interactions.; In the second part of this work a density-matrix functional for isolated impurities was developed. The density-matrix functional for the electron interaction energy, was based on two theorems proved in this work. It was shown that the second-moment approximation yields the exact ground state for a dimer molecule with arbitrary on-site and inter-site Coulomb interactions. The second-moment approximation is implemented as a variational method. By comparison to results from exact diagonalization and the Hartree-Fock method it was shown that the functional was accurate in the case of isolated impurities. The combined effect of disorder and electron interactions for the model of an Anderson impurity in a random alloy were investigated and unexpected crossover behavior in the effects of disorder and electron interactions on the spin fluctuations was found. As a first application of the second-moment approximation, the electronic structure of dangling-bond defects in amorphous silicon was studied. In the second-moment approximation the splitting of the defect state in the energy gap is smaller than expected from Hartree-Fock calculations and approaches a finite limit of 0.55 eV for large values of the Coulomb repulsion. In agreement with experimental results and spin-polarized density functional calculations, it was found that the spin of the defect state is strongly localized on the dangling bond orbital while the charge is mostly delocalized.