Ab initio methods for the calculation of the electronic excitation properties of semiconductors and insulators under regardment of many-particle effects

The accurate prediction and description of electronic excitation properties of real materials, like for instance the band structure or optical spectra, is one of the greatest challenges of modern solid-state theory. The essential difficulty lies hereby in the many-particle character of these excitation, so therein that generally because of the long-range Coulomb interaction very much electrons contribute to an excitation. An efficient description of electronic excitation properties becomes possible in the framework of the many-particle perturbation theory basing on the theory of Green's functions, especially together with the 1965 proposed GW approximation of the exchange-correlation self-energy. The thesis presented here is dedicated to equal parts to the development and study of methods for the calculation of the electronic excitation properties of semiconductors and insulators as well as to the application of these methods on the from physical and technical view intersetting materials indium nitride and indium oxide. In the first part of the thesis for this the commonly approach pursued in the calculation of quasi-particle energies is varied and the usefulness of starting points of the type of generalized Kohn-Sham functionals for the determination of the quasi-particle band structure studied. In the second part of the thesis the interest applies to the study of isolated excitonic excitations. For this a numerically very efficient approach is proposed, which allows the calculation of the energetically lowest exciton eigenvalues. The materials indium nitride and indium oxide are detailedly studied in this thesis and concerningly their properties compared with numerous actual experimental data. To the experiment not yet accessible properties are predicted