Development and application of advanced methods for electronic structure calculations

This thesis relates to improvements and applications of beyond-DFT methods for electronic structure calculations that are applied in computational material science. The improvements are of both technical and principal character.
The well-known GW approximation is optimized for accurate calculations of electronic excitations in two-dimensional materials by exploiting exact limits of the screened Coulomb potential. This approach reduces the computational time by an order of magnitude, enabling large scale applications.
The GW method is further improved by including so-called vertex corrections. This turns out to yield ionization potentials and electron affinities that are in better agreement with experiments for both bulk and 2D materials. This newly developed method requires the calculation of an exchange-correlation kernel known from time-dependent DFT. The computational cost of the kernel is negligible compared with the cost of the GW calculation itself, and the kernel even improves the convergence performance. Literature shows and this thesis confirms that the representation of the individual atomic elements through their PAW setup crucially affects the results of GW calculations. For this reason, part of this thesis relates to developing and applying a new method for constructing so-called norm-conserving PAW setups, that are applicable to GW calculations by using a genetic algorithm. The effect of applying the new setups significantly affects the absolute band positions, both for bulk and 2D materials. The new PAW setups are used for producing most of the results presented in this thesis.
A lack of accurate experimental and theoretical data on adsorption energies, relevant to surface chemistry and catalysis, are identified. The RPA method and beyond, that is known to yield accurate ground state energies, is used to calculate accurate adsorption energies for a wide range of reactions. The results are in good agreement with experimental values, where available. Additionally, a database consisting of 200 highly accurate adsorption energies is constructed to benchmark the accuracy of current DFT functionals and to guide future development of new xc functionals for DFT, especially useful for surface science.
Given the accuracy of existing DFT functionals, they were in turn applied in search for catalysts to be used in electrochemical methanol production from methane. Two different types of surfaces were investigated for this reaction; the (110) surface of rutile transition metal oxides and a fairly new class of two-dimensional materials called MXenes. Promising candidates were found within the MXenes.