Heyd-Scuseria-Ernzerhof screened exchange hybrid functional for complex materials : all-electron implementation and application

The design of suitable materials for application in future devices requires a detailed understanding of their electronic and structural properties. The ab initio method density functional theory (DFT) has emerged as the most commonly applied technique based on its high accuracy predicting characteristics of a wide range of materials. The limits of the predictive power of DFT are set by the availability of precise approximations to the exchange-correlation functional. In this thesis, we developed a scheme to realize screened nonlocal potentials within the full-potential linearized augmented plane-wave (FLAPW) method and applied it, in particular, to the screened Heyd-Scuseria-Ernzerhof (HSE) functional. Incorporating a certain fraction of nonlocal exchange, hybrid functionals improve on the conventional local functionals by partly correcting for the spurious self interaction. This self interaction is most prominent in materials with localized states, so that we expect an improved description of transition-metal and rare-earth compounds. The strong localization of the d and f electrons in these materials complicates a description by pseudopotential methods, so that they are particularly suited for the all-electron FLAPW scheme. The nonlocal exchange is computationally very demanding, hence, we discuss two approximations to improve the computation time of hybrid functional calculations: a spacial restriction of the nonlocal exchange and the employment of a smaller k-point mesh in the calculation of the nonlocal exchange. We demonstrate that both schemes are feasible for selected materials, but not in general for all materials. Employing our implementation of hybrid functionals, we analyze the electronic, structural, and magnetic properties of the rare-earth compounds GdN, EuO, EuS, EuSe, and EuTe and compare to results of DFT+U calculations from the literature. We find that GdN is close to a semi-metal/semiconductor phase transition, which may explain that both states are observed experimentally. In the EuX series, we reproduce the major trends in the series, i.e., the opening of the band gap as well as the transition from a ferromagnetic to an antiferromagnetic ground state. In a systematic study of several simple cubic perovskites, we assess the improvement of the HSE hybrid functional over the local PBE functional concerning the prediction of the lattice constant and the band transitions. Finally, we analyze the ground state of PbCrO3, where the experimental semiconducting ground state could not be reproduced in previous DFT calculations. We determine the relaxed structure for all possible space groups, which are accessible by a combination of tilting and Jahn-Teller distortion of the oxygen octahedra as well as a polar displacement. Depending on the Hubbard U employed in the calculation, we obtain two different energetically optimal structures. Both structures exhibit a band gap and a polar displacement indicating that PbCrO3 may be multiferroic