X-ray absorption using the projector augmented-wave method and the Bethe-Salpeter equation

We present an implementation of the Bethe-Salpeter equation (BSE) for core-conduction band pairs within the framework of the projector augmented-wave method. For validation, the method is applied to the $K$ edges of diamond, graphite and hexagonal boron-nitride, as well as four lithium-halides (LiF, LiCl, LiI, LiBr). We compare our results with experiment, previous theoretical BSE results, and the density functional theory-based supercell core-hole method. In all considered cases, the agreement with experiment is excellent, in particular, for the relative position of the peaks as well as the fine structure. Comparing BSE to supercell core-hole spectra, we find that the latter often qualitatively reproduces the experimental spectrum, however, it sometimes lacks important details. This is shown for the $K$ edges of diamond and nitrogen in hexagonal boron nitride, where we can resolve within the BSE experimental features that are lacking in the supercell core-hole method. Additionally, we show that in certain systems the supercell core-hole method performs better if the excited electron is added to the background charge rather than to the lowest conduction band. We attribute this improved performance to a reduced self-interaction.