the lack of eigenvalues and eigenfunctions limits the detailed knowledge of excitons, e.g., their real-space representation.[@note4]

The investigation of the fine structure of optical absorption spectra, especially near the absorption edge and for low energy optical transitions, requires finer *k*-point samplings than those necessary for the ground-state calculations. Due to the large number of bands and high cutoffs involved we have, however, to restrict ourselves to a rather limited number of *k*-points. For the GW and BSE calculations, we apply a $\Gamma$-centered 888 mesh. Furthermore, a sufficiently large number of conduction bands has to be included in the calculations to describe the electron-hole pair interaction properly. The number of empty states is limited by introducing a cutoff energy for the electron-hole single-particle transitions (without QP corrections) that contribute to the excitonic Hamiltonian of Eq.(\[eq:3\]). This transition energy cutoff was chosen to be 60 eV, corresponding to up to 50 unoccupied bands. A rank of the excitonic Hamiltonian matrix of the order of 210.000 results from this setup. In addition, for the calculation of the full frequency dependent dielectric function, screened exchange integrals, and four-orbit integrals in the GW and BSE schemes, one may introduce a lower plane-wave cutoff than for 