Accuracy of the pseudopotential approximation in ab initio theoretical spectroscopies

A large number of today\textquoterights ab initio calculations, in particular in solid-state physics, are based on density-functional theory using first-principles pseudopotentials. This approach, initially developed for the ground state, is nowadays widely used as a starting point for the calculation of excited-state properties, as, for instance, those involved in optical spectroscopy. In this paper we investigate the validity and the accuracy of the pseudopotential approximation, analyzing how different choices within the latter can influence the calculated electronic response of silicon and silicon carbide. We consider norm-conserving first-principles pseudopotentials, both in the fully nonlocal (Kleinman-Bylander) and the semilocal forms, with different choices for the reference (local) component. The effects of the inclusion of outer-core states in the valence shell are analyzed in order to obtain a detailed comparison with all-electron calculations. We present accurate results for different pseudopotential descriptions of Kohn-Sham and quasiparticle band structures and of many spectroscopic quantities in the linear and the nonlinear response regimes for different momentum transfers Q. Moreover, the effects of the pseudopotential nonlocality have been analyzed for electron-energy-loss spectra in the limit of vanishing momentum transfer. Our results show that the pseudopotential approximation can be quite safely applied to excited-state calculations, even when they involve Kohn-Sham eigenvalues and eigenvectors several tens of eV above the Fermi energy.