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We present an accurate method for computing X-ray photoelectron spectra based on the GW approximation that overcomes the limitations of density functional theory (DFT) approaches. The GW method is routinely used to predict charged valence excitations in molecules and solids. However, GW core-level spectroscopy has thus far been poorly explored. This in parts related to the fact that numerically very efficient techniques such as the analytic continuation, which treat the frequency dependence on the imaginary axis, break down for inner-shell excitations. We implemented a full-frequency approach on the real axis in the all-electron code FHI-aims [1] using a localized basis to enable the treatment of core levels in GW [2]. Our scheme is based on the contour deformation technique and facilitates precise and efficient calculations of the self-energy, which has a complicated pole structure for core states. We present benchmark studies for 1s excitations of small- and medium-sized molecules and discuss the optimization of the starting point as well as self-consistent approaches. We find that the absolute core-level binding energies deviate on average by less than 0.5 eV from experiment outperforming the DFT-based Delta Self-Consistent Field approach. Relative core excitations are also well reproduced with average deviations of less 0.2 eV from the experimental reference. Furthermore, our calculations reveal that the GW excitation spectrum exhibits satellite features in addition to the photoelectric peak, which might provide access to interesting many-body physics.

[1] V. Blum et al., Comput. Phys. Commun. 2009, 180, 2175
[2] D. Golze, J. Wilhelm, M. J. van Setten, P. Rinke, J. Chem. Theory Comput. 2018, 14 (9), 4856