Electron removal energies in noble gas atoms up to 100 keV: ab initio GW vs XPS

X-ray photoelectron spectroscopy (XPS) measures electron removal energies, providing direct access to core and valence electron binding energies, hence probing the electronic structure. In this work, we benchmark for the first time the ab initio many-body GW approximation on the complete electron binding energies of noble gas atoms (He-Rn), which spans 100~keV. Our results demonstrate that GW achieves an accuracy within 1.2% in XPS binding energies, by systematically restoring the underestimation from density-functional theory (DFT, error of 14%) or the overestimation from Hartree-Fock (HF, error of 4.7%). Such results also imply the correlations of $d$ electrons are very well described by GW.