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 Letter, we benchmark the ab initio many-body $GW$ approximation on the complete electron binding energies of noble-gas atoms (He-Rn), which span 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 (error of 14%) or the overestimation from Hartree-Fock (error of 4.7%). Such results also imply the correlations of $d$ electrons are very well described by $GW$.

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• Atomic orbital
• Density functional theory
• Electron correlation calculations for atoms & ions
• Electronic structure
• Electronic structure of atoms & molecules
• Quantum many-body systems
• GW method
• Photoelectron techniques
• Photoemission spectroscopy