Simulation of X-ray photoelectron spectroscopy in atoms, molecules, and clusters: Core-electron excitation from ab initio many-body approach

X-ray photoelectron spectroscopy (XPS) technique, measuring directly core-electrons binding energies (BEs), provides information about electronic structure, chemical bonding, and stoichiometry for molecules/solids. This work presents the benchmark study of core electrons BEs in noble gas atoms between theories, including density functional theory (DFT), Hartree-Fock (HF) and many-body theory perturbation theory (GW approach) against experiments first, pointing out significant improvement of computed BEs from HF/DFT to GW. Furthermore, XPS of noble gas clusters with 3000 atoms were studied with embedded many-body theory to estimate the environmental polarization effect on relative BEs (chemical shifts). While the polarization energy remains consistent for different core orbitals within a given atom, it varies with the ionized atom's position in the cluster. An analytical formula derived from classical electrostatics accurately describes these polarization effects, aligning well with experimental XPS for noble gas clusters. Finally, by investigating the core-electron excitation in carbon 1s among various molecules, we found that the main contribution to chemical shift comes from classical electrostatic interaction and is one order of magnitude larger than the correlation effects.