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Theoretical calculations of core electron binding energies are important foraiding the interpretation of experimental core level photoelectron spectra. Inprevious work, the $\Delta$-Self-Consistent-Field ($\Delta$-SCF) method basedon density functional theory has been shown to yield highly accurate 1s and 2pbinding energies in free molecules. However, most experimental work isconcerned with solids, not gases. In this study, we demonstrate the applicationof the all-electron $\Delta$-SCF method to periodic systems. A consideration ofthe experimentally accessible points of reference leads to the definition of acore electron binding energy in a solid as the difference between the totalenergies of two $N-1$ electron systems: one with an explicit, localized corehole, and one with an electron removed from the highest occupied state. Thecalculation of each of these quantities is addressed. In addition, the analogybetween a localized core hole and a charged defect in a solid is highlighted,and the extrapolation of calculated core electron binding energies to theinfinite supercell limit is discussed. It is found that the extrapolated valuesof the core electron binding energies from periodic $\Delta$-SCF calculationsagree well with experimental results for both metallic and insulating systems,with a mean absolute error of 0.24 eV for the 15 core levels considered in thisstudy.

Core Electron Binding Energies in Solids from Periodic All-Electron $\Delta$-Self-Consistent-Field Calculations