OpenMX supports a general method to calculate absolute binding energies of core levels in metals and insulators, based on a penalty functional and an exact Coulomb cutoff method in the framework of density functional theory . With the method the spurious interaction of core holes between supercells is avoided by the exact Coulomb cutoff method, while the variational penalty functional enables us to treat multiple splittings due to chemical shift, spin-orbit coupling, and exchange interaction on equal footing. It has been demonstrated that the absolute binding energies of core levels for both metals and insulators are calculated by the proposed method in a mean absolute (relative) error of 0.4 eV (0.16%) for eight cases compared to experimental values measured with x-ray photoemission spectroscopy (XPS) within a generalized gradient approximation to the exchange-correlation functional.
By considering the energy conservation for the excitation process in the XPS measurements as schematically
shown in Fig. 78, the absolute binding energies of core levels in gaseous and bulk systems
are respectively given by