A new formalism for calculating core electron binding energies in periodic solids

In reference [1], a formalism for calculating core electron binding energies in periodic solids, as measured in experimental X-ray Photoelectron Spectroscopy (XPS), was presented. In this formalism, the core electron binding energy is calculated as the total energy difference between two N-1 electron systems: one with a core hole, and one with a hole in the highest occupied state.

However, at the limit of infinite supercell size, the total energy difference between the ground state of N-electron system and the state with a hole in the highest occupied orbital converges to the DFT eigenvalue at the valence band maximum (VBM). This allows us to present an alternative formalism, where the core electron binding energy is calculated in terms of the total energy of the N-electron ground state, the N-1 electron final state with a core hole, and the VBM eigenvalue.

This new formalism also allows us to identify the origin of the unexpectedly large errors in previously calculated core electron binding energies in some wide band gap solids, and it suggests a general route for improving the accuracy of calculated core electron binding energies in insulating materials.

[1] – J.M. Kahk et al., J. Phys. Chem. Lett. 12, 9353 (2021)