Core-hole delocalization for modeling x-ray spectroscopies: A cautionary tale

The influence of core-hole delocalization for x-ray photoelectron, x-ray absorption, and x-ray emission spectrum calculations is investigated in detail using approaches including response theory, transition-potential methods, and ground state schemes. The question of a localized/delocalized vacancy is relevant for systems with symmetrically equivalent atoms, as well as near-degeneracies that can distribute the core orbitals over several atoms. We show that the issues relating to core-hole delocalization are present for calculations considering explicit core-hole states, e.g., when using a core-excited or core-ionized reference state or for fractional occupation numbers. As electron correlation eventually alleviates the issues, but even when using coupled-cluster single-double and perturbative triple, there is a notable discrepancy between core-ionization energies obtained with localized and delocalized core-holes (0.5 eV for the carbon K-edge). Within density functional theory, the discrepancy correlates with the exchange interaction involving the core orbitals of the same spin symmetry as the delocalized core-hole. The use of a localized core-hole allows for a reasonably good inclusion of relaxation at a lower level of theory, whereas the proper symmetry solution involving a delocalized core-hole requires higher levels of theory to account for the correlation effects involved in orbital relaxation. For linear response methods, we further show that if x-ray absorption spectra are modeled by considering symmetry-unique sets of atoms, care has to be taken such that there are no delocalizations of the core orbitals, which would otherwise introduce shifts in absolute energies and relative features. (C)2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/)

Automated summary

The influence of core-hole delocalization on x-ray spectroscopy calculations is investigated using different methods. The study finds significant discrepancies between localized and delocalized core-holes, even with electron correlation effects considered.