First principles correction scheme for linear-response time-dependent density functional theory calculations of core electronic states

Linear-response time-dependent density functional theory (LR-TDDFT) for core level spectroscopy using standard local functionals suffers from self-interaction error and a lack of orbital relaxation upon creation of the core hole. As a result, LR-TDDFT calculated X-ray absorption near edge structure (XANES) spectra need to be shifted along the energy axis to match experimental data. We propose a correction scheme based on many body perturbation theory to calculate the shift from first principles. The ionization potential of the core donor state is first computed and then substituted for the corresponding Kohn--Sham orbital energy, thus emulating Koopmans' condition. Both self-interaction error and orbital relaxation are taken into account. The method exploits the localized nature of core states for efficiency and integrates seamlessly in our previous implementation of core level LR-TDDFT, yielding corrected spectra in a single calculation. We benchmark the correction scheme on molecules at the K- and L-edges as well as for core binding energies and report accuracies comparable to higher order methods. We also demonstrate applicability in large and extended systems and discuss efficient approximations.