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Linear-response time-dependent density functional theory (LR-TDDFT) for corelevel spectroscopy using standard local functionals suffers fromself-interaction error and a lack of orbital relaxation upon creation of thecore hole. As a result, LR-TDDFT calculated X-ray absorption near edgestructure (XANES) spectra need to be shifted along the energy axis to matchexperimental data. We propose a correction scheme based on many bodyperturbation theory to calculate the shift from first principles. Theionization potential of the core donor state is first computed and thensubstituted for the corresponding Kohn--Sham orbital energy, thus emulatingKoopmans' condition. Both self-interaction error and orbital relaxation aretaken into account. The method exploits the localized nature of core states forefficiency and integrates seamlessly in our previous implementation of corelevel LR-TDDFT, yielding corrected spectra in a single calculation. Webenchmark the correction scheme on molecules at the K- and L-edges as well asfor core binding energies and report accuracies comparable to higher ordermethods. We also demonstrate applicability in large and extended systems anddiscuss efficient approximations.

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