| Summary: | It is demonstrated that the challenging core-hole particle (CHP) orbital relaxation for core electron spectra can be readily achieved by the mixed-reference spin-flip (MRSF)–time-dependent density functional theory (TDDFT). With the additional scalar relativistic effects on K-edge excitation energies of 24 second- and 17 third-row molecules, the particular ΔCHP–MRSF(R) exhibited near perfect predictions with RMSE ∼0.5 eV, featuring a median value of 0.3 and an interquartile range of 0.4. Overall, the CHP effect is 2–4 times stronger than relativistic ones, contributing more than 20 eV in the cases of sulfur and chlorine third-row atoms. Such high precision allows to explain the splitting and spectral shapes of O, N, and C atom K-edges in the ground state of thymine with atom as well as orbital specific accuracy. The same protocol with a double hole particle relaxation also produced remarkably accurate K-edge spectra of core to valence hole excitation energies from the first (n₀₈π*) and second (ππ*) excited states of thymine, confirming the assignment of 1s → n excitation for the experimentally observed 526.4 eV peak. Regarding both accuracy and practicality, therefore, MRSF–TDDFT provides a promising protocol for core electron spectra of both ground and excited electronic states alike. This work was supported by the Samsung Science and Technology Foundations (SSTF-BA1701-12) for the fundamental theory developments and the NRF funded by the Ministry of Science and ICT (2020R1A2C2008246 and 2020R1A5A1019141). This work was also supported by the Korea Polar Research Institute (KOPRI, PE22120) funded by the Ministry of Oceans and Fisheries. MAS and MHR acknowledge financial support by the "Agence Nationale pour la Recherche" through the project MULTICROSS (ANR-19-CE29-0018-01). Centre de Calcul Intensif d'Aix-Marseille is acknowledged for granting access to its high-performance computing resources. The authors thank the financing through the program PHC STAR 2019 granted by the "Ministère de ...
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