Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory for Accurate X-ray Absorption Spectroscopy

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 (n_O8π^∗) 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.