Modeling Nonresonant X-ray Emission of Second- and Third-Period Elements without Core-Hole Reference States and...

Nonresonant X-ray emission (XE) energies and oscillator strengths are obtained using the effective potential of the generalized Kohn-Sham semi-canonical projected random phase approximation (GKS-spRPA) method. XE energies are estimated as a difference between the valence and core ionization eigenvalues, while the oscillator strengths are obtained within a frozen orbital approximation. This straightforward approach provides accurate XE energies without any need for core-hole reference states, empirical shifting parameters, or tuning of density functionals. To account for relativistic corrections to the core orbitals, we have formulated a scalar relativistic (sr) GKS-spRPA approach based on the spin-free X2C one-electron Hamiltonian. The sr-GKS-spRPA method provides highly reliable XE energies using uncontracted basis-sets on atoms where the core-hole is created prior to emission. For the largest basis-sets used in our study, using completely uncontracted polarized core-valence Dunning basis-sets, the mean absolute errors (MAEs) are within 0.7 eV compared to experimental reference values for a test-set consisting of 27 valence-to-core XE energies of molecules with second- and third-period elements. Considering a balance of accuracy and computational effort, we recommend the use of s-uncontracted def2-TZVP for second-period and all-uncontracted def2-TZVP for third-period elements. For this recommended basis-set, the MAE is 0.2 eV. The analytically continued sr-GKS-spRPA approach, with an $$ computational cost, enables efficient computation of XE spectra of molecules such as S₈ and C₆₀ with several core-hole states.