Excitations in lanthanide ions: a systematic evaluation of two-component CAS-CI and GW

This paper presents a thorough prediction and investigation of ionization energies, atomic levels, and crystal-field splittings in lanthanide ions. We show that a two-component complete active space (CAS) configuration interaction (CI) approach based on two-component density functional theory (DFT) reference states is suitable to yield accurate excitation energies for lower energy terms. DFT references are further shown to be superior to Hartree-Fock (HF) references for predicting both atomic levels and ionization energies. Especially in the Green's function based <i>GW</i> method used to determine ionization energies, the deficiencies of the wave function based HF references are severe, leading to sizable errors. Two-electron contributions to spin-orbit coupling are found to be an important ingredient for obtaining accurate atomic levels. These contributions are taken into account using a screened-nuclear-spin-orbit (SNSO) approach, which is shown to be very accurate. DFT based CAS-CI is further used to calculate crystal-field splittings. The results are well suited to predict the subtle splittings in complexes with unpaired 4f electrons.