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 GW 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.