Development and applications of the LFDFT: the non-empirical account of ligand field and the simulation of the f–d transitions by density functional theory

Abstract

Ligand field density functional theory (LFDFT) is a methodology consisting of non-standard handling of DFT calculations and post-computation analysis, emulating the ligand field parameters in a non-empirical way. Recently, the procedure was extended for two-open-shell systems, with relevance for inter-shell transitions in lanthanides, of utmost importance in understanding the optical and magnetic properties of rare-earth materials. Here, we expand the model to the calculation of intensities of f → d transitions, enabling the simulation of spectral profiles. We focus on Eu²⁺-based systems: this lanthanide ion undergoes many dipole-allowed transitions from the initial 4f⁷(⁸S_7/2) state to the final 4f⁶5d¹ ones, considering the free ion and doped materials. The relativistic calculations showed a good agreement with experimental data for a gaseous Eu²⁺ ion, producing reliable Slater–Condon and spin–orbit coupling parameters. The Eu²⁺ ion-doped fluorite-type lattices, CaF₂:Eu²⁺ and SrCl₂:Eu²⁺, in sites with octahedral symmetry, are studied in detail. The related Slater–Condon and spin–orbit coupling parameters from the doped materials are compared to those for the free ion, revealing small changes for the 4f shell side and relatively important shifts for those associated with the 5d shell. The ligand field scheme, in Wybourne parameterization, shows a good agreement with the phenomenological interpretation of the experiment. The non-empirical computed parameters are used to calculate the energy and intensity of the 4f⁷–4f⁶5d¹ transitions, rendering a realistic convoluted spectrum.