The d-d transitions and ligand field parameters for Cr³⁺/Co²⁺ doped (Mg, Zn)Al₂O₄: Multi-reference Ab initio investigations

The normal spinels (Mg, Zn)Al₂O₄ doped with transition metal (TM) ions Cr³⁺/Co²⁺ are versatile materials with important electronic, optical and spectral properties. In addition to being used in many applications, they are excellent systems for testing some models and simulation features. The aim of this paper is to present, in the unified frame, the results on d-d transitions and ligand field parameters (LFPs) for the title systems, based on ab initio calculations, combining periodic density functional theory (DFT) supercell approach with ab initio (AI) multi -reference perturbation theory (MRPT) and multi-reference configuration interaction (MRCI) methods. These AI methods, based on complete active space self-consistent-field (CASSCF) reference, allow to calculate and investigate the energy levels of TM ions and the d-d transitions between them. From the AI results the B and C Racah parameters, the spin-orbit coupling (SOC) constant and the LFPs in the frame of the angular overlap model (AOM) were accurately extracted with ab initio ligand field theory (AILFT) protocol, all with subsequent comparison with the experimental data or existing theoretical results in the literature. The calculation technique presented in this paper serves as a predictive formalism for further studies of larger monomer clusters, for which experimental data is unreliable or unavailable.