Absorption spectra, ligand field parameters and g factors of Cr³⁺ doped α-Al₂O₃ laser crystal: ab initio calculations

In this paper we present, in the unified frame, the results of the ab initio investigations of absorption spectra, ligand field parameters and g factors for three valence chromium doped α-Al₂O₃ crystal. Our calculations are based on a new methodology applied to a cluster [CrO₆]⁹⁻ embedded in an extended point charge field of host matrix ligands. After the differential functional theory optimization of the doped crystal, a vibrational theoretical spectroscopic study based on infrared spectroscopy has been employed in order to confirm the stability of the optimized doped crystal structure. The ab initio energy calculation of the electronic states and corresponding wave functions of Cr³⁺ are documented from the complete active space self-consistent field. The improved energy states from the N-electron valence second order perturbation theory, second order dynamic correlation dressed complete active space (DCD-CAS2), difference dedicate configuration interaction with three degrees of freedom (MRDDCI3) and spectroscopy-oriented configuration interactions, were analyzed. Based on the ab initio ligand field theory procedure we extracted ligand field parameters and spin–orbit coupling constant which were used to recalculate the energy levels of the studied system. In addition, g factors for the ground state ⁴A₂ of Cr³⁺ ion in corundum are calculated taking into account the full configuration interaction. The results obtained are discussed and the comparisons with measured values from literature show a reasonable agreement, which justifies and recommend this new route of investigation. (paper)