Herein, we study the electronic structure, energies, and vibronic structure of optical d-d transitions of Cr 3+ ions doped in beryl (Be 3 Si 6 Al 2 O 18 :Cr 3+ , emerald). A computational protocol is developed that combines periodic density functional theory (for modeling of the bulk crystalline lattice of emerald) and the multireference configuration interaction complete active space self-consistent field method supplemented with n-electron valence second-order perturbation theory (for the calculation of the energy levels, wave functions, and spin-Hamiltonian and ligand-field parameters of the trigonal Cr 3+ centers in the [CrO 6 ] 9− clusters embedded in an extended point charge field). Ligand-field parameters were extracted from mapping the effective ligand-field Hamiltonian onto the full many-particle Hamiltonian from one side and from a direct fit to energies of computed d-d transitions on the other side. These have been analyzed using ab initio ligand-field theory. The quality of the theoretical predictions is critically assessed through a detailed comparison with the available experimental data.
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.
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