A First-Principles Investigation of the Crystal-Field and Racah Parameters of Transition Metal Ions: Cr³⁺ in Alumina

The crystal-field and Racah parameters of ruby were evaluated based on the first-principles calculations using the relationship between the ligand-field theory and the molecular orbital theory derived by Sambe and Felton. It is found that the combination of the discrete variational (DV)-X calculations and the discrete variational multi-electron (DVME) calculations is effective for prediction of reasonable values for the crystal-field and Racah parameters for Cr 3+ in alumina. These results indicate that the corrections to the DVME calculations based on the DV-X method provide a theoretical basis for the configuration-dependent correction and the correlation correction which were introduced in the previous calculation based on an intuition that the average transition energy should be reproduced better by one-electron calculations than many-electron calculations. This method could be used to predict the d-d transitions for Mn 4+ to find a suitable host for a red phosphor for LED applications.