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We carried out a comparative study on R-line and U-band energies of α-Al 2 O 3 : Cr 3+  material, or the so-called ruby, estimated from one-electron and many-electron first-principles calculations. The estimations were performed without relating to any observed parameter. Although there are numerous reports on the  ab-initio  calculations of absorption spectra and multiplet energies of ruby based on many-electron approach, the investigation based on one-electron approach is basically impossible except for some particular states such as  4 T2 and  2 E. Here we compared the transition energies from the  4 A2 state (ground state) to  4 T2 state (U-band) and to  2 E (R-line) of ruby estimated by one-electron and many-electron first-principles approaches. The one-electron calculations were carried out utilizing using discrete variational Χα (DV-Χα) method combined with ligand field theory, while the many-electron calculations were carried out utilizing using the discrete variational multi-electron (DVME) method. The results show that generally both of the one-electron and the many-electron first-principles calculations can be utilized to estimate the multiplet energies such as U-band and R-line energies. Nevertheless, the refined formula to estimate the R-line energy based on one-electron approach is necessary to enhance the concurrence with the observed data.

Comparative Study on R-line and U-band Energies of Ruby Estimated from One-Electron and Many-Electron First-Principles Approaches