Quasiparticle Self-Consistent <i>GW</i> Analysis of Excited States and Model Construction of 3<i>d</i><sup>2</sup> Luminescent Centers in α-Aluminum Oxide

Cr4+-doped crystals are promising materials for infrared solid laser applications. In order to choose proper host materials of Cr4+ from the wide variety of crystals, multiplet energy levels of Cr4+ should be evaluated without experimental information. A newly developed first-principles method for determining the mean-field Hamiltonian of the localized luminescent center based on quasiparticle self-consistent GW was applied to 3d2 transition metal ions (Cr4+ and V3+) in α-Al2O3. Our method gave good agreement with the effective Coulomb parameters and crystal-field parameters estimated from experimental data. Multiplet energy structures were therefore well reproduced by our method. These results show the possibility of designing new laser host materials within the framework of the first-principles calculations.