Pressure-dependent multiplet-excitation energies of α-Al2O3:Cr3+ by the first-principles method

We apply a method [Phys. Rev. B108, 035141 (2023)], which can treat the multiplet excitations in the first-principles method, to a typical pressure indicator α-Al2O3:Cr3+. After optimizing the crystal structure under hydrostatic pressure from 0.0 to 35.0 GPa in the usual first-prinicple calculations, we obtain the multiplet energies in the method. That is, we conduct the exact diagonalization of the crystal-field model Hamiltonian which is directly determined based on the result of the quasiparticle self-consistent GW method. Our method has no parameters by hand. The calculated pressure dependences of the excitation energies agree well with those of experiments.