First-principles calculation of ground and excited-state absorption spectra of ruby and alexandrite considering lattice relaxation

We performed first-principles calculations of multiplet structures and the corresponding ground-state absorption and excited-state absorption spectra for ruby (Cr³⁺:α-Al₂O₃) and alexandrite (Cr³⁺:BeAl₂O₄) which included lattice relaxation. The lattice relaxation was estimated using the first-principles total energy and molecular-dynamics method of the CASTEP code. The multiplet structure and absorption spectra were calculated using the configuration-interaction method based on density-functional calculations. For both ruby and alexandrite, the theoretical absorption spectra, which were already in reasonable agreement with experimental spectra, were further improved by consideration of lattice relaxation. In the case of ruby, the peak positions and peak intensities were improved through the use of models with relaxations of 11 or more atoms. For alexandrite, the polarization dependence of the U band was significantly improved, even by a model with a relaxation of only seven atoms.