Franck-Condon relaxation in photo-excited YAG:Ce studied using real-time time-dependent density functional theory

First-principles calculations of electron-ion dynamics based on real-time time-dependent density functional theory were performed to study the lattice dynamics in yttrium aluminum garnet (YAG) doped with cerium (Ce) following photoexcitation. The dynamics induced by the optical transitions from the valence band to the conduction band of the YAG host and from the Ce 4f to 5 d levels were examined. Significant lattice motion was observed in the latter case. This lattice motion (Franck-Condon relaxation) decreased the Ce–O bond length by 0.05 Å and increased the energy of the Ce 4f level by 0.5 eV, suggesting a Stokes shift in the light emission due to the Ce 5 d→4f transition. The calculated Stokes shift is consistent with the recently reported experimental value, despite the approximations used in the present calculations. The effect of lattice temperature was also examined up to 300 K.