First-principles calculations of the self-trapped exciton in crystalline NaCl

The atomic and electronic structure of the lowest triplet state of the off-center ${(C}_{2v}$ symmetry) self-trapped exciton in crystalline NaCl is calculated using the local-spin-density (LSDA) approximation. In addition, the Franck-Condon broadening of the luminescence peak and the $a_{1g}\to b_{3u}$ absorption peak are calculated and compared to experiment. LSDA accurately predicts transition energies if the initial and final states are both localized or delocalized, but 1 eV discrepancies with experiment occur if one state is localized and the other is delocalized.