The atomic and electronic structure of the lowest triplet state of the off-
center (C-2 nu symmetry) self-trapped exciton in crystalline NaCl is calcul
ated using the local-spin-density (LSDA) approximation. In addition, the Fr
anck-Condon broadening of the luminescence peak and the a(1g) --> b(3u) abs
orption peak are calculated and compared to experiment. LSDA accurately pre
dicts transition energies if the initial and final states are both localize
d or delocalized, but I eV discrepancies with experiment occur if one state
is localized and the other is delocalized.