Table 5 Probabilities for the transition from Ti to Tf, calculated using direct products.

From: QM-sym, a symmetrized quantum chemistry database of 135 kilo molecules

T if Polarization of light Direct products Resulting characters P T
E C 2 i σ h
T HOMOLUMO x, y Bg × Bu × Ag 1 −1 −1 1 ×
z Bg × Au × Ag 1 1 −1 −1 ×
T HOMO−2→ LUMO x, y Au × Bu × Ag 1 −1 1 −1 ×
z Au × Au × Ag 1 1 1 1
  1. Only the last one is bright since only the direct product Au × Au × Ag contains the total symmetry Ag. PT is the probability of each transition, the transition is bright with √ and dark with ×.