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 i→ f

Polarization of light

Direct products

Resulting characters

P T

E

C 2

i

σ h

T HOMO→ LUMO

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 ×.
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