 Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2022/paper-1/a5/c/iv/solution

A_{1 g}

and the final one is

E_{1 u}

, so an in-plane dipole component satisfies

E_{1 u} \otimes E_{1 u} \otimes A_{1 g} = A_{1 g} + A_{2 g} + E_{2 g} .

The product contains the totally symmetric representation. The combined electronic–vibrational transition is therefore symmetry-allowed, with an in-plane electric dipole transition moment.

A nonzero intensity still needs vibronic coupling. In a coordinate-independent separation, the forbidden electronic matrix element would remain zero. Its first derivative with respect to the

E_{2 g}

coordinate can instead be nonzero, and the vibrational factor

⟨ 1∣ Q ∣0 ⟩

supplies the required one-quantum transition. This is vibrational activation of an electronic transition and explains why the band can be weak.

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