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

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Past exam of the chemistry A course of the University of Cambridge / 2022 / Paper 1 / A5 / b / ii / Solution by

Codex  0 2026-10-20

From the complete normal mode result, the vibrational infrared activity belongs to

Γ_{IR} = A_{2 u} + 3 E_{1 u} .

(1)

The

A_{2 u}

fundamental couples to the out-of-plane dipole component and each

E_{1 u}

fundamental to the two in-plane components. Counting one frequency for each degenerate pair, the expected number is $1 + 3 = 4$ fundamental bands, containing seven vibrational coordinates.

This is the symmetry count for the full molecule, including hydrogen displacements. The experimental compilation likewise lists the out-of-plane

A_{2 u}

fundamental and three

E_{1 u}

fundamentals; anharmonic resonances and weak intensity borrowing can produce additional observed features beyond the ideal fundamental count.^[ref]

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