Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2025/paper-1/a4/b/iii/solution

In this C2v point group convention, , , and . Therefore all six normal modes have symmetry-allowed infrared fundamentals: , absent accidental coincidences or vanishing intensities.
For Raman spectroscopy, examine the polarizability tensor: , , and ; is also Raman-allowed but no vibration occurs here. All six vibrations are therefore Raman-active too, giving . The centrosymmetric mutual-exclusion rule does not apply to formaldehyde.

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