 Solution

ID: past-exam-of-the-condensed-matter-physics-major-option-course-of-the-university-of-oxford/2019/1/a/iii/solution

There are six atoms in the nonlinear oxalate ion, hence

3 \cdot 6 = 18

positional degrees of freedom. Subtract three rigid translations and three rigid rotations to obtain

3 N - 6 = 12

vibrational normal modes. Planarity does not remove out-of-plane motions. Since three modes have been displayed,

12 - 3 = 9 additional vibrational normal modes .

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