Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / 49 / a / ii / Solution

An ordinary molecular point group consists of the identity, proper rotations $C_n$, and, when present, reflections $\sigma$, inversion $i$, and improper rotations $S_n$. Each operation leaves the nuclear geometry and chemical labels equivalent, so only identical nuclei can be interchanged. Translations are not elements of the point group of a finite isolated molecule. The molecular symmetry operations determine how electronic and vibrational coordinates transform.