Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section B / 21 / a / iv / Solution

The square-planar rotor is an oblate symmetric top. A parallel band has $\Delta K=0$ and $\Delta J=0,\pm 1$, producing P and R progressions with approximate spacing $2\tilde{B}$ and a central Q contribution from $K\ne 0$; the $K=0$ parallel Q branch is absent. At modest resolution many nearly coincident $K$ components merge.

A perpendicular band has $\Delta K=\pm 1$ and $\Delta J=0,\pm 1$. Its Q subbranches produce a characteristic series of sharper features on the broader unresolved P/R envelope. Neglecting changes of rotational constants on vibration, successive perpendicular Q features are separated by approximately $2|\tilde{B}-\tilde{C}|$. These are rotational contours rather than extra normal-mode fundamentals.