Solution (source code)

= Solution

The resolved lines arise from simultaneous changes of vibration and rotation in <hydrogen cyanide>. A vibrational fundamental connects many populated lower rotational levels to different upper rotational levels, giving the fine structure of a <rovibrational spectrum>.

The prominent central <Q branch>, together with flanking <P branch> and <R branch> lines, identifies a perpendicular band. For linear HCN, this is the \b[doubly degenerate bending fundamental], not either stretching fundamental. Bending creates a transition-dipole component perpendicular to the molecular axis; its <vibrational angular momentum> permits $\Delta J=0$ as well as $\Delta J=\pm1$.

The two perpendicular bending coordinates share one vibrational frequency. Their degeneracy is different from the series of resolved rotational transitions superimposed on that fundamental. The stretches have their <electric dipole transition moment> along the molecular axis and would give the usual parallel-band P/R pattern without this strong central Q feature.