Species Classification and Rotational Energy Level Patterns of Non-Linear Triatomic Molecules

With the object of making existing knowledge more readily available, the quantized energy levels of symmetrical and asymmetrical tops are discussed from the viewpoint of their classification into species defined by symmetry operations; and simple species nomenclatures are proposed. These are then applied in a discussion of the rotational levels of symmetrical non-linear triatomic molecules A${\mathrm{B}}_2$. With S${\mathrm{O}}_2$ as an example, the pattern of rotational levels is studied as a function of the apex angle $2\alpha$ (near-prolate-symmetrical case for large $\alpha$, oblate or near-oblate case for intermediate $\alpha$, second near-prolate case for small $\alpha$). The classification of the over-all wave functions with respect to behavior for exchange of equal nuclei and for inversion is then considered. This gives rise to level patterns like those of diatomic and linear molecules in the first near-prolate case, but of interesting unfamiliar types (expected also in molecules such as B${\mathrm{Cl}}_3$ or N${\mathrm{H}}_3$) in the oblate case, and of relatively unfamiliar types (known for the molecule ${\mathrm{H}}_2$CO) in the second near-prolate case. Rotational-vibrational and rotational-electronic perturbations are discussed in relation to the species classifications. The concept of gyrovibronic species, and a corresponding nomenclature, are introduced. Top selection rules are discussed, using a convenient tabular formulation. Tables are given, for the case of symmetry $C_{2\nu }$, showing what types of transitions are allowed by the vibronic selection rules for every type of electronic transition, allowed or forbidden; the use of these tables is illustrated by application to the near-ultraviolet absorption spectrum of formaldehyde. Finally, non-linear ABC molecules are considered.