A Note Concerningl-Type Doubling in Axially Symmetric Molecules, in Particular with Reference to Molecules Belonging to the Symmetry GroupsC4vandVd

Abstract

The theory of the $l$-type doubling for axially symmetric polyatomic molecules is applied to molecules belonging to the symmetry groups ${C}_{4v}$ and ${V}_{d}$. It is shown that here $l$-type doubling may be expected in both degenerate Coriolis levels (referring to a positive and a negative product of the quantum numbers $K$ and $l$, respectively). A detailed analysis of a pyramidal $X{Y}_{4}$ model reveals that the doubling in these two levels is of the same order. On the basis of our discussion a microwave absorption pattern is predicted for the transitions $J=1\ensuremath{\rightarrow}J=2$, $\ensuremath{\Delta}K=0$, where a molecule of ${C}_{4v}$ or ${V}_{d}$ symmetry is in an excited degenerate vibration state. An interesting example may be provided by I${\mathrm{F}}_{5}$ if this molecule has the ${C}_{4v}$ structure recently proposed.