Knowledge Bank

Rotational energy $surfaces1$ (RES) are radial plots of the energy of a molecule as a function of the direction of the total angular momentum in the molecular fixed frame. RES are organized by the location and type of their stationary points, i.e., those points for which the gradient of the surface vanishes. Stationary points are important because classically, stable rotations can occur around axes from the origin to either maxima or minima on the RES. The number if stationary points may change with the variation of some external parameter, as for example the total angular momentum J. Such changes are associated with stationary points for which the hessian vanishes. They are called catastrophe points and their distribution can explain quantitative changes in the energy level pattern of the molecule. We have studied the catastrophe map for three torsional states of acetaldehyde below the barrier to internal rotation ($\nu t=0,1,2$) and the first state above the barrier ($vt=3$), for both A and E torsional symmetry species, and for values of J . The number of stationary points $vt=0,1,2$ A states is six for all J values examined, a result identical to that obtained for any rigid asymmetric rotor. For $vt=0,1$ E states, where torsion-rotation interactions are larger, the number is still six. However, the E states for $vt=2$ present a number of catastrophes as J increases which create or annihilate pairs of stationary points. For $vt$=3 E states the situation is even more complicated, so that for J=25 there are 20 stationary points. The catastrophe history (with J) of there RES can be followed, beginning with the stationary points (2 maxima, 1 saddle, 1 minima) which exist for J=1. the relevance of these catastrophes for the energy levels of acetaldehyde will be discussed in terms of the changes in the trajectories of the angular momentum vector as a consequence of the changes in the topology of RES.