Knowledge Bank

We investigate theoretically the rotational dynamics of pyramidal XY$3$ molecules in highly excited rotational states. Towards this end we compute, by a variational method,% } \textbf{103}, 359-378 (2005) and references therein.} the rotational energy levels in the vibrational ground state of PH$3$ for $J$ $\le$ 80 from a potential energy surface determined previously.% } \textbf{290}, 59-67 (2003).} At $J$ $\ge$ 50 the calculated energy levels show a distinct cluster pattern. By monitoring the cluster formation we follow the various stages of the rotational dynamics. We analyze the wavefunctions for the cluster states and compute expectation values which show that the $C3v$ geometrical symmetry of PH$3$ is broken at high rotational excitation. The conclusions drawn from the quantum-mechanical calculations are confirmed by semi-classical theory, i.e., by an analysis of the stationary points on the rotational energy surface.