THEORETICAL EVIDENCE FOR THE FORMATION OF ROTATIONAL ENERGY LEVEL CLUSTERS IN THE VIBRATIONAL GROUND STATE OF PH$_3$

{S. N. Yurchenko, M. Carvajal, P. Jensen, H. Lin, J. Zheng, and W. Thiel, \textit{Mol. Phys.{S. N. Yurchenko, M. Carvajal, P. Jensen, F. Herregodts, and T. R. Huet, \textit{Chem. Phys.Author Institution: Max-Planck-Institut f{u}r Kohlenforschung,; Kaiser-Wilhelm-Platz 1, D--45470 M{u}lheim an der Ruhr, Germany; Steacie Institute for Molecular Sciences,; National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6; FB C -- Theoretische Chemie,; Bergische Universit{a}t, D--42097 Wuppertal, GermanyWe 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 ${\mathbf C}_{3{\rm v}}$ 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