Highly excited vibrational states of HCP and their analysis in terms of periodic orbits: The genesis of saddle-node states and their spectroscopic signature

We present quantum mechanical bound-state calculations for HCP(X̃) using an ab initio potential energy surface. The wave functions of the first 700 states, corresponding to energies roughly 23 000 cm above the ground vibrational state, are visually inspected and it is found that the majority can be uniquely assigned by three quantum numbers. The energy spectrum is governed, from the lowest excited states up to very high states, by a pronounced Fermi resonance between the CP stretching and the HCP bending mode leading to a clear polyad structure. At an energy of about 15 000 cm above the origin, the states at the lower end of the polyads rather suddenly change their bending character. While all states below this critical energy avoid the isomerization pathway, the states with the new behaviour develop nodes along the minimum energy path and show large-amplitude motion with H swinging from the Cto the P-end of the diatomic entity. How this structural change can be understood in terms of periodic classical orbits and saddle-node bifurcations and how this transition evolves with increasing energy is the focal point of this article. The two different types of bending motion are clearly reflected by the rotational constants. The relationship of our results with recent spectroscopic experiments is discussed. © 1997 American Institute of Physics. @S0021-9606~97!01546-8#