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

Abstract

We present quantum mechanical bound-state calculations for HCP(X) using an ab initio potential energy surface. The wave functions of the first 700 states, corresponding to energies roughly 23 000 cm Ϫ1 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 Ϫ1 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 C-to 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.

Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra

“…64,65 Inspired by this prediction, Ishikawa et al 40 have searched for these states and indeed found a series of states, which could not be assigned in the way the other levels were assigned. Moreover, these states showed a large anharmonicity and had unusually large rotational B 0 constants, just the criteria typical for the isomerization states.…”

Observation of the νCHExcited Vibrational Levels in theÃ1A″State of HCP by IR–UV Double Resonance Spectroscopy

“…Such a qualitative change in the vibrational character had been predicted in a theoretical study carried out by Schinke and co-workers (10,11). Our analysis has been restricted to deal exclusively with the interaction between the bend and CP stretch modes, since there had been no experimental observations of highly excited vibrational levels with v CH 0.…”

“…On the other hand, the HCP 7 CPH isomerization reaction in the high-energy region in the X 1 ⌺ ϩ state has been extensively studied experimentally (6 -9) and theoretically (10,11) recently. To observe highly excited vibrational levels in the X 1 ⌺ ϩ state, dispersed fluorescence (DF) and stimulated emission pumping (SEP) spectroscopies are very useful, since excited electronic states have a bent configuration, whereas the X state is linear.…”

Periodic orbits and vibrational wave functions for DCP: nonlinear resonances in isotopically substituted molecules

“…In two previous publications [4,5] we have presented a detailed classical and quantum mechanical study of its vibrational motion up to an energy range of about 3 eV above the minimum of the potential.…”