| Part I. The effective spectroscopic Hamiltonian fitted to experiment by Troellsch and Temps {lcub}A. Troellsch, F. Temps Zeitschrift fuer Physikalische Chemie 215, 207, (2001){rcub} and describing high vibrational excitation to bound and resonant states, is used in conjunction with methods of nonlinear classical dynamics and semiclassical mechanics to extract for all the observed highly excited resonance levels in Polyad 8, the molecular motions upon which they are quantized. Two types of interlaced dynamically distinct ladders of states are revealed. The rungs of these ladders intersperse making the spectra complex. The resonant 2:2:1 frequency ratio of the DC, CO stretches and the bend respectively is what causes the complexity and is what caused past attempts at interpretation to be at best incomplete. All states are assigned with physically meaningful quantum numbers corresponding to quasiconserved quantities. Most interestingly it is pointed out that much of the information and assignment can be done without any calculations at all, using only the qualitative ideas from nonlinear, semiclassical and quantum mechanics along with the information supplied by the experimentalist.; Part II. In systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods. However, this situation can be reversed with increasing dimension of the problem. For a three-dimensional system, viz. the hyperbolic four-sphere scattering system, we demonstrate the superiority of semiclassical versus quantum calculations. Semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques. |
