Howard Taylor
Department of Chemistry, University of Southern California, Los Angeles, CA 90089-0482, USA
The complex FTIR spectra involving the excitation of the CH bond in
CHBrClF is analysed to yield the detailed motions of the hydrogen atom
that when quantized yield the observed energy levels. The starting point
for the analysis is the encoding by the Quack group of their spectra into
an effective spectroscopic, four resonance, algebraic Hamiltonian. This
is followed by a classical nonlinear dynamic analysis in the reduced phase
space of the system. For polyad 5, the highest for which the parametrization
of the Hamiltonian has been shown to hold, five different types of motion
are shown to underlay the dynamics. The relation between the classical
phase space structures found in the analyses and the observed and fitted
quantum levels is established most often by the use of semiclassical KAM
quantization to obtain agreement with the quantum spectra. The molecular
motions associated with an eigenstate are then obtained by transforming
the corresponding reduced phase space structure back to displacement coordinates.
Besides the expected Fermi resonances, a secondary resonance zone associated
with a resonance between the two bend normal modes is found. The motions
associated with the quantum states in this zone are shown to cause such
states to appear to have symmetries as Cs and C3v;
as such this chiral molecule, excited properly will not act in a manner
typical of a chiral molecules.
It will also be shown how the use of the polyad constant of the motion
greatly simplifies the dynamic analysis by causing the reduced phase space
of each high polyad to be reduced to a point at its maximum and minimum
energy. This intern causes a great simplicity in the search for and the
bifurcation structure of the periodic orbits relative to an analysis using
a potential surface. The phase space of the latter is unbounded from above
and leads to an evermore complicated and uninterpretable periodic orbit
pattern as energy increases.