K. Efstathiou(1), M. Joyeux(2), and D. A. Sadovskií(1)

(1) Université du Littoral, UMR 8101 du CNRS, 59140 Dunkerque, France

(2) Laboratoire de Spectrométrie Physique, 
    Université Joseph Fourier - Grenoble I, 
    UMR 5588 du CNRS, B.P. 87, 38402 St. Martin d'Hčres, France 

  Global bending quantum number and the absence of monodromy in
  the HCN<->CNH molecule

ms. AG9012 submitted to Physical Review A 
received Jul 18, 2003 
revised  Oct 22, 2003

Phys. Rev. A 69(3), 032504-1--15 (2004)
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Abstract:
We introduce and analyze a model system based on a deformation of a spherical
pendulum that can be used to reproduce large amplitude bending vibrations of
floppy triatomic molecules with two stable linear equilibria.  On the basis of
our model and the recent vibrational potential in [J. Chem. Phys. 115, 3706
(2001)], we analyze the HCN/CNH isomerizing molecule.  We find that HCN/CNH has
no monodromy and introduce the second global bending quantum number for this
system at all energies where the potential is expected to work. We also show
that LiNC/LiCN is a qualitatively different system with monodromy.

Acknowledgments:  
We thank Boris Zhilinskií and Richard Cushman for helpful discussions and
comments on the manuscript.  This work was made possible by the CNRS research
position granted to D.S. for the 6 month in 2002--2003.  D.S. and K.E.
acknowledge the support by the EU network project Mechanics and Symmetry in
Europe (MASIE), contract HPRN-CT-2000-00113.

PACS:
33.20.Vq, Vibration-rotation analysis 
03.20+i,  Classical mechanics of discrete systems
03.65Sq,  Semiclassical theories and applications
33.15.Mt  Rotation, vibration, and vibration-rotation constants