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Spectroscopic signatures of a saddle point

Spectroscopic signatures of a saddle point. Modelled on HCP as a perturbed spherical pendulum. Spherical pendulum. P. C. θ. H. Outline. Model Hamiltonian Properties of spherical pendulum states Classical trajectories of the coupled model Anharmonic resonances Polyad structure

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Spectroscopic signatures of a saddle point

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  1. Spectroscopic signatures of a saddle point Modelled on HCP as a perturbed spherical pendulum

  2. Spherical pendulum P C θ H

  3. Outline • Model Hamiltonian Properties of spherical pendulum states Classical trajectories of the coupled model Anharmonic resonances Polyad structure • Rotation/vibrational dynamics of HCP bending states Extended RKR potential function Anomalous magnitudes of vibn/rotn parameters • Summary

  4. Model Hamiltonian

  5. Quantum pendulum states 2.0 1.0 E/V0 Diagonalize in a spherical harmonic basis 0.0 -1.0 k

  6. Semiclassical pendulum states Complete analytical solution in terms of Elliptic integrals, which yields the following limiting formulae for k=0

  7. Surfaces of section and periodic orbits

  8. Periodic orbit bifurcations

  9. Periodic orbit frequencies

  10. Polyad structure E<B Inside Fermi res Outside Measured from lowest level of polyad Mean polyad number np=2vs+vb

  11. Polyad structure 0<E<2B Vibrating states Rotating states

  12. Importance of resonance terms ΔE np E

  13. HCP extended RKR bending potential

  14. HCP bend monodromy plot

  15. l doubling

  16. Vibration rotation constants

  17. Summary • Classical and semiclassical methods used to illuminate dynamics of HCP-like model • Classical bending frequency function and Heisenberg matrix elements used to model occurrence and strength of 1:n resonances • RKR plus ab initio information used to determine realistic HCP bending potential • Anomalously large vibn/rotn interaction parameters explained and predicted

  18. Acknowledgements • M P Jacobson (UCSF) • C D Cooper (Oxford) • UK EPSRC References • M P Jacobson and M S Child JCP 114, 250 (2001) • M P Jacobson and M S Child JCP 114, 262 (2001) • M P Jacobson and M S Child JPC 105, 2834 (2001) • M S Child, M P Jacobson and C D Cooper JPC 105, 10791 (2001)

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