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

2. Spherical pendulum P C θ H

3. Outline Properties of spherical pendulum states Model Hamiltonian
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

8. Surfaces of section and periodic orbits

9. Periodic orbit bifurcations

10. Periodic orbit frequencies

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

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

14. Importance of resonance termsnp E

15. HCP extended RKR bending potential

16. HCP bend
monodromy
plot

17. l doubling

18. Vibration rotation constants

19. 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

20. Acknowledgements References 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, (2001)