Spectroscopic signatures of a saddle point

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Spectroscopic signatures of a saddle point

• Modelled on HCP as a perturbed spherical pendulum

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Spherical pendulum
P
C
?
H
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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

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Model Hamiltonian
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Quantum pendulum states
2.0
1.0
E/V0
Diagonalize in a spherical harmonic basis
0.0
-1.0
k
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Semiclassical pendulum states
Complete analytical solution in terms of Elliptic
integrals, which yields the following limiting
formulae for k0
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Surfaces of section and periodic orbits
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Periodic orbit bifurcations
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Periodic orbit frequencies
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Polyad structure EltB
Inside Fermi res
Outside
Measured from lowest level of polyad
Mean polyad number np2vsvb
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Polyad structure 0ltElt2B
Vibrating states
Rotating states
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Importance of resonance terms
?E
np
E
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HCP extended RKR bending potential
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HCP bend monodromy plot
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l doubling
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Vibration rotation constants
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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 1n resonances
• RKR plus ab initio information used to determine
  realistic HCP bending potential
• Anomalously large vibn/rotn interaction
  parameters explained and predicted

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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)