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## Spectroscopic signatures of a saddle point

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**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 • Rotation/vibrational dynamics of HCP bending states Extended RKR potential function Anomalous magnitudes of vibn/rotn parameters • Summary**Quantum pendulum states**2.0 1.0 E/V0 Diagonalize in a spherical harmonic basis 0.0 -1.0 k**Semiclassical pendulum states**Complete analytical solution in terms of Elliptic integrals, which yields the following limiting formulae for k=0**Polyad structure E<B**Inside Fermi res Outside Measured from lowest level of polyad Mean polyad number np=2vs+vb**Polyad structure 0<E<2B**Vibrating states Rotating states**Importance of resonance terms**ΔE np E**HCP bend**monodromy plot**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**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)