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

Spherical pendulum P C θ H

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

Model Hamiltonian

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

Surfaces of section and periodic orbits

Periodic orbit bifurcations

Periodic orbit frequencies

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 np E

HCP extended RKR bending potential

HCP bend monodromy plot

l doubling

Vibration rotation constants

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 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, 10791 (2001)