Spectroscopic signatures of a saddle point

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    09-Feb-2016
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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 - PowerPoint PPT Presentation

Transcript of Spectroscopic signatures of a saddle point

  • Spectroscopic signatures of a saddle pointModelled on HCP as a perturbed spherical pendulum

  • Spherical pendulumCPH

  • OutlineModel HamiltonianProperties of spherical pendulum statesClassical trajectories of the coupled modelAnharmonic resonancesPolyad structure Rotation/vibrational dynamics of HCP bending statesExtended RKR potential functionAnomalous magnitudes of vibn/rotn parametersSummary

  • Model Hamiltonian

  • Quantum pendulum statesDiagonalize in a spherical harmonic basisE/V02.01.00.0-1.0k

  • Semiclassical pendulum statesComplete 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
  • Polyad structure 0
  • Importance of resonance termsEEnp

  • HCP extended RKR bending potential

  • HCP bendmonodromyplot

  • l doubling

  • Vibration rotation constants

  • SummaryClassical and semiclassical methods used to illuminate dynamics of HCP-like modelClassical bending frequency function and Heisenberg matrix elements used to model occurrence and strength of 1:n resonancesRKR plus ab initio information used to determine realistic HCP bending potentialAnomalously large vibn/rotn interaction parameters explained and predicted

  • AcknowledgementsM P Jacobson (UCSF)C D Cooper (Oxford)UK EPSRCReferencesM 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)