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)