1. The role of asymptotic states in H 3 + Jonathan Tennyson Department of Physics and Astronomy Royal Society University College London Jan 2006 HPCx supercomputer: Daresbury Laboratory

2. Spectroscopy of H 3 + “Solved problem” at low energy How about near dissociation? Nature of (rotation-)vibration states? Radiative association: H 2 + H +  H 3 + + h Isotope exchange eg HD + H 3 +  H 2 + H 2 D + Meilke et al, Phys. Rev. Lett. 91, 063201 (2003)

3. Accurate H 3 + PES Realistic potential energy surface: Polyansky et al, Mol. Phys., 98, 261 (2000). r R  Jacobi coordinates

4. Density of states: requires serious computer power Even states

5. H 3 + near dissociation vibrational state

8. Calculated rotational constants for H 3 + JJ Munro, J Ramanlal & J Tennyson, New J Phys, 7, 196 (2005)

10. r R  =90 Classical trajectory at 19600 cm -1

11. Poincare surface of section at 19600 cm -1 r p

12. Classical trajectory above dissociation r R  =90 “Feshbach” resonance

13. Poincare surface of section for D 0 > E > D e

14. Creates H 3 + Detects H + CO 2 laser: 800 – 1000 cm -1 H 3 + + h  H 2 + H + Near-dissociation photodissociation experiment of Carrington et al

15. Quantum states at dissociation: Near dissociation spectrum of H 3 + by Carrington et al 25000+ discrete lines in 222 cm -1

17. Technique for characterising resonances 1.Solve H 0  0 = E  0  for all E including > D 0. 2.Solve H = H 0 + i  U(R) for  0 dropping bound solutions; i U(R) is complex absorbing potential (CAP). 3. Vary to identify resonances in complex plane.

18. Continuum wavefunction r R  = 90

19. Complex Absorbing Potential (CAP) comparison

20. Position Width Locating resonances using a CAP

21. Vibrational (Feshbach) resonances Width (  ) > 1 cm -1 Too short lived to be important for photodissociation spectrum

22. Shape resonances: rotational states trapped by centrifugal barrier KE release

23. Complete model of H 3 + near-dissociation photodissocation spectrum Vibrational states @ dissociation + above Rotational states @ dissociation + above Resonances: lifetime effects Dipole transitions: spectroscopy Asymptotic Vibrational States (AVS) Robust Present in other (all?) molecules eg O 3, NO 2

24. Bruno Silva Paolo Barletta James Munro ChemReact High Performance Computing Consortium