1. Near-Infrared Spectroscopy of H 3 + Above the Barrier to Linearity Jennifer L. Gottfried Department of Chemistry, The University of Chicago *Current address: U. S. Army Research Laboratory, Aberdeen Proving Ground, Maryland Royal Society Discussion Meeting, January 16, 2005

2. Introduction to H 3 + Geometry of H 3 + Simplest polyatomic molecule Ground state equilibrium structure is an equilateral triangle: Spectroscopy of H 3 + No allowed rotational spectrum No discrete electronic spectrum Vibrational spectroscopy symmetric stretch 1 not IR active 3178.36 cm -1 the doubly degenerate mode 2 is IR active 2521.38 cm -1 vibrational angular momentum ℓ

3. McCall 25 years of laboratory spectroscopy of H 3 + Jupiter ISM Galactic Center Saturn & Uranus OkaGottfried Lindsay & McCall, JMS 210, 60 (2001).

4. 2323 2222 2323 2 2020 2222 2121 2020 2424 2121 2525 11   1 + 2 1+21+2 1 11  1 + 2 1+21+2 1+21+2 2020 2222 2424 2626 1 + 2 1 +  2 0 1 +  2 2 1 +  2 1 +  2 Vibrational Bands Hot bands Overtones Forbidden transitions Combination bands 2 fundamental band [T. Oka, Phys. Rev. Lett. 45, 531 (1980)]

5. Motivation for Studying H 3 + at High Energies Astronomical importance The first overtone (2 2  0) has been observed in emission in Jupiter, as have hot band transitions from the 3 2 level 6669 cm -1 in overtone bands 7993 cm -1 in hot bands Theoretical importance Benchmark for first principle quantum mechanics calculations Comparison between experimental and calculated energy levels  important diagnostic tool [P. Drossart, J. P. Maillard, J. Caldwell et al., Nature (London) 340, 539 (1989).] [E. Raynaud, E. Lellouch, J.-P. Maillard, G. R. Gladstone, et al. Icarus 171, 133 (2004).]

6. Barrier to Linearity 

7. Expectation Values (Watson) J=0-2, J=3-5, J=6-10, J=11-15, J=16-20

8. 4 passes through cell clockwise 4 passes through cell counter- clockwise Discharge driven at 19 kHz = velocity modulation Electro-optic modulator (EOM) driven at 500 MHz = frequency modulation Signal demodulated by double- balance mixer (DBM) and lock-in amplifiers (PSD) external wavemeter, I 2 cell and 2-GHz étalon provide frequency calibration continuous coverage from ~10,650-13,800 cm -1 938-725 nm (3 optics sets) Near-Infrared Spectrometer Burleigh WA-1500 J. L. Gottfried, “Near-infrared spectroscopy of H 3 + and CH 2 + ” Ph.D. Thesis, University of Chicago, August 2005.

9. 2323 2222 2323 2 2020 2222 2121 2020 2424 2121 2525 11   1 + 2 1+21+2 1 11  1 + 2 1+21+2 1+21+2 2020 2222 2424 2626 1 + 2 1 +  2 0 1 +  2 2 1 +  2 1 +  2 Vibrational Bands 22 new transitions above the barrier to linearity J. L. Gottfried, B. J. McCall, and T. Oka, J. Chem. Phys. 118, 10890 (2003). 15 new transitions C. F. Neese, C. P. Morong, T. Oka, in progress (see Exhibit).

10. Improvement in Sensitivity Sensitivity ~1.5×10 -2 Sensitivity ~10 -8

11. Hydrogen Rydberg Transitions Pure H 2 (500 mTorr) discharge H 2 * is only interferent H 2 excited by e - bombardment acquires momentum, usually anion lineshape Quenched by metastable He* 10 Torr He added for discrimination

12. Near-infrared Transitions of H 3 + combination long/mid- wavelength optics set: 10,725-10,790 cm -1 (8 lines) midwavelength optics set: 11,019-12,419 (22 lines)

13. Visible Transitions of H 3 + short wavelength optics set: 12,502-13,677 cm -1 (7 lines) (midwavelength optics set)

14. Importance of Theoretical Calculations B 0 = 43.565 cm -1 C 0 = 20.605 cm -1 q = - 5.372 cm -1 Oka, Phys. Rev. Lett. 45, 531 (1980). ζ = - 1 Strong vibration- rotation interaction

15. Observed Spectrum of H 3 +  1  2 ℓ  G {P |Q |R } (J,G ) u/l J < 4 4 th 5 th observed lines, predicted lines by Neale, Miller, Tennyson 1996

16. Röhse, Kutzelnigg, Jaquet, Klopper (RKJK) Cencek, Rychlewski, Jaquet, Kutzelnigg (CRJK) Dinelli, Polyansky, Tennyson (DPT) Jaquet (Jaq02) Alijah, Hinze, Wolniewicz (AHW) Neale, Miller, Tennyson (NMT) Schiffels, Alijah, Hinze (SAH) Jaquet (Jaq03) error < ±0.1 cm -1

17. [Neale, Miller, Tennyson, Astrophys. J. 464, 516 (1996).] [Jaquet, Prog. Theor. Chem. Phys. 13, 503 (2003).] [Alijah, Hinze, Wolniewicz, Ber. Bunsenges. Phys. Chem. 99, 251 (1995)] [Schiffels, Alijah, Hinze, Mol. Phys. 101, 189 (2003).] [Alijah, private communication (2003).] Comparison to Theory purely ab initio calculation!empirical correction for nonadiabatic effects

18. Errors in calculated energy levels significantly larger above the barrier to linearity Conclusions Neese, Morong, Oka (in progress) Gottfried, McCall, Oka 2003

19. First principle ab initio theory on H 3 + has reached spectroscopic accuracy only nonadiabatic and QED corrections missing H 2 : W. Kołos, L. Wolniewicz 1964 – 1975 J. Mol. Spectrosc. 54, 303 (1975) H 3 + : Schiffels, Alijah, Hinze, Mol. Phys. 101, 175, 189 (2003) Conclusions Nearly 30 years to progress from a two- particle problem to a three-particle problem!

20. Expect to observe an additional 90 transitions of H 3 + with current spectrometer Future Prospects

21. Continuing climb up energy ladder (6 2 4  0, 7 2 1  0,…) Future Prospects Pseudo-low resolution convolution of experimental data [Carrington, Kennedy, J. Chem. Phys. 81, 1 (1984)] Energy diagram showing significant energies of H 3 + [Kemp, Kirk, McNab, Phil. Trans. R. Soc. Lond. A 358, 2403 (2000)] Improvements in experimental sensitivity needed! visible dye laser

22. Takeshi Oka Ben McCall Chris Neese and Chris Morong J. K. G. Watson and A. Alijah National Science Foundation Graduate Research Fellowship NSF Grants Acknowledgements