1. High-Resolution Near-Infrared Spectroscopy of H 3 + Above the Barrier to Linearity Jennifer Gottfried and Takeshi Oka University of Chicago Benjamin J. McCall University of California, Berkeley

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 stable electronic excited states Vibrational spectroscopy  the doubly-degenerate bending mode, 2, is IR active

3. Recent NIR Bands Oka (1980) - 1 st experimental detection of H 3 + ! Hot Bands Forbidden Bands 1st and 2nd Overtone Bands Vibrational Bands 0 2 2020 2222 2121 2323 2020 2222 2424 2121 1 + 2 1 1 +2 2 0 1 +2 2 2 1 + 3 2 1 + 4 2 11  1 + 2  1 +2 2  1 +3 2 2323 2525 11 0 2000 4000  1 + 2  1 +2 2 6000 8000 10000 12000 14000 Energy (cm -1 ) [B.J. McCall, JCP 113, 3104 (2000)]

4. 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 Improvements in the sensitivity of astronomical observations may eventually allow the detection of even higher energy levels in Jupiter and/or in hot astronomical objects (e.g. planetary nebulae)

5. Motivation for Studying H 3 + at High Energies Theoretical importance Benchmark for first principle quantum mechanics calculations simplest polyatomic molecule Comparison between experimental and calculated energy levels  important diagnostic tool Closing the 25,000 cm -1 gap current experimental energy levels ~10,000 cm -1 enigmatic predissociation spectrum ~35,000 cm -1

6. Predissociation Spectrum Energy diagram showing significant energies of H 3 + Pseudo-low resolution convolution of experimental data [Carrington, Kennedy, J. Chem. Phys. 81, 1 (1984)] [Kemp, Kirk, McNab, Phil. Trans. R. Soc. Lond. A 358, 2403 (2000)]

7. Motivation for Studying H 3 + at High Energies Theoretical importance, cont’d Breaking the barrier to linearity Interesting challenge for theorists at linear configurations h

8. Barrier to Linearity  The singularity in the kinetic energy operator above the barrier to linearity is difficult to deal with computationally  Current theoretical calculations above the barrier:  J.K.G. Watson  J. Tennyson  A. Alijah

9. Production of H 3 + ~500 mTorr H 2, 500 mA, n(H 3 + ) ~ 10 11 cm -3

11. Detection of H 3 + Mid-Wavelength Optics Set: ~11,000-12,700 cm -1

12. Improvements in Sensitivity Very weak signals, need to increase sensitivity fractional absorption ~ 2 × 10 -5 Unidirectional Multipassing (8 m path length) Noise Subtraction Co - addition (~100 scans,  =30 ms/scan) Modulation Techniques Velocity modulation (~20 kHz) Frequency modulation (500 MHz) Mike Lindsay, Chris Neese and Takeshi Oka: WJ10

13. Vibrational Bands 0 2 2020 2222 2121 2323 2020 2222 2424 2121 1 + 2 1 1 +2 2 0 1 +2 2 2 1 + 3 2 1 + 4 2 11  1 + 2  1 +2 2  1 +3 2 2323 2525 11 0 2000 4000  1 + 2  1 +2 2 6000 8000 10000 12000 14000 Energy (cm -1 ) 20 new lines above the barrier! [manuscript in preparation]

14. Strongest H 3 + line observed in an ordinary molecule, the fourth overtone would be 3 million times weaker than the fundamental! in H 3 +, it is "only" 5000 times weaker! Fit to second derivative Gaussian lineshape double-modulation Example Spectrum

15. Comparison to Theory All experimental energy levels below 9000 cm -1 have been compared to theoretical values Average calculation errors ( ):  Jaquet98 (Cencek) ~ -0.68 cm -1 ▬ Jaquet99 (Cencek) ~ 0.08 cm -1 oAlijah (Röhse) ~ 0.92 cm -1 ▼ Alijah (Cencek) ~ 0.50 cm -1 Rotational and vibrational dependencies observed  can now be corrected for by theorists [Lindsay and McCall, J. Mol. Spectrosc. 210, 60 (2001)]

16. Theoretical Calculations Watson: inserted an artificial wall in the potential at linear geometries Morse oscillator-like wavefunctions vanish at  =  [private communication, 1996] Tennyson: Jacobi coordinates with spherical oscillator functions convergence problems at high J [Neale, Miller, Tennyson, Astrophys. J. 464, 516 (1996)] Alijah: hyperspherical coordinates with hyperspherical harmonics singularity handled naturally in basis set [Alijah, Schiffels, Hinze, manuscript in preparation, 2001]

17. Comparison to Theory Watson: not accurate near barrier, as expected Neale, Miller & Tennyson (NMT): ~0.68 cm -1 high Alijah (corrected): ~0.22 cm -1 low

18. Comparison to Theory

20. Conclusions Theoretical calculations on H 3 + are rapidly approaching spectroscopic accuracy More energy levels above 12,000 cm -1 would be useful in determining the accuracy of Alijah’s correction factors Especially important as the mixing between vibrational bands becomes worse The short-wave (and long-wave) optics set of the Ti:Sapphire laser