1. Progress Towards a High-Precision Infrared Spectroscopic Survey of the H 3 + Ion Adam J. Perry, James N. Hodges, Charles Markus, G. Stephen Kocheril, Paul A. Jenkins II, and Benjamin J. McCall 70 th International Symposium on Molecular Spectroscopy University of Illinois at Urbana-Champaign 22 June 2015 MF05

2. Overview Motivation: H 3 + as a benchmark for ab initio theory Spectroscopic technique Current data Future directions

3. The Interplay Between Experiment and Theory Theoretical Prediction of Transition Frequencies Experimental Measurement Refinement of Calculations Improved Measurements

4. The Goal for Theory: Approaching “Spectroscopic Accuracy” To date it is only possible to calculate rovibrational energy levels/transitions for a select few molecular systems to accuracies of < 1 cm -1 : H2+H2+ H2H2 HeH + H3+H3+ Accuracy: ~10 -5 cm -1 (~300 kHz) Accuracy: ~2 x 10 -4 cm -1 (~6 MHz) Accuracy: ~10 -2 cm -1 (~300 MHz) Accuracy: 10 -2 -10 -1 cm -1 (~300 MHz - 3 GHz) V. Korobov, Phys. Rev. A., 77 022509, (2008) G.D. Dickenson, M.L. Niu, E.J. Salumbides, J. Komasa, K.S.E. Eikema, K. Pachucki, and W. Ubachs, Phys. Rev. Lett., 110, 193601, (2013) K. Pachucki, and J. Komasa, J. Chem. Phys., 137, 204314, (2012) M. Pavanello, L. Adamowicz, A. Alijah, N.F. Zobov, I.I. Mizus, O.L. Polyansky, J. Tennyson, T. Szidarovszky, and A.G. Csaszar, J. Chem. Phys., 136, 184303, (2012)

5. The Goal for Theory: Approaching “Spectroscopic Accuracy” To achieve such accuracies it is necessary to go beyond the Born-Oppenheimer approximation Corrections: – Adiabatic – Non-adiabatic – Relativistic – Quantum Electrodynamic (QED) Highly accurate and precise measurements of rovibrational transitions allow theorists to benchmark their calculations

6. The Marriage of Theory and Experiment: H 3 + First spectrum of H 3 + observed by Oka (1980) – Aided by ab initio calculations of Carney and Porter (1976) Calculation accuracy now on order of experimental uncertainties – Time for improved measurements T. Oka, Phys. Rev. Lett., 45, 531-534, (1980) G.D. Carney and R.N. Porter, J. Chem. Phys., 65, 3547, (1976) First observation of the R(1,0) transition of H 3 +

7. Ion Spectroscopy: Velocity Modulation Spectroscopy (VMS) Detector Laser Lock-In Amplifier C.S. Gudeman, M.H. Begemann, J. Pfaff, and R.J. Saykally. Phys. Rev. Lett. 50, 727-731, (1983)

8. Pushing the Limits of VMS Velocity Modulation (Ion-neutral discrimination) Velocity Modulation (Ion-neutral discrimination) B. M. Siller, et al. Opt. Express 19, 24822-7, (2011) Heterodyne Modulation (Reduction of 1/f technical noise) Heterodyne Modulation (Reduction of 1/f technical noise) Cavity Enhancement (Increase signal strength) Noise Immune Cavity Enhanced Optical Heterodyne Velocity Modulation Spectroscopy (NICE-OHVMS) NICE-OHVMS

9. NICE-OHVMS Spectrometer YDFL EOM Lock-In Amplifier X & Y Channels Lock-In Amplifier X & Y Channels ~ 80 MHz 90 o Phase Shift 2f = 80-100 kHz idler  pump  signal 40-50 kHz AOMAOM AOMAOM OPO Wavemeter Frequency Comb Lock Box PZT Slow Fast to PZT ~2-4 MHz ν 3.2-3.9 µm

10. H 3 + Spectra J.N. Hodges et al. J. Chem. Phys. (2013), 139, 164201. Relative Frequency (MHz) Frequency (cm -1 )

11. New Transition Frequencies Freq. (MHz)Prev. Value (MHz)Us-Prev. (MHz) R(3,3) u 87480191.43(117)87480219(300) a -27.28 R(3,2) u 87640201.59(254)87640158(300) a 43.61 R(5,5) l 88620962.34(144)88620809(300) a 153.25 R(4,3) u 90394720.09(232)90394651(150) b 69.01 R(4,2) u 90673895.29(179)90673968(150) b -72.52 R(4,1) u 90831978.56(177)90832078(150) b -99.70 a.T. Oka. Phil Trans R. Soc. London A (1981) 303, 543-549. b.C. M. Lindsay et al. J. Mol. Spectrosc. (2001) 210, 51-59. Transition Notation:

12. Measured Transitions to Date TransitionFreq. (MHz)TransitionFreq. (MHz) R(1,1) l 80687424.25(165)R(4,3) l 86778433.66(76) R(1,0)81720377.29(86)R(3,3) u 87480191.43(117) R(1,1) u 81730020.44(84)R(3,2) u 87640201.59(254) R(2,2) l 82804769.99(70)R(3,1) u 87789812.71(130) R(2,1) l 82908940.58(279)R(3,0)87844195.67(122) R(2,2) u 84635537.25(121)R(5,5) l 88620962.34(144) R(2,1) u 84724846.57(85)R(6,6) l 90368280.18(102) R(3,3) l 84839013.46(88)R(4,3) u 90394720.09(232) R(3,2) l 84907118.76(299)R(4,2) u 90673895.29(179) R(4,4) l 86774648.52(128)R(4,1) u 90831978.56(177) 20 rovibrational transitions measured to ~1 MHz precision!

13. P(3,3) P(5,0) R(1,1) l Q(2,1) l t R(1,0) Q(3,3) R(3,0) (3,0) (5,0) (4,0) (2,1) l (1,1) Ground (3,3) (2,3) (1,0) (2,1) Fundamental band transitions Selection Rule: ΔG = 0 Ground state energy level spacings Overtone transitions: Selection Rule: ΔG = ±3 Tie “G ladders” together

14. ortho G = 3n para G = 3n±1 (1,0) (1,1) (3,0) (5,0) G = |k-l| Energy (cm -1 ) (2,1) (3,1) (4,1) (5,1) C.M. Lindsay and B.J. McCall. J. Molec. Spectrosc. (2001), 210, 60-83. ortho and para “G ladders” tied together by a fit to the ground state energy levels

15. Conclusions

16. Acknowledgments Advisor: Ben McCall Group Members: James Hodges Charles Markus George Kocheril Funding Agencies