1. Xinchuan Huang, 1 David W. Schwenke, 2 Timothy J. Lee 2 1 SETI Institute, Mountain View, CA 94043, USA 2 NASA Ames Research Center, Moffett Field, CA 94035, USA Columbus, Ohio June 23, 2009 The 64 th International Symposium on Molecular Spectroscopy Accurate Rovibrational Energy Levels for 14 NH 3 / 15 NH 3 IR Linelists up to 6000 cm -1 --- Success of “Best Theory + High-res Exp” Strategy

2. Acknowledgements Theoretical  Timothy J. Lee (NASA Ames, USA)  David W. Schwenke (NASA Ames, USA)  Joel M. Bowman (Emory Univ., USA) Funding NPP/ORAU Spitzer / Herschel (NASA) 2 Experimental  Li-Hong Xu (UNB, Canada)  John C. Pearson (NASA JPL, USA)  Isabelle Kleiner (LISA, CNRS, France)  Linda R. Brown (NASA JPL, USA)

3. Introduction & Review Wide existence in universe Environment-sensitive NH 3 – ND 3 observed LAM: Inversion/Umbrella mode Difficulties in spectra analysis Limitations of HITRAN data: up to 5500 cm -1 above ZPE   0.1 cm -1 beyond 3000 cm -1 intensity data limited to 296 K Not perfect for future high-res, high-energy and high-temp astronomical analysis “Best Theory + High-res Exp” strategy (1 st applied on H 2 O) What we want: Line Positions:  rms < 0.05 cm -1 Intensities: |  | < 10% Up to 20,000 cm -1 above ZPE A pure ab initio PES, HSL-0: CBS/rel/Core/DBOC/ACPF/…  rms = 2.1 cm -1 up to 10,300 cm -1 HSL-1, refined with J = 0-2 energy levels (HITRAN-based) --- see JCP 129, 214304 (2008) Why do NH 3 IR linelists ?Goal & What’s done before ? 3

4. Quick Summary of Latest results 482 of 1012 HITRAN-based energy levels of 14 NH 3 (J up to 6) Non-adiabatic corrections (critical for rms  0.04 cm -1 )  HSL-2 Note: J  6 4111 trans  1012 levels J  22 25229 trans  3391 levels Exact quantum ro-vib calc Reproduce >99.5% 14 NH 3 levels and transition freq in HITRAN (J up to 6),  = 0.01 – 0.02 cm -1   0.03 cm -1 for 15 NH 3 transitions Similar accuracy for predictions: 4 2 line positions and splits New assignments / levels for HITRAN 15 N Isotopic shifts for all HITRAN- related levels (J up to 6) Beyond 6000 cm -1 : ~1 cm -1 accuracy in 6000-7000 cm -1 What’s NEW for HSL-2 ?What can we provide on HSL-2 ? 4

5. Ammonia in Universe: 0 – 1500 K 5 Titan Neptune NGC 253, 140-400 K Uranus 50 – 100 K Gl 229B ( 1000 K, Artist ) Sgr B2, 700 K

6. 1597.5 E (cm -1 ) 1882.2 968.1 932.4 0.79 0.00 3-3- 3+3+ 1-1- 1+1+ 0-0- 0+0+ Barrier Height  1785 cm -1 2895.5 2384.2 2-2- 2+2+ 4-4- 4+4+ 4061.8 3462.5 6 N Inversion / Umbrella mode  All rovibrational levels split  Temperature & Pressure sensitive  More complete data expected for high- energy, high-temperature, and inversion- related spectra.  Very few data for isotopologues ( ND 3 detected in 2002 ) Inversion Splits of 14 NH 3

7. 7 Accurately measured and analyzed < 50% bands fully analyzed Some  > 0.1 cm -1 High-res data or analysis Unavailable 3-4 bands by Lees & Xu  = 0.5 – 1 cm -1 14 NH 3 : Density of States Energy / cm -1

8. Goal, Procedure & Progress Update 1) Compute the best possible ab initio data : (Done, reported in 08) <6000 selected geometries, CBS+core+rel+DBOC+ACPF corr 2) Get accurate global PES/DMS : (Done, HSL-0 reported in 08) V=V short + V long,  rms = 0.1 cm -1 below 40,000 cm -1, DMS tested. Best PES balanced between high & low energy region 3) Empirical Refinement: using selected HITRAN data : HSL-1 reported in 08’ OSU Symposium & JCP 129, 214304 (2008) Now HSL-2: non-adiabatic corrections included,  = 0.01-0.03 cm -1 Accuracy / Quality will depend on and are limited by high-res data 4) Compute accurate intensities for all possible transitions (09-10) 5) Release to public the sorted IR linelists. 8 Compute highly-accurate IR line lists for 14 NH 3, 15 NH 3, 14 ND 3, 14 NHD 2, and 14 NH 2 D, up to 20,000 cm -1 above ZPE

9. 9 HSL-0 Our Best ab initio PES before any refinements

10. 1 ST Refinement with J=0-2 Levels: HSL-1 10 HSL-1 JCP 2008 129, 214304 Non-adiabatic corrections excluded from refinements & exact rovibrational CI

11. 11 HSL-2 (in prep) Non-adiabatic corrections are necessary for rms < 0.04 cm -1. 2 nd Refinement with J=0-6 Levels: HSL-2

12. 12 rms = 0.015 cm -1, for 982 paired states rms = 0.011 cm -1, for 491 inv splits HSL-2 HSL-0 HSL-1 Improving Accuracy (HSL-0  HSL-1  HSL-2)

13. 13 HSL-0 HSL-2HSL-1 rms = 0.015 cm -1, for 982 paired states rms = 0.011 cm -1, for 491 inv splits Improving Accuracy (HSL-0  HSL-1  HSL-2)

14. J IR-related states Paired States rms for ALL 982 paired states +/- ∆ +/∆ 0 21140.0140.012 1 64580.0120.009 2 105980.0130.009 3 1471400.0130.0090.010 4 1891820.0140.011 5 2312240.0160.0110.012 6 2732660.0170.0120.013 Total10309820.0150.011 14 Due to expensive computing cost at higher J’s, it is extremely important to keep rms stable when J rises Stable Accuracy (  rms ) for Higher J Levels

15. Band Used in Opt Paired states rms for ALL 982 paired states +/- ∆ +/∆ GS26440.006<0.0010.004 4 68980.0080.0030.006 2 4 * 561400.0080.0090.008 3 46980.0080.0090.008 2 + 4 52980.0260.0130.017 2 + 3 52980.0060.007 3 + 4 38980.0140.0130.014 2 24420.0260.0220.018 2 20420.0340.0130.022 3 2 22420.0120.0200.016 1 18420.0110.0050.007 1 + 4 36980.0100.0080.009 1 + 2 24420.0210.0110.013 Total4829820.0150.011 Accuracy of energy levels of 13 Bands (J  6) 15 * 12 suspicious trans (and 4 levels) are excluded from statistics

16. Accuracy on Line positions (J  6) Bands No. of Trans  rms  (min)  (max) 0 0 1620.005-0.0150.012 0 1 0 03170.023-0.0040.036 0 2 0 01710.037-0.053-0.017 0 3 0 01140.014-0.0300.017 0 0 0 14770.005-0.0110.016 0 0 0 2 0 *1650.011-0.0280.027 0 0 0 2 2 *3390.007-0.0200.016 0 0 1 1 02950.010-0.0260.010 0 0 1 1 1 1 2140.011-0.0340.031 0 1 0 1 1 2290.030-0.054-0.002 0 1 1 1 02050.009-0.0250.006 1 0 0 01270.015-0.024-0.002 1 0 0 1 1 1580.010-0.0290.029 1 1 0 01140.024-0.042-0.005 Total30870.017 -0.0530.036 * 12 suspicious trans (and 4 levels) are excluded from statistics Bands No. of Trans  rms  (min)  (max) 0 1 0 01630.015-0.0220.026 0 2 0 01140.057-0.081-0.042 0 3 0 0930.027-0.043-0.010 0 1 0 1 1 3140.051-0.079-0.015 0 0 1 1 01900.029-0.0580.005 0 0 0 2 0 250.025-0.0400.027 0 0 0 2 2 1120.027-0.041-0.001 Total10110.039 -0.0810.027 14 fundamental bands 7 hot-bands rising from 2

17. 17 15 NH 3 : 0.00 – 0.03 cm -1 for 3 HITRAN bands 25 rot Trans (J ≤ 4)  = 0.0003 cm -1 10 MHz 1 1 (+)  0 0 (-) 44 2 Trans (J ≤ 4)  = 0.0299 cm -1 55 3+ 4 Trans (J ≤ 4)  = 0.0093 cm -1 25 states (J ≤ 4) Model  = 0.57 cm -1 25 states (J ≤ 4) Model  = 0.58 cm -1 39 states (J ≤ 4) Model  = 0.33 cm -1

18. Isotopic shifts: from 14 NH 3 to 15 NH 3 18 E( 14 NH 3 ) – E( 15 NH 3 ) For all J ≤ 6 levels available in HITRAN

19. 19 4 2, Kleiner et al, J. Mol. Spectrosc. 193, 46 (1999). 49 tentative assignments, 22 rovibrational levels (J  6) 41 transitions verified, 18 levels verified  = 0.017 cm -1 4 levels can not match: JKs=11s,51s,52s,55s 4 2  2, Cottaz et al, J. Mol. Spectrosc. 209, 30 (2001). 34 tentative assignments, 19 rovibrational levels (J  6) 33 transitions verified, 18 levels verified (2 new levels)  = 0.021 cm -1 1 new level cannot match: JKs=62s Level 11s now matches ! (Levels 51s, 52, 55s are not in Cottaz et al.) Predictions: 14 NH 3 4 2 and beyond n01234567  (cm -1) 0.7935.7284.7511.4599.3665.5706.7744.1 __________________ Predictions Inversion Splits of n 2 band origins, n = 0 – 7 ______________________________ 0.00 – 0.03 cm -1 accuracy * “can not match”  differences > 0.04 cm -1

20. More Assignments & 1 ST 2 2 + 4 Level 20 2 4 – 6 2 0 s/a: missing from HITRAN E calc = 3637.1061 cm -1 / 3643.3490 cm -1 Following trans can be fully assigned: (lower state assigned in HITRAN) 1 st level for 2 2 + 4 band, 6 0 1s, found in existing HITRAN data E calc = 3622.8616 cm -1. 6 0 1 s  0000–7 2 0 a,  = 0.0025 cm -1 6 0 1 s  0000–7 5 0 s,  = 0.0026 cm -1 6 0 1 s  0000–5 2 0 a,  = 0.0025 cm -1 6 0 1 s  0000–5 5 0 s,  = 0.0025 cm -1 6 2 0 s  0000–7 1 0 s,  = -0.0081 cm -1 6 2 0 s  0000–7 2 0 a,  = -0.0083 cm -1 6 2 0 s  0000–7 5 0 s,  = -0.0084 cm -1 6 2 0 s  0000–6 5 0 s,  = -0.0083 cm -1 6 2 0 s  0000–5 2 0 a,  = -0.0085 cm -1 6 2 0 a  0000–7 2 0 s,  = 0.0021 cm -1 6 2 0 a  0000–7 5 0 a,  = 0.0022 cm -1 6 2 0 a  0000–6 5 0 a,  = 0.0022 cm -1 6 2 0 a  0000–5 1 0 a,  = 0.0025 cm -1 *Note: 5 other trans need further investigation *Note: 1 more trans needs further investigation

21. Calc Band Origin (s) Calc – Exps Exp Assignment Our Assignment Leading CI coeff Split Calc Split Exp * 6556.8 (E)0-1 1 +2 4 2 0.840 1.51 6605.7 (A)0-2 2 1 0.6260.97 6610.3 (E)1-2 1 + 3 3 +2 4 0 0.640 0.930.94 6650.8 (A)??? 3 +2 4 2 (A) 0.8541.17 6666.2 (E)??? 3 +2 4 2 (E) 0.755-0.48 6679.4 (E)1-2 3 +2 4 2 (E) 1 + 3 0.612 0.680.79 6797.9 (A)1-2 2 3 0 0.763-1.39 21 * Exp splits were reported by Lees & Xu, 2004 – 2008. Beyond 6000 cm -1 : Inversion Splits Accuracy / Quality will depend on and are limited by high-res data

22. 22 * Exp values were reported by Lees & Xu, 2004 – 2008. 14 NH 3 - 2 3 l=0 14 NH 3 - 1 + 3 15 NH 3 - 1 + 3 14 NH 3 - 1 +2 4 (E) ~1.2 ~0.4 ~1.5 Beyond 6000 cm -1 : ~1 cm -1 Deviations

23. Goal & Impact 2 nd molecular high-resolution IR line list for coming golden age of high-resolution IR astronomy, most important N-containing molecule GOAL: Accurate IR line list up to 20,000 cm -1 above ZPE. Current Stage Have reached 0.01 – 0.03 cm -1 accuracy for line positions Reliable predictions on new bands & transition assignments Future work High-energy spectra calibrations Higher J calc for 14 NH 3 / 15 NH 3 Nonadiabatic corrections for 14 ND 3, 14 NHD 2, 14 NH 2 D, and 14 NT 3 IR Intensity Calculations ! -- Ultimate proof 23 Summary & Next Step

24. Future Projects: Methanol, H 3 O +, etc. “Best Theory + High-res Exp” Strategy Better than 0.05 cm -1 Accuracy Reliable Predictions & Extrapolations Straightforward Assignments Similar Accuracy for Isotopologues Next molecule: methanol (CH 3 OH) Low-temperature IR spectra Future: H 3 O +, CH 3 CN, CH 3 OCH 3, etc… 24