Ab initio calculations of highly excited NH3 levels Oleg Polyansky Physics and Astronomy University College London Urbana June 2016 Image credit Shutterstock

Completeness: Absorption of ammonia (T=300 K) BYTe Less than 30,000 NH3 lines are known experimentally: our list contains 1.1 billion lines, or about 40,000 times as many! They represent all the allowed transitions between 1.2 million upper and lower ro-vibrational states, whose individual quantum numbers are detailed in the list. For comparison, it is worth noting that our earlier T=300 K NH3 line list comprises only 3.25 million transitions between 184,400 states. It has an upper energy cut-off of 12,000 cm-1 and a maximum rotational quantum number J=20. Less than 30,000 NH3 lines known experimentally: BYTe contains 1.1 billion lines, about 40,000 times as many! S.N. Yurchenko, R.J. Barber & J. Tennyson, Mon. Not. R. astr. Soc., 413, 1828 (2011) 2

Frontier Problems in Exoplanet Characterization Non-equilibrium processes in exoplanet atmospheres (Stevenson et al. 2010; Madhusudhan & Seager 2011; Moses et al. 2013) CH4, CO, NH3 Constraints on thermal inversions in hot Jupiters (Fortney et al. 2008; Spiegel et al. 2009) TiO, VO, H2S C/O ratios and Carbon-rich atmospheres (Fortney et al. 2008; Spiegel et al. 2009) H2O, CO, HCN, CH4, C2H2,TiH, FeH Constraints on exoplanet formation conditions (Madhusudhan et al. 2011; Oberg et al. 2011) H2O, CO, CH4 Atmospheres and interiors of super-Earths (Bean et al. 2011; Desert et al. 2011; Miller-Ricci Kempton et al. 2011 ) H2O, CO2 Frontier Problems in Exoplanet Characterization Polish this slide. Order the points properly, etc.. Slide courtesy of N Madhusudhan (Cambridge)

Results Hot Jupiter, eclipse Retrieve majority of temperature profile, H2O, CO2 and CH4 well. Not so good at CO and NH3 – not so many absorption lines and those present are contaminated by H2O/CO2. Only upper limit on CO and NH3 achievable where VMR falls below 100 ppmv. Barstow et al. 2013a

Transmission of main candidate molecules (H2O, CO2, CO, CH4,NH3)

Completeness: Absorption of ammonia (T=300 K) BYTe Less than 30,000 NH3 lines are known experimentally: our list contains 1.1 billion lines, or about 40,000 times as many! They represent all the allowed transitions between 1.2 million upper and lower ro-vibrational states, whose individual quantum numbers are detailed in the list. For comparison, it is worth noting that our earlier T=300 K NH3 line list comprises only 3.25 million transitions between 184,400 states. It has an upper energy cut-off of 12,000 cm-1 and a maximum rotational quantum number J=20. Less than 30,000 NH3 lines known experimentally: BYTe contains 1.1 billion lines, about 40,000 times as many! S.N. Yurchenko, R.J. Barber & J. Tennyson, Mon. Not. R. astr. Soc., 413, 1828 (2011) 6

H2OF+H2O H2F+ NH3 H3O+ CH4 H2O H2F+ NH3 H3O+ CH4 Молекулы с числом электронов : 10 H2OF+H2O H2F+ NH3 H3O+ CH4 H2O H2F+ NH3 H3O+ CH4 Вариационные программы: TROVE (3,4 атома) DVR3D (3 атом)

Figure 1. Schematic energy level diagram employed in experiment. Our prediction 41 146.0 cm-1 Global ab initio PES so far ~10 cm-1

H2O pokazatel 0 1 0 1594.74 0.01 3 0 2 17458.21 0.06 0 0 1 3755.92 -0.02 2 1 3 18989.95 -0.05 0 2 0 3151.63 0.04 1 0 4 17748.1 -0.04 0 1 1 5331.26 0.00 3 4 1 19679.19 -0.07 1 0 0 3657.05 5 1 0 18392.77 0 2 1 6871.52 5 0 1 19781.1 0 3 0 4666.79 6 0 0 19781.32 0.02 1 0 1 7249.81 -0.08 4 2 1 19865.28 1 1 0 5234.97 6 1 0 21221.56 0.05 0 3 1 8373.85 2 2 3 20442.77 0 4 0 6134.01 7 0 0 22529.29 -0.06 1 1 1 8806.99 3 0 3 20543.12 1 2 0 6775.09 5 3 2 27502.66 -0.23 0 4 1 9833.58 -0.01 5 1 1 21221.82 2 0 0 7201.54 9 0 0 27540.69 0.15 1 2 1 10328.72 4 3 1 21314.44 0.03 0 0 2 7445.04 6 1 2 27574.91 2 0 1 10613.36 6 0 1 22529.43 0 5 0 7542.43 9 1 0 28934.14 0.83 0 0 3 11032.4 7 0 1 25120.27 1 3 0 8273.97 10 0 0 29810.85 0.42 1 3 1 11813.2 9 0 1 29810.87 0.43 2 1 0 8761.58 10 1 0 31071.57 -0.03 2 1 1 12151.25 11 0 1 33835.22 0.16 0 6 0 8869.95 -0.16 8 0 2 31207.09 -1.72 0 1 3 12565 9 0 3 35509.68 -8.18 0 1 2 9000.14 11 0 0 31909.68 0.67 2 2 1 13652.65 12 0 1 35586.01 -0.56 2 2 0 10284.36 11 1 0 33144.71 3 0 1 13830.93 12 1 1 36684.88 -2.05 0 2 2 10521.76 12 0 0 33835.25 0.19 0 7 1 13835.37 9 1 3 36739.78 -2.31 3 0 0 10599.68 13 0 0 35585.96 0.41 0 2 3 14066.19 13 0 1 37122.72 0.56 1 0 2 10868.87 12 2 0 36179.32 -5.56 1 0 3 14318.81 11 3 1 37309.85 0.22 2 3 0 11767.38 13 1 0 36684.05 -2.84 1 5 1 14647.97 13 1 1 38153.31 0 3 2 12007.77 10 1 2 36740.6 0.54 2 3 1 15119.03 14 0 1 38462.54 1.11 3 1 0 12139.31 14 0 0 37122.7 0.52 3 1 1 15347.95 14 1 1 39390.22 1.22 1 1 2 12407.66 12 3 0 37311.28 -0.59 0 3 3 15534.7 15 0 1 39574.54 0.25 4 0 0 13828.27 13 2 0 37765.65 1 1 3 15832.78 14 2 1 40226.31 -4.14 1 2 2 13910.89 14 1 0 38153.25 2 4 1 16546.31 15 1 1 40370.83 -0.72 2 0 2 14221.15 15 0 0 38462.52 1.10 3 2 1 16821.63 16 0 1 40437.26 1.99 0 0 4 14537.5 14 2 0 39123.77 0.24 4 0 1 16898.84 17 0 1 40949.31 3.88 3 3 0 15108.23 0.11 15 1 0 39390.26 1.26 1 2 3 17312.55 4 1 0 15344.5 16 0 0 39574.55 2 0 3 17495.52 2 1 2 15742.8 16 1 0 40370.55 -0.92 3 3 1 18265.82 4 2 0 16823.31 17 0 0 40437.23 2.09 4 1 1 18393.31 2 2 2 17227.37 18 0 0 40947.49 -8.59 1 3 3 18758.63

BT2 (water) – 0.5 Billion lines H216O POKAZATEL BT2 (water) – 0.5 Billion lines POKAZATEL – 10 billion lines, first complete Linelist of polyatomic molecule, every transition Between every bouind state is included POKAZATEL – PolyanskyOleg,Kyuberis Aleksandra, Zobov nikolAi, Tennyson, Lodi,(and Yurchenko)

H216O, J=0-72, T=296K, Pokazatel, 13000-25000cm-1 H216O, J=0-50, T=296K, BT2, 13000-25000cm-1

Structure of the talk Why we did what we did What we did for NH3 How we have done it

Low lying energy levels of NH3

Recently assigned NH3 band origins Band obs. BYTe ab initio (v1 + v2 + 2v42)+ 7572.9549 2.3 2.5 (v1 + v2 + 2v42)- 7603.1713 2.9 3.5 (v1 + v2 + v31)+ 7656.8700 0.6 -2.0 (v2 + 2v32)+ 7854.3892 2.9 -1.8 (v2 + 2v32)- 7864.0831 2.4 -1.7 (2v1 + v41)+ 8086.5926 1.2 -6.0 (v1 + v31 + v41)+ 8174.7017 -1.8 -2.4 (v1 + v31 + v41)- 8177.4358 -0.6 -1.4 (v1 + 3v41)+ 8253.7494 2.3 1.4 (v1 + 3v41)- 8257.5341 2.2 4.3 (v1 + 2v2 + 2v42)+ 8266.3284 1.4 1.5 (2v32 + v41)+ 8463.2901 2.4 4.4 (2v32 + v41)- 8463.8719 2.2 4.9 E. Burton et al., JMS, v.325, p.7 (2016)  

Highly excited experimental energy levels - calculations v1 v2 v3 v4L3L4 Obs (cm-1) Calc (cm-1) Obs-Calc (cm-1) 1 0 0 2 0 0 6520 6521.21 0.79 2 0 0 0 0 0 6606 6606.14 -0.14 1 0 1 4 0 0 9738.839 9741.40 -2.56 2 0 1 0 1 0 9689.722 9692.62 -2.89 1 0 0 6 0 2 12628.20 12627.56 0.64 3 0 1 0 1 0 12675.50 12676.39 -0.89 5 0 0 0 0 0 15450.82 15458.98 -8.16 4 0 1 0 1 0 15451.19 15458.11 -6.92 6 0 0 0 0 0 18107.56 18122.74 -15.18 5 0 1 0 1 0 18109.47 18119.42 -9.95 Lehmann, K et al. exp. NH3

Prediction and reality for vOH=10 (10,0+, 0)

K. Lehmann et al.- exp.

Figure 2 Spectrum of transitions to the states below D0 Figure 2 Spectrum of transitions to the states below D0. Transitions from the gateway state prepared via the pathway: [25154.61 cm1, 110 (80)+0]  [13864.28 cm1, 111 (40)-0]  [79.496 cm1, 212 (00) 0]. The combination of laser polarisation used and selection rules results in final states with J = 1 or 2. State labels are as in Fig. 1

Structure of the talk Why we did what we did What we did How we have done it

12 FACTORS 1. MRCI , MOLPRO ~Full CI Born-Oppenheimer 1. MRCI , MOLPRO ~Full CI 2. Number of points 200 -2000 3-5 cm-1 3. All electrons, CV 10 cm-1 4. Highest basis set aug-cc-pCV6z 5 cm-1 5. CBS 5 cm-1 6. Optimized (higher) CAS 10 cm-1 Corrections 7. Adiabatic (DBOC) 3 cm-1 8.Relativistic (MVD1, Gaunt (Breit), ) 10 cm-1 9. QED 0.5 cm-1 10. SO 0.1 – 40 cm-1 11. Vibration non-adiabatic (D. Schwenke, P. Bunker) 5 cm-1 12. Rotational non-adiabatic (S.Sauer) 10 cm-1

TROVE Yurchenko S. N. , Thiel W., Jensen P. Theoretical ROVibrational Energies (TROVE): A robust numerical approach to the calculation of rovibrational energies for polyatomic molecules J MOL SPECTROSC , 245 (2) 126 – 140, (2007)

CONCLUSIONS Ab initio NH3 PES and DMS has been calculated Energy levels from 6000 cm-1 to 8000 cm-1 calculated more accurately than fitted PES Energy levels between 10 000cm-1 nd 20 000 cm-1 have been calculated ab initio Starting point for a global PES and Linelist