1. Towards experimental accuracy from the first principles Ab initio calculations of energies of small molecules Oleg L. Polyansky, L.Lodi, J.Tennyson and Nikolai F. Zobov 1 Institute of Applied Physics, Russian Academy of Sciences, Uljanov Street 46, Nizhnii Novgorod, Russia 603950 2Department of Physics and Astronomy, University College London, London WC1E 6BT, UK. Columbus, June 2013

2. Ab initio calculations 1 cm -1 => 0.1 cm -1 When we discovered that optimized CAS MRCI could be very close to Full CI, we used 11 more components of accurate ab initio calculation to reproduce known rovibrational energy levels of 5 molecules to near experimental accuracy

3. SUMMARY What? 1-10 cm -1 => 0.1 cm -1 for 5 molecules H 3 +, H 2 O, HF,CO,N 2 How ? 2 discoveries and 12 factors which allowed us to do that Details tables of obs-calcs of different molecules I will show why 0.1cm-1 is crucial, explain the choice of molecules, show what actually helped us to succeed in the such an improvement, describe all 12 factors in the calcs needed to get such high accuracy and finally will demonstrate many results for all molecules.

6. C-O

9. The highest H 3 + line. -3.0 and +8.5 cm -1 – previous predictions

10. Obs-calc. BO+adiabatic –grey, full model – red and yellow

11. Accurate bond dissociation energy of water determined by triple-resonance vibrational spectroscopy and ab initio calculations Oleg V. Boyarkin a, Maxim A. Koshelev a,b, Oleg Aseev a, Pavel Maksyutenko a, Thomas R. Rizzo a, Nikolay F. Zobov b, Lorenzo Lodi c, Jonathan Tennyson c, Oleg L. Polyansky b,c a – Lausanne, Switzerland, b - Nizhny Novgorod, Russia, c- London, UK abstract Triple-resonance vibrational spectroscopy is used to determine the lowest dissociation energy, D 0, for the water isotopologue HD 16 O as 41 239.7 ± 0.2 cm 1and to improve D 0 for H 2 16 O to 41 145.92 ± 0.12 cm -1. Ab initio calculations including systematic basis set and electron correlation convergence studies, relativistic and Lamb shift effects as well as corrections beyond the Born–Oppenheimer approximation, agree with the measured values to 1 and 2 cm -1 respectively. The improved treatment of high-order correlation terms is key to this high theoretical accuracy. Predicted values for D 0 for the other 5 major water isotopologues are expected to be correct within 1 cm -1 Chemical Physics Letters 568–569 (2013) 14–20

12. Figure 1. Schematic energy level diagram employed in experiment.

13. BO Ab initio contributions to the dissociation energies of H 2 16 O and HD 16 O. Contributions A to H are nuclear-mass independent, all others are nuclear-mass dependent (MD). Ref. [8] Ref. [30] This work A CCSD(T) frozen core 43957(52) 43956(6) B Core correlation CCSD(T) +77 +81(2) C All-electron CCSD(T) 44034 44037(6) D Higher-order correlation 7 25 52(3) E Full CI value 44 027 44 000 43 985(7) MRCI+Q value 43 984(60) Ref.8 Ruscic et al., JPCA, v.106, 2727 (2002) Ref.30 Hrding et al., JCP, v.128, 114111(2008)

14. Corrections F Scalar relativistic correction 53 50 53(3) G QED (Lamb shift) correction +3(1) H Spin–orbit effect 65 69.4(1) K BODC, H2O +36 +35 +35.3(0.5) Do(H2O) Calc. [=E + V] 41187(5) 41116 41145(8) (Obs – Calc) Do(H2O) - 42 +30 +1 Do(HDO) Calc. [=E + W] 41238(8) Dobs – Dcalc +2 2 discoveries

15. Calculation of Rotation–Vibration Energy Levels of the Water Molecule with Near-Experimental Accuracy Based on an ab Initio Potential Energy Surface Oleg L. PolyanskyOleg L. Polyansky *†‡, Roman I. Ovsyannikov ‡, Aleksandra A. Kyuberis ‡, Lorenzo Lodi †, Jonathan Tennyson †, and Nikolai F. Zobov ‡*Roman I. Ovsyannikov Aleksandra A. KyuberisLorenzo LodiJonathan TennysonNikolai F. Zobov † Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom ‡ Institute of Applied Physics, Russian Academy of Science, Ulyanov Street 46, Nizhny Novgorod 603950, Russia J. Phys. Chem. A, Article dx.doi.org/10.1021/jp312343z Oka festschrift Key article

16. 12 FACTORS

17. Obs / cm  1 5Z 1 6Z 1 CBS 2 CBS+CV 3 (010) 1594.75  +0.48 (020) 3155.85  +1.16 (030) 4666.73  (040) 6134.01  +3.20 (050) 7542.44  +4.82 (101) 7249.82 +12.51 +10.76 +9.32  (201) 10613.35 +18.72 +16.46 +13.97  (301) 13830.94 +25.72 +22.81 +18.74  8.97 (601) 13805.22 +32.56 +28.92 +23.06   19781.10 +40.72 +35.96 +28.68  10.72  all 22.84  Ab initio calculations for water 1 MRCI calculation with Dunning’s aug-cc-pVnZ basis set 2 Extrapolation to Complete Basis Set (CBS) limit 3 Core—Valence (CV) correction OL Polyansky, AG Csaszar, SV Shirin, NF.Zobov, J Tennyson, P Barletta, DW Schwenke & PJ Knowles Science, 299, 539 (2003)

18. (010)1594.741594.7-0.031594.84-0.101594.83-0.091593.471.271595.19-0.45 (020)3151.633151.6-0.013151.78-0.153151.76-0.133148.892.743152.52-0.89 (100)3657.053657.00.033657.92-0.873656.880.173660.48-3.433656.740.31 (030)4666.784666.8-0.024667.02-0.244667.00-0.224662.354.434668.18-1.40 (110)5234.975234.80.135235.80-0.835234.760.215237.07-2.105234.940.03 (040)6134.016134.0-0.076134.37-0.366134.38-0.376127.546.476136.03-2.02 (120)6775.096774.90.106776.03-0.946774.970.126775.87-0.786775.49-0.40 (200)7201.547201.5-0.027203.30-1.767201.290.257208.49-6.957200.900.64 (002)7445.047444.80.197446.68-1.647444.580.467452.05-7.017443.951.09 (050)7542.437542.6-0.177542.94-0.517543.03-0.607533.279.167545.21-2.78 sd0,141,960,377,621,7 NO NBO NO QED NO REL NO BODC

19. obs – calc state (v 1 v 2 v 3 ) obsadiabatc+NBOsemi- emp 1 semi- emp 2 semi- emp 3 σ 2.07 0.52 0.23 0.27 0.13 (010)1594.74–0.31–0.22 0.00–0.02–0.03 (020)3151.63–0.54–0.40 0.03 0.02–0.01 (100)3657.05–0.84–0.13 0.04 0.03 (030)4666.78–0.81–0.62 0.01 0.02–0.02 (110)5234.97–1.06–0.22 0.00 0.15 0.13 (040)6134.01–1.14–0.90–0.09–0.02–0.07 (120)6775.09–1.37–0.45–0.01 0.13 0.10 (200)7201.54–1.69–0.31 0.00–0.02 (002)7445.04–1.33 0.14 0.15 0.43 0.19 (050)7542.43–1.54–1.26–0.29–0.10–0.17 (130)8273.97–1.71–0.72–0.08 0.07 0.04 (210)8761.58–1.82–0.29–0.06 0.22 0.19 (012)9000.13–1.61–0.06 0.18 0.41 0.16 (220)10284.3–2.07–0.45–0.01 026 0.22 (022)10521.7–1.92–0.32 0.15 0.35 0.07 H 2 16 O

21. state (v 1 v 2 v 3 ) obsadiabatic+NBOsemi- emp 1 semi- emp 2 semi- emp 3 Σ 1.56 0.30 0.24 0.09 0.08 (010)1403.48–0.31–0.09–0.06–0.07 (100)2723.68–0.25–0.02 0.02 0.06 0.04 (020)2782.01–0.46–0.03 0.02 0.00 (001)3707.47–0.83–0.19–0.18–0.05–0.02 (110)4099.96–0.61–0.04 0.01 0.02 (030)4145.47–0.52 0.03 0.09 0.10 0.08 (011)5089.54–1.05–0.19–0.15–0.05–0.02 (200)5363.82–0.54–0.11–0.03 0.05 0.02 (040)5420.04–0.85 0.03 0.07 0.08 0.09 (101)6415.46–1.03–0.13–0.08 0.08 0.09 (021)6451.90–1.20–0.17–0.11 0.00 0.03 (050)6690.41–1.20–0.05–0.07 0.00 0.02 (210)6746.91–0.73–0.05 0.06 0.11 0.08 (002)7250.52–1.63–0.40–0.38–0.13–0.09 (031)7754.61–1.39–0.15–0.08 0.02 0.06 (111)7808.76–1.27–0.14–0.06 0.07 0.08 (060)7914.32–1.58–0.18–0.30–0.11–0.10 (300)7918.17–0.84–0.17–0.08 0.04 0.01 HDO

22. 20 11 106664.140.57–0.13 20 11 96664.170.57–0.13 20 12 96935.430.71–0.12 20 12 86935.430.71–0.12 20 13 87217.560.85–0.13 20 13 77217.560.85–0.13 20 14 77507.540.99–0.15 20 14 67507.540.99–0.15 20 15 67802.711.21–0.10 20 15 57802.711.21–0.10 20 16 58100.291.41–0.09 20 16 48100.291.41–0.09 20 17 48397.651.63–0.06 20 17 38397.651.63–0.06 20 18 38691.931.87–0.03 20 18 28691.931.87–0.03 20 19 28979.882.140.00 20 19 18979.882.140.00 20 20 19257.462.440.05 20 20 09257.462.440.05 state (J, K a, K c ) obsAB σ 1.06 0.10 20 0 204048.250.13 0.09 20 1 204048.250.13 0.09 20 1 194412.320.14 0.05 20 2 194412.320.14 0.05 20 2 184738.620.15 0.01 20 3 184738.630.15 0.01 20 3 175031.790.16–0.03 20 4 175031.980.16–0.03 20 4 165292.100.15–0.07 20 5 165294.040.16–0.06 20 5 155513.240.11–0.10 20 6 155527.050.15–0.09 20 6 145680.790.03–0.15 20 7 145739.230.17–0.12 20 7 135812.070.03–0.17 20 8 135947.310.23–0.12 20 8 125966.820.16–0.15 20 9 126167.720.33–0.12 20 9 116170.830.31–0.14 20 10 116407.080.44–0.13 20 10 106407.440.44–0.13 J=20 (000)

23. HF V obs obs-calc us Ref.1 1 3961.418 -0.05 -0.87 2 7750.814 -0.11 -1.32 3 11374.23 -0.15 -1.43 4 14832.74 -0.18 -1.12 5 18131.29 -0.21 -0.32 6 21272.86 -0.15 0.83 7 24259.73 -0.08 2.45 8 27093.33 0.03 4.54 Ref.1 W. Cardoen and R.J.Gdanitz. JCP, v.123, 024304 (2005)

24. J01020300102030 obs obs-calc 02 050.764 286.9010 323.5619 458.84- 0.02 0.15 0.57 1.07 16 012.188 164.0413 970.1922 746.86- 0.07 0.09 0.46 0.83 29 801.5511 871.2817 452.5925 878.60- 0.18- 0.03 0.28 0.51 313 423.5715 413.1220 774.6828 856.85- 0.33- 0.21 0.05 0.17 416 882.4018 793.5323 939.8131 683.54- 0.51- 0.41- 0.21- 0.14 520 181.7022 015.9226 950.5934 359.66- 0.70- 0.61- 0.44- 0.36 623 324.4725 083.0229 808.8736 884.97- 0.85- 0.77- 0.59- 0.45 726 312.9927 996.7932 515.5139 257.77- 0.93- 0.84- 0.63- 0.35 829 148.7430 758.2935 070.2441 474.47- 0.90- 0.79- 0.49- 0.05 931 832.2033 367.5337 471.4043 528.96- 0.71- 0.57- 0.16 0.30 1034 362.7135 823.2339 715.5345 411.65- 0.34- 0.15 0.33 0.46 HF Rotational non-adiabatic, g-factor O.B. Lutnaes et al. JCP, v.131, 144104 (2009)

25. DF v / J=01020300102030 obs obs-calc 01 490.342 677.905 949.7811 100.69 0.03- 0.01- 0.11- 0.24 14 397.005 552.108 733.9613 741.23 0.07 0.03- 0.07- 0.23 27 212.158 335.4111 428.9316 295.15 0.07 0.03- 0.08- 0.27 39 937.6911 029.6814 036.4418 764.04 0.02- 0.03- 0.15- 0.38 412 575.3613 636.6316 558.1021 149.30- 0.08- 0.13- 0.27- 0.53 515 126.7816 157.8418 995.3723 452.16- 0.21- 0.27- 0.44- 0.73 617 593.4218 594.7221 349.5425 673.68- 0.37- 0.44- 0.63- 0.95 719 976.5820 948.5323 621.7127 814.66- 0.56- 0.63- 0.84- 1.18 822 277.3823 220.3525 812.7929 875.69- 0.75- 0.83- 1.05- 1.40 924 496.7725 411.0327 923.4631 857.09- 0.95- 1.03- 1.25- 1.60 1026 635.4527 521.2329 954.1333 758.85- 1.13- 1.21- 1.43- 1.76

26. TF and De Obs obs-calc 2443.90 0.05 4823.45 0.08 7139.76 0.06 De 49 360.025 obs-calc obs-calc (ref.1) 3 cm -1 83 cm -1 Ref.1 W. Cardoen and R.J.Gdanitz. JCP, v.123, 024304 (2005)

27. CO OBS obs-calc 1 2 1 1081.78, -0.003 7.6 0.35 2 3225.09, -0.040 19.0 0.81 3 5341.92, -0.082 32.8 1.44 4 7432.29, -0.079 44.5 2.20 5 9496.28, -0.039 56.3 3.08 6 11534.0 0.034 77.1 4.05 7 13545.4 0.155 89.6 5.09 8 15530.6 0.331 99.2 6.17 9 17489.7, 0.568 113. 7.27 10 19422.8, 0.868 125. 8.4 11 21329.9, 1.23 137. 8.5 ----------------------------------------------- ~1000 ~50 1. Liu Y.F. et al. JQSRT, v.112,2296(2011) 2. Shi D-H et al., Int.J.Q.Chem.v113 p.934 (2013)

28. CO ab initio high J J=50 J=100 v 0 5944.5 -0.018 19 880.7 -0.148 1 8043.2 -0.046 21 847.1 -0.085 2 10115.4 -0.074 23 786.9 0.033 3 12161.1 -0.053 25 700.2 0.220 4 14180.4 0.021 27 587.1 0.483 5 16173.5 0.139 29 447.7 0.821 6 18140.2 0.305 31 281.9 1.23 7 20080.8 0.508 33 089.9 1.72 Rotational non-adiabatic, g-factor O.B. Lutnaes et al. JCP, v.131, 144104 (2009)

29. Dissociation energy of CO BEST, MRCI 89 697 BEST CC 89 623 Experiment 89 615 obs - calc(CC) =- 8 obs - calc(MRCI) = 83

30. N2N2 Obs 1175.66, 3505.42, 5806.61, 8079.18, 10323.1, 12538.3, 14724.9, 16882.9, 19012.7, 21114.8, Obs-calc 0.138, 0.282, 0.391, 0.319, 0.198, 0.058, -0.309, -0.908, -2.251, -4.917 Dissociation energy in cm -1 BEST, MRCI 78576 BEST CC 78735 Experiment 78719 obs - calc(CC) = - 16 obs - calc(MRCI) = 143

31. CONCLUSIONS Ab initio MRCI calcs 11 components 0.1 cm -1 for H 2 O 2 cm -1 for Dissociation High J ~ 0.1 cm -1 0.1 cm -1 for HF, CO, N 2 HCN nearly finished