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 Department of Physics and Astronomy, University College London, London WC1E 6BT, UK. Columbus, June 2013

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

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.

C-O

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

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

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 ± 0.2 cm 1and to improve D 0 for H 2 16 O to ± 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

Figure 1. Schematic energy level diagram employed in experiment.

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) (2) C All-electron CCSD(T) (6) D Higher-order correlation (3) E Full CI value (7) MRCI+Q value (60) Ref.8 Ruscic et al., JPCA, v.106, 2727 (2002) Ref.30 Hrding et al., JCP, v.128, (2008)

Corrections F Scalar relativistic correction (3) G QED (Lamb shift) correction +3(1) H Spin–orbit effect (1) K BODC, H2O (0.5) Do(H2O) Calc. [=E + V] 41187(5) (8) (Obs – Calc) Do(H2O) Do(HDO) Calc. [=E + W] 41238(8) Dobs – Dcalc +2 2 discoveries

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 , Russia J. Phys. Chem. A, Article dx.doi.org/ /jp312343z Oka festschrift Key article

12 FACTORS

Obs / cm  1 5Z 1 6Z 1 CBS 2 CBS+CV 3 (010)  (020)  (030)  (040)  (050)  (101)  (201)  (301)  8.97 (601)     all  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)

(010) (020) (100) (030) (110) (040) (120) (200) (002) (050) sd0,141,960,377,621,7 NO NBO NO QED NO REL NO BODC

obs – calc state (v 1 v 2 v 3 ) obsadiabatc+NBOsemi- emp 1 semi- emp 2 semi- emp 3 σ (010) –0.31– –0.02–0.03 (020) –0.54– –0.01 (100) –0.84– (030) –0.81– –0.02 (110) –1.06– (040) –1.14–0.90–0.09–0.02–0.07 (120) –1.37–0.45– (200) –1.69– –0.02 (002) – (050) –1.54–1.26–0.29–0.10–0.17 (130) –1.71–0.72– (210) –1.82–0.29– (012) –1.61– (220) –2.07–0.45– (022) –1.92– H 2 16 O

state (v 1 v 2 v 3 ) obsadiabatic+NBOsemi- emp 1 semi- emp 2 semi- emp 3 Σ (010) –0.31–0.09–0.06–0.07 (100) –0.25– (020) –0.46– (001) –0.83–0.19–0.18–0.05–0.02 (110) –0.61– (030) – (011) –1.05–0.19–0.15–0.05–0.02 (200) –0.54–0.11– (040) – (101) –1.03–0.13– (021) –1.20–0.17– (050) –1.20–0.05– (210) –0.73– (002) –1.63–0.40–0.38–0.13–0.09 (031) –1.39–0.15– (111) –1.27–0.14– (060) –1.58–0.18–0.30–0.11–0.10 (300) –0.84–0.17– HDO

– – – – – – – – – – – – – – – – state (J, K a, K c ) obsAB σ – – – – – – – – – – – – – – –0.13 J=20 (000)

HF V obs obs-calc us Ref Ref.1 W. Cardoen and R.J.Gdanitz. JCP, v.123, (2005)

J obs obs-calc HF Rotational non-adiabatic, g-factor O.B. Lutnaes et al. JCP, v.131, (2009)

DF v / J= obs obs-calc

TF and De Obs obs-calc De obs-calc obs-calc (ref.1) 3 cm cm -1 Ref.1 W. Cardoen and R.J.Gdanitz. JCP, v.123, (2005)

CO OBS obs-calc , , , , , , , , ~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)

CO ab initio high J J=50 J=100 v Rotational non-adiabatic, g-factor O.B. Lutnaes et al. JCP, v.131, (2009)

Dissociation energy of CO BEST, MRCI BEST CC Experiment obs - calc(CC) =- 8 obs - calc(MRCI) = 83

N2N2 Obs , , , , , , , , , , Obs-calc 0.138, 0.282, 0.391, 0.319, 0.198, 0.058, , , , Dissociation energy in cm -1 BEST, MRCI BEST CC Experiment obs - calc(CC) = - 16 obs - calc(MRCI) = 143

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 cm -1 for HF, CO, N 2 HCN nearly finished