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, NizhniiNovgorod, Russia 603950

2Department of Physics and Astronomy, University College London, London WC1E 6BT, UK.

Columbus, June 2013

Ab initio calculations

1 cm-1 => 0.1cm-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 H3

+, H2O, HF,CO,N2

• 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 H3+ line. -3.0 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, UKabstractTriple-resonance vibrational spectroscopy is used to determine the lowest dissociation energy, D0, for the water isotopologue HD 16O as 41 239.7 ± 0.2 cm 1and to improve D0 for H2

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 D0 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.

BOAb initio contributions to the dissociation energies of H2

16 O and HD 16O. 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)

CorrectionsF 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 +22 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. Polyansky *†‡, Roman I. Ovsyannikov ‡, Aleksandra A. Kyuberis ‡, Lorenzo Lodi †, Jonathan Tennyson †, and Nikolai 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

12 FACTORS 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

Obs / cm1 5Z1 6Z1 CBS2 CBS+CV3

(010) 1594.75 -2.99 -2.30 -0.32 +0.48 (020) 3155.85 -4.22 -2.38 -0.79 +1.16(030) 4666.73 -6.30 -3.24 -1.52 +2.05(040) 6134.01 -9.81 -5.54 -2.74 +3.20(050) 7542.44 -14.70 -9.19 -4.72 +4.82 (101) 7249.82 +12.51 +10.76 +9.32 -5.35 (201) 10613.35 +18.72 +16.46 +13.97 -7.47(301) 13830.94 +25.72 +22.81 +18.74 -8.97 (601) 13805.22 +32.56 +28.92 +23.06 -10.17(501) 19781.10 +40.72 +35.96 +28.68 -10.72 [104] s all 22.84 19.74 16.56 7.85

Ab initio calculations for water

1 MRCI calculation with Dunning’s aug-cc-pVnZ basis set2 Extrapolation to Complete Basis Set (CBS) limit3 Core—Valence (CV) correction

OL Polyansky, AG Csaszar, SV Shirin, NF.Zobov, J Tennyson, P Barletta, DW Schwenke & PJ KnowlesScience, 299, 539 (2003)

(010) 1594.74 1594.7 -0.03 1594.84 -0.10 1594.83 -0.09 1593.47 1.27 1595.19 -0.45(020) 3151.63 3151.6 -0.01 3151.78 -0.15 3151.76 -0.13 3148.89 2.74 3152.52 -0.89(100) 3657.05 3657.0 0.03 3657.92 -0.87 3656.88 0.17 3660.48 -3.43 3656.74 0.31(030) 4666.78 4666.8 -0.02 4667.02 -0.24 4667.00 -0.22 4662.35 4.43 4668.18 -1.40(110) 5234.97 5234.8 0.13 5235.80 -0.83 5234.76 0.21 5237.07 -2.10 5234.94 0.03(040) 6134.01 6134.0 -0.07 6134.37 -0.36 6134.38 -0.37 6127.54 6.47 6136.03 -2.02(120) 6775.09 6774.9 0.10 6776.03 -0.94 6774.97 0.12 6775.87 -0.78 6775.49 -0.40(200) 7201.54 7201.5 -0.02 7203.30 -1.76 7201.29 0.25 7208.49 -6.95 7200.90 0.64(002) 7445.04 7444.8 0.19 7446.68 -1.64 7444.58 0.46 7452.05 -7.01 7443.95 1.09(050) 7542.43 7542.6 -0.17 7542.94 -0.51 7543.03 -0.60 7533.27 9.16 7545.21 -2.78

sd 0,14 1,96 0,37 7,62 1,7

NO NBO NO QED NO REL NO BODC

obs – calcstate

(v1v2v3)obs adiabatc +NBO semi-

emp 1semi-emp 2

semi-emp 3

σ   2.07 0.52 0.23 0.27 0.13(010) 1594.7

4–0.31 –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 –0.13 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 –0.31 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

H216O

state (v1v2v3)

obs adiabatic +NBO semi-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 –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 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 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

20 11 10 6664.14

0.57 –0.13

20 11 9 6664.17

0.57 –0.13

20 12 9 6935.43

0.71 –0.12

20 12 8 6935.43

0.71 –0.12

20 13 8 7217.56

0.85 –0.13

20 13 7 7217.56

0.85 –0.13

20 14 7 7507.54

0.99 –0.15

20 14 6 7507.54

0.99 –0.15

20 15 6 7802.71

1.21 –0.10

20 15 5 7802.71

1.21 –0.10

20 16 5 8100.29

1.41 –0.09

20 16 4 8100.29

1.41 –0.09

20 17 4 8397.65

1.63 –0.06

20 17 3 8397.65

1.63 –0.06

20 18 3 8691.93

1.87 –0.03

20 18 2 8691.93

1.87 –0.03

20 19 2 8979.88

2.14 0.00

20 19 1 8979.88

2.14 0.00

20 20 1 9257.46

2.44 0.05

20 20 0 9257.46

2.44 0.05

state (J, Ka, Kc)

obs A B

σ   1.06 0.10

20 0 20 4048.25 0.13 0.09

20 1 20 4048.25 0.13 0.09

20 1 19 4412.32 0.14 0.05

20 2 19 4412.32 0.14 0.05

20 2 18 4738.62 0.15 0.01

20 3 18 4738.63 0.15 0.01

20 3 17 5031.79 0.16 –0.03

20 4 17 5031.98 0.16 –0.03

20 4 16 5292.10 0.15 –0.0720 5 16 5294.04 0.16 –0.06

20 5 15 5513.24 0.11 –0.10

20 6 15 5527.05 0.15 –0.09

20 6 14 5680.79 0.03 –0.15

20 7 14 5739.23 0.17 –0.12

20 7 13 5812.07 0.03 –0.17

20 8 13 5947.31 0.23 –0.12

20 8 12 5966.82 0.16 –0.15

20 9 12 6167.72 0.33 –0.12

20 9 11 6170.83 0.31 –0.14

20 10 11 6407.08 0.44 –0.13

20 10 10 6407.44 0.44 –0.13

J=20 (000)

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)

J 0 10 20 30 0 10 20 30

obs obs obs obs obs-calc0 2 050.76 4 286.90 10 323.56 19 458.84 - 0.02 0.15 0.57 1.071 6 012.18 8 164.04 13 970.19 22 746.86 - 0.07 0.09 0.46 0.832 9 801.55 11 871.28 17 452.59 25 878.60 - 0.18 - 0.03 0.28 0.513 13 423.57 15 413.12 20 774.68 28 856.85 - 0.33 - 0.21 0.05 0.174 16 882.40 18 793.53 23 939.81 31 683.54 - 0.51 - 0.41 - 0.21 - 0.145 20 181.70 22 015.92 26 950.59 34 359.66 - 0.70 - 0.61 - 0.44 - 0.366 23 324.47 25 083.02 29 808.87 36 884.97 - 0.85 - 0.77 - 0.59 - 0.457 26 312.99 27 996.79 32 515.51 39 257.77 - 0.93 - 0.84 - 0.63 - 0.358 29 148.74 30 758.29 35 070.24 41 474.47 - 0.90 - 0.79 - 0.49 - 0.059 31 832.20 33 367.53 37 471.40 43 528.96 - 0.71 - 0.57 - 0.16 0.30

10 34 362.71 35 823.23 39 715.53 45 411.65 - 0.34 - 0.15 0.33 0.46

HF

Rotational non-adiabatic, g-factorO.B. Lutnaes et al. JCP, v.131, 144104 (2009)

DF

v / J= 0 10 20 30 0 10 20 30

obs obs obs obs

obs-calc

0 1 490.34 2 677.90 5 949.78 11 100.69 0.03 - 0.01 - 0.11 - 0.24

1 4 397.00 5 552.10 8 733.96 13 741.23 0.07 0.03 - 0.07 - 0.23

2 7 212.15 8 335.41 11 428.93 16 295.15 0.07 0.03 - 0.08 - 0.27

3 9 937.69 11 029.68 14 036.44 18 764.04 0.02 - 0.03 - 0.15 - 0.38

4 12 575.36 13 636.63 16 558.10 21 149.30 - 0.08 - 0.13 - 0.27 - 0.53

5 15 126.78 16 157.84 18 995.37 23 452.16 - 0.21 - 0.27 - 0.44 - 0.73

6 17 593.42 18 594.72 21 349.54 25 673.68 - 0.37 - 0.44 - 0.63 - 0.95

7 19 976.58 20 948.53 23 621.71 27 814.66 - 0.56 - 0.63 - 0.84 - 1.18

8 22 277.38 23 220.35 25 812.79 29 875.69 - 0.75 - 0.83 - 1.05 - 1.40

9 24 496.77 25 411.03 27 923.46 31 857.09 - 0.95 - 1.03 - 1.25 - 1.60

10 26 635.45 27 521.23 29 954.13 33 758.85 - 1.13 - 1.21 - 1.43 - 1.76

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)

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.v113p.934 (2013)

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-factorO.B. Lutnaes et al. JCP, v.131, 144104 (2009)

Dissociation energy of CO

• BEST, MRCI 89 697• BEST CC 89 623

Experiment 89 615

obs - calc(CC) =- 8 • obs - calc(MRCI) = 83

N2• 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 78576BEST CC 78735Experiment 78719

obs - calc(CC) = - 16 obs - calc(MRCI) = 143

CONCLUSIONS

• Ab initio MRCI calcs • 11 components• 0.1 cm-1 for H2O• 2 cm-1 for Dissociation• High J ~ 0.1 cm-1

• 0.1 cm-1 for HF, CO, N2

• HCN nearly finished