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
Ab initio calculations
1 cm => 0.1cm
-1
-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
Chemical Physics Letters 568–569 (2013) 14–20
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,
D0, for the water isotopologue HD 16O as 41 239.7 ± 0.2 cm 1and to improve D0 for H216 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
Figure 1. Schematic energy level diagram employed in experiment.
BO
Ab initio contributions to the dissociation energies of H216 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)
C All-electron CCSD(T)
D Higher-order correlation
E Full CI value
MRCI+Q value
+77
+81(2)
44034
44037(6)
7
44 027
25
44 000
Ref.8 Ruscic et al. , JPCA, v.106, 2727 (2002)
Ref.30 Hrding et al., JCP, v.128, 114111(2008)
52(3)
43 985(7)
43 984(60)
Corrections
F Scalar relativistic correction
53
50
G QED (Lamb shift) correction
H Spin–orbit effect
K BODC, H2O
Do(H2O) Calc. [=E + V]
(Obs – Calc) Do(H2O)
Do(HDO) Calc. [=E + W]
Dobs – Dcalc
2 discoveries
53(3)
+3(1)
65
+36
69.4(1)
+35
+35.3(0.5)
41187(5) 41116
41145(8)
- 42
+30
+1
41238(8)
+2
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
•
•
•
•
•
•
1. MRCI , MOLPRO
2. Number of points 200 -2000
3. All electrons, CV
4. Highest basis set aug-cc-pCV6z
5. CBS
6. Optimized (higher) CAS
~Full CI
3-5 cm-1
10 cm-1
5 cm-1
5 cm-1
10 cm-1
• 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
Ab initio calculations for water
Obs / cm1
(010)
1594.75
(020)
3155.85
(030)
4666.73
(040)
6134.01
(050)
7542.44
(101)
7249.82
(201)
10613.35
(301)
13830.94
(601)
13805.22
(501)
19781.10
s [104]
all
5Z1
2.99
4.22
6.30
9.81
14.70
+12.51
+18.72
+25.72
+32.56
+40.72
22.84
6Z1
2.30
2.38
3.24
5.54
9.19
+10.76
+16.46
+22.81
+28.92
+35.96
19.74
CBS2
0.32
0.79
1.52
2.74
4.72
+9.32
+13.97
+18.74
+23.06
+28.68
16.56
CBS+CV3
+0.48
+1.16
+2.05
+3.20
+4.82
5.35
7.47
8.97
10.17
10.72
7.85
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)
1594.74
3151.63
3657.05
4666.78
5234.97
6134.01
6775.09
7201.54
7445.04
7542.43
sd
1594.7
3151.6
3657.0
4666.8
5234.8
6134.0
6774.9
7201.5
7444.8
7542.6
-0.03
-0.01
0.03
-0.02
0.13
-0.07
0.10
-0.02
0.19
-0.17
0,14
1594.84
3151.78
3657.92
4667.02
5235.80
6134.37
6776.03
7203.30
7446.68
7542.94
NO NBO
NO QED
-0.10
-0.15
-0.87
-0.24
-0.83
-0.36
-0.94
-1.76
-1.64
-0.51
-0.09
-0.13
0.17
-0.22
0.21
-0.37
0.12
0.25
0.46
-0.60
1,96
1594.83
3151.76
3656.88
4667.00
5234.76
6134.38
6774.97
7201.29
7444.58
7543.03
0,37
1593.47
3148.89
3660.48
4662.35
5237.07
6127.54
6775.87
7208.49
7452.05
7533.27
NO REL
NO BODC
1.27
2.74
-3.43
4.43
-2.10
6.47
-0.78
-6.95
-7.01
9.16
-0.45
-0.89
0.31
-1.40
0.03
-2.02
-0.40
0.64
1.09
-2.78
7,62
1595.19
3152.52
3656.74
4668.18
5234.94
6136.03
6775.49
7200.90
7443.95
7545.21
1,7
obs – calc
state
(v1v2v3)
σ
(010)
(020)
(100)
(030)
(110)
(040)
(120)
(200)
(002)
(050)
(130)
(210)
(012)
(220)
(022)
obs
1594.74
3151.63
3657.05
4666.78
5234.97
6134.01
6775.09
7201.54
7445.04
7542.43
8273.97
8761.58
9000.13
10284.3
10521.7
adiabatc +NBO
2.07
–0.31
–0.54
–0.84
–0.81
–1.06
–1.14
–1.37
–1.69
–1.33
–1.54
–1.71
–1.82
–1.61
–2.07
–1.92
0.52
–0.22
–0.40
–0.13
–0.62
–0.22
–0.90
–0.45
–0.31
0.14
–1.26
–0.72
–0.29
–0.06
–0.45
–0.32
semiemp 1
0.23
0.00
0.03
–0.13
0.01
0.00
–0.09
–0.01
–0.31
0.15
–0.29
–0.08
–0.06
0.18
–0.01
0.15
semiemp 2
0.27
–0.02
0.02
0.04
0.02
0.15
–0.02
0.13
0.00
0.43
–0.10
0.07
0.22
0.41
026
0.35
semiemp 3
0.13
–0.03
–0.01
0.03
–0.02
0.13
–0.07
0.10
–0.02
0.19
–0.17
0.04
0.19
0.16
0.22
0.07
H216O
state
(v1v2v3)
Σ
(010)
(100)
(020)
(001)
(110)
(030)
(011)
(200)
(040)
(101)
(021)
(050)
(210)
(002)
(031)
(111)
(060)
(300)
obs
1403.48
2723.68
2782.01
3707.47
4099.96
4145.47
5089.54
5363.82
5420.04
6415.46
6451.90
6690.41
6746.91
7250.52
7754.61
7808.76
7914.32
7918.17
adiabatic
1.56
–0.31
–0.25
–0.46
–0.83
–0.61
–0.52
–1.05
–0.54
–0.85
–1.03
–1.20
–1.20
–0.73
–1.63
–1.39
–1.27
–1.58
–0.84
+NBO
0.30
–0.09
–0.02
–0.03
–0.19
–0.04
0.03
–0.19
–0.11
0.03
–0.13
–0.17
–0.05
–0.05
–0.40
–0.15
–0.14
–0.18
–0.17
semiemp 1
0.24
–0.06
0.02
0.02
–0.18
0.01
0.09
–0.15
–0.03
0.07
–0.08
–0.11
–0.07
0.06
–0.38
–0.08
–0.06
–0.30
–0.08
semiemp 2
0.09
–0.07
0.06
0.00
–0.05
0.02
0.10
–0.05
0.05
0.08
0.08
0.00
0.00
0.11
–0.13
0.02
0.07
–0.11
0.04
semiemp 3
0.08
–0.07
0.04
0.00
–0.02
0.02
0.08
–0.02
0.02
0.09
0.09
0.03
0.02
0.08
–0.09
0.06
0.08
–0.10
0.01
HDO
J=20 (000)
state
(J, Ka, Kc)
σ
20 0 20
20 1 20
20 1 19
20 2 19
20 2 18
20 3 18
20 3 17
20 4 17
20 4 16
20 5 16
20 5 15
20 6 15
20 6 14
20 7 14
20 7 13
20 8 13
20 8 12
20 9 12
20 9 11
20 10 11
20 10 10
obs
4048.25
4048.25
4412.32
4412.32
4738.62
4738.63
5031.79
5031.98
5292.10
5294.04
5513.24
5527.05
5680.79
5739.23
5812.07
5947.31
5966.82
6167.72
6170.83
6407.08
6407.44
A
1.06
0.13
0.13
0.14
0.14
0.15
0.15
0.16
0.16
0.15
0.16
0.11
0.15
0.03
0.17
0.03
0.23
0.16
0.33
0.31
0.44
0.44
B
0.10
0.09
0.09
0.05
0.05
0.01
0.01
–0.03
–0.03
–0.07
–0.06
–0.10
–0.09
–0.15
–0.12
–0.17
–0.12
–0.15
–0.12
–0.14
–0.13
–0.13
20 11 10
6664.14 0.57
–0.13
20 11 9
20 12 9
20 12 8
20 13 8
20 13 7
20 14 7
20 14 6
20 15 6
20 15 5
20 16 5
20 16 4
20 17 4
20 17 3
20 18 3
20 18 2
20 19 2
20 19 1
20 20 1
20 20 0
6664.17
6935.43
6935.43
7217.56
7217.56
7507.54
7507.54
7802.71
7802.71
8100.29
8100.29
8397.65
8397.65
8691.93
8691.93
8979.88
8979.88
9257.46
9257.46
–0.13
–0.12
–0.12
–0.13
–0.13
–0.15
–0.15
–0.10
–0.10
–0.09
–0.09
–0.06
–0.06
–0.03
–0.03
0.00
0.00
0.05
0.05
0.57
0.71
0.71
0.85
0.85
0.99
0.99
1.21
1.21
1.41
1.41
1.63
1.63
1.87
1.87
2.14
2.14
2.44
2.44
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 Ref.1
7 24259.73 -0.08 2.45 W. Cardoen and R.J.Gdanitz.
8 27093.33
0.03 4.54 JCP, v.123, 024304 (2005)
HF
J
0
1
2
3
4
5
6
7
8
9
10
0
10
20
30
obs
2 050.76
6 012.18
9 801.55
13 423.57
16 882.40
20 181.70
23 324.47
26 312.99
29 148.74
31 832.20
34 362.71
obs
4 286.90
8 164.04
11 871.28
15 413.12
18 793.53
22 015.92
25 083.02
27 996.79
30 758.29
33 367.53
35 823.23
obs
10 323.56
13 970.19
17 452.59
20 774.68
23 939.81
26 950.59
29 808.87
32 515.51
35 070.24
37 471.40
39 715.53
obs
19 458.84
22 746.86
25 878.60
28 856.85
31 683.54
34 359.66
36 884.97
39 257.77
41 474.47
43 528.96
45 411.65
0
10
obs-calc
- 0.02
0.15
- 0.07
0.09
- 0.18
- 0.03
- 0.33
- 0.21
- 0.51
- 0.41
- 0.70
- 0.61
- 0.85
- 0.77
- 0.93
- 0.84
- 0.90
- 0.79
- 0.71
- 0.57
- 0.34
- 0.15
20
30
0.57
0.46
0.28
0.05
- 0.21
- 0.44
- 0.59
- 0.63
- 0.49
- 0.16
0.33
1.07
0.83
0.51
0.17
- 0.14
- 0.36
- 0.45
- 0.35
- 0.05
0.30
0.46
Rotational non-adiabatic, g-factor
O.B. Lutnaes et al. JCP, v.131, 144104 (2009)
DF
v/
J=
0
obs
10
obs
20
obs
30
obs
0
10
20
30
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
2443.90
4823.45
7139.76
obs-calc
0.05
0.08
0.06
• De 49 360.025 obs-calc
•
3 cm-1
Ref.1
W. Cardoen and R.J.Gdanitz.
JCP, v.123, 024304 (2005)
obs-calc (ref.1)
83 cm-1
•
•
•
•
•
•
•
•
•
•
•
•
•
•
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
CO
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
v
0 5944.5
1 8043.2
2 10115.4
3 12161.1
4 14180.4
5 16173.5
6 18140.2
7 20080.8
J=100
-0.018
-0.046
-0.074
-0.053
0.021
0.139
0.305
0.508
19 880.7 -0.148
21 847.1 -0.085
23 786.9 0.033
25 700.2 0.220
27 587.1 0.483
29 447.7 0.821
31 281.9 1.23
33 089.9 1.72
Rotational non-adiabatic, g-factor
O.B. Lutnaes et al. JCP, v.131, 144104 (2009)
Dissociation energy of CO
• BEST, MRCI
• BEST CC
Experiment
89 697
89 623
89 615
obs - calc(CC) =- 8
• obs - calc(MRCI) = 83
•
•
•
•
•
•
•
•
•
•
•
Obs
• Obs-calc
1175.66,
0.138,
3505.42,
0.282,
5806.61,
0.391,
8079.18,
0.319,
10323.1,
0.198,
12538.3,
0.058,
14724.9, -0.309,
16882.9, -0.908,
19012.7, -2.251,
21114.8, -4.917
N2
Dissociation energy in cm-1
BEST, MRCI
BEST CC
Experiment
78576
78735
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