Calculation of rovibrational H3+ lines.
New level of accuracy
Slides of invited talk at
Royal Society conference on H3+
Oleg L. Polyansky1,2
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.
9th February, 2012
Calculation of rovibrational H3+ lines.
New level of accuracy
Oleg Polyansky ,
Alex Alijah
Kolya Zobov,
Irina Mizus,
Roman Ovsyannikov
Lorenzo Lodi,
Jonathan Tennyson,
Attila Csaszar,
Analytical PES from the ab initio points
RV- Schroedinger
equation with
exact kinetic
energy and PES
V(r1,r2,q)
HY=EY
The highest H3+ line. -3.0 and +8.5 cm-1 –
previous predictions
Quotation
• ...H3+ spectroscopy which now entered the
visible region with transitions up to
13676 cm-1. For such energies the deviations
from theory are often more than 1 cm-1 and
it gives further challenges to theorists...
Morong, Gottfried and Oka, JMS, v.255, p.13, (2009)
Major goal of this talk is to demonstrate
and prove 3 basic points
1.Before:
0.1 cm-1 up to 10000 cm-1
1 cm-1 between 10 000cm-1 and 13 000 cm-1
2.Now:
1 cm-1 =>0.1cm-1
Up to 17000 cm-1
3. Future:
Opens the way to further progress
0.1cm-1 up to 20,25,30,35 000 cm-1
0.1 cm-1 =>0.01cm-1
Because some aspects of calculations – BO PES, adiabatic correction and relativistic correction are already 0.01 cm-1
Structure of this talk
1.Motivation (helps to appreciate the basic goal)
2. Global
Analytical
PES
(
accurate to 0.1
and comparison with previous PES
3. Accuracy of previous RV calcs (0.1
cm-1)
cm-1 up to
10 000 cm-1 and 1 cm-1 up to 13000 cm-1 )
4. Our RV calcs
(variational calculations and nBO models)
5. Comparison with experiment
17000 cm-1 )
6. Conclusions and Future work
(0.1 cm-1 up to
+
H3
• Motivation
•
•
Will help to appreciate the major goal
Many honorary titles
• Simplest unsolved QM problem
• Smallest large QM system
• Smallest polyatomic molecule
• Smallest poly-electronic system
Ab initio predictions of water levels
Isotopologue
H216O
H217O
H218O
D216O
HD16O
All water
Nlevels
9426
1083
2460
2807
1976
17338
Jmax
20
12
12
12
12
20

1.17
0.56
0.65
0.71
0.47
0.95
O. L. Polyansky, A. G. Csaszar, S. V. Shirin, N. F. Zobov, P. Barletta, J. Tennyson, D. W. Schwenke, P. J. Knowles,
High-accuracy ab initio rotation-vibration transitions for water,
SCIENCE, vol. 299, p. 539-542, 2003.
How it should be and how it is
H2 +
H3+
H2
H2O
Below barrier of 10 000 cm-1
10-5 cm-1 3x10-5 cm-1
10-2 cm-1
1 cm-1
Above barrier
10-5 cm-1 3x10-5 cm-1
1 cm-1
1 cm-1
Water spectrum above disociation.
The density of lines 1000 times lower than in
Carrington-Kennedy predissociation spectrum of
H3+
EXPERIMENTAL AND CALCULATED SPECTRUM OF WATER ABOVE DISSOCIATION
Zobov ,Shirin,Lodi,Siva,Tennyson,Csaszar,and Polyansky, Chem.phys.Lett.v.507,p.48,(2011)
Our Starting point
(from previous talk)
•
Eh accuracy
• 42 000 points
• Dense and global grid
-8
10
• Now I’ll show that all these aspects are
important for our purposes
First 9 MBB-geometry points for various ab initio PES
• N nx ny nz
1
2
3
4
5
6
7
8
9
-4
-3
-2
-1
0
1
2
3
4
0
0
0
0
0
0
0
0
0
Eh
0 -1.255924
0 -1.296828
0 -1.323893
0 -1.339057
0 -1.343835
0 -1.339388
0 -1.326560
0 -1.305893
0 -1.277607
E this work - E x(cm-1)
CRJK
- 0.012
- 0.013
- 0.013
- 0.014
- 0.018
- 0.015
- 0.015
- 0.021
- 0.022
RKJK
LF
-1.206 -2.6
-1.127 -1.8
-0.960 -1.2
-0.724 -1.1
0.000
0.0
-0.037 -2.1
0.528 -6.5
1.323 -15.0
2.473 -49.1
MBB
-40.3
-23.1
-10.9
- 3.4
0.0
- 1.7
1.8
6.3
11.0
CRJK – Cencek,Rychlewski, Jaquet ,Kutzelnigg, JCP, v.108, 2831 (1998)
RKJK - Roese, Kutzelnigg, Jaquet, Klopper, JCP, v.101, 2231 (1994)
LF - Lie and Frye, JCP, v.96, 6784 (1992)
MBB - Meyer, Botschwina , Burton , JCP, v.84, 891 (1986)
Next 12 MBB-geometry points for various ab initio PES
• N nx ny nz
Eh
10 5 0 0 -1.241529
11 0 -4 0 -1.240043
12 0 -3 0 -1.287329
13 0 -2 0 -1.319311
14 0 -1 0 -1.337797
15 0 1 0 -1.337839
16 0 2 0 -1.319646
17 0 3 0 -1.288451
18 -4 -1 0 -1.244891
19 -4 1 0 -1.245426
20 -3 -2 0 -1.257927
21 -3 -1 0 -1.287408
22 -3 1 0 -1.287788
E this work - E x(cm-1)
CRJK RKJK
LF
- 0.021 4.276
-48.0
- 0.017 -2.539
-4.1
- 0.019 -1.849
-0.2
- 0.019 -1.186
-1.1
- 0.018 -0.661
-1.1
- 0.019 -0.741
-1.1
- 0.018 -1.338
-1.1
- 0.014 -1.384
-5.8
- 0.015 -1.286 -113.0
- 0.014 -1.275 -102.1
- 0.015 -1.416 -87.0
- 0.014 -1.205 -55.0
- 0.014 -1.202 -52.2
MBB
14.2
- 7.2
- 3.5
- 1.3
- 0.4
- 0.6
5.6
20.4
-31.9
-40.4
-26.2
-23.8
-23.5
CRJK – Cencek,Rychlewski Jaquet Kutzelnigg, JCP, v.108, 2831 (1998)
RKJK - Roese Kutzelnigg Jaquet Klopper, JCP, v.101, 2231 (1994)
LF - Lie and Frye, JCP, v.96, 6784 (1992)
MBB - Meyer, Botschwina , Burton , JCP, v.84, 891 (1986)
Analytical PES from the ab initio points
Functional form of the fitted PES
Viegas, Alijah, Varandas, JCP,126,074309(2007)
Number of PES points and their sd in
different energy regions of the GLH3P
Comparison of some ab intio points
with Bachorz et. Al, JCP,v.131,24105(2009)
D in
cm-1
10.18
10.27
10.39
Rovibrational energy levels from
Schroedinger equation
Vibrational
Energy
Rotational
Energy
Potential
Energy
HY=EY
Vibrational KE
Vibrational KE
Non-orthogonal coordinates only
Rotational & Coriolis terms
Rotational & Coriolis terms
Non-orthogonal coordinates only
Reduced masses
(g1,g2) define coordinates
Ab initio vibrational band origins
mode Eobs / cm-1
H3+
MBB CP RKJK
(uncorr)
2.5
5
0.3
0.1
7
0.09
5.4
21
1.1
5.0
6
0.8
3.2
14
0.07
011
100
020
022
111
2521.409
3178.290
4778.350
4998.045
5554.155
H2D+
n1
n2
n3
2992.505
2205.869
2335.449
0.0
1.4
2.6
D2H+
n1
n2
n3
2736.981
1968.169
2078.430
0.2
2.0
1.2
PT(BO) PT(nBO)
-0.11
-1.3
0.0
-0.3
-1.4
+0.056
+0.025
+0.020
+0.010
0.000
0.5 -1.46
0.04 -0.47
0.9 +0.47
-0.020
-0.050
+0.090
0.2
0.8
0.4
-1.04
+0.58
-0.74
+0.001
+0.023
-0.004
MBB - - Meyer, Botschwina , Burton , JCP, v.84, 891 (1986)
CP – Carney, Porter, JCP, v.65,3547(1976)
RKJK- - Roese, Kutzelnigg, Jaquet, Klopper, JCP, v.101, 2231 (1994)
PT - Polyansky and Tennyson, J. Chem. Phys., 110, 5056 (1999) – based on the points
of CRJK - Cencek,Rychlewski, Jaquet, Kutzelnigg, JCP, v.108, 2831 (1998)
Correction to potential
Adiabatic effects in H3+
The Born-Handy approximation
Correction to kinetic energy
Nonadiabatic correction
Bunker and Moss, JMS, v.80, p.217 (1980)
Ab initio vibrational band origins
mode Eobs / cm-1
H3+
MBB CP RKJK
(uncorr)
2.5
5
0.3
0.1
7
0.09
5.4
21
1.1
5.0
6
0.8
3.2
14
0.07
011
100
020
022
111
2521.409
3178.290
4778.350
4998.045
5554.155
H2D+
n1
n2
n3
2992.505
2205.869
2335.449
0.0
1.4
2.6
D2H+
n1
n2
n3
2736.981
1968.169
2078.430
0.2
2.0
1.2
PT(BO) PT(nBO)
-0.11
-1.3
0.0
-0.3
-1.4
+0.056
+0.025
+0.020
+0.010
0.000
0.5 -1.46
0.04 -0.47
0.9 +0.47
-0.020
-0.050
+0.090
0.2
0.8
0.4
-1.04
+0.58
-0.74
+0.001
+0.023
-0.004
MBB - - Meyer, Botschwina , Burton , JCP, v.84, 891 (1986)
CP – Carney, Porter, JCP, v.65,3547(1976)
RKJK- - Roese, Kutzelnigg, Jaquet, Klopper, JCP, v.101, 2231 (1994)
PT - Polyansky and Tennyson, J. Chem. Phys., 110, 5056 (1999) – based on the points
of CRJK - Cencek,Rychlewski, Jaquet, Kutzelnigg, JCP, v.108, 2831 (1998)
Ab initio vibrational band origins
mode Eobs / cm-1
011
100
020
022
111
2521.409
3178.290
4778.350
4998.045
5554.155
7870.020
9113.080
11323.100
11658.400
MBB
(uncorr)
2.5
0.1
5.4
5.0
3.2
CP RKJK PT(BO) PT(nBO)
5
7
21
6
14
0.3
0.09
1.1
0.8
0.07
-0.11
-1.3
0.0
-0.3
-1.4
+0.056
+0.025
+0.020
+0.010
0.000
-0.81
+0.93
+0.55
+7.58
MBB - - Meyer, Botschwina , Burton , JCP, v.84, 891 (1986)
CP – Carney, Porter, JCP, v.65,3547(1976)
RKJK- - Roese, Kutzelnigg, Jaquet, Klopper, JCP, v.101, 2231 (1994)
PT - Polyansky and Tennyson, J. Chem. Phys., 110, 5056 (1999) – based on the points
of CRJK - Cencek,Rychlewski, Jaquet, Kutzelnigg, JCP, v.108, 2831 (1998)
Difference between energy levels of H3+
for BO on (PT99 and GLH3P)
2521.51
2521.46
0.05
3179.59
3179.56
0.02
4778.33
4778.16
0.17
4998.31
4998.17
0.14
5555.41
5555.47
-0.05
6264.44
6264.57
-0.14
7006.08
7005.81
0.27
7285.48
7285.44
0.05
7770.18
7770.55
-0.36
7870.83
7871.34
-0.51
8489.36
8490.23
-0.87
9001.00
9000.89
0.10
9112.15
9112.21
-0.06
9254.75
9255.41
-0.66
9653.29
9653.96
-0.67
Difference as it should be for levels below 10000 cm-1
Difference between energy levels of
H3+ for BO only (PT99 and GLH3P)
9966.77
9969.20
-2.43
13283.35
13293.69
-10.34
9997.47
9998.37
-0.90
13306.91
13319.92
-13.01
10592.73
10595.27
-2.55
13388.52
13398.25
-9.72
10643.42
10647.00
-3.58
10856.90
10857.99
-1.09
13432.93
13443.71
-10.78
10918.03
10919.75
-1.72
13579.29
13590.81
-11.53
11322.55
11326.12
-3.57
13705.01
13715.01
-10.00
14044.61
14057.69
-13.08
14139.87
14157.99
-18.11
11650.82
11655.10
-4.28
11809.70
11814.75
-5.05
Ab initio points differ no more than 0.1 cm-1 in 69 MBB geometries
Why this big difference in energies?
GLH3P – PT99
PT99 – Polyansky and Tennyson, JCP,v.110,5056 (1999) –
69 MBB geometries, sd – 4.5 cm-1
GLH3P-PPKT
PPKT – Polyansky, Prosmiti, Klopper and Tennyson,
Mol.Phys,v.98,261(2000) – 200 geometries, sd – 1.0 cm-1
Ab initio vibrational band origins
mode
011
100
020
022
111
Eobs / cm-1
2521.409
3178.290
4778.350
4998.045
5554.155
MBB CP
2.5
5
0.1
7
5.4
21
5.0
6
3.2
14
RKJK
0.3
0.09
1.1
0.8
0.07
PT(BO) PT(nBO)
-0.11 +0.056
-1.3
+0.025
0.0
+0.020
-0.3
+0.010
-1.4
0.000
7870.020
-0.81
9113.080
+0.93
11323.100
+0.55
11658.400
+7.58
THUS the reason for this large discrepancy – BO PES used in
PT
MBB - - Meyer, Botschwina , Burton , JCP, v.84, 891 (1986)
CP – Carney, Porter, JCP, v.65,3547(1976)
RKJK- - Roese, Kutzelnigg, Jaquet, Klopper, JCP, v.101, 2231 (1994)
PT - Polyansky and Tennyson, J. Chem. Phys., 110, 5056 (1999) – based on the points
of CRJK - Cencek,Rychlewski, Jaquet, Kutzelnigg, JCP, v.108, 2831 (1998)
Thus, we proved that better BO PES is needed.
Now we can use this global GLH3P BO PES, which is
now extremely accurate and dense
For rovibrational calculations
Relative contribution of BO-PES, adiabatic,
nonadiabatic and relativistic corrections to the
accuracy of optical lines calculations
Obs-calc. BO+adiabatic –grey, full
model – red and yellow
The highest H3+ line. -3.0 and +8.5 cm-1 –
previous predictions
Part of a table from
Bachorz et. al , JCP, v131, 024105 (2009)
Last column – our calculations
H3+
H2D+
Quotation
• ...Our measurements include high rotational
lines up to J=6 . Such high J lines have high
deviations from theory and are particularly
challenging to theorists...
Morong, Gottfried and Oka, JMS, v.255, p.13, (2009)
Part of the table of Morong, Gottfried and Oka,
JMS, v.255, p.13, (2009) with the mentioned
high J lines
We fitted 4250 dipole moments with the standard deviation 0.001 to DMS.
Using our PES and DMS calculated the intensities of McKellar, Watson JMS,
191, 215(1998)
Table of intensities. Comparison with Watson
and McKellar, JMS, v.191, 215 (1998)
Table of intensities. Comparison with Watson
and McKellar, JMS, v.191, 215 (1998),continued
Intensity calcs
• Strong lines on average 2%, for all lines -4%
• Need more accurate intensity measurements
to be able to demonstrate the full potential of
our DMS, but even now we can state that our
linelists can provide not only 0.1 cm-1 line
positions, but few % lineintensity
CONCLUSIONS
• Accurate ab initio calculations 10-8 Eh
(previous talk)
• Dense grid and 42000 points
• Accurate fit to analytical surface 0.097 cm-1
• Globally accurate PES GLH3P
• 0.1 cm-1 observed – calculated
• Hopefully 0.01 cm-1 of BO, adiabatic,
relativistic
CONCLUSIONS
• 0.1 cm-1 observed – calculated up to 17000 cm
the work done.
• Future work: 0.1 cm for 20,25,30,35 000 cm-1
could demonstrate only if experiment could
be done
0.1 cm-1 => 0.01 cm-1 – improvement of nonadiabatic models and QED calculations