calculation of rovibrational h 3 + lines. new level of accuracy slides of invited talk at royal...
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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, NizhniiNovgorod, 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-10.1 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 talk1.Motivation (helps to appreciate the basic goal)
2. Global Analytical PES (accurate to 0.1 cm-1) and comparison with previous PES
3. Accuracy of previous RV calcs (0.1 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 (0.1 cm-1 up to 17000 cm-1 )
6. Conclusions and Future work
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 Nlevels Jmax H2
16O 9426 20 1.17H2
17O 1083 12 0.56H2
18O 2460 12 0.65D2
16O 2807 12 0.71HD16O 1976 12 0.47
All water 17338 20 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+ H2 H3
+ 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)
• 10-8 Eh accuracy • 42 000 points• Dense and global grid• 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 Eh E this work - E x(cm-1)
CRJK RKJK LF MBB1 -4 0 0 -1.255924 - 0.012 -1.206 -2.6 -40.32 -3 0 0 -1.296828 - 0.013 -1.127 -1.8 -23.13 -2 0 0 -1.323893 - 0.013 -0.960 -1.2 -10.94 -1 0 0 -1.339057 - 0.014 -0.724 -1.1 - 3.45 0 0 0 -1.343835 - 0.018 0.000 0.0 0.06 1 0 0 -1.339388 - 0.015 -0.037 -2.1 - 1.77 2 0 0 -1.326560 - 0.015 0.528 -6.5 1.88 3 0 0 -1.305893 - 0.021 1.323 -15.0 6.39 4 0 0 -1.277607 - 0.022 2.473 -49.1 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)
• N nx ny nz Eh E this work - E x(cm-1)
CRJK RKJK LF MBB 10 5 0 0 -1.241529 - 0.021 4.276 -48.0 14.2
11 0 -4 0 -1.240043 - 0.017 -2.539 -4.1 - 7.212 0 -3 0 -1.287329 - 0.019 -1.849 -0.2 - 3.513 0 -2 0 -1.319311 - 0.019 -1.186 -1.1 - 1.314 0 -1 0 -1.337797 - 0.018 -0.661 -1.1 - 0.415 0 1 0 -1.337839 - 0.019 -0.741 -1.1 - 0.616 0 2 0 -1.319646 - 0.018 -1.338 -1.1 5.617 0 3 0 -1.288451 - 0.014 -1.384 -5.8 20.418 -4 -1 0 -1.244891 - 0.015 -1.286 -113.0 -31.919 -4 1 0 -1.245426 - 0.014 -1.275 -102.1 -40.420 -3 -2 0 -1.257927 - 0.015 -1.416 -87.0 -26.221 -3 -1 0 -1.287408 - 0.014 -1.205 -55.0 -23.822 -3 1 0 -1.287788 - 0.014 -1.202 -52.2 -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)
Next 12 MBB-geometry points for various ab initio PES
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 pointswith Bachorz et. Al, JCP,v.131,24105(2009)
D in cm-1
10.18
10.27
10.39
Rovibrational energy levels from Schroedinger equation
VibrationalEnergy
RotationalEnergy
PotentialEnergy
Vibrational KE
Vibrational KENon-orthogonal coordinates only
Rotational & Coriolis terms
Rotational & Coriolis terms Non-orthogonal coordinates only
Reduced masses (g1,g2) define coordinates
HY=EY
mode Eobs / cm-1 MBB CP RKJK PT(BO) PT(nBO) (uncorr) 011 2521.409 2.5 5 0.3 -0.11 +0.056 100 3178.290 0.1 7 0.09 -1.3 +0.025 020 4778.350 5.4 21 1.1 0.0 +0.020 022 4998.045 5.0 6 0.8 -0.3 +0.010 111 5554.155 3.2 14 0.07 -1.4 0.000
n1 2992.505 0.0 0.5 -1.46 0.020 n2 2205.869 1.4 0.04 -0.47 0.050 n3 2335.449 2.6 0.9 +0.47 +0.090
n1 2736.981 0.2 0.2 -1.04 +0.001 n2 1968.169 2.0 0.8 +0.58 +0.023 n3 2078.430 1.2 0.4 -0.74 0.004
Ab initio vibrational band origins
H2D+
H3+
D2H+
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 potentialAdiabatic effects in H3
+
The Born-Handy approximation
Bunker and Moss, JMS, v.80, p.217 (1980)
Correction to kinetic energyNonadiabatic correction
mode Eobs / cm-1 MBB CP RKJK PT(BO) PT(nBO) (uncorr) 011 2521.409 2.5 5 0.3 -0.11 +0.056 100 3178.290 0.1 7 0.09 -1.3 +0.025 020 4778.350 5.4 21 1.1 0.0 +0.020 022 4998.045 5.0 6 0.8 -0.3 +0.010 111 5554.155 3.2 14 0.07 -1.4 0.000
n1 2992.505 0.0 0.5 -1.46 0.020 n2 2205.869 1.4 0.04 -0.47 0.050 n3 2335.449 2.6 0.9 +0.47 +0.090
n1 2736.981 0.2 0.2 -1.04 +0.001 n2 1968.169 2.0 0.8 +0.58 +0.023 n3 2078.430 1.2 0.4 -0.74 0.004
Ab initio vibrational band origins
H2D+
H3+
D2H+
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)
mode Eobs / cm-1 MBB CP RKJK PT(BO) PT(nBO) (uncorr) 011 2521.409 2.5 5 0.3 -0.11 +0.056 100 3178.290 0.1 7 0.09 -1.3 +0.025 020 4778.350 5.4 21 1.1 0.0 +0.020 022 4998.045 5.0 6 0.8 -0.3 +0.010 111 5554.155 3.2 14 0.07 -1.4 0.000 7870.020 -0.81 9113.080 +0.93 11323.100 +0.55 11658.400 +7.58
Ab initio vibrational band origins
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)
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 between energy levels of H3+ for BO on (PT99 and GLH3P)
Difference as it should be for levels below 10000 cm-1
9966.77 9969.20 -2.43
9997.47 9998.37 -0.90
10592.73 10595.27 -2.55
10643.42 10647.00 -3.58
10856.90 10857.99 -1.09
10918.03 10919.75 -1.72
11322.55 11326.12 -3.57
11650.82 11655.10 -4.28
11809.70 11814.75 -5.05
13283.35 13293.69 -10.34
13306.91 13319.92 -13.01
13388.52 13398.25 -9.72
13432.93 13443.71 -10.78
13579.29 13590.81 -11.53
13705.01 13715.01 -10.00
14044.61 14057.69 -13.08
14139.87 14157.99 -18.11
Difference between energy levels of H3+ for BO only (PT99 and GLH3P)
Ab initio points differ no more than 0.1 cm-1 in 69 MBB geometriesWhy 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
mode Eobs / cm-1 MBB CP RKJK PT(BO) PT(nBO) 011 2521.409 2.5 5 0.3 -0.11 +0.056 100 3178.290 0.1 7 0.09 -1.3 +0.025 020 4778.350 5.4 21 1.1 0.0 +0.020 022 4998.045 5.0 6 0.8 -0.3 +0.010 111 5554.155 3.2 14 0.07 -1.4 0.000 7870.020 -0.81 9113.080 +0.93 11323.100 +0.55 11658.400 +7.58THUS the reason for this large discrepancy – BO PES used in PT
Ab initio vibrational band origins
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 non-adiabatic models and QED calculations