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 isH2

+ 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