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Calculation of rovibrational H 3 + lines. New level of accuracy Slides of invited talk at

Calculation of rovibrational H 3 + lines. New level of accuracy Slides of invited talk at Royal Society conference on H 3 +. Oleg L. Polyansky 1,2 1 Institute of Applied Physics, Russian Academy of Sciences, Uljanov Street 46, Nizhnii Novgorod, Russia 603950

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Calculation of rovibrational H 3 + lines. New level of accuracy Slides of invited talk at

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  1. 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

  2. Calculation of rovibrational H3+ lines.New level of accuracy Oleg Polyansky, Alex Alijah KolyaZobov, Irina Mizus, Roman Ovsyannikov Lorenzo Lodi, Jonathan Tennyson, Attila Csaszar,

  3. Analytical PES from the ab initio points

  4. RV- Schroedinger equation with exact kinetic energy and PES V(r1,r2,q) HY=EY

  5. The highest H3+ line. -3.0 and +8.5 cm-1 –previous predictions

  6. 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)

  7. 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

  8. Structure of this talk 1.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

  9. 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

  10. Ab initio predictions of water levels IsotopologueNlevelsJmax H216O 9426 20 1.17 H217O 1083 12 0.56 H218O 2460 12 0.65 D216O 2807 12 0.71 HD16O 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.

  11. 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

  12. Water spectrum above disociation. The density of lines 1000 times lower than in Carrington-Kennedy predissociation spectrum of H3+

  13. EXPERIMENTAL AND CALCULATED SPECTRUM OF WATER ABOVE DISSOCIATION Zobov ,Shirin,Lodi,Siva,Tennyson,Csaszar,andPolyansky, Chem.phys.Lett.v.507,p.48,(2011)

  14. 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

  15. First 9 MBB-geometry points for various ab initio PES • N nxnynz 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)

  16. Next 12 MBB-geometry points for various ab initio PES • N nxnynz Eh E this work - E x(cm-1) CRJK RKJK LF MBB 10 5 0 0 -1.241529 - 0.021 4.276 -48.0 14.211 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,RychlewskiJaquetKutzelnigg, JCP, v.108, 2831 (1998) RKJK - RoeseKutzelniggJaquetKlopper, JCP, v.101, 2231 (1994) LF - Lie and Frye, JCP, v.96, 6784 (1992) MBB - Meyer, Botschwina , Burton , JCP, v.84, 891 (1986)

  17. Analytical PES from the ab initio points

  18. Functional form of the fitted PES Viegas, Alijah, Varandas, JCP,126,074309(2007)

  19. Number of PES points and their sd in different energy regions of the GLH3P

  20. Comparison of some abintio pointswith Bachorz et. Al, JCP,v.131,24105(2009) D in cm-1 10.18 10.27 10.39

  21. Rovibrational energy levels from Schroedinger equation Potential Energy Vibrational Energy Rotational Energy

  22. 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

  23. Ab initiovibrational band origins mode Eobs / cm-1MBB 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 n32078.430 1.2 0.4 -0.74 0.004 H3+ H2D+ 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)

  24. Correction to potential Adiabatic effects in H3+ The Born-Handy approximation

  25. Correction to kinetic energy Nonadiabatic correction Bunker and Moss, JMS, v.80, p.217 (1980)

  26. Ab initiovibrational band origins mode Eobs / cm-1MBB 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 n32078.430 1.2 0.4 -0.74 0.004 H3+ H2D+ 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)

  27. Ab initiovibrational band origins mode Eobs / cm-1MBB 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 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)

  28. Difference between energy levels of H3+ • for BO on (PT99 and GLH3P) Difference as it should be for levels below 10000 cm-1

  29. 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 geometries Why this big difference in energies?

  30. GLH3P – PT99 PT99 – Polyansky and Tennyson, JCP,v.110,5056 (1999) – 69 MBB geometries, sd – 4.5 cm-1

  31. GLH3P-PPKT PPKT – Polyansky, Prosmiti, Klopper and Tennyson, Mol.Phys,v.98,261(2000) – 200 geometries, sd – 1.0 cm-1

  32. Ab initiovibrational band origins mode Eobs / cm-1MBB 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 +7.58 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)

  33. 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

  34. Relative contribution of BO-PES, adiabatic, nonadiabatic and relativistic corrections to the accuracy of optical lines calculations

  35. Obs-calc. BO+adiabatic –grey, full model – red and yellow

  36. The highest H3+ line. -3.0 and +8.5 cm-1 –previous predictions

  37. Part of a table fromBachorz et. al , JCP, v131, 024105 (2009)Last column – our calculations

  38. H3+

  39. H2D+

  40. 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)

  41. Part of the table ofMorong, Gottfried and Oka, JMS, v.255, p.13, (2009) with the mentioned high J lines

  42. 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)

  43. Table of intensities. Comparison with Watson and McKellar, JMS, v.191, 215 (1998)

  44. Table of intensities. Comparison with Watson and McKellar, JMS, v.191, 215 (1998),continued

  45. 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

  46. 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

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