Vibration-rotation spectra from first principles Lecture 2: Calculations of spectroscopic accuracy

# Vibration-rotation spectra from first principles Lecture 2: Calculations of spectroscopic accuracy

## Vibration-rotation spectra from first principles Lecture 2: Calculations of spectroscopic accuracy

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1. Vibration-rotation spectra from first principles Lecture 2: Calculations of spectroscopic accuracy Jonathan Tennyson Department of Physics and Astronomy University College London OSU, February 2002

2. “Experiments (are) measured to tenths of wave numbers… this level of accuracy in a calculation is meaningless” Freisner, Bentley, Menou and Leforestier, J. Chem. Phys.99, 324 (1993)

3. For triatomics accuracy determined by: • The potential energy surface • The validity of a potential (ie the Born-Oppenheimer approximation) • Potentials: • from electronic structure calculations • spectroscopically determined

4. Potentials:Ab initioorSpectroscopically determined

5. Using spectra to improve a potential? • Guess form eg V(r1,r2,q) = S ci fi (r1,r2,q) • Compute obs - calc and standard deviation • Compute derivatives. Hellman-Feynman theorem d < n | H | n > /dc= < n | dH/dc | n > gives d < n | V | n > /dci = < n | fi (r1,r2,q) | n > • Repeat calculation with improved V(r1,r2,q) • Guesses improved using specialist techniques • eg I-NoLLS: a program for interactive nonlinear least-squares fitting of the parameters of physical models, • M.M. Law & J. M. Hutson, Comp. Phys. Commun., 102, 252 (1997).

6. Fitting to spectroscopic data • Best start: high quality ab initio calculation • (starting point usually determines quality of fit). • Final fit usual in 2 – 3 iterations • (But many tests first!) • Usually fit energy levels rather than spectra • Fit vibrational and rotational data simultaneously • (Essential for light molecules) • Born-Oppenheimer approximation !? • Fit 20 – 30 parameters (only).

7. Spectroscopically determined water potentials Important to treat vibrations and rotations

8. Spectroscopically determined potential Polyansky, Jenson & Tennyson (PJT1), J. Chem. Phys., 101, 7561 (1994) Fit: 1600 term values with J up to 14 a New experimental value: 10899.64 cm-1

9. Ab initio accuracy better than 1cm1 • Adiabatic or Born-Oppenheimer Diagonal Correction (BODC) • Non-adiabatic corrections for vibration and rotation • Electronic (kinetic) relativistic effect • Relativistic Coulomb potential (Breit effect) • Radiative correction (Lamb shift or qed) Can BO electronic structure calculations be done this accurately? Variational rotation-vibration calculations with exact kinetic energy operator accurate to better than 0.001 cm-1

10. Molecule considered at high accuracy H3+ H2O H2S HCN/HNC

11. Ab initio Born-Oppenheimer potentials for H3+ Year Authors Emin / EhE / cm 1975 Carney & Porter 1.33519 1900 1980 Schinke et al 1.34023 790 1985 Burton et al 1.34188 430 1986 Meyer et al 1.34309 160 1990/2 Frye et al 1.343828 9 1994 Rohse et al 1.3438336 1 1998 Cencek et al a1.3438355 0.04 For spectroscopy shape is more important than magnitude a Also electronic relativistic correction, ~ 3 cm-1

12. Adiabatic effects in H3+ The Born-Handy approximation

13. Ab initio vibrational band origins mode Eobs / cm-1 BO +Vad 011 2521.409 0.11 0.24 100 3178.290 1.30 0.40 020 4778.350 0.00 0.50 022 4998.045 0.30 0.64 111 5554.155 1.40 0.50 n1 2992.505 1.46 0.36 n2 2205.869 0.47 0.25 n3 2335.449 +0.47 0.14 n1 2736.981 1.04 0.28 n2 1968.169 +0.58 0.11 n3 2078.430 0.74 0.18 H3+ H2D+ D2H+

14. Non-adiabatic effects in diatomics P.R. Bunker and R.E. Moss, Mol. Phys., 33, 417 (1977)

15. Effective Hamiltonian after intergration over angular and rotational coordinates. Case where z is along r1 Vibrational KE Vibrational KE Non-orthogonal coordinates only Rotational & Coriolis terms Rotational & Coriolis terms Non-orthogonal coordinates only Reduced masses (g1,g2) define coordinates

16. Non-adiabatic effects in the ST Hamiltonian

17. Ab initio vibrational band origins mode Eobs / cm-1 BO +Vad vnuc 011 2521.409 0.11 0.24 +0.056 100 3178.290 1.30 0.40 +0.025 020 4778.350 0.00 0.50 +0.020 022 4998.045 0.30 0.64 +0.010 111 5554.155 1.40 0.50 0.000 n1 2992.505 1.46 0.36 0.020 n2 2205.869 0.47 0.25 0.050 n3 2335.449 +0.47 0.14 +0.090 n1 2736.981 1.04 0.28 +0.001 n2 1968.169 +0.58 0.11 +0.023 n3 2078.430 0.74 0.18 0.004 H3+ H2D+ D2H+ O.L. Polyansky and J. Tennyson, J. Chem. Phys., 110, 5056 (1999).

18. H2D+ : ab initio spectra J Ka Kc J Ka Kc Eobs / cm-1 BO +Vad vnuc + KNBO 3 2 1 3 2 2 2225.501 0.385 0.245 0.062 0.044 3 2 1 2 0 2 2448.627 0.521 0.259 0.011 0.076 2 2 0 2 2 1 2208.417 0.435 0.242 0.050 0.068 2 2 1 2 0 2 2283.810 0.521 0.239 +0.030 0.059 2 2 0 1 0 1 2381.367 0.573 0.250 +0.008 0.060 3 3 1 2 1 2 2512.598 0.647 0.250 +0.075 0.099 n2 2 0 2 3 1 3 2223.706 0.418 0.163 +0.050 +0.068 2 2 1 3 1 2 2242.303 0.753 0.151 +0.140 +0.095 2 1 2 2 2 1 2272.395 0.420 0.168 +0.035 +0.099 2 2 0 2 1 1 2393.633 0.320 0.162 +0.140 +0.087 3 3 1 3 2 2 2466.041 0.224 0.164 +0.190 +0.080 3 3 1 2 2 0 2596.960 0.185 0.177 +0.167 +0.077 3 3 0 2 2 1 2602.146 0.203 0.172 +0.167 +0.080 n3

19. Rotational non-adiabatic effects Use nuc given by nuclear mass Explicit inclusion of effect via rotational g-factors PR Bunker & RE Moss, J. Mol. Spectrosc., 80, 217 (1980) Preliminary results for H3+ Calculations for all observed levels, J up to 15 Reproduces observations to better than 0.001 x J2 cm-1 for vibrational ground state OL Polyansky, MA Kostin, J Tennyson, BT Sutcliffe, I Paidarova & SPA Sauer, to be published

20. Ab initio predictions of water vibrational fundamentals

21. Water: Barrier to linearity Reference Year Barrier height/cm-1 Comment Carter and Handy 1987 11493 Spectroscopic Empirical Jensen 1989 11246 Spectroscopic Empirical Polyansky et al (PJT2) 1994 10966 Spectroscopic Empirical Lanquetin et al 1999 11154 Effective Hamiltonian Partridge & Schwenke (PS) 1997 11155 Ab initio Partridge & Schwenke 1997 11128 Spectroscopic Empirical PS + adiabatic + relativistic 1998 11192 Ab initio Csaszar et al 1998 11046  70 Extrapolated ab initio Tarczay et al 1999 11127  35 High accuracy ab initio Kain et al 2000 11105  5 Corrected ab initio Valeev et al 2001 11119  12 Ab initio (MP2 – R12)

22. Achieving a “perfect” ab initio potential • Need to consider: (for water) • SCF at full basis set limit (done) • Valence CI to full basis set limit (by extrapolating from large basis calculation) • Extension of CI to full CI limit (only possible with v. small, eg DZP, basis set) • Core – valence correlation New high accuracy extrapolated ab initio calculations in progress Polyansky, Csaszar, Tennyson, Barletta, Shirin, Zobov & Schwenke The future: explicit inclusion of r12 into the wavefunction

23. Ab initio: vibrational errors

24. Ab initio + Adiabatic: vib. errors

25. Ab initio + adiabatic + relativistic MVD1 Csaszar, Kain, Polyansky, Zobov and Tennyson, Chem. Phys. Lett., 293, 317 (1998).

26. Relativistic electronic potential effects in water Ab initio +Gaunt1 +Breit2 Obs / cm1 (010) 1598.19 +0.10 +0.04 1594.75 (020) 3158.49 +0.18 +0.09 3151.63 (030) 4677.22 +0.21 +0.10 4666.79 (040) 6148.29 +0.20+0.05 6134.01 (050) 7561.09 +0.100.10 7542.44 (060) 8894.52 0.16 0.35 8869.95 (101) 7249.52 +1.60 +1.32 7249.82 (201) 10612.70 +2.34 +1.94 10613.35 (301) 13829.31 +3.07 +2.54 13830.94 (401) 16896.50 +3.87 +3.20 16898.84 (501) 19776.00 +4.44 +4.04 19781.10 1 Gaunt correction: 1 electron approximation 2 Breit correction: full calculation H.M. Quiney, P. Barletta, G. Tarczay, A.G. Csaszar, O.L. Polyansky and J. Tennyson, Chem. Phys. Lett., 344, 413 (2001). (also D2)

27. The hydrogen atom: n = 2 levels Non- relativistic Fine structure Lamb shift 2p3/2 2p3/2 2s, 2p 0.365 cm-1 2s1/2 0.035 cm-1 2p1/2 2s1/2 2p1/2 Schrodinger Dirac QED

28. One-electron Lamb shift effects in water Ab initio + Lamb Obs / cm1 (010) 1598.19 0.09 1594.75 (020) 3158.49 0.18 3151.63 (030) 4677.22 0.29 4666.79 (040) 6148.29 0.43 6134.01 (050) 7561.09 0.60 7542.44 (060) 8894.52 0.86 8869.95 (101) 7249.52 +0.37 7249.82 (201) 10612.70 +0.54 10613.35 (301) 13829.31 +0.71 13830.94 (401) 16896.50 +0.83 16898.84 (501) 19776.00 +1.01 19781.10 (601) 22519.69 +1.19 22529.44 (701) 25105.51 +1.29 25120.28 P. Pyykko, K.G. Dyall, A.G. Csaszar, G. Tarczay, O.L. Polyansky and J. Tennyson, Phys. Rev. A, 63, 024502 (2001)

29. Born-Oppenheimer corrections for water BO / cm1 +BODC1 + Non-adiabatic vnuc2 diag3 full4 (010) 1597.60 -0.46 -0.19 -0.06 -0.07 (020) 3157.14 -0.94 -0.38 -0.12 -0.15 (100) 3661.00 +0.55 -0.46 -0.72 -0.70 (030) 4674.88 -1.43-0.55 -0.18 -0.23 (110) 5241.83 +0.16 -0.65 -0.77 -0.76 (040) 6144.64 -2.00-0.71 -0.23 -0.30 (120) 6784.56 -0.23 -0.83 -0.83 -0.84 (200) 7208.80 +1.25 -0.88 -1.39 -1.37 (002) 7450.86 +1.47 -0.90 -1.47 -1.57 (050) 7555.62 -2.71-0.84-0.28 -0.32 1 Born-Oppenheimer diagonal correction using CASSCF wavefunction 2 Non-adiabatic correction by scaling vibrational mass, mV 3 Two parameter diagonal correction 4 Full treatment by Schwenke (J. Phys. Chem. A, 105, 2352 (2001).) J. Tennyson, P. Barletta, M.A. Kostin, N.F.Zobov, and O.L. Polyansky, Spectrachimica Acta A (in press).

30. Variational calculations: Assignments using branches Spectroscopically Determined potential Error / cm-1 Ab initio potential J

31. Polyad structure in water absorption spectrum Long pathlength Fourier Transform spectrum recorded by R Schmeraul

32. Weak lines R. Schermaul, R.C.M. Learner, J.W. Brault, A.A.D. Canas, O.L. Polyansky, D. Belmiloud, N.F. Zobov and J. Tennyson J. Molec. Spectrosc. (in press)

33. Weak water lines Very difficult to record Only a few weak lines in HITRAN New experimental measurements • REIMS data • Carleer et al. • Bruker F.T.S • Range :13200 - 25020 cm-1 • T : 291 K • p(H2O) : 18.5 hPa • pathlength ~ 602.32 m • Number of new lines : 2286 • IMPERIAL data (R.A.L) • Schermaul et al. • Bruker F.T.S • Range :13350 - 14750 cm-1 • T : 294.4 K • p(H2O) : 23.02 hPa • pathlength ~ 800.75 m • Number of lines : 3179 • Number of new lines : 963 Also Kitt Peak archive data Also spectra 8000 – 13500 cm-1

34. Water vapour spectrum: new assignments in the blue Long pathlength FTS M Carleer et al, J. Chem. Phys., 111, 2444 (1999)

35. Water: Rotation-Vibration spectra in the near ultra violet Vibrational mode Previous worka This workb band origin Local Normal lines levels lines levels cm1 (4,2)1 (115) 10 5 22513. (7,0)+0 (700) 5 2 90 39 22529.296 (7,0)0 (601) 42 20 57 15 22529.445 (6,0)2 (521) 16 10 22630. (7,0)1 (611) 16 10 23947. (8,0)+0 (800) 24 20 25120. (8,0)0 (701) 12 6 23 18 25120.278 a C. Camy-Peyret et al, J. Mol. Spectrosc., 113, 208 (1985). bN.F. Zobov et al,J. Chem. Phys., 113, 1546 (2000).

36. Intensity data compared to HITRAN-96 by polyad for spectral region 8500 – 15800 cm-1 Numbers are ratio of total intensity to HITRAN HITRAN underestimates intensity of strong lines! D Belmiloud et al, Geophys. Res. Lett., 27, 3703 (2000).

37. Frequency / cm-1 Water absorption by the atmosphere: Standard Model W Zhong, JD Haigh, D Belmiloud, R Schermaul & J Tennyson, Quart. J. Roy. Metr. Soc., 127, 1615 (2001)

38. Water absorption by the atmosphere:correction of Giver et al (2000) Frequency / cm-1

39. Water absorption by the atmosphere:Effect of weak water lines Frequency / cm-1

40. Water absorption by the atmosphere:Effect of ESA-WVR linelist Frequency / cm-1

41. Experiment Atmospheric absorption Radiative Transfer Model Theory Missing absorption due to water:First estimates • In the red and visible : • Unobserved weak lines have a significant effect : ~ 3 Wm-2 • Estimated additional 2.5-3 % absorption in the near I.R/Red. • Estimated additional 8-11 % absorption in the ‘Blue’ ? • Underestimate of strong lines even more important : ~ 8 Wm-2 • Estimated additional 8 % absorption in the near I.R/Red.

42. Missing absorption due to water:Outstanding issues • In the near infrared and red: • Contributions due to H218O, H217O and HDO. • Possible role of water dimer (H2O)2. • In the blue and ultraviolet: • Are H216O line intensities also underestimated? • Contribution due to weak lines

43. Sensitivity of vibrational band origins a Unknown, assumed negligible

44. Water assignments using variational calculations • Long pathlength absoption (T = 296K) 11000 - 25000 cm-1 Fourier Transform and Cavity Ring Down • Laboratory emisson spectra (T =1300 - 1800K) 400 – 6000 cm-1 • Absorption in sunspots (T = 3200 K) N band, L band, K band 10-12 mm 3 mm 2 mm • 25000 new lines assigned Dataset of 12000 measured H216O energy levels J. Tennyson, N.F. Zobov, R. Williamson, O.L. Polyansky & P.F. Bernath, J. Phys. Chem. Ref. Data, 30, 735 (2001).

45. Paolo Barletta Mizuho Tanaka Maxim Kostin Oleg Polyansky Roman Tolchenov Nikolai Zobov