Vibration-rotation spectra from first principles

Lecture 1: Variational nuclear motion calculationsLecture 2: Rotational motion, Spectra, PropertiesLecture 3: Calculations of spectroscopic accuracyLecture 4: Applications

Jonathan TennysonDepartment of Physics and AstronomyUniversity College London

QUASAAR Winter School,Grenoble, Jan/Feb 2006

Obs / cm−1 5Z1 6Z1 CBS2 CBS+CV3

(010) 1594.75 −2.99 −2.30 −0.32 +0.48 (020) 3155.85 −4.22 −2.38 −0.79 +1.16(030) 4666.73 −6.30 −3.24 −1.52 +2.05(040) 6134.01 −9.81 −5.54 −2.74 +3.20(050) 7542.44 −14.70 −9.19 −4.72 +4.82 (101) 7249.82 +12.51 +10.76 +9.32 −5.35 (201) 10613.35 +18.72 +16.46 +13.97 −7.47(301) 13830.94 +25.72 +22.81 +18.74 −8.97 (401) 13805.22 +32.56 +28.92 +23.06 −10.17(501) 19781.10 +40.72 +35.96 +28.68 −10.72σ[104] all 22.84 19.74 16.56 7.85

Ab initio calculations for water

1 MRCI calculation with Dunning’s aug-cc-pVnZ basis set2 Extrapolation to Complete Basis Set (CBS) limit3 Core—Valence (CV) correction

OL Polyansky, AG Csaszar, J Tennyson, P Barletta, SV Shirin, NF Zobov, DW Schwenke & PJ KnowlesScience, 299, 539 (2003)

Ab initio: vibrational errors

Ab initio + Adiabatic: vib. errors

Ab initio + adiabatic + relativistic

MVD1 Csaszar, Kain, Polyansky, Zobov and Tennyson, Chem. Phys. Lett., 293, 317 (1998).

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

Relativistic electronic potential effects in water

1 Gaunt correction: 1 electron approximation2 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)

2s, 2p

2p3/2

2p1/22s1/2

2s1/2

The hydrogen atom: n = 2 levels

Fine structureNon-relativistic

0.365 cm-1

2p1/2

0.035 cm-1

Lamb shift

2p3/2

Schrodinger Dirac QED

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

One-electron Lamb shift effects in water

P. Pyykko, K.G. Dyall, A.G. Csaszar, G. Tarczay, O.L. Polyansky and J. Tennyson, Phys. Rev. A, 63, 024502 (2001)

BO / cm−1 +BODC1 + Non-adiabatic

µv ≠ µ 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

Born-Oppenheimer corrections for water

1 Born-Oppenheimer diagonal correction using CASSCF wavefunction2 Non-adiabatic correction by scaling vibrational mass, µV3 Two parameter diagonal correction4 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, 58, 675 (2002).

Obs / cm−1 CBS+CV1 +relativity +QED +BODC2 PS3

(010) 1594.75 +0.48 −0.81 −0.75 −0.32 −2.79(020) 3155.85 +1.16 −1.57 −1.44 −0.56 −5.38(030) 4666.73 +2.05 −2.37 −2.17 −0.78 −0.73(040) 6134.01 +3.21 −3.30 −3.01 −1.06 −10.38(050) 7542.44 +4.82 −4.45 −4.03 −1.41 −12.90(101) 7249.82 −5.35 +1.70 +1.45 +0.60 −4.78(201) 10613.35 −7.47 +2.98 +2.58 +1.23 −6.96(301) 13830.94 −8.98 +4.59 +4.06 +2.05 −8.41(401) 13805.22 −10.17 +6.11 +5.49 +2.74 −9.47

σ[104] all 7.85 4.23 3.83 1.90 10.44

Ab initio calculations for water

1 Complete Basis Set (CBS) limit plus Core−Valence (CV) correction2 Born-Oppenheimer Diagonal Correction (BODC)3 Partridge & Schwenke, J Chem Phys, 106, 4618 (1997).

OL Polyansky, AG Csaszar, J Tennyson, P Barletta, SV Shirin, NF.Zobov, DW Schwenke & PJ KnowlesScience, 299, 539 (2003)

Sensitivity of vibrational band origins

~ − 3

+ 2

+ 1.5

+ 0.03+ 0.03

− 0.8

− 20

+ 30 b

H2S

+/− 1.5+ 5Adiabatic correction (BODC)

a+ 6 Breit correction

a+1.3QED

Contribution / cm-1Effect

H3+H2O

a+ 5Gaunt correction

− 0.5 − 4 Non-adiabatic correction

a− 0.8Darwin term (2e)

+/− 0.03− 19Relativistic correction (1e)

+/− 0.03+ 30 bBO convergence

a Unknown, assumed negligible

b. The future: explicit inclusion of r12 into the wavefunction

Why calculate VR spectra?• Test potential energy surfaces

construct potentials

• Quantum ``chaology''Classical dynamics of highly excited molecules is chaotic

• Predict assign spectralab, astronomy, etc

• Calculate transition intensitiesphysical data from observed spectra eg n, T,…..atmospheric studies, astrophysics, combustion ….

• Generate bulk data

partition functions à specific heats, opacitiesJANAF, astrophysics, etc

• Link with reaction dynamicseg HCN ↔ HNC

H3+ + hν → H2 + H+

Linelist and assignments• Linelist : theoretically calculated transitions including :

1- transition frequencies : Eupper - Elower

2- Intensities3- Eupper and Elower and quantum numbers

• Spectra : Measured set of transitions in a molecule at given T o

and p

• Assignment : Identify the quantum numbers of the lowerand upper levels.

What for ? Temperature dependencyPressure broadening

3

Vibrating – rotating molecules:Why is the spectrum of water so complicated?

• Three infrared active vibrational modes• Asymmetric top: 3 rotational degrees of freedom• H atoms leads to large rotational constants• H atoms give very anharmonic motion• Polyad structure of vibrations

(traditional methods of assignment fail)

So what is the problem?

Water is well studied (30,000+ lines in HITRAN)

But• Water spectra have huge dynamic range• Difficult to work with experimentally• Spectra very dense: baseline hard to characterise• Strong lines usually saturated (water-air spectra)• Line profiles important (water-air & water-water)• Weak lines can be significant (pure water spectra)• Line assignment difficult (Variational Methods)

M-Dwarf Stars

Barber & Tennyson computed BT2 linelist:All vibration-rotation levels up to 30,000 cm-1

Giving ~ 5 x 108 transitions

Oxygen rich, cool stars: T = 2000 – 4000 KSpectra dominated by molecular absorptionsH2O, TiO, CO most important

Water opacity

Similar lists available for H3

+, HCN, TiO, HeH+, C3?

• 50,000 processor hrs.

• Wavefunctions > 0.8 terabites

• 221,100 energy levels (all to J=50, E = 30,000 cm-1)14,889 experimentally known

• 506 million transitions (PS list has 308m) ~ 100,000 experimentally known

• → Partition function 99.9915% of Vidler & Tennyson’s value at 3,000K

New BT2 linelist

D.P.K. Banerjee, R.J. Barber, N.K. Ashok & J. Tennyson, Astrophys. J., 672, L141 (2005).

0 500 1000

LudwigHitranlinelist

Frequency (cm-1)

3.0

2.0

1.0

0.0Abs

orpt

ion

(cm

-1at

m-1

at S

TP)

Absorption by steam at T = 3000 K

JH Schryber, S Miller & J Tennyson, JQSRT, 53, 373 (1995)

The Sun: T = 5760 K

Sunspots Image from SOHO : 29 March 2001

Molecules on the Sun

T=5760KDiatomicsH2, CO, CH, OH,CN, etc

SunspotsT=3200KH2, H2O,CO, SiO

Sunspot, T ~ 3200 K Penumbra, T ~ 4000 K

Sunspot

lab

Sunspot: N-band spectrum

L Wallace, P Bernath et al, Science, 268, 1155 (1995)

Assigning a spectrum with 50 lines per cm-1

1. Make ‘trivial’ assignments(ones for which both upper and lower level known experimentally)

2. Unzip spectrum by intensity6 – 8 % absorption strong lines4 – 6 % absorption medium2 – 4 % absorption weak< 2 % absorption grass (but not noise)

3. Variational calculations using ab initio potentialPartridge & Schwenke, J. Chem. Phys., 106, 4618 (1997)+ adiabatic & non-adiabatic corrections for Born-Oppenheimer approximation

4. Follow branches using ab initio predictionsbranches are similar transitions defined by

J – Ka = na or J – Kc = nc, n constant

Only strong/medium lines assigned so far

OL Polyansky, NF Zobov, S Viti, J Tennyson, PF Bernath & L Wallace, Science, 277, 346 (1997).

Sunspot

lab

Assignm

entsSunspot: N-band spectrum

L-band & K-band spectra also assigned

Assignments using branches

Ab initio potentialLess accurate but extrapolate well

J

Erro

r / c

m-1

Determined potentialSpectroscopically

Variational calculations:

Accurate but extrapolate poorly

Polyad structure in water absorption spectrum

Long pathlength Fourier Transform spectrum recorded by R Schmeraul

R. Schermaul, R.C.M. Learner, J.W. Brault, A.A.D. Canas, O.L. Polyansky, D. Belmiloud, N.F. Zobov and J. TennysonJ. Molec. Spectrosc., 211, 169 (2002).

Weak lines

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

Weak water lines Very difficult to record

Only a few weak lines in HITRAN

Also Kitt Peak archive data Also spectra 8000 – 13500 cm−1

Water vapour spectrum: new assignments in the blue

Long pathlength FTSM Carleer et al,

J. Chem. Phys., 111, 2444 (1999)

Vibrational mode Previous worka This workb band originLocal 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

Water: Rotation-Vibration spectra in the near ultra violet

a C. Camy-Peyret et al, J. Mol. Spectrosc., 113, 208 (1985).b N.F. Zobov et al, J. Chem. Phys., 113, 1546 (2000).New CRDS results in this region from SPHERS collaboration

Intensity data compared to HITRAN-96by polyad for spectral region 8500 – 15800 cm-1

HITRAN underestimates intensity of strong lines!D Belmiloud et al, Geophys. Res. Lett., 27, 3703 (2000).

Numbers are ratio of total intensity to HITRAN

1.091.251.251.263ν+δ

1.04

1.04

1.31

Ab Initiocalculation

4ν

3ν

2ν+δ

Polyad

0.961.06

1.141.211.19

0.921.26

Correction Giver et al.

Spectral linefits

Integrated absorbance

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)

Frequency / cm-1

Water absorption by the atmosphere:correction of Giver et al (2000)

Frequency / cm-1

Water absorption by the atmosphere:Effect of weak water lines

Frequency / cm-1

Water absorption by the atmosphere:Effect of ESA-WVR linelist

Missing absorption due to water: estimates

Theory

Experiment

Radiative TransferModel

Atmosphericabsorption

• In the red and visible :

• Unobserved weak lines have a significant effect : ~ 3 Wm-2

Ø Estimated additional 2.5-3 % absorption in the near I.R/Red.

Ø Estimated additional 8-11 % absorption in the ‘Blue’ ?• Underestimate of strong lines even more important : ~ 8 Wm-2

Ø Estimated additional 8 % absorption in the near I.R/Red.

MSF spectra: line parameter retrieval using GOBLIN(R. Tolchenov, UCL)

residue from fit

Pure water vapour

Missing absorption due to water:Outstanding issues

• In the near infrared and red:

Ø Contributions due to H218O, H2

17O and HDO.

Ø Possible role of water dimer (H2O)2.

• In the blue and ultraviolet:

Ø Are H216O line intensities also underestimated?

Ø Contribution due to weak lines

Our strategy for a reliable, complete linelist

• Strong lines:water-air spectra, variable path-length

• Weak lines:water vapour spectra, longest path-length & integration times possible

• Isotopomers:Isotopically enhanced samples (Kitt Peak)

• Completeness/assignments:High quality variational calculations

IUPAC Task Group

Water assignments using variational calculations

• Long pathlength absoption (T = 296K) 9000 - 26000 cm-1

Fourier Transform and Cavity Ring Down

• Laboratory emisson spectra (T =1300 − 1800K) 400 – 6000 cm-1

New oxy-acetylene torch spectrum 400 – 13000 cm-1

• Absorption in sunspots (T = 3200 K)N band, L band, K band

10-12 µm 3 µm 2 µm

Ø 30000 new lines assigned

Dataset of ~15000 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).

The Future:

PDVR3D: DVR3D program for parallel computers,Eg Cray-T3E or IBM SP2

H2O• All J = 0 states to dissociation (> 1000 states)

20 minutes wallclock on 64 Cray T3E processors• All J > 0 up to dissociation. Scales as (J+1).Needs reliable potentials!

HY Mussa and J Tennyson, J. Chem. Phys., 109, 10885 (1998).