Calculating the infrared spectra of hot astrophysical molecules

1
Calculating the infrared spectra of hot
astrophysical molecules
Jonathan Tennyson University College London
SELAC, May 2005
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Layers in a star the Sun
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Spectrum of a hot star black body-like
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Infra red spectrum of an M-dwarf star
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Cool stellar atmospheres dominated by molecular
absorption
Brown Dwarf
The molecular opacity problem
M-dwarf
l (mm)
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Cool stars T 2000 4000 K Thermodynamics
equilibrium, 3-body chemistry
C and O combine rapidly to form CO. M-Dwarfs
Oxygen rich, n(O) gt n(C) H2, H2O, TiO, ZrO, etc
also grains at lower T C-stars Carbon rich,
n(C) gt n(O) H2, CH4, HCN, C3, HCCH, CS,
etc S-Dwarfs n(O) n(C) Rare. H2, FeH,
MgH, no polyatomics Also (primordeal)
metal-free stars H, H2, He, H-, H3 only at low
T
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Also sub-stellar objects
CO less important Brown Dwarfs T 1500 K H2,
H2O, CH4 T-Dwarfs T 1000K methane
stars How common are these? Deuterium burning
test using HDO?
Burn D only No nuclear synthesis
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Modeling the spectra of cool stars

• Spectra very dense cannot get T from
  black-body fit.
• Synthetic spectra require huge databases
• gt 106 vibration-rotation transitions per
  triatomic molecule
• Sophisticated opacity sampling techniques.
• Partition functions also important
• Data distributed by R L Kururz (Harvard), see
• kurucz.harvard.edu

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Physics of molecular opacitiesClosed Shell
diatomics

• CO, H2, CS, etc
• Vibration-rotation transitions.
• Sparse 10,000 transitions
• Generally well characterized by lab data and/or
  theory
• (H2 transitions quadrupole only)

HeH
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Physics of molecular opacitiesOpen Shell
diatomics

• TiO, ZrO, FeH, etc
• Low-lying excited states.
• Electronic-vibration-rotation transitions
• Dense 10,000,000 transitions (?)
• TiO now well understood using mixture of
• lab data and theory

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Physics of molecular opacitiesPolyatomic
molecules

• H2O, HCN, H3, C3, CH4, HCCH, etc
• Vibration-rotation transitions
• Very dense 10,000,000 100,000,000
• Impossible to characterize in the lab
• Detailed theoretical calculations
• Computed opacities exist for H2O, HCN, H3

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Ab initio calculation of rotation-vibration spectr
a
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The DVR3D program suite triatomic
vibration-rotation spectra
J Tennyson, MA Kostin, P Barletta, GJ Harris OL
Polyansky, J Ramanlal NF Zobov Computer Phys.
Comm. 163, 85 (2004). www.tampa.phys.ucl.ac.uk/ftp
/vr/cpc03
Potential energy Surface,V(r1,r2,q)
Dipole function m(r1,r2,q)
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Potentials Ab initio or
Spectroscopically determined
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Molecule considered at high accuracy
H3 H2O H2S HCN/HNC HeH
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Partition functions are important
Model of cool, metal-free magnetic white dwarf
WD1247550 by Pierre Bergeron (Montreal)
Is the partition function of H3 correct?
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Partition functions are important
Model of WD1247550 using ab initio H3 partition
function of Neale Tennyson (1996)
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HCN opacity, Greg Harris

• High accuracy ab initio potential and dipole
  surfaces
• Simultaneous treatment of HCN and HNC
• Vibrational levels up to 18 000 cm-1
• Rotational levels up to J60
• Calculations used SG Origin 2000 machine
• 200,000,000 lines computed
• Took 16 months
• Partition function estimates suggest 93 recovery
  of opacity at 3000 K

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Ab initio vs. laboratory

• HNC bend fundamental
• (462.7 cm-1).
• Q and R branches visible.
• Slight displacement of vibrational band centre
• (2.5 cm-1).
• Good agreement between rotational spacing.
• Good agreement in Intensity distribution.
• Q branches of hot bands visible.

Burkholder et al., J. Mol. Spectrosc. 126, 72
(1987)
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GJ Harris, YV Pavlenko, HRA Jones J Tennyson,
MNRAS, 344, 1107 (2003).
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Importance of water spectra

• Astrophysics
• Third most abundant molecule in the Universe
• (after H2 CO)
• Atmospheres of cool stars
• Sunspots
• Water masers
• Ortho-para interchange timescales

• Other
• Models of the Earths atmosphere
• Major combustion product (remote detection of
  forest fires,
• gas turbine engines)
• Rocket exhaust gases H2 ½ O2 H2O (hot)
  
• Lab laser and maser spectra

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Molecules on the Sun
Sunspots Image from SOHO 29 March 2001
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Sunspot N-band spectrum
Sunspot
lab
L Wallace, P Bernath et al, Science, 268, 1155
(1995)
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Assigning a spectrum with 50 lines per cm-1

• Make trivial assignments
• (ones for which both upper and lower level
  known experimentally)
• 2. Unzip spectrum by intensity
• 6 8 absorption strong lines
• 4 6 absorption medium
• 2 4 absorption weak
• lt 2 absorption grass (but not noise)
• 3. Variational calculations using ab initio
  potential
• Partridge Schwenke, J. Chem. Phys., 106,
  4618 (1997)
• adiabatic non-adiabatic corrections for
  Born-Oppenheimer approximation
• 4. Follow branches using ab initio predictions
• branches 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).
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Sunspot N-band spectrum
Sunspot
Assignments
lab
L-band, K-band H-band spectra also
assigned Zobov et al, Astrophys. J., 489, L205
(1998) 520, 994 (2000) 577, 496 (2002).
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Variational calculations
Assignments using branches
Spectroscopically
Determined potential
Accurate but extrapolate poorly
Error / cm-1
Ab initio potential Less accurate but extrapolate
well
J
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Spectrum of M-dwarf star TVLM 513
HRA Jones, S Viti, S Miller, J Tennyson, F Allard
PH Hauschildt (1996)
Water opacities
Observed Ludwig Jorgensen Miller Tennyson
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Computed Water opacity

• Variational nuclear motion calculations
• High accuracy potential energy surface
• Ab initio dipole surface

Viti Tennyson computed VT2 linelist All
vibration-rotation levels up to 30,000
cm-1 Giving 7 x 108 transitions Similar study
by Partridge Schwenke (PS), NASA Ames New
study by Barber Tennyson (BT1/BT2)
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Spectroscopically determined water potentials
Important to treat vibrations and rotations
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Emission spectra of comet 153P/Ikeya-Zhang
(C/2002 C1)
Emission lines
Solar pumping
N. Dello Russo et al, Icarus, 168, 186 (2004)
Astrophys. J., 621, 537 (2005)
Rotational temperatures ortho/para ratios
Gives rotational temperatures
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Water in Mira
vr 92 km s-1
Cooler than sunspot, but what is T?
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Nova V838 Mon Exploded Feb 2002
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DPK Banerjee, R.J. Barber, N.K. Ashok J.
Tennyson, Astrophys. J. Lett (submitted).
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Water assignments using variational calculations

• Long pathlength absoption (T 296K) 9000 -
  27000 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, H band
  
• 10-12 mm 3 mm 2 mm 1.4 mm
• 30000 new lines assigned
• Dataset of 13500 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).
New lab torch spectra (T 3000 K) from Bernath.
100 000 lines.
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Theoretical Atomic and Molecular Physics and
Astrophysics
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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
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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

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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).
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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
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Ab initio calculations for water

• Obs / cm?1 5Z1
  6Z1 CBS2 CBSCV3
• (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
• 13805.22 32.56 28.92 23.06
  -10.17
• (501) 19781.10 40.72 35.96
  28.68 -10.72
• s104 all 22.84
  19.74 16.56 7.85

1 MRCI calculation with Dunnings aug-cc-pVnZ
basis set 2 Extrapolation to Complete Basis Set
(CBS) limit 3 CoreValence (CV) correction
OL Polyansky, AG Csaszar, J Tennyson, P Barletta,
SV Shirin, NF Zobov, DW Schwenke PJ
Knowles Science, 299, 539 (2003)
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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, 58,
663 (2002).
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Ab initio predictions of water levels

• Isotopomer N(levels) J(max) s / cm-1
• H216O 9426 20
  1.17
• H217O 669 12
  0.28
• H218O 2460 12
  0.65
• D216O 2807 12
  0.71
• HD16O 1976 12 0.47
• All water 17338 20 0.95

Rotational non-adiabatic effects very important
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Residual sources of error

• Basis set convergence of MRCI
• need extrapolated 7Z
• Full CI contributes 1 cm-1 at 25,000 cm-1 (?)
• Surface fitting 346 points computed,
  
• need 1000 points, reduce s by 0.2 cm-1
• Full inclusion of non-adiabatic effects
• up to 25,000 cm-1