Vibrationrotation spectra from first principles

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 initio or
Spectroscopically 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 lt n H n
  gt /dc lt n dH/dc n gt
  gives
  
  d lt n V n gt /dci lt
  n fi (r1,r2,q) n gt
• 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
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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
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Polyad structure in water absorption spectrum
Long pathlength Fourier Transform spectrum
recorded by R Schmeraul
33
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)
34
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
35
Water vapour spectrum new assignments in the blue
Long pathlength FTS M Carleer et al, J. Chem.
Phys., 111, 2444 (1999)
36
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). b N.F. Zobov et al, J. Chem. Phys.,
113, 1546 (2000).
37
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).
38
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)
39
Water absorption by the atmospherecorrection of
Giver et al (2000)
Frequency / cm-1
40
Water absorption by the atmosphereEffect of
weak water lines
Frequency / cm-1
41
Water absorption by the atmosphereEffect of
ESA-WVR linelist
Frequency / cm-1
42
Missing absorption due to waterFirst 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.

43
Missing absorption due to waterOutstanding
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

44
Sensitivity of vibrational band origins
a Unknown, assumed negligible
45
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).
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