Infrared high resolution spectra of 16O3 .Two new
weak bands assigned : 32+33 and 42+43
A. Barbe, M.-R. De Backer-Barilly, Vl.G. Tyuterev
Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 6089,
Université de Reims, FRANCE
A. Campargue, D. Romanini, S. Kassi
Laboratoire de Spectrométrie Physique, UMR CNRS 5588,
Université Joseph Fourier, Grenoble, FRANCE
Ozone generation at 77 K : complete conversion O2 → O3
Fourier Transform
Spectrometer
Working in stepping mode, 3
meters path difference.
Recent experimental improvements:
Use of two detectors
The compact fibered CW-CRDS spectrometer (Grenoble)
1480-1687 nm (5800-7000 cm-1)
6nm/diode
40 diodes
Typical sensitivity 310-10 cm-1
Laser diode
Lambdameter
=f(T,I)
Optical isolator
threshold
Laser OFF
laser ON
-50
0
Photodiode
50
100
Coupler
AO
Modulator
Hamiltonian matrix
Vibrational diagonal block
1
1
1


H  E   A   B  C  J   B  C  J  B  C J   J   J J    J 
2
2
2


  J , J   2 J J  H J  H J J  H J  J   H  J   h J , J 
VV
VV
2
2
2
z
K
2
2
z
xy
 h J , J
KJ
where
2
2
z
xy
2
J
J
2
6
xy
K
 2h J
2
J
2
xy
A, B  AB  BA
4
xy
4
z
KJ
2
2
z
JK
2
K
2
z
JK
2
2
z
2
2
z
2
J
3
J
K
4
2
z
xy
J 
2
2
J J J
and
2
2
2
xy
x
y
Ro-vibrational extradiagonal blocks
H
VV '
Coriolis
 J  J   C  J  J  1 / 2    J  1 / 2 J 
 C J  J  1 / 2    J  1 / 2  J   C J  J  J   C J  J 
 C J  J  1 / 2    J  1 / 2  J   C J  J  J  1 / 2    J  1 / 2 J   ...
C
001



011
z

021
2
z

H
VV '
Anharm

201

211
3
z
3
2
z
3
031

z
2


003
3


2
z

z
z

 F  F J  F J  F  J  J   ...
2
000
020
1
i
where J  J  J

2
200
x
z
002
2
2


y
Assignments :
vibration : predictions from Vl. G. Tyuterev – keep the usual label v1 v2 v3.
rotation : use of ASSIGN program (Chichery A.) based on Ground State Combination
Differencies (GSCD) - J Ka Kc
calculation of energy levels, transitions, and intensities : GIP program. (S. A. Taskhun)
Line intensities
The linestrenghths are calculated using the following effective transition
moment operators :
'
For A-Type band : v 3  v 3 odd
( v1v 2 v 3 )( v1' v '2 v '3 ) ~

   12  , iJ  i , J  d 12  ,J
 d 7  x , J x , J z  i y , iJ y , J z  d 8  z , J 2xy 
z  d1z  d 2 z , J 2  d 3 z , J 2z  d 4
x
y
y
x
5
x
x , Jz
 i y , iJ y , J z  d 6 1 x , iJ y  i y , J x 
2
'
For B-Type band : v 3  v 3 even

 


 z  d1 x  d 2  x , J 2  d 3  x , J 2z  d 4 i y , J z  d 5  z , iJ y  d 6  z , J x , J z  d 7
( v1v 2 v 3 )( v1' v '2 v '3 ) ~
 d8


1
 x , J 2xy  i y , iJ x , J y
2
Where A, B  AB  BA and
d i  vv' d i



1
 x , J 2xy  i y , iJ x , J y 
2
Spectroscopic parameters of the (033) state (in cm-1)
Parameter
(033)
(132)
EVV
4991.358999(78)
5042.301(13)
A-(B+C)/2
3.1743889 (48)
(g)
(B+C)/2
0.39986321 (36)
(g)
(B-C)/2
0.02831028 (70)
(g)
DK
103
0.27889267 (83)
(g)
DJK
105
-0.28104(46)
(g)
DJ
106
0.41834 (36)
(g)
δJ
107
0.868(47)
(g)
HK
x106
0.10159 (38)
(g)
C132,034
 0.0004711 (98)
001
Statistics for the rovibrational transitions included in the fit for the (033) state
Vibrational state
(033)
EVV
4991.3
J max
33
Ka max
13
Number of transitions
299
Number of levels
222
rms (103 cm-1)
4.77
Upper state energies derived from 033.obs
v J Ka Kc
033 3 0 3
033 3 1 2
033 3 3 0
033 4 1 4
033 4 2 3
033 4 3 2
033 4 4 1
033 5 0 5
033 5 1 4
033 5 2 3
033 5 3 2
033 5 4 1
033 5 5 0
energy
error(mK) tra
4996.15825 0.770 2
4999.50259 0.000 1
5024.70684 0.000 1
5002.24563 1.050 2
5012.04908 0.360 2
5027.90421 1.765 2
5050.07658 0.000 1
5003.32734 0.000 1
5006.94951 1.080 2
5016.07448 0.000 1
5031.90622 1.620 2
5054.07879 0.620 2
5082.54358 0.000 1
freq.
4937.69584
4941.48068
4942.18638
4944.44900
4945.47904
4945.47900
4945.70400
4946.50300
OBSERVED and CALCULATED ENERGIES
v J Ka Kc
Eobs
Nb error o-c
--------------------------------------------------------------033 21 9 12 5431.5388
3
1.8
-4.0
033 34 2 33 5472.7990
1
1.2
033 21 11 10 5556.4170
1
-3.0
033 20 11 10 5539.6126
2
1.6
-3.1
033 2 1 2 4996.8485
2
1.2
1.1
033 20 13 8 5688.4314
1
-4.3
033 19 0 19 5139.6244
2
1.4
-2.3
033 19 2 17 5158.8338
2
1.5
0.4
033 31 5 26 5468.2616
1
2.5
033 3 1 2 4999.5026
1
1.8
Part of the line-list for the 31+33 band
Int.
vup J Ka Kc vlow J Ka Kc
Elow
0.133E-25 033 34 2 33 000 35 2 34 535.10314
0.103E-25 033 33 5 28 000 34 5 29 579.06128
0.165E-25 033 32 2 31 000 33 2 32 478.43898
0.184E-25 033 31 1 30 000 32 1 31 450.11768
0.146E-25 033 31 4 27 000 32 4 28 495.51739
0.161E-25 033 31 3 28 000 32 3 29 477.12347
0.127E-25 033 31 5 26 000 32 5 27 522.55763
0.201E-25 033 30 2 29 000 31 2 30 424.95173
31+33 : Obs. – Calc.
1.000
0.980
279268
3510349
P175
289278
P174
299288
3610359
P173
309298
P172
P186
0.985
319308
Transmission
0.990
P170
P171
3710369
0.995
31+33
0.975
1+43
CO2
0.970
4969.6
4969.8
4970
4970.2
CO2
4970.4
4970.6
Wavenumber (cm-1)
4970.8
4971
4971.2
4971.4
Spectroscopic parameters of the 044 vibrational state (in cm-1)
Parameter
(044)
EVV
6506.12800(11)
A-(B+C)/2
3.2109622(99)
(B+C)/2
0.39209216(25)
(B-C)/2
0.02782101(25)
DK
103
0.32159(25)
DJK
105
-0.1240(10)
DJ
106
0.60039(19)
δJ
106
0.13131(10)
δK
105
0.69839(16)
Statistics for the rovibrational transitions included in the fit for the (044) state
Vibrational state
(044)
EVV
6506.1
J max
49
Ka max
7
Number of transitions
304
Number of levels
149
rms (103 cm-1)
3.79
Integrated band intensities, Sv, in (cm/molecule at 296K) and Parameters
of the effective transition moment operator (in Debye).
42 +43 B-type (Sv =1.7310-25 cm/molecule)
Operator
Parameters
Value
Number of
transitions
(J max, Ka max)
rms
deviation
(%)
44, 5
X
z ,iJ y 
d1 (×105)
-0.1240(24)
d5 (×106)
0.33071(43)
84
The rms deviation applies to the quantity (Iobs-Icalc)/Iobs
31.0
42+43 : Obs. – Calc.
0.20
Absorption coefficient (10 -6 cm-1)
0.18
0.16
CO2
0.14
0.12
0.10
0.08
171180
0.06
0.04
Int.~5×10-28 cm/molecule
160171
244235
431420
0.02
0.00
6482.9
6483
6483.1
6483.2
6483.3
6483.4
Wavenumber (cm-1)
6483.5
6483.6
6483.7
Comparison between observed and predicted vibrational energies (in cm-1)
(033)
EVV
(044)
Obs (this work)
pred
Obs.-Calc.
Obs (this work)
pred
Obs.-Calc.
4991.359
4991..447
-0.088
6506.128
6508.152
-2.02
Check of the vibrational assignment to the 6506.128 cm-1
observed band
Observed
(044) pred
O-C (044)
(600) pred
O-C (600)
Ev
6506.128
6508.152
-2.02 cm-1
6500.188
+5.9 cm-1
(B-C)/2
0.0278
0.02847
-0.239 %
0.01418
51.0 %
(B+C)/2
0.39209
0.39253
-0.11 %
0.42008
-6.6%
A- (B+C)/2
3.2109
3.19330
0.55 %
0.42008
2.26%
A
3.603
3.5858
0.48 %
3 .5494
1.49 %
B
0.41991
0.42100
-0.25 %
0.43427
-3.41%
C
0.36427
0.36427
0.0 %
0.40590
-11.4 %
Summary of all the known energy levels of 16O3 derived from high
resolution observation and analysis
34 levels ( A1 symmetry)
0.000
700.909
1103.111
1399.284
1796.232
2057.907
2094.965
2201.133
2486.594
2726.128
2886.251
3083.698
3173.894
3289.912
3390.914
3739.327
3966.794
000
010
100
020
110
002
030
200
120
012
210
102
130
300
022
112
310
40 levels ( B1 symmetry)
4001.183
4141.196
4390.492
4632.595
4783.321
4921.987
5171.347
5540.339
5766.322
6048.496
6099.417
6155.100
6344.360
6366.074
6626.891
6749.344
6767.668
004
202
122
014
212
104
302
114
204
034
510
124
124
430
016
520
242
1042.057
1726.540
2110.829
2407.973
2785.191
3046.115
3086.197
3186.389
3455.748
3698.148
3849.786
4021.674
4121.996
4250.194
4346.439
4508.096
4658.670
4896.843
4918.791
4990.985
001
011
101
021
111
003
031
201
121
013
211
103
131
301
023
221
113
311
005
033
5077.184
5291.264
5307.739
5518.676
5697.719
5782.889
5920.061
5946.236
6063.602
6126.043
6197.822
6307.230
6355.496
6386.553
6567.851
6587.535
6721.701
6896.134
6980.691
6991.832
005
123
401
213
015
105
133
411
105
223
331
025
501
223
421
205
233
035
511
233
Conclusion
As the energy increases, the number of interacting levels becomes larger
and larger. Then a confident assignment accounting for interacting “Dark”
states is almost impossible without good predictions of their band centers
and rotational constants. The point is that these good predictions allow
the assignments of weaker and weaker bands (lines of a few 10-28
cm/molecule become possible). The observation of the 42 + 43 band is a
typical example.
The application of this point will be also demonstrated in the next talk.
O3 is then now one of the most studied molecule, where the energy levels
of 74 vibrational states are obtained up to 7500 cm-1, approaching the
dissociation limit.
The range of derived observed intensities is large: One transition of the 3
band is: 410-20 cm/molecule ,which has to be compared with the total
intensity derived in this work: Sv tot (42 + 43 ) =1.7310-25 cm/molecule
Sv tot (3 ) =1.4110-17 cm/molecule, leading to a ratio of 108 between 3
and 42+43 bands