J. Quant. Sptwrosc. Radiar.Transfer Vol. 48, No. 516, pp. 537466, 1992
Printed in GreatBritain
0022-4073/92 SS.00 + 0.00
Fkrmmon Press Ltd
ENERGY LEVELS, INTENSITIES, AND LINEWIDTHS OF
ATMOSPHERIC CARBON DIOXIDE BANDS
L. S. ROTHMAN,t$
R. L. HAwruNs,t R. B. WA~~~ON,$and R. R. GAMACHE~
TPhillips Laboratory, Geophysics Directorate, Hanscom AFB, MA 01731, gvisidyne, Inc., 10 Corporate
Place, Burlington, MA01803, and TUniversity of Massachusetts Lowell, tinter for Atmospheric
Research, 450 Aiken Street, Lowell, MA 01854, U.S.A.
(Received 9 July 1992)
Ahatra&-Spectroscopic constants are given for eight isotopic variants of carbon dioxide
which provide energy levels for transitions required for terrestrial atmospheric i.r. absorption.
A new tabulation is also furnished with bands considered for the latest HITRAN molecular
database. This list provides improved band intensities and Herman-Wallis coetRcients
generated from recent high-resolution measurements and theoretical calculations. Rotationally-dependent air- and self-broadened halfwidths are provided from a survey of recent
experiments.
INTRODUCTION
Carbon dioxide is one of the most important components of the HITRAN database. Although it
is considered a trace gas in the terrestrial atmosphere, its strong opacity in the infrared (i.r.) has
a major impact on the environment. Accurate knowledge of the spectroscopic properties of the
carbon dioxide molecule is necessary for understanding the greenhouse effect, industrial combustion processes, space and aircraft vehicle exhausts, and planetary atmospheres. It is a prime factor
in atmospheric remote sensing of temperature and constituent profiles. COz is often a contaminant
in spectra. For long-path atmospheric transmission problems it has in fact been necessary that eight
naturally-occurring isotopes be considered for the HITRAN database, the most of any molecular
species contained on the compilation.
Since the last publication of carbon dioxide energy-level and band parameters,’ significant
improvements have been made for the three absorption line parameters: the transition frequency,
intensity, and linewidth. The improvements in the line positions or transition frquencies have been
brought about primarily through the use of Direct Numerical Diagonalization (DND) calcu1ationP to extrapolate from observed vibration-rotation
transitions to transitions which have not
been measured, but are of possible significance in the atmosphere, and a refined, global method
of fitting the transitions. In addition, new observations by Benner et a1,4Esplin et al>’ and Blanquet
et al* have been added to the fit. High-vibrational levels in the 4.3 pm region observed by Baill~,~
but not immediately relevant to the atmospheric transmission requirement of HITRAN, have also
been added to the fit. As before, the goal of this effort has been to generate a self-consistent set
of spectroscopic constants from which to calculate the many line transitions on the database.
The greatest amelioration to the database has been in the intensities. This improvement has been
made possible by the use of new measurements by Johns,lO*il Dana et a1,‘2-‘sBenner et al4 as well
as calculations3 made with the DND technique. Herman-Wallis coefficients, where available, are
used to describe deviations from rigid-rotor behavior.
Pressure broadening of CO,, both by air and COz, was determined by fitting polynomials to a
number of recent measurements’2*‘5-‘8 and calculations.‘9
In the discussions that follow, we use the vibrational quantum notation as defined in Ref. 20.
$To whom all correspondenceshould be addressed.
537
538
L. S. ROTHMAN
et al
LINE
POSITIONS
The least -squares fitting procedure
Carbon dioxide line positions v were calculated from the upper and lower state rovibrational
energies:
v = E’(u ‘) J’) - E”(U”, J”)
(1)
where a single prime denotes the upper state, double primes the lower, E is the energy of the state,
v its vibrational mode, and J the rotational quantum number.
The energies, in turn, have been calculated using effective spectroscopic constants:
E(v, J) = G, + B,J(J + 1) - D,[J(J + l)]‘+ H,[(J(J -t l)]‘.
(2)
Wherever possible, the spectroscopic constants G, B, D, and H for a given vibrational state were
determined by weighted linear least-squares fitting of observed line positions involving that state.
This section describes the fitting procedure used.
For each isotopic species of carbon dioxide, for example r2Cr602(626 in the HITRAN short-hand
notation), spectroscopic constants for all vibrational levels were fit simultaneously. Conceptually,
this is a straightforward application of linear least-squares. However, the large amount of data
involved (almost 20,000 experimentally observed line positions for 626) and the large number of
free parameters (almost 500, again for 626) make the practical application less straightforward.
Least-squares fitting was performed using the Givens rotation algorithm.2’ The implementation
was based on a modification of the algorithm described by Gentleman.22 The Givens algorithm is
about 40% slower and proportionately more subject to accumulated roundoff error than more
common algorithms, but is particularly suited to large, sparse problems such as this one. It
processes the data one observation at a time, so that computer memory requirements are
independent of the number of observations. Also, the fact that only a small number of the
spectroscopic constants are involved in any one observation can be used to reduce the amount of
computation required, by properly ordering the observations and the constants. Thus the
sparseness of this particular problem can be used to improve the speed and roundoff characteristics
of the Givens algorithm.
The presence of roundoff error was examined by fitting the 626 data twice. In one fit, the bands
were ordered for maximum efficiency, in the other fit the data were only partially ordered, such
that twice as much computation was required. The resulting spectroscopic constants were printed
out to 10 significant digits and compared. Not a single digit differed between the two fits. This result
indicates that roundoff error was negligible, and that the implementation is more than adequate
for problems of this size.
Corrections to the data
Comparison to DND calculated line positions indicated that a number of lines in the
30001 t 01101 and 11112 c 01101 bands of the 636 isotope had been incorrectly assignedt3 due
to an avoided crossing between the 30001 level and 11112e sublevel. The lines originally assigned
to P27 and higher, and R25 and higher, of the 30001 t 0110 1 band were reassigned to the
11112e t 01101 subband, and vice-versa.
The Q-branch lines of the 22202 + 01101 band of the 626 isotope4 gave extremely large residuals
in the initial fit. It was found that reducing the J values assigned to these lines by 2 quanta (e.g.
QlS was reassigned to Q 13, etc.) gave residuals commensurate with those in the P- and
R-branches.
There appears to be a typographical error in the position of the P 14fline of the 12202 + 01101
band of the 628 isotope in the paper by Rinsland and Benner.” The value published there,
2055.60013 cm-‘, was replaced by the value published in Rinsland et al?’ 2055.62648 cm-‘.
The line positions measured by Guelachvili et a1,2a-2*and measurements by Esplin et al’-’ which
were calibrated against Guelachvili’s, were recalibrated against the rest of the observational
database. A calibration factor was applied to the affected measurements and varied to give the best
global fit. A value not significantly different from that suggested by Brown and Toth2’ was obtained
in this way.
539
Spectroscopic constants for isotopic variants of CO,
Levels without connection to the ground state
The observation-by-observation
nature of the Givens algorithm permits the fit to be easily
updated by adding new observations. This ability was used to address several problems in the data
used. In some of the isotopic species, there were bands in the database which had no connection
to the ground state. Therefore, only the band center, the difference between term values G, for the
upper and lower state, could be determined for these bands; absolute values for G, could not.
Values for the lower state G: were obtained from the literature and added as pseudo-observations,
effectively fixing the lower-level G: to its literature value, and obtaining the upper-level G: relative
to it. Levels treated in this way are denoted by a “C” in the comment field in Table 1.
Extrapolation in J and v
For many levels, observations do not extend to high enough rotational quantum number J to
determine H,. Extrapolation to values of J greater than the highest observed is inaccurate when
H is not known. The ability to extrapolate was tested by fitting observations of the 10001 + 00001,
01111 c 01101, and 00011 t 00001 bands of 626 over a restricted set of J values, and comparing
the fit both to the observed high-J line positions, and to DND calculated line positions up to
J = 180. (The highest laboratory-observed
J values are J = 108 for 10001, J = 140 for 00001,
J = 116 for 01111, J = 122 for 01101, and J = 141 for 00011. The test fits were performed using
only lines with J up to 20, or up to 30, 40, 50 etc.)
When the fit was restricted to lines of such low J that H could not be determined, as indicated
by the estimated standard deviation of H being larger than the retrieved value of H, the
extrapolated line positions were less accurate than DND calculated positions. But when lines of
sufficiently high J to determine H were used, the extrapolated line positions were as accurate as,
or more accurate than, DND calculated line positions. This typically required measurements to
J = 70 or larger.
Since it appeared that, for these well-measured levels, DND provides a better extrapolation than
the fit itself when H cannot be determined, an attempt was made to determine H for poorlymeasured levels by calculating the energy at J = 180 using DND constants, and using this DND
energy as a pseudo-observation. In most cases, this process caused the fit to the observed line
positions to be significantly worse. In these cases the DND energy was not used, and H was not
fit (effectively, it was fixed to zero). The levels where the single DND energy was retained to
determine H are denoted by a “t” in the comment field (last column) in Table 1. Note that the
pseudo-observation is an energy, not a line position, so that only the indicated level is directly
affected.
In addition to this use of DND energies to extrapolate measured levels with insufficiently high
J, DND spectroscopic constants were used for levels which have not been measured at all. These
pure DND levels are indicated by the symbol lXj in the last column.
BAND
New
INTENSITIES
AND
HERMAN-WALLIS
FACTORS
measurements
New measurements since the 1986 edition of HITRANM have improved the intensities of several
bands. Of particular significance is the band at 720.805 cm-‘. This major side band to the v2
fundamental has had its total band intensity altered several times throughout the history of
HITRAN. Recent measurements by Johns and Auwera,” which have been corroborated by others
(Dana,3’ Huet et a1,32and Varanasi and Chudamani33), have increased the intensity of this band
by 6% from the previous value. The band is one of the key channels for remote sensing experiments
proposed for satellite monitoring. The nearby band at 721.584 cm-’ for the 636 isotope has changed
even more. Previously it was based simply on the isotopic ratio related to the same transition of
the principal isotope (the 1973 calculated value).” We calculated a 40% reduction via DND, which
was later confirmed by the observations of Johns and Auwera.” Another band in the long
wavelength region used for remote sensing is at 791.447 cm-‘. New measurements”.‘* show a 15%
decrease from the previous band intensity in HITRAN and also, as with the bands discussed above,
yield values for the Herman-Wallis factors.
540
L. S. R~THMANet al
Other regions of the spectrum have also had new measurements: the laser bands,15 the 2.7 pm
doublets,‘O the 319,overtone band,35 and two bands in the Fermi tetrad%*” around 2.2pm. The
observations of Refs. 35-37 have had a major impact on the dipole-moment determination used
in DND, and hence on many of the band intensities in Table 2.
Table 1. Spectroscopic constants for CO, levels considered for the HITRAN database.
3owl
311018
31101f
mm?
0220le
D2201 f
10001
111020
11102f
D33Ole
Q3301 f
1llOle
1llOlf
DO011
20003
12202e
122025
20002
044Ole
044Olf
122Ole
12201f
20001
Olllle
Ollllf
211030
21103f
13302e
133021
21102e
21102f
055018
05501 f
13301e
13301f
211010
21101f
10012
02211e
02211f
10011
30004
22203e
222031
14402e
14402f
30003
222020
O.OOWO
667.37996
I
1265.40634
1335.13161
I
1366.16432
1932.47013
I
2003.24615
I
2076.65566
1
2349.14291
2546.36707
2565.02213
1
2671.14315
2671.71459
I
2760.72473
"
2797.13591
3004.01227
I
3161.46399
II
3240.62276
I
3339.35602
"
3340.52762
I
3442.21534
"
3500.67217
I
3612.64060
3659.27229
I
3714.76193
37Q2.6a36
3622.01177
"
3698.31366
I
22202f
3942.64327
4007.Bl460
I
Q6601e
D86olf
4009.67664
I
4664.274&I<
0.3QO2166Q
0.3QO63QOO
0.39125465
oaO46223
0.39166676
0.39166676
0.3QO16666
0.3QO74498
0.39169032
0.39237634
0.39237634
0.39040962
0.3Q1333Bo
0.36714135
0.3B110912
0.39194333
0.39194333
0.36956202
0.39306lQ3
0.39306193
0.39154766
0.39154766
0.3BO60563
0.3675@50
0.366lBO27
0.39102314
0.3Q235111
0.39265624
0.39265624
0.3QOO3563
0.39117476
0.39377734
0.39377734
0.39221531
0.3Q221531
0.39038703
0.39171524
0.36750292
OS663604
0.38883804
0.36706302
0.39176146
0.3Q235OOQ
0.39235009
0.36336242
0.39336242
0.36958904
0.3Ql436B6
0.39143698
0.38446573
OS446573
1.33336
1.35295
1.36066
1.57098
1.37452
1.36022
1.14919
1.49447
1.56357
1.4OoOB
1.4OOOB
1.25653
1.21099
1.32998
1.61217
1.3BQ54
1.53364
1.34939
1.42346
1.42346
1.41703
1.26224
0.97386
1.34766
1.35761
1.63934
1.75698
1.50006
1.50006
1.37969
1.38936
1.44701
1.44701
1.36530
1.36530
1.17465
1.06365
1.57367
1.36021
1.37396
1.14163
2.06599
1.36150
1.70097
1.52154
1.52164
1.67149
1.43977
1.41453
1.47606
1.47606
OsQQll
0.077
O.OQB
0.149
2.173
-3.605
0.146
1.646
1.005
1.163
-1.562
-1.179
0.906
0.451
ODD6
5.043
-6.769
1.302
5.394
-1.195
-1.195
-5.QBl
1.013
4.277
0.149
0.172
2.216
1.633
-1.665
-0.727
2.000
2.792
-1.062
-1.062
-2.730
-1.065
2.641
-0.001
1.981
-3.407
0.173
1.630
0.
0.
0.
-0966
-0966
0.
-6.919
1901
0.
0.
2.327
140
1lB
122
106
110
111
106
103
104
101
100
109
104
141
92
98
97
QO
96
96
98
95
92
116
113
B3
66
69
62
79
64
65
65
91
92
63
62
105
106
106
107
46
46
47
60
60
54
62
71
77
77
w22
I
12
12
I
9I
9
12
"
7
I
13
I
5
6
4
I
7
4
I
6
I
6
6
I
3
I
4
"
6
"
2
I
5
I
5
I
5
3
I
5
1
1
I
9t
2
I
9z
1
2
I
2
Ai
[continued.
. .]
Spectroscopic constants for isotopic variants of CO,
Table l-continued
rc
ITk
<
V
144olf
!22Ole
?2201f
SO001
11112e
11112f
133110
>331lf
111110
Illllf
311040
31104f
233Q3e
233031
15!502e
1!5502f
311030
31103f
30021
233020
233021
377010
D7701 f
311020
31102f
155010
15501f
La013
122120
12212f
233Ole
23301f
311010
31101f
044110
044llf
20012
12211s
12211f
20011
322038
322031
011218
01121f
21113e
21113f
40002
13312e
13312f
05511e
055llf
u
I
1197.36118
I
1225.ow61
1247.70488
"
t314.91373
"
13Qo.62656
I
4416.149
"
4467.1164
I
6557.59598
I
4591.11673
I
4873.32546
4676.79054
I
4879.15606
I
4753.45330
I
4601.36463
I
4653.62341
4687.98501
I
48QO.OQ6
I
4938.3535
I
4970.92029
I
4Q77.63500
5061.77018
.
5099.66050
5197.1473
5245.2605
I
5315.71327
I
5475.07444
1
5475.56500
5531.30325
I
5627.3314
I
,=.764QO
).3Q287278
j.39159424
MQ15Q424
L3QOQ8326
NW76212
M8670505
MsQ37642
Mm37642
L38736478
Ml6823509
K3Q136003
).3Q310013
mQ3O3155
MQ3O2753
MQ405725
3.3Q4o5725
3.36QQ26Ql
xiQ121157
M64m6O5
mQ21Q216
3.3Q21Q216
mQ513421
3.39513421
3.36Q71170
3.39119284
D.39352184
mQ352184
D.38819761
3.386Q4150
D.386Q4150
D.3Q2182QO
DS218200
D.3QO12318
0.39217818
D.3QOl1400
0.39011400
D.366533QQ
0.36652520
0.36052520
0.38749948
0.39014077
0.39157517
0.39152343
0.38454736
0.36512822
0.38815515
0.38943597
0.3QOoQ3w
0.38971557
0.38971557
0.39065398
0.3QO64848
0.3670f311
1.36161
I.62725
I.18580
).67819
1.48514
1.56314
1.36853
1.36653
1.24083
l.2OQ6O
I.772
Is6104
I.59639
1.57380
1.54628
I.59626
1.55056
1.42980
1.32645
1.45716
1.45716
1.45354
1.46354
l.z?212
1.12884
1.39491
1.39491
1.61675
1.31111
1.42134
1.61000
1.61000
0.26294
0.94746
1.4062Q
1.40629
1.36836
1.37447
1.26483
0.98452
2.01648
1.5%76
1.57437
1.34194
1.35306
1.61
1.75365
0.6Q5OO
1.46991
1.48991
1.42634
1.40609
1.31657
-3239
0.
0.
-5.057
4.360
1.266
-1.349
-1.005
0.849
0.362
0.
3.149
-2.004
-1.749
-0.947
-0.947
4.011
0.
0.066
-3.684
-0.098
0.
0.
4.413
-0202
-9.509
-9.509
5.612
0.
0.
0.
0.
-34.432
-2.130
-0.675
-0.875
9.598
-4.565
1.179
3.801
10.152
-2.747
3.022
0.
0.
0.
1.223
0.
-1.531
-0.653
0.103
-0.759
76
60
65
52
66
97
86
89
84
91
0
0
0
.
60
60
51
24
98
45
46
62
62
43
0
59
59
85
61
44
0
.
86
86
75
67
66
79
0
0
I
85
Q2
0
57
0
72
79
r
?r
.
3
.
1
4
.
t
2
I
4
I
1
0
0
I
1
I
1
"
4
1
I
1
.
1
0
1
.
t
I
4
1
.
*
0
I
*r
0
I
q
q
*9t
1
I
6
2
.
4
0
0
I
3
I
1
a
II
rd.
L. S. ROTHMANet al
542
Table I-conrinued
0,
5730.80511
I
0.38Q24791
5789.57598
0.38740648
I
0.3886205Q
591521219
0.38452%8
0.38560887
5968.51212
I
0.3858Osw
0.383Q3wl
Bof6.6QOO6
6075.Q8035
0.38880584
6103.8%
0.38QM235
I
0.38939768
0.3QO46QOo
6178.7013
I
omO44888
6178.8922
0.38Q28314
I
0.3Q158614
6227.91708
0.3867lOQ7
0.3Q179878
8284.0882
I
0.39179882
8288.5325
0.38861273
I
0.38846264
8347.85148
0.3864S4%
0.3QOO4831
6387.8675
I
0.39270574
8398.1110
0.39002331
I
0.39027095
8474.534
0.388@364
I
0.38884M4
0.387973%
8503.OaOQO
65a7.85879
0.38481838
I
0.38572340
8801.71318
0.38837502
I
0.38637502
8879.70588
0.38431555
It
0.38513542
8688.177
0.38%4452
I
OJQO25487
8736.7841
0.39014120
"
OJIQO14728
(E883.55646 o.v4
I
0.38839872
0.38Q23044
6944.7345
I
0.38928798
0.38089334
8972.57734
0.38874989
7023.67530
I
0.38811818
0.39101708
7064.8805
I
0.39100320
7133.824
0.38528576
7154.8273
0.38872910
I
0.38841145
7186.0220
0.38570429
I
1.32457
1.32457
1.13098
1.08749
1.57608
1.34912
1.36906
1.13905
2.12821
2.%
1.58
1.54147
1.49278
0.045QO
O.Qmel
1.71434
1.83005
1.82880
1.58610
1.38597
OS8129
0.15822
OS4065
1.44739
2.47711
1.488
1.25
0.71684
1.47088
1.86881
1.383Ql
1.38391
1.23015
1.191%
1.75
1.91
1.s7846
1.58667
1.41194
1.51749
1.24837
1.42639
1.32399
1.20482
1.15475
1.72862
1.69113
1.72
1.78931
0.79298
1.11545
1.23539
o,oo
=T=
@T!l?-=
0.
0.
2.383
0.819
1.810
-2.429
0.2%
2.312
15255
0.
0.
0.232
-1.553
41.247
-1.508
Q.Q88
11.037
11.037
2.030
1.837
5.809
23.424
-0.748
2.971
88.381
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
-l.Q%
-0.534
0.
0.
-6.244
0.776
0.128
5.539
1.717
-8288
-8.088
0.
12.418
-25.940
-10.058
-4.972
0.
66
87
58
59
76
78
77
70
59
0
I
1
”
t
t
;I
2
(1
t
2
3
2
0
I
1
"
0
"
0
I
0
I
83
0
1)
1
0
I
0
I
0
"
83
0
I
1
0
"
0
I
0
.
0
I
1
57
63
62
88
80
53
58
0
I
1
1
I
c
c
II
II
I
a
I
I
a
II
I
II
I
!
0
I
44
41
0
"
91
48
39
0
II
0
0
I
0
h
0
8
"II
5
1
t
"t
0
m
I
1:
0
e
I
e
0
m
*
1;
[continued.
. .]
543
Spectroscopicconstantsfor isotopicvariantsof CO,
Table
l-continued
.
?259.7463
1263.978
m?.6?1?
I)
1338.1573
I
7377.6240
7460.527
7505.2335
.
7593.695
7602.51399
I
7615.5901
I
7694.3684
I
7734.446
7743.6727
I
7697.57300
I
7QOl.47QOO
I
7920.836
6055.9391
I
8081.8348
I
6192.55067
6232.88409
I
8250.632
I
8293.95124
6425.005
I
6676.716
6803270
I
8831.482
8863.67909
I
6944.140
"
6965.225
9137.799
9246.93393
9366.QQ4
9419.1160
I(
9516.969
9589.6190
+==
M6357498
u8Q584m
b.39002484
M6QQ36Ql
KM553755
I.38548534
M64353QQ
3.36734776
x36866573
I.38860454
M6556301
L38150413
M6206Q16
I.36938488
I.39204422
).3666?442
X38626130
3.386QQ702
%38550602
m664Q?32
9.388Q6500
x36698500
3.36400800
3.36512800
D.38854QQQ
LB.38488062
D.36552049
D.36714174
0.38888667
D.38155873
El6257946
0.38257948
0.386251OQ
0.38782425
0.360605?2
0.38682258
0.38851738
0.36618320
0.3816564Q
0.36274510
0.38514656
0.36337322
0.38337322
0.38126452
0.36203190
0.365Q2420
0.38776745
0.37792307
0.36238062
0.36318877
0.38315966
0.38049550
0.38250452
1.56666
!.51
1.37512
I.79615
I A9566
1.23075
I.86925
I .Qs
I.56933
1.54600
1.176
1.33736
1.35007
3.31976
D.Q2?33
2.?6Q63
1.18879
1.151
1.64452
1.67100
1.33000
II.93900
1.31000
1.36000
0.55
2.66Q24
1.06522
1.6Q616
1.83021
1.56724
1.34291
1.36419
1.387
1.346
1.12750
0.999
0.94
2.30
1.47
1.55
0.964
1.37267
1.37267
1.219
1.17
0.746
0.66
1.32018
1.65
1.57657
1.64309
1.389
143905
----
10.090
0.
10.224
0.740
5.769
0.512
-1.851
0.
-0.746
2.740
0.
0.
0.
19.669
-0.309
56.658
2.613
0.
-1.003
-1.201
0.
0.
0.
0.
0.
90.587
1.473
4.381
4.973
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.414
3.887
0.
5.351
B
I
e=
0
0
0
I
0
I
0
0
0
(1
0
66
59
0
I
0
I
0
0
11
0
I
0
"
0
0
II
0
1
63
55
56
0
"
65
0
I
0
0
I
0
68
69
0
n
0
0
70
a
a
.
a
-
C
L. S. R-N
et al
Table I-continwd
-z-
-0,
r
3
”
9891.353
Qw4.45178
I
99872OQQ
I)
10145.509
I
102Q7.083
I
10444.8Q201
10482.42758
I
10548.61303
11100.85249
I
114Q8A3720
12101.57111
I
12707.18932
I
13313.28158
I
13721.13825
1431aQ2343
I
14QO7.22350
I
15Q21.08782
18601.55838
I
17082.5Q233
I
18OQ8.35889
18854.57385
I
20247.03830
2Q803.01874
0
22373.14880
24474.84885
2855221158
0.38124472
0.37848333
Q.37QO132Q
0.38247wO
0.38381013
0.38085571
0.38218714
0.38185513
0.38241578
0.3785Q441
0.37955413
0.37956413
0.37787751
0.38037285
0.38037285
0.3748&w
0.37542465
0.37598060
0.37853145
0.37853145
0.37737817
0.37737817
0.3717918Q
0.37238910
0.37291185
0.37351138
0.37351188
0.3887312Q
0.38QMB85
OXQ86558
0.3704Q8OQ
0.3704QwQ
0.38587447
0.38832883
0.38582577
0.38282179
0.383304Q5
0.38378Q41
0.36957388
0.m
0.35349217
13@c
O.OOOOO
848.47803
"
1285.82778
129728328
"
1370.08211
1898.53799
I
1948.34998
I
0.3QO23754
0.39081133
0.39124542
0.3QOQ15Q2
0.39181380
0.39181380
0.38971788
0.3QOQ8282
0.3Q202155
0.3Q2287Q2
1.333Q3
1.34681
1.552Ql
1.70432
3.288
1.087
1.012
1.25Q
1.58824
1.33148
1.35930
1.12894
1.38122
1.38122
1.31742
1.32896
1.34414
1.32105
1.35995
1.35855
1.35858
1.31530
1.32523
1.34178
1.31002
1.34Q58
1.31300
1.32074
1.33874
1.2W8Q
1.34484
1am3
1.31705
1.33538
1.30878
1.30812
1.3303Q
1.30854
1.3OlQ8
1.2Q824
0
89
55
0
0.
0.
0.
-0.734
-0.310
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0
1
2
I
0
"
1
I
0
I
1
I
0
I
82
-
58
87
84
51
88
77
88
57
57
85
48
45
80
57
54
52
55
79
54
55
51
48
85
51
54
81
50
53
80
55
34
1
2
I
1
2
"
2
2
I
2
I
1
I
2
2
I
2
"
2
2
I
1
I
2
2
I
2
1
I
-
2
2
1
(838)
1.33348
1.35489
1.38377
1.582QO
1.32714
1.38798
1.20251
1.4QO53
1.56117
[conrhcd.
. .]
Speotroscopic constants for isotopic variants of CO2
Table 1-contimred
V
!7m=
1llOlf
QOOll
20003
122020
12202f
D44010
D4401f
s,
0,
-
,.300;oal
I
2283.48711
2507.5252954
2531.87814
1
2595.759
I
2845.08788
2700.28444
I
Olllle
Ollllf
211030
21103f
13302e
13302f
055010
05501 f
211026
21102f
1330le
133Olf
211018
2110lf
10012
02211e
02211f
10011
30001
11112e
11112f
03311e
033llf
111110
lllllf
00021
20013
122120
12212f
044110
044llf
20012
122lle
122llf
20011
0112le
0112lf
211138
21113f
13312e
133121
0551le
-
2750.59644
2920.23782
II
3127.3533
I
3189.4418
I
3245.4464
"
3289.70119
"
3381.3QQ8Q
I
3433.77073
I
3527.73747
3557.31234
I
3832.91028
4145.78887
414723205
I
4184.70585
1
4287.89801
I
4543.54803
4748.0858Q
4770.97523
.
4832.437
I
4887.39069
4938.83470
I
4991.35308
5188.59893
I
5357.00437
I
339725181
1
5470.4704
UQO91848
I.38727344
MQl88590
I.39211394
mQ2113Q4
I.39295427
3.39295427
M8Q88Q83
MQll814Q
1.3911814Q
KMQ72586
3.38788022
xM82Q411
3.39137580
3.39289978
3.39278884
3.3927828Q
3.39382204
3.39382238
x38QQQ405
D.39113417
3.39185731
D.39185731
D.38873278
3.39094098
KM803847
D.38889956
II.38889955
D.38872378
0.39050355
0.38801702
lx38Q14170
D.38940348
0.38Q40348
0.38713084
0.38794439
0.38431127
0.38884257
0.38925882
0.38925882
0.3QOlOQQ2
0.3QOlOQQ2
0.38883530
0.38828219
0.38828219
0.38870813
0.38474991
0.38534498
0.38882235
0.39009954
0.38QQl811
0.38991811
0.39073350
0,
izzr
l.23848
1.32Ql8
1.84888
1.15471
1.48752
I.41097
1.41097
1.3Qsl
1.32808
1.28874
Q.QQ291
1.34923
1.35938
1.82320
1.77443
1.48814
1.43718
l&Q80
1.4308Q
1.44488
1.32892
1.37858
1.37858
1.20884
l.OQ208
1.57718
1.32077
1.38420
1.19863
2.41245
1.30883
1.54833
1.37487
1.37487
1.28083
1.23448
1.32487
1.83742
1.23021
1.53244
1.39303
1.3Q303
1.39009
la083
1.28742
095417
1.34385
1.35457
1.54217
1.70134
1.31004
1.31004
l.wOO7
-
r
T
=mr 2%
97
1.829
0.143
4.501
0.
0.
0.
0.
0.
-1207
-0.174
0.
0.555
0.280
1.517
2.154
-2.030
-2.089
-1.089
-1.028
2.879
-0.QQ2
0.
0.
0.
0.
2.349
0.
0.
2.111
0.
0.
0.
-0.884
0.221
0.841
2.096
0.081
4.324
-7.835
1.401
0.
0.
0.
0.
0.
0.
0.809
0.073
0.
0.
0.
0.
-10054
A
100
123
QO
30
37
95
Q5
82
88
8Q
54
112
115
0
"
0
I
0
I
53
42
45
34
41
32
105
105
104
103
50
72
97
Q4
97
Q8
QQ
104
91
59
56
Q6
96
81
87
80
87
99
86
44
47
42
43
a
-
1
1L
[continued.
. .]
L. S. ROTHMAN
et al
546
Table l-continued
I
211120
21112f
133110
133llf
2111189
21111f
10022
022210
02221 f
10021
30014
222138
22213f
30013
222120
22212f
30012
222lle
22211f
30011
111220
11122f
311149
31114f
31113e
31113f
00031
31112e
31112f
31111e
3llllf
0113le
0113lf
40013
40012
10032
02231e
02231 f
10031
00041
011410
0114lf
00051
0115le
0115lf
00061
01161s
0116lf
00071
0117le
01171f
00061
01161e
5519.92411
"
uJ6706726
x96621673
U36QQ2176
5688.02625
I
K36QO2176
5662.25617
3.36666742
"
3.36798327
5766.16045
3.36615797
5793.99179
3.36578539
I
M6576539
5672.55126
D.36372777
3.36983672
5951.604
D.36997049
5970.9898
I
D.36988827
6119.623
0.36759266
0.36664751
6155.5076
I
0.38850487
0.36565643
6241.972
6326.0756
D.3664OOW
I
0.36607563
0.36702QOO
6363.624
0.36533315
6374.5313
I
0.36626970
0.36QO4363
6552.925
I
0.3QOQ637Q
0.36734610
6736.698
"
0.36667533
6760.21036
0.36135150
8892.1160
0.36704604
I
0.36773646
7046.031
0.36663504
I
0.36623442
73Q356QQ2
0.36162OQ4
I
0.36239897
7461.570
0.36638893
7600.127
0.36567749
7981.166
0.36227763
6007.33146
0.36267276
I
0.36287276
8089.026
0.38073941
6993.50726
0.3763Q366
9695.24601
0.37889274
I
0.37945451
1163.47756
0.37543675
1773.60746
0.37598832
I
0.37661304
3350.16635
0.37246573
3926.72146
0.37304266
I
0.37357533
5493.62510
0.36953621
6060.64231
0.37012259
"
0.37064065
17613.91274 0.3666QOO2
y16Q.43152_ 0.3672@407
0,
m
1.29484
1.33067
1.32031
1.32031
1.16398
1.12698
1.56121
1.31992
1.36236
1.16687
2.349
1.24177
1.66403
1.639
1.3Q602
1.41634
1.102
2.31461
l.WlQ6
0.666
1.41979
1.52616
1.522
2.035
1.52
1.366
1.32266
3.43070
1.25359
o.QQ2
O&Q3
1.34166
1.366Q3
1.446
0.633
1.566
1.31665
1.37511
1.228
1.32Q32
1.33727
1.35369
1.31656
1.32679
1.34949
1.31145
1.32516
1.34956
1.30664
1.32507
1.34755
1.30579
1.31692
T
!37r
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
-9.500
0.552
0.
-2.620
1.576
0.
46.501
-0.337
0.
-2.106
0.422
0.
0.
0.
0.
0.282
23.463
3.495
0.
0.
0.630
0.556
0.
0.
0.
0.
0.
0.
0.465
0.922
0.763
0.620
0.
0.
0.
0.
0.
0.
0.
0.
0.
r
=F
50
47
52
53
52
47
36
46
49
42
0
0
I
1
"
1
2
"
1
1
0
"
0
0
"
0
0
0
"
0
0
0
1)
0
0
I
0
I
73
0
I
0
I
-
1
"
46
53
0
0
0
37
44
0
56
55
64
57
54
63
56
63
62
59
64
53
56
47
s
q
m
18
”
1
”
1
*
1
1
w
2
0
”
1
*
2
a
1
18
1
1
I
n
m
$
q
q
0:
q
m
8
p1
8
9
t
m
q
01
31
t
t
*Q
Q
119
2t
2t
"t
2t
2
11
2
2
n
2
2
I
2
s-
[continued. .]
Spectroscopic constants for isotopic variants of CO2
541
Table I-conhwed
MlQle
311911
MOXl
mOY1
30021
20255.15758
"
21785.24778
23838.45190
25884.79949
oa429083
0.38478554
0.38070904
0.35777449
0.35484531
NO01
311010
31101f
10002
D22010
z201 f
10001
11102e
11102f
D33Ols
03301 f
1llOle
1llOlf
DO011
20003
122020
12202f
20002
044010
D4401f
12201e
12201f
20001
011110
Ollllf
211030
21103f
13302e
13302f
211028
21102f
13301s
133Olf
21101e
PllOlf
10012
02211e
02211f
10011
30003
30002
11112e
11112f
033118
03311 f
111110
O.OOOOO
882.37335
.
0.38818450
0.38880192
0.38915324
0.38812143
0.38958418
0.38958418
0.38851237
0.38852010
0.38931323
0.37023432
0.37028432
0.38882927
0.38950958
0.38528875
0.38849295
0.389859
0.389859
0.38774382
0.37091415
0.37091415
0.38986999
0.38Q88QW
0.38904215
0.38573112
0.38828757
0.38883303
0.38072232
0.370371
0.370371
0.38814783
0.38917925
0.370274
0.370274
0.388759
0.389187
0.38530734
0.38870707
0.38870707
0.38557351
0.387404
0.38823159
0.38571894
0.38849734
0.38743345
0.38743345
0.38575789
‘wwo
1259.42520
1325.141
I
1385.84343
1901.738%
I
1988.328
I
2049.33885
I
2332.11231
2500.75995
2549.449
I
2814.24775
2851.931
"
2728.24134
I
2757.17770
2982.11105
I
3127.35412
I
32OO.lQ2
I
3281.01892
I
3405.082
I
3454.011
I
3571.14018
3832.524
"
3875.13289
3858.858
3987.595
4201.15072
1
4283.373
I
4348.18588
1.31480
1.38082
1.30087
1.29583
1.29229
0.
0.
0.
0.
0.
44
30
48
57
58
(828)
1.18701
1.20878
1.20882
1.38812
1.24872
1.23158
1.W208
1.32318
1.38848
1.29798
1.29795
1.11901
1.08182
1.18424
1.58393
1.30
1.34
l.OW84
1.29018
1.29018
1.32197
1.13708
0.88719
1.20288
1.20389
1.45042
1.54834
1.34
1.34
1.19318
1.18942
1.24
1.24
1.M
1.12
1.37493
1.23511
1.22499
1.01195
1.25
0.984
1.32213
1.37302
1.29394
1.29394
1.11080
-0.015
0.188
-0285
1.819
-3.814
0.803
0.983
1.578
0.443
-0.510
0.517
0.388
0.427
0.014
3.438
0.
0.
3.583
-0.578
-0.578
0.
0.
0.
0.217
-0298
1.588
1.883
0.
0.
0.
0.
0.
0.
0.
0.
1.813
-3.705
0.444
0.808
0.
0.
2.243
0.553
0.
0.
h 1003
119
113
111
103
100
98
100
75
92
97
0
92
99
118
83
0
I
8
3
I
1
"
3
I
48
46
0
I
2
I
AZ
2-t
2
4
1
0
I
1
1
I
102
99
99
99
0
0
74
91
98
0
2
5
3
I
84
98
98
49
44
35
114
110
45
43
0
.
0
I
c
1
I
3
ct
1
2
I
1
I
0
I
:
0
I
0
(1
2
1
I
C
C
3
0
0
2
I
1
I
C
C
=2
[conrinued.
..]
L. S. ROTHMAN
et al
Table I-con&ued
a,*
T
469960157
479125978
4835.559
.
0.38239125
0.38573@52
0.3888QQl8
0.3868OQ?8
0.38484197
-88008
0.38311032
4Q34.680
I
0.388llQ32
5012.815
0.3858163Q
I
0.36881630
5042.58248
0.33813133
52n.15210
0.3%288lQQ
I
os338427
5408.070
0.38589919
"
0.388QQ18Q
0.38521505
5558.588
I
0.36831024
5727.047
0.365Q54
I
0.387160
5858.028
0.3825OOQ8
5915234
0.363842
I
0.383842
5Q5Q.966
0.m
5993.588
0.38835464
0.38161882
8127.783
8254.5Q4
0.38628589
8429.178
0.38883281
osQ4Q7Q7
w2.lQ672
8762.658
0.385047
I
0.388233
8Q27.845
0.385297
I
0.388814
7347.52735
0.35QQQ435
I
0.38050264
8120.109
osQ70328
8220.384
osQ58221
918023221
0.35680734
1413.84Q29
0.35371885
osQ83374
3822.4Q542
0.31795170
5808.825Q4
0.34507337
7986.70358
D102.lQQl4
0.342lQ8QO
!2213.38382 0.333933580
Tm1.57723
0.14472
0.18875
1.07388
1.28169
1.28109
1.22188
1.13812
0.85461
l.lQQ23
1.20185
1.347
1.5Q2
1.238
1.233
O.QQ
1.03
1.385
1.23
1.22
1.018
1.817
1.407
0.8646
0.3227
1.17897
1.20
1.27
1.07
1.02
1.19695
1.19191
1.398
1.004
1.17712
1.17250
1.17083
1.18843
1.18689
1.16180
1.17709
0.080
0.
0.
0.
0.
0.
0.
,20242
8.871
-1.027
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
ig
a
93
80
32
32
54
95
Q5
53
54
51
51
60
0
"
2
1
1
I
0
I
1
I
0
(1
0
I
2
1
I
1
1
1
2
"
1
I
1
0
"
1
1
1
1
1
2
0
1
0
"
50
39
0
0
58
48
52
53
52
37
36
1
I
-
1
1
2
2
2
2
2
2
1
'%Pf
[continued.
Spectroscopic constants for isotopic variants of CO,
549
Table l--Continued
,
I
V
=:
0,
iYszF= I
111010
lllOlf
DO011
2062.09885
I
2340.01370
252424512
2566.646
I
122020
122021
20002
122010
12201f
20001
Dlllle
Ollllf
10012
02211e
02211f
10011
111128
11112f
llllle
lllllf
00021
20013
20012
20011
21112e
21112f
30013
30012
00031
264124036
2743.465
I
2775.55765
2QQ2.310
I
3591251
3644.990
I
3693.346
4223.434
I
4366.612
.
4655204
4621.515
4939.351
5066.930
5593.645
1
6175.954
6298.116
6946.606
4
-
O.OOOOO
643.329
I
1244SOO23
1266.982
(I
134227778
2005.44617
I
2265.97126
2566.16210
2897.709
I
3490.39555
3529.769
"
3567.54964
4506.746
4692.179
4614.570
4925.013
-
T
0.380725 1.32
0.37894151
0.37984267
0.37563150
0.37920541
0.360210
0.360210
0.37604734
0.360019
0.360019
0.37935305
0.376102
0.376684
0.375612
0.377079
0.377079
0.375745
0.376157
0.377014
0.375973
0.378829
0.37285080
0.3763Q562
0.375116
0.376263
0.375625
0.376756
0.374Q6224
0.37531350
0.369871
'b'%
00001
OllOle
OllOlf
10002
022018
02201 f
10001
111Ole
1llOlf
00011
20002
Olllle
Ollllf
10012
02211e
0221lf
10011
00021
20013
20012
20011
3
-L
1.16611
1.13166
1.26053
1.66266
1.35
1.43
1.20449
1.37
1.21
1.46367
1.23
1.23
1.46
1.30
1.28
1.07
1.39
1.45
1.18
1.14
1.25
1.716
1.21
0.91
1.23
1.22
1.512
0.666
1.24
T
T=-=
zr - =
=G
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
50
31
41
39
0
I
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
102
94
101
64
66
77
63
33
36
101
37
Q5
102
63
65
76
82
0
0
0
0
45
0
"
31
0
I
0
0
I
0
0
I
0
I
x
0
0
0
;18
9
9
A
'oow
0.36616116
0.36656153
0.36911244
0.36653201
0.36949264
0.36Q4Q264
0.36602125
0.36625410
0.36908204
0.36539121
0.36757742
0.36560015
0.36633437
0.36562920
0.36674444
0.36674444
0.36518Q60
0.36260620
0.36651099
0.364815
0.365556
1.16498
1.20496
1.20134
1.36123
1222940
1.22800
1.01052
1.07427
1.00379
1.18167
1.31998
1.20125
1.19855
1.36376
1.22423
1.21644
1.00666
1.205
1.643
1.12
0.66
-
-
-
c
/
C
c
C
0’
-
=
[continued.
. .]
550
L. S. ROTHMAN
et al
Table l-continued
00001
01101~
OllOlf
10902
022010
02201 f
10001
Do011
Olllle
Ollllf
10012
02211e
02211f
10911
00001
OllOle
OllOlf
10002
022010
02201 f
10001
00011
011110
Ollllf
10012
022110
02211f
10011
00021
00031
040000
645.744
.
1255.330
1291.827
I
1355.117
2274.09940
2909.197
I
3503.376
3542.825
I
3808.559
0.00000
357.331
I
1230.32420
1315.094
I
1347.09295
2314.04834
2sQ.131
I
3525.20346
3804.953
I
3639.OQ4QO
4603.69909
m63.97331
0.37631700
0.378981
0.37QeOO
0.379142
0.379989
0.379988
0.373233
0.37574440
0.376152
0.376734
0.379353
0.377129
1.24220
1.22
1.23
1.43
1.25
1.30
1.11
1.23940
1.27
1.27
1.43
1.24
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.377129
0.375380
lzcl0
1.29
1.11
0.
0.
0.34QQl727
0.34723371
0.34772525
0.34952340
0.34812573
0.34912573
0.34740293
0.344OQO46
0.34433039
0.34500968
0.34335314
0.34543473
0.34543473
0.34465129
0.34136563
0.33@4346
"0'4
80
T
0
(I
1
-
:(Q29)
1.05353
1.07024
1.07Q9Q
1.16834
1.15233
1.09342
0.91732
1.0511s
1.O3QQ5
1.07486
1.17367
1.14019
1.09974
0.9lOQQ
1.0477s
1.04595
0.042
0.
0.
o.ge5
0.
0.
-0.015
0.048
0.
0.
1.135
0.
0.
-0.090
0.
0.
1uI
111
122
99
84
101
99
127
110
121
97
93
100
97
76
05
3
-
1
1
1
1
1
1
2
1
1
3
1
1
3
4
1
0 c/28)
The notation in the first column is described in Ref. 20 with X = 10, Y = 11, and Z = 12
for the very high vibrational levels of Ref. 9. The units are cm-‘; D, should be
multiplied by IO-’ and H, by IO-“. The sixth column, J_, is the higheat observed
J for the level, or sublevel in the case of d-doubled bands. The seventh column, 0,
indicates the number of different bands in which this level was observed. The
characters in the comments column, $, are interpreted as folows: a = level observed
in Raman spectroscopy (Refs. 86.89); t = a single DND energy at J = 180 was used
to help determine H,; 9 = observed in Venus spectra (Ref. 39); q = DND constants
are given, no observations were available; * = a perturbed level; C = constraint
applied to force lower level of G: in fit to a literature value.*J
Models used
We assume that the transition moment squared I R I2 can be separated into a rotationless dipole
moment squared, I R, I’, a rotational line strength or Hiinl-London factor L(J, d), where G is the
angular momentum associated with the bending mode, and a Herman-Wallis factor F(J), i.e.
IR(2=(R,~2L(J,t’)F(J).
(3)
The total internal partition sum Q(T) can be approximated by the product of a vibrational part
QV(T) and a rotational part Qa( T),
Q(T) =gj Q~(T)QR(TX
(4)
where gj is the state-independent nuclear spin factor, and depends on the isotopic species.
551
Spectroscopic constants for isotopic variants of CO2
Table 2. Intensity parameters for CO, bands on the HITRAN database.
Is0
471.5112
479.8980
508.1863
510.3208
526.4759
535.8935
542.2202
544.2858
557.7860
561.1210
564.9089
568.9082
573.6826
576.5960
578.6313
579.1417
581.3891
581.7760
585.3282
586.8501
594.2873
596.6752
596.4419
597.0518
697.3385
599.0230
599.2747
601.5712
603.1872
607.5550
607.5575
607.9745
608.8285
609.5860
610.9915
611.2204
615.6969
617.3497
618.0283
619.8238
630.7103
633.0969
634.8641
635.1401
636.7508
637.7635
640.5478
642.3118
643.3290
643.6530
644.4065
644.6333
645.1047
645.7440
646.0830
647.0618
647.7121
648.4780
648.7852
649.0887
649.4090
649.6874
2OOO3
13302
12202
21103
11102
Ill02
21102
11102
14402
12202
20002
13302
13302
11102
21102
20002
22203
12202
12202
11102
20002
21103
21103
looo2
11102
2OOO3
11102
looo2
30003
20003
looo2
20002
10012
10002
20003
30004
20003
10002
loo02
21103
11102
21103
11112
12202
01111
13302
22203
11102
01101
02201
11102
21102
23303
01101
02201
11102
12202
01101
02201
03301
04401
05501
11101
12201
11101
20002
loool
loool
-2oool
1WOl
05601
03301
11101
04401
04401
02201
12201
11101
13302
03301
03301
02201
11101
12202
12202
01101
02201
11102
02201
01101
21102
11102
01101
11101
01111
01101
11102
21103
11102
01101
01101
2OOO3
10002
20003
10012
11102
OWll
12202
21103
10002
OooOl
01101
looo2
20002
22203
OooOl
01101
10002
11102
ooool
01101
02201
03301
04401
326
926
526
326
536
328
526
626
626
828
528
826
536
628
526
627
526
626
636
527
526
636
526
628
626
628
536
638
626
627
627
636
626
637
636
626
626
636
626
636
636
636
626
636
636
636
626
628
638
638
627
636
626
637
637
626
628
636
636
636
636
636
p2
0.0115
0.00145
0.0609
0.00470
0.0139
0.0207
o.walo
3.279
0.00302
0.00765
0.00326
0.0807
0.00147
0.193
0.0415
O.OOO72
0.0109
2.16
0.0365
0.0439
0.994
o.oo457
0.280
4.66
56.18
0.0270
0.920
0.055
0.00544
0.0052
1.17
0.0204
0.0190
0.0106
0.111
0.0259
7.36
24.04
1567.5
0.00932
2.84
0.665
0.00278
0.211
0.0127
0.0132
0.045 1
0.950
3.57
0.3
0.15
0.00353
0.00265
0.642
0.055
230.
0.0737
878.3
72.2
4.58
0.258
0.0136
0.00049
0.00098
O.WlO7
0.00063
0.00084
0.00077
0.00096
o.oooa
0.00087
0.00085
0.0009
o.ooo91
0.00094
o.ooo93
O.Wll
0.
0.00101
O.OOO96
0.0010
0.
0.00104
0.00123
0.00117
o.oooa5
0.00095
0.00062
O.Wl13
0.
0.00103
0.
0.
O.WlO2
0.00083
0.
0.00078
0.0008
0.00087
O.Wll4
0.000959
o.oooa7
0.00099
0.00097
o.oooa9
0.00144
0.00094
0.0013
0.~148
o.wo91
0.
0.
0.
0.00113
0.00131
0.
0.
0.001127
O.Wlll
0.00077
0.00126
0.00122
0.00128
0.00135
1
0.898
0.57
0.547
1.54
i .a3
.1.09
.2.37
0.
.0.632
0.468
0.827
0.598
0.551
0.46
0.379
0.
.0.602
0.554
0.483
0.
.o.a74
.3.77
-2.14
a.69
0.
.0.094
-1.93
0.
-0.612
0.
0.
-0.466
-0.368
0.
1.66
1.36
0.468
0.
0.
0.864
0.166
0.196
-0.25
-2.67
-0.073
-0.41
-2.51
-0.22
0.
0.
0.
-0.078
-0.378
0.
0.
0.
-0.259
0.
-0.707
-0.111
-o.o05
0.093
0.
0.
0.
0.
0.
0.
0.
5.7
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
X:
Oo:ae
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
.3.13
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
::
::
-3.58
0.
0.
0.
0.
0.
0.
L. S. ROTHMANet al
552
Table 2-continued
‘0
v’
If*
049.9649
12202
11102
627
652.5520
154.8694
166.2600
tj56.6006
t155.6414
t557.3310
t157.6911
12202
01111
02211
13302
03311
01101
14402
t157.7532
02201
169.2816
15602
11102
00011
01111
12202
02211
OOOOI
13302
01101
14402
626
626
626
626
626
828
626
628
626
13301
01101
12201
00001
12201
11101
t
t
t
t
t
IS0
a,
.
0.0118
16.5
0.898
0.073s
0.966
0.00454
0.343
0.0510
0.0277
0.00263
0.
0.00132
0.00092
0.00108
0.00124
0.00107
0.
0.00129
0.
0.00136
a,
82
0.
-1.03
-0.077
0.112
-0.151
0.086
0.
-0.018
0.
0.096
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
b2
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
R&S
M-r
3
3
3
3
3
3
3
[continued
553
Spectroscopic constants for isotopic variants of CO,
_..,.
1 aole
733.3474
741.7243
748.1330
746.5233
754.3333
755.1458
757.4766
761.0793
765.6407
767.2917
770.5008
771.2656
781.7408
769.8120
789.9136
790.9869
791.4476
803.7264
626.2546
829.5290
857.1932
664.6650
683.1446
898.5476
910.6378
913.4250
315.6600
917.6461
927.1564
941.6976
355.6673
356.5435
960.3506
363.6862
365.6345
366.2663
1017.6693
1023.6999
1043.6387
1057.3651
1060.4847
1063.7346
1064.4737
1066.2409
1067.7271
1071.5421
072.6871
074.2502
078.4966
080.3741
233.3636
244.6002
253.4252
272.2666
342.2776
365.6434
376.0275
'386.9655
646.3324
1680.987 1
683.2001
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696.6360
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21101
11101
12201
20002
21102
22201
12201
30003
13301
22202
13301
11101
14401
11101
11101
21102
11101
12201
12201
21101
13301
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01111
02211
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00011
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10011
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00031
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10002
10002
loo01
loo01
loo01
11101
21103
2OOO3
12202
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11102
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10001
10011
10001
10002
11102
20002
10022
10012
10002
20003
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loo02
11102
10002
12202
10012
11102
01101
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01101
02201
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326
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0.136
63.4
0.0025
0.0194
0.120
0.00481
2.45
0.00435
o.oo115
0.00526
0.0951
0.131
0.00365
0.01
0.0199
0.0357
7.65
0.00329
0.151
0.00633
0.00527
0.042
0.00599
0.0146
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0.080
0.00071
0.00990
0.414
0.0138
0.
0.00015
6.13
0.0046
0.
0.018
0.054
0.00605
0.0158
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0.0002
9.15
0.0318
0.00307
0.0064
0.757
0.036
0.0305
0.
0.00434
0.0223
0.00267
0.320
0.0152
0.00625
0.359
0.0221
0.0342
0.00120
0.01597
0.00160
0.00711
0.0175
0.00096
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0.
O.Ooo87
O.OOO96
0.00092
0.00107
0.ooo84
0.00074
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0.00073
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0.662
0.126
0.203
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0.629
0.025
0.07
0.035
0.749
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0.709
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1.17
0.233
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1.33
1.33
0.835
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0.925
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0.664
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1.52
4.34
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14.11
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3
3
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3
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0.
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71
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8
16
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63
83
63
63
63
03
63
63
72
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0.
64
(I4
84
::6
-
64
554
L. S. ROTHMANet al
Table 2-continued
“0
1901.7370
1905.4911
1916.6931
1917.6422
1932.4701
1951.1717
1996.5698
2003.2462
2003.7632
2004.2245
2005.4462
2023.8734
2037.0933
2049.3388
2051.7864
2053.9477
2062.0987
2063.7086
2064.1365
2065.8680
2075.4444
2076.8659
2093.3448
2094.6044
2102.1184
2107.0838
2110.6265
2112.4878
2119.0225
2120.5053
2129.7559
2131.8047
2136.5075
2148.2407
2157.6763
2165.5406
2167.9430
2170.8490
2180.6991
2162.4803
2194.1150
2205.2967
2215.2638
2224.6565
2224.9910
2225.0240
2227.8102
3229.6611
2230.2229
2236.6624
2236.6764
2236.5703
2239.2971
2240.5362
2240.7666
2242.3228
2242.8071
2245.2719
2245.4953
2248.3669
2248.3610
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11102
13302
11102
12202
11102
21102
20002
03301
2ooo2
21102
11101
21102
11101
11101
12201
21102
11101
21101
13301
12201
22202
11101
12201
20001
20001
13301
20001
21101
14401
22201
20001
30002
21101
30001
10012
21101
21101
11112
20012
20013
22201
10012
21101
10012
01131
05611
13312
21113
21112
00031
04411
12211
12212
20013
20011
20012
02211
10011
10012
03311
01121
11111
1 1 1 12
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gg
ooool
02201
OooOl
01101
OOOOI
loo01
01101
Ooool
01101
02201
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loo02
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ooool
01101
10002
0ooo1
loo01
02201
01101
11102
00001
01101
01101
01101
02201
01101
loo01
03301
11101
01101
11102
02201
11101
1Oool
02201
10002
11101
20001
2OOO2
03301
loo01
looo2
IOOOI
01121
05601
13302
21103
21102
00021
04401
12201
12202
2OOO3
2oool
2ooo2
02iOl
loo01
loo02
03301
01111
11101
628
626
627
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626
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636
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b.01956
0.00990
o.oo329
0.1979
3.425
0.00768
O.oo289
0.
0.01711
o.oo219
0.ooo78
o.ooo99
0.4584
0.1431
0.0461
0.0849
0.0268
0.00297
O.OO610
0.0166
0.0103
41.56
4.01
o.oo92
0.0217
0.289
O.oQ18
0.1700
0.0183
0.0119
2.132
0.0050
0.0022
0.0077
0.00788
0.0920
0.0009
0.0426
0.0012
0.0028
0.0037
0.00517
0.0331
1.19
0.
0.00254
0.00366
0.00447
0.00198
o.oooo1
0.0603
0.0364
0.0818
0.0459
0.0136
0.0229
0.149
0.0665
0.0816
1.43
0.0250
0.897
1.81
-0.0611
-0.0711
-0.0637
-0.067
-0.06044
-0.0469
-0.0483
-0.0413
-0.06703
-0.0279
-0.0366
-0.060
-0.0417
-0.0334
-0.0436
-0.0404
-0.0369
-0.0273
-0.0325
-0.0327
-0.0377
-0.03772
-0.03638
-0.0305
-0.0482
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82
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0.
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64
64
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5.6
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5.55
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0.
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0.021
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24
24
64
64
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64
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
67
61,67
67
61.67
67
67
67
67
67
67
67
67
67
61.67
67
67
67
67
67
61.67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
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3
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0.
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3
3
3
66
3
3
68
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66
66
66
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66
66
555
Spectroscopic constants for isotopic variants of CO,
Table 2-contimed
I80
!250.7980
!253.0460
!253.4420
!254.3798
!260.0491
!260.0809
!261.9097
t281.9859
!262.4530
i262.8481
L265.2792
1265.9713
t271.7599
1274.0884
2274.3720
1274.4217
1275.8424
1277.1728
2277.2812
2277.3385
2277.9842
2278.3874
2280.8180
2281.6742
2282.7286
2283.2960
2283.4871
2283.5786
2284.3738
2285.3738
2288.7994
2286.8007
2286.8036
2287.1097
2288.3898
2289.0771
2289.5689
2289.6508
2289.9038
2290.2539
2290.4988
2290.6123
2290.6805
2290.9719
2293.4088
2293.6104
2294.8793
2295.0411
2295.0453
2296.8471
2299.2137
2299.2398
2299.2519
2299.4138
2301.0534
2301.7998
2301.9081
2302.3714
2302.5246
2302.9628
2305.2663
2306.6919
2306.7409
12211
10012
10011
31111
32211
30021
10012
33331
31111
10011
30031
DO011
31111
00011
02231
06611
14411
22211
10031
10032
30011
14412
22212
22213
04411
30014
00011
30012
12211
30013
03321
01131
05511
12212
13311
11121
02211
00021
21111
11122
20013
20012
13312
10011
21112
21113
10012
01121
03311
11111
04411
02221
00031
11112
12211
01111
10021
10022
20011
12212
20013
20012
11112
02201
10002
10001
01101
02201
00011
10002
03321
01101
10001
00021
00001
01101
00001
02221
08601
14401
22201
10021
10022
30001
14402
22202
22203
04401
30004
00001
30002
12201
30003
03311
01121
05501
12202
13301
11111
02201
00011
21101
11112
20003
20002
13302
10001
21102
21103
10002
01111
03301
11101
04401
02211
00021
11102
12201
01101
10011
10012
20001
12202
20003
20002
11102
63;637
637
638
638
638
636
626
637
636
828
838
636
837
626
626
626
626
826
626
626
628
626
826
628
826
836
628
828
628
826
826
628
628
826
826
828
828
626
626
628
628
626
828
626
626
828
628
628
828
626
826
826
628
626
828
628
826
626
626
626
826
627
-
a,
0.0264
0.0146
0.0098
3.48
33.7
0.279
19.5
0.
0.628
11.6
0.
38.8
771.6
7.15
0.
0.00599
0.00339
0.00231
0.
0.
0.00100
0.0102
0.00584
0.0147
0.0178
0.00843
9286.
0.00216
0.0121
0.00394
0.00273
0.00002
0.156
0.0290
0.0931
0.00185
0.0127
0.00009
0.089
0.00375
0.0181
0.0103
0.252
0.00487
0.151
0.333
0.00796
0.00720
0.452
0.330
4.06
0.0666
0.00037
0.679
2.58
0.31
0.0250
0.0414
1.07
8.13
3.84
1.98
0.116
0.
0.
0.
0.
0.00013
0.00015
~0.00014
0.
0.
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0.
0.
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0.
0.
O.00024
~0.00011
~0.00012
0.
0.
O.00009
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~0.00012
-0.00010
~0.00010
0.00012
-0.00013
~0.00012
-0.00011
mIOo13
-0.00012
0.
-0.00011
0.
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-0.00014
0.
0.
-0.00012
-0.00015
-0.00012
-0.00013
-0.00011
0.
-0.00011
0.
0.
-0.00013
-0.00011
-0.00012
-0.00011
-0.00013
0.
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-0.00012
0.
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-0.00014
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0.00005
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L
b
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.012
0.007
0.005
0.
0.
0.017
0.
0.
0.
0.
0.
0.827
0.152
.0.106
0.
0.
0.043
0.89
.0.034
0.01
0.017
0.033
0.
0.031
0.008
0.1
0.016
0.
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0.
-0.028
-0.001
0.
0.
-0.05
-0.082
-0.019
-0.047
0.002
0.
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0.
0.
0.005
0.019
0.018
0.006
0.014
0.
-0.027
-0.004
0.
0.028
-0.006
0.029
0.243
-0.02
-0.058
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
ll6f-S
I
I
L
b
IO
B
68
53.9
0.68
63
28
63
0
63
63.9
68
28
I
I
L
B
62
62
1
3
3
3
3
3
IO
3
3
3
3
9
3
3
3
30
@
3
3
3
3
3
3
3
3
3
3
3
L
3
3
3
3
3
3
3
3
70
70
46
45.28
28
70
46
55
62
45.62
40
111
[continued. . .1
L. S. ROTWANet al
556
Table 2-continued
v’
!307.3832
!307.3693
!309.2693
!311.6676
!311.7010
!311.7150
!313.7726
!314.0483
!315.1470
L315.2348
L317.3165
i316.9644
t319.7377
!322.4360
!324.1406
L324.1626
t326.5976
t327.4325
t327.6609
Z332.1123
t336.6324
2340.0137
2349.1429
2367.0624
2415.7075
2426.5174
2429.3736
2429.4679
2456.1564
2464.9606
2500.7600
2524.2461
2566.1821
2614.2477
2616.6436
2641.2404
2757.1777
2775.5577
2791.6377
3125.3044
3154.6316
3161.4640
3275.1633
3261.0169
3269.7012
3305.7064
3339.3560
3340.5345
3341.6569
3365.2691
3396.6949
3396.2166
3460.9018
3460.4684
3466.4391
3473.7120
3462.2379
3462.6933
3482.6307
3490.3956
3496.1413
3497.2866
3496.7540
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23
23
23
23
23
23
23
23
23
Spectroscopicconstants
for isotopic variants of CO,
557
Table 2-continued
a,
I50
3500.6721
3504.3331
3504.9067
3506.7130
3506.3760
3509.2272
3511.4177
3517.3266
3516.6639
3524.2004
3526.2035
3527.6133
3527.7375
3527.6076
3526.0571
3529.9612
3531.0346
3533.9465
3536.7774
3539.0167
3542.6043
3543.0949
3649.2284
3550.7156
3552.6534
3556.9090
3556.7739
3557.7167
3556.7049
3563.3235
3566.0693
3566.2151
3571.1402
3560.3249
3567.5496
3569.0641
3569.6507
3591.2510
3608.5690
3612.8408
3621.2910
3621.5629
3623.3862
3625.1648
3632.9103
3638.0646
3639.2199
3641.5714
3641.6762
3645.4349
3656.8291
3659.2723
3667.0644
3667.5471
3675.1327
3675.6934
3676.7083
3676.7390
3677.7082
3679.5500
3682.0925
3683.8125
3684.3193
21101
21113
14412
31114
10012
21112
12212
20012
22213
31113
10012
30014
10012
22212
13312
22201
20013
11122
11112
20012
21113
40002
20013
30012
12212
21112
30013
30001
11112
20012
10022
20013
10012
11112
10011
10021
20012
10012
10011
10012
20011
20012
21112
21111
10011
10011
11111
12211
13311
20012
21112
02211
20012
10021
10011
11121
30012
20011
21111
30013
31113
11111
31112
00001
11102
04401
21103
00001
11101
02201
10001
12202
21102
00001
20003
00001
12201
03301
01101
10002
01111
01101
10001
11102
11102
10002
20001
02201
11101
20002
01101
01101
10001
00011
10002
00001
01101
00001
00011
10001
00001
00001
00001
10001
10002
11102
11101
00001
00001
01101
02201
03301
10002
11102
00001
10002
00011
00001
01111
20002
10001
11101
20003
21103
01101
21102
626
628
626
626
637
628
628
636
626
626
828
626
636
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636
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636
636
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0.124
0.0162
0.0417
0.00899
0.0771
0.00499
0.144
0.128
0.120
0.00378
0.0588
0.0900
56.1
0.0323
1.09
0.0113
0.185
0.0163
3.81
0.0775
2.83
0.
0.0224
0.0167
28.6
0.969
0.0537
0.00536
0.668
0.0135
0.197
30.7
52.5
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0.703
0.00582
16.1
8.41
0.126
9861.
0.413
0.422
0.0381
0.0330
190.
0.0392
15.6
0.657
0.0279
0.146
0.0120
0.
0.0333
0.349
47.3
0.0290
0.0740
0.106
0.00898
0.0797
0.00705
4.17
0.00565
0.128
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0.00003
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15.71
0.763
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0.429
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0.361
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1.51
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0.731
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1.19
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0.695
0.988
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1.23
1.23
0.781
0.354
0.
0.
0.
0.229
1.38
0.598
1.16
23.05
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0.
1.81
1.52
1.06
1.57
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0.641
0.
0.
1.57
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-0.331
-0.223
-0.69
-0.684
0.
-0.516
-0.551
-0.553
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0.
0.
-1.12
-1.32
-0.707
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-0.365
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0.
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56
23
68
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58
65
58
65
68
68
23
23
68
68
23
23
23
23
23
58
23
23
23
68
[continued.
. .]
558
L. S. ROTHMAN et al
Table
2-continued
90
1667.4743
1692.4267
1692.9025
1693.3460
l700.2948
1702.0629
1703.1568
1703.5104
1704.1117
1705.9450
1711.4762
1712.4120
1713.7201
1713.8093
1714.7819
1723.2486
1724.1327
1725.5253
1726.3964
1726.6466
1727.3590
1799.4844
1814.2522
1856.6580
1858.1058
1980.5817
$987.5950
1005.9455
1416.1490
1591.1167
1614.7788
1639.5016
1655.2040
1673.7365
1685.7762
1687.7961
t692.1790
1708.5263
$722.6495
t733.5180
1735.6110
1743.6967
1748.0656
1753.4534
4755.7069
4768.5544
4784.6810
4786.7006
4790.5720
4791.2598
4807.6945
4608.1851
4814.5700
4821.5150
4839.7328
4853.6234
4871.4461
4887.3907
4887.9850
4896.1927
4904.8601
4910.6054
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15511
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12211
13311
30012
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30003
21111
11121
30002
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31104
31103
11121
30021
30021
22213
30014
30014
20013
21113
32214
23313
40015
21113
20013
31102
31114
22213
20023
31113
30014
20013
21113
40002
20012
20013
30013
20013
21112
20012
12212
21112
20012
20022
02201
10002
10001
00001
11102
01101
21101
12202
13302
20001
10001
13301
11101
12201
00001
01101
05501
10002
04401
02201
03301
20003
10002
00001
11102
02201
00001
01101
00001
00001
01101
00001
00001
02201
10002
10001
00001
01101
12202
03301
20003
01101
00001
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11102
02201
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11101
10002
00001
01101
01101
00001
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10001
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i28
526
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E
0.175
36.5
0.0279
10.2
2.93
0.771
0.00318
0.120
0.00489
0.0439
29.7
0.00327
2.30
0.0870
15223.
1199.
0.00292
0.00761
0.0746
48.1
1.90
0.00211
0.624
0.0144
0.0199
0.00294
0.00625
0.0365
0.00024
0.00289
0.0104
0.124
0.0127
0.00239
0.00234
0.00746
0.0026
0.0442
0.00227
0.0146
0.00180
0.0457
0.323
0.00412
0.0465
0.344
0.00154
0.0116
0.409
0.531
7.85
0.
0.0134
0.0744
0.162
78.1
0.219
2.70
0.
0.0928
1.30
0.00752
0.00361
~0.00015
~0.00019
0.
0.
~0.00013
0.
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-0.00018
~0.00017
~0.00020
~.00017
0.
u.00017
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0.00004
0.00004
-0.00037
9.00040
~0.00018
-0.00016
-0.00016
-0.00042
-0.00034
-0.00026
-0.00027
0.0826
0.00004
0.0701
0.144
0.158
0.
0.
0.
-0.00005
-0.00015
-0.00026
0.
0.
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-0.00001
-0.00012
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-0.00009
0.146
-0.00016
-0.00003
-0.00003
0.00008
-0.00008
-0.00008
0.
0.
0.
0.
-0.00011
0.0008
0.00003
-0.00015
0.
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-0.00014
a,
0.691
.0.62
0.
0.
0.499
0.
,1.05
.0.621
0.593
.1.03
.1.09
0.
.0.783
.0.788
.1.14
.1.14
.I.79
0.181
.0.702
-0.688
-0.627
.0.037
.2.34
2.22
-1.26
-3.49
-0.304
-0.479
2.9
0.
0.
0.
0.
1.49
1.59
1.91
0.
0.
1.25
1.34
1.35
1.37
2.84
-9.53
1.19
1.42
3.11
1.17
2.03
2.23
0.
0.
0.
0.
2.07
2.6
0.54
0.996
0.
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-0.627
0.157
0.815
W-S
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D.
0.
0.
0.
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0.
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0.
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0.
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0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
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1
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IO.86
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36
37
14
I4
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3+
l
3
76
3
3
*
3
3
3
3
[conrimed. . .]
Spectroscopic constants for isotopic variants of CO2
559
Table 2-continued
4920.2114
4922.5519
1925.0130
4928.9159
4931.0883
4937.3120
4939.3510
4941.4884
4942.5088
4948.8194
4953.4009
4959.8872
4985.3849
4978.1442
4977.8350
4991.3531
4993.5819
5013.7801
5020.4011
5028.8123
5042.5825
5081.7701
5082.4432
5084.8737
5088.9300
5091.2052
5099.8805
5114.8988
5123.1981
5128.9731
5139.4024
5151.3812
5188.5989
5217.8728
5247.8323
5291.1322
5315.7132
5584.3931
5887.1890
5858.0280
5951.8040
6959.9680
5972.5401
5993.5880
5998.5897
8020.7970
8075.9803
8088.2180
8119.8230
8127.7830
8149.3847
8170.1019
8175.1187
8175.9540
8198.1785
8205.5107
8227.9171
8241.9720
8243.8380
8254.5940
8298.1180
8308.2087
8348.2837
32213
10013
20011
21112
31113
10012
20012
23312
30013
31112
22212
30012
21112
30012
20012
20011
30011
21111
20021
22211
20011
12211
30012
21111
20011
31112
20011
30011
21111
31111
22211
23311
01121
30011
10022
02221
01121
ooo31
00031
10022
30014
10021
32214
30014
40015
31114
30014
31113
30013
30013
41114
32213
40014
30013
31113
40013
30013
30012
31112
30012
30012
40013
40012
12202
20002
Ooool
01101
11102
20001
ooool
03301
10002
11101
02201
10001
01101
10002
ooool
Ooool
10001
01101
00011
02201
00001
OooOl
10002
01101
00001
11102
OooOl
10001
01101
11101
02201
03301
OoOOl
10002
01101
01101
00001
10001
10002
00001
OooOl
00001
02201
00001
10002
01101
00001
01101
OooOl
00001
11102
02201
10002
OOool
01101
10001
Ooool
OooOl
01101
00001
00001
10002
10001
z=
928
628
538
627
628
628
627
628
628
628
628
628
628
638
628
638
638
638
628
638
628
628
628
628
627
628
828
828
628
828
828
828
838
828
828
828
828
828
828
828
838
828
828
828
828
828
828
838
838
828
828
828
828
827
828
828
828
838
838
828
827
828
828
-
s”,
0.00387
0.00358
0.00448
0.0149
0.0994
0.00108
0.231
0.0313
1.28
0.0507
0.851
0.002
23.5
0.00408
347.5
1.97
0.00521
0.184
0.00288
0.00892
0.252
0.
0.252
0.0281
0.0832
0.0232
109.
0.293
10.1
0.0283
0.422
0.0171
o.oo149
0.0208
0.00848
0.0121
0.188
0.00830
0.00883
0.00410
0.00188
0.00332
0.00339
o.oo400
o.oo409
0.0885
0.514
0.00218
0.0214
0.0221
0.00197
0.0124
0.0222
0.0032
0.330
0.0144
4.52
0.0554
o.oo411
0.0121
0.00275
0.0205
0.0130
alslamA
-0.oooo8
-0.ooo12
0.
0.
-0.oooo3
0.
0.
-0.00011
-0.00018
-0.ooo14
-0.00009
-0.ooo13
-0.00009
-o.ooo14
-0.oooo9
-0.00017
-O.OOO85
-0.00015
-o.o0015
-0.ooo22
-0.Ooo18
0.
-0.00020
-0.00021
0.
-0.00014
0.
-0.00023
-0.00014
-0.00018
-0.00022
0.
-0.00008
-0.00033
0.0194
-0.00054
0.00315
-0.oooo7
-0.oooo5
0.00045
-0.00019
-0.00039
-0.00013
-0.00008
-0.00018
-0.00010
0.0018
-0.00008
0.
-0.00029
-0.00007
-0.00007
-0.00013
0.
-0.00001
-0.00008
0.0009
-0.00009
0.
-0.00014
0.
-0.00018
0.
0.332
-0.397
0.
0.
0.31
0.
0.
0.007
0.884
-0.491
0.127
-0.878
0.02
-1.29
-0.47
-2.07
-3.9
-1.38
-2.58
-1.59
-2.54
0.
-2.21
-1.88
0.
-1.49
0.
-2.24
-1.88
-1.88
-1.78
0.
0.099
-4.11
0.438
-1.79
0.288
-0.797
2.07
1.88
3.08
-0.892
1.53
3.12
2.19
2.38
2.5
1.13
0.
0.384
0.884
0.883
1.9
0.
0.831
-0.078
4.2
-0.492
0.
-2.11
0.
-0.835
0.
3.
3.
3.
3.
3.
3.
D.
D.
3.
0.
D.
0.
3.
D.
D.
D.
D.
D.
0.
D.
0.
0.
D.
D.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
ZI
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
-
3
3
3
3
3
3
3
3
3
3
32
3
92.76
32
3
3
3
3
3
3
l
3
3
3
77
62
3
3
82
3
3
3
3
3
3
3
3
82
3
3
3
3
3
3
3
3
3
78
67
3
3
3
3
3
3
3
67
3
78
67
3
3
3
3
3
[continued.. .]
L. S. ROTHMAN~~
560
al
Table 2-continued
8347.8515
8356.2954
6359.2569
8363.6240
6367.6675
8503.0609
6532.6537
5536.4490
6537.9566
5562.4414
8679.7056
6746.1119
6760.2104
6870.7999
6885.1540
6697.7525
6905.7669
6907.1424
6922.1967
6935.1340
6945.6080
6972.5773
7263.9780
7414.4549
7460.5270
7583.252
7593.695
7734.448
7757.625
7901.4791)
7920.6380
7981.1860
8089.0280
8103.5857
8120.1090
8135.8900
8192.5507
8220.3640
8231.5607
8243.1687
8254.6874
8276.7600
8293.9512
9368.9940
9478.1290
9516.9690
9631.353
30012
31112
32212
30011
41101
30011
40011
31111
11122
32211
11121
01131
00031
11132
01131
02231
10031
10032
00031
01131
00031
00031
40015
41114
40014
41113
40013
40012
41112
21122
40011
10032
10031
20033
10032
11132
10032
10031
20032
20031
12231
11131
10031
20033
21132
20032
20031
00001
01101
02201
00001
00001
00001
10001
01101
00001
02201
00001
01101
00001
11102
01101
02201
10001
10002
00001
01101
00001
00001
00001
01101
00001
01101
00001
00001
01101
00001
00001
00001
00001
10002
00001
01101
00001
00001
10002
10001
02201
01101
00001
00001
01101
00001
00001
626
626
626
626
626
636
636
626
626
626
626
628
626
626
626
626
626
626
626
626
626
-
a,
s”,
I80
626
626
626
636
626
626
626
626
626
626
626
636
636
626
628
626
626
626
628
626
627
626
626
626
626
-
4.54
0.341
0.0128
0.0137
0.
0.586
0.00242
0.0725
0.00598
0.00353
0.0148
0.0147
0.164
0.00246
0.00497
0.0526
0.0153
0.0274
0.0591
1.29
0.0112
15.8
0.00401
0.00445
0.0469
0.00753
0.102
0.0281
0.00218
0.00149
0.00175
0.00256
0.00805
0.00139
0.00217
0.0367
0.431
0.00191
0.00139
0.00112
0.00191
0.0465
0.614
0.00424
0.00165
0.0252
0.00912
v,,
is in cm-’ and Sf is in units of cm-‘/(molecule-cm-‘)
0.00095
0.00014
0.00015
0.00062
0.
0.00115
~0.00009
0.00005
0.0116
0.
0.0159
0.
0.
9.00009
0.
-0.ooOO6
-0.00005
-0.00006
0.
-0.00007
0.
-0.000215
-0.00019
-0.00009
-0.00014
0.
0.
0.00025
0.
0.018
0.00075
-0.00002
-0.00010
0.
0.
-0.00005
0.
0.
0.
-0.00012
-0.00012
-0.00011
0.
0.
0.
0.
0.
i7
3.8
.1.02
0.935
4.81
0.
3.8
-2.96
-2.12
.8.18
::668
0.
0.
0.164
0.
0.411
0.801
0.107
0.
0.426
0.
0.
3.71
1.18
2.82
0.
0.
0.
0.
0.
-2.43
2.52
-0.21
0.
0.
1.66
0.
0.
0.
-0.712
-0.38
-0.399
0.
0.
0.
8:
i7
i7
57
57
36.81
3
3
3
82
82
83
83
t
3
3
3
3
3
3
34
3
3
3
3
3
84
91
3
81
81
315
4
lo- u. The Herman-Wallis coelhcients n,, a2. a3 are for the P- and
R-branches, while b, is for the Q-branch. The second-and third-order Herman-Wallis coefficients (ur, (I~,and br) should be
multiplied by 10T5.The non-numeric characters in the Ref-S column are interpreted thus: 1 = HITRAN line intensity cutoff
lowered for significant Q-branch (densely-packed lines); @ = band absent from HITRAN, but included since it was used in
the least-squares determination of energy levels; * = a perturbed band. When there are multiple references under Ref.-S, the
first is the one actually used in HITRAN.
x
(Note that, to derive QR(T) from the Q(T) given by Gamache et a1,3*one must use QR(T) = Q(T)/
kj Q,(T)]. Values of gi are given in Ref. 38 and QJ296K) can be obtained by a simple summation
of exponentials using the G, in Table 1). Then the line intensity S(T) at temperature T is
S(T) =
K8~310-36Y(3hc11
W(siQJT)Q,V)lv
xexp(-Gz/kT)exp(-Ei/RT)[l
-exp(-hv/kT)]IR,12L(Jn,e)F(Jn)
(5)
where h is Planck’s constant, c is the speed of light, Z, is the isotopic abundance, v is the transition
frequency or line position, E; is the rotational energy of the lower state, and k is Boltzmann’s
constant. Often the factor gj is omitted from Eq.(5) by absorbing it into 1R, 1’.
Spectroscopic constants for isotopic variants of CO,
561
The rotationless band strength given in Table 2 is defined as
S:(T) = W”10-~6)/(3~cll Kvo4,)l(giQv(~11ew(--G/W
at T = 296K, where v0 is the band center (G: - G:‘). Substituting
intensity can then be expressed
S(T) = (v/v,,)S,O(T)L(J”, t’) F(J”) [exp( -E;;/kT)/Q,(T)]
l&l*
09
Eq. (6) into Eq. (5), the line
[I - exp( -hv/kT)J.
(7)
S(T) should be used as given by Eq. (7) when at least one of the upper and lower states has zero
vibrational angular momentum (G = 0). When both upper and lower states have nonxero
vibrational angular momentum (/ > 0), the intensity is split between e and f subbands, and S(T)
should be divided by 2.
It should be noted that some of the St values listed in Table 2 were determined with an additional
factor, g,, in the numerator of Eq. 6, where g, = 2 - &,. For such values, the rotational partition
sum of the band in question was used to determine St. This cancels the factor of approx. 2 since
for t # 0 bands, all rotational levels exist and QR (G # 0) = 2 x Q&round state). For these bands,
we have used 2 x QR(ground state) which introduces an error of a few percent for transitions
originating from bands with 8 larger than 0. There are not many bands on the HITRAN database
where this would be a problem, e.g. starting from the P level (/ = 4).
The Hiinl-London factors for parallel bands (A/ = 0) are given by
L(J”, /) = (J” + 1 + G)(J” + 1 - /)/(J” + 1) (R-branch),
(Q-branch),
L(J”, t) = (Zr” + 1)G2/[.P’(.P’+ l)]
L(J”, /) = (J” + d)(J” - 8)/J”
and for perpendicular
(9)
(P-branch),
(10)
bands (be = f 1)
L(J”, e) = (J” + 2 + CA&)(Y’+ 1 + dAd)/Z(J” + 1) (R-branch),
L(J”, e) = (J” + 1 + /At)(.P’ - k’A~)(2.P’+ 1)/[2J”(J” + l)]
L(J”, d) = (J” - 1 - CAC)(.P’- CA/)/U”
The Herman-Wallis
(8)
(Q-branch),
(P-branch).
(11)
(12)
(13)
factor F was assumed to be of the form
F(m) = (1 + a,m + u2m2+ a3m3)2 (P- and R-branches),
(14a)
F(m) = (1 + b2m2)2 (Q-branches),
(14b)
where a,, a,, and a3 are constants for a given band, and where there is potentially a separate b2
constant for e and f lines in the Q-branch of a given band (b; and bi). The running index m is
m = J + 1 in the R-branch, m = J in the Q-branch, and m = -J in the P-branch. The use of up
to three coefficients in the P- and R-branches is a signiticant improvement over the single coefficient
used in the 1986 edition of HITKAN. Other expressions are used to report Herman-Wallis factors
in the literature. These other formulae were algebraically converted to the form of Eq. (14) for use
in generating the values in Table 2.
DND has now been extensively utilized to calculate unobserved band intensities, and especially
Herman-Wallis factors, for the three most abundant species (626, 636 and 628 in HITRAN
notation). On the 1986 HITRAN database, the method2 was utilized only for the parallel band
intensities of the 626 isotopomer. It was decided to supercede DND calculations with experimental
values where available. The DND calculations yielded first and second order coefficients for the
Herman-Wallis coefficients for the P- and R-branches (a, and a~). The experiments occasionally
provided the third-order coefficient u3 and the second-order coefficient for the Q-branch, b2. In a
few cases, the measurement did not supply a, and/or u2.
PRESSURE
BROADENING
General approach
It was assumed that the pressure broadening of CO2 is independent of vibrational transition.
Data from Johnsi and Dana et aV2*”were used for self-broadening. Data from Dana et alI2 provided
562
L. S. ROTHMANet al
nitrogen- and oxygen-broadening, data from John~‘~ provided air-broadening, and data from
Devi et al” and Margottin-Maclou et alI8 provide additional nitrogen-broadening values. The
calculations of Gamache and Rosenmann’ provide a complete set in m for 1 S )m ) < 121 for
nitrogen-, oxygen- and self-broadening.
The measured broadenings y(T) were converted to 296K by
y(T) = Y(Tll)(TITl’)
(15)
setting T,, = 296K and using a value for n calculated by Gamache and Rosenmann.*g Air-broadened
widths were obtained from nitrogen- and oxygen-broadened widths by
Yair =
0*79~nitrogea
+
o*21Yoxygem.
(16)
Where only nitrogen-broadening was available, the m-dependent Ykr/Ynimpn
ratio determined from
the calculations of Gamache and Rosenmann was used to convert to air-broadening. As a test,
these procedures were applied to the data of Dana,” determining yailin two ways: by Eq. (16), and
by multiplying the nitrogen broadening by the calculated ratio. The two methods agreed to better
than 1% in all cases. For comparison, the measurements in the different references cited differ by
as much as 6%, with an average difference of 2.7%.
Air broadening
The air-broadened line widths at 296K used in HITRAN were determined in this way: because
the polynomial fit did not work well for m = 1, the only available experimental valuei was used:
rtii,(1) = 0.09489 cm- '/atm.
(17)
Yair(m= 2 to 45) = 0.09259 - 1.749 10m3m+ 4.263 lo-’ m* - 3.6793 lo-’ m3
(18)
For m = 2 to m = 45 inclusive,
in cm-‘/atm, obtained by least-squares fitting the experimental data.
For m = 46 to 121 inclusive,
yti,(m = 46 to 121) = 0.039313 + 1.7806 10e3 m - 3.7746 10m5m*
+ 2.9570 lo-’ m3 - 7.969 10m4m4
(19)
in cm-“/atm, obtained from the calculated widths, with the requirements that Eq. (18) match
Eq. (19) at m = 45, and go smoothly to 0.055 at m = 121. However, HITRAN does not include
any lines above m = 108. Figure 1 shows a plot of yail as a function of m chosen for HITRAN.
Self-broadening
The self-broadened widths at 296K used averages of the experimental values’5,‘6 for m = l-4,
again because of poor polynomial fits:
y&l)
= 0.1279 cm-‘/atm,
(20)
~~“(2) = 0.1228 cm-‘/atm,
(21)
y,,,(3) = 0.1204 cm-‘/atm,
(22)
y,‘,(4) = 0.1190 cm-‘/atm.
(23)
For m = 5 to 121 inclusive,
y&m)
= 0.12223 - 1.4039 10d3 m + 9.1762 10e6m2 - 2.0051 lo-* m3
(24)
in cm-‘/atm, obtained by least-squares fitting of the experimental data. Figure 2 illustrates the
function chosen for the HITRAN database.
Related parameters
The temperature dependence of the air-broadened
HITRAN was taken from the calculations of Ref.
parameter, which is applied as in Eq. (15). Pressure
v3 fundamental; these data were from the work of
halfwidths, n, used for the current edition of
19. These calculations provide a J-dependent
shifts for the lines were only provided for the
Devi et a1.17
563
Spectroscopic constants for isotopic variants of CO*
0
20
40
60
80
100
m
Fig. 1. Air-broadened halfwidths of carbon dixode as a function of m. The data are: 0 Ref. 12, + Ref.
) represent the values on HITRAN92.
16, 0 Ref. 17, and A Ref. 18. (CONCLUSION
The improvement in the method of fitting observed CO, line positions did not, in general,
signiflcantly change those lines which also appeared in the 1986 edition of HITRAN. However,
the global fit procedure makes full use of the experimental data, where the old method required
40
60
a0
m
Fig. 2. Self-broadened halfwidths of carbon dioxide as a function of m. The data are: 0 Ref. 12, A Ref.
15, and +Ref. 16. (-)
represents the values on HITRAN92.
564
L. S. ROTHMAN
et al
a subset of the measured bands to be chosen. Also, it is more flexible, allowing use of information
from other sources. Extrapolation to unobserved levels via DND does represent a significant
improvement.
Line intensities are greatly improved, through inclusion of new measurements, and DND
calculations which now include Herman-Wallis coefficients. Line broadening is improved by use
of new measurements and calculations. A single m-dependence of the line broadening was used
for all CO2 bands.
There remains a fair amount of research, both experimental and theoretical, to be performed
to adequately simulate carbon dioxide spectra in problems such as remote sensing and high-temperature applications. There is the need to obtain more intensity measurements of lines, especially
isotopically-enriched samples. There is still a dearth of observations of the line positions of the “0
isotopomers. Further advancements of the Direct Numerical Diagonalization approach will lead
to better Herman-Wallis factors, but more importantly, to proper representation of perturbed
bands.
Acknowledgements-Many colleagues have graciously provided their data prior to publication for this project. We wish
to thank in particular J. W. C. Johns, V. Dana, M. P. Esplin, M. L. Hoke, D. C. Benner, V.M. Devi, M. A. H. Smith,
C. P. Rinsland, and C. Boulet for their valuable inputs. This project has been supported by the Air Force Oflice of Scientific
Research under Task 231OGl.
REFERENCES
L. S. Rothman, Appl. Opt. 25, 1795 (1986).
: : R. B. Wattson and L. S.‘Rothman, J. Molec. Spectrosc. 119, 83 (1986); R. B. Wattson, L. S. Rothman,
A. Newburgh, and R. Pavelle, Paper TE9,43rd Molecular Spectroscopy Symposium, Ohio State University
(1988).
3. R. B. Wattson and L. S. Rothman, JQSRT 48, 763 (1992).
4. D. C. Benner, V. Malathy Devi, C. P. Rinsland, and P. S. Ferry-Leeper, Appl. Opt. 27, 1588 (1988).
5. M. P. Esplin, private communication (1987).
6. M. P. Esplin, R. B. Wattson, M. L. Hoke, R. L. Hawkins, and L. S. Rothman, Appl. Opt. 2& 409 (1989).
7. M. P. Esplin and M. L. Hoke, paper TE6,44th Molecular Spectroscopy Symposium, Ohio State University
(1989).
8. G. Blanquet, J. Walrand, and J.-L. Teffo, Appl. Opt. 27, 2098 (1988).
9. D. Bailly, Thesis, Universitk de Paris-Sud, France (1983).
10. J. W. C. Johns, .I. Molec. Spectrosc. 134, 433 (1989).
11. J. W. C. Johns and J. Vander Auwera, J. Molec. Spectrosc. 140, 71 (1990).
12. V. Dana, A. Valentin, A. Hamdouni, and L. S. Rothman, Appl. Opt. 28, 2562 (1989).
13. A. Hamdouni and V. Dana, Appl. Opt. 29, 1570 (1990).
14. V. Dana, A. Hamdouni, R. B. Wattson, and L. S. Rothman, Appl. Opt. 29, 2474 (1990).
R. B. Wattson, and L. S.
15. V. Dana, J.-Y. Mandin, G. Guelachvili, Q. Kou, M. Morillon-Chapey,
Rothman, J. Molec. Spectrosc. 152, 328 (1992).
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