The intensities, widths, and positions of lines of three CO2 bands near 2750/cm were determined. The results are in general agreement with other measured and estimated values

Hoke, M. L.

Shaw, J. H.

English

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t(NKSA-C?-1693C 9)
	 Pj.PAPIF:Fr- rf r C2 B-ANDS
NEAP 3.6 nICFC'VS (Ohio State Univ.,
Columbus.)
	 21 P HC A02/MF AC1	 CS"L 07D
h82-32438
Unclas
G3/zS 28897
Parameters of CO2
Sands Near 3.6um*
M. L. Hoke
J. H. Shaw	 i
Department of Physics
The Ohio State University
`^.	 SFP 1,C82
	 Columbus Ohio 43210
	
a
R c	 UED	 i
NASA STI FACILITY
11
 ACCESS DEPT
-This work was supported in part by NASA Grant NSG-7469.
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Abstract
The intensities, widths, and positions of lines of three CO )
 bands near
2750 cm-1 have been determined. The results are in general agreement with
other measured and estimated values.
i
i
4
f
t
i
Introduction
A group of CO2
 bands near 2600cm-1
 has recently been investigated by the
12
nonlinear, least-squares method (NLLS) of whole-band analysis.
	 The spectra
-1
of a similar set of bands near 2750cm , shown in Fig. 1, have also been
analyzed by this technique. These spectra were obcained by coadding 750 inter-
ferograms collected by a Nicolet Fourier transform spectrometer. No apodization
was applied to the composite interferograms before transformation. Tlie SNR of
the upper spectrum, Spectrum I, is about 600 and that of the lower spectrum,
Spectrum II, is about 350. The spectral resolution of both is about 0.07cm-1
Spectrum I was obtained with a path length of 476m through a naturally-occurring
sample of CO2
 at a presr ••
	of 177 torr and a temperature of 294K	 ,1 path length
of 994m at 741 torr and 292K was used to obtain Spectrum II.
The descriptions of the CO, bands in 'Table 1 were obtained from the work of
Rothman and Toung. 3
 The strongest band in Table 1 is about ten times weaker than
the corresponding band near 2bl4cm-1 . Thus, although reasonable values for the
widths of the lines near 2600cm 
-1
have been obtained fron. previous analyses l
 of these
bands in Spectrum 1, accurate line widths could nut he obtained from the upper
spectrum in Fig. 1 althou g h the positions of the lines could be well-determined.
Estimates of the line widths were obtained from Spectrum IT,although these lines
ate too wide to :1T low their posieions to be determined as precisely as those in
Spectrum I.
Tines of all three bands are present in these spectra. Information from
aproximately 100 lines of band I, sixty .lines of band II, and 40 lines of the
suhhand, of hind III, most. of which are unresolved, contributed to the analysis.
Spectral Analysis
The method of analysis and the models used to describe the spectra are very
similar to those used previously. 1,2
The vibration-rotation, energy-level models and the expressions for the
relative intensities of the CO 2 bands have been described by Rothman and Young.3
We were able to actermine band origins for all of tae '*ands in Table 1. In
a
i
addition,
	 the quantities B",	 D", B'	 and D' were estimated for band I,and by
fixing B" and D" to the values reported by Guelachvili, 4 estimates of B' and D'
for the upper state of band II were obtained. However, only the sums B' + B"	 }
were obtained for the subbands of band III.
The term (1 +^ m) 
2
was used to describe the influence of vibration-rotation
interactions on CO2 line intensities. The value of C obtained for the strongest
band was less than the standard deviation of 10 -3 ; no attempt was made to estimate
for the other bands.
The profiles of the lines were found to be adequately described by the
Lorent4 shape and the Iml-dependence of the widths was described bythe expression
of Winters et al.5
a
mI = wl + W2 exp [-WV ImI1 + 1J4 ImI exn [ - B"Iml (ImI- 1)/kTJ.	 (1)
This expression, which has four adjustable parameters, described the jmj dependence
o* the CO 2 lines near 2600cm-1 satisfactorily. 0)
The influence of instrumental effects due to the finite optical-path-difference,
the finite source size, and dlte to residual phase error b'_1 on the spectra were
included by usi;ig the models described by Hoke. 	 In those cases where they could
be compared, the parameter value:- in these models agreed with those obtained from
1u
other analvses.
The influence of continuous absorption by the wings of distant CO 2 bands
2
L..
Alt r^
OMOINAI. PAGE 0
OF POOR QL*LRY
Table 1. The band origins, identifications, and intensities of CO2 bands bets
2700 and 2800cm 
1 from the tabulation of Rothman and Young (Ref. 3).
Band Band Center Molecule Transition sand Intensity 
(cm-1 ) (1024 CM- 1 /Mol cm-2
I 2757.229 628 20001-00001 2.20
II 2776.000 627 20001-00001 0.23
III 2791.616 628 21101-01101 0.15
a These band intensities were obtained by assuming the isotopic abundances iL
naturally-occurring CO2.
ME
nwi+ a
OWN
Rotational Constants 	 r
^ -	 J
Four seta of rotational constants lob band fare given
• *	 art.
with experimental values obtained by Guelseth U I and 4**
estimated by Chedin 9
 and Rothman and Young . 3 The expsr,10iiiat=
obtained from other band systems. The ranges of values reporter
	
_
Shawl are caused by correlations among the rotational constants and otior re-
trieved parameters and also by the non-uniqueness of NLLS solutions.
Two sets of constants are reported from each spectrum. In-one ems ; the
, S7re^-
B" and D" values were retrieved from the spectra and, in the other call, these
were fixed to the values of Guelachvili. 4 As in the previous anlly►s",of the
corresponding band at 2 F' ?. 11 ^m-1 , it was found that the retrieved villues' of B" wane
consistently smaller than that reported by Guelachvili4 and that' the STIR obtained
with B" fixed was always smaller than that obtained by retrieving B".
The standard deviations in Table 2 were obtained from the analysii and, as
noted previously , 2 they are often optimistically small. The estimated correlation
coefficients between the retrieved parameters are also obtained. These show vari-
ations from retrieval to retrieval but the correlations between the parameters in
Table 2 agree, in both their relative values and absolute magnitudes, with those
which would be obtained by performing a linear, least-squares analysis of :he
line positions. 10
The largest SDR value was obtained for retrieval A in Table 2. Me differences
in the line positions calculated from these parameters and the other sets of
parameters are shown in Fig. 3. For Iml < 50, all the line positions obtained
from the retrieved parameter sets are consistent to ± 0.003cm 1 . Although the
line positions obtained from the spectrum of the higher pressure sample are less
precise than those obtained from spectrum I the results confirm the conclusions of
Freed et al 11 and of Hollins and Jordan 
12 
that the pressure shifts of infrared
._
4
kCO2 lines are small compared with their wide. s
The lines of the 1601 C
17
0 band are such weaker than those of band I Aiw tot i
upper state constants B' and D', given in Table 3, were obtained by'€
and D". These sets of constants give positions of lines with _MI
which agree within ± 0.005cm-1 . This is less than one tenth of the observed
line width.
Information about the weakest of the bands was only obtained from spectrult:_UI.
Initial estimates of the rotational constants were obtained by calculating the
spectrum of bands I and Il only and subtracting this from the observed spectrum.
Many of the lines of band III, including the Q branch could then be seen. Since
the lines of the two subbatids were only resolved for Iml > 15 it was not possible
to obtain satisfactory individual B' and B" values in the subsequent NLLS analysis.
Absolute values for the band origins were obtained by calibrating the spectra
against the previously-measured positions 13 ' 14 of water vapor lines present in
the spectra. The estimated accuracy of the band originsls ±2 x 10-3	 1. is
smaller than the precision, about 10 -µ cm-1 , estimated by the NLLS analyses.
These band origins are compared with those of Rothman and Young and Ched,in5 in
Table 4.
Line Widths
It was assumed that the corresponding lines in each of the bands had the
same width and all the widths were reduced to standard conditions of 296K, 760
torr by the relation
a(lml, P,T) - a(l m l, P 0 T 0 ) ( P/Po ) (To /T) ;5	(2)
The widths obtained from spectrum II are compared with those obtained from
the previous analyses of the bands near 2600cm
-1
 in Fig. 4. In both cases the
16 12 18
dominant band is due to	 0 C 0 and the brcadening is due to the isotope
12	 51
C 02 . The precision of each set of results in estimated to be about 2-3%.
Since the maximum difference between the two sets of widths is lsn than
	 A
effects due to differences in the vibrational transitions involved are i11.
The values of the constants Wi in Eq.(1), which are given in Table 5, are those
which produced the curves in Fig. 4. They were obtained from the solutions wi4*
the largest SDRs. Other sets of values of W is obtained from retrievals with almost
equally good fits to the experimental data,gave curves almost identical to that
shown in Fig. 5, even though the values of the constants differed by several
times the standard deviations given in Table 5. This behavior is consistent
with that found for most of the other parameter values. 1,2
Intensities
The band sums, the sums of the intensities of all the lines in each band,
were calculated as described previously. l The values in Table 6 were obtained
from the analysis with the largest SDR. The spreads obtained from almost equally
good retrievals are also given together with the values estimated by Rothman
and Young. 3 These spreads are an order of magnitude larger than the standard
deviations obtained by the NLLS analyses. The results for bands ;I and III were
obtained only from spectrum II and, in order to obtain band sum III, it was
necessary to fix the sums B' + B". The experimental intensities for two of the
3
bands are significantly larger than those estimated by Rotham and Young.
Conclusions
The values for the band sum, the line widths, and the rotational parameters
of band I have been obtained with accuracies sufficient for use in most atmospheric
transmittance calculations. The corresponding values for sands II and III
describe the experimental data available adequately. The results are in satis-
factory agreement with the previous measurements of Guelachavili 4 and Hoke and
Shaw 
1,2,8 
and with the estimates of Rothman and Young.3
6
mr•,—
1. M. L. Hoke and J. H. Shaw, "Analysis of CO2 bands near 2600cn 1,.".Appl.
Opt., 21, 929 (1982).
2. M. L. Hoke and J. H. Shaw, "Rotational analysis of CO, bands near 4un,"
Appl. Opt., 21, 935 (1982).
3. L. S. Rothman and L. D. S. Young, "Infrared energy levels and intensities
of carbon dioxide-II," Jour. Quant. Spectrosc. Radl.at. Transfer, 25, 505
(1981).
4. G. Guelachvili, "High resolution Fourier spectra of carbon dioxide and
three of its isotopic species near 4.3um," J. Mol. Spec., 79, 72 (1980).
5. B. H. Winters, S. SiiveLman, and W. S. Benedict, "Line shape in the Wing
beyond the band head of the 4.3u band of CO 2111 Jour. Quant. Spectrosc .
Radiat. Transfer, 4, 527 (1964).
6. G. A. Vanasse and H. Sakai, "Fourier Spectroscopy" in "Progress in Optics,
Vol. VI," E. Wolf ed., North-Holland, Amsterdam (1967).
7. C. R. Anderson and D. R. Mattson, "Phase correction techniques in Fourier
transform-infrared (FT-IR)," Soc. Photo-Opt. Instru. Eng. 289, 199 (1981).
8. M. L. Hoke "Analysis of CO2 bai,ds near 2600cm-1 , Ph.D disc. Ohio State
Univ. (1982).
9. A. Chedin, "The carbon dioxide molecule," J. Mol. Spec., 76, 430 (1979).
10. D. L. Albritton, A. L. Schmeltekopf and R. N. Zare, "An introduction to the
least-squares fitting of spectroscopic data" in "Modern Spectroscopy. Modern
Research II," K. Narahari Rao, ed., Academic Press New York (1966).
11. C. Freed and R. G. O'Donnell, "Advances in CO 2 laser stabilization using
the 4.31im fluorescence technique" Metrologia, 13, 151 (1977).
12. R. C. Hollins and D. L. Jordan, "Pressure shift in an atmospheric pressure
CO 29N2, He gas mixture," J. Plays. B. 15, L 491 (1982).
- "WimW"'13. L. A. Pugh, Pb.D dissertatiou t'"A detailed study
	
	 "OW a`af the nab taf 
of water vapor," Ohio State University (1972).
14. C. Camy-Payret and J. M. Flaud, "Line positions and intensities in. -ilia v2.
band of H2160," Mol. Phys., 32, 523 (1976).
15. R. L. Hawkins, M. L. Hoke, and J. H. Shaw "Wavenumber calibration of Fourier
transform spectra," Appl. Spectrosc. (accepted).
It i
ORIOM PA09 9
OF POOR QUALITY
Table 1. The band origins, identifications, and intensities of CO2 bands between
2700 and 2800cm 1 from the tabulation of Rothman and Young (Ref. 3).
Band Band Center Molecule Transition Band Intensity 
(cm-1 ) (1024 cm-1 /mol cm 
2)
I 2757.229 628 20001-00001 2.20
II 2776.000 627 20001-00001 0.23
III 2791.616 628 21101-01101 0.15
a These band intensities were obtained by assuming the isotopic abundances U.
naturally-occurring CO2.
CW
Table 2. Rotational constants for Band I (20001-00001,628) obtained is this work a"-
other studies.
Retrieval Spectrum SDR B11	 (cmll ) B I	 (cm 1 ) 108 D"
(cm 1 )
108 D'
--- (CM-1
 )
A I 400 0.36818217(56) 0.36903714(22) 12.130(37) 8.882(36)
B I 392 0.36818571a 0.369036189(46) 11.9030' 8.494(96)
C II 170 0.3681616(75) 0.3690155(76) 11.75(35) 8.416(35)
D II 168 0.36818571 a
0.36818571(52)'
0.36903951(87) 11.9030a
11.9030(186)°
8.550(52)
0.3681771 b 0.369039b 11.7b 7.7b
J.368186 c 0.369024c 11.9c 8.8c
0.36816235(22) d 11.5660(49)d
0.36818571 1 ' d 12.413(18)d
aGtielachivili (Ref. 4)
bRothman and Young (Ref. 3)
cChedin (Ref. 9)
dRange of values obtained by Hoke and Shaw (Ref. 2)
ORKM& PAGE IS
OF POOR QUALITY
Table 3. Upper State Rotational Constants for Band 11 (20001-0001.627).
Source B	 (Cm 108 6	 (CM-1
Retrieval Bt 0.379172(7) 0.0
Retrieval D t 0.379327(17) 16.15(12)
othman. a 0.379270 8.8
Chedin b 0.379248 9.3
twee Table 2 for details
standard deviation not obtained
a (Re f . 3)
b (Ref . 9)
Table 4- Origins Of CO2 ts+ =1ig ^^T
Band Molecule Rothman Chedl*
and Young Work
(see Table 2) cm 1( -1 (cm-, )` (^^1)
I 628 2757.229 2757.211 2757.183(2)1':
627 2776.000 2775.610 2775.595(2)
III 628 2791.616 2791.593 2791.512(2)
Ref. 3
Ref. 10
'a
w
  
(cm t /ate) 8.34(2)x10a 8.0732(8)x10 2
w2 (Cm 1 /ate) 5.83(6)x10 
2 6.15(x)x10 2
w3 -0.1539(4) -0.179(4)
w4 (Cm^1 /atm) 1.82(2)x10 
3 1.89(9)x10 3
See Reference 1.
*e
Corrected to 290K, 760 turr.
t
ORIGINAL PAGE 1^
OF POOR QUALITY
Table 6. Band Intensities.
Band Molecule
Intensity	 (1024 cm-1 /mol cm-2
Rothman Spectrum	 I Spectrum	 IIa
and Young
I 628 2.20 3.31	 (12) 3.28	 (1.2)
II 627 0.23 - 0.214	 (12)
III 628 0.15 - 0.255(15)
The values in brackets represent the total scatter in the estimated
values.
a See Ref. 3.
14
Fig. 1. Top: Spectrum of a 476m path of .CO2,pressure,177 torr,
294K; bottom: spectrum of a 994m path of CO 2
, 
pressure
,-
741 tarr
-
, tompwature
292K. These are referred to as Spectrum I and Spectrum 11, respectively,-
the text.
Fig. 2. Upper left: a portion of Spectrum II in a region where there it 11"1011
line absorption. Upper right. a portion of the same spectrum. Bottom: tb*
difference between the observed and calculated values, shown on an expanded scale.
Fig. 3. The differences in the line positions calculated from the constants 3e
retrieval A, Table 3 and the positions calculated from the other retrievals
(labeled according to the retrieval identification in Table 3). including
those calculated from rho constants of Rothman and Young (R) and Chedin (Ch).
Fig. 4. The Iml dependence of the widths of 16012CI80 lines broadened by 12C1602
(reduced to 296K, 760 torr). The top curve was obtained from the analysis of the
20002-0001 band at 2614 cm -1 (see reference 1). The bottom curve was obtained
from the analysis of the 20001-00001 band at 2757 cm- 
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Parameters of CO2 bands near 3.6 microns

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