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Relative intensity calculations for carbon dioxide
J. Quon?. Spectrosc.
Radial.
Pcrgamon PressLtd., 1965.Printedin GreatBritain
Transfer. Vol. 5, pp. 291-301.
RELATIVE INTENSITY CALCULATIONS CARBON DIOXIDE L. D. Jet Propulsion
Laboratory,
GRAY
JUDITH E. SELVIDGE
and
California
FOR
Institute
of Technology,
Pasadena,
California
(Received 6 August 1964) Abstract-Internal and vibrational partition functions of WYOZ are tabulated for the temperature range 150-1200°K at 10°K intervals. Rotational line intensities, relative to the total intensity of the band at 3OO”K, are presented for transitions arising from the state 0000 and from the state 0110.
Part I. Internal Partition Function I. INTRODUCTION
To INTERPRET the results of experimental studies of carbon dioxide absorption in the infrared, it is necessary to know how the intensity of each rotational line varies with temperature. This variation requires a knowledge of the internal and vibrational partition functions. The internal partition function of carbon dioxide has already been calculated at many temperatures in order to obtain the corresponding thermodynamic functions(r*s), but the only explicit tabulation of the partition function is that of TOURIN and HENRY(~) which considers six temperatures ranging from 298 to 1273°K. The values which we present were calculated for the temperature range from 150 to 1200°K in increments of 10°K. II.
THE
INTERNAL
PARTITION
FUNCTION
The internal partition function, qint, is given by qint = C,gV exp[ -4Wk
Cl zJg7 exp[ -44
Q/k Tl
(1)
where r,(z$ is the vibrational energy above the zero point vibrational energy of the molecule, EJ(.~,vt) the rotational energy, g, the degeneracy of the vibrational level (without rotation), and gJ the degeneracy of the rotational sublevel (without vibration). The summation is over all rotational levels for each vibrational level. If the interaction between vibration and rotation is neglected, so that EJ(J, Q) = lJ(a, then the internal partition function can be written as the product of two factors: the vibrational and the rotational partition functions, qVib and qrot; i.e. qint =
qvibqrot
(2)
where qvib =
&;t+
exP[-+(U#)/kT]
291
(3)
292
L. D.
and
GRAY
and qrot =
c
.gJ
JUDITH
E.
SELVIDGE
exp[-dJ)/kT].
In the present calculations, the internal partition function was evaluated directly from equation (1) and the vibrational partition function was obtained from equation (3). For comparison, the partition function for a harmonic-oscillator rigid-rotator was also calculated. The results are given in Table 1. TABLE 1. VIBRATIONAL AND STERNAL
Temperature (“K)
Internal
PARTI~ON
Partition
Function
~LJNCTIONS OF lzC’BOz
Vibrational
Partition
Function
FOR THE TBMPERATURE RANCE 150 to 1200°K
Harmonic
Oscillator
Vibrational
Partition
Function
Rigid-rotor Oscillator Partition
Harmonic Internal Function
150.0
0.13421232E
03
0.1003329lE
01
0.10033275E
01
0.1335442lE
160.0
0.14338238E
03
0.10049753E
01
0.10049720E
01
0.14268064E
03
170.0
0.15265334E
03
0.10070969E
01
0~10070908E
01
0.151917796
03
180.0
0.16204501E
03
0.10097385E
01
0~1009728lE
01
0.161275368
03
190.0
0.171577336
03
0.10129359E
01
0.101291928
01
0.170773llE
03
ZOO.0
0.1812702SE
03
0.1016719lE
01
0~101669dEE
01
0.180430526
03
210.0
0.191142756
03
0.10211056E
01
0.102106226
01
0.190266625
03
220.0
0.201213636
03
0.10261085E
01
0.1026046lE
01
0~20029987E
03
230.0
0~21150100E
03
0.103173668
01
0.10316496E
01
0.210548038
03
240.0
0.22202230E
03
0.103799338
01
0.103787596
01
0.221028236
03
250.0
0.232794408
03
0.10448799E
01
0.1044724lE
01
0.231756926
03
260.0
0.2438333lE
03
0.10523920E
01
0.105219llE
01
0.242749916
03
270.0
0.25515532E
03
0.106052878
01
0.106027208
01
0.25402249E03
280.0
0.26677556E
03
0.10692839E
01
0~106896038
01
0.26558938E
03
290.0
0.27870768E
03
0.10786462E
01
0~10782486.E
01
0.277464888
03
300.0
0.29096700E
03
0~1088613l.E
01
0.10881294E
01
0.289662908
03
310.0
0.30356683E
03
0.10991734E
01
0.109859448
01
0~302197008
03
320.0
0.3165213X
03
0.111032208
01
0.110963568
01
0.31508047E
03
330.0
0.32984382E
03
0.11220509E
01
0.11212455E
01
0.32832636B
03
340.0
0.34354800E
03
0.11343542E
01
0.113341648
01
0.341947568
03
350.0
0.35764652E
03
0.11472240I.S
01
0.11461412E
01
0.35595680E
03
360.0
0.37215216E
03
0.11606517E
01
0.11594135E
01
0.37036672E
03
370.0
0.38707808E
03
0.11746328E
01
0.11732270E
01
0~38518988E
03
380.0
0.402438066
03
0.11891649E
01
0.118757626
01
0~400438826
03 03
03
390.0
0.41824380.E
03
0.120423908
01
0.1202456lE
01
0.41612607E
400.0
0.43450981E
03
0.12198558E
01
0~1217862lE
01
0.43226414E
03
410.0
0.45124673E
03
0.12360040E
01
0.123379048
01
0.4488656lE
03
420.0
0.468470428
03
0.12526892E
01
0.125023758
01
0.46594314E
03
430.0
0.48619244E
03
0.12699039E
01
0.12672006E
01
0.4835094lE
03
440.0
0.504427098
03
0.1287648lE
01
0.12846772B
01
0.50157722E
03
450.0
0,52318493/Z
03
0.13059137E
01
0.130266553
01
0.52015947E
03
460.0
0.54248147E
03
0.132470448
01
0.132116386
01
0.53926921E
03
470.0
0$6232926E
03
0~1344017lE
01
0~13401713E
01
0.55891953E
03
480.0
0$8274207E
03
0.136385086
01
0.13596873E
01
0.57912376E
03
01
490.0
0.60373640E
03
0.13842125E
0.13797115E
01
0.59989530E
03
500.0
0.62532185E
03
0.14050912E
01
0~1400244lE
01
0.621247788
03
510.0
0~64751808E
03
0.142650086
01
0.142128558
01
520.0
0.67033339E
03
0.14484283E
01
0.14428366E
01
530.0
0.69378683E
03
0.147088496
01
0.14648985E
01
0.64319490E03 0.66575065803 0.68892908E03 0.71274449E03 O-73721135E03 0.76234433E03 0~78815828E03 0.81466828603 0~8418896lE03 0.86983770E03 0.89852829E03 0.92797727E03 0.95820077E03
540.0
0.7178906lE
03
0.149386708
01
0.14874727E
01
550.0
0.74266212E
03
0.15173817E
01
0.151056088
01
560.0
0.76811563E
03
0.15414290B
01
0.153416493
01
570.0
0.79426213E
03
0.1566002lE
01
0.1558287lE
01
580.0
0.82112707E
03
0.159112478
01
0.158293008
01
590.0
0.848713993
03
0.16167739E
01
0.16080962E
01
600.0
0.877051208
03
0.16429783E
01
0.16337886E
01
610.0
0.90614243E
03
0.16697159E
01
0.16600104E
01
620.0
0*93601304E
03
0.1697008lB
01
0.168676498
01
630.0
0.96667497E
03
0.17248496E
01
0.17140555E
01
293
Relative intensity calculations for carbon dioxide TABLE
1-contd.
Internal Partition Function
Harmonic Oscillator Vibrational Partition Function
Rigid-rotor Oscillator Partition
Harmonic Internal Function
640.0
0.998150938
03
0.175325518
01
0.174188588
01
0.98921511/Z
03
650.0
0.10304554E
04
0.178222368
01
0.177025976
01
0~10210369E
04
660.0
0.10635983E
04
0.181174578
01
0.17991812E
01
670.0
0.10976071E
04
0.184184348
01
0.18286544E
01
680.0
0.11324990E
04
0.18725199E
01
0.185868368
01
690.0
0.11682893E
04
0.19037753E
01
0.1889273lE
01
0.105368298 0~10871702E 0.11215160E 0.11567378E
04 04 04 04
700.0
0.12049899E
04
0.19356032E
01
0.19204275E
01
0.119285348
04
710.0
0.12426347E
04
0.19680346E
01
0.195215168
01
0.12298807/I
04
720.0
0.128122998
04
0.200105226
01
0~198444986
01
0.12678378E
04
730.0
0.13208006E
04
0.203467218
01
0.20173273E
01
0.13067434.Y
04
740.0
0.13613568&Y
04
0.206888528
01
0~20507891E
01
0.1346616lE
04
750.0
0.14029364.E
04
0.21037245E
01
0.20848400E
01
0.138747486
04
760.0
0.14455457E
04
0.21391750E
01
0.21194855E
01
0.14293387E
04
770.0
0.148920158
04
0.217523698
01
0.21547309E
01
0.14722273E
04
780.0
0.153393816
04
0.22119372E
01
0.21905813E
01
0.1516160lE
04
790.0
0.15797585E
04
0.224925476
01
0.22270425E
01
0.15611574E
04
800.0
0.16267072E
04
0.22872297E
01
0.22641198E
01
0.16072391E
03
810.0
0.167478858
04
0.23258446E
01
0.16544258E
04
820.0
0.17240296E
04
0.23651124E
01
0~23018190E 01 0.234014606 01
0.17027383E
04
830.0
0.177444108
04
0.24050236E
01
0.23791063E
01
0.17521974E
04
840.0
0.18260676E
04
0.244561718
01
0.24187059E
01
0’18028244E
04
850.0
0.187890788
04
0.248686546
01
0.24589508E
01
0.185464lOE
04
860.0
0~19330015E
04
0.252879878
01
0.24998470E
01
0.19076688E
04
870.0
0.198837238
04
0,25714234/Z
01
0.25414006E
01
0.19619299B
04
880.0
0.20450184E
04
0.26147141E
01
0.25836179E
01
0.20174466E
04
890.0
0.210299478
04
0.26587201E
01
0.26265050E
01
0.20742416E
04
900.0
0.21623026E
04
0.2703414lE
01
0.26700684E
01
0.21323377E
04
910.0
0.22229873E
04
0.27488339E
01
0.27143142E
01
0.219175806
04
920.0
0.228505298
04
0.279495878
01
0.275924906
01
0,22525260&Z
04
930.0
0.23485445E
04
0.28418223E
01
0.28048792E
01
0.231466538
04
940.0
0.241347038
04
0.28894090E
01
0.28512116E
01
0.2378200lE
04
950.0
0.24798582E
04
0.29377305E
01
0.28982525E
01
0.24431545E
04
960.0
0.25477374E
04
0.29867982E
01
0.29460088E
01
0.25095530E
04
970.0
0.26171415E
04
0.30366269E
01
0.299448728
01
0.25774206B
04
980.0
0.26880939,X?
04
0.3087222lE
01
01
0.26467824E
04
990.0
0.27605897E
04
01
01
0.27176637E
04
1000~0
0.28347041E
04
01
0.314432318
01
0.27900903E
04
1010.0
0.291042958
04
0.31385539E 0.319068538 0.32435838E
0.30436946E 0.30936375E
01
0.31957584E
01
0.28640883E
04
1020.0
0.29878139.E
04
0.329728078
01
0.32479502E
01
0.293968386
04
1030.0
0.30668955E
04
0.33517949E
01
0.33009056E
01
0.30169035E
04
10400
0.31476676E
04
0.3407094lE
01
0.33546319E
01
0.30957744E
04
1050~0
O-32301845E
04
0.34632155E
01
0.34091360E
01
0.31763234E
04
1060.0
0.3314447OE
04
0.352013598
01
0.34644254E
01
0.325857838
04
1070.0
0.34005164E
04
O-35778982/?
01
0.3520507lE
01
0.33425668E
04
1080.0
0.348842178
04
0.36365096E
01
0.357738866
01
0.34283170E
04
1090.0
0.357815646
04
0.36959396E
01
0.36350773E
01
0.35158572E
04
1100.0
04
0.375624548
01
0.36935804E
01
0.36052164E
04
1110~0
0.36697980E 0.37633492E
04
0.38174061E
01
0.375290558
01
0.369642328
04
1120.0
0~385885808
04
0.38794477E
01
0.38130602E
01
04
1130.0
0.39563326E
04
0.39423546E
01
0~38740519E
01
0.378950768 0.388449866
1140.0
0.40558112E
04
0.400613658
01
0.39358882E
01
0.398142658
04
1150.0
0.415732118
04
0.40708125E
01
0.39985769E
01
0.40803216E
04
1160.0
0.426092598
04
0.41364083E
01
0.40621256E
01
0.41812144E
04
1170.0
0.43666232E
0.420290216
01
0.41265421E
01
0.42841358E
04
1180.0
044744692E
04
0.42703234E
01
0.419183418
01
0.43891173E
04
1190.0
0.45844820E
04
0.433866688
01
0.42580095E
01
17.00~0
0.46967071E
04
044079517fi
01
0.43250762E
01
044961902E @46053867E
04 04
04
04
The vibrational energies observed by COURTOY@)for Wl‘302 were used where available, otherwise the values calculated by PLASS et ai.(5) from Courtoy’sconstants were employed.
294
L. D. GRAYand Jumrn E. SELVIDGE
When calculating the value of the partition function for a given temperature, one must obviously include all the vibrational levels that are significantly populated at that temperature. To insure that all possible levels were included, the following scheme was employed: for C02, the energy +(ui, ~2~,us) of level ZQUZ~U~ can be regarded as corresponding to some integral multiple of l ,(0110), i.e. E~(v~,z$, us) 21 (2~+ va+4us) Ed (0110). The vibrational levels with the coefficient K = (2s + aa + 4~s) the same were grouped together. Thus, group 4 consisted of the seven levels 0440, 0420, 1220,0400, 1200, 2000, and 0001. The number of vibrational levels in the Kth group is given by the sum of the binomial coefficients
(K*2’2)+ (y)+ (K*y2)+. . . -I (2)or
(32)
(5)
where K* = K/2 for K even and K* = (K- 1)/2 for K odd. The total number of levels K*+4 included in groups 0 through K (for even K only) is Thus, group 10 contains ( 4 )34 levels and 126 levels are included in groups 0 through 10. The number of vibrational levels which must be included in calculating the partition function at high temperatures makes the evaluation by direct summation impractical. For example, at 1200”K, 277 rotational levels were summed for each of 652 vibrational states. It required 1.5 min in IBM 7090 to compute the total partition function at this temperature. The rotational energy levels for the vth vibrational state are given by EJ = hc[&J(J+
1) --&J2(.7+
1)2]
where
Bv = Bo-
(6)
xaruc+ Cytprvj. rcj B
Values of the rotational constants were obtained either from COURTOY@)or calculated from equation (7) using Courtoy’s constants. The Bv values obtained from equation (7) should in many cases be corrected for Fermi resonance and, for states with I # 0, for Z-doubling. To check the effect of neglecting the Fermi resonance correction to the rotational constants, the sum S sl = {exp[-E,(lO’O)/kT]
c(u+
1) eXp[-CJ(loOO)/kT]
+ exp[ - ev(0200)/k T’j c(W+
1) exp [ -e&0200)/k T]}
was evaluated at 300°K using both the perturbed and the unperturbed values of the rotational constants. The results are given in Table 2a. The superscript 0 denotes unTABLE2a. THE PARTIAL SUM Sl AT 300’K Sl
(% Q) (e, vO)
(C”O,vO)
0.904998 0.904357
0.878434
perturbed values. The error introduced by neglecting the Fermi resonance in the rotational constants is 0.06 per cent, while the error amounts to 3 per cent if the resonance is
Relative intensity calculations for carbon dioxide
295
completely neglected as in column 3 of Table 2a. In the present calculation, the rotational partition function for each vibrational level was evaluated for states with 2 # 0 by summing over all J 2 I, i.e. the Z-splitting was neglected?. To estimate the effect of this approximation, the sum Sa, S2 = Jsddexp[ -~-(Ol~o)/kT]+ 2 exp[ -~+(Ol~o)/kT], J even
where the superscripts + and - denote the rotational energy computed for the even and odd J levels using the appropriate rotational constants, was compared with the similar sum over all lines using the average value of the rotational constant at 300°K. The results are given in Table 2b. The error in neglecting Z-doubling is seen to be 0.008 per cent. TABLE 2b. THE ROTATIONALPARlTTIONFUNCTIONFORTHEIXvEL(01’0) AT 300°K sz
#
III.
lJ-
532.747 532.706
RESULTS
The internal and vibrational partition functions are given in columns 1 and 2 of Table 1 for WrsOe as a function of temperature. Columns 3 and 4 show the corresponding values of the harmonic oscillator vibrational partition function and the classical internal partition function. At 12OO”K, both the internal and the vibrational partition functions are seen to be about 2 per cent larger than the values obtained using the harmonic oscillator approximation, while at 300°K they are approximately 0.5 and 0.05 per cent larger, respectively. The numerical values shown in Table 1 have the exponent of the power 10 indicated to the right of the number. Thus, qrnt(280”K) = 266.775. REFERENCES 1. H. W. WOOLLEY,Thermodynamic functions for carbon dioxide in the ideal gas state, J. Res. Nat. Bur. Stand. Wash. 52, 289-292 (1954). 2. National Bureau of Standards Circulars No. 500 (1952) and No. 564 (1955). 3. R. H. TOURINand P. M. HENRY. Infrared snectral emissivities and internal enerxv distribution of carbon dioxide at high temperatures. Part I. Internal energy calculations, Scientific-Report No. 2 on Contract AF 19(604)-2223, Warner and Swasey, Flushing, New York (1958). 4. C. P. COURTOY,Spectres de vibration-rotation de molecules simples diatomiques ou polyatomiques avec long parcours d’absorption, Canad. J. Phys. 35, 608-648 (1957); C. P. COURTOY,Spectre infrarouge a grande dispersion et constants moleculaires du COZ, Ann. Sac. Sci. Bruxelles, 75,5-230 (1959). 5. V. R. STULL,P. J. WYATTand G. N. PLASS,Vibrational energies of the COa molecule, J. Chem. Phys. 37, 1442-1445, (1962); see also V. R. STULL, P. J. WYATTand G. N. PLASS. Infrared transmission studies, Final Report, Volume III, The infrared absorption of carbon dioxide, Report SSD-TDR62-127-Volume III, Aeronutronic Division, Ford Motor Company, Newport Beach, California (31 January, 1963). t Average values of the rotational constants were used.
L. D. GRAY
296
Part II. Relative Intensity of Carbon Dioxide Lines in VibrationRotation Bands arising from Transitions from the Ground State and from the First Excited State L. D. GRAY Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California (Received
6 August 1964)
I. INTRODUCTION INTENSITIES of rotational lines, relative to the integrated intensity of a vibration-rotation band, depend primarily upon the rotational constants of the lower vibrational state. For temperatures of interest in planetary atmospheres many of the strong absorbing bands of carbon dioxide have either the (OOOO)or (0110) state as the lower vibrational state. As an aid in interpreting observed spectra, we have tabulated the relative intensities for X-E,, X-Il, Il-Xi, II-II, and II-A transitions at 300°K. II.
THEORY
The integrated intensity SW,>,J”, 1” -+ v’, J', I', of a rotational line (J” +J’) vibrational band (a”, I” + v’, 1’) is given by-j-
S u”,
in the
87~~Nv~<,J" J”,Z”
~
.$,
J’,l’
=
3hc
-(I+)”
x (l?:::+y]/32[1
J” p
.
-exps]
,l”,v’,J’,l’
(1)
where NW!), Jr//p is the number of molecules per unit volume per unit pressure in the lower state with the vibrational quantum numbers denoted by v” and the rotational quantum number J”, I is the quantum number of the angular momentum associated with the doubly degenerate vibration ~2, /3 = fl(v” -+ v’) is the matrix element for the vibrational transition, wvu”, J,', lo, + 2)f,J,, 2' is the wave number of the transition (v”, J”, I” 1” -91’ is the rotational matrix element. In terms of the integrated -+ v’, J’, I’) and R ( J"+J, > intensity Q,,, 1rp+vj,l~ for the band, 8~3 N,y dcz)~‘,J”-t v’,l’ = --wv”,l”,v’,l 3hc p equation (1) may be written as
(2)
(3) t Ref. 1, equation
(7-128a).
Relative intensity calculations
297
for carbon dioxide
It is apparent from equation (2) and the ideal gas law that the temperature of the band intensity is given by
[l -exp( -hcw/kT)]
(4)
-h~wpcroj]
x [l -exp(
dependence
In terms of the band intensity at To, the integrated intensity of a line can be written as
[l
-exp(-hcWf,J-,
~/kT$j
“&,J’
(5)
where SOv’t,J,,(T)
ToQv( To) EZ
TQv(
T>
x gJexpt - wJ,,hc/kT] &Y(T)
here Qv is the vibrational partition function, QR is the rotational partition function C&L”‘, is the energy (in cm-i) of the lower vibrational state, WJ” is the energy of the lower rotational state and is given by WJ” = &J”(J”
+ 1) - Dv#“(J”
+ 1)]2.
(7)
The quantity Sov I ,, J, JT) is given in Table 3 as a function of J” for transitions from the ground state (i.e. C -+ X and X +II) and for transitions from the first excited state (i.e. Il -+ Z, Il. -+ lT, and II-+ A) for a temperature of 300°K. To obtain the intensity of a line in any particular band, the constants of the upper vibrational state which appear in equation (5) must be used. As a first approximation, however, equation (5) can be replaced by &“,Js’~“+
,,‘,J,‘l’
2:
&,“,l”
+
v’
v(
To)~“v~~,J*,(
T).
(8)
The reference temperature chosen was To = 300°K. Equation (4) may be used to obtain the band intensity at this temperature from measurements made at other temperatures. It should be noted that many investigators choose 273°K as a reference temperature in reporting band intensities. REFERENCE 1. S. S. PENNER,Quantitative Molecular Spectroscopy and Gas Emissivities, Addison (1959).
Wesley, Reading,
L. D. GRAY
298
PI-PI
J
R-branch
Q-branch
PI-DELTA P-branch
R-branch
Q-branch
P-branch
1
0~2805OE-02
0~28OSOE-02
0.
0~561OlE-02
0.
2
0.49495E-02
0.15467E-02
0.27841E-02
0.61868Eo2
0.30934E-02
0.
3
0.68823E-02
0.10706E-02
0~48941E-02
0.68823E-02
0.53529E-02
0.61176E-03
4
0~86783E-02
0~81359E-03
0.67799-2
0.75935m2
0.73223E-02
0~1356OE-02
5
0~10351E-O1
0.6506lE-03
0.8517lE-02
0~82805E-02
0.91085E-02
0.21293E-02
6
O~11897B-Ol
0~537OOE-03
0~10120E-01
0.89224E-02
0~1074OE-01
0.28915E-02
7
0~13309E-01
0.45267E-03
0~11588E-01
0.95061B-02
0.12222E-01
0.36214%02
0.
8
0.14578E-01
0.38723E-03
0.12915E-01
0~10022E-01
0.13553E-01
0~43051E-02
9
0~15698E-01
0.33474M3
0~14094E-01
0~10465E-01
0.14729E-01
0.4933OE-02
10
0~16661E-01
0.29157E-03
0~15120E-01
0~10830&01
0.15745E-01
0.54981E-02
11
0.17464E-01
0.25536E-03
0~15988E-01
0~11114E-01
0~16598Gol
0.59954E-02
12
0~18106E-O1
0.22453E-03
0.16696E-01
0~11316E-01
0~17289E-01
0.64216E-02
13
0~18587E-01
0.19796E-03
0.17245E-01
0~114383-01
0~17817E-01
0.67747&02
14
0~18908E-01
0.17485%03
0.176363-01
0~11480E-01
0~18185E-01
0.70544E-02
15
0.19076E-01
0~1546OE-03
0.17874E-01
0.11446E-01
0~18398601
0.72614E-02
16
0~19097E-01
0.13676E-03
0~179663-01
0~11339&01
0.18463E-01
0.73976E-02
17
0.18979E-01
0.12097E-03
0~17918E-01
0~11164E-01
0.18388&01
0.74657E-02
18
0~18732E-01
0.10696E-03
0~17740601
0~10927E-01
0~18183E-01
0.74697E-02
19
0~18367E-01
0.9448913-04
0~17444E~l
0~10634E-01
0~17858E-01
0.74138E-02
20
0.17897E-61
0~83382E-04
0~1704OE-01
0,10291E-01
0.17427s01
0~73031E-02
21
0.17333E-01
0.7348lE-04
0.16542E-01
0.99046602
0~169OlE-01
0.71431E-02
22
0~16689E-01
0.64654E-04
0.15961E-01
0.94826E-02
0.16293E-01
23
0.15979E-01
0.56787E-04
0~15311E-O1
0.90316E-02
0~15617E-01
24
0~15215E-01
0.49782E-04
0~14604E-01
0~85584E-02
0~14885E-01
0.69396E-02 0.66985E-02 0.64259E-02
2.5
0~14410&01
0.4355OE-04
0~13854E-01
0.80695E-02
0~14110&01
0.61277E-02
26
0.13576Ml
0.38014E-04
0.13072&01
0.75713E-02
0~13305E-01
27
0.12725%01
0.33106E-04
0.1227OE-01
0~12481E-01
0.58097E-02 0.54775E-02
28
0~11868E-01
0~28761E-04
0~11458E-01
0.70696E-02 0.65697E-02
0~11648E-01
0.51361E-02
29
0~11014E-01
0.2492413-04
0.10646E-01
0.607641342
0~10817E-01
0.47905E-02
30
0~10171E-01
0.21543E-04
0.98424E-02
0.55942E-02
0.9996lEXt2
0.444501342
31
0.93484E-02
0~1857lE-04
0.90557E-02
051266&02
0.91928E-02
0.41034E32
32
0.85517E-02
0.15966E-04
0.82921602
0.4676713102
0.84139E-02
0.37691Ea2
33
0.77865E-02
0.13687&04
0~75571E-02
0.42472E-02
34
0.7057
0~11701E-04
0.68551E-02
0.38399E-02
0.76649E-02 0.69503E-02
0.31338E-02 0.2837OE-02 0.25563E-02
lE-02
0.34451Ea2
35
0.63669E-02
0.99736ZXl5
0~61898E-02
0.34563E-02
0.62734E-02
36
O-57184E-02
0.84763605
0.55636E-02
0.30975E-02
0.56368602
37
0~5113OE-02
0.71824E-05
0.49782EO2
0.27638B-02
0.5042OE-02
0.22926E-02
38
0.45514E-02
0.60675E-05
0.44346E-02
0.24554Ea2
0~449OOE-02
0.20467E-02
39
0.40338E-02
0~51101E-05
0.39328E-02
0.2172OE-02
0.39808E-02
0~18189E-02
40
0.35594E-02
0.42904E-05
0.34725E-02
0.19132&02
0.35138E-02
0.16092E-02
41
0.31273E-02
0.359lOE-05
0.30527E-02
0.1678lE-02
0.30882E-02
0.14173E-02
42
0~27358E-02
0.2996lE-05
0.267213-02
0~14656E-02
0~27025E-02
0~12428B.02
43
0.23831E-02
0.24918Ea5
0.23289E-02
0.12747E-02
0.23548E-02
0.10851E-02
44
0.20671E-02
0~20658E-05
0~2021lE~2
0~1104OE-02
0.2043OE-02
0.94317E-03
45
0.17854E-02
O.l7071E-05
0.1746513-02
0.9522OC03
0.17651E-02
0.81631E-03
46
0~15356E-02
O.l4061E-05
0.15029E-02
0~81787E--o3
0~15185E-02
0,70348E-03
47
0.13152E-02
0.11543E-05
0~12878E-02
0.6996OE-03
0.13009Ea2
0.60366E-03
48
0~11218E-02
0.59597E-03
0~11099&02
0.51581E-03
0.95288E-03
0,94459E-06 0.77039E-06
0.10989E-02
49
0.9338lE-03
0.50561E-03
0.94296E-03
0~43889E-03
50
0~80605E-03
0.62624E-06
0.79023E-03
0.42721E-03
0.79783%03
0~37187E-03
51
0.67904Ea3
0.50736E-06
0.35949E-03
0.67225E-03
0.31378E-03
52
0.56971E-03
0.40968E-06
0.66597E-03 0.55895E-03
0~30129E-03
0.56412603
0.26366E-03
53
0~47603E-03
0.32969E-06
0.46721E-03
0.25149E-03
0.47145603
0.22062E-03
54
0.39614E-03
0.26442E-06
0.38893E-03
0,20907E-03
0,3924OE-03
0~18386E-03
55
0.32832E-03
0~21136E-06
0.32245E-03
0.1731lE-03
0.32528E-03
0.15259E-03
56
0.271OlE-03
0.16837E-06
0.26625E-03
0.14276E-03
0~26855E-03
0.12612E-03
57
0.2228lE-03
0.13367B-06
0.21896E-03
0.11727E-03
0.22082E-03
0.10382E-03
58
O.l8244E-03
0.10575E-06
0.17935E-03
0.95939E-04
0~18084cO3
0~85114E-04
59
0.14879E-03
0.83385E-07
0.14631E-03
0.78178E-04
O.l4751E-03
0.69497E-04
60
0.12086SO3
0.6552lE-07
0~11888Eo3
0.63452E-04
0.11984E-03
0.5651613-04
Relative intensity calculations for carbon dioxide Tmm
3-contd. PI-DELTA
PI-PI
R-branch
J
299
Q-branch
P-branch
R-branch
Q-branch
P-branch
61
0.9778SE-04
0.51307E-07
0.96207E-04
0.51297E-04
0.96970%04
0.45776604
62
0~78800%04
0~40038E-07
0.77548E-04
0.41306E-04
0.78154E-04
0~36928E-04
63
0.63249E-04
0.31136607
0.62260604
0.3313OE+t
0.627393104
0.29671E-04
64
0~50566E-04
0.24129&07
0.49788E-04
0.26468604
0~50165E-04
0.23745E-04
65
0.40267E-04
0.18635&07
0.39657E-04
0~21063E-04
0~39952GO4
0.18927E-04
66
0.31939E-04
0~14341E-07
0.31462604
0.16696E-04
0.31694E-04
O.l5027E-04
67
0.25234604
0.10998&07
0.24863E-04
0~13182E-04
0.25043E-04
0~11883E-04
68
0~19859E-04
0~84053E-08
0~19571&04
0.10367E-04
0~1971OE-04
0.93599E-05
69
0~15567E-04
0%4012&08
0.15344E-04
0.81219E-05
0.15452E-04
0.73434-5
70
0~121SSE-04
0~48579E-08
0.11984Eo4
0~6338OE-05
0.12067E-04
0.57387E-05
71
0~94539E-05
0.36737E-08
0.93225605
0.49267E-05
0.93864E-05
0.44670E-05
72
0.73244E-05
0.2768SE-08
0.7224OE-05
0.38148E-OS
0.72728E-05
0.346363-05
73
056525E-05
0~2079OE-08
0~55761&05
0.29424E-05
0.56132E-05
0.2675OCOS
74
0.43453605
0~15557E-08
0.42873Ea5
0.22607B-05
0~43155605
0~20579E-05
75
0~33274E-05
0~116OOE-08
0.32836E-05
0~17303E-05
0~33049E-05
0~15770%05
76
0.25381E-05
0.8619SE-09
0~25052E-05
0.13 192E-05
0.25212E-05
0~12038E-05
77
0.19286&05
0.63821609
0~19038EX5
0~10019E-O5
0~19159&05
0.91531E-06
78
0~14598E-05
0.47087-
0.14413E-05
0.75795&06
0~14503&05
0.69327E-06
79
0~11007E-05
0~34618E-09
0~10869E-05
0.57122E-06
0.10936E-05
0.52306E-06
80
0.82669606
0.25361E-09
0.81648E~36
0~42884E-06
0.82146E-06
0.39312E-06
81
0~61853E-06
0~18514E-09
0,61098&06
0.32072606
0.61466E-06
0.29432E-06
82
0.461OlE-06
0.13467M9
0.4554SE-06
0,23894E-06
0.45816M6
0.219SOE-06 0.16307E-06
83
0.34229&06
0.97618610
0.33821&06
0.17733E-06
0.3402OE-06
84
0~25316E-06
0~70507610
0.25018E-06
0~1311OE-06
0.25164E-06
0.12068M6
85
0~18653E-06
0~50745610
0.18436E-06
0.96557%07
0.18542E-06
0.8896SE-07
86
0.13691E-06
0.36392610
0.13534&06
0.70843E-07
0~13611E-06
0.6533SE-07
87
O~lOOllE-06
0.26006E-10
0.98969E-07
0.51779E-07
0.99524%07
0.47797607
88
0.72917E-07
0~18518E-10
0.72097E-07
0~37701&07
0.72498&07
0.34834E-07
89
0.5291oE-07
0.13139IC10
0.52322E-07
0.27347E-07
0.52609M7
0.25289E-07
90
0.38247E-07
0,92896E-11
0,37826&07
0.19761E-07
0.38032E-07
0~1829OE-07
91
0.27542&07
0.65445611
0.27242607
0.1422SE07
0.27389E-07
0.13177607
92
0.19758607
0.45942611
0.1954SM7
O.l0201E-07
0.19649E-07
0~9457SE-08
93
0.1412OE-07
0.32136611
0.1397OE-07
0~72879E-08
0~140443-07
0.67621E-08
94
0~10053&07
0,22399&l
0.99471E-08
0~51869E-08
0,99989&4l8
0~4816SE-08
9s
0~71302E-08
0~15557E-11
0.70559E-08
0.36777E-08
0.70922&08
0.34177E-08
96
0.5038OE-08
O.l0766E-11
0.49861608
0.25977E-08
0.501 lSE-08
0.24159E-08
97
0.35463=8
0.742393-12
0~35101&08
0~1828OE-08
0.35278E-08
0~17013E-08
98
0.24869E-08
0~51011612
0.24617E-08
0~12815E-08
0~2474OE-08
0.11936E-08
99
0.17373E-08
0,34926E-12
0~17200608
0,89499&09
0~1728SE-08
0.83418E-09
100
0.12092608
0.23827612
O.l1972E-08
0.62271E-09
0~1203OE-08
0.58081E-09
101
0~83838E-09
0.16198612
0.83016609
0.43164609
0.83419E-09
0.40287E-09
102
0.5791 lE-09
O.l0972E-12
0.573493-09
0.29807E-09
0.5762SE-09
0~27839E-09
103
0.3985X-09
0.74056613
0.39469E-09
0~20507609
0.39657E-09
SUM
0~51379E-Oa
0~10995E-O1
0~47519?&00
0.31868&00
0~48914C-00
1
0.1916SE-09
L. D. GRAY
300
TABLE PI-SIGMA R-branch
.I
3-conrd. Transitions Q-branch
P-branch
1
0~187OOE-02
0~56101E-02
3
0~55059E-02
0.12847E-01
0,3740OE-02 0.73412E-02
5
0~88719JG02
0,19518E-01
0.10646E-01
I
0~11830&01
0,2535OE-01
0,1352OE-01
9
0.1427OE-01
0,30127E-01
O.l5856E-01
11
O.l612lE-01
0.33708E-01
0~17587E-01
13
0~17347E-01
0,36029E-01
0.18682E-01
15
O.l7954E-01
0.37105E-01
0~1915lE-01
17
0’1798OE-01
0,37018E-01
O.l9038E-01
19
0.17493E-01
0.35906E-01
0.18413601
21
0,16579E-01
0~33948&01
0.17369E-01
23
0~1534OE-01
0.31347s01
0~16007E-01
25
O.l387bE-01
0,28307E-01
0~14431&01
27
0,12286E-01
0~25028E-01
0.1274lE-01
29
0~10658E-01
0.21684E-01
O.l1026E-01
31
0.906528-02
O.l8423E-01
33
0~7564OE4l2
O.l5357E-01
35
0,61949E-02
0~12567E-01
37
0.49819E-02
0~10098E-01
39
0,39354E-02
0.79717E-02
41
0.30546E-02
0,61836E-02
43
0.23302E-02
0.47145E-02
45
0~17474E-02
0.35336E-02
47
O.l2884E-02
0.26042E-02
49
0.9342OE-03
0.18875E-02
51
0.66623E-03
0.13455E-02
53
0.46737E-03
0.94356E-03
55
0.32256E-03
0.65098E-03
57
0.21903E-03
0.44190603
59
O.l4635E-03
0.29518E-03
61
0.96233E-04
O.l9404E-03
63
0.62276E-04
0.12554E-03
65 67 69
0.396bbE-04
0.79942604
0,24869E-04
0,50108E-04
0,15348E-04
0.30918E-04
71
0.93244E-05
0~1878Ofi~04
0.9357bE-02 0~77932E-02 0.63719E-02 0.51165E-02 0.40363E-02 0.3129lE-02 0,23843E-02 0~17862E-02 0~13158E-02 0.9532bE-03 0.67929E-03 0.47619E-03 0,32842E-03 0.22287E-03 O.l4883E-03 0.978lOE-04 0.63264E-04 0.40276M4 0~2524OE-04 0,1557OE-04 0.94557605
73
0,5577lE-05
O.l1231E-04
0.56535E-05
75
0.32842E-05
0.66122E-05
0,3328OE-05
77
0.19042E-05
0.3833lE-05
0,19289E-05
79
0~1087lE-05
0.21879E-05
0~11008E-05
81
0~61108E-06
0,12297E-05
0.71862E36
83
0.3382bE-06
0.68059E-06
0.34233E-06
85
0.18439E-06
0.37094E-06
0.18656E-06
87
0.98982607
0~199lOE-06
0~10012E-06
89
0.52329E-07
0.10525E-06
0,52917E-07
91
0.2724bE-07
0.54791E-07
0,27545E-07
93
0~13972fi-07
0.28093E-07
0.14122E-07
95
0~7056bE-08
0.14188607
0.61309&08
97
0.35105s08
0~7057lE-08
0.35467E-08
99
0~172OlE-08
0.34577E-08
0.1737SE-08
0.83024E-09
0.16687E-08
0.83846E-09
101 SUM
0.241 lbE-00
0.2599lE-00
Relative intensity calculations TABLE
for carbon dioxide
3-conrd. SIGMA-PI
SIGMA-SIGMA
Transitions
Transitions P-branch
R-branch
J
301
R-branch
Q-branch
P-branch
0.
0.
0’18942E-02 0.54042&02 0,86436E-02
0
0,37402E-02
0.
2
0~11095E-01
0.73968E-02
0,37402E-02 0.73968E-02
4
O.l8014E-01
0~14411E-01
0~10808E4ll
6
0.24202E-01
0~20745E-01
0.1383OE-01
8
0~29418E-01
0.2165OE-01
0~16343E-01
0.9246OE-02 0~16212E-01 0.22473E-01 0.27784E-01
10
0~33488E-01
0~30443E-01
O.l8266E-01
0,31965E-01
0,13699E-01
12
0.36312E-01
0~33519E-01
0.19553E-01
0,34916E-01
O.l5363E-01
14
0.37872E-01
0.35347E-01
0,20198E-01
0,36609E-01
0~16411E-01
16
0~3822OE-01
0.35972E-01
0.20234E-01
0.37096E-01
O.l6862E-01
18
0.37473E-01
0.35JOlE-01
0.19723E-01
0.36487E-01
O.l6764E-01
20
0.35793E-01
0.34089E-01
O.l8749E-01
0,34941E-01
O.l6192E-01
22
0.33376E-01
0~31925E-01
O.l7414E-01
0,32651E-01
0.15237E-01
24
0.30428E-01
0~29211E-01
O.l5823E-01
0,2982OE-01
0.13997E-01
26
0,27154E-01
0,26149E-01
0’1408OE-01
0.26652E-01
0.12571E-01
28
0.23742E-01
0.22923E-01
O.l228OE-01
0,23333E-01
O.l1052E-01
30
0.20353E-01
0.19697E-01
0~10505E-01
0.20025G01
0.952OlE-02
32
0~17118E-01
0.16599E-01
0,88183E-02
0~16859601
0.80402E-02
34
0~14131E-01
0.13728E-01
0.72675E-02
0.13929E-01
0.66619&L02
36
0~11455E-01
0~11146E-01
0.58824E-02
O.l13OOE-01
0.5418OE-02
38
0.91216E-02
0.88877E-02
0,46778E-02
0.90047E-02
0.43269E-02
40
0.7137OE-02
0,69629E-02
0.36555E-02
0.705OOE-02
0.33944E-02
42
0.54884E-02
0.53607E-02
0.2808OE-02
0.54246E-02
0.26166E-02
44
0.41491E-02
0.40569E-02
0.21207E-02
0.4103OE-02
0,19823E-02
46
0~30841E-02
0.30185E-02
0.15749E-02
0~30513E-02
O.l4764E-02
48
0.22545E-02
0.22085E-02
0.11502E-02
0.22315E-02
0,10812E-02
50
0~16209E-02
0.15892E-02
0.82636E-03
0~16051E-02
0,77869E-03
52
0’11464E-02
0.11248E-02
0.58404E-03
0,11356E-02
0.55159E-03
54
0.79773E-03
0.78323E-03
040612E-03
0.79048E-03
56
0.54616%03
0.53658E-03
0.27787%03
0~54137E-03 0.36484E-03
0.38436E-03 0,2635OE-03 0,17774E-03
O.l144OE-01
58
0.36795E-03
0,36172E-03
0.1871OE-03
60
0,24396E-03
0,23996E-03
0.12398E-03
0.24196E-03
0,11798E-03
62
0~15919E-03
O.l5666E-03
0~80857E-04
0.15792E-03
0,77067E-04
0~51906fi-04
O.l0145E-03
0,49547x%04
0.32800%04
0,64153E-04
0.31353E-04
0~20404E--o4
0.39933E-04
0.19529E-04
0.12496&L04
0,2447OE-04
0.11975E-04
0.7534lE-05
0,14763E-04
0.72286E-05
044725E-05
0.87685E-05
0.4296OE-05
0.26143E-05
0.5128OE-05
0.25137605
0.15047605 0.85279E-06 0.47595E-06 0.2616OE-06 0.1416OE-06 0.75486E-07 0.39633E-07 0.20495E-07 0.10439E-07 052373E-08 0,25882E-08 0~12599E-08
0.29529E-05 0.16744E-05 0.93491E-06
0.14482E-05
64
0.10224E-03
66
0.64635E-04
68
040225E-04
76
0.51615E-05
0~10067E-03 0.6367OE-04 0.39642E-04 0.24297E-04 0.14661E-04 0,87097E-05 0~50945E-05
78
0,29717E-05
0.29341E-05
80
0.16848E-05
O.l664OE-05
82
0~94058E-06
0.92924E-06
84
0.51711E-06
0~51103fi-06
86
0~27998E-06
0,27676E-06
88
0.14929E-06
0~14762E-06
90
0.78405E-07
0.77543E-07
92
0~40555E-07
0.40118E-07
94
0.20661E-07
0~20443E-07
96
0.10368E-07
0~10261E-07
98
0.51246608
0.50728E-08
0.24951E-08
0.24704E-08
70
0.24644E-04
72
0,14864E-04
74
0.88274E-05
100 SUM
0.27952E-00
0.82159E-06 0.45896E-06
0.51407E-06
0.25247E-06
0.27837E-06
0.13677E-06
0.14846E-06
0.7297OE-07
0.77974Ea7
0,38341E-07
040337E-07
O.l9841E-07
0.20552E-07
0,10113E-07
0~10314E-07
0.5077OE-08
0,50987E-08
0.25105E-08
0.24827E-08
O.l2228E-08
Radial.
Pcrgamon PressLtd., 1965.Printedin GreatBritain
Transfer. Vol. 5, pp. 291-301.
RELATIVE INTENSITY CALCULATIONS CARBON DIOXIDE L. D. Jet Propulsion
Laboratory,
GRAY
JUDITH E. SELVIDGE
and
California
FOR
Institute
of Technology,
Pasadena,
California
(Received 6 August 1964) Abstract-Internal and vibrational partition functions of WYOZ are tabulated for the temperature range 150-1200°K at 10°K intervals. Rotational line intensities, relative to the total intensity of the band at 3OO”K, are presented for transitions arising from the state 0000 and from the state 0110.
Part I. Internal Partition Function I. INTRODUCTION
To INTERPRET the results of experimental studies of carbon dioxide absorption in the infrared, it is necessary to know how the intensity of each rotational line varies with temperature. This variation requires a knowledge of the internal and vibrational partition functions. The internal partition function of carbon dioxide has already been calculated at many temperatures in order to obtain the corresponding thermodynamic functions(r*s), but the only explicit tabulation of the partition function is that of TOURIN and HENRY(~) which considers six temperatures ranging from 298 to 1273°K. The values which we present were calculated for the temperature range from 150 to 1200°K in increments of 10°K. II.
THE
INTERNAL
PARTITION
FUNCTION
The internal partition function, qint, is given by qint = C,gV exp[ -4Wk
Cl zJg7 exp[ -44
Q/k Tl
(1)
where r,(z$ is the vibrational energy above the zero point vibrational energy of the molecule, EJ(.~,vt) the rotational energy, g, the degeneracy of the vibrational level (without rotation), and gJ the degeneracy of the rotational sublevel (without vibration). The summation is over all rotational levels for each vibrational level. If the interaction between vibration and rotation is neglected, so that EJ(J, Q) = lJ(a, then the internal partition function can be written as the product of two factors: the vibrational and the rotational partition functions, qVib and qrot; i.e. qint =
qvibqrot
(2)
where qvib =
&;t+
exP[-+(U#)/kT]
291
(3)
292
L. D.
and
GRAY
and qrot =
c
.gJ
JUDITH
E.
SELVIDGE
exp[-dJ)/kT].
In the present calculations, the internal partition function was evaluated directly from equation (1) and the vibrational partition function was obtained from equation (3). For comparison, the partition function for a harmonic-oscillator rigid-rotator was also calculated. The results are given in Table 1. TABLE 1. VIBRATIONAL AND STERNAL
Temperature (“K)
Internal
PARTI~ON
Partition
Function
~LJNCTIONS OF lzC’BOz
Vibrational
Partition
Function
FOR THE TBMPERATURE RANCE 150 to 1200°K
Harmonic
Oscillator
Vibrational
Partition
Function
Rigid-rotor Oscillator Partition
Harmonic Internal Function
150.0
0.13421232E
03
0.1003329lE
01
0.10033275E
01
0.1335442lE
160.0
0.14338238E
03
0.10049753E
01
0.10049720E
01
0.14268064E
03
170.0
0.15265334E
03
0.10070969E
01
0~10070908E
01
0.151917796
03
180.0
0.16204501E
03
0.10097385E
01
0~1009728lE
01
0.161275368
03
190.0
0.171577336
03
0.10129359E
01
0.101291928
01
0.170773llE
03
ZOO.0
0.1812702SE
03
0.1016719lE
01
0~101669dEE
01
0.180430526
03
210.0
0.191142756
03
0.10211056E
01
0.102106226
01
0.190266625
03
220.0
0.201213636
03
0.10261085E
01
0.1026046lE
01
0~20029987E
03
230.0
0~21150100E
03
0.103173668
01
0.10316496E
01
0.210548038
03
240.0
0.22202230E
03
0.103799338
01
0.103787596
01
0.221028236
03
250.0
0.232794408
03
0.10448799E
01
0.1044724lE
01
0.231756926
03
260.0
0.2438333lE
03
0.10523920E
01
0.105219llE
01
0.242749916
03
270.0
0.25515532E
03
0.106052878
01
0.106027208
01
0.25402249E03
280.0
0.26677556E
03
0.10692839E
01
0~106896038
01
0.26558938E
03
290.0
0.27870768E
03
0.10786462E
01
0~10782486.E
01
0.277464888
03
300.0
0.29096700E
03
0~1088613l.E
01
0.10881294E
01
0.289662908
03
310.0
0.30356683E
03
0.10991734E
01
0.109859448
01
0~302197008
03
320.0
0.3165213X
03
0.111032208
01
0.110963568
01
0.31508047E
03
330.0
0.32984382E
03
0.11220509E
01
0.11212455E
01
0.32832636B
03
340.0
0.34354800E
03
0.11343542E
01
0.113341648
01
0.341947568
03
350.0
0.35764652E
03
0.11472240I.S
01
0.11461412E
01
0.35595680E
03
360.0
0.37215216E
03
0.11606517E
01
0.11594135E
01
0.37036672E
03
370.0
0.38707808E
03
0.11746328E
01
0.11732270E
01
0~38518988E
03
380.0
0.402438066
03
0.11891649E
01
0.118757626
01
0~400438826
03 03
03
390.0
0.41824380.E
03
0.120423908
01
0.1202456lE
01
0.41612607E
400.0
0.43450981E
03
0.12198558E
01
0~1217862lE
01
0.43226414E
03
410.0
0.45124673E
03
0.12360040E
01
0.123379048
01
0.4488656lE
03
420.0
0.468470428
03
0.12526892E
01
0.125023758
01
0.46594314E
03
430.0
0.48619244E
03
0.12699039E
01
0.12672006E
01
0.4835094lE
03
440.0
0.504427098
03
0.1287648lE
01
0.12846772B
01
0.50157722E
03
450.0
0,52318493/Z
03
0.13059137E
01
0.130266553
01
0.52015947E
03
460.0
0.54248147E
03
0.132470448
01
0.132116386
01
0.53926921E
03
470.0
0$6232926E
03
0~1344017lE
01
0~13401713E
01
0.55891953E
03
480.0
0$8274207E
03
0.136385086
01
0.13596873E
01
0.57912376E
03
01
490.0
0.60373640E
03
0.13842125E
0.13797115E
01
0.59989530E
03
500.0
0.62532185E
03
0.14050912E
01
0~1400244lE
01
0.621247788
03
510.0
0~64751808E
03
0.142650086
01
0.142128558
01
520.0
0.67033339E
03
0.14484283E
01
0.14428366E
01
530.0
0.69378683E
03
0.147088496
01
0.14648985E
01
0.64319490E03 0.66575065803 0.68892908E03 0.71274449E03 O-73721135E03 0.76234433E03 0~78815828E03 0.81466828603 0~8418896lE03 0.86983770E03 0.89852829E03 0.92797727E03 0.95820077E03
540.0
0.7178906lE
03
0.149386708
01
0.14874727E
01
550.0
0.74266212E
03
0.15173817E
01
0.151056088
01
560.0
0.76811563E
03
0.15414290B
01
0.153416493
01
570.0
0.79426213E
03
0.1566002lE
01
0.1558287lE
01
580.0
0.82112707E
03
0.159112478
01
0.158293008
01
590.0
0.848713993
03
0.16167739E
01
0.16080962E
01
600.0
0.877051208
03
0.16429783E
01
0.16337886E
01
610.0
0.90614243E
03
0.16697159E
01
0.16600104E
01
620.0
0*93601304E
03
0.1697008lB
01
0.168676498
01
630.0
0.96667497E
03
0.17248496E
01
0.17140555E
01
293
Relative intensity calculations for carbon dioxide TABLE
1-contd.
Internal Partition Function
Harmonic Oscillator Vibrational Partition Function
Rigid-rotor Oscillator Partition
Harmonic Internal Function
640.0
0.998150938
03
0.175325518
01
0.174188588
01
0.98921511/Z
03
650.0
0.10304554E
04
0.178222368
01
0.177025976
01
0~10210369E
04
660.0
0.10635983E
04
0.181174578
01
0.17991812E
01
670.0
0.10976071E
04
0.184184348
01
0.18286544E
01
680.0
0.11324990E
04
0.18725199E
01
0.185868368
01
690.0
0.11682893E
04
0.19037753E
01
0.1889273lE
01
0.105368298 0~10871702E 0.11215160E 0.11567378E
04 04 04 04
700.0
0.12049899E
04
0.19356032E
01
0.19204275E
01
0.119285348
04
710.0
0.12426347E
04
0.19680346E
01
0.195215168
01
0.12298807/I
04
720.0
0.128122998
04
0.200105226
01
0~198444986
01
0.12678378E
04
730.0
0.13208006E
04
0.203467218
01
0.20173273E
01
0.13067434.Y
04
740.0
0.13613568&Y
04
0.206888528
01
0~20507891E
01
0.1346616lE
04
750.0
0.14029364.E
04
0.21037245E
01
0.20848400E
01
0.138747486
04
760.0
0.14455457E
04
0.21391750E
01
0.21194855E
01
0.14293387E
04
770.0
0.148920158
04
0.217523698
01
0.21547309E
01
0.14722273E
04
780.0
0.153393816
04
0.22119372E
01
0.21905813E
01
0.1516160lE
04
790.0
0.15797585E
04
0.224925476
01
0.22270425E
01
0.15611574E
04
800.0
0.16267072E
04
0.22872297E
01
0.22641198E
01
0.16072391E
03
810.0
0.167478858
04
0.23258446E
01
0.16544258E
04
820.0
0.17240296E
04
0.23651124E
01
0~23018190E 01 0.234014606 01
0.17027383E
04
830.0
0.177444108
04
0.24050236E
01
0.23791063E
01
0.17521974E
04
840.0
0.18260676E
04
0.244561718
01
0.24187059E
01
0’18028244E
04
850.0
0.187890788
04
0.248686546
01
0.24589508E
01
0.185464lOE
04
860.0
0~19330015E
04
0.252879878
01
0.24998470E
01
0.19076688E
04
870.0
0.198837238
04
0,25714234/Z
01
0.25414006E
01
0.19619299B
04
880.0
0.20450184E
04
0.26147141E
01
0.25836179E
01
0.20174466E
04
890.0
0.210299478
04
0.26587201E
01
0.26265050E
01
0.20742416E
04
900.0
0.21623026E
04
0.2703414lE
01
0.26700684E
01
0.21323377E
04
910.0
0.22229873E
04
0.27488339E
01
0.27143142E
01
0.219175806
04
920.0
0.228505298
04
0.279495878
01
0.275924906
01
0,22525260&Z
04
930.0
0.23485445E
04
0.28418223E
01
0.28048792E
01
0.231466538
04
940.0
0.241347038
04
0.28894090E
01
0.28512116E
01
0.2378200lE
04
950.0
0.24798582E
04
0.29377305E
01
0.28982525E
01
0.24431545E
04
960.0
0.25477374E
04
0.29867982E
01
0.29460088E
01
0.25095530E
04
970.0
0.26171415E
04
0.30366269E
01
0.299448728
01
0.25774206B
04
980.0
0.26880939,X?
04
0.3087222lE
01
01
0.26467824E
04
990.0
0.27605897E
04
01
01
0.27176637E
04
1000~0
0.28347041E
04
01
0.314432318
01
0.27900903E
04
1010.0
0.291042958
04
0.31385539E 0.319068538 0.32435838E
0.30436946E 0.30936375E
01
0.31957584E
01
0.28640883E
04
1020.0
0.29878139.E
04
0.329728078
01
0.32479502E
01
0.293968386
04
1030.0
0.30668955E
04
0.33517949E
01
0.33009056E
01
0.30169035E
04
10400
0.31476676E
04
0.3407094lE
01
0.33546319E
01
0.30957744E
04
1050~0
O-32301845E
04
0.34632155E
01
0.34091360E
01
0.31763234E
04
1060.0
0.3314447OE
04
0.352013598
01
0.34644254E
01
0.325857838
04
1070.0
0.34005164E
04
O-35778982/?
01
0.3520507lE
01
0.33425668E
04
1080.0
0.348842178
04
0.36365096E
01
0.357738866
01
0.34283170E
04
1090.0
0.357815646
04
0.36959396E
01
0.36350773E
01
0.35158572E
04
1100.0
04
0.375624548
01
0.36935804E
01
0.36052164E
04
1110~0
0.36697980E 0.37633492E
04
0.38174061E
01
0.375290558
01
0.369642328
04
1120.0
0~385885808
04
0.38794477E
01
0.38130602E
01
04
1130.0
0.39563326E
04
0.39423546E
01
0~38740519E
01
0.378950768 0.388449866
1140.0
0.40558112E
04
0.400613658
01
0.39358882E
01
0.398142658
04
1150.0
0.415732118
04
0.40708125E
01
0.39985769E
01
0.40803216E
04
1160.0
0.426092598
04
0.41364083E
01
0.40621256E
01
0.41812144E
04
1170.0
0.43666232E
0.420290216
01
0.41265421E
01
0.42841358E
04
1180.0
044744692E
04
0.42703234E
01
0.419183418
01
0.43891173E
04
1190.0
0.45844820E
04
0.433866688
01
0.42580095E
01
17.00~0
0.46967071E
04
044079517fi
01
0.43250762E
01
044961902E @46053867E
04 04
04
04
The vibrational energies observed by COURTOY@)for Wl‘302 were used where available, otherwise the values calculated by PLASS et ai.(5) from Courtoy’sconstants were employed.
294
L. D. GRAYand Jumrn E. SELVIDGE
When calculating the value of the partition function for a given temperature, one must obviously include all the vibrational levels that are significantly populated at that temperature. To insure that all possible levels were included, the following scheme was employed: for C02, the energy +(ui, ~2~,us) of level ZQUZ~U~ can be regarded as corresponding to some integral multiple of l ,(0110), i.e. E~(v~,z$, us) 21 (2~+ va+4us) Ed (0110). The vibrational levels with the coefficient K = (2s + aa + 4~s) the same were grouped together. Thus, group 4 consisted of the seven levels 0440, 0420, 1220,0400, 1200, 2000, and 0001. The number of vibrational levels in the Kth group is given by the sum of the binomial coefficients
(K*2’2)+ (y)+ (K*y2)+. . . -I (2)or
(32)
(5)
where K* = K/2 for K even and K* = (K- 1)/2 for K odd. The total number of levels K*+4 included in groups 0 through K (for even K only) is Thus, group 10 contains ( 4 )34 levels and 126 levels are included in groups 0 through 10. The number of vibrational levels which must be included in calculating the partition function at high temperatures makes the evaluation by direct summation impractical. For example, at 1200”K, 277 rotational levels were summed for each of 652 vibrational states. It required 1.5 min in IBM 7090 to compute the total partition function at this temperature. The rotational energy levels for the vth vibrational state are given by EJ = hc[&J(J+
1) --&J2(.7+
1)2]
where
Bv = Bo-
(6)
xaruc+ Cytprvj. rcj B
Values of the rotational constants were obtained either from COURTOY@)or calculated from equation (7) using Courtoy’s constants. The Bv values obtained from equation (7) should in many cases be corrected for Fermi resonance and, for states with I # 0, for Z-doubling. To check the effect of neglecting the Fermi resonance correction to the rotational constants, the sum S sl = {exp[-E,(lO’O)/kT]
c(u+
1) eXp[-CJ(loOO)/kT]
+ exp[ - ev(0200)/k T’j c(W+
1) exp [ -e&0200)/k T]}
was evaluated at 300°K using both the perturbed and the unperturbed values of the rotational constants. The results are given in Table 2a. The superscript 0 denotes unTABLE2a. THE PARTIAL SUM Sl AT 300’K Sl
(% Q) (e, vO)
(C”O,vO)
0.904998 0.904357
0.878434
perturbed values. The error introduced by neglecting the Fermi resonance in the rotational constants is 0.06 per cent, while the error amounts to 3 per cent if the resonance is
Relative intensity calculations for carbon dioxide
295
completely neglected as in column 3 of Table 2a. In the present calculation, the rotational partition function for each vibrational level was evaluated for states with 2 # 0 by summing over all J 2 I, i.e. the Z-splitting was neglected?. To estimate the effect of this approximation, the sum Sa, S2 = Jsddexp[ -~-(Ol~o)/kT]+ 2 exp[ -~+(Ol~o)/kT], J even
where the superscripts + and - denote the rotational energy computed for the even and odd J levels using the appropriate rotational constants, was compared with the similar sum over all lines using the average value of the rotational constant at 300°K. The results are given in Table 2b. The error in neglecting Z-doubling is seen to be 0.008 per cent. TABLE 2b. THE ROTATIONALPARlTTIONFUNCTIONFORTHEIXvEL(01’0) AT 300°K sz
#
III.
lJ-
532.747 532.706
RESULTS
The internal and vibrational partition functions are given in columns 1 and 2 of Table 1 for WrsOe as a function of temperature. Columns 3 and 4 show the corresponding values of the harmonic oscillator vibrational partition function and the classical internal partition function. At 12OO”K, both the internal and the vibrational partition functions are seen to be about 2 per cent larger than the values obtained using the harmonic oscillator approximation, while at 300°K they are approximately 0.5 and 0.05 per cent larger, respectively. The numerical values shown in Table 1 have the exponent of the power 10 indicated to the right of the number. Thus, qrnt(280”K) = 266.775. REFERENCES 1. H. W. WOOLLEY,Thermodynamic functions for carbon dioxide in the ideal gas state, J. Res. Nat. Bur. Stand. Wash. 52, 289-292 (1954). 2. National Bureau of Standards Circulars No. 500 (1952) and No. 564 (1955). 3. R. H. TOURINand P. M. HENRY. Infrared snectral emissivities and internal enerxv distribution of carbon dioxide at high temperatures. Part I. Internal energy calculations, Scientific-Report No. 2 on Contract AF 19(604)-2223, Warner and Swasey, Flushing, New York (1958). 4. C. P. COURTOY,Spectres de vibration-rotation de molecules simples diatomiques ou polyatomiques avec long parcours d’absorption, Canad. J. Phys. 35, 608-648 (1957); C. P. COURTOY,Spectre infrarouge a grande dispersion et constants moleculaires du COZ, Ann. Sac. Sci. Bruxelles, 75,5-230 (1959). 5. V. R. STULL,P. J. WYATTand G. N. PLASS,Vibrational energies of the COa molecule, J. Chem. Phys. 37, 1442-1445, (1962); see also V. R. STULL, P. J. WYATTand G. N. PLASS. Infrared transmission studies, Final Report, Volume III, The infrared absorption of carbon dioxide, Report SSD-TDR62-127-Volume III, Aeronutronic Division, Ford Motor Company, Newport Beach, California (31 January, 1963). t Average values of the rotational constants were used.
L. D. GRAY
296
Part II. Relative Intensity of Carbon Dioxide Lines in VibrationRotation Bands arising from Transitions from the Ground State and from the First Excited State L. D. GRAY Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California (Received
6 August 1964)
I. INTRODUCTION INTENSITIES of rotational lines, relative to the integrated intensity of a vibration-rotation band, depend primarily upon the rotational constants of the lower vibrational state. For temperatures of interest in planetary atmospheres many of the strong absorbing bands of carbon dioxide have either the (OOOO)or (0110) state as the lower vibrational state. As an aid in interpreting observed spectra, we have tabulated the relative intensities for X-E,, X-Il, Il-Xi, II-II, and II-A transitions at 300°K. II.
THEORY
The integrated intensity SW,>,J”, 1” -+ v’, J', I', of a rotational line (J” +J’) vibrational band (a”, I” + v’, 1’) is given by-j-
S u”,
in the
87~~Nv~<,J" J”,Z”
~
.$,
J’,l’
=
3hc
-(I+)”
x (l?:::+y]/32[1
J” p
.
-exps]
,l”,v’,J’,l’
(1)
where NW!), Jr//p is the number of molecules per unit volume per unit pressure in the lower state with the vibrational quantum numbers denoted by v” and the rotational quantum number J”, I is the quantum number of the angular momentum associated with the doubly degenerate vibration ~2, /3 = fl(v” -+ v’) is the matrix element for the vibrational transition, wvu”, J,', lo, + 2)f,J,, 2' is the wave number of the transition (v”, J”, I” 1” -91’ is the rotational matrix element. In terms of the integrated -+ v’, J’, I’) and R ( J"+J, > intensity Q,,, 1rp+vj,l~ for the band, 8~3 N,y dcz)~‘,J”-t v’,l’ = --wv”,l”,v’,l 3hc p equation (1) may be written as
(2)
(3) t Ref. 1, equation
(7-128a).
Relative intensity calculations
297
for carbon dioxide
It is apparent from equation (2) and the ideal gas law that the temperature of the band intensity is given by
[l -exp( -hcw/kT)]
(4)
-h~wpcroj]
x [l -exp(
dependence
In terms of the band intensity at To, the integrated intensity of a line can be written as
[l
-exp(-hcWf,J-,
~/kT$j
“&,J’
(5)
where SOv’t,J,,(T)
ToQv( To) EZ
TQv(
T>
x gJexpt - wJ,,hc/kT] &Y(T)
here Qv is the vibrational partition function, QR is the rotational partition function C&L”‘, is the energy (in cm-i) of the lower vibrational state, WJ” is the energy of the lower rotational state and is given by WJ” = &J”(J”
+ 1) - Dv#“(J”
+ 1)]2.
(7)
The quantity Sov I ,, J, JT) is given in Table 3 as a function of J” for transitions from the ground state (i.e. C -+ X and X +II) and for transitions from the first excited state (i.e. Il -+ Z, Il. -+ lT, and II-+ A) for a temperature of 300°K. To obtain the intensity of a line in any particular band, the constants of the upper vibrational state which appear in equation (5) must be used. As a first approximation, however, equation (5) can be replaced by &“,Js’~“+
,,‘,J,‘l’
2:
&,“,l”
+
v’
v(
To)~“v~~,J*,(
T).
(8)
The reference temperature chosen was To = 300°K. Equation (4) may be used to obtain the band intensity at this temperature from measurements made at other temperatures. It should be noted that many investigators choose 273°K as a reference temperature in reporting band intensities. REFERENCE 1. S. S. PENNER,Quantitative Molecular Spectroscopy and Gas Emissivities, Addison (1959).
Wesley, Reading,
L. D. GRAY
298
PI-PI
J
R-branch
Q-branch
PI-DELTA P-branch
R-branch
Q-branch
P-branch
1
0~2805OE-02
0~28OSOE-02
0.
0~561OlE-02
0.
2
0.49495E-02
0.15467E-02
0.27841E-02
0.61868Eo2
0.30934E-02
0.
3
0.68823E-02
0.10706E-02
0~48941E-02
0.68823E-02
0.53529E-02
0.61176E-03
4
0~86783E-02
0~81359E-03
0.67799-2
0.75935m2
0.73223E-02
0~1356OE-02
5
0~10351E-O1
0.6506lE-03
0.8517lE-02
0~82805E-02
0.91085E-02
0.21293E-02
6
O~11897B-Ol
0~537OOE-03
0~10120E-01
0.89224E-02
0~1074OE-01
0.28915E-02
7
0~13309E-01
0.45267E-03
0~11588E-01
0.95061B-02
0.12222E-01
0.36214%02
0.
8
0.14578E-01
0.38723E-03
0.12915E-01
0~10022E-01
0.13553E-01
0~43051E-02
9
0~15698E-01
0.33474M3
0~14094E-01
0~10465E-01
0.14729E-01
0.4933OE-02
10
0~16661E-01
0.29157E-03
0~15120E-01
0~10830&01
0.15745E-01
0.54981E-02
11
0.17464E-01
0.25536E-03
0~15988E-01
0~11114E-01
0~16598Gol
0.59954E-02
12
0~18106E-O1
0.22453E-03
0.16696E-01
0~11316E-01
0~17289E-01
0.64216E-02
13
0~18587E-01
0.19796E-03
0.17245E-01
0~114383-01
0~17817E-01
0.67747&02
14
0~18908E-01
0.17485%03
0.176363-01
0~11480E-01
0~18185E-01
0.70544E-02
15
0.19076E-01
0~1546OE-03
0.17874E-01
0.11446E-01
0~18398601
0.72614E-02
16
0~19097E-01
0.13676E-03
0~179663-01
0~11339&01
0.18463E-01
0.73976E-02
17
0.18979E-01
0.12097E-03
0~17918E-01
0~11164E-01
0.18388&01
0.74657E-02
18
0~18732E-01
0.10696E-03
0~17740601
0~10927E-01
0~18183E-01
0.74697E-02
19
0~18367E-01
0.9448913-04
0~17444E~l
0~10634E-01
0~17858E-01
0.74138E-02
20
0.17897E-61
0~83382E-04
0~1704OE-01
0,10291E-01
0.17427s01
0~73031E-02
21
0.17333E-01
0.7348lE-04
0.16542E-01
0.99046602
0~169OlE-01
0.71431E-02
22
0~16689E-01
0.64654E-04
0.15961E-01
0.94826E-02
0.16293E-01
23
0.15979E-01
0.56787E-04
0~15311E-O1
0.90316E-02
0~15617E-01
24
0~15215E-01
0.49782E-04
0~14604E-01
0~85584E-02
0~14885E-01
0.69396E-02 0.66985E-02 0.64259E-02
2.5
0~14410&01
0.4355OE-04
0~13854E-01
0.80695E-02
0~14110&01
0.61277E-02
26
0.13576Ml
0.38014E-04
0.13072&01
0.75713E-02
0~13305E-01
27
0.12725%01
0.33106E-04
0.1227OE-01
0~12481E-01
0.58097E-02 0.54775E-02
28
0~11868E-01
0~28761E-04
0~11458E-01
0.70696E-02 0.65697E-02
0~11648E-01
0.51361E-02
29
0~11014E-01
0.2492413-04
0.10646E-01
0.607641342
0~10817E-01
0.47905E-02
30
0~10171E-01
0.21543E-04
0.98424E-02
0.55942E-02
0.9996lEXt2
0.444501342
31
0.93484E-02
0~1857lE-04
0.90557E-02
051266&02
0.91928E-02
0.41034E32
32
0.85517E-02
0.15966E-04
0.82921602
0.4676713102
0.84139E-02
0.37691Ea2
33
0.77865E-02
0.13687&04
0~75571E-02
0.42472E-02
34
0.7057
0~11701E-04
0.68551E-02
0.38399E-02
0.76649E-02 0.69503E-02
0.31338E-02 0.2837OE-02 0.25563E-02
lE-02
0.34451Ea2
35
0.63669E-02
0.99736ZXl5
0~61898E-02
0.34563E-02
0.62734E-02
36
O-57184E-02
0.84763605
0.55636E-02
0.30975E-02
0.56368602
37
0~5113OE-02
0.71824E-05
0.49782EO2
0.27638B-02
0.5042OE-02
0.22926E-02
38
0.45514E-02
0.60675E-05
0.44346E-02
0.24554Ea2
0~449OOE-02
0.20467E-02
39
0.40338E-02
0~51101E-05
0.39328E-02
0.2172OE-02
0.39808E-02
0~18189E-02
40
0.35594E-02
0.42904E-05
0.34725E-02
0.19132&02
0.35138E-02
0.16092E-02
41
0.31273E-02
0.359lOE-05
0.30527E-02
0.1678lE-02
0.30882E-02
0.14173E-02
42
0~27358E-02
0.2996lE-05
0.267213-02
0~14656E-02
0~27025E-02
0~12428B.02
43
0.23831E-02
0.24918Ea5
0.23289E-02
0.12747E-02
0.23548E-02
0.10851E-02
44
0.20671E-02
0~20658E-05
0~2021lE~2
0~1104OE-02
0.2043OE-02
0.94317E-03
45
0.17854E-02
O.l7071E-05
0.1746513-02
0.9522OC03
0.17651E-02
0.81631E-03
46
0~15356E-02
O.l4061E-05
0.15029E-02
0~81787E--o3
0~15185E-02
0,70348E-03
47
0.13152E-02
0.11543E-05
0~12878E-02
0.6996OE-03
0.13009Ea2
0.60366E-03
48
0~11218E-02
0.59597E-03
0~11099&02
0.51581E-03
0.95288E-03
0,94459E-06 0.77039E-06
0.10989E-02
49
0.9338lE-03
0.50561E-03
0.94296E-03
0~43889E-03
50
0~80605E-03
0.62624E-06
0.79023E-03
0.42721E-03
0.79783%03
0~37187E-03
51
0.67904Ea3
0.50736E-06
0.35949E-03
0.67225E-03
0.31378E-03
52
0.56971E-03
0.40968E-06
0.66597E-03 0.55895E-03
0~30129E-03
0.56412603
0.26366E-03
53
0~47603E-03
0.32969E-06
0.46721E-03
0.25149E-03
0.47145603
0.22062E-03
54
0.39614E-03
0.26442E-06
0.38893E-03
0,20907E-03
0,3924OE-03
0~18386E-03
55
0.32832E-03
0~21136E-06
0.32245E-03
0.1731lE-03
0.32528E-03
0.15259E-03
56
0.271OlE-03
0.16837E-06
0.26625E-03
0.14276E-03
0~26855E-03
0.12612E-03
57
0.2228lE-03
0.13367B-06
0.21896E-03
0.11727E-03
0.22082E-03
0.10382E-03
58
O.l8244E-03
0.10575E-06
0.17935E-03
0.95939E-04
0~18084cO3
0~85114E-04
59
0.14879E-03
0.83385E-07
0.14631E-03
0.78178E-04
O.l4751E-03
0.69497E-04
60
0.12086SO3
0.6552lE-07
0~11888Eo3
0.63452E-04
0.11984E-03
0.5651613-04
Relative intensity calculations for carbon dioxide Tmm
3-contd. PI-DELTA
PI-PI
R-branch
J
299
Q-branch
P-branch
R-branch
Q-branch
P-branch
61
0.9778SE-04
0.51307E-07
0.96207E-04
0.51297E-04
0.96970%04
0.45776604
62
0~78800%04
0~40038E-07
0.77548E-04
0.41306E-04
0.78154E-04
0~36928E-04
63
0.63249E-04
0.31136607
0.62260604
0.3313OE+t
0.627393104
0.29671E-04
64
0~50566E-04
0.24129&07
0.49788E-04
0.26468604
0~50165E-04
0.23745E-04
65
0.40267E-04
0.18635&07
0.39657E-04
0~21063E-04
0~39952GO4
0.18927E-04
66
0.31939E-04
0~14341E-07
0.31462604
0.16696E-04
0.31694E-04
O.l5027E-04
67
0.25234604
0.10998&07
0.24863E-04
0~13182E-04
0.25043E-04
0~11883E-04
68
0~19859E-04
0~84053E-08
0~19571&04
0.10367E-04
0~1971OE-04
0.93599E-05
69
0~15567E-04
0%4012&08
0.15344E-04
0.81219E-05
0.15452E-04
0.73434-5
70
0~121SSE-04
0~48579E-08
0.11984Eo4
0~6338OE-05
0.12067E-04
0.57387E-05
71
0~94539E-05
0.36737E-08
0.93225605
0.49267E-05
0.93864E-05
0.44670E-05
72
0.73244E-05
0.2768SE-08
0.7224OE-05
0.38148E-OS
0.72728E-05
0.346363-05
73
056525E-05
0~2079OE-08
0~55761&05
0.29424E-05
0.56132E-05
0.2675OCOS
74
0.43453605
0~15557E-08
0.42873Ea5
0.22607B-05
0~43155605
0~20579E-05
75
0~33274E-05
0~116OOE-08
0.32836E-05
0~17303E-05
0~33049E-05
0~15770%05
76
0.25381E-05
0.8619SE-09
0~25052E-05
0.13 192E-05
0.25212E-05
0~12038E-05
77
0.19286&05
0.63821609
0~19038EX5
0~10019E-O5
0~19159&05
0.91531E-06
78
0~14598E-05
0.47087-
0.14413E-05
0.75795&06
0~14503&05
0.69327E-06
79
0~11007E-05
0~34618E-09
0~10869E-05
0.57122E-06
0.10936E-05
0.52306E-06
80
0.82669606
0.25361E-09
0.81648E~36
0~42884E-06
0.82146E-06
0.39312E-06
81
0~61853E-06
0~18514E-09
0,61098&06
0.32072606
0.61466E-06
0.29432E-06
82
0.461OlE-06
0.13467M9
0.4554SE-06
0,23894E-06
0.45816M6
0.219SOE-06 0.16307E-06
83
0.34229&06
0.97618610
0.33821&06
0.17733E-06
0.3402OE-06
84
0~25316E-06
0~70507610
0.25018E-06
0~1311OE-06
0.25164E-06
0.12068M6
85
0~18653E-06
0~50745610
0.18436E-06
0.96557%07
0.18542E-06
0.8896SE-07
86
0.13691E-06
0.36392610
0.13534&06
0.70843E-07
0~13611E-06
0.6533SE-07
87
O~lOOllE-06
0.26006E-10
0.98969E-07
0.51779E-07
0.99524%07
0.47797607
88
0.72917E-07
0~18518E-10
0.72097E-07
0~37701&07
0.72498&07
0.34834E-07
89
0.5291oE-07
0.13139IC10
0.52322E-07
0.27347E-07
0.52609M7
0.25289E-07
90
0.38247E-07
0,92896E-11
0,37826&07
0.19761E-07
0.38032E-07
0~1829OE-07
91
0.27542&07
0.65445611
0.27242607
0.1422SE07
0.27389E-07
0.13177607
92
0.19758607
0.45942611
0.1954SM7
O.l0201E-07
0.19649E-07
0~9457SE-08
93
0.1412OE-07
0.32136611
0.1397OE-07
0~72879E-08
0~140443-07
0.67621E-08
94
0~10053&07
0,22399&l
0.99471E-08
0~51869E-08
0,99989&4l8
0~4816SE-08
9s
0~71302E-08
0~15557E-11
0.70559E-08
0.36777E-08
0.70922&08
0.34177E-08
96
0.5038OE-08
O.l0766E-11
0.49861608
0.25977E-08
0.501 lSE-08
0.24159E-08
97
0.35463=8
0.742393-12
0~35101&08
0~1828OE-08
0.35278E-08
0~17013E-08
98
0.24869E-08
0~51011612
0.24617E-08
0~12815E-08
0~2474OE-08
0.11936E-08
99
0.17373E-08
0,34926E-12
0~17200608
0,89499&09
0~1728SE-08
0.83418E-09
100
0.12092608
0.23827612
O.l1972E-08
0.62271E-09
0~1203OE-08
0.58081E-09
101
0~83838E-09
0.16198612
0.83016609
0.43164609
0.83419E-09
0.40287E-09
102
0.5791 lE-09
O.l0972E-12
0.573493-09
0.29807E-09
0.5762SE-09
0~27839E-09
103
0.3985X-09
0.74056613
0.39469E-09
0~20507609
0.39657E-09
SUM
0~51379E-Oa
0~10995E-O1
0~47519?&00
0.31868&00
0~48914C-00
1
0.1916SE-09
L. D. GRAY
300
TABLE PI-SIGMA R-branch
.I
3-conrd. Transitions Q-branch
P-branch
1
0~187OOE-02
0~56101E-02
3
0~55059E-02
0.12847E-01
0,3740OE-02 0.73412E-02
5
0~88719JG02
0,19518E-01
0.10646E-01
I
0~11830&01
0,2535OE-01
0,1352OE-01
9
0.1427OE-01
0,30127E-01
O.l5856E-01
11
O.l612lE-01
0.33708E-01
0~17587E-01
13
0~17347E-01
0,36029E-01
0.18682E-01
15
O.l7954E-01
0.37105E-01
0~1915lE-01
17
0’1798OE-01
0,37018E-01
O.l9038E-01
19
0.17493E-01
0.35906E-01
0.18413601
21
0,16579E-01
0~33948&01
0.17369E-01
23
0~1534OE-01
0.31347s01
0~16007E-01
25
O.l387bE-01
0,28307E-01
0~14431&01
27
0,12286E-01
0~25028E-01
0.1274lE-01
29
0~10658E-01
0.21684E-01
O.l1026E-01
31
0.906528-02
O.l8423E-01
33
0~7564OE4l2
O.l5357E-01
35
0,61949E-02
0~12567E-01
37
0.49819E-02
0~10098E-01
39
0,39354E-02
0.79717E-02
41
0.30546E-02
0,61836E-02
43
0.23302E-02
0.47145E-02
45
0~17474E-02
0.35336E-02
47
O.l2884E-02
0.26042E-02
49
0.9342OE-03
0.18875E-02
51
0.66623E-03
0.13455E-02
53
0.46737E-03
0.94356E-03
55
0.32256E-03
0.65098E-03
57
0.21903E-03
0.44190603
59
O.l4635E-03
0.29518E-03
61
0.96233E-04
O.l9404E-03
63
0.62276E-04
0.12554E-03
65 67 69
0.396bbE-04
0.79942604
0,24869E-04
0,50108E-04
0,15348E-04
0.30918E-04
71
0.93244E-05
0~1878Ofi~04
0.9357bE-02 0~77932E-02 0.63719E-02 0.51165E-02 0.40363E-02 0.3129lE-02 0,23843E-02 0~17862E-02 0~13158E-02 0.9532bE-03 0.67929E-03 0.47619E-03 0,32842E-03 0.22287E-03 O.l4883E-03 0.978lOE-04 0.63264E-04 0.40276M4 0~2524OE-04 0,1557OE-04 0.94557605
73
0,5577lE-05
O.l1231E-04
0.56535E-05
75
0.32842E-05
0.66122E-05
0,3328OE-05
77
0.19042E-05
0.3833lE-05
0,19289E-05
79
0~1087lE-05
0.21879E-05
0~11008E-05
81
0~61108E-06
0,12297E-05
0.71862E36
83
0.3382bE-06
0.68059E-06
0.34233E-06
85
0.18439E-06
0.37094E-06
0.18656E-06
87
0.98982607
0~199lOE-06
0~10012E-06
89
0.52329E-07
0.10525E-06
0,52917E-07
91
0.2724bE-07
0.54791E-07
0,27545E-07
93
0~13972fi-07
0.28093E-07
0.14122E-07
95
0~7056bE-08
0.14188607
0.61309&08
97
0.35105s08
0~7057lE-08
0.35467E-08
99
0~172OlE-08
0.34577E-08
0.1737SE-08
0.83024E-09
0.16687E-08
0.83846E-09
101 SUM
0.241 lbE-00
0.2599lE-00
Relative intensity calculations TABLE
for carbon dioxide
3-conrd. SIGMA-PI
SIGMA-SIGMA
Transitions
Transitions P-branch
R-branch
J
301
R-branch
Q-branch
P-branch
0.
0.
0’18942E-02 0.54042&02 0,86436E-02
0
0,37402E-02
0.
2
0~11095E-01
0.73968E-02
0,37402E-02 0.73968E-02
4
O.l8014E-01
0~14411E-01
0~10808E4ll
6
0.24202E-01
0~20745E-01
0.1383OE-01
8
0~29418E-01
0.2165OE-01
0~16343E-01
0.9246OE-02 0~16212E-01 0.22473E-01 0.27784E-01
10
0~33488E-01
0~30443E-01
O.l8266E-01
0,31965E-01
0,13699E-01
12
0.36312E-01
0~33519E-01
0.19553E-01
0,34916E-01
O.l5363E-01
14
0.37872E-01
0.35347E-01
0,20198E-01
0,36609E-01
0~16411E-01
16
0~3822OE-01
0.35972E-01
0.20234E-01
0.37096E-01
O.l6862E-01
18
0.37473E-01
0.35JOlE-01
0.19723E-01
0.36487E-01
O.l6764E-01
20
0.35793E-01
0.34089E-01
O.l8749E-01
0,34941E-01
O.l6192E-01
22
0.33376E-01
0~31925E-01
O.l7414E-01
0,32651E-01
0.15237E-01
24
0.30428E-01
0~29211E-01
O.l5823E-01
0,2982OE-01
0.13997E-01
26
0,27154E-01
0,26149E-01
0’1408OE-01
0.26652E-01
0.12571E-01
28
0.23742E-01
0.22923E-01
O.l228OE-01
0,23333E-01
O.l1052E-01
30
0.20353E-01
0.19697E-01
0~10505E-01
0.20025G01
0.952OlE-02
32
0~17118E-01
0.16599E-01
0,88183E-02
0~16859601
0.80402E-02
34
0~14131E-01
0.13728E-01
0.72675E-02
0.13929E-01
0.66619&L02
36
0~11455E-01
0~11146E-01
0.58824E-02
O.l13OOE-01
0.5418OE-02
38
0.91216E-02
0.88877E-02
0,46778E-02
0.90047E-02
0.43269E-02
40
0.7137OE-02
0,69629E-02
0.36555E-02
0.705OOE-02
0.33944E-02
42
0.54884E-02
0.53607E-02
0.2808OE-02
0.54246E-02
0.26166E-02
44
0.41491E-02
0.40569E-02
0.21207E-02
0.4103OE-02
0,19823E-02
46
0~30841E-02
0.30185E-02
0.15749E-02
0~30513E-02
O.l4764E-02
48
0.22545E-02
0.22085E-02
0.11502E-02
0.22315E-02
0,10812E-02
50
0~16209E-02
0.15892E-02
0.82636E-03
0~16051E-02
0,77869E-03
52
0’11464E-02
0.11248E-02
0.58404E-03
0,11356E-02
0.55159E-03
54
0.79773E-03
0.78323E-03
040612E-03
0.79048E-03
56
0.54616%03
0.53658E-03
0.27787%03
0~54137E-03 0.36484E-03
0.38436E-03 0,2635OE-03 0,17774E-03
O.l144OE-01
58
0.36795E-03
0,36172E-03
0.1871OE-03
60
0,24396E-03
0,23996E-03
0.12398E-03
0.24196E-03
0,11798E-03
62
0~15919E-03
O.l5666E-03
0~80857E-04
0.15792E-03
0,77067E-04
0~51906fi-04
O.l0145E-03
0,49547x%04
0.32800%04
0,64153E-04
0.31353E-04
0~20404E--o4
0.39933E-04
0.19529E-04
0.12496&L04
0,2447OE-04
0.11975E-04
0.7534lE-05
0,14763E-04
0.72286E-05
044725E-05
0.87685E-05
0.4296OE-05
0.26143E-05
0.5128OE-05
0.25137605
0.15047605 0.85279E-06 0.47595E-06 0.2616OE-06 0.1416OE-06 0.75486E-07 0.39633E-07 0.20495E-07 0.10439E-07 052373E-08 0,25882E-08 0~12599E-08
0.29529E-05 0.16744E-05 0.93491E-06
0.14482E-05
64
0.10224E-03
66
0.64635E-04
68
040225E-04
76
0.51615E-05
0~10067E-03 0.6367OE-04 0.39642E-04 0.24297E-04 0.14661E-04 0,87097E-05 0~50945E-05
78
0,29717E-05
0.29341E-05
80
0.16848E-05
O.l664OE-05
82
0~94058E-06
0.92924E-06
84
0.51711E-06
0~51103fi-06
86
0~27998E-06
0,27676E-06
88
0.14929E-06
0~14762E-06
90
0.78405E-07
0.77543E-07
92
0~40555E-07
0.40118E-07
94
0.20661E-07
0~20443E-07
96
0.10368E-07
0~10261E-07
98
0.51246608
0.50728E-08
0.24951E-08
0.24704E-08
70
0.24644E-04
72
0,14864E-04
74
0.88274E-05
100 SUM
0.27952E-00
0.82159E-06 0.45896E-06
0.51407E-06
0.25247E-06
0.27837E-06
0.13677E-06
0.14846E-06
0.7297OE-07
0.77974Ea7
0,38341E-07
040337E-07
O.l9841E-07
0.20552E-07
0,10113E-07
0~10314E-07
0.5077OE-08
0,50987E-08
0.25105E-08
0.24827E-08
O.l2228E-08