- Email: [email protected]
Diode laser measurements of line strengths and collisional half-widths in the ν1 band of OCS at 298 and 200K
J. Quant. Speetrosc. Radiat. Transfer Vol. 36, No. 4, pp. 295-306, 1986
0022-4073/86 $3.00+ 0.00 Copyright © 1986PergamonJournals Ltd
Printed in Great Britain. All rights reserved
DIODE AND
LASER
MEASUREMENTS
COLLISIONAL OF
OF
HALF-WIDTHS OCS
AT
298 AND
LINE IN
STRENGTHS
THE
v1 BAND
200K
J.-P. BOUANICH Laboratoire d'Infrarouge, Associ6 au C.N.R.S., Universit6 de Paris-Sud, B~timent 350, F-91405 Orsay Cedex, France and G. BLANQUET, J. WALRAND and C. P. COURTOY Laboratoire de Spectroscopie Mol6culaire, Facult6s Universitaires Notre-Dame de la Paix, Rue de Bruxelles 61, B-5000-Namur, Belgium (Received 15 November 1985)
Abstract--Absolute line strengths and self-broadened half-widths have been measured at 298 and 200 K for spectral lines ranging from J = 1 to 55 in the vI band (860 cm -I) of J6OI2C32S,using a tunable diode laser spectrometer. The vibrational transition moment (6.412 +0.16 x 10-2D) as well as the absolute intensity (29.63 _+ 1.48 cm-2-atm t at 298 K), of the vt band are determined from these line-strength measurements. By applying two semi-classical impact theories of collisional broadening, we have obtained results for half-widths at 298 and 200 K which are significantly larger than the experimental data for [m[ < 50. However, the variation of the linewidths with temperature is well reproduced theoretically. INTRODUCTION A l t h o u g h the self-broadening coefficients for pure rotational transitions o f O C S have been the subject o f several experimental investigations, especially for low J values, l-7 accurate values are not available for rovibrational transitions. In the infrared, the collisional linewidths, as well as the line strengths, are difficult to measure accurately, even with a high-resolution spectrometer, because m o s t o f the v i b r a t i o n - r o t a t i o n lines o f 16O12 C32S exhibit a varying degree o f overlap increasing with pressure, especially at r o o m temperature. Using a natural sample o f OCS, spectra o f the v~ lines o f 16OI2C32S,recorded between 835 and 875 cm -~, are generally complex owing to the presence o f weak lines arising mainly from the hot bands (vl + v 2l ) - v 2t and (2Vl - Vl) and f r o m the v I b a n d o f 16OI2C34S. The only previous accurate determinations o f vl line strengths were performed by Wells e t al. 9 These were m a d e from intensity measurements o f two lines in the R - b r a n c h . Using a high-resolution tunable diode laser ( T D L ) spectrometer, we have measured, for relatively high pressures o f OCS, the absolute strengths o f 35 lines at 298 K and 30 lines at 200 K, and the half-widths o f 36 lines at 298 K and 31 lines at 200 K. These measurements include several blended lines: six at r o o m temperature and two at low temperature. The experimental conditions, as well as the procedure used in data reduction, are described in the following sections. F r o m line-strength measurements, we deduce the vibrational transition m o m e n t and the total integrated intensity o f the vl band, from which we calculate s m o o t h e d values o f the line strengths. The results obtained are c o m p a r e d with available literature values. The experimentally determined pressure-broadened linewidths are c o m p a r e d with the results o f calculations derived from the A n d e r s o n - T s a o - C u r n u t t e (ATC) theory and from a m o r e recent semi-classical impact theory, I° which has been applied with some simplifications. The temperature dependence o f linewidths is deduced from the experimental results and f r o m the calculated results at 298 and 200 K. EXPERIMENTAL
PROCEDURE
The spectra were recordecl on a commercial diode laser spectrometer (Spectra Physics) operating in the 800-900 c m - 1 region, interfaced to a minicomputer. ~l The collimated o u t p u t beam from the T D L was passed t h r o u g h a variable temperature absorption cell containing the gas sample. This 295
296
J.-P. BOUANICH et al.
cell, with a maximum optical pathlength of 4.80cm, and its cryostat have been described previously. 12 Two OCS gas samples were obtained--one from Matheson Co. with a stated purity better than 97.5% and one from l'Ah" Liquide with a stated purity of 99.9% - - a n d were used without further purification. A natural sample of OCS contains 93.74% of the isotopic species 16OI2C32S. In order to obtain the collisional linewidths, we must choose OCS pressures carefully. Low pressures ( < 4 0 mbar) lead to relatively small overlap of adjacent lines, but corrections for the Doppler and T D L linewidth are still important. Much higher pressures increase the linewidths, which are predominantly collision-broadened. Higher pressures also increase the line overlap and the baseline may be less well defined as well. Therefore, we estimate that several pressures are required to obtain reasonably accurate data. We used OCS pressures of about 40, 55, 70, and 85 mbar at room temperature and about 30, 45, 60, and 75 mbar at low temperature. These pressures were measured with a capacitance manometer with an accuracy better than 1 mbar and with a Bourdon-tube gauge having an accuracy of 0.5% of full scale (0-130 mbar). During the experiments, the cell was not isolated from the gauges so that the pressures of OCS in the cell at low temperature were measured without any corrections. It should be noted that the line strengths could have been determined at much lower pressures (which are difficult to measure accurately), but with the advantages (less interferences, well defined background) and the disadvantages (larger corrections) mentioned. The temperature of the gas sample was measured with a platinum resistance thermometer mounted inside the cell and was kept constant at 298 and 200 K with a maximum variation of + 2 K. The P(J) and R(J) lines with J < 6 and J / > 39 were recorded with an optical pathlength of 4 . 8 0 _ 0.02 cm, whereas the other lines were recorded with a pathlength of 1.90_ 0.02 cm. Relative wavelength calibration was performed using an air-spaced Fabry-Perot etalon with a fringe spacing of 0.029851 cm -~, which could be introduced into the laser beam. Spectral purity of the modes was checked by observation of the smoothness of the etalon fringe pattern. The following data were recorded for each absorption line: the diode emission without absorption (this was used for normalization of spectra); the spectrum of OCS at low pressure (about 5 mbar) (this allowed to unambiguous identification of the transition and aided determination of the background, i.e. 100% transmission level); the spectra of the pressure-broadened OCS line; the spectrum of the F a b r y - P e r o t etalon with the absorption cell evacuated. The successive recordings were monitored and stored by a minicomputer. The digitized absorption spectra and etalon fringes were analyzed by a computer program to obtain the line center and etalon fringe-peak positions. A roughly fiat background level was also obtained by normalization to the true emission profile of the diode.It Figure 1 shows an example of the normalized spectra of a line and the corresponding fringe pattern from the etalon scan. A slight anomalous rise of the peak absorption and of the far wings appeared for some lines as the pressure increased. This was probably caused by an absorption continuum from the neighboring lines and was accounted for in the determination of the baseline. It is noteworthy that for an isolated mode of the TDL, the shuttered scan level corresponded to exactly the 100% absorption level produced by a saturated line. This result was checked systematically in the study of OCS lines broadened by N2 .~3 DATA REDUCTION The measured absorption coefficient, K(v), at the wavenumber v is obtained from
K(v)
= ln[/o (v)/I, (v)] l - ~,
(1)
where Io and It are, respectively, the incident and transmitted light intensities and 1 is the optical pathlength. The measured linewidths, 27obs, were taken directly from the spectra at a transmission equal to x/Io(vo)I~(vo) where v0 is the line center wavenumber. ~3 To determine the collisional half-widths, Yc, corrections have been made for the effects of instrumental and Doppler broadenings on the absorption line profiles. These corrections are small (-,.<3%) because the T D L linewidth (estimated to be on average 1.3 × 10-3cm -l) and the Doppler width (which around the band center is 1.37 x 1 0 - 3 c m - l at 298 K and 1.12 x 1 0 - 3 c m - I at 200 K) are almost negligible compared to the observed widths (10-35 x 10 -3 cm-t). A detailed description of the corrections is given in
Line strengths and collisionat half-widths in the v~ band
0% T r l n s m i s s i o n
Fabry-
Psr ot
etaton
297
lever
trace
/
/
r~
i i
Ii !'
"/'
!1/
,I
/
!, r
I
I11 i,'
!It
iI~
~/'
100% Transmitted
j
!
i///
I'
I
intensity
Fig. 1. The normalized spectra of the R(36) line recorded for pure OCS at 8, 30, 45, 59.8 and 74.9mbar and 200 K. Ref. [13]. A plot o f the m e a s u r e d and collisional broadening coefficients vs O C S pressure P is shown in Fig. 2. It m a y be seen that, even for m e a s u r e m e n t s at 30 mbar, Yc is close to 7obs- The straight lines obtained are a verification o f the proportionality o f )'c with P. The self-broadening coefficients Y0 (in c m - t - a t m -~) are derived f r o m the slopes o f these lines.
30
A
T
2O
E u
m
I o
t~
10
I 20
I
I
I
40
60
80
P
(mbar)
Fig. 2. Linewidth vs OCS pressure for the self-broadened R(36) line of OCS; ( x ) measured linewidths, 27ob,; (C)) collisional linewidths, 27,-
J.-P. BOUANICHet al.
298
If we assume a Lorentz shape for the pressure-broadened lines, then the line strengths, S, are obtained from S = Kc(vo) rtTc, where Kc(vo) is the collisional peak absorption coefficient. Corrections for the Doppler and T D L linewidth contributions are, in principle, necessary to determine Kc(vo) from K(vo). The corrections for instrumental (TDL) distortions were made on the measured parameters K(vo) and 7 by using Tables 4 and 5 of Ref. [14] established for the convolution of a Lorentz profile by a Gaussian function. This procedure is justified because the effective T D L lineshape may be approximated by a Gaussian function ~5 and, for the pressures used, the absorption lines are nearly Lorentzian and are theoretically described by a Voigt function. With these corrections, we have obtained K,,(v0), the peak absorption coefficient resulting from the superposition of Doppler and collisional broadenings. Next Kc(vo) was calculated from the following relations derived from Ref. [16]:
K~(vo)=Kv(vo)/[xf-Hy(1--erfy)exp(y2)]=Kv(vo)/[1+
~ (-1) "1'3"''(2m-1)] m=, "~y~
,
(2)
where y = (In 2)t/2(yc/yD), 7D is the Doppler half-width. For y > 4, we use
Kc(vo) = K~.(Vo)/[1 -- (1/2 y2) + (3/4 y4)].
(3)
Except for the lowest pressures considered (about 40 mbar at 298 K and 30 mbar at 200 K), these corrections are much smaller than our experimental uncertainties for K(vo) so that K~(vo) ~- K(vo). Therefore, for P > 50 mbar, the line-center absorption coefficient should be constant as the pressure increases, a result which is roughly verified experimentally. Assuming that the line strengths are proportional to the pressure, we have determined, for each line and temperature, an average value of line strength (So) expressed in cm 2-atm ~ such that So = S/P' with P ' ( a t m ) = P ( m b a r ) x 0.9374 x Ce/1.01325 103. The first factor represents the proportion of 16012C32S in natural OCS. The second factor (Cr) is the overall purity of the OCS gas. Cp is set equal to 0.98 for the first gas sample and 1 for the second sample. These two factors were not considered in determining 70. The main sources of uncertainties in the determination of 70 and So arise from: (1) the presence of weak overlapping lines; in the case of a single, strong overlapping line, measurements were performed on the half of the line away from the interfering line; (2) the baseline location; this is difficult to determine for Lorentzian pressure-broadened lines; (3) the non-linear tuning of the laser; this may be seen from the variation of the Fabry-Perot fringe spacings; (4) the small fringes appearing in the transmission curves (Fig. 1); these are due to parasitic interferences; (5) uncertainties in the pathlength (these occur in the intensity measurements only); (6) errors in the temperature and pressure measurements; (7) the improbable occurrence of a non-isolated mode of the TDL; this would imply a 100% absorption level lower than that considered.
LINE STRENGTHS
Experimental and calculated results The line strengths, So, normalized to 100% 16OI2C325, were determined for the v~ band at 298 and 200 K with an estimated relative error of + 10%. The measured strengths of unblended lines are given in Table 1. In addition, we have measured the strengths of the blended lines P(55), P(33), P(10), P(6), R(1), and R(10) at 298 K. The lines P(33), P(6) and R(1) coincide, respectively, with the P(7), R(22) and R(31) lines of the v~ band of 16012C345,17whereas the P(55), P(10) and R(10) lines are, respectively, blended by the lines P(40), R(6) and R(28) of the (vl + v,~) - v~ hot bands. 8 At low temperature, the strengths of the blended lines P(6) and R(1) were also measured. Because the hot-band lines become much weaker at 200K, the R(10) line may be considered to be unblended. The strength So of an infrared absorption line at the wavenumber v0 is related to the dipole moment matrix element of the rovibrational transition IRvjj v,s,I by
So(T) = 8113 Nr 3h~ Qv(T)Qr(T) Voexp
hcE,(J) ~
Imt l R : f l = ×
1 - exp
--kT- ]]
(4)
Line strengths and collisional half-widths in the vI band
299
where N r is the number of OCS molecules in 1 cm 3 at I atm and absolute temperature T. Here, we used N r = N L x 273.15/T, where N L is the Loschmidt's number. For the pressures considered, OCS behaves as a perfect gas but this is not the case for higher pressures; at 1 atm and 0°C, the number of molecules cm -3 is 1% larger than NL, 18 and the difference increases with increasing density and/or decreasing temperature. E,(J) is the energy (in cm -~) of the lower rotational level of the transition; m = - J for a P(J) line and m = J + 1 for a R(J) line. The induced emission term, 1 - e x p ( - h c v o / k T ) , is almost unity for the v] band. Q~. and Q, are the vibrational and rotational partition functions given by Q~ = E~gv e x p [ - G ( v ) , hc/kT] and Q, = Es(2J + 1) exp[-hcE~(J)/kT].19 Because the OCS molecule has a doubly-degenerate vibration v2 centred at 520.4 c m - ], Q~ is significantly larger than unity. By considering the B and D rotational constants for the v~ band of ]60~2C32S given in Ref. [9], we obtained, at 298 K, Q,, = 1.203, Q~ = 1021.7911 (J varying from 0 to 132); at 200 K, Q~ = 1.051, Qr = 685.7767 (J varying from 0 to 108). By introducing the measured values of line strengths given in Table 1 and all known quantities into equation (4), IR~J'I2 was calculated for each line. N o clear J-dependencies were observed in the IR 12values and the Herman-Wallis factors 2° were not determined. The mean IR~'I value derived from the measurements at 298 and 200 K is 6.412 x 10-2D, with an absolute error estimated to be +0.16 x 10-2D. By using this value of IR~'I and assuming that the vibration-rotation interaction function 2° F(m)= 1, we have obtained the calculated line strengths listed in Table 1. These results are in reasonable agreement with the experimental data at 298 K, as well as those at 200 K. The absolute intensity of the v~ band of ~60]2C32S was evaluated by summing the calculated values of So(T) over all the lines considered for the calculation of Q,(T). We thus obtain the following values: S,,o = 29.63 cm-2-atm -~ at 298 K, S~o = 33.82 cm-2-atm -~ at 273.15 K (STP conditions), S Vl ° = 51.21 cm-2-atm -] at 200 K, with an estimated uncertainty of 5%. Table 1. Observed and calculated line strengths ~ (in cm ]-atm ~ ) i n the v~ band of 16012C32S at 298 and 2 0 0 K 298 K
200 K
298 K
Line
200 K
Line ohmeryed
calculated
obBex'ved
ca/cuJated
ol~e.rved
ca3cuJated
observed
caJ c u ] a t c d
0.5823
0.5868
P( ss )
0.0759
0,0447
P(9)
0.2333
0,2380
p( 52 )
0.0987
0.0695
0.0679
P(8)
0.2237
0.2154
0.5358
P( 81 )
0.1097
0.1073
0.0762
o.o??s
P(6)
p( 48 )
0.3368
0.1357
0.1129
0.1132
P(4)
;)(~)
0.1789
0.1794
0.1800
o.1788
p(3)
0.2531
0.3125
0.3203
P(2)
0.3487
R(1)
0.3783
R(2)
0.0845
0.0866
0.2059
0.1098
0.1349
0.2801
0.2941
0.3426
0.3?43
0.3635
p(38) ]P(37)
0.2660
0.2656
;)( 36 )
0.2873
0.2780
;)(34)
0,3069
0.3020
0.4397
R(3)
0.3135
0,4716
R(4)
;)( 33 ) ]P( 31 )
0.3349
0.3623
0.5655
0.3665
0.4202
0.3141
0.3136
0.2896
o.o888
0.0859
0.228?
0.2198
0.0576
0,1486
0.1479
-
--
0.0580
0.1491 0.2224
0.5361
R(6)
0.1956
0.5161
0.4933
P( 30 )
0.3480
0.34.45
0.5682
R(3o)
-
0.2881
0.7033
0.?033
;)(29)
0.3589
0.3534
0.5998
R(36)
0.4,012
0.3810
P( 25 )
0.3793
0.3787
0.7074
o.7342
R(37)
-
0.3903
;)(22 )
0.3844
0.7330
0.7?6?
R(18)
0.3960
0.3979
0.8690
P( 21 )
0.3833
0.8178
o.79o9
R(24)
o.3877
0.4079
0.7868
0.39?4
0.8604 0.8892
0.8673
P(2o)
0.3743
0.3805
0.8013
R(25)
P(ls)
0.3769
0.3?62
0.8074
R(26)
0.4124
0.3990
;)(38)
0.3709
0.3703
0.8089
R(28)
0.3786
0.3853
0.7378
0.6733
0.8056
R(36)
0.2909
0.2964
0.3987
0.4024
0.7643
R(39)
0.2497
0.256?
0.3114
0.3123
0.2356
0.2434
0.2809
0,2850
0.2302
0.2396
0,2592
;)(17)
0.3622
0,8184
;)(14)
0.3285
0.3282
;)(13)
0.3205
0.3134
0.7307
0,7397
e(,dJK))
;)( 12 )
0.2969
0.7106
0.?096
R(41)
;)(.)0)
0.2591
0,6330
-
-
0.4043
0.7676
O.76JJ 0.7329
300
J,-P. BOUANICHet a/. Table 2. Relative difference (in percent) between the strengths of blended lines (BL) and unblended lines (UL)
Line
T(K)
[Sobs(BL) - Scalc (UL)] x 100
Scalc (UL)
Estimated from the calculated relative line strengths
P(55)
298
+ 11.1
9.65
P(33)
298
+
8.0
2.7
P(IO)
298
+
9.2
6.0
P(6)
298
+
5,3
10.9
R(1)
298
+ 26.4
27.3
R(IO)
298
÷ 10.1
10.9
P(6)
200
+
1.6
8.7
R(1)
200
÷ 18.4
16.9
As may be seen in Table 2, we have evaluated the relative difference between the measured strengths of blended lines and their calculated strengths (given in Table 1). In addition, we have determined the strength ratios of the two components of blended lines by considering the relative line intensities given in Table 2 of Ref. [8], our calculated results, and by assuming that the line strengths So for the isotopic species OC32S and OC34S are the same. Within the experimental errors (~< 10%), corresponding line strengths in Table 2 are in reasonable agreement. We have thus obtained experimentally the expected result: the intensity of a blended line is the sum of the intensities of the individual components of the blended line.
Comparison with other data From our results, we are able, in principle, to calculate line strengths for any transition in the v~ band of OCS. This permits comparisons between our results and those of previous studies to be made. The calculated results of Devi et al. 2~ at 300 K for J ~< 50 are 20-30% lower than our results at 298 K. This is outside the range of our estimated experimental error. However, the agreement is better for P lines with higher J values [for P(75) and P(76), we obtain the same calculated values]. Considering these differences, it is surprising that these authors obtained a band strength of 26.93 cm-2-atm -~ (close to our value, i.e. 29.63 cm-2-atm -I at 298 K) and a squared transition moment IR~'I2 of only 2.85 x 10 -3 D 2 (our result is 4.11 x 10 -3 D2). The calculated results given by Wells et al. 9, derived from the measured R(28) and R(33) line strengths, are about 7.5% smaller than our calculated values of So. However, the resulting transition moment, 6.32 x 10 -2 D (a value identical to that given in Ref. [22]), is only 1.5% lower than our value. This difference could be approximately accounted for if their calculated line strengths had not been normalized to 100% ~60~C~2S. Kagann 22 has recently measured the total intensity of the vt band. The result obtained, 35.5 cm-2-atm -~ , probably included all hot bands and isotopic transitions in the v t region, but is consistent with our determination at 298 K. (A rough estimation 23 of the total strength in the vt region would be to multiply Sv~ by Qv. This gives 35.6cm-2-atm -t which is close to Kagann's value.) COLLISIONAL
HALF-WIDTHS
Experimental results The values we have determined for the collisional half-widths, Y0, at the four pressures studied are given in Table 3 for 298 K and in Table 4 for 200 K. The relative error in 70 is estimated to
Line strengths and collisional half-widths in the v~ band
-g v
~
0
~
,
7
~
~
,
,
0
~
;
,
,
~
0
~
~
~
~
~
~
o
~
301
o
~
, ~ = ~
~
.~z
.
•
,
u
~
j
~
o
.
j
j
~
~
. . . . . . . . .
0"0
J~
~.~ "~..~ L m •
,
.
.
.
.
.
.o x
~
~J
~
~
. . . .
~
~
,
~
~
~
~ J ~ ,
~
~
'~ ~
~
,
~
,
~
~ r ' ~
.3
~-.~7
~.~ 3
i
v
°
J~
o
L
uJ 0.
.
.
.
.
"~ ~
,
~
~, •
,
,
o
E
~
~
~
~
~
•
J.-P. BOUAN1CFI et al.
302
be about + 6% and is, a priori, still larger for values given in parentheses. These values correspond to the blended lines P(33), P(6) and R(1) at 298 and 200 K, P(55), P(10) and R(10) at 298 K, to the P(52) line at 200 K which is overlapped by a strong isotopic line [P(28) of OC34S] and to the very weak P(55) line at 200 K. Within this uncertainty, the linewidths are only Iml dependent, in accordance with the impact theories in which the imaginary parts of the differential cross section are generally negligible. The smoothed values given in Tables 3 and 4 arise from the smooth curves (Fig. 3) that fit the experimental data. An uncertainty of _+5% on these values seems reasonable. It appears that the scatter of the data, especially of the blended lines, around the average curves is small. This result seems to indicate that for two overlapping lines with v e r y different intensities, the weaker line has no detectable influence on the linewidth of the stronger line. Comparison with other experimental data
Assuming that the vibrational dependence of the self-broadened linewidths is very small, we may compare our results for 70 with those obtained for pure rotational transitions J + 1 , - - J in the microwave region. This comparison is summarized in Table 5 (units are converted from M H z / T o r r to c m - L a t m ~). Our smoothed and interpolated values of 70 are smaller, especially for Iml = 10, than the values of Battaglia et al. 3 and are larger for Iml = 2,3,4 than the results obtained recently by Matsuo e t al. 24 for the ground and vibrational excited states. Our data are also somewhat larger for Irnl= 32,34,37,41,43 than the results of measurements in the excited vibrational state (01~0) by Mehrotra and M~ider} 5 By considering all these data, the following conclusions may be drawn: our results are on the whole larger than those obtained for pure rotational transitions; the results given by Battaglia et al. 3 are larger; those given by Matsuo et al. 24 are smaller. The values of 70 obtained in the v~ band by Devi et al. 2~ range from 40 to 60% higher than the experimental results presented in Tables 3 and 5. However, from direct half-width measurements of P(67), P(72) and P(76), these authors determined a mean value of (0.108 + 0.005) c m - L a t m ~ which is consistent with an extrapolation of our results to these lines. Concerning the linewidths at low temperature, the only previous result which may be compared with our data at 200 K is the one obtained by Britt and Boggs ~ for the microwave transition J = 2 - 1 at 195 K: (0.208 4- 0.006) c m - L a t m -~ , which is in excellent agreement with the smoothed value for Iml -- 2 (Table 4), 70 = (0.2085 -t- 0.0104) c m - L a t m -~ .
0.25
20OK.+. '" ~.o~+O"
7" 'IE T
--o.+ \ . '....'~
0.20 E o
+o" +
OoO
~2 0.15
6"~+
+
o'"
o9.....'~,,,, +-
÷*. .
,
+
%" . + + ,
010
I 5
I 10
I 15
I 20
I 25
I 30
I 55
I 40
I 45
.+
l 50
Iml Fig. 3. Self-broadened OCS line halfwidths 70 in the v~band at 298 and 200 K; (+) P-lines; (O) R-lines; (...) smoothed and interpolated values fitting the experimental data; the solid lines represent the theoretical values [calculation (b)].
Line strengthsand collisionalhalf-widthsin the v~ band
303
Theoretical results
The collisional half-widths of self-perturbed OCS were first calculated by applying the ATC theory [calculation (a)]. For the intermolecular potential, we have considered electrostatic contributions produced by dipolar and quadrupolar interactions, and anisotropic dispersion contributions in which we have added a repulsive part ]3'26such that the anisotropic intermolecular potential is: 6
V = V~Iu2 "I- V..Q2 "{- Vu:Q, "k VQIQ2 "I- 4Erl
-- -R
"1-
P 2 (COS 01).
(5)
where the subscript 1 refers to the active molecule, and 2 to the perturbing molecule;/~ and Q are the dipolar and quadrupolar moments of the molecules; ~ denotes here the polarizability anisotropy of OCS [~] =(~I!-~±)/3~]. The values used in the ~0-calculations for ~ , the Lennard-Jones parameters e and a, and the rotational constants B and D of the v~ band are given for OCS in Table 2 of Ref. [13]. We have taken into account the dipole moment for the ground vibrational state of OCS, i.e. 0.715 D. For the quadrupole moment, we have considered the value obtained for ~6012C32S from molecular-beam electric-resonance spectroscopyy i.e. 0.786DA, which seems to be more accurate than the value 0.88 DA, derived from molecular Zeeman effect experiments. 28 Because the contributions arising from the quadrupole moment are relatively small, the 70 values calculated with Q = 0.786 DA are only slightly lower (< 1%) than the values calculated with Q = 0.88 DA. The value 2.79 D/~ deduced from linewidth calculations29 has been disregarded because such calculations do not allow an accurate determination of the quadrupole moment. The self-broadening coefficients, ~0, were computed for Iml ~<55 by including the contributions from collisions with perturbing OCS molecules have J2 values ranging from 0 to 132 for T = 298 K Table 5. Comparison between experimental values of ~0 (in 10 3cm-Latm ]) at room temperature in the microwave region and in the vt band of OCS. Our values are averaged over P- and R-lines, smoothed and interpolated Nil z'eBulbs
transition
J'--,3 159.2,1 2-I
I R L.ine Im;
Prement mtud¥ (m mo o r b e d
valueB)
.157.7, 2 1 5 5 . 9 , 3
.152.9, 5 ] 5 4 . 1 , 6 .144(a), 24"1"
.154
1 3 3 . 8 ( b ) 24t" 3-2
.158,4, 3 .1#7. 4 .144.5, 7
.154.5
. 1 4 8 , 3 ( a ) , 24 . 1 3 8 . 7 ( b ) 24 4-3
.16.1.5, 3 ] 5 . 1 . 6 ( a ) , 24
155
] 3 9 . 4 ( b ) 24
t
5-4
.163.03
5
]55.5
6-5
.165.33
6
356.5
11.0-9
181.33
J0
161
30-29
1165.825
30
165
32-31
.156.425
32
363
34.-33
1154.425
34
360
37-36
114725
37
154.5
4.l - 4 0
.14325
4.1
.147
43-42
.139.? 25
43
.143
In Re~.
24, r e s u l t s o~ r o t a t l o n a l ~ e l a x a t i o n t a r e Conetants a ~ e obtained ~ot
the g~ound orate Lnd £ive v i b r a t i o n a l eXCited atates. (&) ~efe~s t o the ground state and ( b ) t o the v L otate (tOO).
304
J.-P. BOUANICHet al.
and 0 to 108 for T = 200 K. For the interruption function, the following cutoff procedure has been used: S2(b ~d~, the distance of closest approach for a head-on collision. Therefore, the problem of close collisions does not occur, and the contribution of the repulsive anisotropic potential is very small. On the other hand the contribution of the semi-empirical term -4ETl(tr/R)6p2(cos 01), which not only represents the anisotropic dispersion but also the dipoleinduced dipole interaction potential, cannot be neglected especially for 1mI< 10. This calculation yields values of 70 at 298 K [Table 3 (a)] and at 200 K [Table 4 (a)] that are much larger, than our experimental values for [m[ < 55 at 298 K and Im[ < 48 at 200 K. The difference increases from about 13% at Im[ = 2 to about 23% at Iml = 20-30 and decreases for higher [ml. Another calculation, denoted as calculation (a'), has been performed by taking into account the Maxwell-Boltzmann distribution of velocities (instead of the mean collisional velocity ~) through the modified resonance functions ~(k), ~j(k), Fj(k), t~j(k) defined by Cattani. 3°'3~ Including the velocity distribution does not affect the calculated linewidths appreciably [Tables 3(a') and 4(a')]. Agreement with our experimental results is only slightly improved for Im[~>48 at 200 K. In the preceding calculations, the same value of the dipole moment has been used for the lower and upper states of the active molecule. Using/~ = 0.694 D 32 for the vibrational v~ state of OCS leads to 70 values we estimate to be about 1% lower than the calculated results given in Tables 3 and 4. Thus, using a more accurate value of p~ for OCS in v~ state cannot explain the discrepancy with experimental data. A second type of calculation, denoted as calculation (b), has been carried out on the basis of the semi-classical impact theory developed by Robert and Bonamy. ~° This theory includes a non-perturbative treatment of the differential cross sections which does not require a cutoff procedure, as well as an improved kinematic model of binary collisions. We used the formalism presented in Refs [13] and [26] for our calculations. By considering the intermolecular potential defined by Equation (5), the theoretical results [Tables 3(b) and 4(b)] are greatly improved, but they are still larger than our experimental data (Fig. 3). The relative difference is approximately the same at 298 and 200K, and varies from 8-10% for Iml = 2 to about 15% for Iml = 24. The fact that for higher Iml the theoretical halfwidths decrease faster, than the measured halfwidths, as Iml increases, has been observed previously for CO self-perturbed, 26 CO perturbed by N2, ~2 and for OCS perturbed by N2 .13 This.may be caused by underestimation of short-range repulsive forces and neglect of higher-order interactions involving especially the octopole and hexadecapole moments of the molecules. Comparison with recent calculated results
A calculation has been performed by Leavitt and Sattler, 33 using their own formalism (notably improved with regard to the ATC theory) which includes an elaborated intermolecular potential especially for the dispersion and induction interactions. Their results are slightly smaller for Iml < 10 and Iml > 40 than the results of calculation (b). The differences at low J would indicate that our dispersion potential energy in R-6, which implicitly includes the induction interaction, may be slightly overestimated. Using a diode laser heterodyne technique, they measured pressurebroadening coefficients for four lines in the 2v~ band of OCS. For the lines R(3), R(7) and R(I 1), their experimental results, which are not explicitly given, are somewhat lower than the calculated values of halfwidths. Matsuo et al. 24 used the ATC theory to calculate the relaxation rate constants of OCS for the rotational transitions 1-0 to 4-3 in six different vibrational states. They obtained an overall agreement with their experimental data. We estimate that this agreement is not significant because they considered only the dipole-dipole interaction and neglected the dispersion and induction forces which provide an important contribution at low Iml values. If we consider the electrostatic (dipole and quadruple) interactions only, the calculated half-widths derived from the ATC theory are also in agreement at low Iml with the experimental data. For example, we obtain the following 70(Iml) values (in cm ~-atm-~): 0.1534 for Iml = 4 instead of 0.1749, 0.1622 for Iml = 7 instead of 0.1793, 0.2068 for Iml = 25 instead of 0.2073. Thus, the discrepancy remains for Iml > 10 and the calculated and experimental curves 70 = f ( I m l ) do not have the same behavior. Mehrotra and Milder25 used the modified Murphy-Boggs theory to calculate the OCS half-
Line strengths and collisional half-widthsin the v, band
305
widths for the rotational transitions 30-29 to 43--42. Their theoretical values range from 1 to 4% lower than the results of calculations (b) and are notably larger than their experimental results. However, they were able to obtain good agreement by limiting the potential to the dipole-dipole interaction potential. From this investigation, it may be concluded that, regardless of the semi-classical theory used, the use of intermolecular potentials that include the most important long- and middle-range interactions leads to self-broadening coefficients which are significantly larger than the experimental values for Iml < 50. This discrepancy which does not seem to occur for other active and/or perturbing molecules is difficult to explain. We believe that the relative failure of these calculations may originate in one of the common assumptions included in the theories of linewidths or their applications, specifically: not including the effects of correlations between active molecules; the neglect of induction effects in the active molecules (this assumption is questionable for molecules with large dipole moment and polarizability components); and the assumption that all the perturbing molecules are in the ground vibrational state (the contribution of the non-linear OCS molecules in the v2 state has been disregarded).
Temperature dependence of linewidths To determine the variation of half-widths with temperature, we use the usual relation: ?0(T) = ?0(T0)" (T/To)-".
(6)
This procedure is probably an oversimplification, but it has the advantage of allowing comparisons between measurements at different temperatures. In the present work, To = 298 K and T = 200 K. By comparing the experimental (smoothed and averaged) values of ~0 given in Table 3 for 298 K with those given in Table 4 for 200 K, we obtain for the exponent n, values which are strongly Im[ dependent: n increases from 0.76 for Iml = 2 to 0.90 for Iml--- 18, then regularly decreases to 0.34 for Iml = 55 (Fig. 4). Assuming nearly independent errors in the experimental values at 298 and 200K, the error limit in n is estimated to be +0.20. Within this uncertainty, the temperature dependence of halfwidths determined experimentally is in satisfactory agreement with that derived from calculation (b). The resulting n exponent increases from 0.79 for Iml --- 2 to 0.95 for Iml = 17, then decreases to 0.35 for Iml = 51 and increases slightly (0.38 for Iml = 55). The ATC theory provides poorer agreement, especially for Iml > 35: n increases from 0.78 for Iml = 2 to 0.97 or 0.96 for Iml = 17, then decreases for higher Iml to - 0 . 1 0 or 0.01 for Ira[ = 55 [the first value arises from
1.0
q: 0 . 5 •
(o)
0.0
I
I 10
I 20
I 30
I 40
o
. .
~-
"-
I 50
Iml
Fig. 4. Variation of the temperatureexponentn with Iml d e t e r m i n e d for TO= 298 K a n d T = 200 K; (...) experimental results arising from smoothedand interpolatedvalues of ~0; (---) results of calculation(a); (. . . . . . ) calculation (a'); ( ) calculation (b). Q.SR.T. 36/4~
306
J.-P. BOUANICHet al.
calculation (a), the second value from calculation (a')]. A negative value for n, which corresponds to linewidths ~0 larger at 298 K t h a n at 200 K, seems to be unrealistic. It thus appears that the A T C theory does n o t yield a satisfactory v a r i a t i o n of ~0 with T for high Iml values. T h e self-broadened linewidths of OCS have been m e a s u r e d by Srivastava et al. 7 for the 3-2 r o t a t i o n a l t r a n s i t i o n at v a r i o u s t e m p e r a t u r e s r a n g i n g from 233 to 348 K. These a u t h o r s o b t a i n e d n = 0.77-4-0.08, a value in excellent a g r e e m e n t with o u r result for Lml = 3: n = 0.78. F r o m m e a s u r e m e n t s o f linewidths for the r o t a t i o n a l t r a n s i t i o n 2-1 o f OCS at five t e m p e r a t u r e s in the range 297-346 K, Creswell et al. 5 o b t a i n e d n - 0 . 9 . F o r Iml = 2 o u r result is 0.76. These results suggest to us two c o m m e n t s . First, as m e n t i o n e d by these authors, the experimental data are n o t sufficient to d e t e r m i n e in a small t e m p e r a t u r e range ( < 100 K) the precise v a r i a t i o n of ?0 with T. M o r e o v e r it is n o t o b v i o u s that we should find the same value o f n from m e a s u r e m e n t s at t e m p e r a t u r e s below a m b i e n t a n d m e a s u r e m e n t s at t e m p e r a t u r e s above a m b i e n t , because n is p r o b a b l y n o t c o n s t a n t with T over a large t e m p e r a t u r e range. 34 F r o m this study, it m a y be c o n c l u d e d that, a l t h o u g h the theoretical iinewidths are larger t h a n the e x p e r i m e n t a l values, the t e m p e r a t u r e d e p e n d e n c e is nearly identical for b o t h the theoretical a n d e x p e r i m e n t a l values.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.
C. O. Britt and J. E. Boggs, J. chem. Phys, 45, 3877 (1966). Krishnaji and S. L. Svrivastava, J. chem. Phys. 47, 1885 (1967). A. Battaglia, M. Cattani and O. Tarrini, Nuovo Cimento 61B, 193 (1969). W. R. MacGillivray, J. Phys. B: Atom. Molec. Phys. 9, 2511 (1976). R. A. Creswell, S. R. Brown and R, H. Schwendeman, J. chem. Phys. 64, 1820 (1976). P. L. Hewitt, JQSRT 17, 227 (1977). G. P. Srivastava, D. Kumar and A. Kumar, J. chem. Phys. 66, 20 (1977). A. G. Maki, W, B. Olson and R. L. Sams, J. molec. Spectrosc. 81, 122 (1980). J. S. Wells, F. R. Petersen, A. G. Maki and D. J. Sukle, Appl. Opt. 9, 1676 (1981). D. Robert and J. Bonamy, J. Phys (Paris) 40, 923 (1979). G. Blanquet and J. Walrand, Comp. Enhanced Spectrosc. 2, 135 (1984). J. P. Bouanich, R. Farrenq and C. Brodbeck, Can. J. Phys. 61, 192 (1983). A. Mouchet, G. Blanquet, P. Herbin, J. Walrand, C. P. Courtoy and J. P. Bouanich, Can. J. Phys. 63, 527 (1985). J. Deltour, Infrared Phys. 9, 125 (1969). A. Mouchet, Graduate Dissertation, Facult6s Universitaires Notre-Dame de la Paix, Namur, Belgium (1983). B. H. Armstrong, JQSRT 7, 61 (1967). K. Jolma, J. Kauppinen and V. M. Horneman, J. molec. Spectrosc. 101, 300 (1983). D. G. Robinson and N. H. Senturk, J. Chem. Thermodynam. 11, 875 (1979). G. Herzberg, Molecular Spectra and Molecular Structure H. Infrared and Raman Spectra of Polyatomic Molecules, p. 502. Van Nostrand, New York (1964). R. Herman and R. F. Wallis, J. chem. Phys. 23, 637 (1955). V. M. Devi, P. P. Das, A. Bano and K. N. Rao, J. molec. Spectrosc. 87, 578 (1981). R. H. Kagann, J. molec. Spectrosc. 94, 192 (1982). A. C. Maki, A. S. Pine and M. Dang-Nhu, J. molec. Spectrosc. 112, 459 (1985). Y. Matsuo, T. Minowa, H. Komatsu and T. Shimizu, J. chem, Phys. 82, 3127 (1985). S. C. Mehrotra and H. M~ider, Can. J. Phys. 62, 1280 (1984). J. P. Bouanich, JQSRT 31, 561 (1984). F. H. de Leeuw and A. Dymanus, Chem. Phys. Lett. 7, 288 (1970). W. H. Flygare, W. Hiittner, R. L. Shoemaker and P. D. Foster, J. chem. Phys. 50, 1714 (1969). J. S. Murphy and J. E. Boggs, J. chem. Phys. 49, 3333 (1968). M. Cattani, J. chem. Phys. 52, 4566 (1970). V. Prakash and J. E. Boggs, J. chem. Phys. 55, 1492 (1971). A. Foord and D. H. Whiffen, Molec. Phys. 26, 959 (1973). R. P. Leavitt and J. P. Sattler, JQSRT 29, 179 (1983). J. Bonamy, D. Robert and C. Boulet, JQSRT 31, 23 (1984).
0022-4073/86 $3.00+ 0.00 Copyright © 1986PergamonJournals Ltd
Printed in Great Britain. All rights reserved
DIODE AND
LASER
MEASUREMENTS
COLLISIONAL OF
OF
HALF-WIDTHS OCS
AT
298 AND
LINE IN
STRENGTHS
THE
v1 BAND
200K
J.-P. BOUANICH Laboratoire d'Infrarouge, Associ6 au C.N.R.S., Universit6 de Paris-Sud, B~timent 350, F-91405 Orsay Cedex, France and G. BLANQUET, J. WALRAND and C. P. COURTOY Laboratoire de Spectroscopie Mol6culaire, Facult6s Universitaires Notre-Dame de la Paix, Rue de Bruxelles 61, B-5000-Namur, Belgium (Received 15 November 1985)
Abstract--Absolute line strengths and self-broadened half-widths have been measured at 298 and 200 K for spectral lines ranging from J = 1 to 55 in the vI band (860 cm -I) of J6OI2C32S,using a tunable diode laser spectrometer. The vibrational transition moment (6.412 +0.16 x 10-2D) as well as the absolute intensity (29.63 _+ 1.48 cm-2-atm t at 298 K), of the vt band are determined from these line-strength measurements. By applying two semi-classical impact theories of collisional broadening, we have obtained results for half-widths at 298 and 200 K which are significantly larger than the experimental data for [m[ < 50. However, the variation of the linewidths with temperature is well reproduced theoretically. INTRODUCTION A l t h o u g h the self-broadening coefficients for pure rotational transitions o f O C S have been the subject o f several experimental investigations, especially for low J values, l-7 accurate values are not available for rovibrational transitions. In the infrared, the collisional linewidths, as well as the line strengths, are difficult to measure accurately, even with a high-resolution spectrometer, because m o s t o f the v i b r a t i o n - r o t a t i o n lines o f 16O12 C32S exhibit a varying degree o f overlap increasing with pressure, especially at r o o m temperature. Using a natural sample o f OCS, spectra o f the v~ lines o f 16OI2C32S,recorded between 835 and 875 cm -~, are generally complex owing to the presence o f weak lines arising mainly from the hot bands (vl + v 2l ) - v 2t and (2Vl - Vl) and f r o m the v I b a n d o f 16OI2C34S. The only previous accurate determinations o f vl line strengths were performed by Wells e t al. 9 These were m a d e from intensity measurements o f two lines in the R - b r a n c h . Using a high-resolution tunable diode laser ( T D L ) spectrometer, we have measured, for relatively high pressures o f OCS, the absolute strengths o f 35 lines at 298 K and 30 lines at 200 K, and the half-widths o f 36 lines at 298 K and 31 lines at 200 K. These measurements include several blended lines: six at r o o m temperature and two at low temperature. The experimental conditions, as well as the procedure used in data reduction, are described in the following sections. F r o m line-strength measurements, we deduce the vibrational transition m o m e n t and the total integrated intensity o f the vl band, from which we calculate s m o o t h e d values o f the line strengths. The results obtained are c o m p a r e d with available literature values. The experimentally determined pressure-broadened linewidths are c o m p a r e d with the results o f calculations derived from the A n d e r s o n - T s a o - C u r n u t t e (ATC) theory and from a m o r e recent semi-classical impact theory, I° which has been applied with some simplifications. The temperature dependence o f linewidths is deduced from the experimental results and f r o m the calculated results at 298 and 200 K. EXPERIMENTAL
PROCEDURE
The spectra were recordecl on a commercial diode laser spectrometer (Spectra Physics) operating in the 800-900 c m - 1 region, interfaced to a minicomputer. ~l The collimated o u t p u t beam from the T D L was passed t h r o u g h a variable temperature absorption cell containing the gas sample. This 295
296
J.-P. BOUANICH et al.
cell, with a maximum optical pathlength of 4.80cm, and its cryostat have been described previously. 12 Two OCS gas samples were obtained--one from Matheson Co. with a stated purity better than 97.5% and one from l'Ah" Liquide with a stated purity of 99.9% - - a n d were used without further purification. A natural sample of OCS contains 93.74% of the isotopic species 16OI2C32S. In order to obtain the collisional linewidths, we must choose OCS pressures carefully. Low pressures ( < 4 0 mbar) lead to relatively small overlap of adjacent lines, but corrections for the Doppler and T D L linewidth are still important. Much higher pressures increase the linewidths, which are predominantly collision-broadened. Higher pressures also increase the line overlap and the baseline may be less well defined as well. Therefore, we estimate that several pressures are required to obtain reasonably accurate data. We used OCS pressures of about 40, 55, 70, and 85 mbar at room temperature and about 30, 45, 60, and 75 mbar at low temperature. These pressures were measured with a capacitance manometer with an accuracy better than 1 mbar and with a Bourdon-tube gauge having an accuracy of 0.5% of full scale (0-130 mbar). During the experiments, the cell was not isolated from the gauges so that the pressures of OCS in the cell at low temperature were measured without any corrections. It should be noted that the line strengths could have been determined at much lower pressures (which are difficult to measure accurately), but with the advantages (less interferences, well defined background) and the disadvantages (larger corrections) mentioned. The temperature of the gas sample was measured with a platinum resistance thermometer mounted inside the cell and was kept constant at 298 and 200 K with a maximum variation of + 2 K. The P(J) and R(J) lines with J < 6 and J / > 39 were recorded with an optical pathlength of 4 . 8 0 _ 0.02 cm, whereas the other lines were recorded with a pathlength of 1.90_ 0.02 cm. Relative wavelength calibration was performed using an air-spaced Fabry-Perot etalon with a fringe spacing of 0.029851 cm -~, which could be introduced into the laser beam. Spectral purity of the modes was checked by observation of the smoothness of the etalon fringe pattern. The following data were recorded for each absorption line: the diode emission without absorption (this was used for normalization of spectra); the spectrum of OCS at low pressure (about 5 mbar) (this allowed to unambiguous identification of the transition and aided determination of the background, i.e. 100% transmission level); the spectra of the pressure-broadened OCS line; the spectrum of the F a b r y - P e r o t etalon with the absorption cell evacuated. The successive recordings were monitored and stored by a minicomputer. The digitized absorption spectra and etalon fringes were analyzed by a computer program to obtain the line center and etalon fringe-peak positions. A roughly fiat background level was also obtained by normalization to the true emission profile of the diode.It Figure 1 shows an example of the normalized spectra of a line and the corresponding fringe pattern from the etalon scan. A slight anomalous rise of the peak absorption and of the far wings appeared for some lines as the pressure increased. This was probably caused by an absorption continuum from the neighboring lines and was accounted for in the determination of the baseline. It is noteworthy that for an isolated mode of the TDL, the shuttered scan level corresponded to exactly the 100% absorption level produced by a saturated line. This result was checked systematically in the study of OCS lines broadened by N2 .~3 DATA REDUCTION The measured absorption coefficient, K(v), at the wavenumber v is obtained from
K(v)
= ln[/o (v)/I, (v)] l - ~,
(1)
where Io and It are, respectively, the incident and transmitted light intensities and 1 is the optical pathlength. The measured linewidths, 27obs, were taken directly from the spectra at a transmission equal to x/Io(vo)I~(vo) where v0 is the line center wavenumber. ~3 To determine the collisional half-widths, Yc, corrections have been made for the effects of instrumental and Doppler broadenings on the absorption line profiles. These corrections are small (-,.<3%) because the T D L linewidth (estimated to be on average 1.3 × 10-3cm -l) and the Doppler width (which around the band center is 1.37 x 1 0 - 3 c m - l at 298 K and 1.12 x 1 0 - 3 c m - I at 200 K) are almost negligible compared to the observed widths (10-35 x 10 -3 cm-t). A detailed description of the corrections is given in
Line strengths and collisionat half-widths in the v~ band
0% T r l n s m i s s i o n
Fabry-
Psr ot
etaton
297
lever
trace
/
/
r~
i i
Ii !'
"/'
!1/
,I
/
!, r
I
I11 i,'
!It
iI~
~/'
100% Transmitted
j
!
i///
I'
I
intensity
Fig. 1. The normalized spectra of the R(36) line recorded for pure OCS at 8, 30, 45, 59.8 and 74.9mbar and 200 K. Ref. [13]. A plot o f the m e a s u r e d and collisional broadening coefficients vs O C S pressure P is shown in Fig. 2. It m a y be seen that, even for m e a s u r e m e n t s at 30 mbar, Yc is close to 7obs- The straight lines obtained are a verification o f the proportionality o f )'c with P. The self-broadening coefficients Y0 (in c m - t - a t m -~) are derived f r o m the slopes o f these lines.
30
A
T
2O
E u
m
I o
t~
10
I 20
I
I
I
40
60
80
P
(mbar)
Fig. 2. Linewidth vs OCS pressure for the self-broadened R(36) line of OCS; ( x ) measured linewidths, 27ob,; (C)) collisional linewidths, 27,-
J.-P. BOUANICHet al.
298
If we assume a Lorentz shape for the pressure-broadened lines, then the line strengths, S, are obtained from S = Kc(vo) rtTc, where Kc(vo) is the collisional peak absorption coefficient. Corrections for the Doppler and T D L linewidth contributions are, in principle, necessary to determine Kc(vo) from K(vo). The corrections for instrumental (TDL) distortions were made on the measured parameters K(vo) and 7 by using Tables 4 and 5 of Ref. [14] established for the convolution of a Lorentz profile by a Gaussian function. This procedure is justified because the effective T D L lineshape may be approximated by a Gaussian function ~5 and, for the pressures used, the absorption lines are nearly Lorentzian and are theoretically described by a Voigt function. With these corrections, we have obtained K,,(v0), the peak absorption coefficient resulting from the superposition of Doppler and collisional broadenings. Next Kc(vo) was calculated from the following relations derived from Ref. [16]:
K~(vo)=Kv(vo)/[xf-Hy(1--erfy)exp(y2)]=Kv(vo)/[1+
~ (-1) "1'3"''(2m-1)] m=, "~y~
,
(2)
where y = (In 2)t/2(yc/yD), 7D is the Doppler half-width. For y > 4, we use
Kc(vo) = K~.(Vo)/[1 -- (1/2 y2) + (3/4 y4)].
(3)
Except for the lowest pressures considered (about 40 mbar at 298 K and 30 mbar at 200 K), these corrections are much smaller than our experimental uncertainties for K(vo) so that K~(vo) ~- K(vo). Therefore, for P > 50 mbar, the line-center absorption coefficient should be constant as the pressure increases, a result which is roughly verified experimentally. Assuming that the line strengths are proportional to the pressure, we have determined, for each line and temperature, an average value of line strength (So) expressed in cm 2-atm ~ such that So = S/P' with P ' ( a t m ) = P ( m b a r ) x 0.9374 x Ce/1.01325 103. The first factor represents the proportion of 16012C32S in natural OCS. The second factor (Cr) is the overall purity of the OCS gas. Cp is set equal to 0.98 for the first gas sample and 1 for the second sample. These two factors were not considered in determining 70. The main sources of uncertainties in the determination of 70 and So arise from: (1) the presence of weak overlapping lines; in the case of a single, strong overlapping line, measurements were performed on the half of the line away from the interfering line; (2) the baseline location; this is difficult to determine for Lorentzian pressure-broadened lines; (3) the non-linear tuning of the laser; this may be seen from the variation of the Fabry-Perot fringe spacings; (4) the small fringes appearing in the transmission curves (Fig. 1); these are due to parasitic interferences; (5) uncertainties in the pathlength (these occur in the intensity measurements only); (6) errors in the temperature and pressure measurements; (7) the improbable occurrence of a non-isolated mode of the TDL; this would imply a 100% absorption level lower than that considered.
LINE STRENGTHS
Experimental and calculated results The line strengths, So, normalized to 100% 16OI2C325, were determined for the v~ band at 298 and 200 K with an estimated relative error of + 10%. The measured strengths of unblended lines are given in Table 1. In addition, we have measured the strengths of the blended lines P(55), P(33), P(10), P(6), R(1), and R(10) at 298 K. The lines P(33), P(6) and R(1) coincide, respectively, with the P(7), R(22) and R(31) lines of the v~ band of 16012C345,17whereas the P(55), P(10) and R(10) lines are, respectively, blended by the lines P(40), R(6) and R(28) of the (vl + v,~) - v~ hot bands. 8 At low temperature, the strengths of the blended lines P(6) and R(1) were also measured. Because the hot-band lines become much weaker at 200K, the R(10) line may be considered to be unblended. The strength So of an infrared absorption line at the wavenumber v0 is related to the dipole moment matrix element of the rovibrational transition IRvjj v,s,I by
So(T) = 8113 Nr 3h~ Qv(T)Qr(T) Voexp
hcE,(J) ~
Imt l R : f l = ×
1 - exp
--kT- ]]
(4)
Line strengths and collisional half-widths in the vI band
299
where N r is the number of OCS molecules in 1 cm 3 at I atm and absolute temperature T. Here, we used N r = N L x 273.15/T, where N L is the Loschmidt's number. For the pressures considered, OCS behaves as a perfect gas but this is not the case for higher pressures; at 1 atm and 0°C, the number of molecules cm -3 is 1% larger than NL, 18 and the difference increases with increasing density and/or decreasing temperature. E,(J) is the energy (in cm -~) of the lower rotational level of the transition; m = - J for a P(J) line and m = J + 1 for a R(J) line. The induced emission term, 1 - e x p ( - h c v o / k T ) , is almost unity for the v] band. Q~. and Q, are the vibrational and rotational partition functions given by Q~ = E~gv e x p [ - G ( v ) , hc/kT] and Q, = Es(2J + 1) exp[-hcE~(J)/kT].19 Because the OCS molecule has a doubly-degenerate vibration v2 centred at 520.4 c m - ], Q~ is significantly larger than unity. By considering the B and D rotational constants for the v~ band of ]60~2C32S given in Ref. [9], we obtained, at 298 K, Q,, = 1.203, Q~ = 1021.7911 (J varying from 0 to 132); at 200 K, Q~ = 1.051, Qr = 685.7767 (J varying from 0 to 108). By introducing the measured values of line strengths given in Table 1 and all known quantities into equation (4), IR~J'I2 was calculated for each line. N o clear J-dependencies were observed in the IR 12values and the Herman-Wallis factors 2° were not determined. The mean IR~'I value derived from the measurements at 298 and 200 K is 6.412 x 10-2D, with an absolute error estimated to be +0.16 x 10-2D. By using this value of IR~'I and assuming that the vibration-rotation interaction function 2° F(m)= 1, we have obtained the calculated line strengths listed in Table 1. These results are in reasonable agreement with the experimental data at 298 K, as well as those at 200 K. The absolute intensity of the v~ band of ~60]2C32S was evaluated by summing the calculated values of So(T) over all the lines considered for the calculation of Q,(T). We thus obtain the following values: S,,o = 29.63 cm-2-atm -~ at 298 K, S~o = 33.82 cm-2-atm -~ at 273.15 K (STP conditions), S Vl ° = 51.21 cm-2-atm -] at 200 K, with an estimated uncertainty of 5%. Table 1. Observed and calculated line strengths ~ (in cm ]-atm ~ ) i n the v~ band of 16012C32S at 298 and 2 0 0 K 298 K
200 K
298 K
Line
200 K
Line ohmeryed
calculated
obBex'ved
ca/cuJated
ol~e.rved
ca3cuJated
observed
caJ c u ] a t c d
0.5823
0.5868
P( ss )
0.0759
0,0447
P(9)
0.2333
0,2380
p( 52 )
0.0987
0.0695
0.0679
P(8)
0.2237
0.2154
0.5358
P( 81 )
0.1097
0.1073
0.0762
o.o??s
P(6)
p( 48 )
0.3368
0.1357
0.1129
0.1132
P(4)
;)(~)
0.1789
0.1794
0.1800
o.1788
p(3)
0.2531
0.3125
0.3203
P(2)
0.3487
R(1)
0.3783
R(2)
0.0845
0.0866
0.2059
0.1098
0.1349
0.2801
0.2941
0.3426
0.3?43
0.3635
p(38) ]P(37)
0.2660
0.2656
;)( 36 )
0.2873
0.2780
;)(34)
0,3069
0.3020
0.4397
R(3)
0.3135
0,4716
R(4)
;)( 33 ) ]P( 31 )
0.3349
0.3623
0.5655
0.3665
0.4202
0.3141
0.3136
0.2896
o.o888
0.0859
0.228?
0.2198
0.0576
0,1486
0.1479
-
--
0.0580
0.1491 0.2224
0.5361
R(6)
0.1956
0.5161
0.4933
P( 30 )
0.3480
0.34.45
0.5682
R(3o)
-
0.2881
0.7033
0.?033
;)(29)
0.3589
0.3534
0.5998
R(36)
0.4,012
0.3810
P( 25 )
0.3793
0.3787
0.7074
o.7342
R(37)
-
0.3903
;)(22 )
0.3844
0.7330
0.7?6?
R(18)
0.3960
0.3979
0.8690
P( 21 )
0.3833
0.8178
o.79o9
R(24)
o.3877
0.4079
0.7868
0.39?4
0.8604 0.8892
0.8673
P(2o)
0.3743
0.3805
0.8013
R(25)
P(ls)
0.3769
0.3?62
0.8074
R(26)
0.4124
0.3990
;)(38)
0.3709
0.3703
0.8089
R(28)
0.3786
0.3853
0.7378
0.6733
0.8056
R(36)
0.2909
0.2964
0.3987
0.4024
0.7643
R(39)
0.2497
0.256?
0.3114
0.3123
0.2356
0.2434
0.2809
0,2850
0.2302
0.2396
0,2592
;)(17)
0.3622
0,8184
;)(14)
0.3285
0.3282
;)(13)
0.3205
0.3134
0.7307
0,7397
e(,dJK))
;)( 12 )
0.2969
0.7106
0.?096
R(41)
;)(.)0)
0.2591
0,6330
-
-
0.4043
0.7676
O.76JJ 0.7329
300
J,-P. BOUANICHet a/. Table 2. Relative difference (in percent) between the strengths of blended lines (BL) and unblended lines (UL)
Line
T(K)
[Sobs(BL) - Scalc (UL)] x 100
Scalc (UL)
Estimated from the calculated relative line strengths
P(55)
298
+ 11.1
9.65
P(33)
298
+
8.0
2.7
P(IO)
298
+
9.2
6.0
P(6)
298
+
5,3
10.9
R(1)
298
+ 26.4
27.3
R(IO)
298
÷ 10.1
10.9
P(6)
200
+
1.6
8.7
R(1)
200
÷ 18.4
16.9
As may be seen in Table 2, we have evaluated the relative difference between the measured strengths of blended lines and their calculated strengths (given in Table 1). In addition, we have determined the strength ratios of the two components of blended lines by considering the relative line intensities given in Table 2 of Ref. [8], our calculated results, and by assuming that the line strengths So for the isotopic species OC32S and OC34S are the same. Within the experimental errors (~< 10%), corresponding line strengths in Table 2 are in reasonable agreement. We have thus obtained experimentally the expected result: the intensity of a blended line is the sum of the intensities of the individual components of the blended line.
Comparison with other data From our results, we are able, in principle, to calculate line strengths for any transition in the v~ band of OCS. This permits comparisons between our results and those of previous studies to be made. The calculated results of Devi et al. 2~ at 300 K for J ~< 50 are 20-30% lower than our results at 298 K. This is outside the range of our estimated experimental error. However, the agreement is better for P lines with higher J values [for P(75) and P(76), we obtain the same calculated values]. Considering these differences, it is surprising that these authors obtained a band strength of 26.93 cm-2-atm -~ (close to our value, i.e. 29.63 cm-2-atm -I at 298 K) and a squared transition moment IR~'I2 of only 2.85 x 10 -3 D 2 (our result is 4.11 x 10 -3 D2). The calculated results given by Wells et al. 9, derived from the measured R(28) and R(33) line strengths, are about 7.5% smaller than our calculated values of So. However, the resulting transition moment, 6.32 x 10 -2 D (a value identical to that given in Ref. [22]), is only 1.5% lower than our value. This difference could be approximately accounted for if their calculated line strengths had not been normalized to 100% ~60~C~2S. Kagann 22 has recently measured the total intensity of the vt band. The result obtained, 35.5 cm-2-atm -~ , probably included all hot bands and isotopic transitions in the v t region, but is consistent with our determination at 298 K. (A rough estimation 23 of the total strength in the vt region would be to multiply Sv~ by Qv. This gives 35.6cm-2-atm -t which is close to Kagann's value.) COLLISIONAL
HALF-WIDTHS
Experimental results The values we have determined for the collisional half-widths, Y0, at the four pressures studied are given in Table 3 for 298 K and in Table 4 for 200 K. The relative error in 70 is estimated to
Line strengths and collisional half-widths in the v~ band
-g v
~
0
~
,
7
~
~
,
,
0
~
;
,
,
~
0
~
~
~
~
~
~
o
~
301
o
~
, ~ = ~
~
.~z
.
•
,
u
~
j
~
o
.
j
j
~
~
. . . . . . . . .
0"0
J~
~.~ "~..~ L m •
,
.
.
.
.
.
.o x
~
~J
~
~
. . . .
~
~
,
~
~
~
~ J ~ ,
~
~
'~ ~
~
,
~
,
~
~ r ' ~
.3
~-.~7
~.~ 3
i
v
°
J~
o
L
uJ 0.
.
.
.
.
"~ ~
,
~
~, •
,
,
o
E
~
~
~
~
~
•
J.-P. BOUAN1CFI et al.
302
be about + 6% and is, a priori, still larger for values given in parentheses. These values correspond to the blended lines P(33), P(6) and R(1) at 298 and 200 K, P(55), P(10) and R(10) at 298 K, to the P(52) line at 200 K which is overlapped by a strong isotopic line [P(28) of OC34S] and to the very weak P(55) line at 200 K. Within this uncertainty, the linewidths are only Iml dependent, in accordance with the impact theories in which the imaginary parts of the differential cross section are generally negligible. The smoothed values given in Tables 3 and 4 arise from the smooth curves (Fig. 3) that fit the experimental data. An uncertainty of _+5% on these values seems reasonable. It appears that the scatter of the data, especially of the blended lines, around the average curves is small. This result seems to indicate that for two overlapping lines with v e r y different intensities, the weaker line has no detectable influence on the linewidth of the stronger line. Comparison with other experimental data
Assuming that the vibrational dependence of the self-broadened linewidths is very small, we may compare our results for 70 with those obtained for pure rotational transitions J + 1 , - - J in the microwave region. This comparison is summarized in Table 5 (units are converted from M H z / T o r r to c m - L a t m ~). Our smoothed and interpolated values of 70 are smaller, especially for Iml = 10, than the values of Battaglia et al. 3 and are larger for Iml = 2,3,4 than the results obtained recently by Matsuo e t al. 24 for the ground and vibrational excited states. Our data are also somewhat larger for Irnl= 32,34,37,41,43 than the results of measurements in the excited vibrational state (01~0) by Mehrotra and M~ider} 5 By considering all these data, the following conclusions may be drawn: our results are on the whole larger than those obtained for pure rotational transitions; the results given by Battaglia et al. 3 are larger; those given by Matsuo et al. 24 are smaller. The values of 70 obtained in the v~ band by Devi et al. 2~ range from 40 to 60% higher than the experimental results presented in Tables 3 and 5. However, from direct half-width measurements of P(67), P(72) and P(76), these authors determined a mean value of (0.108 + 0.005) c m - L a t m ~ which is consistent with an extrapolation of our results to these lines. Concerning the linewidths at low temperature, the only previous result which may be compared with our data at 200 K is the one obtained by Britt and Boggs ~ for the microwave transition J = 2 - 1 at 195 K: (0.208 4- 0.006) c m - L a t m -~ , which is in excellent agreement with the smoothed value for Iml -- 2 (Table 4), 70 = (0.2085 -t- 0.0104) c m - L a t m -~ .
0.25
20OK.+. '" ~.o~+O"
7" 'IE T
--o.+ \ . '....'~
0.20 E o
+o" +
OoO
~2 0.15
6"~+
+
o'"
o9.....'~,,,, +-
÷*. .
,
+
%" . + + ,
010
I 5
I 10
I 15
I 20
I 25
I 30
I 55
I 40
I 45
.+
l 50
Iml Fig. 3. Self-broadened OCS line halfwidths 70 in the v~band at 298 and 200 K; (+) P-lines; (O) R-lines; (...) smoothed and interpolated values fitting the experimental data; the solid lines represent the theoretical values [calculation (b)].
Line strengthsand collisionalhalf-widthsin the v~ band
303
Theoretical results
The collisional half-widths of self-perturbed OCS were first calculated by applying the ATC theory [calculation (a)]. For the intermolecular potential, we have considered electrostatic contributions produced by dipolar and quadrupolar interactions, and anisotropic dispersion contributions in which we have added a repulsive part ]3'26such that the anisotropic intermolecular potential is: 6
V = V~Iu2 "I- V..Q2 "{- Vu:Q, "k VQIQ2 "I- 4Erl
-- -R
"1-
P 2 (COS 01).
(5)
where the subscript 1 refers to the active molecule, and 2 to the perturbing molecule;/~ and Q are the dipolar and quadrupolar moments of the molecules; ~ denotes here the polarizability anisotropy of OCS [~] =(~I!-~±)/3~]. The values used in the ~0-calculations for ~ , the Lennard-Jones parameters e and a, and the rotational constants B and D of the v~ band are given for OCS in Table 2 of Ref. [13]. We have taken into account the dipole moment for the ground vibrational state of OCS, i.e. 0.715 D. For the quadrupole moment, we have considered the value obtained for ~6012C32S from molecular-beam electric-resonance spectroscopyy i.e. 0.786DA, which seems to be more accurate than the value 0.88 DA, derived from molecular Zeeman effect experiments. 28 Because the contributions arising from the quadrupole moment are relatively small, the 70 values calculated with Q = 0.786 DA are only slightly lower (< 1%) than the values calculated with Q = 0.88 DA. The value 2.79 D/~ deduced from linewidth calculations29 has been disregarded because such calculations do not allow an accurate determination of the quadrupole moment. The self-broadening coefficients, ~0, were computed for Iml ~<55 by including the contributions from collisions with perturbing OCS molecules have J2 values ranging from 0 to 132 for T = 298 K Table 5. Comparison between experimental values of ~0 (in 10 3cm-Latm ]) at room temperature in the microwave region and in the vt band of OCS. Our values are averaged over P- and R-lines, smoothed and interpolated Nil z'eBulbs
transition
J'--,3 159.2,1 2-I
I R L.ine Im;
Prement mtud¥ (m mo o r b e d
valueB)
.157.7, 2 1 5 5 . 9 , 3
.152.9, 5 ] 5 4 . 1 , 6 .144(a), 24"1"
.154
1 3 3 . 8 ( b ) 24t" 3-2
.158,4, 3 .1#7. 4 .144.5, 7
.154.5
. 1 4 8 , 3 ( a ) , 24 . 1 3 8 . 7 ( b ) 24 4-3
.16.1.5, 3 ] 5 . 1 . 6 ( a ) , 24
155
] 3 9 . 4 ( b ) 24
t
5-4
.163.03
5
]55.5
6-5
.165.33
6
356.5
11.0-9
181.33
J0
161
30-29
1165.825
30
165
32-31
.156.425
32
363
34.-33
1154.425
34
360
37-36
114725
37
154.5
4.l - 4 0
.14325
4.1
.147
43-42
.139.? 25
43
.143
In Re~.
24, r e s u l t s o~ r o t a t l o n a l ~ e l a x a t i o n t a r e Conetants a ~ e obtained ~ot
the g~ound orate Lnd £ive v i b r a t i o n a l eXCited atates. (&) ~efe~s t o the ground state and ( b ) t o the v L otate (tOO).
304
J.-P. BOUANICHet al.
and 0 to 108 for T = 200 K. For the interruption function, the following cutoff procedure has been used: S2(b ~
A calculation has been performed by Leavitt and Sattler, 33 using their own formalism (notably improved with regard to the ATC theory) which includes an elaborated intermolecular potential especially for the dispersion and induction interactions. Their results are slightly smaller for Iml < 10 and Iml > 40 than the results of calculation (b). The differences at low J would indicate that our dispersion potential energy in R-6, which implicitly includes the induction interaction, may be slightly overestimated. Using a diode laser heterodyne technique, they measured pressurebroadening coefficients for four lines in the 2v~ band of OCS. For the lines R(3), R(7) and R(I 1), their experimental results, which are not explicitly given, are somewhat lower than the calculated values of halfwidths. Matsuo et al. 24 used the ATC theory to calculate the relaxation rate constants of OCS for the rotational transitions 1-0 to 4-3 in six different vibrational states. They obtained an overall agreement with their experimental data. We estimate that this agreement is not significant because they considered only the dipole-dipole interaction and neglected the dispersion and induction forces which provide an important contribution at low Iml values. If we consider the electrostatic (dipole and quadruple) interactions only, the calculated half-widths derived from the ATC theory are also in agreement at low Iml with the experimental data. For example, we obtain the following 70(Iml) values (in cm ~-atm-~): 0.1534 for Iml = 4 instead of 0.1749, 0.1622 for Iml = 7 instead of 0.1793, 0.2068 for Iml = 25 instead of 0.2073. Thus, the discrepancy remains for Iml > 10 and the calculated and experimental curves 70 = f ( I m l ) do not have the same behavior. Mehrotra and Milder25 used the modified Murphy-Boggs theory to calculate the OCS half-
Line strengths and collisional half-widthsin the v, band
305
widths for the rotational transitions 30-29 to 43--42. Their theoretical values range from 1 to 4% lower than the results of calculations (b) and are notably larger than their experimental results. However, they were able to obtain good agreement by limiting the potential to the dipole-dipole interaction potential. From this investigation, it may be concluded that, regardless of the semi-classical theory used, the use of intermolecular potentials that include the most important long- and middle-range interactions leads to self-broadening coefficients which are significantly larger than the experimental values for Iml < 50. This discrepancy which does not seem to occur for other active and/or perturbing molecules is difficult to explain. We believe that the relative failure of these calculations may originate in one of the common assumptions included in the theories of linewidths or their applications, specifically: not including the effects of correlations between active molecules; the neglect of induction effects in the active molecules (this assumption is questionable for molecules with large dipole moment and polarizability components); and the assumption that all the perturbing molecules are in the ground vibrational state (the contribution of the non-linear OCS molecules in the v2 state has been disregarded).
Temperature dependence of linewidths To determine the variation of half-widths with temperature, we use the usual relation: ?0(T) = ?0(T0)" (T/To)-".
(6)
This procedure is probably an oversimplification, but it has the advantage of allowing comparisons between measurements at different temperatures. In the present work, To = 298 K and T = 200 K. By comparing the experimental (smoothed and averaged) values of ~0 given in Table 3 for 298 K with those given in Table 4 for 200 K, we obtain for the exponent n, values which are strongly Im[ dependent: n increases from 0.76 for Iml = 2 to 0.90 for Iml--- 18, then regularly decreases to 0.34 for Iml = 55 (Fig. 4). Assuming nearly independent errors in the experimental values at 298 and 200K, the error limit in n is estimated to be +0.20. Within this uncertainty, the temperature dependence of halfwidths determined experimentally is in satisfactory agreement with that derived from calculation (b). The resulting n exponent increases from 0.79 for Iml --- 2 to 0.95 for Iml = 17, then decreases to 0.35 for Iml = 51 and increases slightly (0.38 for Iml = 55). The ATC theory provides poorer agreement, especially for Iml > 35: n increases from 0.78 for Iml = 2 to 0.97 or 0.96 for Iml = 17, then decreases for higher Iml to - 0 . 1 0 or 0.01 for Ira[ = 55 [the first value arises from
1.0
q: 0 . 5 •
(o)
0.0
I
I 10
I 20
I 30
I 40
o
. .
~-
"-
I 50
Iml
Fig. 4. Variation of the temperatureexponentn with Iml d e t e r m i n e d for TO= 298 K a n d T = 200 K; (...) experimental results arising from smoothedand interpolatedvalues of ~0; (---) results of calculation(a); (. . . . . . ) calculation (a'); ( ) calculation (b). Q.SR.T. 36/4~
306
J.-P. BOUANICHet al.
calculation (a), the second value from calculation (a')]. A negative value for n, which corresponds to linewidths ~0 larger at 298 K t h a n at 200 K, seems to be unrealistic. It thus appears that the A T C theory does n o t yield a satisfactory v a r i a t i o n of ~0 with T for high Iml values. T h e self-broadened linewidths of OCS have been m e a s u r e d by Srivastava et al. 7 for the 3-2 r o t a t i o n a l t r a n s i t i o n at v a r i o u s t e m p e r a t u r e s r a n g i n g from 233 to 348 K. These a u t h o r s o b t a i n e d n = 0.77-4-0.08, a value in excellent a g r e e m e n t with o u r result for Lml = 3: n = 0.78. F r o m m e a s u r e m e n t s o f linewidths for the r o t a t i o n a l t r a n s i t i o n 2-1 o f OCS at five t e m p e r a t u r e s in the range 297-346 K, Creswell et al. 5 o b t a i n e d n - 0 . 9 . F o r Iml = 2 o u r result is 0.76. These results suggest to us two c o m m e n t s . First, as m e n t i o n e d by these authors, the experimental data are n o t sufficient to d e t e r m i n e in a small t e m p e r a t u r e range ( < 100 K) the precise v a r i a t i o n of ?0 with T. M o r e o v e r it is n o t o b v i o u s that we should find the same value o f n from m e a s u r e m e n t s at t e m p e r a t u r e s below a m b i e n t a n d m e a s u r e m e n t s at t e m p e r a t u r e s above a m b i e n t , because n is p r o b a b l y n o t c o n s t a n t with T over a large t e m p e r a t u r e range. 34 F r o m this study, it m a y be c o n c l u d e d that, a l t h o u g h the theoretical iinewidths are larger t h a n the e x p e r i m e n t a l values, the t e m p e r a t u r e d e p e n d e n c e is nearly identical for b o t h the theoretical a n d e x p e r i m e n t a l values.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.
C. O. Britt and J. E. Boggs, J. chem. Phys, 45, 3877 (1966). Krishnaji and S. L. Svrivastava, J. chem. Phys. 47, 1885 (1967). A. Battaglia, M. Cattani and O. Tarrini, Nuovo Cimento 61B, 193 (1969). W. R. MacGillivray, J. Phys. B: Atom. Molec. Phys. 9, 2511 (1976). R. A. Creswell, S. R. Brown and R, H. Schwendeman, J. chem. Phys. 64, 1820 (1976). P. L. Hewitt, JQSRT 17, 227 (1977). G. P. Srivastava, D. Kumar and A. Kumar, J. chem. Phys. 66, 20 (1977). A. G. Maki, W, B. Olson and R. L. Sams, J. molec. Spectrosc. 81, 122 (1980). J. S. Wells, F. R. Petersen, A. G. Maki and D. J. Sukle, Appl. Opt. 9, 1676 (1981). D. Robert and J. Bonamy, J. Phys (Paris) 40, 923 (1979). G. Blanquet and J. Walrand, Comp. Enhanced Spectrosc. 2, 135 (1984). J. P. Bouanich, R. Farrenq and C. Brodbeck, Can. J. Phys. 61, 192 (1983). A. Mouchet, G. Blanquet, P. Herbin, J. Walrand, C. P. Courtoy and J. P. Bouanich, Can. J. Phys. 63, 527 (1985). J. Deltour, Infrared Phys. 9, 125 (1969). A. Mouchet, Graduate Dissertation, Facult6s Universitaires Notre-Dame de la Paix, Namur, Belgium (1983). B. H. Armstrong, JQSRT 7, 61 (1967). K. Jolma, J. Kauppinen and V. M. Horneman, J. molec. Spectrosc. 101, 300 (1983). D. G. Robinson and N. H. Senturk, J. Chem. Thermodynam. 11, 875 (1979). G. Herzberg, Molecular Spectra and Molecular Structure H. Infrared and Raman Spectra of Polyatomic Molecules, p. 502. Van Nostrand, New York (1964). R. Herman and R. F. Wallis, J. chem. Phys. 23, 637 (1955). V. M. Devi, P. P. Das, A. Bano and K. N. Rao, J. molec. Spectrosc. 87, 578 (1981). R. H. Kagann, J. molec. Spectrosc. 94, 192 (1982). A. C. Maki, A. S. Pine and M. Dang-Nhu, J. molec. Spectrosc. 112, 459 (1985). Y. Matsuo, T. Minowa, H. Komatsu and T. Shimizu, J. chem, Phys. 82, 3127 (1985). S. C. Mehrotra and H. M~ider, Can. J. Phys. 62, 1280 (1984). J. P. Bouanich, JQSRT 31, 561 (1984). F. H. de Leeuw and A. Dymanus, Chem. Phys. Lett. 7, 288 (1970). W. H. Flygare, W. Hiittner, R. L. Shoemaker and P. D. Foster, J. chem. Phys. 50, 1714 (1969). J. S. Murphy and J. E. Boggs, J. chem. Phys. 49, 3333 (1968). M. Cattani, J. chem. Phys. 52, 4566 (1970). V. Prakash and J. E. Boggs, J. chem. Phys. 55, 1492 (1971). A. Foord and D. H. Whiffen, Molec. Phys. 26, 959 (1973). R. P. Leavitt and J. P. Sattler, JQSRT 29, 179 (1983). J. Bonamy, D. Robert and C. Boulet, JQSRT 31, 23 (1984).