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High-resolution infrared spectrum of the ν3 band of CD3Br
JOURNAL
OF
MOLECULAR
SPECTROSCOPY
High-Resolution
75,
Infrared
70-80 (1979)
Spectrum
of the v3 Band of CD,Br
R. ANTTILA, T. KARKKAINEN, AND Department
of Physics,
University
J. KAUPPINEN
of Oulu, 90100 Oulu 10, Finland
AND G. GRANER Laboratoire
d’lnfrarouge,
Laboratoire
associt au CNRS, UniversitC 91405 Orsay, France
de Paris-Sud,
Bcitiment 350,
The lowest frequency fundamental band v, of CDSBr has been studied at a resolution limit of 0.03 cm-‘. About 250 J lines belonging to both isotopic species CDS70Brand CDa8iBr have been measured in the P and R branches of this parallel band. In the analyses, leastsquares fits and simulations have been applied. The band centers, 577.286(2) and 575.975(2) cm-r, respectively, have been obtained together with B, DJ, and 4 values. In addition to the main bands, the hot bands 2v3 - V~and vS + vs - v6 have been investigated. I. INTRODUCTION
Due to the two bromine isotopes, which are almost equally abundant, there are two isotopic species of CD,Br. The ground state rotational constant B as well as the centrifugal distortion constants DJ and DJK for both isotopic molecules have been determined by Garrison et al. (I) using microwave spectroscopy. Somewhat later, Morino and Hirose (2) measured with the same method the rotational constants at several excited vibrational states. The constant A,, has recently been determined by Edwards and Brodersen (3) from a vibration-rotation Raman band. The infrared spectrum of methyl bromide-d,, including the lowest fundamental v3, has been studied by Jones et al. (4). In the parallel band u3 they observed two Q branches, but in the P and R branches they only saw one series of lines. As this band around 580 cm-’ seemed to be well suited to our spectrometer, we decided to reinvestigate it. The first aim was to resolve the isotopic structure in the P and R branches. Having recorded the spectrum, we saw that values for several constants could be obtained. An analyses of some hot bands proved to be possible, too. II. EXPERIMENTAL
DETAILS
The measurements were performed with the Fourier spectrometer at the University of Oulu (5). The resolution attained was about 0.03 cm-‘. The computed wavenumbers were checked with water vapor lines (6, 7). The sample gas was purchased from Merck, Sharp and Dohme and it was used 0022-2852/79/040070-11$02.00/0 Copyright
0 1979 by Academic
All rights of reproduction
Press,
Inc.
in any form reserved.
70
vI BAND OF CD,Br
FIG. 1. A recording of the ~a band of CD8Br (upper trace) together with the synthetized (lower trace). Experimental conditions: Path length 1 m, pressure 5.5 Totr. The simulation computed with a resolution of 0.03 cm-’ and it includes, besides the va fundamentals, the 215 - V, and V, + vg - vs. Water vapor absorptions, marked with a dot, are strong because allowed to remain for calibration purposes.
71
spectrum has been hot bands they were
72
ANTTILA ET AL.
Br01
Br01
I I
Br79
Br79 Y I
I
I
I
FIG. 2. Two small regions of the y3 band of CD,Br in detail together with simulations. The conditions are the same as in Fig. 1. In both cases the upper trace is the experimental spectrum, while the lower trace represents the simulation. The first part illustrates the effects of the K structure on P(J) lines near the end of the P branch. Lines belonging to the hot bands 2~ - V, are also visible. In the latter part the effects of the hot bands are discernible at the beginning of the R branch. The lines due to different hot hands are indicated in both parts as follows: (0) 2~3 - vg of CD37sBr; (U) 25 - v3 of CDsslBr; and (+) q + vg - V, of CDaT8Br.
without any further treatment. The gas was in a triple-pass cell giving a path length of 1 m. Several recordings at pressures varying between 0.5 and 5.5 Torr were made. The wavenumbers given are mainly based on five different interferograms. The best spectra were obtained by using a low-pass interference filter, from Optical Coating Laboratory, Inc., and KBr windows to depress the radiation outside the measurement region. III. ANALYSIS OF THE YeBAND
Spectrum
A recording of the parallel vQband is presented in Fig. 1 together with a simulation using the constants derived. Two Q branches due to CD,7gBr and CD,*lBr with a separation of 1.3 cm-l are observed. In addition, the isotopic structure is clearly discernible in the P and R branches. The two series of lines corresponding to the isotopic species cross each other three times. On the other hand, it is not possible to resolve the fine K structure of each “line.” At high J values, however, the effects of the K structure are apparent, because the J “lines” are sharp on the high-frequency side and clearly degrade to lower frequencies. These fea-
q BAND OF CD,Br
73
tures are better seen on the P side, e.g., around 545 cm-‘, where the spectrum is less packed, and they are presented in the first part of Fig. 2. Additional absorptions attributable to the “hot” bands were also detected there as well as just above the main Q branches in the latter part of Fig. 2. Analysis The assignment of the J values was first confirmed with the aid of ground state combination differences. The literature values for the ground state constants are given in Table I. The observed frequencies of the peaks in the main bands are given in Table II. Lower weights are given to the incompletely resolved lines near the coincidences of the bands, to the weak lines at high or very low J values and also to other lines where the frequencies from different measurements are more scattered. Zero weights are given to those lines which are not resolved, but which can be concluded to be composed of two noncoincident lines. In the analysis of the spectrum, a series of least-squares fits and simulations was used. The observed frequencies, neglecting those corresponding to the lowest J values, were first fitted as a polynomial in m. Based on the resulting v,, and B’ - B” values as well as the literature data in Table I, a set of simulations over the Q-branch region was performed. The value for A' - A” thus obtained was then checked with the shape of the P(J) lines at high J values. From the simulations the effective K values for the R and P “lines” were also drawn. From about J = 10 onwards, the peak maxima correspond to Kz = 8. The shifts of the first lines in the P and R branches, due to their smaller values of K*, served as a test for A’ - A”, too. Finally, all these considerations led to A’ - A” = -(2.7 + 0.2) x 10V3cm-‘. We could have fitted the observed transitions to a classical formula for an unperturbed symmetric top band, where A’ - A” would have been fixed TABLE I Literature Values for the Ground State Rotation and Centrifugal Distortion Constants of CD3Br CDJB’B,
Constant
BJ-CIX-~
nw arb
A&m-']
Raman
DJn0-7cm-1]
field
Force
field
DJK~O-'cm-~
cal~.~
1.95
1.94
2.12 cal~.~
Raman' Force
(I). (2). (3). (8).
2.6004
MU a
DK[,0-4cm-']
a Ref. b Ref. c Ref. d Ref.
'
MU a Force
field
0.257332
cal~.~
2.11
t 3x10 -6 + 0.0010
t 0.13
0.256219 2.6004 1.96
f 3x10 -6 f 0.0010
f 0.07
1.94 f 0.02
2.11 2.09
1.72
1.72
1.965
1.967
t 0.02
74
ANTTILA ET AL. TABLE II Observed Line Positions (cm-‘) in the V, Bands of CD,BI-a P(J)
R(J)
79Br
J 0
1 2 z
577.800 78.308 78.811 79.308 79.805
80.300 80.790
z f3 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 :; 29 :: ;i :z 37 38 43: 41 42
A
al.272 81.761 82.243 82.724 83.197
: 2
0 0
I
-: 1 z
i
K472' 11 84:602 f: 85.060 85.511 -3 85.957 -11 86.403 -15 86.840 -16
89.049 89.475 89.897 90.317 90.735 91.147 91.557 91.959 592.363 92.762 93.156 93.548 93.936 94.322 94.703 95.079 95.456 x6" 96:564 96.918 97.269 97.616
:43 45 46
-I -I -2 -2
0 0
-: -1 -1 -2 -1 -1 0 0 -1 2 : z -3 -a
:87 49 50 :: :: :z :87
z6345 99:992 600.315 00.633 00.950 01.265
1 3
:
-1 -1
I
2 ’
X~
02:lao 02.481 02.775 03.o>g 03.344
65: :: :: a The
; -: -7
diierences
W
0.1 0.3 0.3 0.5 0.5 1.0 1.0 0.3 1.0 1.0 1.0 0.5 0.3 0.0 0.0 0.1 0.3 0.0 0.0 0.0 0.1 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 A:; 1.0 0.5 1.0 1.0 1.0 1.0 1.0 1.0 0":: 0.5 0.1 0.0 0.0 0.3 0.0 0.0 0.1 0.5 1.0 1.0 i:: 1.0 1.0 1.0 1.0 0.5 0.3 1.0 0.1 0.5 0.3 0.3
*‘B,
A
78.973 -1 79.461 -2 79.944 -3 80.429 -I 80.908 0 al.383 -I al.856 0 82.325 82.791 l 83.252 -I 83.708 -4 84.142 -26 84.602 -la 85.060 -9 85.511 -3 FE a61840 87.270 87.695 88.117 88.537 88.955 89.370 89.783 90.190 90.591 590.991 91.3a9 91.782 92.173 92.559 92.944 93.323 93.699 94.072
’
1: 9 5 2
I I :
3 -1 -1 -I -1 -1 -2 0 -1 -1 -1
95.528 -I 95.882 -2 96.240 96.564 -1;
Ei 9a:604 98.924 99.241 99.560 99.866 600.178 00.481 00.784 01.078 01.376 01.665
l5 6' 3 0 -: 0 -2 -: 0 -2
W
0.3 0.3 0.5 1.0 1.0 0.5 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.3 0.0 0.0 0.1 0.3 0.1.
0.0 0.0
0.3 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 A:; 0.3 0.1 0.0 0.0 0.3 0.0 0.0 0.1 0.5 0.5 Fl:: 0.3 A:; 0.5 0.3 1.0 0.3
798,
A
575.733 2 75.203 -1 74.677 3 74,144 2 73.610 2 73.070 72.527 i 71.983 1 71.435 1 70.883 0 70.329 0 69.772 69.214 68.645 -2 68.077 -2 67.506 -3 66.931 -4 66.355 -3 65.777 -1 65.192 -3 64.603 -4 64.014 -3 63.425 62.824 -: 62.227 -I 61.625 0 60.992 -27 60.394 -16 59.787 -10 559.176 -5 58.561 -1 57.944 4 57.325 10 56.696 2 56.061 55.419 -1 54.788 6 54.144 3
W
i::
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 i:," 0.5 0.3 0.1 0.0 0.0 0.0 0.1 0.3 0.1 0.0 0.0 0.3 0.3 0.5 1.0 0.5 1.0 1.0 1.0 1.0 A:; 0.5
46.202 45.521 44.834 44.145 43.450 42.762 42.065 41.362 40.654 39.948 39.239 38.525 37.815
0 1 -I -1 3 : o -t -3 -3
2
i:: 0.5 1.0 ii:; 0.5 1.0 ::5" 0.5 i:: 0.5 0.3 0.1
alB,
A
W
574.945 74.426 73.902
-1 0 0
0.3 0.5 0.5
71.237 70.695 70.150 69.600 69.050 68.493
1 1 1 -1
A:; 1.0
66.806 66.240 65.668 65.097 64.518
-1 -1 -2
62.181 61.588 60.992 60.394
I
-1
i
2 7 9
557.944 -9 57.325 -12 56.696 -22 56.095 -1
53.574 52.940 52.299 51.652 51.004 50.354 49.700 49.043 48.384 47.720 47.054 46.382 45.709 45.038 44.360 43.678 42.995 42.303 41.615 40.922 40.222
-1 3 3 o
0
0 0 0
Ci 0 -3 -4
I I
: -1 2 3 0
1.0 1.0 1.0 1.0
A:; 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Ii:: 0.5 0.3 0.3 0.0 0.0 0.1 0.1 0.3 0.0 0.0 0.0 0.1 0.1 0.3 1.0 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 i:; 0.5 A:; ;:; 0.5 A:; i:; 0.5 0.5 0.1 0.5
A = vobS- v,,,, (toe3 cm-l) and the weights used in the analyses are also given.
q BANDOF CD,Br
75
to -2.7 x 10e3 cm-’ and ground state values constrained to the values of Table I. We preferred another approach, better adapted to the nearly total absence of K structure. First, the P and R lines with low J values were corrected to correspond to K2 = 8, as did the other lines. (This correction is only a few thousandths of cm-‘.) Then, all the transitions were fitted to a polynomial v = a, + a,m + agr? + a3m3 + af14.
(1)
The coefficients from this fit are given in the upper part of Table III. For an unperturbed parallel band, the coefficients of Eq. (1) have the following values: a q, = Y,, + (A’ - A” - B’ + B”)K2 - (DI( - D;I)K4; al = B’ + B” - (D& + D’;K)K*; a 2 = B’ - B” - D; + Di; - (Dix - D’;K)K*; a3 = -2(D;
(2)
+ DI;);
a4 = 0’; - 0;. If we make the approximation D;K = Dl;x, we can derive values for B’, B”, D;, and DL;. They are given in the lower part of Table III. It is very satisfactory to find that our results for B, are in good agreement with the microwave values, TABLE III Results from The
values
of
the
the
Analysis
coefficients
of the vg Band of CD,BP
in
Eq. (1):
CD3'YBr a0 [w-q
577.2779(4)
a, [c:cm_'1
0.513003(15)
0.510763(13)
a2 D0-3cm-']
-1.6650(7)
-1.6536(6)
a3 n0-7cm-']
-7.884(58)
-7.668(52)
a4 pa-Ycm-']
-1.2(2)
-0.9(2)
Std.
dev.
Molecular
v
0
S D" J
constants:
km-‘]
577.286(2)
575.975(2)
0.257351(10)
0.256225(10)
no-3crn-lJ
1.6650(7)
1.6536(6)
p0-7cm-1]
1.965(15)
1.913(14)
D; - 0;'po-Ycm-'] a;
2.0
2.3
~O-3cm-'j
6" = B. km-']
a
CD3% 575.9665(4)
po-3,,-']
The error limits in parentheses
1.2(2)
0.9(2)
2.7
2.7
? 0.2
are standard deviations
+ 0.2
here, as in the rest of this work.
76
ANTTILA
ET AL.
the deviation being less than 2 and 0.6 standard deviations, respectively. On the other hand, our results for af = B,, - B3 are more accurate than Morino and Hirose’s values (2): 1.663(3) and 1.650(3) x 10m3cm-l, with which they are in good agreement. Our results for DI; and 0; also seem to be more accurate than the microwave values. Our DI: value for CD37QBris slightly larger than that for CD381Br, as predicted by force constant calculations (8). To get the u,, values presented in Table III, we further approximated Dk = 0;. The whole analysis, and especially the fact that 0; - Di; is only a very small fraction ofDI;, suggests that y3 can be interpreted as an unperturbed band. Although TABLE
IV
Observed Line Positions (cm-‘) in the Hot Bands 2% - vQof CDaBr
R(J)
P(J)
J
81 CO "Br 3
CD
3
Br
CD3"Br
CD3%
568.842 68.317 574.365 '4.852
577.091 77.561 78.041
12
17 18
564.700 64,143 63.582 63.016 62.454
19 20 21 22
61.885 61.315 60.732 60.156
23 24
59.574
25 26
:t:::i 57.804
27 28
55.721 56.608
15 16
:; 4’: 41 :: 44
62.350 61.786 61.228 60.657 60.088
58:356 57.771 57.189
::
82.113
84.2'3
8’. 52.373 51.757 51.141 50.520 51.075 50.443 49.809 49.170 48.526 47.891 47.244 46.593 45.938
43.959 43.300 42.630 41.962 41.281
81.686 82.113 82.536 82.962 i;::;:
49.89' 49.269 48.639 48.008 47.366 46.729 46.081 45.443
44.634 49 50
81.686
:i.;:i
:i :i
'8.579 79.033
62.903
32 ;43 35 36
76:738 77.665 '8.128
13 14
75.330 75.806
42.826 42.159 41.490
145
87.540 86.611 86.989
89.600
77
v3 BAND OF CD3Br
the Coriolis interaction term 5” 36 with lr6 is probably not negligible, the levels y6 and v3 cross only for very high K values, so that the interaction has only a global effect on the Q band. IV. “HOT” BANDS
The molecule has two low-lying vibrational levels, the v3 = 1 level treated above and the us = 1 level around 715 cm-’ (4). The transitions starting from these levels give rise to appreciable hot bands. Their relative intensities were computed to be 12.7 and 6.5%, respectively. Starting from theP side, where the separations between the main lines are larger, two series of lines could be easily found and they might be attributed to the transitions 2~ - Q of the two isotopic species. Using the values of B3 and a? as a starting point, the assignment was found. The small extra absorptions around the main band P lines at 571.983 and 570.695 cm-’ were recognized as being due to the Q branches of these hot bands. Using lower-state combination differences, it was possible to find some lines even on the R side. The observed lines are given in Table IV. The analyses were performed as in the case of the fundamentals. However, only a third-order polynomial was used and identical TABLE V Results from the Analysis of the Hot Bands 2q - v3 of CD,Br The
a
values
Cc"-']
a2 a3 Std.
dev.
l4slecular
8" = B
3
B" _ B'
OJ Fit of
the
B3 B33 (v3-2)
in Eq.
(1):
CD3'9Br
COJB'B,
572.1590(13)
570.8905(10)
0.509558(55)
[lo-3cm-'1
-1.6566(15)
[lo-'cm-']
-7.25(42)
[10-3cm-']
0.507565i47) 1.64'4('1) -8.15(35)
3.6
3.7
constants:
[an-‘]
0
OJ
the coefficients
[cm-']
0
al
”
of
572.'67(3)
570.899(3)
cm-11
0.255624(29)
po-3cm-']
1.6566(15)
1.6474(11)
Do-7c"‘y
1.81(11)
2.04(9)
upper
state
rotational
0.254623(26)
levels:
[cm“]
0.255667
[cm-']
0.254012(5)
0.252918(5)
Do-7c,-'1
'.99(3)
'.92(3)
c Constrained.
=
0.254565'
78
ANTTILA ET AL. TABLE VI Observed Line Positions (cm-*) in the Hot Bands v3 + vg - vu of CD,Br
P(J)
J
R(J) CD3'%
CD3'%
6 ; 9
78.813
22
560.571
23 24
59.997 59.413
26 57.651 57.033 56.429
z 29 30 31
557.651 57.033 56.429 55.806
55.835 55.230
:: 34 j5 36
53.957 53.325 51.443 50.786
$Z
weights were given to all the observed lines. The results from the fits are presented in Table V. It has been assumed that DJK is a constant and has the same value as in the ground state. The values obtained for B3 agree, within about two standard deviations, with those computed with the aid of B, from Table I and 4 from the fundamentals yg (Table III). The latter values are presented in the last part of Table V. The differences B” - B’ are slightly smaller than in the corresponding main bands Ye, indicating that B is not a strictly linear function of the vibrational quantum number u3. On the other hand, the isotope effect is the same within the error limits. In the derivation of the v. values, d’ from the main bands was assumed. TABLE VII Results from the Analysis of the Hot Bands v, + v6 - v6 of CD,Br CD3%
CD3”Sr
”
0
+
[A'
B6[Cm-!i
-
A"
-
(8’
-
B”)]? [cm-‘]
573.872(5)
572.579(9)
0.25661a
0.25550a
0.25494(l)
0.25384(2)
constrained
*36[cm-ki
Constrained were
used
a Ref. (2).
values for both
0; = D;' = 1 .95x10-'cm-' the
bands.
and
DJK =
'JK
= 2 12x10-6cm-' '
79
v3 BAND OF CD,Br TABLE VIII Some Vibrational Constants (cm-‘) of CD,Br CDj7'Br
v3 2v 3 -v
CD"Br
577.286(Z)
575.975w
572.167(3)
570.899(3)
” 3 +v 6 -v 6
573.880(5)
572.587(g)
u”
579.846(5)
578.514(5)
3
Xi3 ‘;6
-7..560(3)
-2.538(3)
-3.‘+06(7)
-3.388(g)
Another method was also applied to the analyses of the isotopic hot bands 2v, - v,. The upper-state energy levels were fitted to a second-order polynomial ofJ(J + 1). The lower-state rotational constants B3 were constrained to the values given together with the results. The DJ values at the levels uQ = 1 were taken from the results of the fundamental bands. In addition, the same assumptions concerning DJK as above were used together with K2 = 8. The fits with standard deviations 3.7 x 1O-3 and 4.0 x 10e3 cm-’ led to the results given in the last part of Table V. Since the v. values were equal to those obtained with the first method, they are not repeated. Only a dozen lines to each of the isotopic hot bands v3 + v6 - v6 could be assigned. They are given in Table VI. The assignments were supported by tiny absorptions attributable to the Q branches. As the detected lines were almost entirely from the end of the P branches, no accurate rotational analyses were possible. The method for fitting the upper-state rotational levels was applied. The constrained lower-state values as well as the results are given in Table VII. The differences B” - B’ are very near to the a$ values of the corresponding isotopic species. Using the vibrational energy expression
Go(v~,Q,.
. -1
=
7
dvi
+
7
kzi
x~kvivk
+
C C i kai
gikeiek,
(3)
some vibrational constants were calculated. They are given in Table VIII together with the v. values of the investigated bands. As can be seen, the anharmonicities xi3 and ~30,are nearly equal for both the isotopic species. It is good, however, that the values for the lighter molecule CD37gBr are slightly larger. The anharmonicity constants can be compared with the corresponding values of CH,Br. According to Morino et al. (9), xi3 is roughly -4 cm-l. It is normal that the present value is smaller. Betrencourt-Stimeman et al. (10) have indirectly determined& = -4.2 cm-‘. Again, it is normal that the present value for the deuterated molecule is smaller.
80
ANTTILA
ET AL.
ACKNOWLEDGMENT Financial support from the Academy of Finland is gratefully acknowledged. RECEIVED:
May
26, 1978 REFERENCES
1. 2. 3. 4.
A. Y. T. E.
K. GARRISON,J. W. SIMMONS,AND C. ALEXANDER, J. Chem. Phys. 45, 413-415 (1%6). MORINO AND C. HIROSE, .I. Mol. Spectrosc. 24, 204-224 (1%7). H. EDWARDS AND S. BRODERSEN,.~.Mol. Spectrosc. 54, 121-131 (1975). W. JONES,R. J. L. POPPLEWELL,AND H. W. THOMPSON,Spectrochim. Acta 22, 639-646
5. 6. 7. 8. 9. 10.
J. J. J. J. Y. C.
(1%6). KAUPPINEN,Appl. Opt. 14, 1987-1992 (1975); Acta Univ. 0~1. A 38 (1975). M. FLAUD AND C. CAMY-PEYRET,Mol. Phys. 26, 811-823 (1973). KAUPPINEN,T. KARKKAINEN,AND E. KYR~, J. Mol. Spectrosc. 71, 15-45 (1978). L. DUNCAN,J. Mol. Spectrosc. 60, 225-238 (1976). MORINO,J. NAKAMURA,AND S. YAMAMOTO,Bull. Chem. Sot. Japan 38,459-468 (1965). BETRENCOURT-STIRNEMANN, G. GRANER,D. E. JENNINGS,AND W. E. BLASS,.I. Mol. Spectrosc. 69, 179- 198 (1978).
OF
MOLECULAR
SPECTROSCOPY
High-Resolution
75,
Infrared
70-80 (1979)
Spectrum
of the v3 Band of CD,Br
R. ANTTILA, T. KARKKAINEN, AND Department
of Physics,
University
J. KAUPPINEN
of Oulu, 90100 Oulu 10, Finland
AND G. GRANER Laboratoire
d’lnfrarouge,
Laboratoire
associt au CNRS, UniversitC 91405 Orsay, France
de Paris-Sud,
Bcitiment 350,
The lowest frequency fundamental band v, of CDSBr has been studied at a resolution limit of 0.03 cm-‘. About 250 J lines belonging to both isotopic species CDS70Brand CDa8iBr have been measured in the P and R branches of this parallel band. In the analyses, leastsquares fits and simulations have been applied. The band centers, 577.286(2) and 575.975(2) cm-r, respectively, have been obtained together with B, DJ, and 4 values. In addition to the main bands, the hot bands 2v3 - V~and vS + vs - v6 have been investigated. I. INTRODUCTION
Due to the two bromine isotopes, which are almost equally abundant, there are two isotopic species of CD,Br. The ground state rotational constant B as well as the centrifugal distortion constants DJ and DJK for both isotopic molecules have been determined by Garrison et al. (I) using microwave spectroscopy. Somewhat later, Morino and Hirose (2) measured with the same method the rotational constants at several excited vibrational states. The constant A,, has recently been determined by Edwards and Brodersen (3) from a vibration-rotation Raman band. The infrared spectrum of methyl bromide-d,, including the lowest fundamental v3, has been studied by Jones et al. (4). In the parallel band u3 they observed two Q branches, but in the P and R branches they only saw one series of lines. As this band around 580 cm-’ seemed to be well suited to our spectrometer, we decided to reinvestigate it. The first aim was to resolve the isotopic structure in the P and R branches. Having recorded the spectrum, we saw that values for several constants could be obtained. An analyses of some hot bands proved to be possible, too. II. EXPERIMENTAL
DETAILS
The measurements were performed with the Fourier spectrometer at the University of Oulu (5). The resolution attained was about 0.03 cm-‘. The computed wavenumbers were checked with water vapor lines (6, 7). The sample gas was purchased from Merck, Sharp and Dohme and it was used 0022-2852/79/040070-11$02.00/0 Copyright
0 1979 by Academic
All rights of reproduction
Press,
Inc.
in any form reserved.
70
vI BAND OF CD,Br
FIG. 1. A recording of the ~a band of CD8Br (upper trace) together with the synthetized (lower trace). Experimental conditions: Path length 1 m, pressure 5.5 Totr. The simulation computed with a resolution of 0.03 cm-’ and it includes, besides the va fundamentals, the 215 - V, and V, + vg - vs. Water vapor absorptions, marked with a dot, are strong because allowed to remain for calibration purposes.
71
spectrum has been hot bands they were
72
ANTTILA ET AL.
Br01
Br01
I I
Br79
Br79 Y I
I
I
I
FIG. 2. Two small regions of the y3 band of CD,Br in detail together with simulations. The conditions are the same as in Fig. 1. In both cases the upper trace is the experimental spectrum, while the lower trace represents the simulation. The first part illustrates the effects of the K structure on P(J) lines near the end of the P branch. Lines belonging to the hot bands 2~ - V, are also visible. In the latter part the effects of the hot bands are discernible at the beginning of the R branch. The lines due to different hot hands are indicated in both parts as follows: (0) 2~3 - vg of CD37sBr; (U) 25 - v3 of CDsslBr; and (+) q + vg - V, of CDaT8Br.
without any further treatment. The gas was in a triple-pass cell giving a path length of 1 m. Several recordings at pressures varying between 0.5 and 5.5 Torr were made. The wavenumbers given are mainly based on five different interferograms. The best spectra were obtained by using a low-pass interference filter, from Optical Coating Laboratory, Inc., and KBr windows to depress the radiation outside the measurement region. III. ANALYSIS OF THE YeBAND
Spectrum
A recording of the parallel vQband is presented in Fig. 1 together with a simulation using the constants derived. Two Q branches due to CD,7gBr and CD,*lBr with a separation of 1.3 cm-l are observed. In addition, the isotopic structure is clearly discernible in the P and R branches. The two series of lines corresponding to the isotopic species cross each other three times. On the other hand, it is not possible to resolve the fine K structure of each “line.” At high J values, however, the effects of the K structure are apparent, because the J “lines” are sharp on the high-frequency side and clearly degrade to lower frequencies. These fea-
q BAND OF CD,Br
73
tures are better seen on the P side, e.g., around 545 cm-‘, where the spectrum is less packed, and they are presented in the first part of Fig. 2. Additional absorptions attributable to the “hot” bands were also detected there as well as just above the main Q branches in the latter part of Fig. 2. Analysis The assignment of the J values was first confirmed with the aid of ground state combination differences. The literature values for the ground state constants are given in Table I. The observed frequencies of the peaks in the main bands are given in Table II. Lower weights are given to the incompletely resolved lines near the coincidences of the bands, to the weak lines at high or very low J values and also to other lines where the frequencies from different measurements are more scattered. Zero weights are given to those lines which are not resolved, but which can be concluded to be composed of two noncoincident lines. In the analysis of the spectrum, a series of least-squares fits and simulations was used. The observed frequencies, neglecting those corresponding to the lowest J values, were first fitted as a polynomial in m. Based on the resulting v,, and B’ - B” values as well as the literature data in Table I, a set of simulations over the Q-branch region was performed. The value for A' - A” thus obtained was then checked with the shape of the P(J) lines at high J values. From the simulations the effective K values for the R and P “lines” were also drawn. From about J = 10 onwards, the peak maxima correspond to Kz = 8. The shifts of the first lines in the P and R branches, due to their smaller values of K*, served as a test for A’ - A”, too. Finally, all these considerations led to A’ - A” = -(2.7 + 0.2) x 10V3cm-‘. We could have fitted the observed transitions to a classical formula for an unperturbed symmetric top band, where A’ - A” would have been fixed TABLE I Literature Values for the Ground State Rotation and Centrifugal Distortion Constants of CD3Br CDJB’B,
Constant
BJ-CIX-~
nw arb
A&m-']
Raman
DJn0-7cm-1]
field
Force
field
DJK~O-'cm-~
cal~.~
1.95
1.94
2.12 cal~.~
Raman' Force
(I). (2). (3). (8).
2.6004
MU a
DK[,0-4cm-']
a Ref. b Ref. c Ref. d Ref.
'
MU a Force
field
0.257332
cal~.~
2.11
t 3x10 -6 + 0.0010
t 0.13
0.256219 2.6004 1.96
f 3x10 -6 f 0.0010
f 0.07
1.94 f 0.02
2.11 2.09
1.72
1.72
1.965
1.967
t 0.02
74
ANTTILA ET AL. TABLE II Observed Line Positions (cm-‘) in the V, Bands of CD,BI-a P(J)
R(J)
79Br
J 0
1 2 z
577.800 78.308 78.811 79.308 79.805
80.300 80.790
z f3 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 :; 29 :: ;i :z 37 38 43: 41 42
A
al.272 81.761 82.243 82.724 83.197
: 2
0 0
I
-: 1 z
i
K472' 11 84:602 f: 85.060 85.511 -3 85.957 -11 86.403 -15 86.840 -16
89.049 89.475 89.897 90.317 90.735 91.147 91.557 91.959 592.363 92.762 93.156 93.548 93.936 94.322 94.703 95.079 95.456 x6" 96:564 96.918 97.269 97.616
:43 45 46
-I -I -2 -2
0 0
-: -1 -1 -2 -1 -1 0 0 -1 2 : z -3 -a
:87 49 50 :: :: :z :87
z6345 99:992 600.315 00.633 00.950 01.265
1 3
:
-1 -1
I
2 ’
X~
02:lao 02.481 02.775 03.o>g 03.344
65: :: :: a The
; -: -7
diierences
W
0.1 0.3 0.3 0.5 0.5 1.0 1.0 0.3 1.0 1.0 1.0 0.5 0.3 0.0 0.0 0.1 0.3 0.0 0.0 0.0 0.1 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 A:; 1.0 0.5 1.0 1.0 1.0 1.0 1.0 1.0 0":: 0.5 0.1 0.0 0.0 0.3 0.0 0.0 0.1 0.5 1.0 1.0 i:: 1.0 1.0 1.0 1.0 0.5 0.3 1.0 0.1 0.5 0.3 0.3
*‘B,
A
78.973 -1 79.461 -2 79.944 -3 80.429 -I 80.908 0 al.383 -I al.856 0 82.325 82.791 l 83.252 -I 83.708 -4 84.142 -26 84.602 -la 85.060 -9 85.511 -3 FE a61840 87.270 87.695 88.117 88.537 88.955 89.370 89.783 90.190 90.591 590.991 91.3a9 91.782 92.173 92.559 92.944 93.323 93.699 94.072
’
1: 9 5 2
I I :
3 -1 -1 -I -1 -1 -2 0 -1 -1 -1
95.528 -I 95.882 -2 96.240 96.564 -1;
Ei 9a:604 98.924 99.241 99.560 99.866 600.178 00.481 00.784 01.078 01.376 01.665
l5 6' 3 0 -: 0 -2 -: 0 -2
W
0.3 0.3 0.5 1.0 1.0 0.5 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.3 0.0 0.0 0.1 0.3 0.1.
0.0 0.0
0.3 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 A:; 0.3 0.1 0.0 0.0 0.3 0.0 0.0 0.1 0.5 0.5 Fl:: 0.3 A:; 0.5 0.3 1.0 0.3
798,
A
575.733 2 75.203 -1 74.677 3 74,144 2 73.610 2 73.070 72.527 i 71.983 1 71.435 1 70.883 0 70.329 0 69.772 69.214 68.645 -2 68.077 -2 67.506 -3 66.931 -4 66.355 -3 65.777 -1 65.192 -3 64.603 -4 64.014 -3 63.425 62.824 -: 62.227 -I 61.625 0 60.992 -27 60.394 -16 59.787 -10 559.176 -5 58.561 -1 57.944 4 57.325 10 56.696 2 56.061 55.419 -1 54.788 6 54.144 3
W
i::
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 i:," 0.5 0.3 0.1 0.0 0.0 0.0 0.1 0.3 0.1 0.0 0.0 0.3 0.3 0.5 1.0 0.5 1.0 1.0 1.0 1.0 A:; 0.5
46.202 45.521 44.834 44.145 43.450 42.762 42.065 41.362 40.654 39.948 39.239 38.525 37.815
0 1 -I -1 3 : o -t -3 -3
2
i:: 0.5 1.0 ii:; 0.5 1.0 ::5" 0.5 i:: 0.5 0.3 0.1
alB,
A
W
574.945 74.426 73.902
-1 0 0
0.3 0.5 0.5
71.237 70.695 70.150 69.600 69.050 68.493
1 1 1 -1
A:; 1.0
66.806 66.240 65.668 65.097 64.518
-1 -1 -2
62.181 61.588 60.992 60.394
I
-1
i
2 7 9
557.944 -9 57.325 -12 56.696 -22 56.095 -1
53.574 52.940 52.299 51.652 51.004 50.354 49.700 49.043 48.384 47.720 47.054 46.382 45.709 45.038 44.360 43.678 42.995 42.303 41.615 40.922 40.222
-1 3 3 o
0
0 0 0
Ci 0 -3 -4
I I
: -1 2 3 0
1.0 1.0 1.0 1.0
A:; 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Ii:: 0.5 0.3 0.3 0.0 0.0 0.1 0.1 0.3 0.0 0.0 0.0 0.1 0.1 0.3 1.0 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 i:; 0.5 A:; ;:; 0.5 A:; i:; 0.5 0.5 0.1 0.5
A = vobS- v,,,, (toe3 cm-l) and the weights used in the analyses are also given.
q BANDOF CD,Br
75
to -2.7 x 10e3 cm-’ and ground state values constrained to the values of Table I. We preferred another approach, better adapted to the nearly total absence of K structure. First, the P and R lines with low J values were corrected to correspond to K2 = 8, as did the other lines. (This correction is only a few thousandths of cm-‘.) Then, all the transitions were fitted to a polynomial v = a, + a,m + agr? + a3m3 + af14.
(1)
The coefficients from this fit are given in the upper part of Table III. For an unperturbed parallel band, the coefficients of Eq. (1) have the following values: a q, = Y,, + (A’ - A” - B’ + B”)K2 - (DI( - D;I)K4; al = B’ + B” - (D& + D’;K)K*; a 2 = B’ - B” - D; + Di; - (Dix - D’;K)K*; a3 = -2(D;
(2)
+ DI;);
a4 = 0’; - 0;. If we make the approximation D;K = Dl;x, we can derive values for B’, B”, D;, and DL;. They are given in the lower part of Table III. It is very satisfactory to find that our results for B, are in good agreement with the microwave values, TABLE III Results from The
values
of
the
the
Analysis
coefficients
of the vg Band of CD,BP
in
Eq. (1):
CD3'YBr a0 [w-q
577.2779(4)
a, [c:cm_'1
0.513003(15)
0.510763(13)
a2 D0-3cm-']
-1.6650(7)
-1.6536(6)
a3 n0-7cm-']
-7.884(58)
-7.668(52)
a4 pa-Ycm-']
-1.2(2)
-0.9(2)
Std.
dev.
Molecular
v
0
S D" J
constants:
km-‘]
577.286(2)
575.975(2)
0.257351(10)
0.256225(10)
no-3crn-lJ
1.6650(7)
1.6536(6)
p0-7cm-1]
1.965(15)
1.913(14)
D; - 0;'po-Ycm-'] a;
2.0
2.3
~O-3cm-'j
6" = B. km-']
a
CD3% 575.9665(4)
po-3,,-']
The error limits in parentheses
1.2(2)
0.9(2)
2.7
2.7
? 0.2
are standard deviations
+ 0.2
here, as in the rest of this work.
76
ANTTILA
ET AL.
the deviation being less than 2 and 0.6 standard deviations, respectively. On the other hand, our results for af = B,, - B3 are more accurate than Morino and Hirose’s values (2): 1.663(3) and 1.650(3) x 10m3cm-l, with which they are in good agreement. Our results for DI; and 0; also seem to be more accurate than the microwave values. Our DI: value for CD37QBris slightly larger than that for CD381Br, as predicted by force constant calculations (8). To get the u,, values presented in Table III, we further approximated Dk = 0;. The whole analysis, and especially the fact that 0; - Di; is only a very small fraction ofDI;, suggests that y3 can be interpreted as an unperturbed band. Although TABLE
IV
Observed Line Positions (cm-‘) in the Hot Bands 2% - vQof CDaBr
R(J)
P(J)
J
81 CO "Br 3
CD
3
Br
CD3"Br
CD3%
568.842 68.317 574.365 '4.852
577.091 77.561 78.041
12
17 18
564.700 64,143 63.582 63.016 62.454
19 20 21 22
61.885 61.315 60.732 60.156
23 24
59.574
25 26
:t:::i 57.804
27 28
55.721 56.608
15 16
:; 4’: 41 :: 44
62.350 61.786 61.228 60.657 60.088
58:356 57.771 57.189
::
82.113
84.2'3
8’. 52.373 51.757 51.141 50.520 51.075 50.443 49.809 49.170 48.526 47.891 47.244 46.593 45.938
43.959 43.300 42.630 41.962 41.281
81.686 82.113 82.536 82.962 i;::;:
49.89' 49.269 48.639 48.008 47.366 46.729 46.081 45.443
44.634 49 50
81.686
:i.;:i
:i :i
'8.579 79.033
62.903
32 ;43 35 36
76:738 77.665 '8.128
13 14
75.330 75.806
42.826 42.159 41.490
145
87.540 86.611 86.989
89.600
77
v3 BAND OF CD3Br
the Coriolis interaction term 5” 36 with lr6 is probably not negligible, the levels y6 and v3 cross only for very high K values, so that the interaction has only a global effect on the Q band. IV. “HOT” BANDS
The molecule has two low-lying vibrational levels, the v3 = 1 level treated above and the us = 1 level around 715 cm-’ (4). The transitions starting from these levels give rise to appreciable hot bands. Their relative intensities were computed to be 12.7 and 6.5%, respectively. Starting from theP side, where the separations between the main lines are larger, two series of lines could be easily found and they might be attributed to the transitions 2~ - Q of the two isotopic species. Using the values of B3 and a? as a starting point, the assignment was found. The small extra absorptions around the main band P lines at 571.983 and 570.695 cm-’ were recognized as being due to the Q branches of these hot bands. Using lower-state combination differences, it was possible to find some lines even on the R side. The observed lines are given in Table IV. The analyses were performed as in the case of the fundamentals. However, only a third-order polynomial was used and identical TABLE V Results from the Analysis of the Hot Bands 2q - v3 of CD,Br The
a
values
Cc"-']
a2 a3 Std.
dev.
l4slecular
8" = B
3
B" _ B'
OJ Fit of
the
B3 B33 (v3-2)
in Eq.
(1):
CD3'9Br
COJB'B,
572.1590(13)
570.8905(10)
0.509558(55)
[lo-3cm-'1
-1.6566(15)
[lo-'cm-']
-7.25(42)
[10-3cm-']
0.507565i47) 1.64'4('1) -8.15(35)
3.6
3.7
constants:
[an-‘]
0
OJ
the coefficients
[cm-']
0
al
”
of
572.'67(3)
570.899(3)
cm-11
0.255624(29)
po-3cm-']
1.6566(15)
1.6474(11)
Do-7c"‘y
1.81(11)
2.04(9)
upper
state
rotational
0.254623(26)
levels:
[cm“]
0.255667
[cm-']
0.254012(5)
0.252918(5)
Do-7c,-'1
'.99(3)
'.92(3)
c Constrained.
=
0.254565'
78
ANTTILA ET AL. TABLE VI Observed Line Positions (cm-*) in the Hot Bands v3 + vg - vu of CD,Br
P(J)
J
R(J) CD3'%
CD3'%
6 ; 9
78.813
22
560.571
23 24
59.997 59.413
26 57.651 57.033 56.429
z 29 30 31
557.651 57.033 56.429 55.806
55.835 55.230
:: 34 j5 36
53.957 53.325 51.443 50.786
$Z
weights were given to all the observed lines. The results from the fits are presented in Table V. It has been assumed that DJK is a constant and has the same value as in the ground state. The values obtained for B3 agree, within about two standard deviations, with those computed with the aid of B, from Table I and 4 from the fundamentals yg (Table III). The latter values are presented in the last part of Table V. The differences B” - B’ are slightly smaller than in the corresponding main bands Ye, indicating that B is not a strictly linear function of the vibrational quantum number u3. On the other hand, the isotope effect is the same within the error limits. In the derivation of the v. values, d’ from the main bands was assumed. TABLE VII Results from the Analysis of the Hot Bands v, + v6 - v6 of CD,Br CD3%
CD3”Sr
”
0
+
[A'
B6[Cm-!i
-
A"
-
(8’
-
B”)]? [cm-‘]
573.872(5)
572.579(9)
0.25661a
0.25550a
0.25494(l)
0.25384(2)
constrained
*36[cm-ki
Constrained were
used
a Ref. (2).
values for both
0; = D;' = 1 .95x10-'cm-' the
bands.
and
DJK =
'JK
= 2 12x10-6cm-' '
79
v3 BAND OF CD,Br TABLE VIII Some Vibrational Constants (cm-‘) of CD,Br CDj7'Br
v3 2v 3 -v
CD"Br
577.286(Z)
575.975w
572.167(3)
570.899(3)
” 3 +v 6 -v 6
573.880(5)
572.587(g)
u”
579.846(5)
578.514(5)
3
Xi3 ‘;6
-7..560(3)
-2.538(3)
-3.‘+06(7)
-3.388(g)
Another method was also applied to the analyses of the isotopic hot bands 2v, - v,. The upper-state energy levels were fitted to a second-order polynomial ofJ(J + 1). The lower-state rotational constants B3 were constrained to the values given together with the results. The DJ values at the levels uQ = 1 were taken from the results of the fundamental bands. In addition, the same assumptions concerning DJK as above were used together with K2 = 8. The fits with standard deviations 3.7 x 1O-3 and 4.0 x 10e3 cm-’ led to the results given in the last part of Table V. Since the v. values were equal to those obtained with the first method, they are not repeated. Only a dozen lines to each of the isotopic hot bands v3 + v6 - v6 could be assigned. They are given in Table VI. The assignments were supported by tiny absorptions attributable to the Q branches. As the detected lines were almost entirely from the end of the P branches, no accurate rotational analyses were possible. The method for fitting the upper-state rotational levels was applied. The constrained lower-state values as well as the results are given in Table VII. The differences B” - B’ are very near to the a$ values of the corresponding isotopic species. Using the vibrational energy expression
Go(v~,Q,.
. -1
=
7
dvi
+
7
kzi
x~kvivk
+
C C i kai
gikeiek,
(3)
some vibrational constants were calculated. They are given in Table VIII together with the v. values of the investigated bands. As can be seen, the anharmonicities xi3 and ~30,are nearly equal for both the isotopic species. It is good, however, that the values for the lighter molecule CD37gBr are slightly larger. The anharmonicity constants can be compared with the corresponding values of CH,Br. According to Morino et al. (9), xi3 is roughly -4 cm-l. It is normal that the present value is smaller. Betrencourt-Stimeman et al. (10) have indirectly determined& = -4.2 cm-‘. Again, it is normal that the present value for the deuterated molecule is smaller.
80
ANTTILA
ET AL.
ACKNOWLEDGMENT Financial support from the Academy of Finland is gratefully acknowledged. RECEIVED:
May
26, 1978 REFERENCES
1. 2. 3. 4.
A. Y. T. E.
K. GARRISON,J. W. SIMMONS,AND C. ALEXANDER, J. Chem. Phys. 45, 413-415 (1%6). MORINO AND C. HIROSE, .I. Mol. Spectrosc. 24, 204-224 (1%7). H. EDWARDS AND S. BRODERSEN,.~.Mol. Spectrosc. 54, 121-131 (1975). W. JONES,R. J. L. POPPLEWELL,AND H. W. THOMPSON,Spectrochim. Acta 22, 639-646
5. 6. 7. 8. 9. 10.
J. J. J. J. Y. C.
(1%6). KAUPPINEN,Appl. Opt. 14, 1987-1992 (1975); Acta Univ. 0~1. A 38 (1975). M. FLAUD AND C. CAMY-PEYRET,Mol. Phys. 26, 811-823 (1973). KAUPPINEN,T. KARKKAINEN,AND E. KYR~, J. Mol. Spectrosc. 71, 15-45 (1978). L. DUNCAN,J. Mol. Spectrosc. 60, 225-238 (1976). MORINO,J. NAKAMURA,AND S. YAMAMOTO,Bull. Chem. Sot. Japan 38,459-468 (1965). BETRENCOURT-STIRNEMANN, G. GRANER,D. E. JENNINGS,AND W. E. BLASS,.I. Mol. Spectrosc. 69, 179- 198 (1978).