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Contribution to the study of the 2ν5 (A1) rovibrational band of CH3Br near 2860 cm−1
JOURNAL
OF MOLECULAR
SPECTROSCOPY
Contribution
51,238-2&l (1974)
to the Study of the 2v5 (Al) Rovibrational of CH,Br near 2860 cm-l
Band
GEORGES GRANER Laboratoire d’lnfrarouge, Laboratoire associe au CNRS, Universitk de PARIS Bdtiment 3.50, 9140.5Orsay, France
VI,
This band was studied on a Fourier Transform spectrum (resolving power of the apparatus: 0.005 cm-l). For each isotopic species CH3 rgBr and CH3 *rBr, about 800 lines were assigned. The band is well explained by a x-y type Coriolis interaction with ~2 + ~5. Several local resonances occur for low K values as well as a doubling of the K = 3 levels. Their study provides interesting information on neighboring bands, especially 3~g(E), ~2 + VI + ~6, and 24E).
The infrared spectrum of Methylbromide has been recorded between 2800 and 4250 cm-’ using the “third generation” Fourier interferometer built at Laboratoire Aim6 Cotton (1). The main characteristics of the recorded spectra have already been given (2). The apodized resolution limit of the apparatus is 0.005 cm-’ and, because of the Doppler broadening, the measured linewidth is about 7 X lop3 cm-‘. The absolute precision on the wavenumbers is estimated to be 2 X lop3 cm-r but the internal consistency of these wavenumbers is much better, probably 0.24.3 X 1O-3 cm-‘. Most of the present work was done on one spectrum run with the interferometer entirely evacuated. The sample pressure was 0.4 Torr and the path length 8 meters. The 2vg band here reported is situated in the lower frequency region of the interferometer; because of absorption by the Infrasil separating plate and of the use of a PbS detector, the Signal-to-Noise ratio is quite a bit poorer than in Ref. (2) and the spectrum was not used below 2830 cm-l. Notations used in this paper are the classical ones. It should be especially noted that K is a signed quantity and that K = 1k I. GROUND STATE CONSTANTS
The set of ground state constants of methyl bromide is divided in two subsets. First, the values of B”, D”.T, and D”JR are of prime importance for us since they enter into the ground-state combination differences (GSCD) such as Q&(J - 1) - QPK(J + 1) which are very useful in making line assignments as was suggested by Blass and Edwards (4). These constants, already well known from microwave work (5)) were slightly rem-red, for CH3 *‘Br only, through the study of the v4 band (2). The second subset, i.e., A” and D”K is far less well known but it has almost no importance for the study of a parallel band where only A’ - A” and D’II. - D”g are significant. Nevertheless, we found it convenient in the present paper to deal with upper 238 Copyright AU rights
Q 1974
by Academic
of reproduction
Press,
in any form
Inc. reserved.
THE 2v.5 BAND TABLE
OF CHzBr
239
I
GROUND-STATE CONSTANTS USED IN THIS WORK
CHJ ‘OBr
CH, *lBr
5.1291~ 8.308 X 10-S” 0.3191607~ 3.30228 X 10Pc 4.27962 X 10-6~
5.1291. 8.492 X 10-h* 0.3179477* 3.274 X lO+* 4.244 x IO-B*
a From Ref. (6). b From Ref. (2). c From Ref. (5). All values are expressed in cm-l.
state energies; Table I gives the values we used. As it is explained in Ref. (Z), A” is taken from Barnett and Edwards (6) while D” K has been modified. The same A” and D”K values have been used for both isotopic species. Since an uncertainty of 0.01 cm-’ on A” is not at all unlikely, cm-r for K = 9, are possible on energy values hereafter quoted. ASSIGNMENT
large errors, up to 1
OF THE TRANSITIONS
Although the parallel component of 2vs has already been quoted in (7) and studied in (8), our drastic improvement in resolution obliged us to use a completely new approach to the problem. Since the QQ branches in the 2856-2862 cm-’ region were not intense and clear enough to be the starting point of the work, we began by looking for series in the QR and QP regions. We were rapidly able to find more than a dozen quite regular R series and fewer P series. In most cases, they appear as almost parallel twin series, obviously related to the existence of the equally abundant isotopic species CHa 79Br and CHI 81Br. This fact, although it doubles the line density, is quite useful in the confirmation of line assignments and helps one to spot a ‘
240
GEORGES
GRANER
K = 1 ones. Nevertheless, the alternative assignment of these series or part of them cannot be completely ruled out. It should be noticed that above J ~40, on our spectrum QP lines are weak and barely recognizable in the noise. Therefore, the GSCD are of no use for assigning or checking high J R-lines, which are thereby slightly less reliable. For this reason, we were puzzled for a long time by several short but clear series of lo-15 lines in the 2890-2900 cm-* region, No convincing J and K numbering was possible with the help of the GSCD and moreover, these short series are clearly perturbed at their lower frequency end, which prohibits their linking to other series. Finally, they were attributed to K = 1, 2, and 3. From the GSCD, low J QQK (J) lines can easily be assigned. A plot of QQx (K) vs K2 also gives QQs (a), QQs (9), and QQr, (10). All identified transitions, 1600 in number, are grouped in Tables V-XII. A part of the spectrum in the region of the QQ branches is shown on Fig. 1. STUDY
OF INDIVIDUAL
SUBBANDS
We were soon convinced that several perturbations were taking place within this band. Therefore, we felt compelled to start this work by a separate analytical study of each K subband. Since the ground state constants B”, D “J, and @‘JR are well known, it is sensible to deal with the upper state energies of the transitions instead of the frequencies. They are obtained through
E’ = Y + (A” - B”),
+ l?“J”(J” + 1) - D”JJ”2(J” + 1)” - D”J~J”(J” + 1)K” - Dt’~K4.
An error on A” and DK” has strictly no effect within a given subband effect on the comparison of different subbands.’ The upper state levels of a subband were fitted to a polynomial :
(1)
and it has little
E’ = a,, + aJ’(J’ + 1) + UZJ’~(J’+ 1)” + u~J’~(J’ + 1)” + . . .,
(2)
up to the point where no statistically significant improvement was obtained by adding a new monomial [see Ref. (z)]. In the least-squares fit, a severe weighting was used. Only pure lines were given a unity weight; slight asymmetries led to weight equal to 0.2 or 0.1 and larger anomalies or overlappings were sanctioned by 0.01 or even 0. The weights are given in Tables V-XII. Some very bad lines, whose frequency may be wrong by as much as 5 X 1w3 cm-l are purposely deleted in these tables. As can be seen from Tables II-III, all the subbands of 2~5 need at least 4, and often more, terms in formula (2) to achieve a satisfactory and significant fit with a standard deviation of OS-O.7 X 1O-3 cm-‘. It is important to note here that the same treatment applied to subbands of v4 (a), which is almost an unperturbed band, shows that 3 parameters only are usually statistically significant and give u N 0.4 X 1e3 cm-’ except for the K’ = 5 and K’ = 7 subbands which require 4 parameters since they are close to the badly perturbed K’ = 6 subbands. 1An equivalent
method
would have consisted
YcDI= Y + ,“,“(J”
in working
+ 1) - D”JJ”‘(J”
with corrected + I)* -
D”Jd”(J”
frequencies +
1)p.
THE
2~5 BAND
241
OF CHaBr
P = 0.4 TORR L=8M.
61
79
79
PO(10)
PO Ill)
l’““““l”“““‘I”““” 2855.50
2856.CUJ
2856.50
‘,““““‘,“‘“‘“’
a
,,,,,,,,,
2857.00
2857.50
@r,,,l
I,,,
,,
10
6
@LIII’PI’
,
I
,
16
’ ’ ’ I ’
,““,““““’
’
’
2858.50
2isT
J
,,,,,,/,,
2859.00
,,,,
285800
,,I,,,,.,
2859.50
286000
I~‘““‘“l”“““‘l”‘“““~~““~
b FIG. 1. Part
2860.50
2 861.00
2861.!io
286208
of the absorption spectrum of CHJBr in the region of the ‘JQ branches. the Q superscript was omitted in every line identification.
Since one has
AK = 0 for all transitions,
Therefore, the fact that we need 4, 5, or 6 terms for the subbands of 2~5 is a first clue that a global resonance occurs. Another sign is the tremendous increase with K of al (i.e., of B’ eff - B”). A third anomaly is the large size and variations of u2 compared to -D”J. Nevertheless, there is clearly a regularity in these variations from K = 8 to 3. It is therefore reasonable to try to fit these subbands together while excluding for the moment the low K subbands which are much more abnormal and are subject to several local resonances. Tables II-III give the results of the individual fits of each subband.
.321729 .321243 .321029 .320684 .320275 .32050 .320666 .320695
3031 &I62
2980.0256
2937.6273
2904.6495
2861.1984
2866..328
2866.8954
2e62.1300
5
4
5
4
6
4 (a) (b)
5 (c)
uu
udw
taldq
(b)
(c)
-
-
+
-
-
5.16
3.80
0
7.3
4.03
4.41
4.16
6.14
up to J’ = 35 and taking “Femi-like”
into account the mo8onance near J’ = 10
transitiona
only transitions
with J’ 2 22
-
.322674
3092.9m
5
- 11.13
- 69,
107 x *2
.32759
*I
3163.201
.0
6.1
sub
reaonancee into account
go.
2a62.13al
2862.Of355
2861 .%OO
2861.W
1.534
1.505
1.34
1.114
1.524
1.868
2.082 2859.8293 zs60.669a
2.566
3.713
8.43
103~ (BLB*)
2858.7665
2857.4668
2855.714
”
-41.
(2)
2e62.019
BY IWMULA
@GO.
- 1000.
-
13.
9.0
3%
185.
53a
‘5
OF C+
II
1O12
OF TEE K SBBAUD
6
-1 All values In cm
1
(a)
K
FOLRWIUAL FIT
PABU
-
-1
dtb
up to J’
oply transitions
uaiw
using transitions
in m
(a)
AI1 vdues
.31948a
.319449
.319454
.319793
= 35 and tekiq
J’ 2 2G
2862.1154
(b)
0
6
.31949
2066.1987
6 (a)
2866.8789
2881.1738
6
2
4 (b)
2904.6411
4
1
.319095
2937.6273
4
4
3 6.29
3.97
4.36
4.72
5.0
3.93
“Femi-like”
-
-
- 22.
+
-
-
-
7.5
resonances
-
-
544.
3.1
-26.
2300.
10'5 E a 4
- 120.
"5
0.23
200.
- 1.46
4.6
10'6 I
BY FORMULA(2)
- 22000.
into account.
200.
29.
9000.
- 922.
-
9.
8.9
36.
.320491
2980.0352
.3m9
3031.8376
5
4
187.
-
6.06
- 11.02
.321625
5m.
10’2T, 3
-
5
3092.9886
5
I
Efi2
68.
IO
7
OF TEE K SUBBAFiW OF ‘X3 “Br
III
.32630
*I
6
3163.260
0
6
II
8
K
POLYNOMIAL. FIT
TABI.
sib
2862.1154
2862.06-R
2861.9876
2861.9305
2861.3477
2e60.6708
2859.8098
2s5a.7466
2851.4466
2855.695
u
1.541
1.501
1.55
1.147
1.5%
I.845
2862
2.543
3.618
8.35
lo3x (BI-BN)
GEORGES
244 CORIOLIS
GRANER
RESONANCE
WITH
~2 + vj
It is well known that a parallel band, in which an A1 vibration is singly excited and a perpendicular band in which an E vibration is singly excited, may be affected by an accidental resonance caused by the term (3) in the first order Hamiltonian. This type of resonance, called Coriolis resonance due to rotation about the x and y axes (z being taken as the top axis), has been studied by various investigators (10-16). The corresponding nondiagonal matrix elements are given by setting vt = V~= 1 in the following formula. (8, - 1, V,, I*, +c+*,
Vt - l,Z1 f
1, K f
1)
= 4[(Va/Vt)f + (Vt/Y*)j].B.TI,I?.[V,(V,
=1=Zt)(J =F K)(J f
k + l)-Ji.
(4)
One of the less disputable examples of this resonance is given by the v2 and v5 bands of the methyl halides where the coupling constant { B2,5has been predicted several times (11,14) and measured (11, 14, 16, 17) ; all values lie in the range 0.45-0.65. More specifically for methyl bromide, this constant was predicted to be 0.61 and the interpretation of microwave transitions (14) yielded values between 0.60 and 0.67. Recently, we had the opportunity, through the kindness of Dr. W. E. Blass, to reexamine infrared data concerning the v2 and v5 bands of CHaBr from M. Kurlat’s thesis (18). Although our present fit is not very good, it gives a value close to 0.61 (19). It was pointed out earlier (17,20) that, as a consequence, the overtones 2~ (Al), 285 (E), 2vz and the combination band v2 + v5 are involved in a sextuple interaction [see Fig. 6 of (17a) or Fig. 4 of (20) J. But it was shown in the case of CHsCl (17) that 2~ (Al) is mainly perturbed by its interaction with v2 + v5 so that it is more or less legitimate, in a first stage, to ignore the other bands. This approximation seems even more justified here than with CH&l since there is a larger frequency difference here between v2 and vs. Moreover, a recent study (9) of 2~2 shows few signs of perturbation except for K = 7, 8, 9. Therefore, we felt entitled to treat the problem simply as a Coriolis resonance between the parallel band 2~5 and the perpendicular band v2 + VS.A rough calculation predicts a crossing of levels between R = 8 and 9 of 2~5. The three levels involved are 1v2 = 0,
v5
=
2,15 = 0, J, k)
and /vz = 1, vs = 1, 15= fl,
J, k f
1)
and the coupling constant is precisely p2,5 as can be seen by setting v, = 2, It = 0 and v, = 1 in formula (5). We had at our disposal a computer least-squares program (1%) adapted for this problem. Unfortunately v2 + v5 is too low to be visible on the present spectra and for the time being, we have poorly resolved spectra (7,8) with only Q-branch frequencies given. Nevertheless, we have decided to use these data in the following way : 17 Q-branch frequencies of vz + v5 from Ref. (7) and about 300 frequencies of the 2~ band with K > 4 were simultaneously fitted. The weights assigned to the v2 + v5 lines were progressively
THE ZVS BAND
yo
2862.2094
t
21
A’
5.03609
?
9
(A’
-
A”)
-
B”)
-
B’
2
u5
D; Dt D;K
2862.1910
t
0.1599
x f
6)x
(7.275
2
85)x
(6.64
+
0.6254
6)x
?
26
10
(3.469
A
7)
(7.335
f
72)
(6.45
2744.459
t
20
-0.367
f
13
8’
_
B”
(1.54
t
4)
f
2
-35
+
were in
in
in
the
determined the
constants dependently
in
second
one
given for
a
both
15
+
the
v5
isotopes
v2 are
+
last
x
the but
&a&m for Table IV: Read - 0.0367 instead of stead of 1.54 X 10-a for B’ - B” of ~2 + Y.S.
10
-3
10-6
_I
related
lines mean
not
x
significant
and v5
10 -5
10 -6
DyK
constants
computation
“hiCh
“*
of five
first
from *or
units
x
D;
-
the
text,
1O-7 x
3
A”
?h
deviations
i
_
-1.218
x
6)
A’
“;
standard
k
0.6251
“;
25
10 -3
10 -6
A5
explained
f x
-7
VO
8
0.09306
0.1516
10 -5
3
19 r
0.3180993
10 -3
(3.510
f
5.03603
0.09300
0.3193206
(B’
(A,)
245
OF CH3Br
“*
subsequently were
of
figure. f0
values
+
AF u5
fixed
excluded. obtained
significantly
0.367 for A’ - A”
The in-
different.
and - 1.54 X 1O-3 in-
lowered to 0.01 (which is still too optimistic!). Out of the constants of Q + ~5, only five were free to float, namely Q, A’, B’, A{S, and D’K.~ In the next step, the lines of v2 + v5 were taken out of the computation and all the the constants of this band were constrained to their previously obtained values. This rather primitive method gave surprisingly good results: the standard deviation in residuals is 0.005 cm-l for both isotopic species and although 79Br and 8’Br were separately treated, they show a remarkable agreement. Values given in Table IV are evidently an *It may seem odd that we try to get a B’ value for a band for which no individual P, Q, or R line is known. But in fact, the resonance between the two bands is so sensitive to B’(vz + ~5) that at least a good approximation of it can he obtained from 2~5 alone.
246
GEORGES
GRANER
5
f.Jl.7096
1.m
60.72la 60.7405
am am
60.65)2
l.c.2
mm.
1
59.cQ94
am
59.9m
1.m
9a.m
1.00
99.9911
1.m
99.9m
1.m
99.9%6(
1x4
99.99%
am
96.3029 0.01
60.099-d
0.m
99.cce9
l.c.2
96.4499
1.m
W.T,%
1.00
m.wo
0.00
99.01
1.m
96.9%4
1.m
%.a64
1.m
99.111,
1.m
95.1610
1.m
91.6%?7
1.m
60.1%9
1.m
59.lW
1.00
n&59
1.m
60.m3
am
99.m9
am
99.m
0.10
60.2ata
0.m
99.nm
1.00
R.u.m
0.m
99.4?e
0.10
99.7628
1.00
99.w,
1.00
%.w¶
1.m
58.8369
I.rn
%.9937
r.m
%a,*
,,W
90.9811
1.m
56.uo9
1.00
6o.mE
0.00
59.om
1.m
96.9m
1.00
%.Yw
1.m
c4.9916
1.m
99.09lo
1.00
%.?sa
1.m
Pm93
1.m
60.9658
am
59.19%
1.m
96.9017
1.W
92.m,
1.m
59.m
1.00
57.0174
1.m
99.m
1.02
57.2624
0.10
61.0689
1.00
59.97%
1.m
99.1625
0.10
59.67u
1.00
59.n49
1.m
99.8m
1.m
%?.4@1 1.m
approximation for v2 + ~5,3 but they could be considered as satisfactory for 215 (Al) ; unfortunately the K = O-3 subbands do not fit with the other ones. We will tackle in the following paragraph the problems of these low K subbands. Among the results of Table IV, we should point out the remarkably low value of B = -7.6 X lO+. These values are B’ - B” which gives lgcz$ = -8.0 X 1OP and *‘cY~ to be compared not only to aEB = - 75 X lO+ in Ref. (8), but also to aP ‘v 18 MHz = -60 X 1P6 in Ref. (14). The Coriolis resonance was not taken into account in (8) aAs an example of the crudeness of the results concerning YZ+ ~6, we should point out the zero isotopic shift on the band centers. It is not surprising since the same line frequencies of this band were used for both species. From the data of 2~9 (13) and the present ones on 21~6,we can predict an isotopic shift of 37 X 1C3 cm-l for VI + VS.
THE
2~5 BAND
OF CH3Br
-
J
m.
1
1
2 3 4 5 6 7 B 9 10 11 12 13 I4 15 (6 !I 18 19 20 21 22 23 24 25 26 R 18 2¶ 30 31 32 33 34 35 36 3l 35 39 +a +1 +2 a ++
+z
92.8985
&co’
43
93.63c4
l.02
++
94.3618
1.m
+5
95.1149
I.rn
,6
95.8912
0.m
+7
96.6791
1.M
+a
9-7.+7+4
1.00
+9
%‘I.2753
t.m
50
99.0785
1.w
51
99.8719
0.m
-
’
247
GEORGES
248
GRANER
81 BIUNCE
BRANCE
I
-
II
BNANCN III
BFaNcE
BruJlcE II
I
J
rm.
Y
3
64.5951
0.x)
4
65.2549
1.00
5
65.9016
0.M
5a.e4%
0.10
6
66.5616
0.50
58.2253
0.10
7
67.2210
I.00
57.6022
0.10
8
67.8846
1.00
56.9e19
0.02
Mao3
0.M
55.7595
0.02
ma.
Y
Pm.
Y
Pm. 59.4778
9 10
Y
Y
Pm.
III
Y
0.10
11
69.8896
o.M
55.1501
0.02
12
70.5655
0.50
54.5442
0.10
13
71.24i2
0.M
14
71.9176
1.00
15
72.5977
1.W
16
n.n93
0.70
52.1376
0.10
73.9626
1.00
51.5458
0.10
18
74.6471
1.00
1.00
77
rmrp.
muicx
19
75.m
1.W
20
76.0175
o.5O
49.7731
21
76.7008
1.00
49.1w1
1.00
22
77.3m6
1.00
48.5948
0.10
23
78.0493
1.00
48.0068
0.70
24
76.6788
1.00
m.9440
1.00
47.4140
1.00
25
79.1837
I.00
79.5169
0.10
46.8105.
l.W
26
80.1547
1.00
46.1691
1.00
27
80.7997
1.00
82.0941
1.00
45.734o
1.00
28
81.4m
1.00
82.6117
1.00
45.1019
0.0s
29
82.0289
1.W
44.4750
0.M
45.Wl5
0.00
3o
82.5891
1.00
83.7293
1.00
43.0358
1.00
45.0174
1.w
84.3384
t.m
43.1666
0.00
31
46.4350
0.w
32
83.6069
0.W
84.9769
t&W
43.5953
0.M
33
&(A652
o.f!O
65.6375
1.W
42.9344
0.20
34
acwo
0.W
42.3ceu
0.m
35
86.9812
0.00
41.7018
l.M
37
ea.4364
1.00
40.5151
0.10
30
89.1797
1.0
1.00
36
39
89.8891
0.10
10
90.6045
1.w
3E.9167
41
91.3250
1.00
30.3614
1.w
42
92.0484
1.W
37.0150
0.00
43
92.n29
1.00
37.2723
1.00
44
93.4981
1.W
36.7320
0.00
45
94.2268
1.00
9.1961
1.00
46
94.955s
1.w
35.6620
0.w
47
95.6836
1.W
35.13oo
0.w
48
96.4134
1.00
49
97.1415
1.00
so
97.6709
1.00
51
98.6012
0.10
52
99.3309
l.w
53
00.0568
0.10
54
00.7816
1.00
-
249
8, BRANCH I
2P.ANcli
BRANCH III
II
J
PREQ.
w
0.00
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O.lC
-
250
GEORGES GRANER
but was considered in (14). It is a new illustration of the danger of extracting from microwave data, as was pointed out in Ref. (16). THE LOW K
SUBBANDS
For K < 3, a certain number of “abnormal” phenomena occur, namely: (a) one local resonance for J LX 10 and K = 0 of CHa ‘@Br; (b) two local resonances for J N 23 and J ‘V 30 for K = 1;
as values
2.51
THE 2~s BAND OF CH3Br
a level splitting for high J values of K = 3 ; (d) probable resonances for high J values (J = 40-G) of K = 0, 1,2 ; (e) a noticeable shift of the QQK (K) lines for low K values.
(c)
The small local resonance in the K = 0 subband of CH3 7gBr is depicted in Fig. 2. From an analytical study of this resonance (see Ref. (2) for methods), one can find that the perturbing level has an effective value B’-I?” = -5.34 X low3 cm-‘. The coupling
6
5
5 Kaa.
Y
MB&
”
?mP.
8
7 Y
m.
”
252
term can be represented either by WO = 0.0867 cm-’ or W = W,(J(J + 1) - K(K+ l))i with W, = 807 X 1OP cm-’ and we have no way to choose between them. The fact that no similar perturbation is visible on the K = 0 subband of CHs 81Br can be interpreted by assuming that for this species, the perturbing level is notably lower than the level of 2~5, for all J values. This hypothesis leads to the conclusion that the (unknown) perturbing level has a vibrational isotopic shift larger than 0.8 cm-l. For the I( = 1 subbands, the situation is more intricate since there are at least two local resonances occurring for relatively close values of J’ (25 and 30 for 7gBr, 23 and 30 for 81Br). The frequencies of the QQr transitions are plotted on Fig. 3. Several treatments of this problem are possible. By assuming a simple model, where two dije~nt subbands are responsible of the two resonances, we can get some information about them. Low J resonance (J ‘V 24) :
B'eff - B” = -4.51
X 1OP cm-l.
0.152 cm-r for alBr. Vibrational 4Assumed J-independent. and 0.0064 cm-l.
Coupling
term4 Wo = 0.136 cm-* for 7sBr and
isotopic shift ‘V 0.660 cm-l.
If a Coriolis type term is taken, the values are respectively W, = 0.0053
THE 2~5 BAND
OF CHsBr
253
High J resonance (J N 30) : B’cff - B” = -3.38
X 10e3 cm-l.
Coupling
term5 W,, = 0.562 cm-l.
Vibrational
isotopic shift = 0.189 cm-‘. The K = 3 subband shows a splitting visible from J’ ‘V 36 on both isotopic species, and at least for the first J values, in the P as well as in the R branch. The splittings are given in Table XIII. They can be reasonably well represented by a formula like Av= uJn(J + 1)” with n slightly larger than 3 (n = 3.3 and a = 4.3 X 1CP cm-r). It should be pointed out that these splittings are much smaller than those found in a few perpendicular bands. Other probable resonances in the K = 0, 1, and 2 subbands for very high J values will not be emphasized here. Due to the lower quality of the spectrum under 2840 cm-‘, P lines are difficult to find to check assignments of R transitions. Therefore, the upper branch of the K = 0 subband can be misnumbered by f 1 in J. We think the numbering is correct for J > 35 in K = 1. For K = 2, no convincing upper branch was assigned. 6 See footnote 4. Coriolis type term W, = 0.0183 cm-l.
254
GEORGES
GRANER
v. + h)
ki N._
l
cl-l
+ ****
.+
++*
8, Br 79
FIG. 2. Plot of the frequencies of the hypothetical Q&(J) lines as computed from experimental Q& and QPo lines. This curve refers to CHX ‘aBr. The corresponding curve for CHa 81Br shows no resonance.
The last “abnormal” phenomenon in the low K subbands is the position of the @QK(K) lines. They are observed for K 3 3 and can be computed or extrapolated from R and P lines for lower K values. They are plotted with an extended scale for Bromine 81 on Fig. 4. It is obvious on this figure as well as on the similar one for Bromine 79 that the K = 0, 1, 2 values are displaced from the regular curve given by the other ones; if it is to be interpreted as a resonance, it has a WO of ~~0.1 cm-’ and a crossing point approximately equidistant from K = 1 and K = 2. Similar phenomena can be detected by plotting the origin V,,b of the subbands.
QRIand QPr lines. FIG. 3. Plot of the frequencies of the Q@(J) 1ines as computed from experimental Note the two “large” local resonances and the smaller one for J’ = 36. This curve refers to CHa *rBr but the corresponding one for the other species is very similar.
THE
2~5 BAND TABLE
255
OF CHaBr XIII
SPLITTINGS IN THE K = 3 SUBBANDS= CHs ?gBr
J’
u Splittings
7.3 7.3 9.0 11.7 13.6
(30.4)
are given in 10-a cm-‘. Imprecise
values are between
EXPLANATION
P branch
(7.2) 8.1 9.5 12.6 12.3 17.0 21.1 25.2 26.6 33.9 37.4 44.2 49.8 57.1 65.6 73.7 83.4 89.2
(8.1) 10.8 10.2 (13.8) (14.)
18.7 (21.9) (28.3) (25.6) 34.2 38.4 45.6 51.6 58.7 66.9 76.9 88.7 95.9
TENTATIVE
R branch
P branch
R branch
3.5 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
CHs *lBr
OF THE
LOW
(8.8) (8.2) 10.6 10.6 15.8 (19.7) (20.7) (25.9) (27.0)
brackets.
K RESONANCES
The first task before attempting any interpretation of these phenomena is to find the energy levels responsible for the perturbations. From data given in Ref. (7) and (8), it is possible to compute the band centers within a few wavenumbers and to plot the corresponding energy levels to see if they are likely to cross the levels of 2~. We can thus reasonably eliminate 3v6(& = f3), predicted near 2744 cm-* and 3~3 + vg near 2762, whose levels can only interact with (US = 2 Z5 = 0) if we accept large K changes between interacting levels. PCevertheless,rtherelis an interesting phenomenon with 3v~(E6 = f 1). While the band center of the component Z6 = 3 of this band is relatively well known from the knowledge
I
~409 K2
3
CH,
I
.2 .l
2m62.0
.9l" 012
%r
x
x
x
x
x
x L
I
1 3
' 4
11 9 9
11 7 9
x
11 970
x
. K
FIG. 4. Plot of experimental (or deduced from R and P lines) QQK(K) line frequencies for CHJ arBr. A similar curve can be drawn for CHa ‘sBr. The frequency of QQK(K) is almost exactly a linear function of K2 except for low K values. To emphasize this anomaly, the quantity 0.09 Ke has been added to each frequency.
GEORGES GRANER
256 of 2v~(& = f2) given by
and of vg (7, S), the band center of 3v6(.& = &l) (3&-l
is unknown.
It is
= (3YfJL3 - sgm.
From Ref. (2) and (3), it can be deduced that v6 has the following constants 7g~gB= 1.131 X 10m3cm-‘,
%ysB = 1.124 X 10m3cm-r,
and ‘Ig(yg) - *I(Q) = 63.8 X 1O-3 cm-‘, from which 3~ can be predicted to have B’ - B” = -3.393 or -3.372 X 103 cm-’ and an isotopic shift of 0.1914 cm-l. They are precisely the B’ - B” and the isotopic shift found for the J ‘V 30 resonance in the K = 1 subband (see earlier). This fact could be considered as an amazing coincidence but for the following fact: 3ve(Za = 1) has already been detected for CH3Cl at 3042.753 cm-’ (21) or 3043.532 cm-’ (22) which gives for this compound a value of (3~~)~~~ - 3 X (Y,J = 6~“~~ - 2gsa=
-9.6
cm-‘.
It seems reasonable to assume a similar anharmonicity for methyl bromide, so that (3yg)l_1 can be predicted to be S-10 cm-* lower than 3 X 954.3 = 2862.9 cm-‘. The best fit is found by putting the band center of 3vs(E = 1) at 2856.46 for 7gBr and 2856.26 for 81Br, i.e., with 6x”~s - 2g66 = -6.54 cm-‘. With this value, the levels (~1~= 2, Z5 = 0, K = 1) and (~6 = 3, Ze = 1, K = 2) are interacting through a x-y Coriolis interaction. From V6 = 954.3 (7), 2V6(i = 2) = 1868.8 (7) and 3vS(l = 1) = 2856.36, one can deduce6 0’6 = 974.2, A valuable 1925 cm-‘. The vz -!- v3 f
3co66= -5.8,
&is = -14.1.
check would be, of course, to find the parallel
component
of
2vS
near
V6Band
Since this band is predicted to be centered almost at the same frequency as 2~ (Al), it is important to ascertain its characteristics. They can be obtained by different ways, not entirely converging. Its band center can probably be best attained from the band center of v5 + v3 + VP,which is reasonably well known from Ref. (2) to be 2996.403 cm-’ for 7gBr and 2995.041 cm-’ for 81Br. Assuming that (V6 + V3 + v6) - (V2 + V3 + v6) N (l’s + v6) - (l’~ + v6) = 133.30 Cl+ (7), the band center of v2 + v3 f v6 is predicted near 2862 cm-’ with an isotopic shift of 1.271 cm-‘. The prediction of B’ - B” for this band is more delicate because of the already mentioned Coriolis resonance between v2 and vs. From ~6 + v3 + v6 in Ref. (2) (B’ - B” = -3.34 X lop3 cm-l) and the difference Bg - Bz of Ref. (19) where the Coriolis one would resonance is taken into account (Bs - B2 = - 1.04 X 10e3 cm-l), predict B’ - B” = -4.38 X 103 cm-l for v2 + v3 •l- v6. On the other hand, taking cxaB 6if Y.Y = 954.6 as in Ref. (h’), one gets&
= 974.92, S’P,P, = -6.02,
and gee = -14.24 cm-l.
THE 2~5 BAND
OF CH3Br
257
from (23), (Y~ B from (24) and (Y~ B from (9), one gets B’ - B” = -5.52 X 1V cm-l. These conflicting values agree more or less with the experimental values found earlier in the K = 0 resonance (B’ - B” = -5.34 X 1P cm-r) for one, in the K = 1, J E 24 resonance (B’ - B” = -4.51 X 10m3err-l) for the other. Similar problems arise with oA values. Plotting reasonable energy levels for v2 + v3 + v6 leads us to the provisional conclusion that a Coriolis resonance occurs between the following levels: v5 = 1,lj = 0, K = 0 and for 7sBr); v5=2,/5=0,X=
z12= 03 = z’~= Is = 1, K = 1, (crossing
1andvz=v3=v6=&=1,K=2,
for JZ
10
(crossingforJIV24);
z5 = 2, l5 = 0, K = 2 and v2 = 2’3= y6 = &, = 1, K = 3, (crossing for J N 41). Nevertheless, it is probably an oversimplification to consider these two vibrational levels alone since the values of the coupling terms, the values of B’ - B” as well as the isotopic shifts are only half-satisfying. The VI Band Near 2973 cm-r It has been traditionally (Al) for all methyl halides of this band from the same tive. In any case, it is hard by an interaction with ~1. The Perpendicular
admitted that a Fermi resonance occurs between vr and 2~5 but its importance is more and more denied. Since a study Fourier spectra is still in progress (H), we cannot be affirmato imagine how the local resonances in 2v6 could be explained
2v5 Band (15 = ~2)
It is the most elusive of all concerned bands since it was never observed, as far we know, for any methyl halide. One can guess that its band center is not too far away from the center of the parallel component so that level crossings are probable. As was mentioned earlier, both components are implied in a sextuple Coriolis resonance together with 2vz and v2 + v5 but they are only indirectly linked through v2 + vs. Nevertheless, a direct link is possible through the l(2, 2) resonance. Unfortunately, no definite value of the relevant constant 45 can be obtained from Ref. (14) although it is obviously very small. One of the phenomena whigh might be explained by the influence of 2v5(E) is the uplifting of the K = 2 subband, even for low J values (Fig. 4). We can assume for instance that the K = 0, 1~ = -2 level of 2~5 is very slightly lower than K = 2 15 = 0. If both levels are linked to a third one E, which is far lower, they will both be displaced upwards, giving the observed effect. Of course, other levels of the perpendicular component could also explain this effect. We can, in the same way, try to explain the splitting of the QQ3series by this invisible v5 = 2, 1~ = f2 level. Let us assume that the 16 = 0 and 15 = f2 sublevels are interacting not only through the l-type (2, 2) resonance, but also through the l-type (2, -1) resonance (25). (Vt, It, KI HI V[, lt f = FC(J(J
2, k f
2)
+ 1) - k(k f
l))(J(J
+ 1) -
(K f
l)(K f
2))(vt + It + 2)(v, =F z,>p
GEORGES
2.58
GRANER
SUBLEVELS
Ofvs.Z,J.4 Nl-193p ONLY)
FIGURE 5
=
E(2K =I=l)[(J
+ 1) - K(k F l)(Vt f
I, + 2)(V, =F &)I*.
In this case, the 3(2J + 1) levels of ~5 = 2 corresponding to a J value7 are linked in three chains. Each chain contains 2J+ 1 levels of the same rovibrational symmetry. One contains the levels with K - I = 3p (type A I+ A 2) ; the other two chains are in fact equivalent and link the levels with k - Z = 3p f 1. Let us consider only the first chain, and limit the discussion to a simple example where J = 4 (Fig. 5). The 9 levels involved here comprised # (k = 0, Z= 0) and four pairs [# (k, I), # (- K, -Z)]. If we introduce, as usual new base functions #* = (l/a) (&,i f #_-k,l), four of them are of A 2 type and five of A 1 type* according to Ref. (26) : A:
#+(4, -2),
-42: #-(4,
-2),
C(3,
O), #+(2,2),
#+(3,0),
#-(2,2),
ti-(1,
-2)
#+(I,
-2).
and +(O, O),
The perturbed levels are therefore obtained by diagonalizing one 5 X 5 and one 4 X 4 matrix. Since q-(3,0) and #+(3,0) belong to different matrices, their perturbed energies will be different so that a splitting into Ar and AZ sublevels will occur in the ~5 = 2, Z = 0, K = 3 level. Since the lower levels of the Q&(J) and QPa(J) transitions are also of type Ar + AZ (26), these transitions themselves will be split. Similar effects but of much smaller size can be expected for the K = 6 levels. The present author is conscious of the entirely conjectural nature of the explanations involving 2~b(E) in the absence of any information on the band center of this band. the author noticed the publication of a While this paper was being written, work by Maki, Sams, and Olson (27) concerning the parallel band 3~ of PH,. Two different kinds of splittings of K = 3 levels are mentioned therein. The first one concerns 7Neglecting the M-degeneracy. 8 +(O, 0) is of AI type if J is even and of A2 type if J is odd.
THE
2~s BAND
OF CHaBr
259
the ZJ:,= 3 level. It is quite different from our splitting, although it is also an AJ2 splitting. First it is much larger than ours by a factor of lo5 for J = 10; second, it varies roughly like [J(J + l)p.” instead of [J(J + l)]“.” and finally no I quantum number can intervene in their problem. A second splitting mentioned in Ref. (27) affects the ground state of PHS and is described by a formula Av = au + bu2 where u = [J(J + l)][J(J + 1) - 21 [J(J + 1) - 61. This splitting is clearly proven by Davies el al. (28) and it is striking that it varies as [J(J + l)]” a 1most as in our finding. A least-squares fit does not clearly discriminate between the formula in [J(J + l)]“.” and a formula in au + bd with a = 4 X lo-l2 cm-’ = 0.12 Hz. This new hypothesis might appear attractive but for the following two objections. (1) If we accept the affirmation of Davies et al., namely, that u~n~/uc~~B~ru (BP& to be roughly 1.6 X lop4 Hz and not &Ha&)’ = 5 x 105, we would expect UCH~B~ 0.12 as found. (2) More important is the fact that neither in the parallel band ~1 (24) nor in the perpendicular band ~4 (2) of methyl bromide any K = 3 splitting or anomaly in ground state combination differences was ever found, as could be expected if our splitting was due to the ground state. Therefore, we prefer to think for the moment that the K = 3 splitting here observed is occuring in the 85 = 2 level, and is probably explainable by an interaction with 2~~2. DISCUSSION
AND
CONCLUSION
While writing the last words of this paper the author is aware that new questions that have arisen from this work are more numerous than those which have been solved. This will probably often be the case in the future with high resolution spectra of overtones and combination bands, since favorable cases as Ref. (2) are quite rare. We have assigned about sixteen hundred lines, found reasonable band centers and isotopic shifts for 2~5. The existence and size of the Coriolis coupling with v2 + v5 have been undoubtly proved and, hopefully, the B’ - B” and A’ - A” values published in Table IV are better than previous values. Moreover, we tried to convince the reader that we found correctly the band center of 3v6(/6 = ~1) and that the v2 + v3 + v6 and 2vb(&, = f2) bands are responsible for other local effects. Improvement of this work would demand better spectra of the region 2600-2840 cm-’ as well as a complete elucidation of the region of v2 and vh fundamentals. ACKNOWLEDGMENTS The author is indebted to Dr. Guy Guelachvili and Mr. Claude Amiot who provided CHzBr. He wishes to acknowledge the usefulness of many conversations with other Polyatomic Molecules group. RECEIVED:
September
the spectrum of members of the
13, 1973 REFERENCES
1. J. CONNES, H. DELOUIS, P. CONNES, G. GUELACHVILI,J. P. MAILLARD, AND G. MICKEL, Nom. Rev. Opt. Apfd. 1, 3-22 (1970). 2. C. BETRENCOURT,G. GBANER, AND G. GUELACHVILI,J. Mol. Spectrosc. 15, 216-237 (1974).
260
GEORGES GRANER
3. (a) N. BENSABI, C. ALAMICHEL,AND C. AMIOT,Mol. Phys. (1974); (b) 4. (a) (a) 5. W. 6. (a)
N. BENSARI,These de 3eme Cycle, Paris, 1973. W. E. BLASS, Ph.D. Dissertation, University of Michigan, 1963; W. E. BLASS ANDT. H. EDWARDS,J. Mol. Spectrosc. 24, 111-115 (1967). J. 0. THOMAS,J. T. Cox, ANDW. GORDY,J. Chem. Phys. 22, 1718-1722 (1954). T. L. BARNETTANDT. H. EDWARDS,J. Mol. Spectrosc. 20, 352-358 (1966) ; (b) T. L. BARNETT,Ph.D. Dissertation, University of Michigan, 1967. 7. Y. MORINOANDJ. NAKAM~RA,Bull. Chem. SOL Japan 38, 459468 (1965). 8. E. W. JONES,R. J. L. POPPLEWELL,AND H. W. THOMFSON,Spectrochim. Acta 22, 647-657 (1966). 9. C. BETRENCOURT AND M. MORILLON,J. Mol. Spectrosc. 45, 171-186 (1973). IO. G. AMAT AND H. H. NIELSEN, “MoIecuIar OrbitaIs in Chemistry, Physics and Biology,” p. 293, Academic Press, New York, 1964. Ii. C. DI LAURO ANDI. M. MILLS, J. Mol. Spectrosc. 21, 386413 (1966). 12. R. L. DILLINGANDP. M. PARKER,J. Mol. Spectrosc. 28, 178-196 (1967). 13. W. E. BLASS, J. Mol. Spectrosc. 31, 196-207 (1969). 14. Y. MORINOAND C. H~ROSE,J. Mol. Spectrosc. 24, 204-224 (1967). 15. (a) J. C. DEROCHE,G. GRANER,ANDC. ALAMIC~EL,J. Mol. Spectrosc. 43, 175-189 (1972); (b) J. C. DEROCHE,These de 3eme Cycle, Paris, 1971. 16. G. GRANER,J. Phys. 31, 435-438 (1970). 17. (a) M. MORILLON,G. GRANER,C. ALAMICKEL,C. BETRENCOURT, ANDM. BETRENCOURT, J. Phys. 31, 519-531 (1970); (a) M. MORILLON,These, Paris, 1970, Chap. IX. 18. M. KURLAT, Ph.D. Dissertation, University of Tennessee, Knoxville, 1969. 19. W. E. BLASS ANDG. GRANER,in preparation. 20. M. BETRENCOURT AND G. GRANER,Spectrodim. Acta 28A, 1019-1027 (1972). 21. [a) M. MORILIDN, G. GRANER,AND C. ALAMICHEL,C. R. Ad. Sci. Paris 266B, 240-243 (1968) ; (6) M. MORILLON,These, Paris, 1970, Chap. VII. 22. A. G. MAKI ANDR. THIBAULT,J. Chew Phys. 48, 2163-2167 (1968). 23. D. R. ANDERSONANDJ. OVEREND,Spectrochim. Acta 27A, 2013-2015 (1971). 24. M. BETRENCOURT AND M. MORILLON,private communication. 25. M. L. GRENIER-BESSON, J. Phys. Rad. 21, 555-565 (1960). 26. G. TARRAGO,These, Paris, 1965. 27. A. G. MAIU, R. L. SAYS, ANDW. B. OLSON,J. Chem. Phys. 58,45024512 (1973). 28. P. B. DAVIES, R. M. NEUMANN,S. C. WOFSY, AND W. KLE~ERER, J. Chem. Phys. 55,3564-3568
(1971).
OF MOLECULAR
SPECTROSCOPY
Contribution
51,238-2&l (1974)
to the Study of the 2v5 (Al) Rovibrational of CH,Br near 2860 cm-l
Band
GEORGES GRANER Laboratoire d’lnfrarouge, Laboratoire associe au CNRS, Universitk de PARIS Bdtiment 3.50, 9140.5Orsay, France
VI,
This band was studied on a Fourier Transform spectrum (resolving power of the apparatus: 0.005 cm-l). For each isotopic species CH3 rgBr and CH3 *rBr, about 800 lines were assigned. The band is well explained by a x-y type Coriolis interaction with ~2 + ~5. Several local resonances occur for low K values as well as a doubling of the K = 3 levels. Their study provides interesting information on neighboring bands, especially 3~g(E), ~2 + VI + ~6, and 24E).
The infrared spectrum of Methylbromide has been recorded between 2800 and 4250 cm-’ using the “third generation” Fourier interferometer built at Laboratoire Aim6 Cotton (1). The main characteristics of the recorded spectra have already been given (2). The apodized resolution limit of the apparatus is 0.005 cm-’ and, because of the Doppler broadening, the measured linewidth is about 7 X lop3 cm-‘. The absolute precision on the wavenumbers is estimated to be 2 X lop3 cm-r but the internal consistency of these wavenumbers is much better, probably 0.24.3 X 1O-3 cm-‘. Most of the present work was done on one spectrum run with the interferometer entirely evacuated. The sample pressure was 0.4 Torr and the path length 8 meters. The 2vg band here reported is situated in the lower frequency region of the interferometer; because of absorption by the Infrasil separating plate and of the use of a PbS detector, the Signal-to-Noise ratio is quite a bit poorer than in Ref. (2) and the spectrum was not used below 2830 cm-l. Notations used in this paper are the classical ones. It should be especially noted that K is a signed quantity and that K = 1k I. GROUND STATE CONSTANTS
The set of ground state constants of methyl bromide is divided in two subsets. First, the values of B”, D”.T, and D”JR are of prime importance for us since they enter into the ground-state combination differences (GSCD) such as Q&(J - 1) - QPK(J + 1) which are very useful in making line assignments as was suggested by Blass and Edwards (4). These constants, already well known from microwave work (5)) were slightly rem-red, for CH3 *‘Br only, through the study of the v4 band (2). The second subset, i.e., A” and D”K is far less well known but it has almost no importance for the study of a parallel band where only A’ - A” and D’II. - D”g are significant. Nevertheless, we found it convenient in the present paper to deal with upper 238 Copyright AU rights
Q 1974
by Academic
of reproduction
Press,
in any form
Inc. reserved.
THE 2v.5 BAND TABLE
OF CHzBr
239
I
GROUND-STATE CONSTANTS USED IN THIS WORK
CHJ ‘OBr
CH, *lBr
5.1291~ 8.308 X 10-S” 0.3191607~ 3.30228 X 10Pc 4.27962 X 10-6~
5.1291. 8.492 X 10-h* 0.3179477* 3.274 X lO+* 4.244 x IO-B*
a From Ref. (6). b From Ref. (2). c From Ref. (5). All values are expressed in cm-l.
state energies; Table I gives the values we used. As it is explained in Ref. (Z), A” is taken from Barnett and Edwards (6) while D” K has been modified. The same A” and D”K values have been used for both isotopic species. Since an uncertainty of 0.01 cm-’ on A” is not at all unlikely, cm-r for K = 9, are possible on energy values hereafter quoted. ASSIGNMENT
large errors, up to 1
OF THE TRANSITIONS
Although the parallel component of 2vs has already been quoted in (7) and studied in (8), our drastic improvement in resolution obliged us to use a completely new approach to the problem. Since the QQ branches in the 2856-2862 cm-’ region were not intense and clear enough to be the starting point of the work, we began by looking for series in the QR and QP regions. We were rapidly able to find more than a dozen quite regular R series and fewer P series. In most cases, they appear as almost parallel twin series, obviously related to the existence of the equally abundant isotopic species CHa 79Br and CHI 81Br. This fact, although it doubles the line density, is quite useful in the confirmation of line assignments and helps one to spot a ‘
240
GEORGES
GRANER
K = 1 ones. Nevertheless, the alternative assignment of these series or part of them cannot be completely ruled out. It should be noticed that above J ~40, on our spectrum QP lines are weak and barely recognizable in the noise. Therefore, the GSCD are of no use for assigning or checking high J R-lines, which are thereby slightly less reliable. For this reason, we were puzzled for a long time by several short but clear series of lo-15 lines in the 2890-2900 cm-* region, No convincing J and K numbering was possible with the help of the GSCD and moreover, these short series are clearly perturbed at their lower frequency end, which prohibits their linking to other series. Finally, they were attributed to K = 1, 2, and 3. From the GSCD, low J QQK (J) lines can easily be assigned. A plot of QQx (K) vs K2 also gives QQs (a), QQs (9), and QQr, (10). All identified transitions, 1600 in number, are grouped in Tables V-XII. A part of the spectrum in the region of the QQ branches is shown on Fig. 1. STUDY
OF INDIVIDUAL
SUBBANDS
We were soon convinced that several perturbations were taking place within this band. Therefore, we felt compelled to start this work by a separate analytical study of each K subband. Since the ground state constants B”, D “J, and @‘JR are well known, it is sensible to deal with the upper state energies of the transitions instead of the frequencies. They are obtained through
E’ = Y + (A” - B”),
+ l?“J”(J” + 1) - D”JJ”2(J” + 1)” - D”J~J”(J” + 1)K” - Dt’~K4.
An error on A” and DK” has strictly no effect within a given subband effect on the comparison of different subbands.’ The upper state levels of a subband were fitted to a polynomial :
(1)
and it has little
E’ = a,, + aJ’(J’ + 1) + UZJ’~(J’+ 1)” + u~J’~(J’ + 1)” + . . .,
(2)
up to the point where no statistically significant improvement was obtained by adding a new monomial [see Ref. (z)]. In the least-squares fit, a severe weighting was used. Only pure lines were given a unity weight; slight asymmetries led to weight equal to 0.2 or 0.1 and larger anomalies or overlappings were sanctioned by 0.01 or even 0. The weights are given in Tables V-XII. Some very bad lines, whose frequency may be wrong by as much as 5 X 1w3 cm-l are purposely deleted in these tables. As can be seen from Tables II-III, all the subbands of 2~5 need at least 4, and often more, terms in formula (2) to achieve a satisfactory and significant fit with a standard deviation of OS-O.7 X 1O-3 cm-‘. It is important to note here that the same treatment applied to subbands of v4 (a), which is almost an unperturbed band, shows that 3 parameters only are usually statistically significant and give u N 0.4 X 1e3 cm-’ except for the K’ = 5 and K’ = 7 subbands which require 4 parameters since they are close to the badly perturbed K’ = 6 subbands. 1An equivalent
method
would have consisted
YcDI= Y + ,“,“(J”
in working
+ 1) - D”JJ”‘(J”
with corrected + I)* -
D”Jd”(J”
frequencies +
1)p.
THE
2~5 BAND
241
OF CHaBr
P = 0.4 TORR L=8M.
61
79
79
PO(10)
PO Ill)
l’““““l”“““‘I”““” 2855.50
2856.CUJ
2856.50
‘,““““‘,“‘“‘“’
a
,,,,,,,,,
2857.00
2857.50
@r,,,l
I,,,
,,
10
6
@LIII’PI’
,
I
,
16
’ ’ ’ I ’
,““,““““’
’
’
2858.50
2isT
J
,,,,,,/,,
2859.00
,,,,
285800
,,I,,,,.,
2859.50
286000
I~‘““‘“l”“““‘l”‘“““~~““~
b FIG. 1. Part
2860.50
2 861.00
2861.!io
286208
of the absorption spectrum of CHJBr in the region of the ‘JQ branches. the Q superscript was omitted in every line identification.
Since one has
AK = 0 for all transitions,
Therefore, the fact that we need 4, 5, or 6 terms for the subbands of 2~5 is a first clue that a global resonance occurs. Another sign is the tremendous increase with K of al (i.e., of B’ eff - B”). A third anomaly is the large size and variations of u2 compared to -D”J. Nevertheless, there is clearly a regularity in these variations from K = 8 to 3. It is therefore reasonable to try to fit these subbands together while excluding for the moment the low K subbands which are much more abnormal and are subject to several local resonances. Tables II-III give the results of the individual fits of each subband.
.321729 .321243 .321029 .320684 .320275 .32050 .320666 .320695
3031 &I62
2980.0256
2937.6273
2904.6495
2861.1984
2866..328
2866.8954
2e62.1300
5
4
5
4
6
4 (a) (b)
5 (c)
uu
udw
taldq
(b)
(c)
-
-
+
-
-
5.16
3.80
0
7.3
4.03
4.41
4.16
6.14
up to J’ = 35 and taking “Femi-like”
into account the mo8onance near J’ = 10
transitiona
only transitions
with J’ 2 22
-
.322674
3092.9m
5
- 11.13
- 69,
107 x *2
.32759
*I
3163.201
.0
6.1
sub
reaonancee into account
go.
2a62.13al
2862.Of355
2861 .%OO
2861.W
1.534
1.505
1.34
1.114
1.524
1.868
2.082 2859.8293 zs60.669a
2.566
3.713
8.43
103~ (BLB*)
2858.7665
2857.4668
2855.714
”
-41.
(2)
2e62.019
BY IWMULA
@GO.
- 1000.
-
13.
9.0
3%
185.
53a
‘5
OF C+
II
1O12
OF TEE K SBBAUD
6
-1 All values In cm
1
(a)
K
FOLRWIUAL FIT
PABU
-
-1
dtb
up to J’
oply transitions
uaiw
using transitions
in m
(a)
AI1 vdues
.31948a
.319449
.319454
.319793
= 35 and tekiq
J’ 2 2G
2862.1154
(b)
0
6
.31949
2066.1987
6 (a)
2866.8789
2881.1738
6
2
4 (b)
2904.6411
4
1
.319095
2937.6273
4
4
3 6.29
3.97
4.36
4.72
5.0
3.93
“Femi-like”
-
-
- 22.
+
-
-
-
7.5
resonances
-
-
544.
3.1
-26.
2300.
10'5 E a 4
- 120.
"5
0.23
200.
- 1.46
4.6
10'6 I
BY FORMULA(2)
- 22000.
into account.
200.
29.
9000.
- 922.
-
9.
8.9
36.
.320491
2980.0352
.3m9
3031.8376
5
4
187.
-
6.06
- 11.02
.321625
5m.
10’2T, 3
-
5
3092.9886
5
I
Efi2
68.
IO
7
OF TEE K SUBBAFiW OF ‘X3 “Br
III
.32630
*I
6
3163.260
0
6
II
8
K
POLYNOMIAL. FIT
TABI.
sib
2862.1154
2862.06-R
2861.9876
2861.9305
2861.3477
2e60.6708
2859.8098
2s5a.7466
2851.4466
2855.695
u
1.541
1.501
1.55
1.147
1.5%
I.845
2862
2.543
3.618
8.35
lo3x (BI-BN)
GEORGES
244 CORIOLIS
GRANER
RESONANCE
WITH
~2 + vj
It is well known that a parallel band, in which an A1 vibration is singly excited and a perpendicular band in which an E vibration is singly excited, may be affected by an accidental resonance caused by the term (3) in the first order Hamiltonian. This type of resonance, called Coriolis resonance due to rotation about the x and y axes (z being taken as the top axis), has been studied by various investigators (10-16). The corresponding nondiagonal matrix elements are given by setting vt = V~= 1 in the following formula. (8, - 1, V,, I*, +c+*,
Vt - l,Z1 f
1, K f
1)
= 4[(Va/Vt)f + (Vt/Y*)j].B.TI,I?.[V,(V,
=1=Zt)(J =F K)(J f
k + l)-Ji.
(4)
One of the less disputable examples of this resonance is given by the v2 and v5 bands of the methyl halides where the coupling constant { B2,5has been predicted several times (11,14) and measured (11, 14, 16, 17) ; all values lie in the range 0.45-0.65. More specifically for methyl bromide, this constant was predicted to be 0.61 and the interpretation of microwave transitions (14) yielded values between 0.60 and 0.67. Recently, we had the opportunity, through the kindness of Dr. W. E. Blass, to reexamine infrared data concerning the v2 and v5 bands of CHaBr from M. Kurlat’s thesis (18). Although our present fit is not very good, it gives a value close to 0.61 (19). It was pointed out earlier (17,20) that, as a consequence, the overtones 2~ (Al), 285 (E), 2vz and the combination band v2 + v5 are involved in a sextuple interaction [see Fig. 6 of (17a) or Fig. 4 of (20) J. But it was shown in the case of CHsCl (17) that 2~ (Al) is mainly perturbed by its interaction with v2 + v5 so that it is more or less legitimate, in a first stage, to ignore the other bands. This approximation seems even more justified here than with CH&l since there is a larger frequency difference here between v2 and vs. Moreover, a recent study (9) of 2~2 shows few signs of perturbation except for K = 7, 8, 9. Therefore, we felt entitled to treat the problem simply as a Coriolis resonance between the parallel band 2~5 and the perpendicular band v2 + VS.A rough calculation predicts a crossing of levels between R = 8 and 9 of 2~5. The three levels involved are 1v2 = 0,
v5
=
2,15 = 0, J, k)
and /vz = 1, vs = 1, 15= fl,
J, k f
1)
and the coupling constant is precisely p2,5 as can be seen by setting v, = 2, It = 0 and v, = 1 in formula (5). We had at our disposal a computer least-squares program (1%) adapted for this problem. Unfortunately v2 + v5 is too low to be visible on the present spectra and for the time being, we have poorly resolved spectra (7,8) with only Q-branch frequencies given. Nevertheless, we have decided to use these data in the following way : 17 Q-branch frequencies of vz + v5 from Ref. (7) and about 300 frequencies of the 2~ band with K > 4 were simultaneously fitted. The weights assigned to the v2 + v5 lines were progressively
THE ZVS BAND
yo
2862.2094
t
21
A’
5.03609
?
9
(A’
-
A”)
-
B”)
-
B’
2
u5
D; Dt D;K
2862.1910
t
0.1599
x f
6)x
(7.275
2
85)x
(6.64
+
0.6254
6)x
?
26
10
(3.469
A
7)
(7.335
f
72)
(6.45
2744.459
t
20
-0.367
f
13
8’
_
B”
(1.54
t
4)
f
2
-35
+
were in
in
in
the
determined the
constants dependently
in
second
one
given for
a
both
15
+
the
v5
isotopes
v2 are
+
last
x
the but
&a&m for Table IV: Read - 0.0367 instead of stead of 1.54 X 10-a for B’ - B” of ~2 + Y.S.
10
-3
10-6
_I
related
lines mean
not
x
significant
and v5
10 -5
10 -6
DyK
constants
computation
“hiCh
“*
of five
first
from *or
units
x
D;
-
the
text,
1O-7 x
3
A”
?h
deviations
i
_
-1.218
x
6)
A’
“;
standard
k
0.6251
“;
25
10 -3
10 -6
A5
explained
f x
-7
VO
8
0.09306
0.1516
10 -5
3
19 r
0.3180993
10 -3
(3.510
f
5.03603
0.09300
0.3193206
(B’
(A,)
245
OF CH3Br
“*
subsequently were
of
figure. f0
values
+
AF u5
fixed
excluded. obtained
significantly
0.367 for A’ - A”
The in-
different.
and - 1.54 X 1O-3 in-
lowered to 0.01 (which is still too optimistic!). Out of the constants of Q + ~5, only five were free to float, namely Q, A’, B’, A{S, and D’K.~ In the next step, the lines of v2 + v5 were taken out of the computation and all the the constants of this band were constrained to their previously obtained values. This rather primitive method gave surprisingly good results: the standard deviation in residuals is 0.005 cm-l for both isotopic species and although 79Br and 8’Br were separately treated, they show a remarkable agreement. Values given in Table IV are evidently an *It may seem odd that we try to get a B’ value for a band for which no individual P, Q, or R line is known. But in fact, the resonance between the two bands is so sensitive to B’(vz + ~5) that at least a good approximation of it can he obtained from 2~5 alone.
246
GEORGES
GRANER
5
f.Jl.7096
1.m
60.72la 60.7405
am am
60.65)2
l.c.2
mm.
1
59.cQ94
am
59.9m
1.m
9a.m
1.00
99.9911
1.m
99.9m
1.m
99.9%6(
1x4
99.99%
am
96.3029 0.01
60.099-d
0.m
99.cce9
l.c.2
96.4499
1.m
W.T,%
1.00
m.wo
0.00
99.01
1.m
96.9%4
1.m
%.a64
1.m
99.111,
1.m
95.1610
1.m
91.6%?7
1.m
60.1%9
1.m
59.lW
1.00
n&59
1.m
60.m3
am
99.m9
am
99.m
0.10
60.2ata
0.m
99.nm
1.00
R.u.m
0.m
99.4?e
0.10
99.7628
1.00
99.w,
1.00
%.w¶
1.m
58.8369
I.rn
%.9937
r.m
%a,*
,,W
90.9811
1.m
56.uo9
1.00
6o.mE
0.00
59.om
1.m
96.9m
1.00
%.Yw
1.m
c4.9916
1.m
99.09lo
1.00
%.?sa
1.m
Pm93
1.m
60.9658
am
59.19%
1.m
96.9017
1.W
92.m,
1.m
59.m
1.00
57.0174
1.m
99.m
1.02
57.2624
0.10
61.0689
1.00
59.97%
1.m
99.1625
0.10
59.67u
1.00
59.n49
1.m
99.8m
1.m
%?.4@1 1.m
approximation for v2 + ~5,3 but they could be considered as satisfactory for 215 (Al) ; unfortunately the K = O-3 subbands do not fit with the other ones. We will tackle in the following paragraph the problems of these low K subbands. Among the results of Table IV, we should point out the remarkably low value of B = -7.6 X lO+. These values are B’ - B” which gives lgcz$ = -8.0 X 1OP and *‘cY~ to be compared not only to aEB = - 75 X lO+ in Ref. (8), but also to aP ‘v 18 MHz = -60 X 1P6 in Ref. (14). The Coriolis resonance was not taken into account in (8) aAs an example of the crudeness of the results concerning YZ+ ~6, we should point out the zero isotopic shift on the band centers. It is not surprising since the same line frequencies of this band were used for both species. From the data of 2~9 (13) and the present ones on 21~6,we can predict an isotopic shift of 37 X 1C3 cm-l for VI + VS.
THE
2~5 BAND
OF CH3Br
-
J
m.
1
1
2 3 4 5 6 7 B 9 10 11 12 13 I4 15 (6 !I 18 19 20 21 22 23 24 25 26 R 18 2¶ 30 31 32 33 34 35 36 3l 35 39 +a +1 +2 a ++
+z
92.8985
&co’
43
93.63c4
l.02
++
94.3618
1.m
+5
95.1149
I.rn
,6
95.8912
0.m
+7
96.6791
1.M
+a
9-7.+7+4
1.00
+9
%‘I.2753
t.m
50
99.0785
1.w
51
99.8719
0.m
-
’
247
GEORGES
248
GRANER
81 BIUNCE
BRANCE
I
-
II
BNANCN III
BFaNcE
BruJlcE II
I
J
rm.
Y
3
64.5951
0.x)
4
65.2549
1.00
5
65.9016
0.M
5a.e4%
0.10
6
66.5616
0.50
58.2253
0.10
7
67.2210
I.00
57.6022
0.10
8
67.8846
1.00
56.9e19
0.02
Mao3
0.M
55.7595
0.02
ma.
Y
Pm.
Y
Pm. 59.4778
9 10
Y
Y
Pm.
III
Y
0.10
11
69.8896
o.M
55.1501
0.02
12
70.5655
0.50
54.5442
0.10
13
71.24i2
0.M
14
71.9176
1.00
15
72.5977
1.W
16
n.n93
0.70
52.1376
0.10
73.9626
1.00
51.5458
0.10
18
74.6471
1.00
1.00
77
rmrp.
muicx
19
75.m
1.W
20
76.0175
o.5O
49.7731
21
76.7008
1.00
49.1w1
1.00
22
77.3m6
1.00
48.5948
0.10
23
78.0493
1.00
48.0068
0.70
24
76.6788
1.00
m.9440
1.00
47.4140
1.00
25
79.1837
I.00
79.5169
0.10
46.8105.
l.W
26
80.1547
1.00
46.1691
1.00
27
80.7997
1.00
82.0941
1.00
45.734o
1.00
28
81.4m
1.00
82.6117
1.00
45.1019
0.0s
29
82.0289
1.W
44.4750
0.M
45.Wl5
0.00
3o
82.5891
1.00
83.7293
1.00
43.0358
1.00
45.0174
1.w
84.3384
t.m
43.1666
0.00
31
46.4350
0.w
32
83.6069
0.W
84.9769
t&W
43.5953
0.M
33
&(A652
o.f!O
65.6375
1.W
42.9344
0.20
34
acwo
0.W
42.3ceu
0.m
35
86.9812
0.00
41.7018
l.M
37
ea.4364
1.00
40.5151
0.10
30
89.1797
1.0
1.00
36
39
89.8891
0.10
10
90.6045
1.w
3E.9167
41
91.3250
1.00
30.3614
1.w
42
92.0484
1.W
37.0150
0.00
43
92.n29
1.00
37.2723
1.00
44
93.4981
1.W
36.7320
0.00
45
94.2268
1.00
9.1961
1.00
46
94.955s
1.w
35.6620
0.w
47
95.6836
1.W
35.13oo
0.w
48
96.4134
1.00
49
97.1415
1.00
so
97.6709
1.00
51
98.6012
0.10
52
99.3309
l.w
53
00.0568
0.10
54
00.7816
1.00
-
249
8, BRANCH I
2P.ANcli
BRANCH III
II
J
PREQ.
w
0.00
Pm.
r
0.10
4
65.2126
1.00
59.4625
5
65.8641
1.00
58.83fYl
I.00
6
66.5FJ9
1.00
58.2172
0.10
7
61.1186
1.00
51.6022
0.10
8
67.G87
,.oO
56.9849
c.10
9
68.5022
1.N)
56.3703
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-
250
GEORGES GRANER
but was considered in (14). It is a new illustration of the danger of extracting from microwave data, as was pointed out in Ref. (16). THE LOW K
SUBBANDS
For K < 3, a certain number of “abnormal” phenomena occur, namely: (a) one local resonance for J LX 10 and K = 0 of CHa ‘@Br; (b) two local resonances for J N 23 and J ‘V 30 for K = 1;
as values
2.51
THE 2~s BAND OF CH3Br
a level splitting for high J values of K = 3 ; (d) probable resonances for high J values (J = 40-G) of K = 0, 1,2 ; (e) a noticeable shift of the QQK (K) lines for low K values.
(c)
The small local resonance in the K = 0 subband of CH3 7gBr is depicted in Fig. 2. From an analytical study of this resonance (see Ref. (2) for methods), one can find that the perturbing level has an effective value B’-I?” = -5.34 X low3 cm-‘. The coupling
6
5
5 Kaa.
Y
MB&
”
?mP.
8
7 Y
m.
”
252
term can be represented either by WO = 0.0867 cm-’ or W = W,(J(J + 1) - K(K+ l))i with W, = 807 X 1OP cm-’ and we have no way to choose between them. The fact that no similar perturbation is visible on the K = 0 subband of CHs 81Br can be interpreted by assuming that for this species, the perturbing level is notably lower than the level of 2~5, for all J values. This hypothesis leads to the conclusion that the (unknown) perturbing level has a vibrational isotopic shift larger than 0.8 cm-l. For the I( = 1 subbands, the situation is more intricate since there are at least two local resonances occurring for relatively close values of J’ (25 and 30 for 7gBr, 23 and 30 for 81Br). The frequencies of the QQr transitions are plotted on Fig. 3. Several treatments of this problem are possible. By assuming a simple model, where two dije~nt subbands are responsible of the two resonances, we can get some information about them. Low J resonance (J ‘V 24) :
B'eff - B” = -4.51
X 1OP cm-l.
0.152 cm-r for alBr. Vibrational 4Assumed J-independent. and 0.0064 cm-l.
Coupling
term4 Wo = 0.136 cm-* for 7sBr and
isotopic shift ‘V 0.660 cm-l.
If a Coriolis type term is taken, the values are respectively W, = 0.0053
THE 2~5 BAND
OF CHsBr
253
High J resonance (J N 30) : B’cff - B” = -3.38
X 10e3 cm-l.
Coupling
term5 W,, = 0.562 cm-l.
Vibrational
isotopic shift = 0.189 cm-‘. The K = 3 subband shows a splitting visible from J’ ‘V 36 on both isotopic species, and at least for the first J values, in the P as well as in the R branch. The splittings are given in Table XIII. They can be reasonably well represented by a formula like Av= uJn(J + 1)” with n slightly larger than 3 (n = 3.3 and a = 4.3 X 1CP cm-r). It should be pointed out that these splittings are much smaller than those found in a few perpendicular bands. Other probable resonances in the K = 0, 1, and 2 subbands for very high J values will not be emphasized here. Due to the lower quality of the spectrum under 2840 cm-‘, P lines are difficult to find to check assignments of R transitions. Therefore, the upper branch of the K = 0 subband can be misnumbered by f 1 in J. We think the numbering is correct for J > 35 in K = 1. For K = 2, no convincing upper branch was assigned. 6 See footnote 4. Coriolis type term W, = 0.0183 cm-l.
254
GEORGES
GRANER
v. + h)
ki N._
l
cl-l
+ ****
.+
++*
8, Br 79
FIG. 2. Plot of the frequencies of the hypothetical Q&(J) lines as computed from experimental Q& and QPo lines. This curve refers to CHX ‘aBr. The corresponding curve for CHa 81Br shows no resonance.
The last “abnormal” phenomenon in the low K subbands is the position of the @QK(K) lines. They are observed for K 3 3 and can be computed or extrapolated from R and P lines for lower K values. They are plotted with an extended scale for Bromine 81 on Fig. 4. It is obvious on this figure as well as on the similar one for Bromine 79 that the K = 0, 1, 2 values are displaced from the regular curve given by the other ones; if it is to be interpreted as a resonance, it has a WO of ~~0.1 cm-’ and a crossing point approximately equidistant from K = 1 and K = 2. Similar phenomena can be detected by plotting the origin V,,b of the subbands.
QRIand QPr lines. FIG. 3. Plot of the frequencies of the Q@(J) 1ines as computed from experimental Note the two “large” local resonances and the smaller one for J’ = 36. This curve refers to CHa *rBr but the corresponding one for the other species is very similar.
THE
2~5 BAND TABLE
255
OF CHaBr XIII
SPLITTINGS IN THE K = 3 SUBBANDS= CHs ?gBr
J’
u Splittings
7.3 7.3 9.0 11.7 13.6
(30.4)
are given in 10-a cm-‘. Imprecise
values are between
EXPLANATION
P branch
(7.2) 8.1 9.5 12.6 12.3 17.0 21.1 25.2 26.6 33.9 37.4 44.2 49.8 57.1 65.6 73.7 83.4 89.2
(8.1) 10.8 10.2 (13.8) (14.)
18.7 (21.9) (28.3) (25.6) 34.2 38.4 45.6 51.6 58.7 66.9 76.9 88.7 95.9
TENTATIVE
R branch
P branch
R branch
3.5 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
CHs *lBr
OF THE
LOW
(8.8) (8.2) 10.6 10.6 15.8 (19.7) (20.7) (25.9) (27.0)
brackets.
K RESONANCES
The first task before attempting any interpretation of these phenomena is to find the energy levels responsible for the perturbations. From data given in Ref. (7) and (8), it is possible to compute the band centers within a few wavenumbers and to plot the corresponding energy levels to see if they are likely to cross the levels of 2~. We can thus reasonably eliminate 3v6(& = f3), predicted near 2744 cm-* and 3~3 + vg near 2762, whose levels can only interact with (US = 2 Z5 = 0) if we accept large K changes between interacting levels. PCevertheless,rtherelis an interesting phenomenon with 3v~(E6 = f 1). While the band center of the component Z6 = 3 of this band is relatively well known from the knowledge
I
~409 K2
3
CH,
I
.2 .l
2m62.0
.9l" 012
%r
x
x
x
x
x
x L
I
1 3
' 4
11 9 9
11 7 9
x
11 970
x
. K
FIG. 4. Plot of experimental (or deduced from R and P lines) QQK(K) line frequencies for CHJ arBr. A similar curve can be drawn for CHa ‘sBr. The frequency of QQK(K) is almost exactly a linear function of K2 except for low K values. To emphasize this anomaly, the quantity 0.09 Ke has been added to each frequency.
GEORGES GRANER
256 of 2v~(& = f2) given by
and of vg (7, S), the band center of 3v6(.& = &l) (3&-l
is unknown.
It is
= (3YfJL3 - sgm.
From Ref. (2) and (3), it can be deduced that v6 has the following constants 7g~gB= 1.131 X 10m3cm-‘,
%ysB = 1.124 X 10m3cm-r,
and ‘Ig(yg) - *I(Q) = 63.8 X 1O-3 cm-‘, from which 3~ can be predicted to have B’ - B” = -3.393 or -3.372 X 103 cm-’ and an isotopic shift of 0.1914 cm-l. They are precisely the B’ - B” and the isotopic shift found for the J ‘V 30 resonance in the K = 1 subband (see earlier). This fact could be considered as an amazing coincidence but for the following fact: 3ve(Za = 1) has already been detected for CH3Cl at 3042.753 cm-’ (21) or 3043.532 cm-’ (22) which gives for this compound a value of (3~~)~~~ - 3 X (Y,J = 6~“~~ - 2gsa=
-9.6
cm-‘.
It seems reasonable to assume a similar anharmonicity for methyl bromide, so that (3yg)l_1 can be predicted to be S-10 cm-* lower than 3 X 954.3 = 2862.9 cm-‘. The best fit is found by putting the band center of 3vs(E = 1) at 2856.46 for 7gBr and 2856.26 for 81Br, i.e., with 6x”~s - 2g66 = -6.54 cm-‘. With this value, the levels (~1~= 2, Z5 = 0, K = 1) and (~6 = 3, Ze = 1, K = 2) are interacting through a x-y Coriolis interaction. From V6 = 954.3 (7), 2V6(i = 2) = 1868.8 (7) and 3vS(l = 1) = 2856.36, one can deduce6 0’6 = 974.2, A valuable 1925 cm-‘. The vz -!- v3 f
3co66= -5.8,
&is = -14.1.
check would be, of course, to find the parallel
component
of
2vS
near
V6Band
Since this band is predicted to be centered almost at the same frequency as 2~ (Al), it is important to ascertain its characteristics. They can be obtained by different ways, not entirely converging. Its band center can probably be best attained from the band center of v5 + v3 + VP,which is reasonably well known from Ref. (2) to be 2996.403 cm-’ for 7gBr and 2995.041 cm-’ for 81Br. Assuming that (V6 + V3 + v6) - (V2 + V3 + v6) N (l’s + v6) - (l’~ + v6) = 133.30 Cl+ (7), the band center of v2 + v3 f v6 is predicted near 2862 cm-’ with an isotopic shift of 1.271 cm-‘. The prediction of B’ - B” for this band is more delicate because of the already mentioned Coriolis resonance between v2 and vs. From ~6 + v3 + v6 in Ref. (2) (B’ - B” = -3.34 X lop3 cm-l) and the difference Bg - Bz of Ref. (19) where the Coriolis one would resonance is taken into account (Bs - B2 = - 1.04 X 10e3 cm-l), predict B’ - B” = -4.38 X 103 cm-l for v2 + v3 •l- v6. On the other hand, taking cxaB 6if Y.Y = 954.6 as in Ref. (h’), one gets&
= 974.92, S’P,P, = -6.02,
and gee = -14.24 cm-l.
THE 2~5 BAND
OF CH3Br
257
from (23), (Y~ B from (24) and (Y~ B from (9), one gets B’ - B” = -5.52 X 1V cm-l. These conflicting values agree more or less with the experimental values found earlier in the K = 0 resonance (B’ - B” = -5.34 X 1P cm-r) for one, in the K = 1, J E 24 resonance (B’ - B” = -4.51 X 10m3err-l) for the other. Similar problems arise with oA values. Plotting reasonable energy levels for v2 + v3 + v6 leads us to the provisional conclusion that a Coriolis resonance occurs between the following levels: v5 = 1,lj = 0, K = 0 and for 7sBr); v5=2,/5=0,X=
z12= 03 = z’~= Is = 1, K = 1, (crossing
1andvz=v3=v6=&=1,K=2,
for JZ
10
(crossingforJIV24);
z5 = 2, l5 = 0, K = 2 and v2 = 2’3= y6 = &, = 1, K = 3, (crossing for J N 41). Nevertheless, it is probably an oversimplification to consider these two vibrational levels alone since the values of the coupling terms, the values of B’ - B” as well as the isotopic shifts are only half-satisfying. The VI Band Near 2973 cm-r It has been traditionally (Al) for all methyl halides of this band from the same tive. In any case, it is hard by an interaction with ~1. The Perpendicular
admitted that a Fermi resonance occurs between vr and 2~5 but its importance is more and more denied. Since a study Fourier spectra is still in progress (H), we cannot be affirmato imagine how the local resonances in 2v6 could be explained
2v5 Band (15 = ~2)
It is the most elusive of all concerned bands since it was never observed, as far we know, for any methyl halide. One can guess that its band center is not too far away from the center of the parallel component so that level crossings are probable. As was mentioned earlier, both components are implied in a sextuple Coriolis resonance together with 2vz and v2 + v5 but they are only indirectly linked through v2 + vs. Nevertheless, a direct link is possible through the l(2, 2) resonance. Unfortunately, no definite value of the relevant constant 45 can be obtained from Ref. (14) although it is obviously very small. One of the phenomena whigh might be explained by the influence of 2v5(E) is the uplifting of the K = 2 subband, even for low J values (Fig. 4). We can assume for instance that the K = 0, 1~ = -2 level of 2~5 is very slightly lower than K = 2 15 = 0. If both levels are linked to a third one E, which is far lower, they will both be displaced upwards, giving the observed effect. Of course, other levels of the perpendicular component could also explain this effect. We can, in the same way, try to explain the splitting of the QQ3series by this invisible v5 = 2, 1~ = f2 level. Let us assume that the 16 = 0 and 15 = f2 sublevels are interacting not only through the l-type (2, 2) resonance, but also through the l-type (2, -1) resonance (25). (Vt, It, KI HI V[, lt f = FC(J(J
2, k f
2)
+ 1) - k(k f
l))(J(J
+ 1) -
(K f
l)(K f
2))(vt + It + 2)(v, =F z,>p
GEORGES
2.58
GRANER
SUBLEVELS
Ofvs.Z,J.4 Nl-193p ONLY)
FIGURE 5
=
E(2K =I=l)[(J
+ 1) - K(k F l)(Vt f
I, + 2)(V, =F &)I*.
In this case, the 3(2J + 1) levels of ~5 = 2 corresponding to a J value7 are linked in three chains. Each chain contains 2J+ 1 levels of the same rovibrational symmetry. One contains the levels with K - I = 3p (type A I+ A 2) ; the other two chains are in fact equivalent and link the levels with k - Z = 3p f 1. Let us consider only the first chain, and limit the discussion to a simple example where J = 4 (Fig. 5). The 9 levels involved here comprised # (k = 0, Z= 0) and four pairs [# (k, I), # (- K, -Z)]. If we introduce, as usual new base functions #* = (l/a) (&,i f #_-k,l), four of them are of A 2 type and five of A 1 type* according to Ref. (26) : A:
#+(4, -2),
-42: #-(4,
-2),
C(3,
O), #+(2,2),
#+(3,0),
#-(2,2),
ti-(1,
-2)
#+(I,
-2).
and +(O, O),
The perturbed levels are therefore obtained by diagonalizing one 5 X 5 and one 4 X 4 matrix. Since q-(3,0) and #+(3,0) belong to different matrices, their perturbed energies will be different so that a splitting into Ar and AZ sublevels will occur in the ~5 = 2, Z = 0, K = 3 level. Since the lower levels of the Q&(J) and QPa(J) transitions are also of type Ar + AZ (26), these transitions themselves will be split. Similar effects but of much smaller size can be expected for the K = 6 levels. The present author is conscious of the entirely conjectural nature of the explanations involving 2~b(E) in the absence of any information on the band center of this band. the author noticed the publication of a While this paper was being written, work by Maki, Sams, and Olson (27) concerning the parallel band 3~ of PH,. Two different kinds of splittings of K = 3 levels are mentioned therein. The first one concerns 7Neglecting the M-degeneracy. 8 +(O, 0) is of AI type if J is even and of A2 type if J is odd.
THE
2~s BAND
OF CHaBr
259
the ZJ:,= 3 level. It is quite different from our splitting, although it is also an AJ2 splitting. First it is much larger than ours by a factor of lo5 for J = 10; second, it varies roughly like [J(J + l)p.” instead of [J(J + l)]“.” and finally no I quantum number can intervene in their problem. A second splitting mentioned in Ref. (27) affects the ground state of PHS and is described by a formula Av = au + bu2 where u = [J(J + l)][J(J + 1) - 21 [J(J + 1) - 61. This splitting is clearly proven by Davies el al. (28) and it is striking that it varies as [J(J + l)]” a 1most as in our finding. A least-squares fit does not clearly discriminate between the formula in [J(J + l)]“.” and a formula in au + bd with a = 4 X lo-l2 cm-’ = 0.12 Hz. This new hypothesis might appear attractive but for the following two objections. (1) If we accept the affirmation of Davies et al., namely, that u~n~/uc~~B~ru (BP& to be roughly 1.6 X lop4 Hz and not &Ha&)’ = 5 x 105, we would expect UCH~B~ 0.12 as found. (2) More important is the fact that neither in the parallel band ~1 (24) nor in the perpendicular band ~4 (2) of methyl bromide any K = 3 splitting or anomaly in ground state combination differences was ever found, as could be expected if our splitting was due to the ground state. Therefore, we prefer to think for the moment that the K = 3 splitting here observed is occuring in the 85 = 2 level, and is probably explainable by an interaction with 2~~2. DISCUSSION
AND
CONCLUSION
While writing the last words of this paper the author is aware that new questions that have arisen from this work are more numerous than those which have been solved. This will probably often be the case in the future with high resolution spectra of overtones and combination bands, since favorable cases as Ref. (2) are quite rare. We have assigned about sixteen hundred lines, found reasonable band centers and isotopic shifts for 2~5. The existence and size of the Coriolis coupling with v2 + v5 have been undoubtly proved and, hopefully, the B’ - B” and A’ - A” values published in Table IV are better than previous values. Moreover, we tried to convince the reader that we found correctly the band center of 3v6(/6 = ~1) and that the v2 + v3 + v6 and 2vb(&, = f2) bands are responsible for other local effects. Improvement of this work would demand better spectra of the region 2600-2840 cm-’ as well as a complete elucidation of the region of v2 and vh fundamentals. ACKNOWLEDGMENTS The author is indebted to Dr. Guy Guelachvili and Mr. Claude Amiot who provided CHzBr. He wishes to acknowledge the usefulness of many conversations with other Polyatomic Molecules group. RECEIVED:
September
the spectrum of members of the
13, 1973 REFERENCES
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260
GEORGES GRANER
3. (a) N. BENSABI, C. ALAMICHEL,AND C. AMIOT,Mol. Phys. (1974); (b) 4. (a) (a) 5. W. 6. (a)
N. BENSARI,These de 3eme Cycle, Paris, 1973. W. E. BLASS, Ph.D. Dissertation, University of Michigan, 1963; W. E. BLASS ANDT. H. EDWARDS,J. Mol. Spectrosc. 24, 111-115 (1967). J. 0. THOMAS,J. T. Cox, ANDW. GORDY,J. Chem. Phys. 22, 1718-1722 (1954). T. L. BARNETTANDT. H. EDWARDS,J. Mol. Spectrosc. 20, 352-358 (1966) ; (b) T. L. BARNETT,Ph.D. Dissertation, University of Michigan, 1967. 7. Y. MORINOANDJ. NAKAM~RA,Bull. Chem. SOL Japan 38, 459468 (1965). 8. E. W. JONES,R. J. L. POPPLEWELL,AND H. W. THOMFSON,Spectrochim. Acta 22, 647-657 (1966). 9. C. BETRENCOURT AND M. MORILLON,J. Mol. Spectrosc. 45, 171-186 (1973). IO. G. AMAT AND H. H. NIELSEN, “MoIecuIar OrbitaIs in Chemistry, Physics and Biology,” p. 293, Academic Press, New York, 1964. Ii. C. DI LAURO ANDI. M. MILLS, J. Mol. Spectrosc. 21, 386413 (1966). 12. R. L. DILLINGANDP. M. PARKER,J. Mol. Spectrosc. 28, 178-196 (1967). 13. W. E. BLASS, J. Mol. Spectrosc. 31, 196-207 (1969). 14. Y. MORINOAND C. H~ROSE,J. Mol. Spectrosc. 24, 204-224 (1967). 15. (a) J. C. DEROCHE,G. GRANER,ANDC. ALAMIC~EL,J. Mol. Spectrosc. 43, 175-189 (1972); (b) J. C. DEROCHE,These de 3eme Cycle, Paris, 1971. 16. G. GRANER,J. Phys. 31, 435-438 (1970). 17. (a) M. MORILLON,G. GRANER,C. ALAMICKEL,C. BETRENCOURT, ANDM. BETRENCOURT, J. Phys. 31, 519-531 (1970); (a) M. MORILLON,These, Paris, 1970, Chap. IX. 18. M. KURLAT, Ph.D. Dissertation, University of Tennessee, Knoxville, 1969. 19. W. E. BLASS ANDG. GRANER,in preparation. 20. M. BETRENCOURT AND G. GRANER,Spectrodim. Acta 28A, 1019-1027 (1972). 21. [a) M. MORILIDN, G. GRANER,AND C. ALAMICHEL,C. R. Ad. Sci. Paris 266B, 240-243 (1968) ; (6) M. MORILLON,These, Paris, 1970, Chap. VII. 22. A. G. MAKI ANDR. THIBAULT,J. Chew Phys. 48, 2163-2167 (1968). 23. D. R. ANDERSONANDJ. OVEREND,Spectrochim. Acta 27A, 2013-2015 (1971). 24. M. BETRENCOURT AND M. MORILLON,private communication. 25. M. L. GRENIER-BESSON, J. Phys. Rad. 21, 555-565 (1960). 26. G. TARRAGO,These, Paris, 1965. 27. A. G. MAIU, R. L. SAYS, ANDW. B. OLSON,J. Chem. Phys. 58,45024512 (1973). 28. P. B. DAVIES, R. M. NEUMANN,S. C. WOFSY, AND W. KLE~ERER, J. Chem. Phys. 55,3564-3568
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