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The ν4 band of CD3I with perturbations: A high-resolution infrared study
JOURNAL
OF MOLECULAR
SPECTROSCOPY
The
108,99-I
I8 (I 984)
Band of CD31 with Perturbations: A High-Resolution infrared Study v4
G. GUELACHVILI Laboratoire d’lnfiarouge, Associh au CNRS, UniversitP de Paris&d, Bcit. 350, 91405 Orsay Cedex. France
AND
M. KOIVUSAARI AND R. ANTTILA Department of Physics, University of Oulu. SF-905 70 Oulu 5 7, Finland
The infrared band Ye of CDs1 between 2220 and 2390 cm-’ has been investigated at a resolution of 5.4 X IO-) cm-‘. More than 2000 lines were assigned to subbands with KAK from - 18 to 21, including J values up to 70. In the analysis the Coriolis resonances with V, + v:’ + v:‘, Ye + 2@, Ye + 2~2, and 2u, + 2@ were taken into account. The molecular constants concerning the fundamental v,, as well as the parameters describing the combination kVeh, were derived. 0 1984 Academic Press. Inc. INTRODUCTION
The infrared spectra of methyl halides, both of CH,X and CDsX, have been widely investigated. However, the heaviest member of this family, CDJI, has received least attention. The whole region from 500 to 5000 cm-’ was studied by Jones et ul. (I) in 1965. Their resolution varied between 0.1 and 0.3 cm-‘. Of the fundamentals, u4 was studied under higher resolution (0.05 cm-‘) by Peterson and Edwards (2) in 197 1. They were able to assign ‘PK(J) and ‘&(J) lines, but the overlapping of the lines from different subbands caused problems. The other perpendicular fundamentals us and vg were studied by Anderson and Overend (3). Matsuura and Shimanouchi (4) later analyzed the Coriolis resonance between u2 and vs. The lowest fundamentals v3 and & were recently analyzed using the Fourier spectra recorded in Oulu (5, 6). As there seemed to exist no investigation of v1 after Jones et al. (I), and since the knowledge of u4 was not complete and, of the interacting bands 2v2, v2 + us and 2vs, only the parallel component of 2~ was measured (I), we decided to record the spectrum of CD31 around 2000 cm-‘. During the course of this work there appeared a Raman investigation of the v4 band by Poulsen and Brodersen (7). EXPERIMENTAL DETAILS
The spectra were recorded on the Fourier transform spectrometer of Laboratoire d’brfrarouge in Orsay. The instrumental resolution was 5.4 X lop3 cm-‘. Two 99
0022-2852184 $3.00 Copyright 0
1984 by Academic Press, Inc.
All rights of reproduction in any foonn reserved
100
GUELACHVILI,
KOIVUSAARI,
AND
ANTTILA
spectra between 1830 and 2580 cm-’ were registered, in both of them the absorption path length was 52 m and the sample pressures were 0.9 and 0.07 Torr. Only the recording with higher pressure was used in the study of the v4 band. The sample was obtained from Merck Sharp & Dohme. The existence of small amounts of CHDzI was revealed by the v2 band around 2200 cm-‘. DESCRIPTION
OF THE
SPECTRUM
The v4 band covers the range from 2220 to 2390 cm-‘. At first sight it looks like a regular unperturbed perpendicular band with the Q-branch spacing of about 4 cm-‘, as the small part from the P side in Fig. 1 indicates. It was easy to observe the starting of most ‘P&) and RRK(J) series according to the requirement J I K. Hence, unambiguous assignments for the majority of the lines produced no difficulties. We could assign lines to 40 subbands from KAK = - 18 to KAK = 2 1,
a.9
po1* r--“ 2252
I
_
_
_~__~.
___.
a.9
_..
.__
.
2254
.7~, 2255
1OlW
‘Qll ._ ._~__‘i_ 22;6'
2259
_
2253
2260
. . .
. . -... 2258
2251
2261
2262
FIG. I. A small regular part from the P side of the v4 band of CDJ. Within this region the lines in addition to the Q branches are of ‘P&r) type. For them the assignments are given in the form K(J) or by representing merely the K value. Especially starting of the P branches in the subbands KAK = -9, - 10,and - 11 is indicated. The figure shows how heavily the lines from different subbands may overlap, even at the resolution of 0.0054 cm-‘. Experimental conditions (also concerning figs. 2, 4 and 5): Absorption path length, 52 m; sample pressure, 120 Pa (0.9 Torr); room temperature.
101
yq BAND OF CDJ
altogether more than 2300 lines were identified in u4 with J,,,,, x 70. Both P and R lines could be detected in the subbands -7 S KAK 2 9, and Q lines when 6 S KA K i 16. In some regions the lines from different subbands happened to be widely coincident even with the resolution available in the present study. Such is the case especially for ‘PK(J) lines with K = 8-l 1. This situation can be seen in Fig. 1. The only place where a perturbation is striking is the Q branch RQs. This can be seen in Fig. 2, where the structure of RQs together with that of RQ9 is presented. When performing the assignments we observed, however, local perturbations in several subbands. Because it was illustrative to study them graphically, we systematically plotted in every subband, versus J’(J’ + l), the observed lines reduced by 2B,,m - 4D$m3 - D$K[K’2J’(J’ + 1) - K”‘J”(J” + l)], where m = J’ when AJ = fl and m = -J” when AJ = - 1. A collection of these plots is given in Fig. 3.
6
61161 ;I 7 6
FIG. 2.The most striking perturbations in the Y, band of CD& The Q branches RQs and RQs with assignments. In addition to MJ) lines, there are RRK(J) lines whose assignments are presented in the form K(J) or by giving only the K value.
2255.3. ppl,
JIJ.11 2251.6
2250
L5ol
JIJ*ll 2255.7
2250
L500
JIJ4 228L.O
2500
5000
2288.5
JlJ*ll
.
2295.7 2540
SOW
2300.1 pp3
1
RPO
'.
JIJ*il 2288.0
2299.6 L
22923
i’
pp2
4
2291.8
2500
5000
2301.0 RR1 ..
.. ‘. ‘.,
2540
JIJ*ll * 5ow
JlJ*ll 2303.2 /_ 25O+l
2334.3
2330.5
I....
-..
JIJ.11
JIJ*ll 232a5
1254
2Mo
2332.3
2250
235t.O
1500
%6
%‘
'.
JIJ.11 2354.5 i
15c-l
MOO
JIJ.11 2363.9
FIG. 3. Plots of RRx(J) - f?J”(J”
1500
3ooo
or ‘&(J) lines (corrected with 2Eom - 4D$n” - Df[KzJ’(J’ + I) + I)]) versus J’(J’ + 1) to illustrate different observed resonances in the Yeband of CDJ. The
graphs have been produced with the aid of a digital plotter. 102
“4 BAND OF CD31
lU.3
To start the numerical analysis we fixed the ground state constants to those in Table I, and separately fitted the upper state energies of every subband in a secondorder polynomial of J’(J’ + l), cf. (10). When looking at the plots of Fig. 3 it is evident that there are subbands which do not fit in this simple model. Such was the case especially for KAK = -12, -11, -8, -1, 0, 1, 8, 9, 10, 12, 14, 15, and 18. In most subbands, or at least in their low-J parts, this model worked well, and the standard deviations were between 0.2 and 0.6 X 10e3 cm-‘, even when some blended lines were included. However, the systematic changes in the coefficients of these polynomials revealed that the perturbations were not localized only in those subbands where crossings or other obvious effects were detectable. Trials to treat the whole u4 as an unperturbed band led to the conclusion that perhaps one-third of the lines could be satisfactorily fitted. By using 740 lines selected from almost every subband, but including mainly low-J values, we could reach a standard deviation of 0.0009 cm- ‘. The results from this fit gave initial values for the u4 band constants. It was evident that there are several vibrational levels which cause perturbations in v4. By applying the information available in literature, all the vibrational levels from about 1900 to 2400 cm-’ were estimated, as well as their rotational K structures. In addition to IQ, v4, 2v2, u2 + v=,, and 2~) there are ternary or quaternary combination levels including y3 and/or &. By using a graphical presentation of the K structure of altogether 23 vibrational states and by applying Amat’s rule (II), the possible perturbing levels were sought. The asymptotes from the plots in Fig. 3 gave estimates for B, - B. values of the perturbing states. The strongest perturbations in v4 can be grouped into four regions. On the R side there is the subband with KAK = 14, then KAK = 8 and 9 together with adjacent subbands. The third place is around KAK = 0, and the fourth one on the P side with KAK = -11 and -12. 1. In the v4 bands of CH3Br (IO, 12) and CD3Br (13) the strongest perturbations have been due to a xy-Coriolis resonance with u3 + u;’ + ut’, Naturally we tried the same in CD31. Using this level to explain the most striking perturbation in the subband KAK = 8, such large positive anharmonicities would be needed that it was judged unreasonable. On the other hand, according to our estimates, the level K = 16, 1~= Z, = 1 of the vibrational state o3 = o5 = ug = 1 is very near to the level K = 15, 1 = 1 of o4 = 1. The evidence including the value of B’ - B. lead us to accept the Coriolis resonance between these levels as the source of the perturbation TABLE I Constrained Ground State Constants of CD,1 Ref. A0
[cm-']
2.59608
(1,
60
[cm-'1
0.2014825
(9)
D", [10 -6 cm-']
0.1244
(2)
D;'
1.611
(8)
D;
[1O-6 [lo -6
cm-']
cm-‘1
19.8
(?_I
104
GUELACHVILI,
KOIVUSAARI,
AND
ANTTILA
in the KA K = 14 subband. The subband KA K = 13 looks regular. The perturbation at high values of J in RRlS lines could not be explained with the aid of the above resonance. 2. The interpretation of the Q branches RQs and RQs presented in Fig. 2 was performed by simultaneously using the R lines and the ground state combination differences. The resonance region of the RR8 branch is shown in Fig. 4 and that of RR9 in Fig. 5. The plot of the R lines of KA K = 7 looked regular, whereas the corresponding plot of KAK = 10 indicated evident curvature, especially when J > 50, and slight similar effects were also observed in KAK = 11. All these perturbations seem to be caused by the same factor. When comparing the plots for KAK = 8 and 9 in Fig. 3, it can be seen that the ratio of the spacings between V+ and u- lines in the crossing region is about the same as the ratio of the corresponding J(J + 1) values. We conclude that there is a Coriolis-type interaction. The only vibrational state which we could find to explain the observed effects is v2 + 2~:~. The estimated asymptotes from the plots also agree with (B’ - &) prediction for this level. A scheme of the interacting levels is given in Fig. 6. 3. In the plots for the subbands KAK = - 1, 0, and + 1 in Fig. 3, one can see crossings around J’ = 35, 50, and 60, respectively. The growth of the resonance effects with J indicates a Coriolis interaction, and again we have interpreted the perturber to be an E-type level, 2v3 + 2ug2 in this case. The energy level diagram based on our results is presented in Fig. 7. 4. In the subband KA K = - 11 there are relatively strong resonance effects, with the crossing around J’ = 33, and in the subband KA K = - 12 the effects are still more pronounced, with the crossing around S = 55 as the plots in Fig. 3 show. The plot for the next subband, KA K = - 13, is clearly curved at high J, whereas that for KA K = - 10 is a straight line. These effects have been interpreted to be due to u2 + 2~8, i.e., there is now a Coriolis resonance between Ye and a vibrational state of A symmetry. Figure 6 illustrates the situation for the energy levels in this case, too. ANALYSIS
In the analysis, transitions were included from both v4 and those four combinations which were stated above as the perturbers in the main resonances observed. Although
RRB(J),
1,5
20 20
15
!
2336
25 u+ I
I
2337
25
I
2338
V-
I
2339
FIG. 4. The Y+ and V- series of R&(J) lines in the resonancecrossingregion.Some lines belonging to other subbands are presented in the form K(J).
I
23LO
assignmentsfor
105
vq BAND OF CDJl
u-
RRS(J)
L5
L9
v+ L7
I .
.I
- ____--2350
2351
! 2353
2352
2351
A 2353
2355
2351
2356
2357
FIG. 5. The Y+and Y- series of RR9(J) lines in the resonance crossing region. The other assignments as in Fig. 4. The lines with dots are due to CO*.
2600-
K =12 ----.....
K:[ 12 ....7
K-l11 i---*
2550-
*I-*% ,-
11-e.......-
~ 11
I 10 I.....'
...I
FIG. 6. Part of the energy level diagram of CD,1 to illustrate the interaction of Yewith ~2 + 2~: and with Y?+ 2~:~. The crossing has been observed in those four cases marked with the dots in the diagram. The behavior of the K levels as a function of J can be seen in the respective plots in Fig. 3.
106
GUELACHVILI,
KOIVUSAARI,
2v,+zv,o
v, ! :-I
Elm-'1
AND ANTTILA
+I
I
2320
K=;
K=3----.
3
K=j
I
3
I
2310
2-.
.-
. j
2300-
1 -...
I
1
_:
/
: ___
.... ;.
...* .
.... '..
o-
FIG. 7. Part of the energy level diagram of CD31 to illustrate the resonances of v4 with 2v, + 2~: and with 2q + 2~:~. The crossing has been observed in those cases where the interactions have been denoted in the scheme.
other possibilities were considered, all the interactions turned out to be of xyCoriolis type as mentioned above. The off-diagonal coupling matrix elements are of the forms (Y$‘, J, k(i&
+ v:’ + vf’, J, k+
1) = W,,iJ(J+
(u;l, J, kjEj,lv2 + 2@, J, k f 1) = H&vJ(J (v,+‘, J, klEj,12vj + 2v;‘, J, k f 1)=
H&tJ(J+
1) - k(k+-
I),
+ 1) - k(k + l), I)-k(k?
l),
and (u;‘, J, klficlvz + 24, J, k 7 1) = W,,\lJ
(1)
In the first element the operator is of the type r3r4rsr6Pa where rk is a vibrational operator connected to the normal mode Vkand the rotational operator P, is P, or P,, (12). The forms of the other operators are analogous. The coefficients W, are molecular parameters which can be experimentally determined. The first three resonances are between two vibrational levels of symmetry E. For all pairs of values J and k14 at u4 = 1, each of these resonances can be described by a 2 X 2 matrix. The last resonance is between E and A levels. Because the K(+I) levels in u4 = 1 are far from K - 1 levels in v2 + 214 we neglected the coupling between them for simplicity and described even this resonance with a 2 X 2 matrix.
v, BAND
OF CD,1
107
Hence, the energy levels were calculated as the eigenvalues of 5 X 5 matrices, when all the four resonances were included. For the diagonal element F4(J, k, I,), the expression F,(J, k. 14) = v: + (A, - B#? + &(.I
+ BJ(J
+ 1) - 2(,4<)4kl, + r#k31,
+ l)kl, - D;J*(J + 1)’ - D;“J(J + l)k* - Dfk’
(2)
was used. When k14 = 1, an additional term +q4/2 J(J + 1) was applied to take into account the 1 doubling; 1 resonance was neglected. In the term values for the perturbing states no n terms were included, and the D constants were fixed to ground state values. The resonances are rather well separated from each other. Thus, initial values for the coupling parameters Wi, and also for the constants of the perturbing levels were obtained by treating the resonances one by one. Already in this phase of the work we noticed that the standard deviation and the systematic deviations in the fit of the subbands KAK = 7-10 could be remarkably diminished if W3, in Eq. (1) was substituted by W3, + W>,J(J + 1). In the global fit an essential question is the choice of the free parameters and the constraints. We tried to fix the A and B values of v2 + 2vz2 and v2 + 2~2 to be equal as well, as the A[ constants for v2 + 2vt* and 2v3 + 24’. In the course of the study we had to diminish the restrictions, however; especially the subband KAK = - 12 was problematic. A satisfactory fit was obtained when we allowed the B values for the levels K = 11 and K = 12 of v2 + 24 to be different. There is a Coriolis resonance between v2 and v5, with the crossing around k = 15 (4). The same interaction also exists between v2 + 2~: and v:’ + 24 as well as between v2 + 2vb* and v:’ + 2&*. Hence, there may be large differences in the effective B values for those levels of v2 + 2~: and v2 + 2vg* which play the most important roles in the resonances with v4. A large number of fits using different constraints was performed. The final set of free parameters is seen in Table V representing the results. The observed line positions together with the assignments are presented in Table II. The lines marked with C have been left out from the global fit. They are either heavily blended or they are perturbed by weaker resonances. RESULTS
The results for v4 are given in Table III. The upper state constants in the first column have error limits which are smaller than those of the fixed ground state values. So, the differences of the constants are those which are more important, and (Y$’= 8.655(6) X lop5 cm-’ and & = 13.5021(9) X 10e3 cm-’ are obtained. As compared with the recent results from Raman spectra (7), it may be said that our values have narrower error limits but, within approximately three times the standard deviations in Ref. (7), the values for a4‘, 4 and (An4 agree. Because RQo is broader than the adjacent Q branches, the l-doubling constant q4 is positive according to the sign convention of Cartwright and Mills (14). All the changes in the D constants between the ground state and the state v4 = 1 are small. Two comments concerning the results may be added. A wider simultaneous analysis, including, e.g., the vI
TABLE II
TABLE II-Conhued hl i. 1,1
081
0-c
K,,K’ 11,1’
085
o-c
K”I( 1”I
lx5
0-c
TABLE II-Continued
TABLE II-Continued
Y
111
TABLE II-Continued
E3 El
: : : -:
E,
::
112
TABLE II-Continued
114
GUELACHVILI,
KOIVUSAARI,
AND ANTTILA
TABLE II-Continued
’ 2000 cm-’ should be added to the wavenumbers given. The lines marked with C have not been included in the fit. The symbols (E2-E5) in the crossing regions of the main resonances refer to transitions whose upper state is more due to a perturbed combination level.
band, should probably lead to somewhat different band constants. The values of (An4 and 75 are dependent on the constrained values of A,, and H. To study the purely K-dependent terms in the energy expression without fixing any values, we evaluated most subband origins and then made a fit of them in the polynomial vrb(K) = a0 f a& + a&* + a3K3 + afi4. The results are presented in Table IV. By combining the coefficients a3 and a4 we get D$ - 1/47# = 1.590(4) TABLE III Molecular Constants of CDs1 Connected to the Fundamental Vibration y4 v,
[cm -'I
A4
[cm“] =
B4
[cm-'I
cl; [lo-6
= 2298.54431(2)
2.5825779(v)
m-1
[IO
Number
.a The
-6
=
lines
error
standard
[lo-3
n;' [IO
1.6188(4)
cm-‘1 =
of
q4
I = 0.'2375(2)
DqJK I10 -6cm'l D;
[cm -‘I
(Ai)4
= 0.20139595(6)
n;
110
-6 -6
= 0.463800(3)
1 = 0.02811(12)
m-'
cm-']
=
-0.36'(3)
cm-‘1 =
14.59(4!
20.276(j)
2132,
limits
std.
here
deviations
dev.
as well
1.15
as
in the units
x 10
-3 cm-l
in Tables of
the
IV, V and
last
digit
VI are
given.
v4 BAND OF CD,1
115
TABLE IV
Results from the Polynomial Fit of the Subband Origins in the v4 Band of CDJ (The corresponding combinations of the molecular constants from Table III are given for comparison.) Pal. a0 = v. + al a2
= 2;A
(A - 8) - Z(At,) + nK - DK - 6) - Z(A<)
=A-A0
-
- 4DK
+ 3nK
(6 - aJ
+ 3n
[cm
K
(cm
-1 -1 -1
- 6~~
[cm
III
1
229Y.S972(3)
1
3.83457(3)
3.83473(l)
1
-0.013492(4)
-0.013493(l)
a3 = r,K - 40"
(lo-5
&'I
a4 = DoK
[IO_7
cm-']
- DK
Table
fit.
2299.99789(~)
-6.550(12)
-6.651(5)
-4.74(11)
-4.760)
__~
X 10e5 cm-‘. It is not possible to obtain L$ and r/f separately without further assumptions. If we make the slightly questionable supposition that A - A0 is not dependent on the choice of the constrained A,, we can use A - A0 as well as B - B,, from Tables I and III. Then, a2, u3, and a4 together lead to 0;: = 1.96(9) X IO-’ cm-’ and qf = 1.49(33) X 10e5 cm- ‘. The value for L$ is in good agreement with the result of Poulsen and Brodersen (7), which we have used as a constrained value. The force field prediction of Duncan (15) is 629.6 kHz (2.100 X IO-’ cm-‘). The results for the perturbing levels are given in Table V. The parameters ~0, A, and A& which appear in the K-dependent terms in the energy expressions, are strongly correlated. Therefore, the statistical errors, in v. and A are of little importance. TABLE V
Results Concerning the Combination Levels which Cause the Largest Perturbations in the Fundamental Band “a of CD31
t, u3 +
t2
14
KAK a
v.
-1 [cm I
A
[cm-'lb
B
(cm
-1
1
v2 + 2U6O
J2 + 2V6
v5
2197.5241(2) 2.59136
-11:12
-l,O,l
5.9 2259.348113)
2301.9060(2)
2254.3639(l)
2.59199
2.631965(6)
0.199916(3)
O.lYYl839(43
a.l982356(5)
1
0.36704
-0.92658
-0.92658
110‘3cm-'1
4.91(2)
12.63(l)
2.63(2)
2.62933(j) o.199092(4~c 0.198991(2)
[cm
(Q',ff
WC WC
c B. - B
[lo-6
-1 b
cm-‘1
[lo-3 cm-'Id
.567
oh.
I
talc
1.337
a Values of KOK b
3.247 3.462
2.239 2.062
indicate those subbands of v,, where
the crossings
ere
2.391C 2.062
observed.
The parameters A and A< without error limit5 were fixed at least i? the final calculation
= Refers to the level K = II, see text. d
3.793(7)
0.490(S)
The other B is for the level K = 12.
Our re5"Its for B. - B are compared with those calculated
with the aid of the
(2, 6, _ 9)
y4 BAND OF CDJ
117
sponding fundamentals (4-6) gives x35 + x36 + x56 + & = -9.08 cm-‘. The coherence of this value with those in CH3Br (10, 12) and CD3Br (13, 16) gives further support to the interpretation. When the difference between 2u3 + 2~:’ and v2 + 2vg2 from Table V is combined with that between 2u3 and v2 (4, 5) x26 - 2x36 = 3.54 cm-’ iS obtained. Together with x26 = -3.24 Cm-' (1, 4, 6), we get x36 = -3.39 Cm-'. If we further apply ws + vg from Ref. (I), the above result from q + &’ + vg’ leads to x35 = -2.47 cm-‘. The error limits of the constants are at least some tenths of a cm-‘. The values themselves are all small and negative, and hence they look reasonable. Our values for u2 + 2ui2 and v2 + 2~: give &6 = 1.25 cm-‘. The results of Anderson and Overend (17) from the 2Vg region are contradictory in this respect, whereas the position of 2Vg(11)around 13 10 cm-’ (17) is in good agreement with our interpretation. To check the g66 value, we tried to find, in addition to 2v1 + 2vb2, the other component 216 + 2~:. In the plots of the ‘P&r) lines (K = l4) in Fig. 3, there are tiny perturbations (marked with arrows) so that the crossings take place around J’ values 21, 38, 52, and 64, when K” grows from 1 to 4. These very small effects, which seem to increase with the crossing J(J + 1), can be explained in terms of a xy-Coriolis resonance between v4 and 2v3 + 2~:. When the parameters q, = 2297.62 cm-‘, B = 0.198085 cm-‘, and A = 2.6170 cm-’ are used for 2v3 + 2& the crossings take place at proper positions. The coupling parameter W, is about 3 X 10m4cm-‘. The energy level diagram is presented in Fig. 7. The spacing between v0 values of the components of 2~ + 2@ is 4.34 cm-‘, which means &6 = I .09 cm-‘. This is of the same order of magnitude as the result 1.25 cm-’ from the u2 + 2ug levels above. Among the RRl8(J) lines there is a perturbation, with the crossing around J’ = 34 as shown in Fig. 3, and the lines with J” > 25 were excluded from the fit. Likewise, RR,7(J) lines with .I” > 40 were rejected because of irregularities, with a probable crossing around J’ = 49. Both the perturbations may be of the same origin and one possibility is a resonance with ~5’ + 2~2~. The tall of the RRl5(J) is also clearly perturbed, and only the lines .I” =G25 were used. The plot of ‘P&I) lines shows a small resonance almost in the beginning of the branch, but no corresponding effects are visible in the adjacent subbands. The asymptote from the fit indicates so small an absolute value for B' - B" that some component of v5 + 2vg seems to be the only possible perturber. The observed characteristics of this perturbation can be explained by a 1(2, - 1) resonance between the states vq = 1, l4 = -1, K = 7 and v5 = 1, 1, = - 1, 2)6= 2, 16 = 2, K = 6. As all the lines of this subband after the crossing region are coincident with those from other subbands, the subband KAK = -8 was completely excluded from the fit. ACKNOWLEDGMENT The authors are grateful to Dr. Georges Graner for valuable comments. RECEIVED:
March 15. 1984 REFERENCES
I. E. W.JONES, R.J. L. POPPLEWELL, AND H. W.THOMPSON, hoc. R. Sot. SerA 288, 39-49 (1965). 2. R. W. PETERSON AND T. H. EDWARDS, J. Mol. Spectrosc. 38, l-15 (1971).
118
GUELACHVILI,
KOIVUSAARI,
AND ANTTILA
3. D. R. ANDERSONAND J. OVEREND,Spectrochim.Acta A 28, 1231-1251 (1972). 4. H. MATSUURAAND T. SHIMANOIJCHI, J. Mol. Specfrosc. 60,93-l 10 (1976). 5. R. A~~FITILA, M. KOIW~AARI, J. KAUPPINEN, E. KYR~, AND F. HEGELUND,J. Mol. Spectrosc. 84, 225-233 (1980). 6. M. KOIWSAARI, J. KAUPPINEN, A.-M. KJZLH&&AND R. ANTTILA,J. Mol. Spectrosc. 84, 342-354 7. 8. 9. 10.
Il. 12. 13. 14.
15. 16. 17.
(1980). POUISENAND S. BRODERSEN, J. Raman Spectrosc.14, 77-82 (1983). K. GARRISON,J. W. SIMMONS,AND C. ALEXANDER,J. Chem. Phys. 45,413-415 (1966). L. KUCZKOWSKI,J. Mol. Spectrosc.45, 26 I-270 (1973). BETRENC~URT-STIRNEMANN, G. GRANER,AND G. GUELACHVILI, J. Mol. Spectrosc.51,216-237 (1974). G. AMAT, C. R. Acud. SC. B 250, 1439-1440 (1960). C. BETRENCOURT-STIRNEMANN, Thise, Orsay, 1975. P. M. WILT, F. W. HECKER,J. D. FEHRIBACH,D. E. BARDIN, AND T. H. EDWARDS,J. Mol. Spectrosc. 90, 33-42 (1981). G. J. CARNRIGHT AND I. M. MILLS,J. Mol. Specfrosc. 34, 415-439 (1970). J. L. DUNCAN,J. Mol. Spectrosc. 60, 225-238 (1976). G. GRANER,J. Mol. Spectrosc. 90, 394-438 (198 1). D. R. ANDERSONAND J. OVEREND,Spectrochim. Acta A 28, 1637-1647 (1972). C. A. R. C.
OF MOLECULAR
SPECTROSCOPY
The
108,99-I
I8 (I 984)
Band of CD31 with Perturbations: A High-Resolution infrared Study v4
G. GUELACHVILI Laboratoire d’lnfiarouge, Associh au CNRS, UniversitP de Paris&d, Bcit. 350, 91405 Orsay Cedex. France
AND
M. KOIVUSAARI AND R. ANTTILA Department of Physics, University of Oulu. SF-905 70 Oulu 5 7, Finland
The infrared band Ye of CDs1 between 2220 and 2390 cm-’ has been investigated at a resolution of 5.4 X IO-) cm-‘. More than 2000 lines were assigned to subbands with KAK from - 18 to 21, including J values up to 70. In the analysis the Coriolis resonances with V, + v:’ + v:‘, Ye + 2@, Ye + 2~2, and 2u, + 2@ were taken into account. The molecular constants concerning the fundamental v,, as well as the parameters describing the combination kVeh, were derived. 0 1984 Academic Press. Inc. INTRODUCTION
The infrared spectra of methyl halides, both of CH,X and CDsX, have been widely investigated. However, the heaviest member of this family, CDJI, has received least attention. The whole region from 500 to 5000 cm-’ was studied by Jones et ul. (I) in 1965. Their resolution varied between 0.1 and 0.3 cm-‘. Of the fundamentals, u4 was studied under higher resolution (0.05 cm-‘) by Peterson and Edwards (2) in 197 1. They were able to assign ‘PK(J) and ‘&(J) lines, but the overlapping of the lines from different subbands caused problems. The other perpendicular fundamentals us and vg were studied by Anderson and Overend (3). Matsuura and Shimanouchi (4) later analyzed the Coriolis resonance between u2 and vs. The lowest fundamentals v3 and & were recently analyzed using the Fourier spectra recorded in Oulu (5, 6). As there seemed to exist no investigation of v1 after Jones et al. (I), and since the knowledge of u4 was not complete and, of the interacting bands 2v2, v2 + us and 2vs, only the parallel component of 2~ was measured (I), we decided to record the spectrum of CD31 around 2000 cm-‘. During the course of this work there appeared a Raman investigation of the v4 band by Poulsen and Brodersen (7). EXPERIMENTAL DETAILS
The spectra were recorded on the Fourier transform spectrometer of Laboratoire d’brfrarouge in Orsay. The instrumental resolution was 5.4 X lop3 cm-‘. Two 99
0022-2852184 $3.00 Copyright 0
1984 by Academic Press, Inc.
All rights of reproduction in any foonn reserved
100
GUELACHVILI,
KOIVUSAARI,
AND
ANTTILA
spectra between 1830 and 2580 cm-’ were registered, in both of them the absorption path length was 52 m and the sample pressures were 0.9 and 0.07 Torr. Only the recording with higher pressure was used in the study of the v4 band. The sample was obtained from Merck Sharp & Dohme. The existence of small amounts of CHDzI was revealed by the v2 band around 2200 cm-‘. DESCRIPTION
OF THE
SPECTRUM
The v4 band covers the range from 2220 to 2390 cm-‘. At first sight it looks like a regular unperturbed perpendicular band with the Q-branch spacing of about 4 cm-‘, as the small part from the P side in Fig. 1 indicates. It was easy to observe the starting of most ‘P&) and RRK(J) series according to the requirement J I K. Hence, unambiguous assignments for the majority of the lines produced no difficulties. We could assign lines to 40 subbands from KAK = - 18 to KAK = 2 1,
a.9
po1* r--“ 2252
I
_
_
_~__~.
___.
a.9
_..
.__
.
2254
.7~, 2255
1OlW
‘Qll ._ ._~__‘i_ 22;6'
2259
_
2253
2260
. . .
. . -... 2258
2251
2261
2262
FIG. I. A small regular part from the P side of the v4 band of CDJ. Within this region the lines in addition to the Q branches are of ‘P&r) type. For them the assignments are given in the form K(J) or by representing merely the K value. Especially starting of the P branches in the subbands KAK = -9, - 10,and - 11 is indicated. The figure shows how heavily the lines from different subbands may overlap, even at the resolution of 0.0054 cm-‘. Experimental conditions (also concerning figs. 2, 4 and 5): Absorption path length, 52 m; sample pressure, 120 Pa (0.9 Torr); room temperature.
101
yq BAND OF CDJ
altogether more than 2300 lines were identified in u4 with J,,,,, x 70. Both P and R lines could be detected in the subbands -7 S KAK 2 9, and Q lines when 6 S KA K i 16. In some regions the lines from different subbands happened to be widely coincident even with the resolution available in the present study. Such is the case especially for ‘PK(J) lines with K = 8-l 1. This situation can be seen in Fig. 1. The only place where a perturbation is striking is the Q branch RQs. This can be seen in Fig. 2, where the structure of RQs together with that of RQ9 is presented. When performing the assignments we observed, however, local perturbations in several subbands. Because it was illustrative to study them graphically, we systematically plotted in every subband, versus J’(J’ + l), the observed lines reduced by 2B,,m - 4D$m3 - D$K[K’2J’(J’ + 1) - K”‘J”(J” + l)], where m = J’ when AJ = fl and m = -J” when AJ = - 1. A collection of these plots is given in Fig. 3.
6
61161 ;I 7 6
FIG. 2.The most striking perturbations in the Y, band of CD& The Q branches RQs and RQs with assignments. In addition to MJ) lines, there are RRK(J) lines whose assignments are presented in the form K(J) or by giving only the K value.
2255.3. ppl,
JIJ.11 2251.6
2250
L5ol
JIJ*ll 2255.7
2250
L500
JIJ4 228L.O
2500
5000
2288.5
JlJ*ll
.
2295.7 2540
SOW
2300.1 pp3
1
RPO
'.
JIJ*il 2288.0
2299.6 L
22923
i’
pp2
4
2291.8
2500
5000
2301.0 RR1 ..
.. ‘. ‘.,
2540
JIJ*ll * 5ow
JlJ*ll 2303.2 /_ 25O+l
2334.3
2330.5
I....
-..
JIJ.11
JIJ*ll 232a5
1254
2Mo
2332.3
2250
235t.O
1500
%6
%‘
'.
JIJ.11 2354.5 i
15c-l
MOO
JIJ.11 2363.9
FIG. 3. Plots of RRx(J) - f?J”(J”
1500
3ooo
or ‘&(J) lines (corrected with 2Eom - 4D$n” - Df[KzJ’(J’ + I) + I)]) versus J’(J’ + 1) to illustrate different observed resonances in the Yeband of CDJ. The
graphs have been produced with the aid of a digital plotter. 102
“4 BAND OF CD31
lU.3
To start the numerical analysis we fixed the ground state constants to those in Table I, and separately fitted the upper state energies of every subband in a secondorder polynomial of J’(J’ + l), cf. (10). When looking at the plots of Fig. 3 it is evident that there are subbands which do not fit in this simple model. Such was the case especially for KAK = -12, -11, -8, -1, 0, 1, 8, 9, 10, 12, 14, 15, and 18. In most subbands, or at least in their low-J parts, this model worked well, and the standard deviations were between 0.2 and 0.6 X 10e3 cm-‘, even when some blended lines were included. However, the systematic changes in the coefficients of these polynomials revealed that the perturbations were not localized only in those subbands where crossings or other obvious effects were detectable. Trials to treat the whole u4 as an unperturbed band led to the conclusion that perhaps one-third of the lines could be satisfactorily fitted. By using 740 lines selected from almost every subband, but including mainly low-J values, we could reach a standard deviation of 0.0009 cm- ‘. The results from this fit gave initial values for the u4 band constants. It was evident that there are several vibrational levels which cause perturbations in v4. By applying the information available in literature, all the vibrational levels from about 1900 to 2400 cm-’ were estimated, as well as their rotational K structures. In addition to IQ, v4, 2v2, u2 + v=,, and 2~) there are ternary or quaternary combination levels including y3 and/or &. By using a graphical presentation of the K structure of altogether 23 vibrational states and by applying Amat’s rule (II), the possible perturbing levels were sought. The asymptotes from the plots in Fig. 3 gave estimates for B, - B. values of the perturbing states. The strongest perturbations in v4 can be grouped into four regions. On the R side there is the subband with KAK = 14, then KAK = 8 and 9 together with adjacent subbands. The third place is around KAK = 0, and the fourth one on the P side with KAK = -11 and -12. 1. In the v4 bands of CH3Br (IO, 12) and CD3Br (13) the strongest perturbations have been due to a xy-Coriolis resonance with u3 + u;’ + ut’, Naturally we tried the same in CD31. Using this level to explain the most striking perturbation in the subband KAK = 8, such large positive anharmonicities would be needed that it was judged unreasonable. On the other hand, according to our estimates, the level K = 16, 1~= Z, = 1 of the vibrational state o3 = o5 = ug = 1 is very near to the level K = 15, 1 = 1 of o4 = 1. The evidence including the value of B’ - B. lead us to accept the Coriolis resonance between these levels as the source of the perturbation TABLE I Constrained Ground State Constants of CD,1 Ref. A0
[cm-']
2.59608
(1,
60
[cm-'1
0.2014825
(9)
D", [10 -6 cm-']
0.1244
(2)
D;'
1.611
(8)
D;
[1O-6 [lo -6
cm-']
cm-‘1
19.8
(?_I
104
GUELACHVILI,
KOIVUSAARI,
AND
ANTTILA
in the KA K = 14 subband. The subband KA K = 13 looks regular. The perturbation at high values of J in RRlS lines could not be explained with the aid of the above resonance. 2. The interpretation of the Q branches RQs and RQs presented in Fig. 2 was performed by simultaneously using the R lines and the ground state combination differences. The resonance region of the RR8 branch is shown in Fig. 4 and that of RR9 in Fig. 5. The plot of the R lines of KA K = 7 looked regular, whereas the corresponding plot of KAK = 10 indicated evident curvature, especially when J > 50, and slight similar effects were also observed in KAK = 11. All these perturbations seem to be caused by the same factor. When comparing the plots for KAK = 8 and 9 in Fig. 3, it can be seen that the ratio of the spacings between V+ and u- lines in the crossing region is about the same as the ratio of the corresponding J(J + 1) values. We conclude that there is a Coriolis-type interaction. The only vibrational state which we could find to explain the observed effects is v2 + 2~:~. The estimated asymptotes from the plots also agree with (B’ - &) prediction for this level. A scheme of the interacting levels is given in Fig. 6. 3. In the plots for the subbands KAK = - 1, 0, and + 1 in Fig. 3, one can see crossings around J’ = 35, 50, and 60, respectively. The growth of the resonance effects with J indicates a Coriolis interaction, and again we have interpreted the perturber to be an E-type level, 2v3 + 2ug2 in this case. The energy level diagram based on our results is presented in Fig. 7. 4. In the subband KA K = - 11 there are relatively strong resonance effects, with the crossing around J’ = 33, and in the subband KA K = - 12 the effects are still more pronounced, with the crossing around S = 55 as the plots in Fig. 3 show. The plot for the next subband, KA K = - 13, is clearly curved at high J, whereas that for KA K = - 10 is a straight line. These effects have been interpreted to be due to u2 + 2~8, i.e., there is now a Coriolis resonance between Ye and a vibrational state of A symmetry. Figure 6 illustrates the situation for the energy levels in this case, too. ANALYSIS
In the analysis, transitions were included from both v4 and those four combinations which were stated above as the perturbers in the main resonances observed. Although
RRB(J),
1,5
20 20
15
!
2336
25 u+ I
I
2337
25
I
2338
V-
I
2339
FIG. 4. The Y+ and V- series of R&(J) lines in the resonancecrossingregion.Some lines belonging to other subbands are presented in the form K(J).
I
23LO
assignmentsfor
105
vq BAND OF CDJl
u-
RRS(J)
L5
L9
v+ L7
I .
.I
- ____--2350
2351
! 2353
2352
2351
A 2353
2355
2351
2356
2357
FIG. 5. The Y+and Y- series of RR9(J) lines in the resonance crossing region. The other assignments as in Fig. 4. The lines with dots are due to CO*.
2600-
K =12 ----.....
K:[ 12 ....7
K-l11 i---*
2550-
*I-*% ,-
11-e.......-
~ 11
I 10 I.....'
...I
FIG. 6. Part of the energy level diagram of CD,1 to illustrate the interaction of Yewith ~2 + 2~: and with Y?+ 2~:~. The crossing has been observed in those four cases marked with the dots in the diagram. The behavior of the K levels as a function of J can be seen in the respective plots in Fig. 3.
106
GUELACHVILI,
KOIVUSAARI,
2v,+zv,o
v, ! :-I
Elm-'1
AND ANTTILA
+I
I
2320
K=;
K=3----.
3
K=j
I
3
I
2310
2-.
.-
. j
2300-
1 -...
I
1
_:
/
: ___
.... ;.
...* .
.... '..
o-
FIG. 7. Part of the energy level diagram of CD31 to illustrate the resonances of v4 with 2v, + 2~: and with 2q + 2~:~. The crossing has been observed in those cases where the interactions have been denoted in the scheme.
other possibilities were considered, all the interactions turned out to be of xyCoriolis type as mentioned above. The off-diagonal coupling matrix elements are of the forms (Y$‘, J, k(i&
+ v:’ + vf’, J, k+
1) = W,,iJ(J+
(u;l, J, kjEj,lv2 + 2@, J, k f 1) = H&vJ(J (v,+‘, J, klEj,12vj + 2v;‘, J, k f 1)=
H&tJ(J+
1) - k(k+-
I),
+ 1) - k(k + l), I)-k(k?
l),
and (u;‘, J, klficlvz + 24, J, k 7 1) = W,,\lJ
(1)
In the first element the operator is of the type r3r4rsr6Pa where rk is a vibrational operator connected to the normal mode Vkand the rotational operator P, is P, or P,, (12). The forms of the other operators are analogous. The coefficients W, are molecular parameters which can be experimentally determined. The first three resonances are between two vibrational levels of symmetry E. For all pairs of values J and k14 at u4 = 1, each of these resonances can be described by a 2 X 2 matrix. The last resonance is between E and A levels. Because the K(+I) levels in u4 = 1 are far from K - 1 levels in v2 + 214 we neglected the coupling between them for simplicity and described even this resonance with a 2 X 2 matrix.
v, BAND
OF CD,1
107
Hence, the energy levels were calculated as the eigenvalues of 5 X 5 matrices, when all the four resonances were included. For the diagonal element F4(J, k, I,), the expression F,(J, k. 14) = v: + (A, - B#? + &(.I
+ BJ(J
+ 1) - 2(,4<)4kl, + r#k31,
+ l)kl, - D;J*(J + 1)’ - D;“J(J + l)k* - Dfk’
(2)
was used. When k14 = 1, an additional term +q4/2 J(J + 1) was applied to take into account the 1 doubling; 1 resonance was neglected. In the term values for the perturbing states no n terms were included, and the D constants were fixed to ground state values. The resonances are rather well separated from each other. Thus, initial values for the coupling parameters Wi, and also for the constants of the perturbing levels were obtained by treating the resonances one by one. Already in this phase of the work we noticed that the standard deviation and the systematic deviations in the fit of the subbands KAK = 7-10 could be remarkably diminished if W3, in Eq. (1) was substituted by W3, + W>,J(J + 1). In the global fit an essential question is the choice of the free parameters and the constraints. We tried to fix the A and B values of v2 + 2vz2 and v2 + 2~2 to be equal as well, as the A[ constants for v2 + 2vt* and 2v3 + 24’. In the course of the study we had to diminish the restrictions, however; especially the subband KAK = - 12 was problematic. A satisfactory fit was obtained when we allowed the B values for the levels K = 11 and K = 12 of v2 + 24 to be different. There is a Coriolis resonance between v2 and v5, with the crossing around k = 15 (4). The same interaction also exists between v2 + 2~: and v:’ + 24 as well as between v2 + 2vb* and v:’ + 2&*. Hence, there may be large differences in the effective B values for those levels of v2 + 2~: and v2 + 2vg* which play the most important roles in the resonances with v4. A large number of fits using different constraints was performed. The final set of free parameters is seen in Table V representing the results. The observed line positions together with the assignments are presented in Table II. The lines marked with C have been left out from the global fit. They are either heavily blended or they are perturbed by weaker resonances. RESULTS
The results for v4 are given in Table III. The upper state constants in the first column have error limits which are smaller than those of the fixed ground state values. So, the differences of the constants are those which are more important, and (Y$’= 8.655(6) X lop5 cm-’ and & = 13.5021(9) X 10e3 cm-’ are obtained. As compared with the recent results from Raman spectra (7), it may be said that our values have narrower error limits but, within approximately three times the standard deviations in Ref. (7), the values for a4‘, 4 and (An4 agree. Because RQo is broader than the adjacent Q branches, the l-doubling constant q4 is positive according to the sign convention of Cartwright and Mills (14). All the changes in the D constants between the ground state and the state v4 = 1 are small. Two comments concerning the results may be added. A wider simultaneous analysis, including, e.g., the vI
TABLE II
TABLE II-Conhued hl i. 1,1
081
0-c
K,,K’ 11,1’
085
o-c
K”I( 1”I
lx5
0-c
TABLE II-Continued
TABLE II-Continued
Y
111
TABLE II-Continued
E3 El
: : : -:
E,
::
112
TABLE II-Continued
114
GUELACHVILI,
KOIVUSAARI,
AND ANTTILA
TABLE II-Continued
’ 2000 cm-’ should be added to the wavenumbers given. The lines marked with C have not been included in the fit. The symbols (E2-E5) in the crossing regions of the main resonances refer to transitions whose upper state is more due to a perturbed combination level.
band, should probably lead to somewhat different band constants. The values of (An4 and 75 are dependent on the constrained values of A,, and H. To study the purely K-dependent terms in the energy expression without fixing any values, we evaluated most subband origins and then made a fit of them in the polynomial vrb(K) = a0 f a& + a&* + a3K3 + afi4. The results are presented in Table IV. By combining the coefficients a3 and a4 we get D$ - 1/47# = 1.590(4) TABLE III Molecular Constants of CDs1 Connected to the Fundamental Vibration y4 v,
[cm -'I
A4
[cm“] =
B4
[cm-'I
cl; [lo-6
= 2298.54431(2)
2.5825779(v)
m-1
[IO
Number
.a The
-6
=
lines
error
standard
[lo-3
n;' [IO
1.6188(4)
cm-‘1 =
of
q4
I = 0.'2375(2)
DqJK I10 -6cm'l D;
[cm -‘I
(Ai)4
= 0.20139595(6)
n;
110
-6 -6
= 0.463800(3)
1 = 0.02811(12)
m-'
cm-']
=
-0.36'(3)
cm-‘1 =
14.59(4!
20.276(j)
2132,
limits
std.
here
deviations
dev.
as well
1.15
as
in the units
x 10
-3 cm-l
in Tables of
the
IV, V and
last
digit
VI are
given.
v4 BAND OF CD,1
115
TABLE IV
Results from the Polynomial Fit of the Subband Origins in the v4 Band of CDJ (The corresponding combinations of the molecular constants from Table III are given for comparison.) Pal. a0 = v. + al a2
= 2;A
(A - 8) - Z(At,) + nK - DK - 6) - Z(A<)
=A-A0
-
- 4DK
+ 3nK
(6 - aJ
+ 3n
[cm
K
(cm
-1 -1 -1
- 6~~
[cm
III
1
229Y.S972(3)
1
3.83457(3)
3.83473(l)
1
-0.013492(4)
-0.013493(l)
a3 = r,K - 40"
(lo-5
&'I
a4 = DoK
[IO_7
cm-']
- DK
Table
fit.
2299.99789(~)
-6.550(12)
-6.651(5)
-4.74(11)
-4.760)
__~
X 10e5 cm-‘. It is not possible to obtain L$ and r/f separately without further assumptions. If we make the slightly questionable supposition that A - A0 is not dependent on the choice of the constrained A,, we can use A - A0 as well as B - B,, from Tables I and III. Then, a2, u3, and a4 together lead to 0;: = 1.96(9) X IO-’ cm-’ and qf = 1.49(33) X 10e5 cm- ‘. The value for L$ is in good agreement with the result of Poulsen and Brodersen (7), which we have used as a constrained value. The force field prediction of Duncan (15) is 629.6 kHz (2.100 X IO-’ cm-‘). The results for the perturbing levels are given in Table V. The parameters ~0, A, and A& which appear in the K-dependent terms in the energy expressions, are strongly correlated. Therefore, the statistical errors, in v. and A are of little importance. TABLE V
Results Concerning the Combination Levels which Cause the Largest Perturbations in the Fundamental Band “a of CD31
t, u3 +
t2
14
KAK a
v.
-1 [cm I
A
[cm-'lb
B
(cm
-1
1
v2 + 2U6O
J2 + 2V6
v5
2197.5241(2) 2.59136
-11:12
-l,O,l
5.9 2259.348113)
2301.9060(2)
2254.3639(l)
2.59199
2.631965(6)
0.199916(3)
O.lYYl839(43
a.l982356(5)
1
0.36704
-0.92658
-0.92658
110‘3cm-'1
4.91(2)
12.63(l)
2.63(2)
2.62933(j) o.199092(4~c 0.198991(2)
[cm
(Q',ff
WC WC
c B. - B
[lo-6
-1 b
cm-‘1
[lo-3 cm-'Id
.567
oh.
I
talc
1.337
a Values of KOK b
3.247 3.462
2.239 2.062
indicate those subbands of v,, where
the crossings
ere
2.391C 2.062
observed.
The parameters A and A< without error limit5 were fixed at least i? the final calculation
= Refers to the level K = II, see text. d
3.793(7)
0.490(S)
The other B is for the level K = 12.
Our re5"Its for B. - B are compared with those calculated
with the aid of the
(2, 6, _ 9)
y4 BAND OF CDJ
117
sponding fundamentals (4-6) gives x35 + x36 + x56 + & = -9.08 cm-‘. The coherence of this value with those in CH3Br (10, 12) and CD3Br (13, 16) gives further support to the interpretation. When the difference between 2u3 + 2~:’ and v2 + 2vg2 from Table V is combined with that between 2u3 and v2 (4, 5) x26 - 2x36 = 3.54 cm-’ iS obtained. Together with x26 = -3.24 Cm-' (1, 4, 6), we get x36 = -3.39 Cm-'. If we further apply ws + vg from Ref. (I), the above result from q + &’ + vg’ leads to x35 = -2.47 cm-‘. The error limits of the constants are at least some tenths of a cm-‘. The values themselves are all small and negative, and hence they look reasonable. Our values for u2 + 2ui2 and v2 + 2~: give &6 = 1.25 cm-‘. The results of Anderson and Overend (17) from the 2Vg region are contradictory in this respect, whereas the position of 2Vg(11)around 13 10 cm-’ (17) is in good agreement with our interpretation. To check the g66 value, we tried to find, in addition to 2v1 + 2vb2, the other component 216 + 2~:. In the plots of the ‘P&r) lines (K = l4) in Fig. 3, there are tiny perturbations (marked with arrows) so that the crossings take place around J’ values 21, 38, 52, and 64, when K” grows from 1 to 4. These very small effects, which seem to increase with the crossing J(J + 1), can be explained in terms of a xy-Coriolis resonance between v4 and 2v3 + 2~:. When the parameters q, = 2297.62 cm-‘, B = 0.198085 cm-‘, and A = 2.6170 cm-’ are used for 2v3 + 2& the crossings take place at proper positions. The coupling parameter W, is about 3 X 10m4cm-‘. The energy level diagram is presented in Fig. 7. The spacing between v0 values of the components of 2~ + 2@ is 4.34 cm-‘, which means &6 = I .09 cm-‘. This is of the same order of magnitude as the result 1.25 cm-’ from the u2 + 2ug levels above. Among the RRl8(J) lines there is a perturbation, with the crossing around J’ = 34 as shown in Fig. 3, and the lines with J” > 25 were excluded from the fit. Likewise, RR,7(J) lines with .I” > 40 were rejected because of irregularities, with a probable crossing around J’ = 49. Both the perturbations may be of the same origin and one possibility is a resonance with ~5’ + 2~2~. The tall of the RRl5(J) is also clearly perturbed, and only the lines .I” =G25 were used. The plot of ‘P&I) lines shows a small resonance almost in the beginning of the branch, but no corresponding effects are visible in the adjacent subbands. The asymptote from the fit indicates so small an absolute value for B' - B" that some component of v5 + 2vg seems to be the only possible perturber. The observed characteristics of this perturbation can be explained by a 1(2, - 1) resonance between the states vq = 1, l4 = -1, K = 7 and v5 = 1, 1, = - 1, 2)6= 2, 16 = 2, K = 6. As all the lines of this subband after the crossing region are coincident with those from other subbands, the subband KAK = -8 was completely excluded from the fit. ACKNOWLEDGMENT The authors are grateful to Dr. Georges Graner for valuable comments. RECEIVED:
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