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Microwave spectrum of methylene fluoride in excited vibrational states
JOWNALOFMOLECULARSPECTBOSCOPY
69,409-420
(1978)
Microwave Spectrum of Methylene Fluoride in Excited Vibrational States ELZI HIROTA’ Department of Chemistry, Faculty of Science, Kyushu University, Fzlkuoka 812, Japan, and Institute for Molecular Science, Okazaki 444, Japan The rotational spectra of WHSF~ in seven of the nine fundamental vibrational states and also in overtone and combination states involving the ~1 mode were observed and assigned. Coriolis interactions between ~1 and ~7, YZ and ~8, ~3 and ye, and ~6 and Y, were analyzed by using approximate expressions for the rotational levels. An effective Hamiltonian with the Coriolis term in the off-diagonal block was applied to stronger interaction between ~3 and VS. Fermi resonance between VI and 2~4 was found to be negligible. The ground state spectra of YHzF2 and of YHzFz were remeasured to improve the accuracy of the rotational and centrifugal distortion constants. The Coriolis coupling constants and the energy differences between two vibrational levels in resonance, which were obtained through an analysis of the satellite spectra, are compared with the results derived from a normal coordinate analysis.
INTRODUCTION Because of high resolution attained by microwave spectroscopy, rotational spectra of a molecule in excited vibrational states provide detailed information on the intramolecular vibrations. This sort of information is particularly important in cases where two or more vibrational levels are nearly degenerate and vibration-rotation spectra obtained by conventional vibrational spectroscopy are not sufficiently well resolved. An analysis of a Coriolis resonance may give us the vibrational energy difference and the Coriolis coupling constant involved in the resonance. Provided that we could observe the spectra in the overtone state, a Fermi resonance may also be analyzed. It is well known that, although microwave spectroscopy allows us to determine rotational constants with an accuracy of five to eight significant figures, the structural parameters derived from these rotational constants are much less precise, because vibration-rotation interaction obscures the geometrical meaning of the rotational constants. The vibrational contribution to the rotational constants includes terms from the cubic potential constants, which are most difficult to estimate. It is thus worth observing vibrational satellites, which may make it possible to evaluate the anharmonic potential constants and to derive the equilibrium structure. Analyses of the vibration-rotation interaction have hitherto been carried out in detail only on diatomic, triatomic, and a few symmetric top molecules. Here, we under-
1Present address : Institute
for Molecular
Science,
Okazaki
444, Japan.
0022-2852/78/0693-0409$02.00/O Copyright 0 19713by Academic Press. Inc. Allrights of reproduction in any form reserved.
410
EIZI HIROTA
took a little more complicated molecule, methylene fluoride. The following considerations led to the choice of this molecule. Because it is an asymmetric top, we may determine three rotational constants for each vibrational state. Among the asymmetric top molecules it belongs to the highest symmetry Czo. The absence of any nuclei with the quadrupole moments makes the rotational spectrum simple enough to observe weak vibrational satellites. By investigating not only the normal species but also 13Cand D isotopesubstituted species, additional information may be obtained. In a previous paper (I) we reported rotational constants of CDzFz in excited vibrational states. We analyzed the Coriolis resonances in cases where they were significant. In the present paper we will describe an analogous analysis of the microwave spectra of CH,Fz, and we will discuss in a subsequent paper the molecular structure and the anharmonic potential constants, of methylene fluoride, using the data on the two main species and a few other minor species. Table I lists intensities of the rotational transitions of CHZFZ calculated at T = 300 K. The line strength X is taken as unity and the transition frequency is chosen to be 20 000 MHz. The vibrational frequencies are taken from Ref. (2). It is obvious that we will be able to observe the rotational spectra in all the fundamental states except the VI and vg states. Table I includes also a few overtone and combination states of VHZFZ and the ground state of 13CHzFz in natural abundance. The spectra in these states could also be detected. As is obvious from Table I, the ~2, ~3, US, VI, US,and vg states may be coupled by TABLE I
Intensities of the Rotational Transitions of CHZFZin the Vibrational State (cm-‘)a symmetry
5
G.S.
vs(cm
-1
ee,oo
1
eo,oe
0.0
4.66
1
2948.0
3.37
2 3 4
1508.0 1113.2 528.5
10-12 2.02 10-12 3.37 10-Y 2.02 10-Y 2.23 10-8 1.34 10-8 3.70 10-7 2.22 10-7
a2
5
1262.0
1.10
10-8
%
6 7
3014.3 1177.9
1.46 9.84
10-12 2.44 10-Y 1.64
10-12 10-8
b2
8 9
1435.0 1090.1
2.88 1.49
lo-' 10-8
4.80 2.49
10-9 lO-8
2x4
(1057) (1586) (1642)
2.93
10-8
1.76
10-8
Al
9
*2 61 B2 a1
a.
s
3x4 3+4 4+5 4+7 4+9 %,G.S. l3c, 4
(1791) (1706) (1619) 0.0 (528.5)
T=300K, vo=20 OOOMHZ,
10%
2.79
6.57
10%
10-Y
2.32 lo-' 1.79 10-T 8.72 lO-1o 7.80 10-10 1.18 10-~
1.40 10-Y 1.06 lo-T 5.21 10-l' 1.30 10-Y 1.97 10-9
5.21 4.13
3.13 2.48
lO-8 10-Y
(Av)~=ZOMHZ.
10-a lfg
411
MICROWAVE SPECTRUM OF CHzFz TABLE II Possible Effects of the Coriolis Interactions in Methylene Fluoride TYPO a
b
c
a.
Ref.
b.
For
A’($
(a))*/,,
s
S’
Ik,,,Pv
2
7
0.0606
3
7
0.3818
-181.45
5
8
0.0231
-0.25
5
9
0.0685
2
5
0.6088
3
5
0.0576
-0.08 -3.25
s,
0.89
SS’
b
MHZ
2.20 5.65
7
8
0.4717
7
9
0.4663
9.29
2
8
0.7778
23.65
2
9
0.0828
0.05
3
0
0.0345
-0 .Ol
3
9
0.6236
48.04
5
7
0.7254
17.86
(1). the
replaced
bby
and
c-type
B and
b,
interactions and
C and
A and c,
a are
to
be
respectively.
Coriolis interactions. As a measure of the effect of the interaction on the rotational spectra we calculated A2(tbr8t (0))2/AEd8f, B2({B,8t0))2/AE8.~, or C2([B,Bf(C))2/AEd5f in Table II. The largest value is due to the v3-V’I coupling, associated with the a-axis. However, as discussed earlier (I), the actual contributions may be larger for the b- and c-axis interactions than for the a-axis interaction. Therefore, the v3-vg, v2-v8, and vg-vr couplings may be more important, but these are probably not as large as the VZ-vg mteraction m CD2F2. The microwave spectrum of CH2F2 in the ground state was first observed by Lide (3), and we added more lines to evaluate the centrifugal distortion constants (4). Recently Koutcher et aE. (5) improved the rotational as well as the centrifugal distortion constants by adding a few transition frequencies precisely measured by a beam maser technique (6). Flygare and his co-workers (7) measured the Zeeman effect on the rotational spectrum of CHzFr, and determined the g factors, the magnetic susceptibilities, and the molecular quadrupole moment. Kukolich et al. (6,s) refined these constants by using a beam maser. However, all the constants were associated with the ground vibrational state, and no vibrational satellites have ever been analyzed. A few papers have appeared on the vibration-rotation spectra of methylene fluoride (2,9), but rotational structures were resolved only in a few cases and then with much lower resolution than that achieved by microwave spectroscopy. EXPERIMENTAL
DETAILS
A sample of methylene fluoride was provided us through the courtesy of Dr. J. J. Drysdale of DuPont Co. It was used in our previous work (4). The microwave spectrometer used in the present work was of the Hughes-Wilson type with 1 IO-kHz squarewave Stark modulation. The spectra were recorded at room temperature.
412
EIZI HIROTA ROTATIONAL
SPECTRUM
AND ANALYSIS
A Q-branch series Jw-,I-JO,= with J = 1, 2, 3, . . . provides us with the most convenient clue to the assignment of the vibrational satellites. We thus scanned the spectrum in the region of 38.5-48.5 GHz carefully. A Q-branch transition is easily differentiated from a P- or R-branch transition because the former has a larger Stark effect in most cases. Several cross points were found on a usual Q-branch plot [(A-C)/2 vs K] and were assigned to particular vibrational states. These assignments are based upon consideration of Coriolis coupling and observation of the relative intensities. As will be discussed in a subsequent paper the vibration-rotation constants of CHzFz are dominated by the Coriolis terms. The statistical spin weight is 10 for the (K__r, K+r) = (even, even) and (odd, odd) transitions in a vibrational state of al or a2 symmetry and for the (K-1, K+i) = (even, odd) and (odd, even) transitions in a state of br or b2 symmetry, whereas it is 6 for other transitions. The observed spectrum clearly reflects these spin weights. The 111~ 000 transition is the most convenient of the P- or R-branch lines for completing the rotational assignment. Although this transition has a positive Stark effect in many cases, the Stark effect observed for the ground state transition is negative. This fact is ascribed to a near degeneracy between the llr and the 202 states. In the ground state the separation is about 1136 MHz, the 2,,2 state being higher. It is interesting to note that the A constant increases with excitation of the v4 mode and the Stark effect tends to be more negative on going from the ground state to v4 and then to 2~4 [the observed Stark coefficient is -5.02, -9.4’1, and -34.5 for the ground, v4, and 2~4 states, in units of 1c5 MH~/(v/cm)~]. The Stark effect becomes positive in the 3~4 state, which means that the 111level is higher than the 202level in this state. This sort of correlation between the A constant and the Stark effect facilitates searching for the 111~ OOotransitions in other excited vibrational states as well. Unfortunately, for the VTstate the 111t 000 line is overlapped by a strong line, but the Stark component is observed, because the Stark coefficient is negative and large c-32.0 X 10m5 MHz/ (V/cm)2]. Because of Stark mixing two forbidden transitions, 2,n t 0~ and 2r1+ 111, are made allowed at finite Stark fields, by borrowing intensities from 111t 000 and 211+ 202, respectively. In fact, such transitions were observed for the ground and the v4 states. Recently, Kawaguchi and Tanaka (10) observed the vg band of methylene fluoride by laser Stark spectroscopy. The transitions they observed involve levels which are nearly degenerate with others, like lrr and 202 discussed here. The assignment of lrr + 000 for a particular vibrational state was checked by observing the 303 +- 212 transition, which exhibits three well-resolved Stark components. Higher J, P, or R branches show only barely resolved or unresolved Stark lobes, but were measured for confirmation of the assignment and also for precise determination of the centrifugal distortion constants. All the observed transitions were subjected to a least-squares analysis, by using a Hamiltonian described in detail in the previous paper (1). Because the Hamiltonian includes only the first-order centrifugal distortion terms, the observations were limited to the J value of 20. Each vibrational satellite was analyzed separately. For v3 and VQ a first-order centrifugal distortion treatment is not satisfactory, and an effective Hamiltonian comprising the two vibrational states was used.
MICROWAVE
SPECTRUM
413
OF CH2F4
RESULTS
Ground, v4, ZV+ 3v4 states. Table III summarizes ground and the v4 states. The molecular constants, TABLE Observed and Calculated
Frequencies
1.
1
-
1, 2,
1, 1, 0, 2, 2. 1, o, 2, 2, 1, 0, 2, 2, 1, 1, 2, 3, l,
0
-
1 3 l-3,‘ 0 2 4 2 l 3 5 3 2 4 5 3 ; 1
.3. 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, ;>
3 6 6 5 4 7 8 6
7: 6, 7, 8, 8, 7, 7, 9,
2: 2:
2: 1, 3, 7, 7, 7,
1, 3, 3, 78: 1, 1, !* 3, 8: 9, :: 10, 2, 10, 1, 11, 2. 11, 2: lo, 4; lo, 4, ll, 1, 12, 2, 12, 2, 11. 11; 1: :I :;, 12: 12, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15,
-
0. 1; 2, 2,
$ 8 10 9 16 7 6 11 10 11 8 12 7
I ;, - 9: - 9, - 10. - 10: - 11; -11, - 10, - 11, - 11, -12, - 11, 12,
2, 12
- 12,
? 1: 2, 3, 1, 5, 5, 3, 3, 1, 5, 5,
I:;> - 12: - 13, - 13, - 13, - 15, - 15, - 14, - 14, - 14, - 16, - lb,
:zS 16: 1: :* lb, 16, 5, lb, 5, 17, 1, 3,
; 13 13 11 14 10 9 12 13 15 11 10 16 :: 12 11 l5 17
:'B, 4, 14 1s: 4, 15 18, 1, 18 4, 15 :z, 4, 16 18: 6, 13 18, 6, 12 19, 20, 20, 19, 19.
Ground
J",K_;,K+;
1.
0.
0
0; 0, 1,
l 2 2 ^
1, o, 2, l, o, 2, 2, 2, o, 2, 2, 2.
5 z
2, 3, 2, 3, 3, 3, 3, 2, 3,
2 2 5 7 6 7 6
6 7 ; ; ; ;
:: l: 2, 9 ? l: 3: 11 2. 10
;;
2: 4, 4. 4; 4, 2, 4, 4, 4, - 15, 4, 2, - 17, 4, - 17, 4, I ;;, 4, 2, - 17: 5, - 17, 5, - 17, 2, - 18, 5, - 18, 5, - 19, 5. - 19, 5; 2, 5, 5,
11 ;; 11 12 11 10 12 12 13 12 11 13 13 14 12 14 13 12 15 14 13 14 15 16 15 14
:: :z
III
of l*CHzFz in the Ground and the ~1 State (MHz)
TI-8.tXitX3Il J',K_i,K+i -
the observed transitions in the which are derived, are listed in
atate
"ohs 58 39 41 22 54 62 43 43 31 45 46 65 8 29 50 15 14 55 53 58 39 61 31 38 64 11 9 20 21 14 30 38 15 53 54 37 64 32 $1 i4 42 48 10 14 44 63 11 44 51 52 34 24 43 30 31 58 44 3;
792.098 852.549 282.677 204.183 033.161 196.649 433.373 761.213 543.750 262.944 420,813 695.730 439.239 268.534 342.841 253.722 364.419 312.309 685.951 044.683 501.034 446.773 763.670 956.637 259.415 452.622 091.401 237.586 980.475 417.298 679.093 812.624 633.552 125.242 806.717 400.828 104.958 507.747 974.150 ij5.837 040.860 455.971 365.824 772.429 542.528 291.395 810.708 895.885 758.265 7i2.966 fZ73.iii 760.332 133.486 962.080 897.919 1?9.115 155.747 ;$.;;;
11 63 33 11 9 25 33 29 50 50 16 55 50 29 29
4X3:769 173.042 563.230 430.306 097.145 974.350 159.214 624.489 004.809 180.929 700.568 353.168 127.912 339.007 630.720
ObS-CalC 0.019 0.046 -0.057 -0.017 -0.024 -0.140 0.068 0.111 -0.072 O.cll2 0.068 0.069 -0.041 -0.005 0.040 :.:;: 0:053 0.048 -0.041 0.041 -0.055 0.026 0.051 0.017 0.092
0.007 0.025 -0.064 -0.005 -0.013 0.048 0.062 -0.167 0.092 -0.034 -0.094 0.088 -0.024 0.005 -0.082 0.016 0.092 0.022 0.048 0.036 -0.062 0.047 0.072 -0.255 -0.053 0.002 -0.064 -0.028 0.115 -0.152 0.070 0.066 -0.020 0.076 -0.156 -0.036 -0.045 -0.028 -0.039 0.09l 0.030 0.102 0.051 0.034 0.166 -0,022 -0.056 -0.056
“4
state
'ohs
obs-talc
58 40 41 21 55 63 43 43 32 46 46 65 9 30 50 13 15 55 55 60 38 61 33 41 62 9 11 22 20 12 28 36 13 56 57 35 61 29 35 37 39 45 13 18 41 6;
696.419 263.548 665.244 689.448 260.091 492.213 833.820 205.837 803.583 637.794 846.147 103.464 726.733 730.426 800.704 943.843 922.201 811.071 870.963 262.526 173.345 996.070 987.787 234.985 918.602 k71.198 348.799 579.220 068.652 133.495 621.636 509.622 153.607 262.560 954.886 181.828 790.714 951.178 156.923 956.859 643.494 816.028 590.555 026.531 948.431 w&.;;;
42 55 56 31 21 40 35 36 55 40
087:074 837.710 405.958 377.812 398.299 091.972 089.137 030.350 016.909 737.408
-0.135 0.084 -0.081 0.089 -0.017 -0.012 -0.027 0.058 -0.032 0.024 0.029 0.148 0.045 0.011 0.066 0.105 0.117 0.003 -0.036 -0.022 0.023 -0.001 -0.119 -0.033 0.064 -0.128 -0.062 -0.064 0.084 0.067 -0.024 -0.058 -0.168 -0.091 -0.055 -0.062 -0.102 -0.029 0.092 -0.018 0.165 0.036 0.077 0.118 0.038 0.016 0.024 -0.025 -0.004 0.013 -0.056 0.085 -0.011 -0.063 0.129 -0.114 0.015
14 15 59 30
092.133 600.152 696.395 003.011
0.027 -0.001 -0.063 -0.014
22 28 25 55 55
129.646 901.813 346.547 020.273 197.019
-0.006 0.133 0.016 0.242 -0.018
51 45 34 34
057.892 802.227 402.124 695.236
0.029 -0.047 -0.132 -0.126
414
EIZI
HIROTA
TABLE Rotational
Constants
and Centrifugal
IV
Distortion
Ground and ~1 States
Constants
of WHIFI
Ground state Ref. A
(5)
Ref.
49 142.770(85) 10 604.692(20) 9 249.836(16)
B i: Taaaa 'bbbb Tcccc
in the
(MHz)a v4state
present
(5 )
present
49 142.834(44) 10 604.747(10)
49 142.818(18) 10 604.7050(44)
9 249.807(E)
9 249.8437(33)
49 480.557(19) 10 582.8371(49) 9 216.6002(36)
-2.3049(41) -0.06064(91) -0.02653(71)
-2.3156(27) -o.o6095(47) -0.02672(l)'
-2.30061(77) -0.06151(18) -0.02723(13)
-2.38610(87) -0.06100(21) -0.02690(16)
0.170(12) -0.03648(99)
0.1684(59) -0.03683(47)
0.1575(23) -0.03756(19)
0.1568(28) -0.03682(23)
a. Errors are the standard deviations. b. ~~~~~~~~~ + [(A-B)/(A-c)IT~~~~~and ~~~~~~~~~ + C(B-c)/(A-c)~T,,,, c. The standard deviation given in Ref. (5) seems to be too small.
Table IV. Most ground state transitions reported earlier (4) were remeasured more precisely. Thus, the ground state values are more accurate than those reported in Refs. (4 and 5). Table V shows the observed transition frequencies and the derived molecular TABLE
V
Observed Transition Frequencies and Molecular Constants in the 2~4 and 3~ States (MHz)* Transition
2v>,
- J",K_jl,K+y
J’,K_i,K+i
" 0tJs 996.521 633.678 048.849 172.928 481.984 793.621 238.335 640.834 057.106 024.359 279.565 509.554 272.276 331.266
-0.060 0.071 -0.099 0.027 -0.216 0.056 0.002 0.002 0.150 0.043 -0.074 0.095
59 41 42 20
1, 1, l, 0, 2, 2, 1, 0, 2, 2, 1, 0, 1, 1,
1 0 1 3 1 0 2 4 2 1 3 5 4 5
- 0, - 1, - 2, - 2, - 3, - 3, - 3, - 3, -4, - 4, - 4, - 4, - 5, - 6,
0, 0, O, 1, 1, 1, o, 1, 1, 1, 0, 1, 0, o,
0 1 : 2 3 3 3 3 4 4 4 5 2
58 40 42 21 56 64 44 42 34 48 47 64 51 56
!: 7, 7,
3, 1, 1, 3,
6 3 6 5
- 6, 7, - 7, i:
2, 0, 2,
5 7 ;
62 486.277 36 861.137 62 576.126 36 203.212
'8, 3, > 1,
7 4
- 7, I
2,
6
61 522.751 43 597.083
A
B E Taaaa 'bbbb lcccg Tl T2b
3"1, obs-talc
1, 1, 2, 3, 2, 2, 3, 4, 3, 3, 4, 5, 5, 6,
of ‘“CHzFe
' Ob8 289.923 002.390 434.060 654.985
obs-talc -0.007 0.007 0.044 -0.004
44 648.825
0.041
35 298.270
-0.001
47 725.522 63 914.700
-0.143 0.005
-yl;:
56 884.807
0.101
-0:oso 0.034 0.015 -0.010
63 204.535
-0.039
-0.039 0.031
60 311.272
-0.001
49 815.676(49) 10 560.939(17) 9 181.533(15) -2.489(14) -0.0612(14) -0.0259(20) 0.125(17) -0.0358(15)
50 146.827(90) 10 539.192(87) 9 143.79(10) -2.72(10) -0.060(13) -0.027(11) -0.02(14) -0.056(13)
a. Errors of the molecular constants are the standard deviations. b. See Table IV for definitions.
MICROWAVE
SPECTRUM
415
OF CHzFz
TABLE VI Observed Transition Frequencies and Molecular Constants of 13CHzFzin the Ground and the Y( States (MHz+ Transition
1,
1,
1
l, 2, 3, 2,
l, l, o, 2,
o l 3 l
y> I
0,
, 0, o, > 1,
$9
I - 3,
ii B t ='aaaa 'bbbb lcccc b Tlb T2
"4 state
Ground state
K 1,K I, J'aK_i,K+i _ J 1, ’ -1’ +1
1,
y
; 2
'ohs
obs-Calc
"ohs
38 39 23 49 42 45 27 41 45
929.293 531.189 977.683 501.235 865.485 220.298 048.614 329.622 589.988 344.210
-0.041 -0.007 0.008 0.003 0.043 0.023 0.033 -0.053 -0.023 -0.005
57 38 40 22 51 42 44
25 49 54 46 51 43 61 32 22
829.095 458.021 684.892 710.757 569.383 950.048 151.065 622.587 083.267
%~ 0:010 0.090 I;:;$ -0.040 0.082 0.052
56
47 730.785(39) 10 606.137(14) 9 199.117(11) -2.241(13) -0.0638(12) -0.0290(17) 0.123(14) -0.0386(13)
abs-talc
231.882 901.395 360.045 987.720 087.677 621.668 495.042
-0.113 0.123 -0.022 0.032 0.048 -0.014 0.030
45 771.999
-0.032
49 55 48 53
920.263 190.726 888.610 784.102
0.034 -0.009 0.005 -0.042
61 710.659 34 898.498
0.001 0.028
48 067.173(64) 10 584.479(59) 9 165.404(37) -2.300(45) -0.0644(72) -0.0279(64) 0.103(77) -o.O392(63)
a. Errcr?.of the molecular constants are the standard deviations b. See Table IV for definitions.
constants in the 2vq and 3v, states. The rotational constants change almost linearly with the quantum number 04, and thus the effect of the Fermi resonance between 2v4 and v3 is small as in the case of CDzFz. The data on r3CHzFz in the ground and the v4 states are given in Table VI. In the previous paper (4) we determined the rotational constants in the ground state of 13CHzFz by fixing the centrifugal distortion constants to the values of the 12C species, whereas the present data allow us to determine eight molecular constants simultaneously. ~2, vg, vr, and vs. The observed transitions and the molecular constants derived from them are summarized in Table VII. The effects of the Coriolis couplings mentioned in Table II are apparent in the molecular constants. For example, the A constant in the VTstate is larger than the ground state value by about 750 MHz, which is mainly due to the Coriolis interaction of this state with the vt state. The raaaa constant is also affected. v3 and vg. The observed transition frequencies listed in Table VIII were first analyzed separately for the two states. The results thus obtained are given in Table IX under the heading I. It is noted that the differences between the observed and the calculated frequencies, which are given in Table VIII, are larger than those in other vibrational states. Furthermore, when we calculate the frequencies of next higher J transitions such as 634+ 725 and 633+ 726, they differ from the observed values by 4-26 MHz. This observation indicates clearly that the treatment used on the other states is not
416
EIZI
HIROTA
TABLE Observed Transition
Frequencies
VII
and Molecular
Constants
of WHtF2
in the
YP, ~5, ~7, and vs States (MHz)* TranSition J’,K_i,K+i
-
Vobs / obs-talc
J”,K_;,K+;
y2
1,
1,
1
-
0,
0,
1,
1,
0
- 1,
0,
39
2,
1,
- 2,
0,
40
3,
1,
- 3,
0,
42
4,
1,
- 4,
0,
45
5,
1,
- 5,
0,
49 53
0
“5
-0.098
“2:FTi 40 847:406 0.023
0.013 49 308.411 -0.063 53 932.088 0.001 59 630.454 0.003 22 65;JD4'
6,
1,
- 6,
0,
7,
1,
- 7,
0,
3,
0,
3
- 2,
1,
2
4,
o,
4
- 3,
1,
3
5,
o,
5
- 4,
1,
4
7,
1,
6
- 6,
2,
5
8,
1,
7
- 7,
2,
6
2,
2,
1
- 3,
1,
2
64 283.832 -0.020 53 '";A;;
2,
2,
0
- 3,
1,
3
60 89;:;(;; 60 773.647
3,
2,
2
- 4,
1,
3
3,
2,
1
- 4,
1,
4
43 "?;A;
6,
3,
4
- 7,
2,
5
52 214:567 -0.019 56 036.363 0.001
59 22 624.155 0.037 44 182.222 0.042
6,
3,
3
- 7,
2,
6
7,
3,
4
- 8,
2,
7
48 ‘;;.;U;
a
10 6;7:912 to.022
E
9 34;.;;t _.
~cccc Tlb T2b
a.
Errors
b.
See
43 570.112 0.085 51 957.721 -0.001
58 40 739.450 0.020 42 238.944 41 401.396 -0.007 0.030 44 '"yu; 43 749.881 0.111 47 7961370 47 022.328 0.010 -0.127 52 51 333.820 0.105 "'vz 57 4531625 56 813.519 0.024 -0.070 64 63 594.289 "E.',',; 0.013 21 2771552 22 081.400 -0.049 0.097 42 858.594 43 ""::;g -0.014 64 829.564 65 591.626 -0.059 -0.005 37 861.639 40 421.922 -0.053 0.614 62 878.358 65 442.064 0.003 0.000 56 367.114 53 823.225 0.013 -0.010 65 163.752 62 699.675 -0.017 0.075 33 765.809 -0.026 48 554.692 -0.123 57 53 530.207 0.010 7x43; 62 73;:;;; 58 671.068 -0.007 43 839:022 39 "';A;: -0.095
VII-Continued
A
'bbbb
“yx;
64 480:496 0.030
-0.072
TABLE
Taaaa
44 201:877 -0.024 39
‘8
v7
58 208.478 -0.005 39 '"y;:
58 294.148
48 876.621 to.039 10 604.055 io.013 9 332.448 to.012
-2.247 to.016 IO.0593 ~0.0020 -0.0454 to.0025
-2.300 io.012 -0.0644 +0.0013
0.377 +0.024 IO.0359 +0.0022
0.457 to.014 -0.0254 +0.0013 _
$W~ _ .
49 893.532 49 o:;.;;,’ +0.058 10 6y2.860 10 608.340 to.017 to.019 9 153.129 9 l~F&~%~ to.017 _ .
X: IO.0660 ~0.0014 -0.0144 ~0.0020 -0.079 +0.017 -0.0212 +0.0016
of the molecular constants are the standard deviations. Table IV for definitions.
-2.327 +0.011 IO.0652 +0.0015 IO.0097 +0.0017 10.046 +0.016 IO.0411 +_0.0015
MICROWAVE
SPECTRUM TABLE
417
OF CHoFz
VIII
Observed and Calculated Frequencies of “CHZFZ in the ~8 and VPStates (MHz)
Transition
"' 3
J',K_i,K+i- J",K_;,K+;
'ohs
" Ia
IIb
'ohs
I=
1, 1, 2, 3, 4, 5, 6, 7, 8, 3, 4, 5, 7,
1, 1, 1, 1, 1, 1, 1, 1, 1, 0, o, o, 1,
1
-
0,
0,
0 1 2 3 4 5 6 7 3 4 5 6
-
1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 6,
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2,
0 1 2 3 4 5 6 7 8 2 3 4 5
57 3% 40 41 44 47 51 56 62 23 44
8, 2, 2, 3, 6, 6, 7,
1, 2, 2, 2, 3, 3, 3,
7 1 0 1 4 3 4
-
7, 3, 3, 4, 7, 7, 8,
2, 1, 1, 1, 2, 2, 2,
6 2 3 4 5 6 7
64 067.795 51 603.492
a.
Ohs.-talc. obtained using the molecular constants I of Table IX. Ohs.-talc. obtained using the molecular constants II of Table IX. Not included in a least-squaresanalysis.
b. c.
714.812 861.364 014.692 791.997 248.546 456.596 501.339 475.836 473.217 185.320 603.57%
39 993.01%
40 821.805 49 408.588 52 496.236
-0.366 0.421 0.264 0.270 0.072 -0.103 -0.274 -0.319 0.248 -0.26% 0.485
-0.554 -0.600 -0.858 -0.925 -1.095 -1.067 -0.826 -0.317 0.70% 1.211 0.669
57 678.389
-0.186 -0.775
41 307.500 43 779.712
-0.166 -0.04%
0.031 0.256
47 230.694 51 783.910 57 578.03%
0.152 0.20% 0.203
0.574 0.744 0.832
64 749.842
-0.138
0.543
21 691.418 43 101.409
0.281 0.005 -0.267 0.241 -0.131 0.421 0.049
-0.508 -0.465 0.002 -0.262 -0.837 -0.234
64 -0.172 40 0.289 0.576 65 -0.470 1.925 53 63 0.272 1.777 46 (26.201)' -0.885 53 C-24.156)' 0.392 59 40 -0.485
IIb
897.159 445.162 481.979 666.742 000.937 841.032
0.697 0.820 -0.359 561.774 ('-17.816)'2.042 (4.234)'-1.270 256.394 683.050 (lo.146)c-2.879
enough to account for the v3 and vgspectra. Therefore we also analyzed them simultaneously by using a two-dimensional effective Hamiltonian. The results thus obtained are designated as II in Table IX. The agreement between the observed and the calculated frequencies are not as good as in the case of I for the lines in common. However, in II several lines which could not even be inchrded in I are used. The somewhat poorer fit of II for the common lines may be partly due to the fact that we fixed the centrifugal distortion constants to the ground state values. For example, the T,,.= constant in v1 would be more positive because of Coriolis coupling with vr. We thus assumed a value of -0.8087 MHz for this constant, but obtained a result which was slightly less satisfactory than II in Table IX. In conclusion, the Coriolis interaction between va and vg is not strong enough to allow simultaneous determination of C*s, C*g, D, and va-vg, but is too strong for the independent treatment of the states to be very satisfactory. It is to be noted that P3 + O”/(Q - vg) and Pg - LY/(va - vg) agree respectively with cS and cg of I within 2 MHz. v3 i- ~4, vq + VS,v4 + VT,and v4 -I- vg.Table X summarizes the transition frequencies observed for the four combination states v4 + vs (s = 3, 5, 7, and 9). Because the number of the observed transitions was small, most of the centrifugal distortion constants were fixed either to those of the v8 states or to those of the ground state. The standard deviations attached to the constants of v4 + VT are abnormally small and probably result from a statistical accident. For v4 + vg the 11~t OoOtransition could sufficient
418
EIZI HIROTA
not be observed, and thus the B constant was fixed to a calculated value. For comparison
Table X also lists the rotational constants, which were calculated from those of the fundamental states. Discrepancies, if any, might be due to the fact that the effects of Coriolis interactions change on going from the fundamental states to the combination states. DISCUSSION
The rotational as well as the centrifugal distortion constants, which are listed in Tables VII and IX, indicate clearly the presence of Coriolis couplings between v3 and ~7, v2 and vs, v3 and vg, and v5 and ~7. As pointed out in Ref. (I) we may estimate roughly the Coriolis coupling constant and the vibrational energy difference between the two vibrational states by using changes of the rotational and the centrifugal distortion constants upon excitation of the normal modes. Our approximation requires that the changes of the molecular constants are of the same magnitude, but opposite in sign for the two states: AA = AA, = -_A,#
and AT = - (AT....)~ = (A7aaaa)s* in case of the
u-axis interaction. We may thus calculate
TABLE IX Molecular Constanti of l*CHlFp in the YQand vpStates (MHz)a
II
E C"
48 287.08(35) 10 549.54(13) 9 428.38(15)
9 261.2(95)
Taaaa Tbbbb Tcccg
-0.81(26) -0.045(12) -0.293(11) 4.44(11)
[-2.30061
*lb T2
-0.303(58)
C-O.03761
t
'bbbb Leg *lb *2 D F
v3-v9
b.
C-O.06151 C-O.02721 co.15751
48 698.79(25)
48 704.26(44)
.10 531.112(76)
10 524.25(22)
8 980.550(88)
C" Taaaa
a.
48 295.44(51) 10 544.10(19)
9 147.3(96) -3.29(17)
C-2.30061
-0.1063(823 o.2369(81) -2.805(73) 0.051(27)
[-0.06151 C-O.02721 co.15751 C-O.03761 10
189.(336)
-116.(17) 628.3(78)x103
Values in parentheses are standard deviations, and those in brackets are fixed. See Table IV for feflnltions.
MICROWAVE
SPECTRUM TABLE
419
OF CHzFe
X
Observed Transition Frequencies and Molecular Constants of ‘*CH*Fz in the YI + YI, Ed+ ~5, ~1 + Y,, and ~1 + VPStates (MHz)8 Transition
vobs/obs.-talc.
J',K_i,K+i- J",K_;,K+1" 1,
1,
1 -
0,
0
1,
1,
0 - 1,
0,
0,
1
2,
1,
1 - 2,
0,
2
3,
1,
2 - 3,
0,
3
4,
1,
3 - 4,
0,
4 5
5,
1,
4 - 5,
0,
6,
1,
5 - 6,
0,
6
7,
1,
6-
7,
0,
7
a,
1,
7 - a,
0,
a
v3+v4
v4+v5
v4+y7
58 013.350 0.000 39 277.958 0.019 40 467.488 -0.119 42 301.450 0.053 44 837.567 0.072 48 151.112 0.027
58 502.832 0.000
59 355.127 0.000 41 106.932 0.000 42 612.592 -0.001 44 945.285
57 472.733 -0.099 63 67;:;;;
48 645.900 to.057
o.ooi
46 099.730 48 191.936 -0.003 -0.000 49 802.631 -0.053 54 485.555 0.102 60 2~',:;;5
49 2e$;65;
- .
lo 53,;.;;8' 10 581.442 *0.076 9 367.799 '0.057 c-2.3181 C-1.2331 c-0.0601 [-0.0601 -0.1626 c-o.34131 *0.0011 b T1b T2 A (calc.jC B (calc.)C F (calc.)C a.
b. c.
CO.1761 C-O.03621 48 624.82 10 527.68 9 395.13
50 231.828 to.001 10 589.582 to.002 9 124.164 to.001 L-3.4051 C-O.6211 -0.0521 to.0002
CO.1761 [-0.03621 49 214.360 10 582.187 9 299.204
LO.1761 L-O.03621 50 231.271 10 590.992 9 119.885
v4+v9
40 056.968 0.120 41 "'X 44 OS:435 0.022 47 467.728 0.010 51 952.240 -0.002 57 655.691 0.023 64 713.600 -0.012
49 040.445 io.094 cl0 509.8371 a 9;;.;;; -. L-2.3181 c-o.05791 0.1481 eo.0018 CO.1761 [-0.03621 49 036.53
Errors of the molecular constants are standard deviations. Values in brackets are fixed. See Table IV for definitions. Calculated from the constants in the fundamental states.
18.8w and AE,,l by A /{.,,,‘“’ / = (AA3/A7)+, A&.# = 4A@/Ar.
(la) (lb)
Table XI summarizes the molecular constants for four pairs of states, which are pertinent for the present discussion. They satisfy the conditions required for the approximation within about lOye, except AC of va and v8. The Coriolis coupling constants and vibrational energy differences, which are calculated from them by using Eqs. (I), are compared in Table XI with the values reported in Ref. (2). Agreement is not as satisfactory as in %D2Fz (I), and discrepancies are probably due to contributions of terms other than the Coriolis terms. However, the latter terms are obviously the most dominant in rotational-constant changes in these states. A subsequent paper will deal with detailed analysis of the rotational constants in excited vibrational states.
420
EIZI HIROTA TABLE
XI
Coriolis Coupling Constants and Vibrational Energy Differences in reCHsFzs State AA(MHz)
A~~~~~(Mfiz) %,s' (a) -1.49 1.491 -1.49
State
AT~~~~(MHz)
AC(MHz>
3
94.801
.B.
-114.288 104.545
z3
178.534
a9.
-269.294 223.914
82.604
z5 ai;.
0.380 (0.390) ") 58,s
The
I”
Corlolls
-1 AEs,s'fern f
0.864
(0.788)
81.5 (73.0)
0.704 (0.622)
25.2 (23.1)
0.266 -0.2641 0.265 0.0158
-96.715 89.660
Values
-57.8
(-64.7)
0.0182
-0.0175 0.0179
-0.0128 0.0143
0.768 (0.728)
a.
AE S,S'(cm-11
75.0 (84.1)
parenthesesare taken from Rd.(2). coupling constantsare recalculated. ACKNOWLEDGMENTS
The author would like to thank Dr. J. J. Drysdale for providing us with a sample of methylene fluoride. He is also grateful to Professor R. F. Curl for reading the manuscript. The calculation in the present work was carried out at the Computation Centers of Kyushu University and Nagoya University.
RECEIVED:
August
15. 1977 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
E. HIROTA AND M. SAHARA,J. hfnl. Spectrosc. 56, 21 (1975). I. SUZUKIANDT. SHIMANOUCHI, J. Mol. Spectrosc. 46, 130 (1973). D. R. LIDE, JR., J. Amer. Chem. Sot. 74,3548 (1952). E. HIROTA, T. TANAKA, A. SAKAKIBARA,Y. OHAS~, AND Y. MORINO, J. Mol. Spectsosc. 34, 222 (1970). J. A. KOUTCHER,R. H. LARK~N,J. R. WILLIAMS, AND S. G. KUKOLICH,J. Mol. Spectrosc. 60,373 (1976). S. G. KUKOLICH,J. H. S. WANG, ANDD. J. RUBEN, J. Chem. Phyrys. 58, 5474 (1973). M.-K. Lo ANDW. H. FLYGARE,J. Mol. Spectrosc. 25, 365 (1968); R. P. BLICKENSDERFER, J. H. S. WANG, ANDW. H. FLYGARE,J. Chem. Phys. 51,3196 (1969). S. G. KUKOLICHAND A. C. NELSON,J. Chem. Phys. 564446 (1972) ; A. C. NELSON,S. G. KmoLrcn, ANDD. J. RUBEN, J. Mol. Spectrosc. 51, 107 (1974). H. B. STEWARTANDH. H. NIELSEN,Phys. Rev. 75,640 (1949) ; S. P. S. PORTO,J. Mol. Spectrosc. 3, 248 (1959). K. KAWAGUCHIANDT. TANAKA, J. MoZ. Spectrosc. 68, 12.5 (1977).
69,409-420
(1978)
Microwave Spectrum of Methylene Fluoride in Excited Vibrational States ELZI HIROTA’ Department of Chemistry, Faculty of Science, Kyushu University, Fzlkuoka 812, Japan, and Institute for Molecular Science, Okazaki 444, Japan The rotational spectra of WHSF~ in seven of the nine fundamental vibrational states and also in overtone and combination states involving the ~1 mode were observed and assigned. Coriolis interactions between ~1 and ~7, YZ and ~8, ~3 and ye, and ~6 and Y, were analyzed by using approximate expressions for the rotational levels. An effective Hamiltonian with the Coriolis term in the off-diagonal block was applied to stronger interaction between ~3 and VS. Fermi resonance between VI and 2~4 was found to be negligible. The ground state spectra of YHzF2 and of YHzFz were remeasured to improve the accuracy of the rotational and centrifugal distortion constants. The Coriolis coupling constants and the energy differences between two vibrational levels in resonance, which were obtained through an analysis of the satellite spectra, are compared with the results derived from a normal coordinate analysis.
INTRODUCTION Because of high resolution attained by microwave spectroscopy, rotational spectra of a molecule in excited vibrational states provide detailed information on the intramolecular vibrations. This sort of information is particularly important in cases where two or more vibrational levels are nearly degenerate and vibration-rotation spectra obtained by conventional vibrational spectroscopy are not sufficiently well resolved. An analysis of a Coriolis resonance may give us the vibrational energy difference and the Coriolis coupling constant involved in the resonance. Provided that we could observe the spectra in the overtone state, a Fermi resonance may also be analyzed. It is well known that, although microwave spectroscopy allows us to determine rotational constants with an accuracy of five to eight significant figures, the structural parameters derived from these rotational constants are much less precise, because vibration-rotation interaction obscures the geometrical meaning of the rotational constants. The vibrational contribution to the rotational constants includes terms from the cubic potential constants, which are most difficult to estimate. It is thus worth observing vibrational satellites, which may make it possible to evaluate the anharmonic potential constants and to derive the equilibrium structure. Analyses of the vibration-rotation interaction have hitherto been carried out in detail only on diatomic, triatomic, and a few symmetric top molecules. Here, we under-
1Present address : Institute
for Molecular
Science,
Okazaki
444, Japan.
0022-2852/78/0693-0409$02.00/O Copyright 0 19713by Academic Press. Inc. Allrights of reproduction in any form reserved.
410
EIZI HIROTA
took a little more complicated molecule, methylene fluoride. The following considerations led to the choice of this molecule. Because it is an asymmetric top, we may determine three rotational constants for each vibrational state. Among the asymmetric top molecules it belongs to the highest symmetry Czo. The absence of any nuclei with the quadrupole moments makes the rotational spectrum simple enough to observe weak vibrational satellites. By investigating not only the normal species but also 13Cand D isotopesubstituted species, additional information may be obtained. In a previous paper (I) we reported rotational constants of CDzFz in excited vibrational states. We analyzed the Coriolis resonances in cases where they were significant. In the present paper we will describe an analogous analysis of the microwave spectra of CH,Fz, and we will discuss in a subsequent paper the molecular structure and the anharmonic potential constants, of methylene fluoride, using the data on the two main species and a few other minor species. Table I lists intensities of the rotational transitions of CHZFZ calculated at T = 300 K. The line strength X is taken as unity and the transition frequency is chosen to be 20 000 MHz. The vibrational frequencies are taken from Ref. (2). It is obvious that we will be able to observe the rotational spectra in all the fundamental states except the VI and vg states. Table I includes also a few overtone and combination states of VHZFZ and the ground state of 13CHzFz in natural abundance. The spectra in these states could also be detected. As is obvious from Table I, the ~2, ~3, US, VI, US,and vg states may be coupled by TABLE I
Intensities of the Rotational Transitions of CHZFZin the Vibrational State (cm-‘)a symmetry
5
G.S.
vs(cm
-1
ee,oo
1
eo,oe
0.0
4.66
1
2948.0
3.37
2 3 4
1508.0 1113.2 528.5
10-12 2.02 10-12 3.37 10-Y 2.02 10-Y 2.23 10-8 1.34 10-8 3.70 10-7 2.22 10-7
a2
5
1262.0
1.10
10-8
%
6 7
3014.3 1177.9
1.46 9.84
10-12 2.44 10-Y 1.64
10-12 10-8
b2
8 9
1435.0 1090.1
2.88 1.49
lo-' 10-8
4.80 2.49
10-9 lO-8
2x4
(1057) (1586) (1642)
2.93
10-8
1.76
10-8
Al
9
*2 61 B2 a1
a.
s
3x4 3+4 4+5 4+7 4+9 %,G.S. l3c, 4
(1791) (1706) (1619) 0.0 (528.5)
T=300K, vo=20 OOOMHZ,
10%
2.79
6.57
10%
10-Y
2.32 lo-' 1.79 10-T 8.72 lO-1o 7.80 10-10 1.18 10-~
1.40 10-Y 1.06 lo-T 5.21 10-l' 1.30 10-Y 1.97 10-9
5.21 4.13
3.13 2.48
lO-8 10-Y
(Av)~=ZOMHZ.
10-a lfg
411
MICROWAVE SPECTRUM OF CHzFz TABLE II Possible Effects of the Coriolis Interactions in Methylene Fluoride TYPO a
b
c
a.
Ref.
b.
For
A’($
(a))*/,,
s
S’
Ik,,,Pv
2
7
0.0606
3
7
0.3818
-181.45
5
8
0.0231
-0.25
5
9
0.0685
2
5
0.6088
3
5
0.0576
-0.08 -3.25
s,
0.89
SS’
b
MHZ
2.20 5.65
7
8
0.4717
7
9
0.4663
9.29
2
8
0.7778
23.65
2
9
0.0828
0.05
3
0
0.0345
-0 .Ol
3
9
0.6236
48.04
5
7
0.7254
17.86
(1). the
replaced
bby
and
c-type
B and
b,
interactions and
C and
A and c,
a are
to
be
respectively.
Coriolis interactions. As a measure of the effect of the interaction on the rotational spectra we calculated A2(tbr8t (0))2/AEd8f, B2({B,8t0))2/AE8.~, or C2([B,Bf(C))2/AEd5f in Table II. The largest value is due to the v3-V’I coupling, associated with the a-axis. However, as discussed earlier (I), the actual contributions may be larger for the b- and c-axis interactions than for the a-axis interaction. Therefore, the v3-vg, v2-v8, and vg-vr couplings may be more important, but these are probably not as large as the VZ-vg mteraction m CD2F2. The microwave spectrum of CH2F2 in the ground state was first observed by Lide (3), and we added more lines to evaluate the centrifugal distortion constants (4). Recently Koutcher et aE. (5) improved the rotational as well as the centrifugal distortion constants by adding a few transition frequencies precisely measured by a beam maser technique (6). Flygare and his co-workers (7) measured the Zeeman effect on the rotational spectrum of CHzFr, and determined the g factors, the magnetic susceptibilities, and the molecular quadrupole moment. Kukolich et al. (6,s) refined these constants by using a beam maser. However, all the constants were associated with the ground vibrational state, and no vibrational satellites have ever been analyzed. A few papers have appeared on the vibration-rotation spectra of methylene fluoride (2,9), but rotational structures were resolved only in a few cases and then with much lower resolution than that achieved by microwave spectroscopy. EXPERIMENTAL
DETAILS
A sample of methylene fluoride was provided us through the courtesy of Dr. J. J. Drysdale of DuPont Co. It was used in our previous work (4). The microwave spectrometer used in the present work was of the Hughes-Wilson type with 1 IO-kHz squarewave Stark modulation. The spectra were recorded at room temperature.
412
EIZI HIROTA ROTATIONAL
SPECTRUM
AND ANALYSIS
A Q-branch series Jw-,I-JO,= with J = 1, 2, 3, . . . provides us with the most convenient clue to the assignment of the vibrational satellites. We thus scanned the spectrum in the region of 38.5-48.5 GHz carefully. A Q-branch transition is easily differentiated from a P- or R-branch transition because the former has a larger Stark effect in most cases. Several cross points were found on a usual Q-branch plot [(A-C)/2 vs K] and were assigned to particular vibrational states. These assignments are based upon consideration of Coriolis coupling and observation of the relative intensities. As will be discussed in a subsequent paper the vibration-rotation constants of CHzFz are dominated by the Coriolis terms. The statistical spin weight is 10 for the (K__r, K+r) = (even, even) and (odd, odd) transitions in a vibrational state of al or a2 symmetry and for the (K-1, K+i) = (even, odd) and (odd, even) transitions in a state of br or b2 symmetry, whereas it is 6 for other transitions. The observed spectrum clearly reflects these spin weights. The 111~ 000 transition is the most convenient of the P- or R-branch lines for completing the rotational assignment. Although this transition has a positive Stark effect in many cases, the Stark effect observed for the ground state transition is negative. This fact is ascribed to a near degeneracy between the llr and the 202 states. In the ground state the separation is about 1136 MHz, the 2,,2 state being higher. It is interesting to note that the A constant increases with excitation of the v4 mode and the Stark effect tends to be more negative on going from the ground state to v4 and then to 2~4 [the observed Stark coefficient is -5.02, -9.4’1, and -34.5 for the ground, v4, and 2~4 states, in units of 1c5 MH~/(v/cm)~]. The Stark effect becomes positive in the 3~4 state, which means that the 111level is higher than the 202level in this state. This sort of correlation between the A constant and the Stark effect facilitates searching for the 111~ OOotransitions in other excited vibrational states as well. Unfortunately, for the VTstate the 111t 000 line is overlapped by a strong line, but the Stark component is observed, because the Stark coefficient is negative and large c-32.0 X 10m5 MHz/ (V/cm)2]. Because of Stark mixing two forbidden transitions, 2,n t 0~ and 2r1+ 111, are made allowed at finite Stark fields, by borrowing intensities from 111t 000 and 211+ 202, respectively. In fact, such transitions were observed for the ground and the v4 states. Recently, Kawaguchi and Tanaka (10) observed the vg band of methylene fluoride by laser Stark spectroscopy. The transitions they observed involve levels which are nearly degenerate with others, like lrr and 202 discussed here. The assignment of lrr + 000 for a particular vibrational state was checked by observing the 303 +- 212 transition, which exhibits three well-resolved Stark components. Higher J, P, or R branches show only barely resolved or unresolved Stark lobes, but were measured for confirmation of the assignment and also for precise determination of the centrifugal distortion constants. All the observed transitions were subjected to a least-squares analysis, by using a Hamiltonian described in detail in the previous paper (1). Because the Hamiltonian includes only the first-order centrifugal distortion terms, the observations were limited to the J value of 20. Each vibrational satellite was analyzed separately. For v3 and VQ a first-order centrifugal distortion treatment is not satisfactory, and an effective Hamiltonian comprising the two vibrational states was used.
MICROWAVE
SPECTRUM
413
OF CH2F4
RESULTS
Ground, v4, ZV+ 3v4 states. Table III summarizes ground and the v4 states. The molecular constants, TABLE Observed and Calculated
Frequencies
1.
1
-
1, 2,
1, 1, 0, 2, 2. 1, o, 2, 2, 1, 0, 2, 2, 1, 1, 2, 3, l,
0
-
1 3 l-3,‘ 0 2 4 2 l 3 5 3 2 4 5 3 ; 1
.3. 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, ;>
3 6 6 5 4 7 8 6
7: 6, 7, 8, 8, 7, 7, 9,
2: 2:
2: 1, 3, 7, 7, 7,
1, 3, 3, 78: 1, 1, !* 3, 8: 9, :: 10, 2, 10, 1, 11, 2. 11, 2: lo, 4; lo, 4, ll, 1, 12, 2, 12, 2, 11. 11; 1: :I :;, 12: 12, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15,
-
0. 1; 2, 2,
$ 8 10 9 16 7 6 11 10 11 8 12 7
I ;, - 9: - 9, - 10. - 10: - 11; -11, - 10, - 11, - 11, -12, - 11, 12,
2, 12
- 12,
? 1: 2, 3, 1, 5, 5, 3, 3, 1, 5, 5,
I:;> - 12: - 13, - 13, - 13, - 15, - 15, - 14, - 14, - 14, - 16, - lb,
:zS 16: 1: :* lb, 16, 5, lb, 5, 17, 1, 3,
; 13 13 11 14 10 9 12 13 15 11 10 16 :: 12 11 l5 17
:'B, 4, 14 1s: 4, 15 18, 1, 18 4, 15 :z, 4, 16 18: 6, 13 18, 6, 12 19, 20, 20, 19, 19.
Ground
J",K_;,K+;
1.
0.
0
0; 0, 1,
l 2 2 ^
1, o, 2, l, o, 2, 2, 2, o, 2, 2, 2.
5 z
2, 3, 2, 3, 3, 3, 3, 2, 3,
2 2 5 7 6 7 6
6 7 ; ; ; ;
:: l: 2, 9 ? l: 3: 11 2. 10
;;
2: 4, 4. 4; 4, 2, 4, 4, 4, - 15, 4, 2, - 17, 4, - 17, 4, I ;;, 4, 2, - 17: 5, - 17, 5, - 17, 2, - 18, 5, - 18, 5, - 19, 5. - 19, 5; 2, 5, 5,
11 ;; 11 12 11 10 12 12 13 12 11 13 13 14 12 14 13 12 15 14 13 14 15 16 15 14
:: :z
III
of l*CHzFz in the Ground and the ~1 State (MHz)
TI-8.tXitX3Il J',K_i,K+i -
the observed transitions in the which are derived, are listed in
atate
"ohs 58 39 41 22 54 62 43 43 31 45 46 65 8 29 50 15 14 55 53 58 39 61 31 38 64 11 9 20 21 14 30 38 15 53 54 37 64 32 $1 i4 42 48 10 14 44 63 11 44 51 52 34 24 43 30 31 58 44 3;
792.098 852.549 282.677 204.183 033.161 196.649 433.373 761.213 543.750 262.944 420,813 695.730 439.239 268.534 342.841 253.722 364.419 312.309 685.951 044.683 501.034 446.773 763.670 956.637 259.415 452.622 091.401 237.586 980.475 417.298 679.093 812.624 633.552 125.242 806.717 400.828 104.958 507.747 974.150 ij5.837 040.860 455.971 365.824 772.429 542.528 291.395 810.708 895.885 758.265 7i2.966 fZ73.iii 760.332 133.486 962.080 897.919 1?9.115 155.747 ;$.;;;
11 63 33 11 9 25 33 29 50 50 16 55 50 29 29
4X3:769 173.042 563.230 430.306 097.145 974.350 159.214 624.489 004.809 180.929 700.568 353.168 127.912 339.007 630.720
ObS-CalC 0.019 0.046 -0.057 -0.017 -0.024 -0.140 0.068 0.111 -0.072 O.cll2 0.068 0.069 -0.041 -0.005 0.040 :.:;: 0:053 0.048 -0.041 0.041 -0.055 0.026 0.051 0.017 0.092
0.007 0.025 -0.064 -0.005 -0.013 0.048 0.062 -0.167 0.092 -0.034 -0.094 0.088 -0.024 0.005 -0.082 0.016 0.092 0.022 0.048 0.036 -0.062 0.047 0.072 -0.255 -0.053 0.002 -0.064 -0.028 0.115 -0.152 0.070 0.066 -0.020 0.076 -0.156 -0.036 -0.045 -0.028 -0.039 0.09l 0.030 0.102 0.051 0.034 0.166 -0,022 -0.056 -0.056
“4
state
'ohs
obs-talc
58 40 41 21 55 63 43 43 32 46 46 65 9 30 50 13 15 55 55 60 38 61 33 41 62 9 11 22 20 12 28 36 13 56 57 35 61 29 35 37 39 45 13 18 41 6;
696.419 263.548 665.244 689.448 260.091 492.213 833.820 205.837 803.583 637.794 846.147 103.464 726.733 730.426 800.704 943.843 922.201 811.071 870.963 262.526 173.345 996.070 987.787 234.985 918.602 k71.198 348.799 579.220 068.652 133.495 621.636 509.622 153.607 262.560 954.886 181.828 790.714 951.178 156.923 956.859 643.494 816.028 590.555 026.531 948.431 w&.;;;
42 55 56 31 21 40 35 36 55 40
087:074 837.710 405.958 377.812 398.299 091.972 089.137 030.350 016.909 737.408
-0.135 0.084 -0.081 0.089 -0.017 -0.012 -0.027 0.058 -0.032 0.024 0.029 0.148 0.045 0.011 0.066 0.105 0.117 0.003 -0.036 -0.022 0.023 -0.001 -0.119 -0.033 0.064 -0.128 -0.062 -0.064 0.084 0.067 -0.024 -0.058 -0.168 -0.091 -0.055 -0.062 -0.102 -0.029 0.092 -0.018 0.165 0.036 0.077 0.118 0.038 0.016 0.024 -0.025 -0.004 0.013 -0.056 0.085 -0.011 -0.063 0.129 -0.114 0.015
14 15 59 30
092.133 600.152 696.395 003.011
0.027 -0.001 -0.063 -0.014
22 28 25 55 55
129.646 901.813 346.547 020.273 197.019
-0.006 0.133 0.016 0.242 -0.018
51 45 34 34
057.892 802.227 402.124 695.236
0.029 -0.047 -0.132 -0.126
414
EIZI
HIROTA
TABLE Rotational
Constants
and Centrifugal
IV
Distortion
Ground and ~1 States
Constants
of WHIFI
Ground state Ref. A
(5)
Ref.
49 142.770(85) 10 604.692(20) 9 249.836(16)
B i: Taaaa 'bbbb Tcccc
in the
(MHz)a v4state
present
(5 )
present
49 142.834(44) 10 604.747(10)
49 142.818(18) 10 604.7050(44)
9 249.807(E)
9 249.8437(33)
49 480.557(19) 10 582.8371(49) 9 216.6002(36)
-2.3049(41) -0.06064(91) -0.02653(71)
-2.3156(27) -o.o6095(47) -0.02672(l)'
-2.30061(77) -0.06151(18) -0.02723(13)
-2.38610(87) -0.06100(21) -0.02690(16)
0.170(12) -0.03648(99)
0.1684(59) -0.03683(47)
0.1575(23) -0.03756(19)
0.1568(28) -0.03682(23)
a. Errors are the standard deviations. b. ~~~~~~~~~ + [(A-B)/(A-c)IT~~~~~and ~~~~~~~~~ + C(B-c)/(A-c)~T,,,, c. The standard deviation given in Ref. (5) seems to be too small.
Table IV. Most ground state transitions reported earlier (4) were remeasured more precisely. Thus, the ground state values are more accurate than those reported in Refs. (4 and 5). Table V shows the observed transition frequencies and the derived molecular TABLE
V
Observed Transition Frequencies and Molecular Constants in the 2~4 and 3~ States (MHz)* Transition
2v>,
- J",K_jl,K+y
J’,K_i,K+i
" 0tJs 996.521 633.678 048.849 172.928 481.984 793.621 238.335 640.834 057.106 024.359 279.565 509.554 272.276 331.266
-0.060 0.071 -0.099 0.027 -0.216 0.056 0.002 0.002 0.150 0.043 -0.074 0.095
59 41 42 20
1, 1, l, 0, 2, 2, 1, 0, 2, 2, 1, 0, 1, 1,
1 0 1 3 1 0 2 4 2 1 3 5 4 5
- 0, - 1, - 2, - 2, - 3, - 3, - 3, - 3, -4, - 4, - 4, - 4, - 5, - 6,
0, 0, O, 1, 1, 1, o, 1, 1, 1, 0, 1, 0, o,
0 1 : 2 3 3 3 3 4 4 4 5 2
58 40 42 21 56 64 44 42 34 48 47 64 51 56
!: 7, 7,
3, 1, 1, 3,
6 3 6 5
- 6, 7, - 7, i:
2, 0, 2,
5 7 ;
62 486.277 36 861.137 62 576.126 36 203.212
'8, 3, > 1,
7 4
- 7, I
2,
6
61 522.751 43 597.083
A
B E Taaaa 'bbbb lcccg Tl T2b
3"1, obs-talc
1, 1, 2, 3, 2, 2, 3, 4, 3, 3, 4, 5, 5, 6,
of ‘“CHzFe
' Ob8 289.923 002.390 434.060 654.985
obs-talc -0.007 0.007 0.044 -0.004
44 648.825
0.041
35 298.270
-0.001
47 725.522 63 914.700
-0.143 0.005
-yl;:
56 884.807
0.101
-0:oso 0.034 0.015 -0.010
63 204.535
-0.039
-0.039 0.031
60 311.272
-0.001
49 815.676(49) 10 560.939(17) 9 181.533(15) -2.489(14) -0.0612(14) -0.0259(20) 0.125(17) -0.0358(15)
50 146.827(90) 10 539.192(87) 9 143.79(10) -2.72(10) -0.060(13) -0.027(11) -0.02(14) -0.056(13)
a. Errors of the molecular constants are the standard deviations. b. See Table IV for definitions.
MICROWAVE
SPECTRUM
415
OF CHzFz
TABLE VI Observed Transition Frequencies and Molecular Constants of 13CHzFzin the Ground and the Y( States (MHz+ Transition
1,
1,
1
l, 2, 3, 2,
l, l, o, 2,
o l 3 l
y> I
0,
, 0, o, > 1,
$9
I - 3,
ii B t ='aaaa 'bbbb lcccc b Tlb T2
"4 state
Ground state
K 1,K I, J'aK_i,K+i _ J 1, ’ -1’ +1
1,
y
; 2
'ohs
obs-Calc
"ohs
38 39 23 49 42 45 27 41 45
929.293 531.189 977.683 501.235 865.485 220.298 048.614 329.622 589.988 344.210
-0.041 -0.007 0.008 0.003 0.043 0.023 0.033 -0.053 -0.023 -0.005
57 38 40 22 51 42 44
25 49 54 46 51 43 61 32 22
829.095 458.021 684.892 710.757 569.383 950.048 151.065 622.587 083.267
%~ 0:010 0.090 I;:;$ -0.040 0.082 0.052
56
47 730.785(39) 10 606.137(14) 9 199.117(11) -2.241(13) -0.0638(12) -0.0290(17) 0.123(14) -0.0386(13)
abs-talc
231.882 901.395 360.045 987.720 087.677 621.668 495.042
-0.113 0.123 -0.022 0.032 0.048 -0.014 0.030
45 771.999
-0.032
49 55 48 53
920.263 190.726 888.610 784.102
0.034 -0.009 0.005 -0.042
61 710.659 34 898.498
0.001 0.028
48 067.173(64) 10 584.479(59) 9 165.404(37) -2.300(45) -0.0644(72) -0.0279(64) 0.103(77) -o.O392(63)
a. Errcr?.of the molecular constants are the standard deviations b. See Table IV for definitions.
constants in the 2vq and 3v, states. The rotational constants change almost linearly with the quantum number 04, and thus the effect of the Fermi resonance between 2v4 and v3 is small as in the case of CDzFz. The data on r3CHzFz in the ground and the v4 states are given in Table VI. In the previous paper (4) we determined the rotational constants in the ground state of 13CHzFz by fixing the centrifugal distortion constants to the values of the 12C species, whereas the present data allow us to determine eight molecular constants simultaneously. ~2, vg, vr, and vs. The observed transitions and the molecular constants derived from them are summarized in Table VII. The effects of the Coriolis couplings mentioned in Table II are apparent in the molecular constants. For example, the A constant in the VTstate is larger than the ground state value by about 750 MHz, which is mainly due to the Coriolis interaction of this state with the vt state. The raaaa constant is also affected. v3 and vg. The observed transition frequencies listed in Table VIII were first analyzed separately for the two states. The results thus obtained are given in Table IX under the heading I. It is noted that the differences between the observed and the calculated frequencies, which are given in Table VIII, are larger than those in other vibrational states. Furthermore, when we calculate the frequencies of next higher J transitions such as 634+ 725 and 633+ 726, they differ from the observed values by 4-26 MHz. This observation indicates clearly that the treatment used on the other states is not
416
EIZI
HIROTA
TABLE Observed Transition
Frequencies
VII
and Molecular
Constants
of WHtF2
in the
YP, ~5, ~7, and vs States (MHz)* TranSition J’,K_i,K+i
-
Vobs / obs-talc
J”,K_;,K+;
y2
1,
1,
1
-
0,
0,
1,
1,
0
- 1,
0,
39
2,
1,
- 2,
0,
40
3,
1,
- 3,
0,
42
4,
1,
- 4,
0,
45
5,
1,
- 5,
0,
49 53
0
“5
-0.098
“2:FTi 40 847:406 0.023
0.013 49 308.411 -0.063 53 932.088 0.001 59 630.454 0.003 22 65;JD4'
6,
1,
- 6,
0,
7,
1,
- 7,
0,
3,
0,
3
- 2,
1,
2
4,
o,
4
- 3,
1,
3
5,
o,
5
- 4,
1,
4
7,
1,
6
- 6,
2,
5
8,
1,
7
- 7,
2,
6
2,
2,
1
- 3,
1,
2
64 283.832 -0.020 53 '";A;;
2,
2,
0
- 3,
1,
3
60 89;:;(;; 60 773.647
3,
2,
2
- 4,
1,
3
3,
2,
1
- 4,
1,
4
43 "?;A;
6,
3,
4
- 7,
2,
5
52 214:567 -0.019 56 036.363 0.001
59 22 624.155 0.037 44 182.222 0.042
6,
3,
3
- 7,
2,
6
7,
3,
4
- 8,
2,
7
48 ‘;;.;U;
a
10 6;7:912 to.022
E
9 34;.;;t _.
~cccc Tlb T2b
a.
Errors
b.
See
43 570.112 0.085 51 957.721 -0.001
58 40 739.450 0.020 42 238.944 41 401.396 -0.007 0.030 44 '"yu; 43 749.881 0.111 47 7961370 47 022.328 0.010 -0.127 52 51 333.820 0.105 "'vz 57 4531625 56 813.519 0.024 -0.070 64 63 594.289 "E.',',; 0.013 21 2771552 22 081.400 -0.049 0.097 42 858.594 43 ""::;g -0.014 64 829.564 65 591.626 -0.059 -0.005 37 861.639 40 421.922 -0.053 0.614 62 878.358 65 442.064 0.003 0.000 56 367.114 53 823.225 0.013 -0.010 65 163.752 62 699.675 -0.017 0.075 33 765.809 -0.026 48 554.692 -0.123 57 53 530.207 0.010 7x43; 62 73;:;;; 58 671.068 -0.007 43 839:022 39 "';A;: -0.095
VII-Continued
A
'bbbb
“yx;
64 480:496 0.030
-0.072
TABLE
Taaaa
44 201:877 -0.024 39
‘8
v7
58 208.478 -0.005 39 '"y;:
58 294.148
48 876.621 to.039 10 604.055 io.013 9 332.448 to.012
-2.247 to.016 IO.0593 ~0.0020 -0.0454 to.0025
-2.300 io.012 -0.0644 +0.0013
0.377 +0.024 IO.0359 +0.0022
0.457 to.014 -0.0254 +0.0013 _
$W~ _ .
49 893.532 49 o:;.;;,’ +0.058 10 6y2.860 10 608.340 to.017 to.019 9 153.129 9 l~F&~%~ to.017 _ .
X: IO.0660 ~0.0014 -0.0144 ~0.0020 -0.079 +0.017 -0.0212 +0.0016
of the molecular constants are the standard deviations. Table IV for definitions.
-2.327 +0.011 IO.0652 +0.0015 IO.0097 +0.0017 10.046 +0.016 IO.0411 +_0.0015
MICROWAVE
SPECTRUM TABLE
417
OF CHoFz
VIII
Observed and Calculated Frequencies of “CHZFZ in the ~8 and VPStates (MHz)
Transition
"' 3
J',K_i,K+i- J",K_;,K+;
'ohs
" Ia
IIb
'ohs
I=
1, 1, 2, 3, 4, 5, 6, 7, 8, 3, 4, 5, 7,
1, 1, 1, 1, 1, 1, 1, 1, 1, 0, o, o, 1,
1
-
0,
0,
0 1 2 3 4 5 6 7 3 4 5 6
-
1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 6,
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2,
0 1 2 3 4 5 6 7 8 2 3 4 5
57 3% 40 41 44 47 51 56 62 23 44
8, 2, 2, 3, 6, 6, 7,
1, 2, 2, 2, 3, 3, 3,
7 1 0 1 4 3 4
-
7, 3, 3, 4, 7, 7, 8,
2, 1, 1, 1, 2, 2, 2,
6 2 3 4 5 6 7
64 067.795 51 603.492
a.
Ohs.-talc. obtained using the molecular constants I of Table IX. Ohs.-talc. obtained using the molecular constants II of Table IX. Not included in a least-squaresanalysis.
b. c.
714.812 861.364 014.692 791.997 248.546 456.596 501.339 475.836 473.217 185.320 603.57%
39 993.01%
40 821.805 49 408.588 52 496.236
-0.366 0.421 0.264 0.270 0.072 -0.103 -0.274 -0.319 0.248 -0.26% 0.485
-0.554 -0.600 -0.858 -0.925 -1.095 -1.067 -0.826 -0.317 0.70% 1.211 0.669
57 678.389
-0.186 -0.775
41 307.500 43 779.712
-0.166 -0.04%
0.031 0.256
47 230.694 51 783.910 57 578.03%
0.152 0.20% 0.203
0.574 0.744 0.832
64 749.842
-0.138
0.543
21 691.418 43 101.409
0.281 0.005 -0.267 0.241 -0.131 0.421 0.049
-0.508 -0.465 0.002 -0.262 -0.837 -0.234
64 -0.172 40 0.289 0.576 65 -0.470 1.925 53 63 0.272 1.777 46 (26.201)' -0.885 53 C-24.156)' 0.392 59 40 -0.485
IIb
897.159 445.162 481.979 666.742 000.937 841.032
0.697 0.820 -0.359 561.774 ('-17.816)'2.042 (4.234)'-1.270 256.394 683.050 (lo.146)c-2.879
enough to account for the v3 and vgspectra. Therefore we also analyzed them simultaneously by using a two-dimensional effective Hamiltonian. The results thus obtained are designated as II in Table IX. The agreement between the observed and the calculated frequencies are not as good as in the case of I for the lines in common. However, in II several lines which could not even be inchrded in I are used. The somewhat poorer fit of II for the common lines may be partly due to the fact that we fixed the centrifugal distortion constants to the ground state values. For example, the T,,.= constant in v1 would be more positive because of Coriolis coupling with vr. We thus assumed a value of -0.8087 MHz for this constant, but obtained a result which was slightly less satisfactory than II in Table IX. In conclusion, the Coriolis interaction between va and vg is not strong enough to allow simultaneous determination of C*s, C*g, D, and va-vg, but is too strong for the independent treatment of the states to be very satisfactory. It is to be noted that P3 + O”/(Q - vg) and Pg - LY/(va - vg) agree respectively with cS and cg of I within 2 MHz. v3 i- ~4, vq + VS,v4 + VT,and v4 -I- vg.Table X summarizes the transition frequencies observed for the four combination states v4 + vs (s = 3, 5, 7, and 9). Because the number of the observed transitions was small, most of the centrifugal distortion constants were fixed either to those of the v8 states or to those of the ground state. The standard deviations attached to the constants of v4 + VT are abnormally small and probably result from a statistical accident. For v4 + vg the 11~t OoOtransition could sufficient
418
EIZI HIROTA
not be observed, and thus the B constant was fixed to a calculated value. For comparison
Table X also lists the rotational constants, which were calculated from those of the fundamental states. Discrepancies, if any, might be due to the fact that the effects of Coriolis interactions change on going from the fundamental states to the combination states. DISCUSSION
The rotational as well as the centrifugal distortion constants, which are listed in Tables VII and IX, indicate clearly the presence of Coriolis couplings between v3 and ~7, v2 and vs, v3 and vg, and v5 and ~7. As pointed out in Ref. (I) we may estimate roughly the Coriolis coupling constant and the vibrational energy difference between the two vibrational states by using changes of the rotational and the centrifugal distortion constants upon excitation of the normal modes. Our approximation requires that the changes of the molecular constants are of the same magnitude, but opposite in sign for the two states: AA = AA, = -_A,#
and AT = - (AT....)~ = (A7aaaa)s* in case of the
u-axis interaction. We may thus calculate
TABLE IX Molecular Constanti of l*CHlFp in the YQand vpStates (MHz)a
II
E C"
48 287.08(35) 10 549.54(13) 9 428.38(15)
9 261.2(95)
Taaaa Tbbbb Tcccg
-0.81(26) -0.045(12) -0.293(11) 4.44(11)
[-2.30061
*lb T2
-0.303(58)
C-O.03761
t
'bbbb Leg *lb *2 D F
v3-v9
b.
C-O.06151 C-O.02721 co.15751
48 698.79(25)
48 704.26(44)
.10 531.112(76)
10 524.25(22)
8 980.550(88)
C" Taaaa
a.
48 295.44(51) 10 544.10(19)
9 147.3(96) -3.29(17)
C-2.30061
-0.1063(823 o.2369(81) -2.805(73) 0.051(27)
[-0.06151 C-O.02721 co.15751 C-O.03761 10
189.(336)
-116.(17) 628.3(78)x103
Values in parentheses are standard deviations, and those in brackets are fixed. See Table IV for feflnltions.
MICROWAVE
SPECTRUM TABLE
419
OF CHzFe
X
Observed Transition Frequencies and Molecular Constants of ‘*CH*Fz in the YI + YI, Ed+ ~5, ~1 + Y,, and ~1 + VPStates (MHz)8 Transition
vobs/obs.-talc.
J',K_i,K+i- J",K_;,K+1" 1,
1,
1 -
0,
0
1,
1,
0 - 1,
0,
0,
1
2,
1,
1 - 2,
0,
2
3,
1,
2 - 3,
0,
3
4,
1,
3 - 4,
0,
4 5
5,
1,
4 - 5,
0,
6,
1,
5 - 6,
0,
6
7,
1,
6-
7,
0,
7
a,
1,
7 - a,
0,
a
v3+v4
v4+v5
v4+y7
58 013.350 0.000 39 277.958 0.019 40 467.488 -0.119 42 301.450 0.053 44 837.567 0.072 48 151.112 0.027
58 502.832 0.000
59 355.127 0.000 41 106.932 0.000 42 612.592 -0.001 44 945.285
57 472.733 -0.099 63 67;:;;;
48 645.900 to.057
o.ooi
46 099.730 48 191.936 -0.003 -0.000 49 802.631 -0.053 54 485.555 0.102 60 2~',:;;5
49 2e$;65;
- .
lo 53,;.;;8' 10 581.442 *0.076 9 367.799 '0.057 c-2.3181 C-1.2331 c-0.0601 [-0.0601 -0.1626 c-o.34131 *0.0011 b T1b T2 A (calc.jC B (calc.)C F (calc.)C a.
b. c.
CO.1761 C-O.03621 48 624.82 10 527.68 9 395.13
50 231.828 to.001 10 589.582 to.002 9 124.164 to.001 L-3.4051 C-O.6211 -0.0521 to.0002
CO.1761 [-0.03621 49 214.360 10 582.187 9 299.204
LO.1761 L-O.03621 50 231.271 10 590.992 9 119.885
v4+v9
40 056.968 0.120 41 "'X 44 OS:435 0.022 47 467.728 0.010 51 952.240 -0.002 57 655.691 0.023 64 713.600 -0.012
49 040.445 io.094 cl0 509.8371 a 9;;.;;; -. L-2.3181 c-o.05791 0.1481 eo.0018 CO.1761 [-0.03621 49 036.53
Errors of the molecular constants are standard deviations. Values in brackets are fixed. See Table IV for definitions. Calculated from the constants in the fundamental states.
18.8w and AE,,l by A /{.,,,‘“’ / = (AA3/A7)+, A&.# = 4A@/Ar.
(la) (lb)
Table XI summarizes the molecular constants for four pairs of states, which are pertinent for the present discussion. They satisfy the conditions required for the approximation within about lOye, except AC of va and v8. The Coriolis coupling constants and vibrational energy differences, which are calculated from them by using Eqs. (I), are compared in Table XI with the values reported in Ref. (2). Agreement is not as satisfactory as in %D2Fz (I), and discrepancies are probably due to contributions of terms other than the Coriolis terms. However, the latter terms are obviously the most dominant in rotational-constant changes in these states. A subsequent paper will deal with detailed analysis of the rotational constants in excited vibrational states.
420
EIZI HIROTA TABLE
XI
Coriolis Coupling Constants and Vibrational Energy Differences in reCHsFzs State AA(MHz)
A~~~~~(Mfiz) %,s' (a) -1.49 1.491 -1.49
State
AT~~~~(MHz)
AC(MHz>
3
94.801
.B.
-114.288 104.545
z3
178.534
a9.
-269.294 223.914
82.604
z5 ai;.
0.380 (0.390) ") 58,s
The
I”
Corlolls
-1 AEs,s'fern f
0.864
(0.788)
81.5 (73.0)
0.704 (0.622)
25.2 (23.1)
0.266 -0.2641 0.265 0.0158
-96.715 89.660
Values
-57.8
(-64.7)
0.0182
-0.0175 0.0179
-0.0128 0.0143
0.768 (0.728)
a.
AE S,S'(cm-11
75.0 (84.1)
parenthesesare taken from Rd.(2). coupling constantsare recalculated. ACKNOWLEDGMENTS
The author would like to thank Dr. J. J. Drysdale for providing us with a sample of methylene fluoride. He is also grateful to Professor R. F. Curl for reading the manuscript. The calculation in the present work was carried out at the Computation Centers of Kyushu University and Nagoya University.
RECEIVED:
August
15. 1977 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
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