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Microwave spectra of the ground vibrational state of formaldehyde substituted with 17O and 18O
JOURNAL
OF
MOLECULAR
SPECTROSCOPY
Microwave Spectra Formaldehyde
80,
307-319 (1980)
of the Ground Vibrational State of Substituted with 170 and 1801
DANNY T. DAVIES, RICHARD J. RICHARDS, AND M. C. L. GERRY Department
of
Chemistry,
The University of British Columbia, Vancouver, B. C. V6T I W5, Canada
2075 Wesbrook
Mall,
Pure rotational transitions in the ground vibrational state have been measured for H,YYO, H,*2C*70, H,*3C1B0, and H,W”O in the frequency region 8-75 GHz, These have included both Q- and R-branch transitions, and have permitted accurate evaluation of rotational constants and several quartic centrifugal distortion constants for each species. These in turn have permitted the prediction of several transitions of possible use in radioastronomy. INTRODUCTION
The microwave and millimeter-wave spectra of formaldehyde, in several isotopic forms, have been the subjects of a large number of studies (1). Several reviews have appeared summarizing much of the work (2,3),but new measurements continue to be made. The spectrum, particularly that of the most abundant isotopic species in its ground vibrational state, has been subject to increasingly refined analysis. In 1978, for example, several new measurements were reported for various isotopic species in their ground vibrational states, along with a study of a Coriolis resonance between y4 and vg excited states (4). That year also saw the publication of an extensive analysis combining microwave data with averaged combination differences from five infrared bands (5). Most recently, a rather detailed and complete set of constants for HzlsC1sO and H,13C160 has been published (6). This paper is concerned with the microwave spectra of species containing I70 or l*O. Even though some transitions of two of these, H,1%17O and H21*C180, were reported earlier, the observed spectra were not extensive. For H212C170, five Q-branch transitions, having K, = 1 and 2, have been very accurately measured (7), yielding, besides (B, - C,), accurate values for 170 quadrupole and magnetic coupling constants. There has been, however, no report of any R branches. For H212C180, rather more lines have been reported, including R branches (3, 4, 8-12), but these spectra, too, are not extensive. ’ This work is taken from the B.Sc. theses of Danny T. Davies (1977) and Richard J. Richards (1978), The University of British Columbia. It has been supported by the National Research Council of Canada.
307
0022-2852/80/040307-13$02.00/O Copyright All rights
8
1980 by Academic
of reproduction
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in any fom
Inc. reserved.
308
DAVIES,
RICHARDS,
AND GERRY
Furthermore, many of the early measurements, which were made using labeled species in natural abundance, have been found to be rather inaccurate. One was used in the recent analysis of the spectrum of H,‘V*O by Dangoisse er al. (4), and tends to reduce the value of their analysis, in spite of the inclusion of their own more accurate measurements. The microwave spectrum of formaldehyde is of interest, not only because it gives much structural information about a relatively simple molecule, but also because it has been used to detect this molecule in interstellar space. In particular, three isotopic species, H212C160, H213C60, and H,‘VBO have been found by radioastronomical techniques (1, 13 -15) and an unsuccessful search for H,Yi70 has also been carried out (15). Nevertheless, formaldehyde can be considered a combination of H2 and CO, the two most abundant interstellar molecules. For CO, in particular, several isotopic species have been observed, including substituted =C’60 ) 12C180 and 12C170 (1, 13), so that further isotopically species of formaldehyde remain potentially observable. In the present paper we report the spectra of the species HZIY?*O, H1’V’O, HZ13C1*0, and H213C170, the last two for the first time. In all cases, in order to increase line intensities, artificial substitutions of 13C, 180 and l’0 were made. Both Q and R branches were observed for all four species, and have been analyzed for rotational and centrifugal distortion constants. Predictions of frequencies of several unmeasured transitions, which may be of interest to radioastronomers. are also included. EXPERIMENTAL
METHODS
Formaldehyde enriched with 170 and l*O was prepared by exchange with isotopically enriched water. Initially paraformaldehyde, either as its normal species or 90% enriched with 13C, was depolymerized by heating, and the resulting formaldehyde was collected at liquid nitrogen temperature in a trap containing 5 A4 HCl in isotopically enriched water. In this mixture the formaldehyde not only underwent isotopic exchange, but also repolymerized. After the water had been pumped off in vucuo, the polymer was reheated and the labeled formaldehyde collected in a storage vessel. Isotopic enrichments ivere -10% 170 and -20% I*O. Microwave spectra were obtained using a conventional lOO-kHz Starkmodulated instrument in the frequency region 8-75 GHz. The regions 8-18 and 26.5-40 GHz were covered using a Hewlett-Packard 8400C Microwave Spectroscopy Source. At K band (18-26.5 GHz) an appropriate OK1 Klystron was used. Microwave power above 60 GHz was obtained by doubling the frequency from the Hewlett-Packard Source. Most transitions were measured at room temperature, though occasionally for those lines at low J and K, the measurements were made with the cell cooled with dry ice. Estimated accuracy MHz below 40 GHz and -+-0.1 MHz of the measurements is -20.05 above 60 GHz.
309
SPECTRA OF H,VsO AND H,C”O TABLE 1 Check of the Fitting Procedure Used by Comparison of the Constants Obtained for H,‘V60 with Those of Winnewisser et al. (6) parametera A
Present Workb 281 968.7 (13)'
Wlnnewisser __et al (6). 281 970.72 (18)
B
38 836.066 (48)
38 836.0456 (9)
C
34 002.204 (48)
34 002.2034 (8)
AJ x 10' gK A~ $ x 103 &K
7.57 (30)
7.5295 (14)
1.2918 (60)
1.29051 (24)
19.424a
19.424 (5)
10.434 (23)
10.4568 (6)
1.0307 (21)
1.02603 (17)
a In the present work AK and the sextic coefficients were held fixed at the "Microwave + Optical" values of reference (6). b
12 18 A data set as close as possible to that of Ii2C 0 was used in this analysis.
' All constants are in MHz. Numbers in parentheses are 95 percent confidence limits in units of the last significant figures.
RESULTS AND ANALYSIS
Between 9 and 18 rotational transitions have been newly measured in the present work for each of the four isotopic species. Hyperfine structure due to I70 was observed in many of the transitions of molecules containing this isotope; this could be entirely accounted for, for both H,‘V70 and H213P70, using the I70 quadrupole and magnetic coupling constants of Flygare and Lowe (7), and no attempt was made to refine these constants. The spectra of each isotopic species were analyzed for rotational and centrifugal distortion constants, using Watson’s Hamiltonian for the I’ representation in its A reduction (16). For the 170-containing species the hyperfine structure had been previously subtracted off. Since the data sets used were rather small, and only a few different branches were measured, it was necessary to assume values for some distortion constants. In the initial analyses, for H212C*80, the constant AK was very poorly determined, and was essentially perfectly correlated with aK. Because its contribution to the transition frequencies was, on the other hand, quite significant, and ignoring it would distort the obtained values for the other constants, its value was fixed for the Y-containing species at 19.424 MHz, and for the 13C-containing species at 19.499 MHz, as found by Winnewisser et al. (6). Because it is dependent on the moment of inertia about the symmetry axis, which is essentially the same for all species studied here, this approximation is reasonable. Contributions due to sextic constants could also have been expected to be significant, but none of these were well determined from the present data; to preserve consistency between the various isotopic species the sextic constants
1.2658 (33)
13
2.6
6.6
22
0.98264(40)
9.8430(92)
1.03078(21)
10.4344(23)
1.29183(60)
7.574(30)
26
4.2
o.94538(15)
9.1218(14)
1.1810g(38)
6.861(19)
14
3.4
0.98681(19)
9.6350(11)
1.256gl(31)
7.205(15)
9
4.6
0.9358g (65)
8.9044(80)
1.18321(34)
6.8e
32413.03414(49)
36776.85586(49)
281995.23(28j
H213c170b.c
"Microwave
+
Opticsi" values of ref.
(6).
11
4.5
0.90266(53)
8.312g (69)
1.127g2(30)
6.5=
31698.86363(47)
35859.25637(47)
281984B5 (26)
H213C180b
12 18 g These fits were performed using a data set as close as possible to that of H2 C 0, and are presented for comparison purposes only. A complete set of constants is in ref. (a).
f Standard deviation of the fit.
e Held fixed in the analyses. See text.
d Numbers in parentheses are 95 percent confidence limits in units of the last significant figures of the numbers on the line. Subscript numbers are required for frequency predictions.
'170 hyperfine constants as in ref. (I?.
b~K and sextic coefficients held fixed at the ~~13~160
aAK and sextic coefficients held fixed at the H212C160 "Microwave + Optical" values of ref. (5).
Number of TransitionsI
SDFITfx102
6K
bJX103
AJK
$x102
33213.99163 (25)
32511.53562(30)
34002.20408(48)
C
37811.09962(24)
36904.18116(30)
H213C160boz
38836.06574(48)
H212C180s
281993.167(11)
B
Ii2 12c170s,c
281959.665(9)
d 281968.740(13)
12 II* c160a,g
A
(MHz) Parameter
Derived Rotational and Centrifugal Distortion Constantsa of Various Isotopic Species of Formaldehyde
TABLE II
311
SPECTRA OF H,VBO AND H,C”O TABLE III Measured and Predicted Transition Frequencies TransitIon
Observed Frequency
(in MHz) of H,12C’s0 Calculated Frequency
R-Branches l(O,l) 2CO.2) 2(1,2) 2(1,1) 3(0,3) 3(1,3) 3(1,2) 3(2,2) 3(2,1) 4(0,4) 4(1,4) 4U.3) 4c2.3) 4(2;2) 4(3,2) 4(3,1) -
69 415.44 138 770.90a -_
O(O,O) l(O,l) l(l,l) lU,O) 2(0,2) 2(1,2) 2(1,1) 2(2,1) 212,O) 3(0,3) 3(1,3) 3(1,2) 3c2.2) 3(2;1) 3(3,1) 3(3,0)
-208 006.44a
-_
214 208 208 277
77a.4ga 211.42a 444.63a 062.58a.b
286 277 278 277 277
2;;.96a*b 562.78=3b 145.36aab 675.36a>b 677.9ga8b
4 13 26 43 65
3a8.7969ae 165.95491e 330.17 a7a.07a 803.08
69 138 134 143 208 201 214 208 208 277 268 286 277 278 277 277
415.442 (53)d 770.898 (66) 435 937 (66) 213.093 (66) 006.470 (65) 614.283 (52) 778.442 (51) 211.399 (58) 444.670 (58) 062.65 (27) 745.77 (25) 293.69 (25) 562.71 (22) 145.36 (22) 674.95 (25) 677.85 (25)
4 13 26 43 65 92 122 157 12 18 28
388.797 165.953 330.111 878.027 803.123 093.567 729.89 682.16 107.081 905.551 120.183 0.484 3.384 13.531 744.396 689.013 971.370 901.850 824.281 701.702 267.217 892.679 312.789
Q-Branches l(l,O) - l(l,l) 2U,l) - 2(1,2) 30,2) - 3(1,3) 4(1,3) - 4(1,4) 5U.4) - 5(1,5) 6C1.5) - 6(1,6) 7c1.6) - 7(1,7) 8(1,7) - E(1.8) 8(2,6) - a(2,7) 9(2,7) - 9(2,8) 10(2,8) - 10(2,9) 3(3,0) - 3(3,1) 4(3,1) - 4(3,2) 4(3,2) - 5(3,3) 15(3,12) - 15c3.13) 16(3,13) - 16c3.14) 17(3,14) - 17(3,15) 18(3,15) - 18(3,16) 19(3,16) - 19(3,17) 24(4,20) - 24(4,21) 25c4.21) - 25(4,22) 26(4,22) - 26(4,23) 28(4,24) - 28(4,25)
a Dangoisse --9 et al b
-12 107.08 18 905.52 28 120.11 0.4845C 3.384OC 13.531oc 8 744.37 12 689.02 17 971.47 24 901.85 33 824.30 9 701.71 13 267.21 17 892.62 31 312.80
8 12 17 24 33 9 13 17 31
(4) 03) (26) (43) (65) (94) (13) (18) (18) (27) (40) (0) (0) (0) (23) (27) (31) (39) (53) (45) (46) (45) (79)
ref. (4).
Not included in the fit.
' Chardon g &, ref. (11). d Numbers in parentheses are 95 percent confidence limits for the predicted frequencies. e Tucker et al, ref. (11). -
were also fixed, in the same manner
as A K, to the values of Winnewisser constants and four determined quartic distortion constants were in fact reasonable a fit was carried out to H212C160, using a data set as close as possible to that of H,12C1*0. Excellent agreement of the constants with those of Winnewisser et al. was found, as shown in Table I, implying that reliable, consistent constants could be obtained for the other species using this procedure. et al. (6). To check then that the resulting three rotational
312
DAVIES, RICHARDS, AND GERRY TABLE IV Measured and Predicted Transition Frequencies Transition F'-F"
Observed Frequency
(in MHz) of H,LzC170
Calculated Frequency (splitfingja
Relative Intensityb
R-Branches 1(0,1) 512 J/2 312
- O(O,O) - 512 - 512 - 512 I
2(0,2) 512 712 512 312 912 712 II2 512 312
71026.560 71026.56
2(1,1) 512 712 312 512 J/2 912 512 l/2 312
-
-0.15 -0.12 0.00 0.08
0.11 0.20 0.47 137452.81
S/2 512 512 312 J/2 312 J/2 3;2 712 -
-
lo,*) 312 712 312 712 512 712 512 312 512
0.33 0.44 0.22
141987.27 (10) -0.39 -0.28
- l(O,l) - 312 - J/2 - 712 - 312 - 712 - 512 - 312 - 512 - 512
2(1,2) - l(l,l) 312 512 712 li2 912 312 512 5;2 712
(52)d
-0.29 0.07 0.31
(17) 0.04 0.12 0.17 0.07 0.33 0.09 0.02 0.06 0.10
-2.56 -1.22 -0.92 -0.56
0.01 0.69 2.02 2.03 2.32
--
0.06 0.10 0.02 0.09 0.33 0.17 0.07 0.12 0.04
146639.85
(16)
-2.81 -1.57 -0.85 -0.68 -0.06 0.46 0.83 0.86 2.79
0.06
0.10 0.09 0.02 0.17 0.33 0.12 0.07 0.00
Q-Branches
l(l,O) 5/2 7;2 512 512 312 712 312 2(1,1) 712 712 512 512 912 712 S/2 312 912 3;2 l/2 l/2
- l(l.1) - 512 - 5;2 - 712 - 312 1 - 512 - 7/2 - 312 -
2(1,2) 712 S/2 J/2 512 712 912 312 512 912 lj2 312 l/2
(4593.250)e’f -3. 63Se -2.131 -0.404 -0.004 1.106 3.250 (13780.79)e -2.70Je -2.490 -1.895 -1.598 -0.748
-0.491 -0.266 0.363 1.565 2.953 3.420 --
4593.754 -3.643 -2.135 -0.399 -0.393 0.004
(10)
1.109 3.246
0.02 0.16 0.16 0.16 0.16 0.29 0.07
13780.790 (24) -2.781 -2.484
-1.889 -1.592 -0.748 -0.469 -0.256 0.371 1.565 2.957 3.414 4.605
0.12 0.09 0.09 0.03 0.06 0.06 0.08 0.08 0.27 0.05 0.05 0.02
SPECTRA OF H&?O
313
AND H,C”O
TABLE IV-Continued Transition F'-F" 3(1,2) - 3(1,3) 912 - 712 712 912 712 712 512 912 1112 5/Z 5/2 312 u/2 312 312 l/2 l/2
-
5(1,4)
7l2 912 9/2 I 512 712 1112 912 I 512 \ 312 512 1112 312 112 312 112 - 5(1,5)
1112 - 1112 13/2 - 11/2 1112 U/2 1312 912 912 912 1312 712 712 1512 512
-
6U,5) 1312 1512 1312 1312 1112 1512 1112 1112 912 912 1712 712
-
13;2 912 1312 lll2 912 712 1512 912 712 1512 512
Observed Frequency
Calculated Frequency (splitting) 275S9.607 -2.47
(27559.64)
(38) 0.05 0.16 0.09 0.05 0.05 0.05 0.03 0.03 0.05 0.04 0.04 0.25 0.03 0.03 0.03 0.02
-2.31 -2.25 -2.10 -1.43
27557.38 27558.19 27558.74
-0.89 -0.27 -0.24 -0.07 1.02 1.54 1.80 2.63 3.48 3.85 4.71
27559.42 27560.66 27561.18 27561.41 27562.22 27563.13 -27564.34 (68874.17) 68871.74
68874.184 -2.50 -2.27 -2.06 -2.02 -1.82 -1.61 -1.14 -0.17 0.03 0.33 1.30 2.03 4.01
68872.30 _-_--68875.50 68876.18 68878.16
96388.99 -2.52 -2.20 -2.12 -2.00 -1.74
- 6(1,6) 1312 1312 1112 1512 1312 1512 1112 912 1112 912 1712 712
-1.69 -0.13 -0.41 0.07 1.01 2.08 3.87
Relative Intensity b
(50)
0.14 0.02 0.02 0.02 0.18 0.02 0.11 0.02 0.03 0.02 0.09 0.23 0.08 (13)
0.15 0.02 0.02 0.02 0.02
0.18 0.12 0.02 0.02 0.10 0.22 0.09
-
Accordingly, this procedure was used for the 170 and ‘*O species. Minor variations, depending on the data set, were also required. For H,*2C180 our newly measured transitions were combined with the 2 + 1 and 3 + 2 R-branch frequencies of Dangoisse et al. (4); since the measurements were all given equal weight in the fits the less accurate 4 +- 3 R branch was not included. For the other three species, l,,, +- OoOwas the only R-branch transition measured, so AJ was also fixed. Since the rotational constants of H,12C170 and H,13C160 are very similar, they were assumed to have the same A,. AJ of the other 13C species was then scaled to those of the lzC species. Finally, for comparison purposes, the spectrum of H,13C160 was reanalyzed using a data set similar to that of H,13C1s0. The fitting procedure for the analyses was reported previously (17). A first-
314
DAVIES,
RICHARDS,
TABLE Transition F'_F" 7(1,6) - 7(1,7) 1512 - 1512 I.712- 1712 1312 - 1312 1112 - 1112 19;2 - 19;2 912
-
IV-Continued
Observed Frequency
--
912
6(2,4) - 6(2,5) 13/2 - 1312 1512 - 1512 u/2 - 1112 1 912 - 9/2 1712 - 1712 712 - 712
(4468.19je -0.220=
7(2,5) - 7(2,6) 1512 - 1512 1712 - 1712 1312 - 1312 t 1112 - 1112 1912 - 1912 912 - 912
(8015.28)e -0.308e
8(2,6) - 8(2,7) 1712 - 1712 1512 - 1512
c13292.39je -0.404=
1912
-
1912
t
1312 - 1312 2112 - 2112 1112 - Ill2
-0.140 0.080 0.195 0.360
-0.198 0.103 0.260 0.466
-0.246 0.104 0.348 0.599
9(2,7) - 9C2.8) 1912 - 1912 1712 - 1712 2112 - 2112 1512 - 1512 2312 - 2312 1312 - 1312 I
(20744.01)
10(2,8) - 10(2,9) 2112 - 2112 1912 - 19/2 2312 - 2312 I 17/2 - 1712, 2512 - 2512 1512 - 1512 1
(30830.44)
15(3,12) - 15(3,13) 3112 - 3112 29;2 - 2912 3312 - 3312 27/Z - 2712 3512 - 3512 2512 - 2512
(10068.97)
20743.65
20744.41
30830.01
30830.92
10068.97
AND GERRY
Calculated Frequency (splittine)
Relative Intensitvb
1213448.71(31) -2.52 -1.58 -1.49 0.81 2.11 3.78
0.15 0.18 0.13 0.12 0.22 0.10
4468.198 (12) -0.233 -0.155 -0.126 0.091 0.195 0.356
0.15 0.18 0.12 0.10 0.22 0.09
8015.308 (18) -0.314 -0.195 -0.187 0.098
0.266 0.466
0.15 0.18 0.13 0.12 0.22 0.10
13292.419 (22) -0.403 -0.256 -0.238 0.103 0.346 0.589
0.16 0.14 0.18 0.12 0.21 0.11
20744.013 (28) -0.50 -0.33 -0.28 0.11 0.43 0.72
0.16 0.14 0.18 0.13 0.21 0.12
30830.417 (42) -0.60 -0.41 -0.33 0.11 0.52 0.87
0.16 0.15 0.18 0.13 0.20 0.12
10068.949 (34) -0.14 -0.10 -0.07 0.01 0.12 0.20
0.17 0.16 0.18 0.15 0.19 0.14
order fit in a rigid rotor basis was made to the rotational and quartic centrifugal distortion constants. These constants, including those fixed in the analyses, were then used to predict the transition frequencies exactly. The difference between the exact and first-order frequencies was then subtracted from the measured values, and the procedure was repeated until convergence was obtained. The transition frequencies and results of the analyses for the four oxygensubstituted species are shown in Tables III-VI. These tables include, for H,12C180 and H212C170, some transitions measured previously but, for various
315
SPECTRA OF H,C”O AND H&i’0 TABLE IV-Continued Observed Frequency
Transition F'_,?" 16(3,13) - 16(3,14) 3312 - 3312 3112 - 3112 3512 - 3512 2912 - 2912 3712 - 3712 2712 - 2712
(14600.49)
17C3.14) - 17(3,15) 3512 - 3512 I 3312 - 3312 3712 - 3712 I 3112 - 3112 3912 - 3912 2912 - 2912
(20660.22)
18(3,15) - 18(3,16) 3712 - 3712 35;2 - 35/2 3912 - 3912 3312 - 3312 4112 - 4112 3112 - 3112
(28596.99)
Calculated Frequency (splitting)
Relative Intensityb
14600.484 (32) -0.17 -0.13 -0.09 0.02 0.15 0.25
0.17 0.16 0.18 0.15 0.19 0.14
14600.49
20660.06
20660.244 (28) -0.22 -0.17 -0.11
0.02 0.19 0.31
20660.37
28596.78
28597.21
28596.985 (48) -0.27 -0.20 -0.13 0.02 0.23 0.39
0.17 0.16 0.18 0.15 0.19 0.14 0.17 0.16 0.18 0.15 0.19 P.14
a Splittings of hyperfine components are given below the unsplit transition frequency. To obtain the transition frequency of the hypertke component the splitting value should be added to the unsplit line frequency. b Relative intensities of hyperhne components. p Observed frequencies in parentheses are hypothetical unsplit frequencies, used in the analysis for rotational and centrifugal distortion constants. d These are the unsplit line frequencies. Numbers in parentheses beside calculated frequencies are 95 percent confidence limits of the predictions. e Flygare and Lowe, Ref. (7). Hyperfine components are their reported observed splittings. f This transition was not included in the fit to the rotational and centrifugal distortion constants. There is apparently a misprint in Ref. (7).
TABLE V Measured Rotational Transition Frequencies
(in MHz) of H,Y1*O
Observed Frequency
l( 0. 1) 2( 1. 1) 5( 1, 4) 8( 2. 6) 9( 2. 7) ll( 2, 9) 13( 2,ll) 16( 3.13) 17( 3.14) 19( 3,16) 20( 3,17)
-
O( 2( 5( a( 9( ll( 13( 16( 17( 19( 20(
0, 0) 1. 2) 1, 5) 2, 7) 2, 8) 2.10) 2.12) 3,14) 3,lS) 3,17) 3,18)
67556.86 12472.78 62340.46 10837.12 16933.52 36057.48 66990.10 10741.85 15228.10 28733.24 38381.92
Calculated Frequency
67556.860(90)=
12472.765(26) 62340.463(88) 10837.106(38) 16933.455(S) 36057.546(64) 66990.083(88) 10741.870(58) 15228.092(60) 28733.226(51) 38381.928(80)
a Numbers in parenthesis are 95 percent confidence limits of the predicted frequencies.
316
DAVIES, RICHARDS,
AND GERRY
TABLE VI Measured Rotational Transitions (in MHz) of H,‘3C’70 in Its Ground Vibrational State Transition F'_F"
l(O.1)
- O(O,O)
512 712 312
-
712 712 512 512 912 712 512 312 VI2 312 l/2
-
2U,l)
512 512 512 -
5C1.4) 1112 1312 912 712 1512 512
-
Observed
Calculated Frequency
Frequency
(splitting)a
(69189.62)'
69189.620 (92)d -0.29 0.07 0.31
69189.62 I
(13079.63)
50,5) 1112 1312 VI2 712 1512 512
(65372.00) 65369.66 65370.12 -65373.38 65374.00 65376.02
65372.004 -2.50 -1.82 -1.14 1.30 2.03 4.01
(90)
27746.619 -0.60 -0.41 -0.33
(74)
13077.80 13079.20 13079.98 13081.23 13082.88
10(2,8) 2112 1912 2312 1712 2512 1512
10(2,9) 2112 1912 2312 17f2 2512 / 1512
(27746.58)
-
12(2,10) 2512 2312 2712 2112 2912 1912
- 12(2,11) 2512 2312 2712 2112 2912 1912
(54773.19)
-
13(2,11) 2712 2512 2912 2312 3112 2112
- 13(2,12) 2712 2512 2912 2312 3112 2112
(73485.35)
-
27746.59
-2.78 -2.48 -1.89 -1.59 -0.75 -0.47 -0.26 0.37 1.57 2.96 3.41
0.12 0.09 0.09 0.03 0.06 0.06 0.08 0.08 0.27 0.05 0.05 0.14 0.18 0.11 0.09 0.23 0.08 0.16 0.15 0.18 0.13 0.20 0.12
0.11
0.52 0.87
54773.20
54773.147 -0.78 -0.56 -0.41
(60) 0.16 0.15 0.18 0.14 0.20 0.13
0.11 0.67 1.12
73486.36
0.33 0.44 0.22
13079.611 (28)
2(1,2) 712 t 512 712 i 512 712 VI2 I 312 S/2 VI2 l/2 1 312
13076.97
Relative Intensityb
73485.367 -0.88 -0.64 -0.46 0.12 0.76 1.27
(86)
0.17 0.15 0.18 0.14 0.20 0.13
reasons indicated earlier, as well as in the tables, also present predicted frequencies of transitions unmeasured in the present work, but which may be of interest to radioastronomers. DISCUSSION
The derived rotational and centrifugal distortion constants given in Table II represent for H,12C180 and H,‘V70 a considerable improvement in accuracy over previously published values. For H,13CL*0 and H,‘3C170 they are the first values published. They can be expected to be reliable, in spite of the relatively
317
SPECTRA OF H.$?O AND H,C”O TABLE VI-Continued Transition F'-F"
Observed Frequency
Calculated (splittingja
15(3,12) 3112 2912 3312 2712 3512 2512
- 15(3,13) 3112 2912 3312 2712 3512 2512
(8567.12)
-
17(3,14) 3513 3312 3712 31/Z 3912 2912
- 17(3,15) 3513 3312 3712 3112 3912 2912
(17611.51)
-
19(3,16) 3912 3712 4112 3512 4312 3312
- 19(3,17) 3912 3712 4112 3513 4312 3312
(33158.60)
-
8567.150 -0.12 -0.09 -0.06 0.01 0.11 0.18
(64)
17611.474 -0.20 -0.15 -0.10 0.02 0.17 0.28
(66)
33158.611 -0.29 -0.22 -0.15 0.03 0.25 0.43
(90)
8567.12
17611.51
33158.60
Frequency
a Splittings of hyperfine componentsare given below b Relative intensities of hyperfine components. ' Observed frequencies in parentheses in the analysis for rotational and d
Numbers in parentheses beside limits of the predictions.
Relative Intensityb
0.17 0.16 0.18 0.15 0.19 0.14
0.17 0.16 0.18 0.15 0.19 0.14
0.17 0.16 0.18 0.15 0.19 0.14
unsplit
transition
frequencies.
are hypothetical unsplit frequencies, centrifugal distortion constants.
calculated
frequencies
are
95 percent
used
confidence
small data sets, and the necessity to fix some parameters in the fits. This is confirmed in Table I, where excellent agreement between our values and the precise values of Winnewisser et al. (6) is found. In the case of the species H212C180, Hz12C170, Hz13C180, and Hz13C170, although the fixed constants do make significant contributions to the frequencies of the observed transitions, these frequencies are rather insensitive to small variations in these constants. Indeed, when in an earlier analysis we fixed them to the slightly different values of Brown and Hunt (.5), the derived constants were extremely close to those in Table II. Furthermore, in any case, AK is almost independent of the masses of the heavy atoms (6). Finally, the constants show consistent trends between the isotopic species. Accordingly, within the limitations of the data, predicted frequencies of unmeasured transitions should also be reliable. Such transitions would include u-type Q and R branches having AK, = 0 (e.g., 2,, + 110, 6,, +- 6,,) and selected values of these are given for H,12C180 and H,‘2C170 in Tables III and IV. They seem likely to be the most important for radioastronomical studies. Predictions of other transitions of this type can be made with the constants given in Table II; for the species containing 170 the hyperfine constants of Ref. (7) will also be required. We would be pleased to provide such predictions on request. As a final check of our answers we have calculated the quartic distortion con-
318
DAVIES, RICHARDS,
AND GERRY
TABLE VII Comparison of Observed and Calculateda Centrifugal Distortion Constant@ of Formaldehyde PEXaUieter AJx102
H212C160
12C17 "2
"212c180
H213C160
obs. talc.
7.5295d
7.52
7.2' 7.16
6.86 6.65
7.1525d 7.16
6.8' 6.80
6.5' 6.49
A JK
obs. talc.
1.29051d 1.286
1.266 1.226
1.1811 1.174
1.25749d 1.254
1.183 1.193
1.128 1.141
hK
obs. talc.
19.424d 19.11
19.424= 19.18
19.424= 19.23
19.499= 19.22
19.49gc 19.27
6&03
obs. talc.
10.4568d 9.84
9.843 9.15
9.122 8.56
9.6313d 9.08
8.904 8.42
8.312 7.86
0.9826 0.860
0.9454 0.826
0.98745d 0.863
0.9358 0.825
0.9026 0.791
*K
obs. talc.
1.02603d 0.898
19.49gd 19.15
a Calculated from the force constants of Duncan and Mallinson (lJ). b In MHZ. = Assumed. d Winnewisser -et al (6).
stants for the various isotopic species using the rather precise and complete general valence force field of Duncan and Mallinson (18). The planarity relations were assumed to hold for the distortion constants. The calculated constants are compared with the experimental values in Table VII. The agreement between the two sets is clearly very good for A_,, AJK, and AK. This is especially so for AJ, including our assumed values. For Ax a small isotopic dependence on oxygen isotope is found in the calculation, contrary to the assumption in the fits. However, for a test case of Hz12C1*0 with AK assumed to be 19.57 MHz, following the trend of the calculated values, virtually no difference was found in the distortion constants (changes much less than one standard deviation, except for A,, within two and 6, within three standard deviations), and the frequency predictions were identical. The agreement between calculated and observed values for aJ and SK is poorer than for the other three constants, but the calculated and observed values show the same isotopic dependence, thus confirming our assignments. ACKNOWLEDGMENTS We thank R. W. Davis for his help and advice with some of the experiments, reading the manuscript and offering several helpful suggestions.
and for critically
Note added in proof. Since the acceptance of this paper Dr. G. Winnewisser communicated similar results to us for H,‘*C’“O and H,‘“C’“O. We thank him for this and for bringing to our attention a small but important computing error, which we have corrected.
REFERENCES 1. B.
STARCK, R. MUTTER, C. SPRETER, K. KETTEMANN, A. Boccs, M. BOTSKOR AND M. JONES, “Bibliography of Microwave Spectroscopy 1945- 1975,” Physik Daten 9-1, Sektion fur Strukturdokumentation der Universitat Ulm, 1977.
SPECTRA
319
OF H,C’*O AND H,C”O
2. D. R. JOHNSON, F. J. LOVAS AND W. H. KIRCHHOFF, J. Phvs. Chcm. Ref. Data 1, 1011-1045 (1972). 3. T. OKA, K. TAKAGI, AND Y. MORINO,J. MO/. Specfrosc. 4.
14, 27-52
D. DANGOISSE, E. WILLEMOT. AND J. BELLET, J. Mol. Spectrosc.
5. L. R. BROWN AND R. H. HUNT, J. Mol. Spectrosc.
73, 277-289
(1964).
71, 414-429
(1978).
(1978).
6. G. WINNEWISSER, R. A. CORNET, F. W. BIRSS, R. M. GORDON, D. A. RAMSAY. AND S. N. TILL,
7. 8. 9. 10. II. 12. 13. 14. 15. 16. 17. 18.
J. Mol. Spectrosc. 74, 327-329 (1979). W. H. FLYGARE AND J. T. LOWE, .I. Chem. Phys. 43, 3645-3653 (1965). T. OKA. H. HIRAKAWA, AND K. SHIMODA. J. Phys. Sot. Japan 15, 2265-2273 (1960). T. OKA AND Y. MORINO, J. Phys. Sot. Japan 16, 1235-1242 (1961). K. TAKAGI AND T. OKA, J. Phys. Sot. Japan 18, 1174-1180 (1963). K. D. TUCKER, G. R. TOMASEVI~H AND P. THADDEUS, Asfrophys. J. 169, 429-440 (1971); Astrophys. J. 174, 463-466 (1972). J.-C. CHARDON, C. GENTY, D. GUICHON, N. SUNGUR, AND J.-G. THEOBALD, Rev. Phys. Appl. 9, 961-965 (1974). R. H. GAMMON, Chem. Enp. Nenss. 21-33 (October 2, 1978). F. F. GARDNER, J. C. RIBES, AND B. F. C. COOPER. Astrophys. Lett. 9, 181-183 (1971). B. ZUCKERMAN, D. BUHL, P. PALMER, AND L. E. SNYDER. Astrophys. J. 189, 217-220 (1974). J. K. G. WATSON. “Vibrational Spectra and Structure; a Series of Advances” (J. R. Durig, Ed.). pp. l-89, Elsevier, New York, 1977. M. C. L. GERRY, J. Mol. Spectrosc. 4.5, 71-78 (1973). J. L. DUNCAN AND P. D. MALLINSON, Chem. Phys. Lett. 23, 597-599 (1973).
OF
MOLECULAR
SPECTROSCOPY
Microwave Spectra Formaldehyde
80,
307-319 (1980)
of the Ground Vibrational State of Substituted with 170 and 1801
DANNY T. DAVIES, RICHARD J. RICHARDS, AND M. C. L. GERRY Department
of
Chemistry,
The University of British Columbia, Vancouver, B. C. V6T I W5, Canada
2075 Wesbrook
Mall,
Pure rotational transitions in the ground vibrational state have been measured for H,YYO, H,*2C*70, H,*3C1B0, and H,W”O in the frequency region 8-75 GHz, These have included both Q- and R-branch transitions, and have permitted accurate evaluation of rotational constants and several quartic centrifugal distortion constants for each species. These in turn have permitted the prediction of several transitions of possible use in radioastronomy. INTRODUCTION
The microwave and millimeter-wave spectra of formaldehyde, in several isotopic forms, have been the subjects of a large number of studies (1). Several reviews have appeared summarizing much of the work (2,3),but new measurements continue to be made. The spectrum, particularly that of the most abundant isotopic species in its ground vibrational state, has been subject to increasingly refined analysis. In 1978, for example, several new measurements were reported for various isotopic species in their ground vibrational states, along with a study of a Coriolis resonance between y4 and vg excited states (4). That year also saw the publication of an extensive analysis combining microwave data with averaged combination differences from five infrared bands (5). Most recently, a rather detailed and complete set of constants for HzlsC1sO and H,13C160 has been published (6). This paper is concerned with the microwave spectra of species containing I70 or l*O. Even though some transitions of two of these, H,1%17O and H21*C180, were reported earlier, the observed spectra were not extensive. For H212C170, five Q-branch transitions, having K, = 1 and 2, have been very accurately measured (7), yielding, besides (B, - C,), accurate values for 170 quadrupole and magnetic coupling constants. There has been, however, no report of any R branches. For H212C180, rather more lines have been reported, including R branches (3, 4, 8-12), but these spectra, too, are not extensive. ’ This work is taken from the B.Sc. theses of Danny T. Davies (1977) and Richard J. Richards (1978), The University of British Columbia. It has been supported by the National Research Council of Canada.
307
0022-2852/80/040307-13$02.00/O Copyright All rights
8
1980 by Academic
of reproduction
Press,
in any fom
Inc. reserved.
308
DAVIES,
RICHARDS,
AND GERRY
Furthermore, many of the early measurements, which were made using labeled species in natural abundance, have been found to be rather inaccurate. One was used in the recent analysis of the spectrum of H,‘V*O by Dangoisse er al. (4), and tends to reduce the value of their analysis, in spite of the inclusion of their own more accurate measurements. The microwave spectrum of formaldehyde is of interest, not only because it gives much structural information about a relatively simple molecule, but also because it has been used to detect this molecule in interstellar space. In particular, three isotopic species, H212C160, H213C60, and H,‘VBO have been found by radioastronomical techniques (1, 13 -15) and an unsuccessful search for H,Yi70 has also been carried out (15). Nevertheless, formaldehyde can be considered a combination of H2 and CO, the two most abundant interstellar molecules. For CO, in particular, several isotopic species have been observed, including substituted =C’60 ) 12C180 and 12C170 (1, 13), so that further isotopically species of formaldehyde remain potentially observable. In the present paper we report the spectra of the species HZIY?*O, H1’V’O, HZ13C1*0, and H213C170, the last two for the first time. In all cases, in order to increase line intensities, artificial substitutions of 13C, 180 and l’0 were made. Both Q and R branches were observed for all four species, and have been analyzed for rotational and centrifugal distortion constants. Predictions of frequencies of several unmeasured transitions, which may be of interest to radioastronomers. are also included. EXPERIMENTAL
METHODS
Formaldehyde enriched with 170 and l*O was prepared by exchange with isotopically enriched water. Initially paraformaldehyde, either as its normal species or 90% enriched with 13C, was depolymerized by heating, and the resulting formaldehyde was collected at liquid nitrogen temperature in a trap containing 5 A4 HCl in isotopically enriched water. In this mixture the formaldehyde not only underwent isotopic exchange, but also repolymerized. After the water had been pumped off in vucuo, the polymer was reheated and the labeled formaldehyde collected in a storage vessel. Isotopic enrichments ivere -10% 170 and -20% I*O. Microwave spectra were obtained using a conventional lOO-kHz Starkmodulated instrument in the frequency region 8-75 GHz. The regions 8-18 and 26.5-40 GHz were covered using a Hewlett-Packard 8400C Microwave Spectroscopy Source. At K band (18-26.5 GHz) an appropriate OK1 Klystron was used. Microwave power above 60 GHz was obtained by doubling the frequency from the Hewlett-Packard Source. Most transitions were measured at room temperature, though occasionally for those lines at low J and K, the measurements were made with the cell cooled with dry ice. Estimated accuracy MHz below 40 GHz and -+-0.1 MHz of the measurements is -20.05 above 60 GHz.
309
SPECTRA OF H,VsO AND H,C”O TABLE 1 Check of the Fitting Procedure Used by Comparison of the Constants Obtained for H,‘V60 with Those of Winnewisser et al. (6) parametera A
Present Workb 281 968.7 (13)'
Wlnnewisser __et al (6). 281 970.72 (18)
B
38 836.066 (48)
38 836.0456 (9)
C
34 002.204 (48)
34 002.2034 (8)
AJ x 10' gK A~ $ x 103 &K
7.57 (30)
7.5295 (14)
1.2918 (60)
1.29051 (24)
19.424a
19.424 (5)
10.434 (23)
10.4568 (6)
1.0307 (21)
1.02603 (17)
a In the present work AK and the sextic coefficients were held fixed at the "Microwave + Optical" values of reference (6). b
12 18 A data set as close as possible to that of Ii2C 0 was used in this analysis.
' All constants are in MHz. Numbers in parentheses are 95 percent confidence limits in units of the last significant figures.
RESULTS AND ANALYSIS
Between 9 and 18 rotational transitions have been newly measured in the present work for each of the four isotopic species. Hyperfine structure due to I70 was observed in many of the transitions of molecules containing this isotope; this could be entirely accounted for, for both H,‘V70 and H213P70, using the I70 quadrupole and magnetic coupling constants of Flygare and Lowe (7), and no attempt was made to refine these constants. The spectra of each isotopic species were analyzed for rotational and centrifugal distortion constants, using Watson’s Hamiltonian for the I’ representation in its A reduction (16). For the 170-containing species the hyperfine structure had been previously subtracted off. Since the data sets used were rather small, and only a few different branches were measured, it was necessary to assume values for some distortion constants. In the initial analyses, for H212C*80, the constant AK was very poorly determined, and was essentially perfectly correlated with aK. Because its contribution to the transition frequencies was, on the other hand, quite significant, and ignoring it would distort the obtained values for the other constants, its value was fixed for the Y-containing species at 19.424 MHz, and for the 13C-containing species at 19.499 MHz, as found by Winnewisser et al. (6). Because it is dependent on the moment of inertia about the symmetry axis, which is essentially the same for all species studied here, this approximation is reasonable. Contributions due to sextic constants could also have been expected to be significant, but none of these were well determined from the present data; to preserve consistency between the various isotopic species the sextic constants
1.2658 (33)
13
2.6
6.6
22
0.98264(40)
9.8430(92)
1.03078(21)
10.4344(23)
1.29183(60)
7.574(30)
26
4.2
o.94538(15)
9.1218(14)
1.1810g(38)
6.861(19)
14
3.4
0.98681(19)
9.6350(11)
1.256gl(31)
7.205(15)
9
4.6
0.9358g (65)
8.9044(80)
1.18321(34)
6.8e
32413.03414(49)
36776.85586(49)
281995.23(28j
H213c170b.c
"Microwave
+
Opticsi" values of ref.
(6).
11
4.5
0.90266(53)
8.312g (69)
1.127g2(30)
6.5=
31698.86363(47)
35859.25637(47)
281984B5 (26)
H213C180b
12 18 g These fits were performed using a data set as close as possible to that of H2 C 0, and are presented for comparison purposes only. A complete set of constants is in ref. (a).
f Standard deviation of the fit.
e Held fixed in the analyses. See text.
d Numbers in parentheses are 95 percent confidence limits in units of the last significant figures of the numbers on the line. Subscript numbers are required for frequency predictions.
'170 hyperfine constants as in ref. (I?.
b~K and sextic coefficients held fixed at the ~~13~160
aAK and sextic coefficients held fixed at the H212C160 "Microwave + Optical" values of ref. (5).
Number of TransitionsI
SDFITfx102
6K
bJX103
AJK
$x102
33213.99163 (25)
32511.53562(30)
34002.20408(48)
C
37811.09962(24)
36904.18116(30)
H213C160boz
38836.06574(48)
H212C180s
281993.167(11)
B
Ii2 12c170s,c
281959.665(9)
d 281968.740(13)
12 II* c160a,g
A
(MHz) Parameter
Derived Rotational and Centrifugal Distortion Constantsa of Various Isotopic Species of Formaldehyde
TABLE II
311
SPECTRA OF H,VBO AND H,C”O TABLE III Measured and Predicted Transition Frequencies TransitIon
Observed Frequency
(in MHz) of H,12C’s0 Calculated Frequency
R-Branches l(O,l) 2CO.2) 2(1,2) 2(1,1) 3(0,3) 3(1,3) 3(1,2) 3(2,2) 3(2,1) 4(0,4) 4(1,4) 4U.3) 4c2.3) 4(2;2) 4(3,2) 4(3,1) -
69 415.44 138 770.90a -_
O(O,O) l(O,l) l(l,l) lU,O) 2(0,2) 2(1,2) 2(1,1) 2(2,1) 212,O) 3(0,3) 3(1,3) 3(1,2) 3c2.2) 3(2;1) 3(3,1) 3(3,0)
-208 006.44a
-_
214 208 208 277
77a.4ga 211.42a 444.63a 062.58a.b
286 277 278 277 277
2;;.96a*b 562.78=3b 145.36aab 675.36a>b 677.9ga8b
4 13 26 43 65
3a8.7969ae 165.95491e 330.17 a7a.07a 803.08
69 138 134 143 208 201 214 208 208 277 268 286 277 278 277 277
415.442 (53)d 770.898 (66) 435 937 (66) 213.093 (66) 006.470 (65) 614.283 (52) 778.442 (51) 211.399 (58) 444.670 (58) 062.65 (27) 745.77 (25) 293.69 (25) 562.71 (22) 145.36 (22) 674.95 (25) 677.85 (25)
4 13 26 43 65 92 122 157 12 18 28
388.797 165.953 330.111 878.027 803.123 093.567 729.89 682.16 107.081 905.551 120.183 0.484 3.384 13.531 744.396 689.013 971.370 901.850 824.281 701.702 267.217 892.679 312.789
Q-Branches l(l,O) - l(l,l) 2U,l) - 2(1,2) 30,2) - 3(1,3) 4(1,3) - 4(1,4) 5U.4) - 5(1,5) 6C1.5) - 6(1,6) 7c1.6) - 7(1,7) 8(1,7) - E(1.8) 8(2,6) - a(2,7) 9(2,7) - 9(2,8) 10(2,8) - 10(2,9) 3(3,0) - 3(3,1) 4(3,1) - 4(3,2) 4(3,2) - 5(3,3) 15(3,12) - 15c3.13) 16(3,13) - 16c3.14) 17(3,14) - 17(3,15) 18(3,15) - 18(3,16) 19(3,16) - 19(3,17) 24(4,20) - 24(4,21) 25c4.21) - 25(4,22) 26(4,22) - 26(4,23) 28(4,24) - 28(4,25)
a Dangoisse --9 et al b
-12 107.08 18 905.52 28 120.11 0.4845C 3.384OC 13.531oc 8 744.37 12 689.02 17 971.47 24 901.85 33 824.30 9 701.71 13 267.21 17 892.62 31 312.80
8 12 17 24 33 9 13 17 31
(4) 03) (26) (43) (65) (94) (13) (18) (18) (27) (40) (0) (0) (0) (23) (27) (31) (39) (53) (45) (46) (45) (79)
ref. (4).
Not included in the fit.
' Chardon g &, ref. (11). d Numbers in parentheses are 95 percent confidence limits for the predicted frequencies. e Tucker et al, ref. (11). -
were also fixed, in the same manner
as A K, to the values of Winnewisser constants and four determined quartic distortion constants were in fact reasonable a fit was carried out to H212C160, using a data set as close as possible to that of H,12C1*0. Excellent agreement of the constants with those of Winnewisser et al. was found, as shown in Table I, implying that reliable, consistent constants could be obtained for the other species using this procedure. et al. (6). To check then that the resulting three rotational
312
DAVIES, RICHARDS, AND GERRY TABLE IV Measured and Predicted Transition Frequencies Transition F'-F"
Observed Frequency
(in MHz) of H,LzC170
Calculated Frequency (splitfingja
Relative Intensityb
R-Branches 1(0,1) 512 J/2 312
- O(O,O) - 512 - 512 - 512 I
2(0,2) 512 712 512 312 912 712 II2 512 312
71026.560 71026.56
2(1,1) 512 712 312 512 J/2 912 512 l/2 312
-
-0.15 -0.12 0.00 0.08
0.11 0.20 0.47 137452.81
S/2 512 512 312 J/2 312 J/2 3;2 712 -
-
lo,*) 312 712 312 712 512 712 512 312 512
0.33 0.44 0.22
141987.27 (10) -0.39 -0.28
- l(O,l) - 312 - J/2 - 712 - 312 - 712 - 512 - 312 - 512 - 512
2(1,2) - l(l,l) 312 512 712 li2 912 312 512 5;2 712
(52)d
-0.29 0.07 0.31
(17) 0.04 0.12 0.17 0.07 0.33 0.09 0.02 0.06 0.10
-2.56 -1.22 -0.92 -0.56
0.01 0.69 2.02 2.03 2.32
--
0.06 0.10 0.02 0.09 0.33 0.17 0.07 0.12 0.04
146639.85
(16)
-2.81 -1.57 -0.85 -0.68 -0.06 0.46 0.83 0.86 2.79
0.06
0.10 0.09 0.02 0.17 0.33 0.12 0.07 0.00
Q-Branches
l(l,O) 5/2 7;2 512 512 312 712 312 2(1,1) 712 712 512 512 912 712 S/2 312 912 3;2 l/2 l/2
- l(l.1) - 512 - 5;2 - 712 - 312 1 - 512 - 7/2 - 312 -
2(1,2) 712 S/2 J/2 512 712 912 312 512 912 lj2 312 l/2
(4593.250)e’f -3. 63Se -2.131 -0.404 -0.004 1.106 3.250 (13780.79)e -2.70Je -2.490 -1.895 -1.598 -0.748
-0.491 -0.266 0.363 1.565 2.953 3.420 --
4593.754 -3.643 -2.135 -0.399 -0.393 0.004
(10)
1.109 3.246
0.02 0.16 0.16 0.16 0.16 0.29 0.07
13780.790 (24) -2.781 -2.484
-1.889 -1.592 -0.748 -0.469 -0.256 0.371 1.565 2.957 3.414 4.605
0.12 0.09 0.09 0.03 0.06 0.06 0.08 0.08 0.27 0.05 0.05 0.02
SPECTRA OF H&?O
313
AND H,C”O
TABLE IV-Continued Transition F'-F" 3(1,2) - 3(1,3) 912 - 712 712 912 712 712 512 912 1112 5/Z 5/2 312 u/2 312 312 l/2 l/2
-
5(1,4)
7l2 912 9/2 I 512 712 1112 912 I 512 \ 312 512 1112 312 112 312 112 - 5(1,5)
1112 - 1112 13/2 - 11/2 1112 U/2 1312 912 912 912 1312 712 712 1512 512
-
6U,5) 1312 1512 1312 1312 1112 1512 1112 1112 912 912 1712 712
-
13;2 912 1312 lll2 912 712 1512 912 712 1512 512
Observed Frequency
Calculated Frequency (splitting) 275S9.607 -2.47
(27559.64)
(38) 0.05 0.16 0.09 0.05 0.05 0.05 0.03 0.03 0.05 0.04 0.04 0.25 0.03 0.03 0.03 0.02
-2.31 -2.25 -2.10 -1.43
27557.38 27558.19 27558.74
-0.89 -0.27 -0.24 -0.07 1.02 1.54 1.80 2.63 3.48 3.85 4.71
27559.42 27560.66 27561.18 27561.41 27562.22 27563.13 -27564.34 (68874.17) 68871.74
68874.184 -2.50 -2.27 -2.06 -2.02 -1.82 -1.61 -1.14 -0.17 0.03 0.33 1.30 2.03 4.01
68872.30 _-_--68875.50 68876.18 68878.16
96388.99 -2.52 -2.20 -2.12 -2.00 -1.74
- 6(1,6) 1312 1312 1112 1512 1312 1512 1112 912 1112 912 1712 712
-1.69 -0.13 -0.41 0.07 1.01 2.08 3.87
Relative Intensity b
(50)
0.14 0.02 0.02 0.02 0.18 0.02 0.11 0.02 0.03 0.02 0.09 0.23 0.08 (13)
0.15 0.02 0.02 0.02 0.02
0.18 0.12 0.02 0.02 0.10 0.22 0.09
-
Accordingly, this procedure was used for the 170 and ‘*O species. Minor variations, depending on the data set, were also required. For H,*2C180 our newly measured transitions were combined with the 2 + 1 and 3 + 2 R-branch frequencies of Dangoisse et al. (4); since the measurements were all given equal weight in the fits the less accurate 4 +- 3 R branch was not included. For the other three species, l,,, +- OoOwas the only R-branch transition measured, so AJ was also fixed. Since the rotational constants of H,12C170 and H,13C160 are very similar, they were assumed to have the same A,. AJ of the other 13C species was then scaled to those of the lzC species. Finally, for comparison purposes, the spectrum of H,13C160 was reanalyzed using a data set similar to that of H,13C1s0. The fitting procedure for the analyses was reported previously (17). A first-
314
DAVIES,
RICHARDS,
TABLE Transition F'_F" 7(1,6) - 7(1,7) 1512 - 1512 I.712- 1712 1312 - 1312 1112 - 1112 19;2 - 19;2 912
-
IV-Continued
Observed Frequency
--
912
6(2,4) - 6(2,5) 13/2 - 1312 1512 - 1512 u/2 - 1112 1 912 - 9/2 1712 - 1712 712 - 712
(4468.19je -0.220=
7(2,5) - 7(2,6) 1512 - 1512 1712 - 1712 1312 - 1312 t 1112 - 1112 1912 - 1912 912 - 912
(8015.28)e -0.308e
8(2,6) - 8(2,7) 1712 - 1712 1512 - 1512
c13292.39je -0.404=
1912
-
1912
t
1312 - 1312 2112 - 2112 1112 - Ill2
-0.140 0.080 0.195 0.360
-0.198 0.103 0.260 0.466
-0.246 0.104 0.348 0.599
9(2,7) - 9C2.8) 1912 - 1912 1712 - 1712 2112 - 2112 1512 - 1512 2312 - 2312 1312 - 1312 I
(20744.01)
10(2,8) - 10(2,9) 2112 - 2112 1912 - 19/2 2312 - 2312 I 17/2 - 1712, 2512 - 2512 1512 - 1512 1
(30830.44)
15(3,12) - 15(3,13) 3112 - 3112 29;2 - 2912 3312 - 3312 27/Z - 2712 3512 - 3512 2512 - 2512
(10068.97)
20743.65
20744.41
30830.01
30830.92
10068.97
AND GERRY
Calculated Frequency (splittine)
Relative Intensitvb
1213448.71(31) -2.52 -1.58 -1.49 0.81 2.11 3.78
0.15 0.18 0.13 0.12 0.22 0.10
4468.198 (12) -0.233 -0.155 -0.126 0.091 0.195 0.356
0.15 0.18 0.12 0.10 0.22 0.09
8015.308 (18) -0.314 -0.195 -0.187 0.098
0.266 0.466
0.15 0.18 0.13 0.12 0.22 0.10
13292.419 (22) -0.403 -0.256 -0.238 0.103 0.346 0.589
0.16 0.14 0.18 0.12 0.21 0.11
20744.013 (28) -0.50 -0.33 -0.28 0.11 0.43 0.72
0.16 0.14 0.18 0.13 0.21 0.12
30830.417 (42) -0.60 -0.41 -0.33 0.11 0.52 0.87
0.16 0.15 0.18 0.13 0.20 0.12
10068.949 (34) -0.14 -0.10 -0.07 0.01 0.12 0.20
0.17 0.16 0.18 0.15 0.19 0.14
order fit in a rigid rotor basis was made to the rotational and quartic centrifugal distortion constants. These constants, including those fixed in the analyses, were then used to predict the transition frequencies exactly. The difference between the exact and first-order frequencies was then subtracted from the measured values, and the procedure was repeated until convergence was obtained. The transition frequencies and results of the analyses for the four oxygensubstituted species are shown in Tables III-VI. These tables include, for H,12C180 and H212C170, some transitions measured previously but, for various
315
SPECTRA OF H,C”O AND H&i’0 TABLE IV-Continued Observed Frequency
Transition F'_,?" 16(3,13) - 16(3,14) 3312 - 3312 3112 - 3112 3512 - 3512 2912 - 2912 3712 - 3712 2712 - 2712
(14600.49)
17C3.14) - 17(3,15) 3512 - 3512 I 3312 - 3312 3712 - 3712 I 3112 - 3112 3912 - 3912 2912 - 2912
(20660.22)
18(3,15) - 18(3,16) 3712 - 3712 35;2 - 35/2 3912 - 3912 3312 - 3312 4112 - 4112 3112 - 3112
(28596.99)
Calculated Frequency (splitting)
Relative Intensityb
14600.484 (32) -0.17 -0.13 -0.09 0.02 0.15 0.25
0.17 0.16 0.18 0.15 0.19 0.14
14600.49
20660.06
20660.244 (28) -0.22 -0.17 -0.11
0.02 0.19 0.31
20660.37
28596.78
28597.21
28596.985 (48) -0.27 -0.20 -0.13 0.02 0.23 0.39
0.17 0.16 0.18 0.15 0.19 0.14 0.17 0.16 0.18 0.15 0.19 P.14
a Splittings of hyperfine components are given below the unsplit transition frequency. To obtain the transition frequency of the hypertke component the splitting value should be added to the unsplit line frequency. b Relative intensities of hyperhne components. p Observed frequencies in parentheses are hypothetical unsplit frequencies, used in the analysis for rotational and centrifugal distortion constants. d These are the unsplit line frequencies. Numbers in parentheses beside calculated frequencies are 95 percent confidence limits of the predictions. e Flygare and Lowe, Ref. (7). Hyperfine components are their reported observed splittings. f This transition was not included in the fit to the rotational and centrifugal distortion constants. There is apparently a misprint in Ref. (7).
TABLE V Measured Rotational Transition Frequencies
(in MHz) of H,Y1*O
Observed Frequency
l( 0. 1) 2( 1. 1) 5( 1, 4) 8( 2. 6) 9( 2. 7) ll( 2, 9) 13( 2,ll) 16( 3.13) 17( 3.14) 19( 3,16) 20( 3,17)
-
O( 2( 5( a( 9( ll( 13( 16( 17( 19( 20(
0, 0) 1. 2) 1, 5) 2, 7) 2, 8) 2.10) 2.12) 3,14) 3,lS) 3,17) 3,18)
67556.86 12472.78 62340.46 10837.12 16933.52 36057.48 66990.10 10741.85 15228.10 28733.24 38381.92
Calculated Frequency
67556.860(90)=
12472.765(26) 62340.463(88) 10837.106(38) 16933.455(S) 36057.546(64) 66990.083(88) 10741.870(58) 15228.092(60) 28733.226(51) 38381.928(80)
a Numbers in parenthesis are 95 percent confidence limits of the predicted frequencies.
316
DAVIES, RICHARDS,
AND GERRY
TABLE VI Measured Rotational Transitions (in MHz) of H,‘3C’70 in Its Ground Vibrational State Transition F'_F"
l(O.1)
- O(O,O)
512 712 312
-
712 712 512 512 912 712 512 312 VI2 312 l/2
-
2U,l)
512 512 512 -
5C1.4) 1112 1312 912 712 1512 512
-
Observed
Calculated Frequency
Frequency
(splitting)a
(69189.62)'
69189.620 (92)d -0.29 0.07 0.31
69189.62 I
(13079.63)
50,5) 1112 1312 VI2 712 1512 512
(65372.00) 65369.66 65370.12 -65373.38 65374.00 65376.02
65372.004 -2.50 -1.82 -1.14 1.30 2.03 4.01
(90)
27746.619 -0.60 -0.41 -0.33
(74)
13077.80 13079.20 13079.98 13081.23 13082.88
10(2,8) 2112 1912 2312 1712 2512 1512
10(2,9) 2112 1912 2312 17f2 2512 / 1512
(27746.58)
-
12(2,10) 2512 2312 2712 2112 2912 1912
- 12(2,11) 2512 2312 2712 2112 2912 1912
(54773.19)
-
13(2,11) 2712 2512 2912 2312 3112 2112
- 13(2,12) 2712 2512 2912 2312 3112 2112
(73485.35)
-
27746.59
-2.78 -2.48 -1.89 -1.59 -0.75 -0.47 -0.26 0.37 1.57 2.96 3.41
0.12 0.09 0.09 0.03 0.06 0.06 0.08 0.08 0.27 0.05 0.05 0.14 0.18 0.11 0.09 0.23 0.08 0.16 0.15 0.18 0.13 0.20 0.12
0.11
0.52 0.87
54773.20
54773.147 -0.78 -0.56 -0.41
(60) 0.16 0.15 0.18 0.14 0.20 0.13
0.11 0.67 1.12
73486.36
0.33 0.44 0.22
13079.611 (28)
2(1,2) 712 t 512 712 i 512 712 VI2 I 312 S/2 VI2 l/2 1 312
13076.97
Relative Intensityb
73485.367 -0.88 -0.64 -0.46 0.12 0.76 1.27
(86)
0.17 0.15 0.18 0.14 0.20 0.13
reasons indicated earlier, as well as in the tables, also present predicted frequencies of transitions unmeasured in the present work, but which may be of interest to radioastronomers. DISCUSSION
The derived rotational and centrifugal distortion constants given in Table II represent for H,12C180 and H,‘V70 a considerable improvement in accuracy over previously published values. For H,13CL*0 and H,‘3C170 they are the first values published. They can be expected to be reliable, in spite of the relatively
317
SPECTRA OF H.$?O AND H,C”O TABLE VI-Continued Transition F'-F"
Observed Frequency
Calculated (splittingja
15(3,12) 3112 2912 3312 2712 3512 2512
- 15(3,13) 3112 2912 3312 2712 3512 2512
(8567.12)
-
17(3,14) 3513 3312 3712 31/Z 3912 2912
- 17(3,15) 3513 3312 3712 3112 3912 2912
(17611.51)
-
19(3,16) 3912 3712 4112 3512 4312 3312
- 19(3,17) 3912 3712 4112 3513 4312 3312
(33158.60)
-
8567.150 -0.12 -0.09 -0.06 0.01 0.11 0.18
(64)
17611.474 -0.20 -0.15 -0.10 0.02 0.17 0.28
(66)
33158.611 -0.29 -0.22 -0.15 0.03 0.25 0.43
(90)
8567.12
17611.51
33158.60
Frequency
a Splittings of hyperfine componentsare given below b Relative intensities of hyperfine components. ' Observed frequencies in parentheses in the analysis for rotational and d
Numbers in parentheses beside limits of the predictions.
Relative Intensityb
0.17 0.16 0.18 0.15 0.19 0.14
0.17 0.16 0.18 0.15 0.19 0.14
0.17 0.16 0.18 0.15 0.19 0.14
unsplit
transition
frequencies.
are hypothetical unsplit frequencies, centrifugal distortion constants.
calculated
frequencies
are
95 percent
used
confidence
small data sets, and the necessity to fix some parameters in the fits. This is confirmed in Table I, where excellent agreement between our values and the precise values of Winnewisser et al. (6) is found. In the case of the species H212C180, Hz12C170, Hz13C180, and Hz13C170, although the fixed constants do make significant contributions to the frequencies of the observed transitions, these frequencies are rather insensitive to small variations in these constants. Indeed, when in an earlier analysis we fixed them to the slightly different values of Brown and Hunt (.5), the derived constants were extremely close to those in Table II. Furthermore, in any case, AK is almost independent of the masses of the heavy atoms (6). Finally, the constants show consistent trends between the isotopic species. Accordingly, within the limitations of the data, predicted frequencies of unmeasured transitions should also be reliable. Such transitions would include u-type Q and R branches having AK, = 0 (e.g., 2,, + 110, 6,, +- 6,,) and selected values of these are given for H,12C180 and H,‘2C170 in Tables III and IV. They seem likely to be the most important for radioastronomical studies. Predictions of other transitions of this type can be made with the constants given in Table II; for the species containing 170 the hyperfine constants of Ref. (7) will also be required. We would be pleased to provide such predictions on request. As a final check of our answers we have calculated the quartic distortion con-
318
DAVIES, RICHARDS,
AND GERRY
TABLE VII Comparison of Observed and Calculateda Centrifugal Distortion Constant@ of Formaldehyde PEXaUieter AJx102
H212C160
12C17 "2
"212c180
H213C160
obs. talc.
7.5295d
7.52
7.2' 7.16
6.86 6.65
7.1525d 7.16
6.8' 6.80
6.5' 6.49
A JK
obs. talc.
1.29051d 1.286
1.266 1.226
1.1811 1.174
1.25749d 1.254
1.183 1.193
1.128 1.141
hK
obs. talc.
19.424d 19.11
19.424= 19.18
19.424= 19.23
19.499= 19.22
19.49gc 19.27
6&03
obs. talc.
10.4568d 9.84
9.843 9.15
9.122 8.56
9.6313d 9.08
8.904 8.42
8.312 7.86
0.9826 0.860
0.9454 0.826
0.98745d 0.863
0.9358 0.825
0.9026 0.791
*K
obs. talc.
1.02603d 0.898
19.49gd 19.15
a Calculated from the force constants of Duncan and Mallinson (lJ). b In MHZ. = Assumed. d Winnewisser -et al (6).
stants for the various isotopic species using the rather precise and complete general valence force field of Duncan and Mallinson (18). The planarity relations were assumed to hold for the distortion constants. The calculated constants are compared with the experimental values in Table VII. The agreement between the two sets is clearly very good for A_,, AJK, and AK. This is especially so for AJ, including our assumed values. For Ax a small isotopic dependence on oxygen isotope is found in the calculation, contrary to the assumption in the fits. However, for a test case of Hz12C1*0 with AK assumed to be 19.57 MHz, following the trend of the calculated values, virtually no difference was found in the distortion constants (changes much less than one standard deviation, except for A,, within two and 6, within three standard deviations), and the frequency predictions were identical. The agreement between calculated and observed values for aJ and SK is poorer than for the other three constants, but the calculated and observed values show the same isotopic dependence, thus confirming our assignments. ACKNOWLEDGMENTS We thank R. W. Davis for his help and advice with some of the experiments, reading the manuscript and offering several helpful suggestions.
and for critically
Note added in proof. Since the acceptance of this paper Dr. G. Winnewisser communicated similar results to us for H,‘*C’“O and H,‘“C’“O. We thank him for this and for bringing to our attention a small but important computing error, which we have corrected.
REFERENCES 1. B.
STARCK, R. MUTTER, C. SPRETER, K. KETTEMANN, A. Boccs, M. BOTSKOR AND M. JONES, “Bibliography of Microwave Spectroscopy 1945- 1975,” Physik Daten 9-1, Sektion fur Strukturdokumentation der Universitat Ulm, 1977.
SPECTRA
319
OF H,C’*O AND H,C”O
2. D. R. JOHNSON, F. J. LOVAS AND W. H. KIRCHHOFF, J. Phvs. Chcm. Ref. Data 1, 1011-1045 (1972). 3. T. OKA, K. TAKAGI, AND Y. MORINO,J. MO/. Specfrosc. 4.
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