JOURNAL
OF MOLECULAR
SPECTROSCOPY
(1990)
1@,340-352
Microwave Spectrum of Ketene
RONALD D. BROWN, PETER D. GODFREY, DONALD MCNAUGHTON,
ANTHONY P. PIERLOT, AND WILLIAM H. TAYLOR
Centre for High-Resolution Spectroscopy and Opto-Electronic Technology, Chemistry Department,
Monash University, Wellington Road Clayton, Victoria 3168, Australia
A new Stark-modulated submillimeter-wave spectrometer is described. This spectrometer has
been used to analyze the microwave spectrum of three isotopomers (heavy atoms) of ketene. The
rotational constants determined have been used to calculate the structureof ketene using a variety
of methods. The question of planarity of ketene is also addressed. High-resolution microwave
measurements have been used to determine the spin-rotation interaction in CH2”CO. o 1990
Academic
Press. Inc.
The first measurement of the rotational spectrum of ketene, CH2 = CO, was reported
in 1950 (I) for the main isotopomer and the monodeutero and the dideutero forms.
For the isotopomers 13CH2= CO and CH2 = C 180, the B and C rotational constants
were reported in 1959 (2) but no details of the observed lines or spectra were given.
Independent measurements on the same isotopomers were made by Beaudet (3). No
microwave measurements have been reported for CH2 = 13C0. More recently Johns
et al. (4) reported millimeter-wave and high-resolution infrared measurements for the
main species and Nemes and Winnewisser (5) reported millimeter-wave transitions
for the two deuterated species. Infrared spectra have also been reported by Nemes (6)
(main species), Winther et al. ( 7) ( DZ species), Hegelund et al. (8) ( DZ species),
Duncan et al. (9) (HZ, D2, and both 13C species), and Duncan and Ferguson (IO)
(Hz and both 13Cspecies).
In view of the importance of this small molecule, especially its interesting role as
the first member in the structurally anomalous cumulenone series (11-Z4), and its
detection in the interstellar medium (15-17), we have undertaken an investigation
in both the microwave and the millimeter-wave regions of the ketene spectrum for
the normal species, both 13C species, and the “0 species in order to provide greater
precision in the available spectroscopic constants for ketene, and in so doing, report
any improvements in the molecular geometry. We have also recorded spectra in the
1 GHz region in order to further our experimental and theoretical investigations of
magnetic hypefine structure in small molecules ( 18).
EXPERIMENTAL
DETAILS
Ketene was generated by vacuum pyrolysis of acetic acid or acetic anhydride in a
300 X IO-mm i.d. silicon tube pyrolysis furnace. Spectra were measured with a continuous flow of sample through the cell. When acetic acid was used as a ketene precursor
(on the microwave spectrometer), intermediate trapping of the unwanted pyrolysate
0022-2852190 $3.00
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All rights of reproduction
340
Press, Inc.
in any form reserved.
MICROWAVE SPECTRUM OF KETENE
341
by a dry ice cold trap plus packing the tube with 20 mm of silica packing was found
to reduce pressure broadening
by removing water and unpyrolyzed
acetic acid. On
the millimeter-wave
spectrometer
acetic anhydride was found to produce lines approximately five times more intense than those produced by acetic acid without trapping
and was used for all observations
of isotopomers
in natural abundance.
Pyrolysis
temperatures
to 1100°C were attained through resistive heating and optimized by
observing the intensity of the 10,-000 and the 17 5,11- 165.12lines in the microwave and
the millimeter-wave
regions, respectively. Optimum pyrolysis temperatures varied with
precursor and pumping speed of the spectrometer.
The optimum
temperature
for
pyrolysis of acetic acid on the microwave spectrometer
was 1100°C; the optimum
temperature
for pyrolysis of acetic anhydride was 650 and 1000°C on the microwave
and millimeter-wave
spectrometers,
respectively.
‘3C-enriched acetic acid (Stohler Isotope Chemicals) was used to confirm assignments of the two r3C species of ketene in the microwave region and for accurate
measurements.
None was available at the time of the millimeter-wave
experiments
and all 13C observations
and measurements
were done in natural abundance
in the
higher-frequency
region. For the study of “0-ketene,
180-acetic acid was prepared
from the reaction of l80-water with acetyl chloride.
Microwave spectra of the four ketene isotopomers were recorded using conventional
Stark-modulated
spectrometers.
Microwave sources were referenced to a laboratory
standard which was calibrated against a cesium beam frequency standard operated by
CSIRO Division of Applied Physics. Frequency
measurements
are expected to be
accurate to I part in 10 ‘. Magnetic hyperfine measurements
utilized a 2-kHz detector
system in order to minimize line broadening.
A diagram of the millimeter-wave
spectrometer is presented in Fig. 1. The millimeterwave spectrometer consists of a 0.6-m absorption cell constructed from stainless steel
and internally coated with Teflon. The cell is evacuated with a 6-in. Edwards High
Vacuum Ltd. diffusion pump backed by a dual stage rotary pump. Millimeter-wave
radiation is produced by a Millitech MU4-02T tunable multiplier (quadrupler ) from
a fundamental
frequency produced by an OKI BOV11 or OKI 90V 1OA klystron, phaselocked to a BWO synthesizer operating in X-band. The quadrupled radiation is introduced into the cell via a square cross section microwave horn through a Teflon lens.
The radiation is focused by a second Teflon lens to a beam waist of approximately
20
mm at the center point of the cell and refocused by a further pair of Teflon lenses
into an externally mounted gold-plated circular cross section horn. The output is
directed via a light guide tube to an Advanced Kinetics InSb crystal helium-cooled
bolometer detector. The lens guide system was designed using the principles of Gaussian
optics (19).
In this study, the microwave signal was Stark modulated at 80 kHz by applying a
square wave voltage of up to 2500 V across two parallel plates (26.1 cm X 7 cm x 1
mm) situated transverse to the microwave beam and separated by approximately
2
cm. Both plates are secured by Dehin rods (Fig. 2). One plate was grounded and the
square wave voltage applied to the other plate. This system resulted in a signal-tonoise ratio of 20: 1 for the strongest 13C ketene lines in natural abundance and, unlike
our previous source-modulated
spectrometer (20). resulted in a straight baseline. We
have found Stark modulation
to be ideal at these high frequencies although lines with
very slow Stark effects are difficult to observe.
342
BROWN
ET AL.
UTILITY FORTS
LIGHT
GUIDE
TEFLON COATED
VACIJUMCHAMBER
-3
i
TO
BOLOMETER
i
t
SAMPLE PORT
VACUUM PORT
FIG. 1. Stark-modulated
millimeter-wave
spectrometer.
Analog signals from the phase sensitive detectors were digitized and stored on a
VAX 11/750 computer. This allowed repetitive scanning and computer averaging to
improve the signal-to-noise ratio of the absorption transitions. Line centers were determined by fitting a Lorentzian curve to the average of the accumulated line spectra.
Absorption transitions for the substituted ketenes were originally predicted using
the B and C values of Cox et al. (2), and the centrifugal distortion constants for the
normal species published by Johns et al. (4). Line assignments in the microwave
bbUN FLANGE
STARR
CONNJ3Cl-ION
FIG. 2. Plan view of Stark plates.
MlCROWAVE
SPECTRUM
343
OF KETENE
region were confirmed by comparison of their Stark effects with those of the normal
species and by the closeness of the fit of Watson’s S-reduced Hamiltonian to the data
in a weighted least-squares computer program (I’ representation). Millimeter-wave
transitions were predicted using the resulting rotational and centrifugal distortion constants from the fit to the lower-frequency transitions and the data of Johns ez al. (4).
Theoretical multiplet profiles for the ketene lines affected by the hyperfine structure
were produced utilizing our program SPINRO (21)) which is based upon a general
method for deriving asymmetric rotor hyperfine matrix elements for an arbitrary
number of coupled nuclei and for arbitrary coupling tensors (18). “C-H spin-spin
tensor elements were calculated from an optimized ub initio structure (CO = 1. I68
A, CC = 1.317 A, CH = 1.074 A, HCH = 121.2”) at the MP3/6-13G** level (22).
‘jC spin-rotation tensor elements were calculated on a VAX 1 1 / 780 computer using
the program COLUMBO (23) which utilized the output from an SCF calculation by
Gaussian 80 package, version D (24). The calculations were carried out using the
double zeta (DZ) basis sets of Dunning (25) enhanced with one set of polarization
functions with basis sets contracted to 4~2~1 d on carbon and oxygen and 2slp on
hydrogen. Proton magnetic hyperfine constants ( spin-spin and spin-rotation ) for ketene were taken from Fabricant ef al. (26). Tensor elements required for the prediction
of the hyperfine components of the CH2 = 13C0 2i ,-2i2 transition are given in Table I.
RESULTS
The transitions assigned for the four ketene species are presented in Table II. In the
millimeter-wave region only lines with Kp > 2 were measured due to undermodulation
of the observed lower K lines. Observed line intensities followed the expected spin
statistics (odd Kp = 3 X even I’$). For this reason, not all isotopic lines of even Z$ in
the millimeter-wave region were observed. Also, a few isotopic lines observed were
not measured due to interference from normal species lines.
All transitions measured were fitted to Watson’s S-reduced Hamiltonian in the I’
representation. In addition to the transitions measured for the normal ketene species,
the microwave and IR combination differences (A&, = 2) reported by Johns et al.
(4) were included in the fit in order to best determine the molecular constants with
all available data. Only a small improvement
in the precision of the A rotational
constant resulted from the additional millimeter-wave transitions reported in this work.
TABLE I
Tensors Required for the Prediction of the Hyperfine
of the CH2= “CO 211-312 Transitiona
V(‘T-H)”
-4.13
-0.72
0.0
-0.12
1.31
0.0
Components
M(“C)C
0.0
0.0
3.42
67.00
i::
WI vaIues ill kH2.
Qakxktcdspin-spin
coupling
tensor.
ccalculated
spin-rotadon
WL~ling
tensor.
0.0
3.86
0.0
0.0
0.0
4.19
344
BROWN
ET AL.
TABLE II
Ketene Microwave and Millimeter Transitions
cH2=co
TEWitiOll
173.14 - w3,13
172.16 - 162.15
174.14 - 164.13
174.13- 164.12
175~3 - 165.12
175.12 - IQ.11
176.12 - &,ll
176.11 - l66.10
177.11 - 167.10
177.10 - 167,9
178,lO - 14,9
1789 - 16gS
182.16 - 172~5
183.16- 173.15
183.15 - 173.14
182.17 - 172,16
184.15- 174.14
184.14 - 174.13
185.14 - 175.13
185~3 - 175.12
l&,13 - 176.12
186.12 - 176.11
187.12 - 177.11
1’37.11- 177.10
w7.11 - 178,lO
188.10 - 178.9
192.17 - 182.16
193.17- 183.16
193.16 - 183.15
192.18 - 182.17
194.16- 184.15
194.15 - 184.14
195.15- 185.14
195~4 - 185.13
197.13 - 187.12
197.12- 187~1
cH2=‘3co
Observed Ohs.-Cal.
20209.201
40417.950
40039.022
40793.832
60625.695
60058.127
61190.279
60615.875
60617.162
20753.880
24903.578
343693.935
343384.676
343387.579
343376.133
343250.411
343250.411
343088.615
343088.615
-0.007
0.006
0.013
0.004
-0.043
0.046
-0.052
0.109
-0.166
0.007
-0.004
0.008
0.039
0.040
-0.002
0.044
0.034
-0.019
-0.019
342649.626
342649.626
342357.372
342357.372
363936.886
363580.268
363584.216
363559.732
363436.178
363436.178
363263.913
363263.913
363053.843
363053.843
362798.487
362798.487
362488.987
362488.987
0.047
0.047
-0.064
-0.064
-0.005
-0.027
0.053
-0.021
0.007
-0.008
-0.056
-0.056
-0.097
-0.097
0.066
0.066
-0.022
-0.022
Observed Ohs.-Cal
20209.834
40419.171
40040.246
40795.084
60627.578
60059.984
61192.148
60617.745
60619.041
20754.011
24903.738
343704.011
343395.328
343398.322
0.022
0.019
-0.004
0.011
0.030
0.045
-0.008
-0.018
-0.283
0.005
-0.003
o.ojo
-0.167
-0.068
343261.882 0.490
343261.882 0.480
343099.253 0.129
343099.253 0.129
342658.657 -0.085
342658.657 -0.085
363591.694
363595.537
0.081
0.063
363446.822 -0.791
363446.822 -0.806
363275.178 0.406
363275.178 0.406
(MHZ)
‘QI2=cD
ObSrved ohs.-Cal.
19568.103
39135.818
38780.490
39488.160
0.022
0.075
0.008
0.010
58170.377
59231.828
58693.266
58694.372
19457,562
23348.100
0.048
0.013
0.027
-0.238
0.008
-0.W3
332492.974
332495.348
332490.784
332367.262
332367.262
-0.340
-0.351
-0.253
0.508
0.500
332024.761
332024.761
331801.099
331801.099
-0.039
-0.039
a.090
-0.090
352366.774
352047.816
352051.030
352035.572
351912.906
351912.906
0.050
-0.286
-0.250
-0.004
0.596
0.584
351312.026 0.205
351312.026 0.205
cH2=c’O
obS?ved
19182.333
38364.313
38022.773
38702.993
57545.516
57033.792
58054.100
57536.436
57537.415
18702.844
22442.492
ohs.-Cal.
-0.016
-0.003
0.006
0.008
-0.005
0.001
-0.003
0.222
-0.074
O.W2
-0.004
345401.461 -0.445
345109.839 0.097
345112.685 -0.063
344980.348 0.052
z%z
344824:097
344632720
344632.720
344399.543
344399.543
:z!
0:044
-0.081
-0.081
-0.134
-0.134
364619.840
364278.642
364282.398
364257.590
364140.103
364140.103
363974.456
363974.456
363525.795
363525.795
0.129
0.034
-0.154
O.WO
-0.114
-0.132
0.073
0.073
0.126
0.126
_
The least-squares fit was optimized by including all five quark, two sextic, and one
octic distortion constant. Molecular constants for all isotopic species are presented in
Table III.
Transitions assigned to the CH2= 13C0 species occur at higher frequencies than
the corresponding transitions for the main species, conversely to what is expected.
The rotational constants for this isotopomer are thus larger than those of the main
species. This result, although unpredicted, is not unique. A similar result occurs for
N20 and has been attributed to the effects of zero-point vibrations outweighing changes
in the moments of inertia resulting from substitution near the center of mass of the
MICROWAVE
SPECTRUM
345
OF KETENE
TABLE III
Ketene Rotational and Centrifugal Distortion Constantsa
CH2=COb
A
282071. (11)
CH2=‘3CO
‘3CHz=CO
CH2=C1*0
CHD=C@
282334. (521)
282112. (334)
287350. (910)
194305.(38)
141537.(12)
B
10293.3175(53)
10293.6209(58)
9960.9659(79)
9761.2368 (33)
9647.0664 (13)
9120.8296(14)
C
9915.9036 (53)
9916.2046 (57)
9607.1276 (84)
9421.1236 (33)
9174.6457 (13)
8552.7008(16)
DJ
0.003278 (11)
0.003318 (27)
0.003108(16)
0.002873 (19)
0.0030075(84)
DJK
0.47925 (67)
0.4700 (14)
0.4417 (18)
0.4377 (15)
0.32851 (15)
0.0024652(70)
0.32328 (17)
22.577=
22.54oC
22.54of
DK
22.543 (738)
22.543C
22.561C
dl
-0.000143 (14)
-0.000143(15)
-0.000132(24)
-0.000126(11)
-0.0002241(14)
-0.0002156(17)
&
-0.m500
-O.O%OsoC
-O.@XlO44C
0.000131 (21)
-0.OCGQ847
(39)
-0.0001205(35)
HJK
HKJ
(75)
-0.000486(29)
IJKKK-0.ooooO388(30)
A
_____-__
O.OOOGO318
(55)
0.077058
-0.000831(23)
_-_-__-_
0.078630
-0.001182(74)
o.OOOOO753
(88)
0.077236
___
___
_
O.OOOOO224
(49)
O.OOXlO294
(29)
-0.0001156(65)
-0.OGQ386
(57)
-0.0002410(57)
-0.c0m414 (66)
-0.oooooo490 (60) -O.@XNIOO311
(67)
0.110345
0.096542
0.110008
aAU valuesin MHZ, except A in amu AZ;
transitions
fittedtoa S-reduced Hamiltonian in 1’ representation.
b Constants fitted to microwave data (this work) plus microwave and infrared combination differences calculated from data in Ref.@.
c Fixed in least-squares determination.
d Ref.a
data refitted to S-reduced Hamiltonian.
molecule. The A rotation constant for the CH2 = C “0 isotopomer is also larger than
the normal species A constant, although the transitions for this species are shifted
lower in frequency. The B and C rotational constants for the 13CH2=CO and
CH2 = C I80 species agree well with those reported by Cox et al. ( 2) _
The DK centrifugal distortion constants for the isotopic species were fixed at values
based upon force field calculations utilizing the GHFF force field tensor elements for
ketene of Duncan et al. (27). Calculated constants for the three isotopomers were
scaled by DK (experimental)/ DK (predicted) for the normal species. The dz centrifugal
distortion constants for the two 13Cspecies were fixed by the same procedure because
they were not well determined in the initial least-squares calculations. Higher-order
distortion constants not well determined were eliminated from the fit. None of the
least-squares parameters were significantly affected by varying the value of DK by 1
MHz or by varying the value of d2 (in the 13Ccalculations) by one unit in the most
significant digit.
The hyperfme structure of the CHz= 13C0 2, 1-212transition was observed experimentally to be very similar in its profile to that predicted (Figs. 3 and 4). The components grouped together in Table IV were observed as broad peaks. The first observed
frequency corresponds to the strong central peak consisting of many components.
Multiple scans over a small frequency region in the wings of the spectrum resulted in
an improved signal/noise ratio for the weaker components listed in Table IV.
346
BROWN
1132.16
ET AL.
1132.22
1132.26
Frequency
FIG. 3. Observed
hype&me
multiplet
1132.30
/MHz
of the CH2’3C0
211-2,2 transition.
The frequency differences between the components listed in Table IV have a large
dependence on the 13Cspin-rotation tensor and were used to estimate values of the
tensor elements. A frequency difference of 93 (4) kHz between the unresolved l/2 +
312, 512 + 512, 512 + 712 transitions and the 513 + 312 transition is in good
agreement with that predicted (89.1 kHz). Calculations using a 20% reduced spinrotation tensor predicted a splitting of 75.0 kHz. Therefore, linear interpolation was
used to obtain an estimate of the 13Cspin-rotation tensor assuming that the difference
between the predicted splittings and the measured splittings is due solely to differences
between the predicted and calculated 13Cspin-rotation tensors. This assumption seems
1
1132.252
1132.278
Frequency /MHz
FIG. 4. Predicted
hype&e
multiplet
of the CHZ’~CO 21,-2,2 transition.
1132.305
347
MICROWAVE SPECTRUM OF KETENE
TABLE IV
Observed Hyperfine Components of the CH2= “CO 21,-2,2 Transition”
Observed
Transition
F’cF”
O.-C.
h4Hz
MHZ
1132.242(2)
0.004
1132.202(4)
0.004
14-z
: :
1132.283(I)
0.007
5,1
2
2
1132.295(l)
0.008
UNtXOlVd
+21
I+1
2
2
1
2+-2
aAUvaluesin MHz.
reasonable
since the other variables contributing
to the hyperfine structure (H-H
spin-spin,
H spin-rotation,
13C-H spin-spin tensors) have been accurately measured
or calculated. The measured and calculated r3C spin-rotation
tensor components
are
presented in Table V.
DISCUSSION
Cox et al. (2) reported the first substitution
structure (Y,) of ketene in 1959. Moore
and Pimentel (28) reassigned the ketene infrared spectrum for the H2, HD, and Dz
isotopomers in 1962, resulting in a new b-coordinate for the hydrogen atoms and thus
new rS hydrogen parameters. In 1976, Mallinson and Nemes (29) calculated an average
structure (Y,), an effective structure ( ro), and a new substitution
structure (Y,) utilizing
all the then available data. These structures appear to combine isotopic data derived
from spectral fits differing in the level of treatment.
The hydrogen substitution
calculations were made without reference to which data (and which equations)
were
utilized (see discussion below). Duncan and Munro (30) published in 1987 a new
average structure and an estimated equilibrium
structure (r,) (based upon a diatomic
approximation)
utilizing the previous data plus newer high- and medium-resolution
TABLE V
Calculated (DZP) and Measured Nuclear and Electronic Contributions to Spin-Rotation
M
ww
M”ww
W&HZ)
M (kHz)a
7W)
4.1(4)
4.4(5)
tt
67.00
3.86
-2.59
-1.22
68.23
6.45
cc
4.18
-2.55
6.73
aMeasmd values;
this work.
Interaction
348
BROWN
ET AL.
infrared Dz-species data ( 7, 8). Additional high-resolution infrared studies of all the
isotopic ketenes except the I80 isotopomer, made by Duncan et al. (9, ZO), were
further utilized in a new force field calculation for ketene (31)) but no newer structure
refinements were reported.
The rotational constants determined in this work have been used here (along with
deuterium isotopomer data (5)) to calculate the structure of ketene in a variety
of ways.
1. Substitution Structure (r,)
For planar molecules, substitution structures may be calculated by sets of two rotational constants, making use of the relation AZ, = AZ, + AZ, in Kraitchman’s (32)
equations. For on-axis atoms, coordinates may be calculated with sets of single rotational constants, AZ, = 0; AZb = AZ,. As reported by Staley et al. (33), substantial
structural errors may be incurred through an arbitrary choice of data, when all the
data are not of similar precision. For all of the ketene isotopomers, the A rotational
constants are 2 to 4 orders of magnitude less precise, as determined in least-squares
fits, than the B and C rotational constants. Furthermore, all B and C constants reported
here are determined to better than 1 part in 106. The normal species B and C rotational
constants differ by less than 3 parts in lo8 (3 X 10M4MHz) when determined using
a data set of both microwave and IR combination-differences frequencies compared
to a microwave data set only. (The combination-difference frequencies affect mainly
the A rotational constant and certain of the centrifugal distortion constants.) Hence
calculations based on both microwave and IR combination-difference
frequencies
(where available) or microwave data only for the various isotopomers of ketene should
yield a consistent structure.
Rotational constants for determining hydrogen coordinates are calculated from
microwave data published by Nemes and Winnewisser (5) which were refitted to the
same Watson’s S-reduced Hamiltonian used here for the heavy (nonhydrogen) atoms.
When all three HDCCO rotational constants are used in Kraitchman’s equations, the
c-coordinate for hydrogen becomes small and imaginary, supporting the planarity
assumptions utilized in further calculations (see below). Hydrogen coordinates were
subsequently calculated setting c = 0 (planar Kraitchman’s equations) and using B
and C data only. B and C data were also used in Chutjian’s equations (34) utilizing
the doubly deuterated ketene data and the two results were averaged. The hydrogen
coordinates calculated from the two sets of data vary by +-0.00025 A (a-coordinate)
and +-0.00046 A (b-coordinate), well within the uncertainties quoted as Ag = 0.00 15/
g, g = a, 6, as recommended by Costain (35) and Harmony et al. (36).
When AZ, or AZcdata (aXiS eqUatiOnS)
or AZband AZcdata (planar t?qUatiOnS) are
used to calculate the coordinates of the heavy atoms, the a-coordinates of the oxygen
and methylene carbon change by less than 1 X 10e4 A. These results are averaged and
presented in Table VI. The carbonyl carbon a-coordinates are imaginary due to the
negative AZ’s and vary by less than 2 X low3 .& in the three calculations. The real acoordinate for the carbonyl carbon, presented in Table VI, was calculated by the first
moment condition, Llm,zi = 0. Uncertainties are calculated as A, = 0.0015/g, g = a,
6. The substitution structure calculated from the coordinates in Table VI is presented
in Table VII.
MICROWAVE
SPECTRUM
349
OF KETENE
TABLE VI
Substitution
Coordinates
for Ketene”
a
b
0
1.1828(13)
_____._
carbony
C
O.o208(721)b
Inethylene
C
1.2929( 12)
H
1.8131(g)
_____ _
-__-__.
0.9493( 16)
aAl1values in A.Uncertainties calculated as Ag=O.O015/g, g=a,b.
bDeterminedby fust moment condition.
2. IZffective Structure (rO)
Several least-squares fits of the four molecular parameters to the data have been
performed. The least-squares fits result in larger bond lengths and angles than in the
substitution calculations, as is expected. When the carbonyl carbon is allowed to move
off the u-axis (but remaining in the ab plane), no significant difference in the results
is obtained; i.e., within the uncertainty of the fit, the b-coordinate remains zero. The
effective r. structure, determined as an average of two data sets including HDCCO or
DDCCO rotational constants and utilizing only B and C constants (five isotopomers
each), is presented in Table VII. Both fits assume a linear CC0 chain. Uncertainties
are presented as m,
where ArO’sare the uncertainties in the least-squares fits.
3. .4pproximate Equilibrium Structure (rf’,,)
Recently, Harmony et al. (37-40) have presented methods based upon Watson’s
(41,42) mass-dependence I, calculations whereby experimental ground state moments
of inertia (lo’s) are scaled by a factor, 2p - 1 (p = Is/IO), in order to approximate
equilibrium moments ( le’s). As described in those papers, the resulting (scaled) moments (If,,) must be corrected in the case of deuterium-substituted data to account
TABLE VII
Ketene StructurePb
co
1.1626 (57)
1.1620 (721)
1.1600 (58)
1.1609 (4)
1.1681
cc
1.3147 (60)
1.3137 (721)
1.3140 (62)
1.3142 (5)
1.3166
CH
1.G905 (18)
1.0825 (15)
1.0740 (19)
1.0753(17)
1.0745
HCH
123.46 (29)
122.56 (1)
a Bond distances in A;angle in degrees
b For uncertainties see text
c Values from Ref.m.
121.58 (29)
121.76 (33)
121.249
350
BROWN
ET AL.
for overscaling due to the larger vibrational contribution to the ground state moments
in the deuterium compound. The complete set of Z& moments (rotational constants)
are then least-squares fitted to obtain structures, r;, which are better approximations
to equilibrium structures than those obtained by the conventional r. or Y, methods.
r& structures are expected to be within - 10m3A of the equilibrium structure. In this
work, pa and pb values for both HD and DD substitution data sets were used to
calculate rA structures. The deuterium correction of 0.0028 1 A along the substitution
CH bond axes was applied to the deuterium moments and the resulting least-squares
fits of the two data sets were averaged. Results are presented in Table VII.
The heavy-atom r. and rs parameters calculated in this work agree with the previously
published values within the errors reported in all data sets. Our r. and I, hydrogen
parameters do not agree with the previously published values (29).
Of particular interest is the newly calculated rf,, structure. Early calculations demonstrated that heavy-atom parameters could often be reproduced within 0.001 A of
equilibrium values, and generally within the hoped-for 0.002-0.003 A. (Harmony
refers to the work of Whiffen and co-workers (43-45). who have shown that errors
of 0.001 A may result even in conventional re determinations if Coriolis coupling
contributions are ignored.) Subsequent papers (39, 40) have described methods for
accommodating hydrogen-containing molecules. Except for the CO bond length, all
of the r$ parameters reported here agree with Duncan and Munro’s (30) estimated
Y, structure within the uncertainties quoted for both sets of calculations. The CO bond
determined here by the rL method is smaller than that determined by Duncan and
Munro by 0.0009 A, still well within the expected precision for the r$ calculation and
only slightly outside the error limits reported by those authors. This discrepancy may
be a product of either or both calculations: Duncan and Munro used a combination
empirical/ah initio general harmonic force field to calculate their average structure
and they assumed bond anharmonic parameters in the diatomic approximation to
calculate an r, structure. With the rL method, molecules containing large-amplitude,
low-frequency bending modes have been shown (HNC (39), ethylene (40)) to scale
poorly (i.e., the vibration-rotation
contributions of these modes do not cancel well:
hence the hydrogen-deuterium
correction) and for ketene both the CH2 wag and the
CC0 out-of-plane bend fall below 600 cm-’ (31). It is worth noting that the effect of
not correcting the large-amplitude bond stretching-rotation contributions (e.g., hydrogens) is a resultant bond length too small relative to the equilibrium bond. This
is precisely the effect suspected in the r& calculation for the CO bond in ketene. Data
allowing us to correct for heavy-atom, low-frequency vibrations in a manner similar
to the hydrogen correction, however, are not presently available. This would require
equilibrium structures for molecules having low-frequency bending of analogous heavyatom groups (in this case, CO). For the present, it is mainly of interest in support of
both approximate equilibrium calculations that they agree so well.
Table VII also contains the results of a full geometry optimization of ketene at the
MP3 /6-3 1G * * level of theory. In this calculation the hydrogens were allowed to bend
out of the plane of the heavy atoms and the CC0 angle was allowed to vary from
180”. The minimum energy position is with the hydrogens coplanar with the heavy
atoms. Both the calculated approximate equilibrium structures agree well with the
calculated geometry, although the CO distance is overestimated by the MP3 / 6-3 1G* *
calculation.
MICROWAVE
SPECTRUM
OF KETENE
351
The question of planarity for this molecule, central to the studies of the cumulenones
ever since propadienone was synthesized and determined to be kinked at the central
carbon atom ( 11, 13), is resolved in the affirmative (i.e., ketene is planar, Cl”) to the
extent of the following evidence:
(i) Inertial defect values determined from normal coordinate analysis (5) and force
field calculations (29) based upon a planar C 2Vmolecule compare favorably with
experimental values. In the latter calculations, the components Avib, Acent,Aelec( Aelec
from molecular g values (46)) account for better than 99% of the experimental ground
state inertial defect.
(ii) Treatment of the HDCCO data with Kraitchman’s equations (32) for the nonplanar asymmetric rotor yields a small (0.123 A (this work)) imaginary coordinate
along the c-principal axis.
(iii) The ab initio molecular structure optimized using large MO basis functions
and including the effects of electron correlation predicts a planar Cz, structure.
ACKNOWLEDGMENT
This
work was supported by a grant from the Australian Research
RECEIVED:
Council.
December 19, 1989
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