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The microwave spectrum of methyl isoselenocyanate: CH3NCSe as a quasi-symmetric top
JOURNAL
OF MOLECULAR
SPECTROSCOPY
140, 3 l-45 (1990)
The Microwave Spectrum of Methyl Isoselenocyanate: CH,NCSe as a Quasi-symmetric Top J. KOPUT Depurtment qf Chemistrv, Adam Mickiewicz University. 60- 780 Poznati. Poland AND
F. STROH AND M. WINNEWISSER Phpical Chemistry Institut, Justus Liebig University8 6300 Giesren. Federal Republic of Germuq The microwavespectrum of methyl isoselenocyanate. CH,NCSe, has been measured in the region 18-40 GHz. The a-type J + 1 + J rotational transitions (J = 5 to 10) in the ground vibrational state of the molecule have been assigned for the three isotopic species with ‘*Se, “Se. and ‘%e. For the most abundant isotopic species, with *‘Se, the rotational transitions in the excited states of the CNC bending mode or0 = 1 and 2 have also been assigned. Contrary to the previous investigation [T. Sakaizumi et al., Bull. Chem. Sot. Japan 59, 1614-16 16 ( 1986)], it has been shown that the observed spectrum is consistent with that of a quasi-symmetric top molecule. The rotation-vibration constants have been determined. showing an unusual variation with excitation of the CNC bending mode. The CNC bending potential function has been determined in preliminary calculations using a quasi-symmetric top model. The potential function is calculated to be very anharmonic, with an equilibrium CNC angle of about 162” and a barrier to linearity of the CNCSe skeleton of about 25 cm _I. From accidental resonances observed for the ground state transitions the barrier to internal rotation of the methyl group was estimated to be about 3 cm~‘. 0 1990 Academic Press, Inc. I. INTRODUCTION
In a series of papers [see Ref. ( 1) and references therein] the microwave spectra and molecular structures of isocyanates and isothiocyanates have been studied using a quasi-symmetric top approach. In the present paper, an extension of previous studies, we report the first results of an analysis of the microwave spectrum of methyl isoselenocyanate, CH3NCSe. The microwave spectrum of methyl isoselenocyanate was recently reported by Sakaizumi et al. (2). The authors analyzed the rotational spectrum in the ground vibrational state of the molecule within the standard asymmetric-rigid-rotor approximation. The assignment of several lines in the region 9-40 GHz was proposed and the rotationvibration constants A, B, C, AJ, and A, were determined for the two isotopic species, CH3NC *‘Se and CH3NC ‘*Se. The methyl isoselenocyanate molecule was found to be a near symmetric top with the CNC angle of 157 -t 4”. Sakaizumi et al. concluded that though the microwave spectra of methyl isocyanate, CH3NC0. and methyl isothiocyanate, CHjNCS, could not be fitted within the standard semirigid-rotor ap31
0022-2852190 Copyright
0
$3.00
1990 by Academtc
All rights of reproduction
Press
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in any form reserved.
32
KOPUT,
STROH,
AND WINNEWISSER
proximation (the rigid-frame/rigid-top model), the observed spectrum of methyl isoselenocyanate could be fitted within the rigid-rotor approximation. This in turn led the authors to the conclusion that the barrier to internal rotation of the methyl group in methyl isoselenocyanate might be higher than some 0.3 kcal/mol. On the other hand, an analysis of the infrared spectrum reported by Franklin et al. (3) showed essentially free internal rotation of the methyl group in gaseous methyl isoselenocyanate. Also, the frequency of the CNC bending mode was found to be low; the weak band near 370 cm-’ in . the infrared spectra of the solid and liquid states was assigned to be equally well the fundamental or first overtone of the CNC bending mode. The infrared measurements of Franklin et al. (3)) along with the previous analysis of the microwave spectra of methyl isocyanate and methyl isothiocyanate by one of us ( I ), suggest that methyl isoselenocyanate is not a rigid, near symmetric top, but rather another example of a quasi-symmetric top molecule. This possibility is further supported by microwave (4) as well as millimeter-wave and infrared studies (5) of isoselenocyanic acid, HNCSe. It was shown that in the series including isocyanic acid, HNCO, isothiocyanic acid, HNCS, and isoselenocyanic acid the latter is the most quasilinear molecule. Although the shape of the HNC bending potential function was not explicitly determined, the large-amplitude HNC bending motion in isoselenocyanic acid was found by Vogt and Winnewisser (5) to be the most anharmonic in the series. That is why we decided to reinvestigate the microwave spectrum of methyl isoselenocyanate. We report here the measurement and assignment of the rotational spectrum in the ground vibrational state and some excited states of the CNC bending mode, and also the results of preliminary calculations on the CNC bending potential function. II. EXPERIMENTAL
DETAILS
Samples of methyl isoselenocyanate were prepared by refluxing the mixture of methyl isocyanide and selenium powder in chloroform (2) or petroleum ether (3). The samples were purified by trap-to-trap vacuum distillation. The microwave spectra were recorded using a Hewlett-Packard Model 8460A MRR spectrometer. All spectra were taken at room temperature. The half-life of methyl isoselenocyanate was observed to be approximately 1 min in the metal microwave cell, and the spectra were therefore taken in a slow flow with sample pressures of about 10 mTorr ( 1 mTorr = 0.13 Pa) measured at the cell end. Lines were recorded at Stark field strengths ranging from 10 to 1400 V/cm. Frequency calibration was checked by comparison with lines of OCS (6). The accuracy of the measured frequencies is estimated to be f0.05 MHz for well-resolved lines. The positions of overlapping lines were determined by band shape analysis-a computer simulation of a band envelope using a Lorentzian lineshape function. The spectra of the molecules with different selenium isotopes were observed in natural abundance. No quadrupole hyperfine structure due to the 14N nucleus was observed. III. SPECTRUM
AND ANALYSIS
The microwave spectrum of methyl isoselenocyanate consists of a-type R-branch rotational transitions of a near-prolate symmetric rotor with a rotational constant B
CHjNCSe
AS A QUASI-SYMMETRIC
33
TOP
of about 1.6 GHz. Each J + 1 + J rotational transition contains many lines of comparable intensity. The observed great complexity of each rotational transition and the high density of lines are partly due to the presence of several isotopic species containing different isotopes of selenium; the selenium atom has five important isotopes with mass numbers and relative abundances being, respectively, 80-49.82%, 7823.52%, 82-9.19%, 76-9.02%, and 77-7.58%. This is also partly due, as suggested above, to the presence of two-large amplitude motions in the methyl isoselenocyanate molecule, namely the internal rotation of the methyl group and the CNC bending motion. As these two motions are of a low frequency a large number of the excited states can be populated at room temperature giving rise to several significantly intense lines in the rotational spectrum. A survey microwave spectrum between 29.1 and 30.0 GHz, in the region of the J = 9 + 8 rotational transition, is shown in Fig. 1. The assignment of the observed spectrum proposed by Sakaizumi et al. (2) was made in terms of the asymmetric-rigid-rotor model. In the region shown in Fig. 1 (we will restrict ourselves the discussion to the J = 9 + 8 rotational transition only), the pair of lines at 29 539 and 29 622 MHz was assigned on the basis of the observed Stark effect and intensity to the K, = 1 asymmetry-doublet transitions in the ground vibrational state of the most abundant isotopic species CH3NCs0Se. The strongest line in this region, at 29 582 MHz, lying midway between the K, = 1 lines, was assigned to the K, = 0 ground state transition. The other two lines in the vicinity of the K, = 0 line, at 29 576 and 29 569 MHz, were assigned to the unresolved K, = 2 and Ku = 3 ground state transitions, respectively. As shown in Ref. (I) (compare Figs. 1 and 2 therein) for molecules of the WH3XYZ type, such an assignment is characteristic of an asymmetric top molecule with a well-
29 1
293
FIG. 1. Survey microwave of the J = 9 + 8 rotational V/cm.
29 5
297
29 9GHr
spectrum of methyl isoselenocyanate between 29.1 and 30.0 GHz, in the region transition, recorded as described in the text, with a Stark field strength of 1200
34
KOPUT,
STROH,
AND WINNEWISSER
bent equilibrium configuration of the WXYZ skeleton. For a molecule with a large WXY angle, as that found for methyl isoselenocyanate (2), the observed spectral pattern is expected to closely resemble that of a symmetric top molecule. In the latter case, the K, = 0 ground state transition should be clearly displaced to lower frequency with respect to the K, = 1 asymmetry-doublet transitions. For a molecule close to the symmetric-top limit ( I ) , the ground-state transition, in terms ofthe usual symmetrictop formalism, ’ should form a regular series of lines showing the characteristic Stark behavior and relative intensities. The K = 0 transition should have a normal secondorder Stark effect, whereas the K P 0 transitions should have a very fast first-order Stark effect. Since the molecule is of C’s”symmetry the K = 3n ground state transitions, where n is an integer, should show an enhanced intensity, as being unresolved doublets due to the rotational transitions between energy levels of A, and A2 symmetry. The observed frequencies Yof the J + 1 + J ground-state transitions should also follow the symmetric top formula ( 7) V = 2B(J+
1) - 4DJ(J+
1>3 -
2DJK(J+
l)K2
+ 4HJK(J+
1)3K2 + 2HK,(J+
l)K4,
(1)
where B, DJ, DJ~, HJK, and HxJ are the usual rotation-vibration constants. The first clue to such an assignment came when the region about 29.3 GHz was analyzed. As shown in Fig. 2 the series of lines, beginning with the line at 29 377 MHz, can be assigned on the basis of the above-mentioned criteria to the J = 9 + 8 ground state transition of the most abundant isotopic species, CH3NCa0Se. A similar series of lines can be found in this region beginning with the line at 29 172 MHz. As the relative peak heights of the lines are of about one-fifth of those assigned to the ground state transition of CH3NC8’Se this series can be assigned to the ground state transition of the other isotopic species, CH3NC8*Se. If this assignment is correct, a similar series of lines, arising from the CH3NC ‘*Se molecules, is expected to be found displaced by about 200 MHz to higher frequency with respect to the ground state transition of CH3NCa0Se. Indeed, such a series can be found beginning, as shown in Fig. 3 below, with the line at 29 592 MHz. The relative peak heights of these lines are of about one-half of those assigned to the ground state transition of CH3NC8’Se, as expected from the relative natural abundances of the selenium isotopes. The lines of the ground state transitions of the other two isotopic species, CH3NC77Se and CH3NC7%e, are expected to be found around 29.7 and 29.8 GHz, respectively. Since these Iines are of a small intensity and the regions mentioned are overcrowded (see Fig. 1) we did not attempt to make a detailed assignment. The frequencies of the J + 1 f J ground-state transitions, with J = 5,6, 8, 9, and 10, have been measured for the three isotopic species, with 82Se, 80Se, and 78Se, and have been fitted using the symmetric top formula ( 1) . The observed frequencies and the differences between the observed and calculated frequencies are given in Table I. As shown by the results, it is possible to fit the observed frequencies with standard deviation about 0.1 MHz. Although this deviation is bigger than the experimental ’ The energy levels and wavefunctions of a quasi-symmetric top molecule can be described in two ways, using either the usual asymmetric or symmetric top formalism (I ). We use hereafter the symmetric top notation in which the rotational quantum number K of a prolate symmetric top corresponds to K,.
CH,NCSe
29.1
292
AS A QUASI-SYMMETRIC
35
TOP
29.4 GHr
293
FIG. 2. Part of the / = 9 + 8 rotational transition in the ground vibrational states of CH,NC*‘Se and CH,NC%e, with the lines labeled by K values. The upper spectrum was recorded using 1400 V/cm Stark modulation, while the lower spectrum was recorded using 100 V/cm Stark modulation; note that the K = 0 lines are not fully modulated even at the electric held strength of 1400 V/cm. The enhanced intensity of the K = 3 and K = 6 lines is clearly shown.
295
296GHz
FIG. 3. Part of the J = 9 8 rotational transition in the ground vibrational state v’ = 0’ of CH3NC7”Se and in the excited states Y’ = 1” and 2” of CH3NC**Se. The lines for the 0’ and 2’ states are labeled by A’ values: note the difference in the K structures. The asterisks mark the K = 1 I-type doublet lines in the excited state u’ = 1” of CHJNCEOSe.
KOPUT,
36
STROH,
AND
WINNEWISSER
TABLE I Observed Frequencies (obs.) and Differences Between the Observed and Calculated Frequencies (o-c), in MHz, for the J+ 1 + JRotational Transitions in the Ground Vibrational State ofCH,NC”Se, CH,NC*“Se, and CH3NC%e CHsNCs%
CH3NCsoSe
J
K
obs.
5 5 5 5 5 5 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10
0 1 2 3 4 5 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 10
19448.33 19444.04 19431.30 19409.91 19380.06 _
0.05 0.00 0.00 -0.09 -0.01
22689.59 22684.61 22669.76 22644.90 22610.16 22566.97” 22509.49 29172.19 29165.82 29146.66 29114.74 29070.19 29014.77a 28941.03 _
0.00 -0.04 -0.03 -0.07 0.09 2.00 0.03 0.09 0.07 -0.04 -0.11 0.10 2.55 0.01
32413.40 32406.27 32385.05 32349.60 32300.20 32238.74” 32156.91 32062.63 _ _
0.11 0.02 -0.05 -0.17 0.11 2.86 0.05 -0.10
35654.54 35646.70 35623.38 35584.44 35530.17 35462.65” 35372.84 35269.38 _
0.12 0.01 -0.09 -0.22 0.08 3.09 0.07 0.01
a Perturbed
_
obs.
O-C
19584.83 19580.51 19567.72 19545.93 19515.72 19478.28” 22848.89 22843.87 22828.85 22803.58 22768.45 22724.71” 22666.52 29377.02 29370.55 29351.19 29318.82 29273.77 29217.65” 29143.00 29056.98 28957.42 32640.98 32633.78 32612.31 32576.37 32526.38 32464.11” 32381.32 32285.91 32175.55 32049.19 35904.84 35896.96 35873.35 35833.90 35778.98 35710.59” 35619.71 35515.00 35393.90 35255.28 35098.78
line, excluded from the fit.
CH3NC7sSe o-c -0.07 -0.08 0.08 -0.08 0.09 1.89 -0.08 -0.08 0.00 -0.07 0.21 2.19 0.19 0.02 0.00 -0.01 -0.07 0.28 2.78 0.17 -0.16 -0.09 0.04 -0.01 -0.02 -0.11 0.25 3.01 0.13 -0.22 -0.06 -0.09 0.01 -0.03 -0.07 -0.16 0.21 3.22 0.08 -0.25 0.00 0.09 0.11
obs.
O-C
19728.06 19723.63 19710.45 19688.48 19658.06 _
0.04 -0.02 -0.09 -0.15 0.20
23015.93 23010.79 22995.49 22969.90 22934.38 22890.02” _
-0.01 -0.06 -0.08 -0.14 0.20 2.14
29591.68 29585.15 29565.49 29532.68 29487.08 29430.19” 29354.65 29267.47 _
0.03 0.02 -0.04 -0.13 0.25 2.72 0.15 -0.24
32879.48 32872.22 32850.40 32813.99 32763.41 32700.31” 32616.52 32519.88 32408.19 32280.18 36167.22 36159.26 36135.22 36095.29 36039.72 35970.38” 35878.50 35772.32 35649.66 35509.32
0.05 0.02 -0.06 -0.17 0.24 3.00 0.14 -0.21 0.04 0.00 0.06 0.04 -0.14 -0.21 0.21 3.18 0.17 -0.29 -0.04 0.14
CHSNCSe
AS A QUASI-SYMMETRIC
37
TOP
accuracy, it is not unexpected when the symmetric top formula is applied to fit the rotational spectrum of a near-symmetric top molecule (8). The K = 5 transitions were found to be perturbed for all the isotopic species; as shown below (see Section IV) these perturbations are due to internal rotation of the methyl group. The calculated rotation-vibration constants are given in Table II. For a symmetric top molecule of C,, symmetry, the sum of quartic centrifugal distortion constants (DJK + 2DJ) is proportional to the square of the rotational constant B ( 7, 9). Since the proportionality constant includes the rotational constant A and vibrational factors, which all can be expected to be approximately constant for the isotopic species under consideration, the calculated relative values of (DJK + 2DJ) should be the same as those of B*. It follows indeed from the results of Table II that for the isotopic species with 82Se, “Se, and 78Se, the relative values of ( DJK + 2DJ) are 0.983, 1, and 1.O13, while the relative values of B* are 0.986, 1, and 1.O15, respectively. Similarly, the quartic centrifugal distortion constant DJ is expected to be proportional to B4 ( 7, 9). For the isotopic species with “Se, 80Se and 78Se, the calculated relative values of DJ are 0.932, 1, and 1.059, while the relatibe values of B4 are 0.972, 1, and 1.030, respectively. Since the ground state transitions of methyl isoselenocyanate are satisfactorily described as those of a symmetric top molecule the other rotational transitions observed for the different isotopic species can be assigned as those in excited states of the lowestfrequency bending mode vIo, this being from the infrared study (3) the CNC bending mode. The Ka = 1 asymmetry doublet, assigned unambiguously on the basis of the Stark effect (2), is thus assigned as the K = 1 I-type doublet in the first excited state V Lo = 1. Ilo = fl ( vlo and Ilo are hereafter written simply as I.Jand I). The other lines observed in the vicinity of the I-type doublet lines, shown for the J = 9 + 8 rotational transition in Fig. 3, can then be also assigned to transitions arising from molecules in the excited state v’ = 1 ‘I. However, when this region was examined thoroughly it appeared that at least three different types of rotational transitions could be recognized. The first series of lines was assigned to the above-mentioned rotational transition in the ground vibrational state of CH3NC78Se. The second series of lines was assigned
TABLE II Calculated
Rotation-Vibration CH,NC’%e,
B/
MHz
Constants’ for the Ground Vibrational States of CH3NC8*Se. and CHINC%e as Symmetric Top Molecules
1620.7051(42)
1632.0907(61)
1644.0182(70)
DJ/ kHz
0.204(22)
0.219(32)
0.232(36)
DJK/~HZ
354.26(31)
360.36(25)
364.91(39)
HJK/HZ
12.3( 14)
15.8( 13)
16.0( 19)
HKJ/HZ
-120.5(50)
-99.0( 18)
-101.2(28)
’ Figures digit
in parentheses
quoted.
are one standard
deviation
in units
of the last
KOPUT,
38
STROH,
AND
WINNEWISSER
on the basis of the Stark effect and relative intensities to the rotational transition in the excited state v1 = 1 *’ of CH3NC8’Se. For a symmetric top molecule, these lines should appear in the rotational spectrum as two branches corresponding to the kl > 0 and kl -c 0 transitions and having the k = 0 transition as a common origin (k is the signed rotational quantum number, K = 1k I); the I k - I( = 3n transitions, where n is an integer, should show an enhanced intensity. It appeared that several of the observed transitions coalesced into single, broad-and-structured lines; for example, the strongest line in the region shown in Fig. 3, at 29 582 MHz, was found to consist of the three transitionswith(v’,k)being(l’,O),(l’,-l),and(1’,-2).Thethirdseriesoflines showed a pattern characteristic of the rotational transition in a nondegenerate vibrational state of a symmetric top. Since the intensity of lines was about the same as that of the ground state transition of CH3NC7’Se this series could only be assigned to the rotational transition in the excited state v’ = 2’ of CH3NCSoSe. The other weak lines observed in this region are most likely due to the rotational transitions in the excited states of CH3NC 82Se. The measured frequencies of the J + 1 + J rotational transitions, with J = 5, 6, 8,9, and 10, in the excited states v’ = 1” and 2’ of the most abundant isotopic species CH3NCs0Se are given in Table III. The transition frequencies u in the 1*’ state have been fitted to the symmetric top formula ( 7) v = 2B(J+
1) - 4DJ(J+
+2H&J+
1)3 - 2DJK(J+
l)k4i-2v.,(J+
l)k2
l)kl+48J,(J+
+ 4I&(J+ 1)3kl+20,(J+
1)3k2 l)k31+Av,
(2)
where Av = fqe(J+ Av
=
d(J+
1)
l)[(J II2 - (kl4(kll)(A - Al - B) +
U21
for
kl=
1,
for
kl#
1.
(3)
The transition frequencies in the 2’ state have been fitted to formula ( 1)) neglecting interactions with the 2’2 state. As for the ground vibrational state, the standard deviations of both fits, of about 0.3 MHz, are bigger than the experimental accuracy. The calculated rotation-vibration constants are given in Table IV. The rotational transitions in the excited states v ’ = 1*’ and 2 ’ of CH3NC ‘*Se have also been assigned; since the transition frequencies were measured only to t-O.5 MHz they are not reported here. The calculated rotation-vibration constants show an unusual variation with excitation of the CNC bending mode vlo. For a rigid, symmetric top molecule, the rotational constant B is expected to change linearly with the vibrational quantum number v, while the centrifugal distortion constant DJKis expected to be almost constant. Changes in the constants B and DJK determined for CH3NCE0Se indicate that the methyl isoselenocyanate molecule is far from being a true rigid, symmetric top. Similar changes in the constants B and DJx have been observed for silyl isocyanate, SiH3NC0, the molecule being a prominent example of a quasi-symmetric top ( 9). A comparison of the constants B and DJK for methyl isoselenocyanate and silyl isocyanate is presented
CH4NCSe AS A QUASI-SYMMETRIC
TOP
39
TABLE III Observed Frequencies (obs.) and Differences Between the Observed and Calculated Frequencies (o-c). in MHz, for the J + 1 + J Rotational Transitions in the Excited States u’ = 1” and 2’ of CH9NCs0Se ?J’ = 20
n’ = l*’ kl 10 J 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10
K 0 1 1 2 3 4 5 0 1 1 2 3 4 5 6 0 1 1 2 3 4 5 6 0 1 1 2 3 4 5 6 0 1 1 2 3 4 5 6
obs.
kl < 0 o-c
19721.66” 19692.84 19747.88 19717.42n 19713.06” 19706.60 _
0.03 0.11 0.15 -0.09 0.04 -0.08
23008.37 22974.93 23039.09 23003.77 22998.44 22990.95 _ _
-0.04 0.17 0.16 0.03 -0.05 -0.14
29581.77 29538.90 29621.44 29576.17 29569.20 29559.68 29547.18
0.01 0.20 0.24 0.01 -0.16 -0.19 0.18
32868.39 32820.85 32912.52 32862.37 32854.57 32843.98 32830.17 _
0.09 0.26 0.26 0.02 -0.20 -0.25 0.21
36154.93 36102.76 36203.57 36148.55 36139.89 36128.20 36113.14
0.19 0.34 0.31 0.03 -0.26 -0.37 0.25
obs.
19721.66” 19721.42a
-0.42 -0.07
19717.42” 19714.11°
-0.09 0.02
23008.48” 23008.01
-0.47 -0.25
23003.42” 22999.56 22994.41
-0.18 -0.04 0.06
29582.12 29581.36 _
-0.37 -0.23
29575.51 29570.71 29563.48
-0.04 0.33 -0.11
32868.71 32867.92
-0.44 -0.22
32861.45 32855.97 32847.83
0.06 0.34 -0.24
36155.27 36154.42 _
-0.44 -0.17
36147.26 36141.17 36132.11
0.14 0.41 -0.31
’ Strongly overlapped line, excluded from the fit. b Perturbed
O-C
line, excluded from the fit.
obs.
O-C
19744.89
-0.07
19743.33 19738.85 19730.39 _ _
-0.05 0.25 -0.17
23035.60
-0.14
23033.80 23028.59 23018.84
-0.10 0.26 -0.12
22987.58b 22966.46 29617.13
-0.65 0.02 -0.11
29614.73 29608.09 29595.55 29580.04b 29555.48b 29528.32 32907.86
-0.14 0.37 -0.15 1.41 -0.79 0.00 -0.09
32905.19 32897.79 32883.82 _
-0.13 0.40 -0.23
32839.43’ 32809.30 36198.52
-0.86 0.02 -0.11
36195.60 36187.48 36172.18 _
-0.14 0.45 -0.19
36123.31’ 36090.23
-1.00 -0.01
40
KOPUT, STROLL AND WINNEWISSER TABLE IV Calculated Rotation-Vibration Constants” for the Excited States uf = 1*’ and 2“ of CHsNC8”Se as a Symmetric Top Molecule v’ = 1*r
?Jr= 20
1643.499( 12)
1645.423( 12)
0.279(59)
0.126(58)
Bl MHz DJ/
kHz
DJK/
kHz
47.0( 11)
132.3(13)
HJK/
Hz
0.3(41)
4.5(40)
HKJ/
Hz
-211(28)
-158(28)
SJ/ kHz
-79.4(34)
@JJ/ Hz
34( 15)
@JK/ Hz
-2270( 110)
qe/ MHz
4.5838(92)
(A - AC - B)/ MHz
9100(2100)
L1Figures in parentheses
are one standard
deviation in
units of the last digit quoted.
in Table V. Although we did not yet assign unequivocally the rotational transitions in higher excited states of the vlo mode, the methyl isoselenocyanate molecule appears to be another example of a quasi-symmetric top. This explains the inadequacy of the usual symmetric top formalism when it is applied to describe the observed rotational spectrum. TABLE V Comparison of the Constants B and DJKDetermined for Various States of the vIo Mode of CHsNC*‘Se (This Work) and SiH,NCO (9) d = 00
9J’= 1*1
ur =z 20
CHsNCSe B/ MHz
1632.091
1643.499
1645.423
DJK/
360.4
47.0
132.3
kHz
SiHsNCO B/ MHz
2517.932
2542.349
2543.064
DJK/
642.0
58.4
226.6
kHz
CH3NCSe AS A QUASI-SYMMETRIC IV. CALCULATION
41
TOP
USING THE QUASI-SYMMETRIC
TOP MODEL
The standard symmetric top approach allowed us to understand a part of the observed rotational spectrum of methyl isoselenocyanate in terms of the rotation-vibration constants. To get a deeper insight into the structure and dynamics of the molecule we used the quasi-symmetric top approach. The quasi-symmetric top model [the reader is referred to Ref. ( 1) and references therein for details] allows one to relate the rotation-vibration energy levels of a nonrigid WH,XYZ molecule directly to the structural constants and shape of the potential energy surface. The energy levels, and the corresponding transition energies, are calculated using an approximate, five-dimensional Hamiltonian, which describes a WHJYZ molecule bending at the WXY angle, internally rotating about the WX bond, and rotating in space. The quantities appearing in the Hamiltonian are functions of coordinates of the two large-amplitude motions, the WXY bending motion and internal rotation of the WH3 group; they depend as well on the assumed structural and potential function parameters. All other vibrations of the molecule are assumed to be of small amplitude and coupled to neither the large-amplitude motions nor overall rotation. The rotation-vibration energy levels are calculated by a variation method assuming some values of the structural and potential function parameters. The other way around, the values of these parameters can be determined by a leastsquares fitting of the calculated transition energies to the observed ones. As contributions of the small-amplitude vibrations are not explicitly included in the Hamiltonian the quasi-symmetric top approach can be used for the rotation-vibration energy levels with low J values, say J d 5; and the determined parameter values can only be considered as effective values, as being averaged over the small-amplitude vibrational coordinates. In the calculations the CNC bending potential function V,(p) was chosen as a quadratic potential with a Lorentzian hump
Hfb2 - PZ)’ “‘(‘)
= fp;
+ (8H --fp3p2
’
(4)
where the CNC bending coordinate p is the supplement of the CNC angle, pe is the equilibrium angle [ Voo(p,) = 01, H is the height of the barrier to linearity of the CNCSe skeleton, and f is the harmonic force constant at p = pe. According to the infrared study on methyl isoselenocyanate (3), and bearing in mind the results of previous studies on the rotational spectra of methyl isocyanate and methyl isothiocyanate ( I ), the internal rotation of the methyl group was assumed to be completely free. The methyl group was assumed to be of C3, symmetry, with the symmetry axis coinciding with the CN bond, and the NCSe group was assumed to be linear. The CNC bending-internal rotation-rotation Hamiltonian involved then the four bond lengths r(CN), r(NC), r(CSe), and r(CH), the HCN valence angle, and the three potential function parameters pe, H, andf. The molecular parameters were adjusted in the least-squares fit to the experimental data. Due to the above-mentioned limitations of the model Hamiltonian we did not attempt to fit the measured transition frequencies. Instead, the molecular parameters were refined to reproduce the effective rotational
KOPUT,
42
STROH,
AND
WINNEWISSER
constants Bvk, for various vlo vibrational states, which in turn were determined fitting the observed and calculated transition frequencies u to the expression v = 2Bok,(J+
1) -40&J+
l)3.
by
(5)
In the final least-squares fit 16 effective rotational constants Bukl, with 1k 1 < 3, were used. Only four of the eight molecular parameters appeared to be refinable and. therefore, the calculations were carried out for fixed structures of the NCSe and CH3 groups. The bond lengths for the NCSe group were held fixed at the values determined for isoselenocyanic acid (4). The CH bond length and the HCN valence angle were fixed at the values determined for methyl isocyanate ( 1). The observed and calculated values of the effective rotational constants Bvkl are given in Table VI and the final values of the molecular parameters are given in Table VII. As shown by the results of Table VII, the CNC bending potential function of methyl isoselenocyanate is determined to be very anharmonic, with a barrier to linearity of at the the CNCSe skeleton of only 25 cm -I. The potential function has a minimum CNC valence angle of 161.7”. The shape of the potential function and location of some of the CNC bending energy levels are shown in Fig. 4. The ground vibrational of the potential function, state is calculated to lie about 28 cm-] above the minimum of the vlo funthat is, about 3 cm-’ above the top of the barrier. The wavenumber damental ( 1” + 0’) is calculated to be about 29 cm-‘, that of the first vlo overtone are much smaller than that (2’ + 0’) about 85 cm-’ ; both vibrational wavenumbers found in the infrared study (3). The determined shape of the potential function and location of the energy levels of the v ,0 mode are clearly similar to those found for silyl isocyanate ( 9).
TABLE VI Observed and Calculated Effective Rotational Constants &,, 2,
k
1
Buk~ (ohs. 1
Bvkl (talc.)
0 0 0 0 1 1 1 1 1 1 1 2 2 2 2 4
0 1 2 3 0 1 1 2 3 -1 -2 0 1 2 3 0
0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0
1632.083 1631.723 1630.650 1628.836 1643.487 1645.673 1641.086 1643.133 1642.760 1643.510 1643.461 1645.416 1645.284 1644.911 1644.208 1660.220”
1631.946 1631.620 1630.639 1629.002 1643.517 1645.593 1641.184 1643.153 1642.800 1643.547 1643.487 1645.329 1645.213 1644.864 1644.282 1660.263
Q Preliminary result
in MHz, of CHjNC’“Se o-c 0.137 0.103 0.011 -0.166 -0.030 0.080 -0.098 -0.020 -0.040 -0.037 -0.026 0.087 0.071 0.047 -0.074 -0.043
CHrNCSe
AS A QUASI-SYMMETRIC
TOP
43
TABLE VII Values of the Molecular Parameters’,* for CHrNCSe r(CN)I
8,
1.43232( 29)
r0JC)I
A
1.195
r(CSe)/ r-(WI
1.717
8,
1.100
8,
L(HCN)/
deg
109.5
Mel deg
l&285(71)
H/ cm-’
25.37(52)
f/
0.03849(57)
mdyne A
’ Figures in parentheses
are one standard
deviation
in units of the last digit quoted. b Parameters
quoted without errors were held fixed.
It was found in the calculations that the perturbations observed for the K = 5 transitions in the ground vibrational state could be attributed to accidental resonances between the (VI, k) = (0’) -t5 ) and ( 3 *3, *5 ) energy levels due to internal rotation of the methyl group. For a molecule of the WH3XYZ type, the nonzero barrier to internal rotation V3 gives rise to interactions between pairs of the energy levels with Av = t 1, *3, Al = -t3, and Ak = 0. The near coincidences between such energy levels give rise to accidental resonances observed in the rotational spectrum as shifts of lines
00
0 u 0
10
20
30
PldW
FIG.4. The calculated CNC bending potential function and location of some of the vIOenergy levels (with k = 0, labeled by 0’ values).
44
KOPUT,
STROH,
AND
WINNEWISSER
from their unperturbed positions. Since the errors introduced by the quasi-symmetric top model are of the same order as the observed deviations we were not able to determine with any confidence the value of the barrier to internal rotation by leastsquares fitting to the effective rotational constants Bvk[.Instead, the barrier height was estimated by performing calculations with different assumed V, values. The observed deviations for the K = 5 ground-state transitions were found to be best reproduced with the barrier to internal rotation of 3 + 1 cm-‘. The estimated barrier height is close to those found for methyl isothiocyanate (1) and germyl isocyanate (lo), and is indeed indicative of nearly free internal rotation of the methyl group in methyl isoselenocyanate. The determined molecular parameters allowed us to reproduce semi-quantitatively the observed rotational spectra of different isotopic species of methyl isoselenocyanate. For example, the region about 29.7-29.8 GHz shown in Fig. 1 is predicted to be dominated by four different J = 9 + 8 rotational transitions, namely those in the excited states 21’= 2” and 3” of CH3NC8’Se and in the excited states u’ = 1iI and 2’ of CH3NC7*Se. As an assignment of the rotational spectrum of methyl isoselenocyanate in the higher excited states of the CNC bending mode requires additional measurements, the data and analysis will be reported in a future publication. Finally, it should be pointed out that the rotational transitions reported by Sakaizumi et al. (2) are correctly assigned to a common vibrational state and their assignment of the rotational quantum number K, corresponds to that of K given in this work [compare the results given in Table 1 of Ref. (2) and Table III (the column headed “kl 2 0”) of this paper]. However, the observed rotational transitions cannot be assigned as those in the ground vibrational state of the molecule but rather as the kl a 0 transitions in the excited state v’ = I*’ of the CNC bending mode. For the 1” state, the rotational constant B and the effective I-type doubling constant qe can be estimated by using the relations [see Eqs. (6) and (7) of Ref. ( 1 )] B NN ;(Ba”Y’” +
Cay”‘)
$(BSY”
pYm),
4e
=
-
(6)
where Basym and Casym are the rotational constants in the usual asymmetric rotor approximation. Taking the values of Basym and Cay” from Table 3 of Ref. (2), the constants B and qe are calculated to be 1643.447 and 4.599 MHz. Both values agree very well with those given for the 1” state in Table IV of this paper. V. CONCLUSION
All of the above-discussed evidence indicates that the observed rotational spectrum of methyl isoselenocyanate is best described as that of a quasi-symmetric top molecule. The observed spectrum is dense and very complex because changes in the rotational transitions due to excitation of the low-frequency mode vlo are irregular and of the same magnitude as those due to the presence of different isotopic species. The present study is only the first step in a fuller understanding of the structure and dynamics of methyl isoselenocyanate; a further analysis of the low-J rotational spectra of specific isotopic species is necessary.
CH3NCSe AS A QUASI-SYMMETRIC
TOP
45
ACKNOWLEDGMENTS We thank Dr. B. P. Winnewisser for critically reading and commenting on the manuscript. One of us (J.K.) is indebted to Professor 1. Yamaguchi and Dr. T. Sakaizumi for very helpful and stimulating correspondence; he is also grateful to the Alexander von Humboldt Foundation for the award of a Research Fellowship 1988. This work was supported in part by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. RECEIVED:
September
20, 1989 REFERENCES
1. J. KOPUT, J. Mol. Specfrosc. 118,448-458 ( 1986). and references therein. 2. T. SAKAIZUMI, A. YASUKAWA,H. MIYAMOTO,0. OHASHI,AND I. YAMAGUCHI,Bull. Chem. Sot. Japan59, 1614-1616(1986). 3. W. J. FRANKLIN,R. L. WERNER,ANDR. A. ASHBY,Specfrochim. Acra Parf A 30, 1293-1304 (1974). 4. B. LANDSBERG,Chem. Phys. Lett. 60,265-270 ( 1979). 5. J. VOGTANDM. WINNEWISSER, Ber. Bunsenges. Phys. Chern. 88,439-443.444-450 ( 1984). 6. A. G. MAKI, J. Phys. Chem. Ref: Data 3,221-244 ( 1974). 7. D. PAPOUSEKANDM. R. ALIEV,“Molecular Vibrational Rotational Spectra,” Academia, Prague, 1982. 8. S. CRADOCK,J. Mol. Spectrosc. 92, 170-183 ( 1982). 9. J. A. DUCKETT,A. G. ROBIETTE,ANDI. M. MILLS,J. Mol. Spectrosc. 62, 34-52 ( 1976). IO. S. CRADOCK,J. R. DURIG, A. B. MOHAMAD,J. F. SULLIVAN,ANDJ. KOPUT, J. Mol. Specirosc. 128, 68-81 (1988).
OF MOLECULAR
SPECTROSCOPY
140, 3 l-45 (1990)
The Microwave Spectrum of Methyl Isoselenocyanate: CH,NCSe as a Quasi-symmetric Top J. KOPUT Depurtment qf Chemistrv, Adam Mickiewicz University. 60- 780 Poznati. Poland AND
F. STROH AND M. WINNEWISSER Phpical Chemistry Institut, Justus Liebig University8 6300 Giesren. Federal Republic of Germuq The microwavespectrum of methyl isoselenocyanate. CH,NCSe, has been measured in the region 18-40 GHz. The a-type J + 1 + J rotational transitions (J = 5 to 10) in the ground vibrational state of the molecule have been assigned for the three isotopic species with ‘*Se, “Se. and ‘%e. For the most abundant isotopic species, with *‘Se, the rotational transitions in the excited states of the CNC bending mode or0 = 1 and 2 have also been assigned. Contrary to the previous investigation [T. Sakaizumi et al., Bull. Chem. Sot. Japan 59, 1614-16 16 ( 1986)], it has been shown that the observed spectrum is consistent with that of a quasi-symmetric top molecule. The rotation-vibration constants have been determined. showing an unusual variation with excitation of the CNC bending mode. The CNC bending potential function has been determined in preliminary calculations using a quasi-symmetric top model. The potential function is calculated to be very anharmonic, with an equilibrium CNC angle of about 162” and a barrier to linearity of the CNCSe skeleton of about 25 cm _I. From accidental resonances observed for the ground state transitions the barrier to internal rotation of the methyl group was estimated to be about 3 cm~‘. 0 1990 Academic Press, Inc. I. INTRODUCTION
In a series of papers [see Ref. ( 1) and references therein] the microwave spectra and molecular structures of isocyanates and isothiocyanates have been studied using a quasi-symmetric top approach. In the present paper, an extension of previous studies, we report the first results of an analysis of the microwave spectrum of methyl isoselenocyanate, CH3NCSe. The microwave spectrum of methyl isoselenocyanate was recently reported by Sakaizumi et al. (2). The authors analyzed the rotational spectrum in the ground vibrational state of the molecule within the standard asymmetric-rigid-rotor approximation. The assignment of several lines in the region 9-40 GHz was proposed and the rotationvibration constants A, B, C, AJ, and A, were determined for the two isotopic species, CH3NC *‘Se and CH3NC ‘*Se. The methyl isoselenocyanate molecule was found to be a near symmetric top with the CNC angle of 157 -t 4”. Sakaizumi et al. concluded that though the microwave spectra of methyl isocyanate, CH3NC0. and methyl isothiocyanate, CHjNCS, could not be fitted within the standard semirigid-rotor ap31
0022-2852190 Copyright
0
$3.00
1990 by Academtc
All rights of reproduction
Press
Inc.
in any form reserved.
32
KOPUT,
STROH,
AND WINNEWISSER
proximation (the rigid-frame/rigid-top model), the observed spectrum of methyl isoselenocyanate could be fitted within the rigid-rotor approximation. This in turn led the authors to the conclusion that the barrier to internal rotation of the methyl group in methyl isoselenocyanate might be higher than some 0.3 kcal/mol. On the other hand, an analysis of the infrared spectrum reported by Franklin et al. (3) showed essentially free internal rotation of the methyl group in gaseous methyl isoselenocyanate. Also, the frequency of the CNC bending mode was found to be low; the weak band near 370 cm-’ in . the infrared spectra of the solid and liquid states was assigned to be equally well the fundamental or first overtone of the CNC bending mode. The infrared measurements of Franklin et al. (3)) along with the previous analysis of the microwave spectra of methyl isocyanate and methyl isothiocyanate by one of us ( I ), suggest that methyl isoselenocyanate is not a rigid, near symmetric top, but rather another example of a quasi-symmetric top molecule. This possibility is further supported by microwave (4) as well as millimeter-wave and infrared studies (5) of isoselenocyanic acid, HNCSe. It was shown that in the series including isocyanic acid, HNCO, isothiocyanic acid, HNCS, and isoselenocyanic acid the latter is the most quasilinear molecule. Although the shape of the HNC bending potential function was not explicitly determined, the large-amplitude HNC bending motion in isoselenocyanic acid was found by Vogt and Winnewisser (5) to be the most anharmonic in the series. That is why we decided to reinvestigate the microwave spectrum of methyl isoselenocyanate. We report here the measurement and assignment of the rotational spectrum in the ground vibrational state and some excited states of the CNC bending mode, and also the results of preliminary calculations on the CNC bending potential function. II. EXPERIMENTAL
DETAILS
Samples of methyl isoselenocyanate were prepared by refluxing the mixture of methyl isocyanide and selenium powder in chloroform (2) or petroleum ether (3). The samples were purified by trap-to-trap vacuum distillation. The microwave spectra were recorded using a Hewlett-Packard Model 8460A MRR spectrometer. All spectra were taken at room temperature. The half-life of methyl isoselenocyanate was observed to be approximately 1 min in the metal microwave cell, and the spectra were therefore taken in a slow flow with sample pressures of about 10 mTorr ( 1 mTorr = 0.13 Pa) measured at the cell end. Lines were recorded at Stark field strengths ranging from 10 to 1400 V/cm. Frequency calibration was checked by comparison with lines of OCS (6). The accuracy of the measured frequencies is estimated to be f0.05 MHz for well-resolved lines. The positions of overlapping lines were determined by band shape analysis-a computer simulation of a band envelope using a Lorentzian lineshape function. The spectra of the molecules with different selenium isotopes were observed in natural abundance. No quadrupole hyperfine structure due to the 14N nucleus was observed. III. SPECTRUM
AND ANALYSIS
The microwave spectrum of methyl isoselenocyanate consists of a-type R-branch rotational transitions of a near-prolate symmetric rotor with a rotational constant B
CHjNCSe
AS A QUASI-SYMMETRIC
33
TOP
of about 1.6 GHz. Each J + 1 + J rotational transition contains many lines of comparable intensity. The observed great complexity of each rotational transition and the high density of lines are partly due to the presence of several isotopic species containing different isotopes of selenium; the selenium atom has five important isotopes with mass numbers and relative abundances being, respectively, 80-49.82%, 7823.52%, 82-9.19%, 76-9.02%, and 77-7.58%. This is also partly due, as suggested above, to the presence of two-large amplitude motions in the methyl isoselenocyanate molecule, namely the internal rotation of the methyl group and the CNC bending motion. As these two motions are of a low frequency a large number of the excited states can be populated at room temperature giving rise to several significantly intense lines in the rotational spectrum. A survey microwave spectrum between 29.1 and 30.0 GHz, in the region of the J = 9 + 8 rotational transition, is shown in Fig. 1. The assignment of the observed spectrum proposed by Sakaizumi et al. (2) was made in terms of the asymmetric-rigid-rotor model. In the region shown in Fig. 1 (we will restrict ourselves the discussion to the J = 9 + 8 rotational transition only), the pair of lines at 29 539 and 29 622 MHz was assigned on the basis of the observed Stark effect and intensity to the K, = 1 asymmetry-doublet transitions in the ground vibrational state of the most abundant isotopic species CH3NCs0Se. The strongest line in this region, at 29 582 MHz, lying midway between the K, = 1 lines, was assigned to the K, = 0 ground state transition. The other two lines in the vicinity of the K, = 0 line, at 29 576 and 29 569 MHz, were assigned to the unresolved K, = 2 and Ku = 3 ground state transitions, respectively. As shown in Ref. (I) (compare Figs. 1 and 2 therein) for molecules of the WH3XYZ type, such an assignment is characteristic of an asymmetric top molecule with a well-
29 1
293
FIG. 1. Survey microwave of the J = 9 + 8 rotational V/cm.
29 5
297
29 9GHr
spectrum of methyl isoselenocyanate between 29.1 and 30.0 GHz, in the region transition, recorded as described in the text, with a Stark field strength of 1200
34
KOPUT,
STROH,
AND WINNEWISSER
bent equilibrium configuration of the WXYZ skeleton. For a molecule with a large WXY angle, as that found for methyl isoselenocyanate (2), the observed spectral pattern is expected to closely resemble that of a symmetric top molecule. In the latter case, the K, = 0 ground state transition should be clearly displaced to lower frequency with respect to the K, = 1 asymmetry-doublet transitions. For a molecule close to the symmetric-top limit ( I ) , the ground-state transition, in terms ofthe usual symmetrictop formalism, ’ should form a regular series of lines showing the characteristic Stark behavior and relative intensities. The K = 0 transition should have a normal secondorder Stark effect, whereas the K P 0 transitions should have a very fast first-order Stark effect. Since the molecule is of C’s”symmetry the K = 3n ground state transitions, where n is an integer, should show an enhanced intensity, as being unresolved doublets due to the rotational transitions between energy levels of A, and A2 symmetry. The observed frequencies Yof the J + 1 + J ground-state transitions should also follow the symmetric top formula ( 7) V = 2B(J+
1) - 4DJ(J+
1>3 -
2DJK(J+
l)K2
+ 4HJK(J+
1)3K2 + 2HK,(J+
l)K4,
(1)
where B, DJ, DJ~, HJK, and HxJ are the usual rotation-vibration constants. The first clue to such an assignment came when the region about 29.3 GHz was analyzed. As shown in Fig. 2 the series of lines, beginning with the line at 29 377 MHz, can be assigned on the basis of the above-mentioned criteria to the J = 9 + 8 ground state transition of the most abundant isotopic species, CH3NCa0Se. A similar series of lines can be found in this region beginning with the line at 29 172 MHz. As the relative peak heights of the lines are of about one-fifth of those assigned to the ground state transition of CH3NC8’Se this series can be assigned to the ground state transition of the other isotopic species, CH3NC8*Se. If this assignment is correct, a similar series of lines, arising from the CH3NC ‘*Se molecules, is expected to be found displaced by about 200 MHz to higher frequency with respect to the ground state transition of CH3NCa0Se. Indeed, such a series can be found beginning, as shown in Fig. 3 below, with the line at 29 592 MHz. The relative peak heights of these lines are of about one-half of those assigned to the ground state transition of CH3NC8’Se, as expected from the relative natural abundances of the selenium isotopes. The lines of the ground state transitions of the other two isotopic species, CH3NC77Se and CH3NC7%e, are expected to be found around 29.7 and 29.8 GHz, respectively. Since these Iines are of a small intensity and the regions mentioned are overcrowded (see Fig. 1) we did not attempt to make a detailed assignment. The frequencies of the J + 1 f J ground-state transitions, with J = 5,6, 8, 9, and 10, have been measured for the three isotopic species, with 82Se, 80Se, and 78Se, and have been fitted using the symmetric top formula ( 1) . The observed frequencies and the differences between the observed and calculated frequencies are given in Table I. As shown by the results, it is possible to fit the observed frequencies with standard deviation about 0.1 MHz. Although this deviation is bigger than the experimental ’ The energy levels and wavefunctions of a quasi-symmetric top molecule can be described in two ways, using either the usual asymmetric or symmetric top formalism (I ). We use hereafter the symmetric top notation in which the rotational quantum number K of a prolate symmetric top corresponds to K,.
CH,NCSe
29.1
292
AS A QUASI-SYMMETRIC
35
TOP
29.4 GHr
293
FIG. 2. Part of the / = 9 + 8 rotational transition in the ground vibrational states of CH,NC*‘Se and CH,NC%e, with the lines labeled by K values. The upper spectrum was recorded using 1400 V/cm Stark modulation, while the lower spectrum was recorded using 100 V/cm Stark modulation; note that the K = 0 lines are not fully modulated even at the electric held strength of 1400 V/cm. The enhanced intensity of the K = 3 and K = 6 lines is clearly shown.
295
296GHz
FIG. 3. Part of the J = 9 8 rotational transition in the ground vibrational state v’ = 0’ of CH3NC7”Se and in the excited states Y’ = 1” and 2” of CH3NC**Se. The lines for the 0’ and 2’ states are labeled by A’ values: note the difference in the K structures. The asterisks mark the K = 1 I-type doublet lines in the excited state u’ = 1” of CHJNCEOSe.
KOPUT,
36
STROH,
AND
WINNEWISSER
TABLE I Observed Frequencies (obs.) and Differences Between the Observed and Calculated Frequencies (o-c), in MHz, for the J+ 1 + JRotational Transitions in the Ground Vibrational State ofCH,NC”Se, CH,NC*“Se, and CH3NC%e CHsNCs%
CH3NCsoSe
J
K
obs.
5 5 5 5 5 5 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10
0 1 2 3 4 5 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 10
19448.33 19444.04 19431.30 19409.91 19380.06 _
0.05 0.00 0.00 -0.09 -0.01
22689.59 22684.61 22669.76 22644.90 22610.16 22566.97” 22509.49 29172.19 29165.82 29146.66 29114.74 29070.19 29014.77a 28941.03 _
0.00 -0.04 -0.03 -0.07 0.09 2.00 0.03 0.09 0.07 -0.04 -0.11 0.10 2.55 0.01
32413.40 32406.27 32385.05 32349.60 32300.20 32238.74” 32156.91 32062.63 _ _
0.11 0.02 -0.05 -0.17 0.11 2.86 0.05 -0.10
35654.54 35646.70 35623.38 35584.44 35530.17 35462.65” 35372.84 35269.38 _
0.12 0.01 -0.09 -0.22 0.08 3.09 0.07 0.01
a Perturbed
_
obs.
O-C
19584.83 19580.51 19567.72 19545.93 19515.72 19478.28” 22848.89 22843.87 22828.85 22803.58 22768.45 22724.71” 22666.52 29377.02 29370.55 29351.19 29318.82 29273.77 29217.65” 29143.00 29056.98 28957.42 32640.98 32633.78 32612.31 32576.37 32526.38 32464.11” 32381.32 32285.91 32175.55 32049.19 35904.84 35896.96 35873.35 35833.90 35778.98 35710.59” 35619.71 35515.00 35393.90 35255.28 35098.78
line, excluded from the fit.
CH3NC7sSe o-c -0.07 -0.08 0.08 -0.08 0.09 1.89 -0.08 -0.08 0.00 -0.07 0.21 2.19 0.19 0.02 0.00 -0.01 -0.07 0.28 2.78 0.17 -0.16 -0.09 0.04 -0.01 -0.02 -0.11 0.25 3.01 0.13 -0.22 -0.06 -0.09 0.01 -0.03 -0.07 -0.16 0.21 3.22 0.08 -0.25 0.00 0.09 0.11
obs.
O-C
19728.06 19723.63 19710.45 19688.48 19658.06 _
0.04 -0.02 -0.09 -0.15 0.20
23015.93 23010.79 22995.49 22969.90 22934.38 22890.02” _
-0.01 -0.06 -0.08 -0.14 0.20 2.14
29591.68 29585.15 29565.49 29532.68 29487.08 29430.19” 29354.65 29267.47 _
0.03 0.02 -0.04 -0.13 0.25 2.72 0.15 -0.24
32879.48 32872.22 32850.40 32813.99 32763.41 32700.31” 32616.52 32519.88 32408.19 32280.18 36167.22 36159.26 36135.22 36095.29 36039.72 35970.38” 35878.50 35772.32 35649.66 35509.32
0.05 0.02 -0.06 -0.17 0.24 3.00 0.14 -0.21 0.04 0.00 0.06 0.04 -0.14 -0.21 0.21 3.18 0.17 -0.29 -0.04 0.14
CHSNCSe
AS A QUASI-SYMMETRIC
37
TOP
accuracy, it is not unexpected when the symmetric top formula is applied to fit the rotational spectrum of a near-symmetric top molecule (8). The K = 5 transitions were found to be perturbed for all the isotopic species; as shown below (see Section IV) these perturbations are due to internal rotation of the methyl group. The calculated rotation-vibration constants are given in Table II. For a symmetric top molecule of C,, symmetry, the sum of quartic centrifugal distortion constants (DJK + 2DJ) is proportional to the square of the rotational constant B ( 7, 9). Since the proportionality constant includes the rotational constant A and vibrational factors, which all can be expected to be approximately constant for the isotopic species under consideration, the calculated relative values of (DJK + 2DJ) should be the same as those of B*. It follows indeed from the results of Table II that for the isotopic species with 82Se, “Se, and 78Se, the relative values of ( DJK + 2DJ) are 0.983, 1, and 1.O13, while the relative values of B* are 0.986, 1, and 1.O15, respectively. Similarly, the quartic centrifugal distortion constant DJ is expected to be proportional to B4 ( 7, 9). For the isotopic species with “Se, 80Se and 78Se, the calculated relative values of DJ are 0.932, 1, and 1.059, while the relatibe values of B4 are 0.972, 1, and 1.030, respectively. Since the ground state transitions of methyl isoselenocyanate are satisfactorily described as those of a symmetric top molecule the other rotational transitions observed for the different isotopic species can be assigned as those in excited states of the lowestfrequency bending mode vIo, this being from the infrared study (3) the CNC bending mode. The Ka = 1 asymmetry doublet, assigned unambiguously on the basis of the Stark effect (2), is thus assigned as the K = 1 I-type doublet in the first excited state V Lo = 1. Ilo = fl ( vlo and Ilo are hereafter written simply as I.Jand I). The other lines observed in the vicinity of the I-type doublet lines, shown for the J = 9 + 8 rotational transition in Fig. 3, can then be also assigned to transitions arising from molecules in the excited state v’ = 1 ‘I. However, when this region was examined thoroughly it appeared that at least three different types of rotational transitions could be recognized. The first series of lines was assigned to the above-mentioned rotational transition in the ground vibrational state of CH3NC78Se. The second series of lines was assigned
TABLE II Calculated
Rotation-Vibration CH,NC’%e,
B/
MHz
Constants’ for the Ground Vibrational States of CH3NC8*Se. and CHINC%e as Symmetric Top Molecules
1620.7051(42)
1632.0907(61)
1644.0182(70)
DJ/ kHz
0.204(22)
0.219(32)
0.232(36)
DJK/~HZ
354.26(31)
360.36(25)
364.91(39)
HJK/HZ
12.3( 14)
15.8( 13)
16.0( 19)
HKJ/HZ
-120.5(50)
-99.0( 18)
-101.2(28)
’ Figures digit
in parentheses
quoted.
are one standard
deviation
in units
of the last
KOPUT,
38
STROH,
AND
WINNEWISSER
on the basis of the Stark effect and relative intensities to the rotational transition in the excited state v1 = 1 *’ of CH3NC8’Se. For a symmetric top molecule, these lines should appear in the rotational spectrum as two branches corresponding to the kl > 0 and kl -c 0 transitions and having the k = 0 transition as a common origin (k is the signed rotational quantum number, K = 1k I); the I k - I( = 3n transitions, where n is an integer, should show an enhanced intensity. It appeared that several of the observed transitions coalesced into single, broad-and-structured lines; for example, the strongest line in the region shown in Fig. 3, at 29 582 MHz, was found to consist of the three transitionswith(v’,k)being(l’,O),(l’,-l),and(1’,-2).Thethirdseriesoflines showed a pattern characteristic of the rotational transition in a nondegenerate vibrational state of a symmetric top. Since the intensity of lines was about the same as that of the ground state transition of CH3NC7’Se this series could only be assigned to the rotational transition in the excited state v’ = 2’ of CH3NCSoSe. The other weak lines observed in this region are most likely due to the rotational transitions in the excited states of CH3NC 82Se. The measured frequencies of the J + 1 + J rotational transitions, with J = 5, 6, 8,9, and 10, in the excited states v’ = 1” and 2’ of the most abundant isotopic species CH3NCs0Se are given in Table III. The transition frequencies u in the 1*’ state have been fitted to the symmetric top formula ( 7) v = 2B(J+
1) - 4DJ(J+
+2H&J+
1)3 - 2DJK(J+
l)k4i-2v.,(J+
l)k2
l)kl+48J,(J+
+ 4I&(J+ 1)3kl+20,(J+
1)3k2 l)k31+Av,
(2)
where Av = fqe(J+ Av
=
d(J+
1)
l)[(J II2 - (kl4(kll)(A - Al - B) +
U21
for
kl=
1,
for
kl#
1.
(3)
The transition frequencies in the 2’ state have been fitted to formula ( 1)) neglecting interactions with the 2’2 state. As for the ground vibrational state, the standard deviations of both fits, of about 0.3 MHz, are bigger than the experimental accuracy. The calculated rotation-vibration constants are given in Table IV. The rotational transitions in the excited states v ’ = 1*’ and 2 ’ of CH3NC ‘*Se have also been assigned; since the transition frequencies were measured only to t-O.5 MHz they are not reported here. The calculated rotation-vibration constants show an unusual variation with excitation of the CNC bending mode vlo. For a rigid, symmetric top molecule, the rotational constant B is expected to change linearly with the vibrational quantum number v, while the centrifugal distortion constant DJKis expected to be almost constant. Changes in the constants B and DJK determined for CH3NCE0Se indicate that the methyl isoselenocyanate molecule is far from being a true rigid, symmetric top. Similar changes in the constants B and DJx have been observed for silyl isocyanate, SiH3NC0, the molecule being a prominent example of a quasi-symmetric top ( 9). A comparison of the constants B and DJK for methyl isoselenocyanate and silyl isocyanate is presented
CH4NCSe AS A QUASI-SYMMETRIC
TOP
39
TABLE III Observed Frequencies (obs.) and Differences Between the Observed and Calculated Frequencies (o-c). in MHz, for the J + 1 + J Rotational Transitions in the Excited States u’ = 1” and 2’ of CH9NCs0Se ?J’ = 20
n’ = l*’ kl 10 J 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10
K 0 1 1 2 3 4 5 0 1 1 2 3 4 5 6 0 1 1 2 3 4 5 6 0 1 1 2 3 4 5 6 0 1 1 2 3 4 5 6
obs.
kl < 0 o-c
19721.66” 19692.84 19747.88 19717.42n 19713.06” 19706.60 _
0.03 0.11 0.15 -0.09 0.04 -0.08
23008.37 22974.93 23039.09 23003.77 22998.44 22990.95 _ _
-0.04 0.17 0.16 0.03 -0.05 -0.14
29581.77 29538.90 29621.44 29576.17 29569.20 29559.68 29547.18
0.01 0.20 0.24 0.01 -0.16 -0.19 0.18
32868.39 32820.85 32912.52 32862.37 32854.57 32843.98 32830.17 _
0.09 0.26 0.26 0.02 -0.20 -0.25 0.21
36154.93 36102.76 36203.57 36148.55 36139.89 36128.20 36113.14
0.19 0.34 0.31 0.03 -0.26 -0.37 0.25
obs.
19721.66” 19721.42a
-0.42 -0.07
19717.42” 19714.11°
-0.09 0.02
23008.48” 23008.01
-0.47 -0.25
23003.42” 22999.56 22994.41
-0.18 -0.04 0.06
29582.12 29581.36 _
-0.37 -0.23
29575.51 29570.71 29563.48
-0.04 0.33 -0.11
32868.71 32867.92
-0.44 -0.22
32861.45 32855.97 32847.83
0.06 0.34 -0.24
36155.27 36154.42 _
-0.44 -0.17
36147.26 36141.17 36132.11
0.14 0.41 -0.31
’ Strongly overlapped line, excluded from the fit. b Perturbed
O-C
line, excluded from the fit.
obs.
O-C
19744.89
-0.07
19743.33 19738.85 19730.39 _ _
-0.05 0.25 -0.17
23035.60
-0.14
23033.80 23028.59 23018.84
-0.10 0.26 -0.12
22987.58b 22966.46 29617.13
-0.65 0.02 -0.11
29614.73 29608.09 29595.55 29580.04b 29555.48b 29528.32 32907.86
-0.14 0.37 -0.15 1.41 -0.79 0.00 -0.09
32905.19 32897.79 32883.82 _
-0.13 0.40 -0.23
32839.43’ 32809.30 36198.52
-0.86 0.02 -0.11
36195.60 36187.48 36172.18 _
-0.14 0.45 -0.19
36123.31’ 36090.23
-1.00 -0.01
40
KOPUT, STROLL AND WINNEWISSER TABLE IV Calculated Rotation-Vibration Constants” for the Excited States uf = 1*’ and 2“ of CHsNC8”Se as a Symmetric Top Molecule v’ = 1*r
?Jr= 20
1643.499( 12)
1645.423( 12)
0.279(59)
0.126(58)
Bl MHz DJ/
kHz
DJK/
kHz
47.0( 11)
132.3(13)
HJK/
Hz
0.3(41)
4.5(40)
HKJ/
Hz
-211(28)
-158(28)
SJ/ kHz
-79.4(34)
@JJ/ Hz
34( 15)
@JK/ Hz
-2270( 110)
qe/ MHz
4.5838(92)
(A - AC - B)/ MHz
9100(2100)
L1Figures in parentheses
are one standard
deviation in
units of the last digit quoted.
in Table V. Although we did not yet assign unequivocally the rotational transitions in higher excited states of the vlo mode, the methyl isoselenocyanate molecule appears to be another example of a quasi-symmetric top. This explains the inadequacy of the usual symmetric top formalism when it is applied to describe the observed rotational spectrum. TABLE V Comparison of the Constants B and DJKDetermined for Various States of the vIo Mode of CHsNC*‘Se (This Work) and SiH,NCO (9) d = 00
9J’= 1*1
ur =z 20
CHsNCSe B/ MHz
1632.091
1643.499
1645.423
DJK/
360.4
47.0
132.3
kHz
SiHsNCO B/ MHz
2517.932
2542.349
2543.064
DJK/
642.0
58.4
226.6
kHz
CH3NCSe AS A QUASI-SYMMETRIC IV. CALCULATION
41
TOP
USING THE QUASI-SYMMETRIC
TOP MODEL
The standard symmetric top approach allowed us to understand a part of the observed rotational spectrum of methyl isoselenocyanate in terms of the rotation-vibration constants. To get a deeper insight into the structure and dynamics of the molecule we used the quasi-symmetric top approach. The quasi-symmetric top model [the reader is referred to Ref. ( 1) and references therein for details] allows one to relate the rotation-vibration energy levels of a nonrigid WH,XYZ molecule directly to the structural constants and shape of the potential energy surface. The energy levels, and the corresponding transition energies, are calculated using an approximate, five-dimensional Hamiltonian, which describes a WHJYZ molecule bending at the WXY angle, internally rotating about the WX bond, and rotating in space. The quantities appearing in the Hamiltonian are functions of coordinates of the two large-amplitude motions, the WXY bending motion and internal rotation of the WH3 group; they depend as well on the assumed structural and potential function parameters. All other vibrations of the molecule are assumed to be of small amplitude and coupled to neither the large-amplitude motions nor overall rotation. The rotation-vibration energy levels are calculated by a variation method assuming some values of the structural and potential function parameters. The other way around, the values of these parameters can be determined by a leastsquares fitting of the calculated transition energies to the observed ones. As contributions of the small-amplitude vibrations are not explicitly included in the Hamiltonian the quasi-symmetric top approach can be used for the rotation-vibration energy levels with low J values, say J d 5; and the determined parameter values can only be considered as effective values, as being averaged over the small-amplitude vibrational coordinates. In the calculations the CNC bending potential function V,(p) was chosen as a quadratic potential with a Lorentzian hump
Hfb2 - PZ)’ “‘(‘)
= fp;
+ (8H --fp3p2
’
(4)
where the CNC bending coordinate p is the supplement of the CNC angle, pe is the equilibrium angle [ Voo(p,) = 01, H is the height of the barrier to linearity of the CNCSe skeleton, and f is the harmonic force constant at p = pe. According to the infrared study on methyl isoselenocyanate (3), and bearing in mind the results of previous studies on the rotational spectra of methyl isocyanate and methyl isothiocyanate ( I ), the internal rotation of the methyl group was assumed to be completely free. The methyl group was assumed to be of C3, symmetry, with the symmetry axis coinciding with the CN bond, and the NCSe group was assumed to be linear. The CNC bending-internal rotation-rotation Hamiltonian involved then the four bond lengths r(CN), r(NC), r(CSe), and r(CH), the HCN valence angle, and the three potential function parameters pe, H, andf. The molecular parameters were adjusted in the least-squares fit to the experimental data. Due to the above-mentioned limitations of the model Hamiltonian we did not attempt to fit the measured transition frequencies. Instead, the molecular parameters were refined to reproduce the effective rotational
KOPUT,
42
STROH,
AND
WINNEWISSER
constants Bvk, for various vlo vibrational states, which in turn were determined fitting the observed and calculated transition frequencies u to the expression v = 2Bok,(J+
1) -40&J+
l)3.
by
(5)
In the final least-squares fit 16 effective rotational constants Bukl, with 1k 1 < 3, were used. Only four of the eight molecular parameters appeared to be refinable and. therefore, the calculations were carried out for fixed structures of the NCSe and CH3 groups. The bond lengths for the NCSe group were held fixed at the values determined for isoselenocyanic acid (4). The CH bond length and the HCN valence angle were fixed at the values determined for methyl isocyanate ( 1). The observed and calculated values of the effective rotational constants Bvkl are given in Table VI and the final values of the molecular parameters are given in Table VII. As shown by the results of Table VII, the CNC bending potential function of methyl isoselenocyanate is determined to be very anharmonic, with a barrier to linearity of at the the CNCSe skeleton of only 25 cm -I. The potential function has a minimum CNC valence angle of 161.7”. The shape of the potential function and location of some of the CNC bending energy levels are shown in Fig. 4. The ground vibrational of the potential function, state is calculated to lie about 28 cm-] above the minimum of the vlo funthat is, about 3 cm-’ above the top of the barrier. The wavenumber damental ( 1” + 0’) is calculated to be about 29 cm-‘, that of the first vlo overtone are much smaller than that (2’ + 0’) about 85 cm-’ ; both vibrational wavenumbers found in the infrared study (3). The determined shape of the potential function and location of the energy levels of the v ,0 mode are clearly similar to those found for silyl isocyanate ( 9).
TABLE VI Observed and Calculated Effective Rotational Constants &,, 2,
k
1
Buk~ (ohs. 1
Bvkl (talc.)
0 0 0 0 1 1 1 1 1 1 1 2 2 2 2 4
0 1 2 3 0 1 1 2 3 -1 -2 0 1 2 3 0
0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0
1632.083 1631.723 1630.650 1628.836 1643.487 1645.673 1641.086 1643.133 1642.760 1643.510 1643.461 1645.416 1645.284 1644.911 1644.208 1660.220”
1631.946 1631.620 1630.639 1629.002 1643.517 1645.593 1641.184 1643.153 1642.800 1643.547 1643.487 1645.329 1645.213 1644.864 1644.282 1660.263
Q Preliminary result
in MHz, of CHjNC’“Se o-c 0.137 0.103 0.011 -0.166 -0.030 0.080 -0.098 -0.020 -0.040 -0.037 -0.026 0.087 0.071 0.047 -0.074 -0.043
CHrNCSe
AS A QUASI-SYMMETRIC
TOP
43
TABLE VII Values of the Molecular Parameters’,* for CHrNCSe r(CN)I
8,
1.43232( 29)
r0JC)I
A
1.195
r(CSe)/ r-(WI
1.717
8,
1.100
8,
L(HCN)/
deg
109.5
Mel deg
l&285(71)
H/ cm-’
25.37(52)
f/
0.03849(57)
mdyne A
’ Figures in parentheses
are one standard
deviation
in units of the last digit quoted. b Parameters
quoted without errors were held fixed.
It was found in the calculations that the perturbations observed for the K = 5 transitions in the ground vibrational state could be attributed to accidental resonances between the (VI, k) = (0’) -t5 ) and ( 3 *3, *5 ) energy levels due to internal rotation of the methyl group. For a molecule of the WH3XYZ type, the nonzero barrier to internal rotation V3 gives rise to interactions between pairs of the energy levels with Av = t 1, *3, Al = -t3, and Ak = 0. The near coincidences between such energy levels give rise to accidental resonances observed in the rotational spectrum as shifts of lines
00
0 u 0
10
20
30
PldW
FIG.4. The calculated CNC bending potential function and location of some of the vIOenergy levels (with k = 0, labeled by 0’ values).
44
KOPUT,
STROH,
AND
WINNEWISSER
from their unperturbed positions. Since the errors introduced by the quasi-symmetric top model are of the same order as the observed deviations we were not able to determine with any confidence the value of the barrier to internal rotation by leastsquares fitting to the effective rotational constants Bvk[.Instead, the barrier height was estimated by performing calculations with different assumed V, values. The observed deviations for the K = 5 ground-state transitions were found to be best reproduced with the barrier to internal rotation of 3 + 1 cm-‘. The estimated barrier height is close to those found for methyl isothiocyanate (1) and germyl isocyanate (lo), and is indeed indicative of nearly free internal rotation of the methyl group in methyl isoselenocyanate. The determined molecular parameters allowed us to reproduce semi-quantitatively the observed rotational spectra of different isotopic species of methyl isoselenocyanate. For example, the region about 29.7-29.8 GHz shown in Fig. 1 is predicted to be dominated by four different J = 9 + 8 rotational transitions, namely those in the excited states 21’= 2” and 3” of CH3NC8’Se and in the excited states u’ = 1iI and 2’ of CH3NC7*Se. As an assignment of the rotational spectrum of methyl isoselenocyanate in the higher excited states of the CNC bending mode requires additional measurements, the data and analysis will be reported in a future publication. Finally, it should be pointed out that the rotational transitions reported by Sakaizumi et al. (2) are correctly assigned to a common vibrational state and their assignment of the rotational quantum number K, corresponds to that of K given in this work [compare the results given in Table 1 of Ref. (2) and Table III (the column headed “kl 2 0”) of this paper]. However, the observed rotational transitions cannot be assigned as those in the ground vibrational state of the molecule but rather as the kl a 0 transitions in the excited state v’ = I*’ of the CNC bending mode. For the 1” state, the rotational constant B and the effective I-type doubling constant qe can be estimated by using the relations [see Eqs. (6) and (7) of Ref. ( 1 )] B NN ;(Ba”Y’” +
Cay”‘)
$(BSY”
pYm),
4e
=
-
(6)
where Basym and Casym are the rotational constants in the usual asymmetric rotor approximation. Taking the values of Basym and Cay” from Table 3 of Ref. (2), the constants B and qe are calculated to be 1643.447 and 4.599 MHz. Both values agree very well with those given for the 1” state in Table IV of this paper. V. CONCLUSION
All of the above-discussed evidence indicates that the observed rotational spectrum of methyl isoselenocyanate is best described as that of a quasi-symmetric top molecule. The observed spectrum is dense and very complex because changes in the rotational transitions due to excitation of the low-frequency mode vlo are irregular and of the same magnitude as those due to the presence of different isotopic species. The present study is only the first step in a fuller understanding of the structure and dynamics of methyl isoselenocyanate; a further analysis of the low-J rotational spectra of specific isotopic species is necessary.
CH3NCSe AS A QUASI-SYMMETRIC
TOP
45
ACKNOWLEDGMENTS We thank Dr. B. P. Winnewisser for critically reading and commenting on the manuscript. One of us (J.K.) is indebted to Professor 1. Yamaguchi and Dr. T. Sakaizumi for very helpful and stimulating correspondence; he is also grateful to the Alexander von Humboldt Foundation for the award of a Research Fellowship 1988. This work was supported in part by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. RECEIVED:
September
20, 1989 REFERENCES
1. J. KOPUT, J. Mol. Specfrosc. 118,448-458 ( 1986). and references therein. 2. T. SAKAIZUMI, A. YASUKAWA,H. MIYAMOTO,0. OHASHI,AND I. YAMAGUCHI,Bull. Chem. Sot. Japan59, 1614-1616(1986). 3. W. J. FRANKLIN,R. L. WERNER,ANDR. A. ASHBY,Specfrochim. Acra Parf A 30, 1293-1304 (1974). 4. B. LANDSBERG,Chem. Phys. Lett. 60,265-270 ( 1979). 5. J. VOGTANDM. WINNEWISSER, Ber. Bunsenges. Phys. Chern. 88,439-443.444-450 ( 1984). 6. A. G. MAKI, J. Phys. Chem. Ref: Data 3,221-244 ( 1974). 7. D. PAPOUSEKANDM. R. ALIEV,“Molecular Vibrational Rotational Spectra,” Academia, Prague, 1982. 8. S. CRADOCK,J. Mol. Spectrosc. 92, 170-183 ( 1982). 9. J. A. DUCKETT,A. G. ROBIETTE,ANDI. M. MILLS,J. Mol. Spectrosc. 62, 34-52 ( 1976). IO. S. CRADOCK,J. R. DURIG, A. B. MOHAMAD,J. F. SULLIVAN,ANDJ. KOPUT, J. Mol. Specirosc. 128, 68-81 (1988).