- Email: [email protected]
The rotation-inversion spectrum of ketenimine, H2CCNH
JOURNAL
OF MOLECULAR
SPECTROSCOPY
(1986)
118,267-276
The Rotation-Inversion Spectrum of Ketenimine, H&=C=NH M. RODLER, R. D. BROWN, P. D. GODFREY, AND B. KLEIB~MER Chemistry Department, Monash University, Clayton, Victoria 3168, Australia High-resolution measurements of p&pe transitions of ketenimine in the 4- to 7-GHz region revealed a splitting of each line caused by the inversion motion of the imino hydrogen. The inversion splitting amounts to 66 kHz. Data from ab initio molecular orbital calculations for the changes of the geometrical parameters during the inversion motion have been used to carry out semirigid bender calculations. A barrier height of 4700 + 200 cm-’ and an equilibrium HNC angle of 115.4+ 0.6” have been derived. In addition, the microwave spectrum of the Ndeuterated species has been assigned. The inversion splitting could not be resolvedbut the quadrupole coupling of the deuterium nucleus has been observed. Attempts to detect the inversion splitting in methanimine, H,C=NH, have been unsuccessful, suggesting a higher barrier than in ketenimine. Q 1986 Academic Press, Inc. I. INTRODUCTION
Ketenimine (etheneimine, vinylideneamine) is a transient tautomer of acetonitrile. It was first generated in cryogenic matrices and spectroscopically identified by observing its infrared spectrum in 1963 (I). The study of isotopic species allowed a normal coordinate analysis of the totally symmetric A’ block by Jacox (2). Recently we succeeded in detecting ketenimine in the gas phase by measuring its microwave spectrum (3). Ketenimine is structurally similar to the isoelectronic allene (H2C=C=CH2) where the planes formed by the two CH2 groups lie perpendicular to each other. In the case of the imine one CH2 group is replaced by NH and the nitrogen lone pair. In principle the imino hydrogen can change its place with the lone pair in an inversion type motion: H
H
‘C=C=N-H H’
‘C=C=N.. H’
.H
or in a general case: H X=N
X=N’
‘H’ This is similar to the inversion motion of ammonia derivatives like cyanamide (N----t--NH2) or monochloramine (Cl-NH3 where the two hydrogen atoms attached to the nitrogen invert simultaneously: H
:H X-N:
X-N’ ‘H 267
*.H’ 0022-2852186 $3.00 Copyright 0
1986 by Academic Rcss. Inc.
All rights of reproduction in any form reserved
RODLER
268
ET AL.
But while the splitting of rotational lines due to this latter motion (which one might generally call amino inversion) has been observed in a number of cases, no such splitting has ever been reported for the former type (imino inversions). In the liquid phase however, inversions of imines have been studied for more than 20 years using NMR-techniques (4). But for experimental reasons the imino hydrogen has always been replaced by larger substituents. We now report the observation of the inversion splitting in the main isotopic species of ketenimine. These data together with the infrared data (2) were used to determine the potential function of the inversion motion applying the semirigid bender model introduced by Bunker and Landsberg (5). The parameters dete~ining the ~rni~~dity were transferred from ab initio calculations at the MP3/6-3 lG** level. The rotational spectrum of the isotopic species H&CND was also assigned. The inversion splitting could not be resolved. Instead the splitting of the lines due to the deuterium quadrupole coupling could be measured and the coupling constants determined. One of the simplest molecules which can perform an imino inversion is methanimine (methyleneimine). But in this case we have been unable to resolve the inversion splitting. 2. EXPERIMENTAL
DETAILS
Besides the two precursors reported in the previous publication (3), two other substances have been found to produce ketenimine: isoxazole and 1,2,3-triazole. Applying the same pressure in the cell they all produced lines of similar intensity. Isoxazole has some advantages owing to its considerably higher vapor pressure (leading to stronger but broader lines) and its commercial availability. Ketenimine-ND was generated by pyrolyzing 3-propionitrile-OD which was produced by an exchange reaction of the nitrile with excess 40 and sub~quent distillation. Aminoacetonit~le was used to generate methanimine. The vapors of the starting materials were pyrolyzed in a silica tube (2 cm inner diameter) which was heated to 1000-l 1OO’Cover a length of 30 cm with an electric furnace. The gases were pumped through the absorption cell at pressures of 0.05- 1 Pa. In the 12- to 60-GHz region a conventional microwave spectrometer was employed with 30-kHz Stark modulation and a cell with G-band dimensions. The microwave sources were phase-locked OK1 klystrons. In the 4- to 7-GHz range where all the highresolution work was done a 5-kHz Stark modulated instrument was used with a waveguide cell of L-band dimensions (16.5 by 8.255 cm). The microwave source was a Hewlett-Packard K03-8690A phase-locked backward-wave oscillator. In cases where the transitions could not be modulated sufficiently in the L-band cell, a cell of G-band size was used instead. The data were collected by a Varian V75 computer, the multiplets being repetitively scanned upward and downward at low pressures (0.05-0.2 Pa) and averaged. The resulting linewidth (full-width at half-maximum) was typically about 35-40 kHz. 3. .ANALYSIS
AND
ASSIGNMENT
OF THE MICROWAVE
SPECTRA
The microwave spectrum of the previously unknown N-deuterated ketenimine has been assigned in the same way as the parent compound (3). Seventeen transitions
ROTATION-INVERSION
269
SPECTRUM
TABLE I Observed Rotational Constants (in MHz) and Centrifugal Distortion Constant (in kHz) for Ketenimine-NH and -ND@’ HZC=ONa
A
163242.42(3)
201445.47(4)
B
9663.144(Z)
9032.951(Z)
C
9470.126(l)
8962.187(I)
233.1(3)
DJK
138.3(7) 10321.(31)
10128.(19)
DK
0.0172(Z)
-0.071(4)
dl
0.0152(l)
-0.004(Z)
d2
-0.085(2)
-0.19(Z)
“KJ
Numbers of
2.78(l)
3.032(6)
DJ
(a)
H2C=C=ND
the
in
parentheses
least
squares
represent
one
standard
deviation
fit.
have been measured. The derived rotational and centrifugal distortion constants are listed in Table I. They are defined according to Watson’s symmetric reduction in a I’ representation (6). Due to an incorrect assignment of the 192,17- 201,i9 transition of HzCCNH the constants given in the previous publication differ slightly from the values now reported. Measurements of additional lines led to the constants given in Table I for this isotopic species. Figure 1 shows the multiplet found for the 9i,s - 10o,10transition of the main isotopic species at 4930 MHz where the inversion- splitting could be observed. The three strongest lines represent the three quadrupole components of the transition from the vibrationally first excited state (O- or v = 1) to the ground state (O+ or v = 0),
I 4930.0
4930.
FREQUENCY
s
/MHz.
FIG. I. Observed quadrupole and inversion splitting of the 9,,8-10 0,10transition in ketenimine-NH. The assignmerit of the components is given in Table II.
270
RODLER ET AL. TABLE II Measured Transition Frequencies of H2CCNH and H2CCND in the 4- to 7-GHz Region H*C
K+i) +
J’(K.i,
9
(1,8>
l
J”(K_i,
$0
p*
K+i)
=
+ F”
9 + IO
fO,iCJ)
c =
NH
“I
+ “”
5+
+ o-
4929.902
6
+ 0+
4930.033
o+ + o-
4930,469
a-
o+
4930.600
o+ f
o-
49JU.535
o-
*
o+
4930.668
o+
f
o-
4254.625
o+ + o-
4254.740
a-
4255.080
Ftequency/Mu7.
SplittinK/kHz
I31
10
*
11
131
8f9
l
133
27(2,25)
+ 28
(1.27)
28
+ z,(a)
115
27
+ 28
*
u+
II? Q- + I?+
H*C
J’(K,i,
K+i)
+ J”(K_1”,K+i),
9(0,9)
*
8
Fi’
(I,71
-
F’
Fi(b)
St
c =
7
4255.
ND
+ F”(‘)
Frequency/MHz
Ef7
6442.582
9 + Sfdf I.0 + 9
9*8
I97
6442.627
10
l
9
6442.653
11
+
m(d)
6442.705
9*8
6443.239 6443.283
(a)
The
(b)
F1 = J FL
quadrupole
is
cmponents
+ IN, still
(cf
P = F1 +
fdf
The
IN being a good
ID,
quadrxxpole
F’ the
quantum
ID being
the
components
= J’
f
nuclear
1 + F”
= j”
f
1 could
not
be
resolved.
spin
quantum
number
of
the
nitrogen
spin
quantvm
numbet
of
the
deuterfum
nucleus;
number. nuclear F”
=F;
f
I-P”
= F;fl
could
not
be
nucleus.
resolved.
whereas the three weaker lines are due to the three components of the O+to O- transition. They each lie 132 kHz higher than in the former triplet and possess only one-third of the intensity. This separation leads to an energy difference between O+ and O- of 66 kHz. The intensity ratio of three to one is due to the different spin statistical weight of the two transitions. Since the inversion splitting is resolvable the appropriate symmetry group is C&(M) (7). In order to study the dependence of the observed splitting on the romtional energy we also measured the 272,2s +- 28~~ transition which also happens to lie in the G-band region, The energy difference of 117 kHz is slightly smaher in this case. Attempts to measure the splitting in higher f%equency ranges f&led
ROTATION-INVERSION SPECTRUM
271
due to increased Doppler broadening. But while all p&pe transitions showed an asymmetric line profile no such asymmetry could be observed for PO-type lines. The measured transition frequencies of the two multiplets and their assignments are listed in Table II. When the 90,9- 8,,, transition of ketenimine-ND was measured with high resolution a pattern very similar to that in Fig. 1 was obtained. But the splitting of the lines is caused by a different effect. Calculations using the WISB method (8) indicated that the inversion splitting for this isotope should be smaller than 1 kHz. The observed structure is due to the partially resolved deuterium quadrupole coupling which splits each component of the nitrogen quadrupole triplet into three lines. Two of them are not resolved. Table II lists the measured transition frequencies whereas in Table III the fitted quadrupole coupling constants are given for HzCCND as well as HzCCNH. Additional information from other transitions has also been used to determine the listed constants. Some measurements were carried out in an attempt to resolve the inversion splitting in methanimine (H&L%NH). Being the lowest lying &,-type Iine the 215,17-224,18transition at 4567.3 MHz was selected. Al~ou~ the full linewidth was less than 40 kHz no sign of a splitting was observed. Both quad~pole components showed a symmetric line profile. 4. AB INITIO MOLECULAR ORBITAL CALCULATIONS
Some information about the change of the geometrical parameters during the inversion motion was needed in order to carry out semirigid bender calculations. Thus ab initio calculations at different geometries have been performed using the 6-3 lG** basis set (9) which includes p and d-type polarization functions on the hydrogen and heavy atoms, respectively. To include the effect of electron correlation on the geometries and energies the M0ller-Ples~t ~~ur~tion theory carried to third order (MP3) was used (10). The core molecular orbitals were frozen. The GAUSSIAN 80 system of programs was employed. The optimized MP3 geometries for ketenimine and methanimine at the minima and saddle points are given in Table IV. Additional calculations have been performed to prove that the C,, structures indeed represent saddle points. In particular it has TABLE III ObservedNuclear Qua~~le
CouplingConsul H*C-C-NH
fin MHz) as Obtainedfrom a Least-SquaresFit I%$-C-ND
XB,(N)
0.030(46)
0.030(a)
XbbW
I .523(40)
1.601(28)
Xa,(0)
-0.011(31)
Xbb( Dt
-0.131(15)
fa)
Was not
fitted.
272
RODLER ET AL. TABLE IV Structures and Energies Obtained for Ketenimine and Methanimine from Ab Initio MP3/6-3 lG** Optimizations
Ketenimine Parameter(a)
c,-symmetry
Methanimine c.-synmetry
c7..-smetw
C?..-syrrrmetrY
CN
1.234
1.189
1.274
1.239
NH
1.017
0.986
1.020
0.985
CH
1.077
1.075
CC
1.315
1.328
1.089/1.085(b)
1.101
113.7
180.
109.7
180.
120.2
119.7
125.l/ll8.7(b)
123.2
174.6
180.
90.5
90.
-132.3207
-132.2931
(a)
Bond
(b)
The same
0.0
1140CLfe)
0.0
5410.
0.0
11040.
(e)
on
the
in value
side
-94.3050
6060.
lengths first
-94.3570
0.0
of
(c)
In Bartrees.
Cd)
In cm -1
(e)
The HF energy cafeuleted to
(1000
;;,
angles
refers
the
cm-l
in
to
double
= 2.859
differenc 10670 cm-*
the
bond
degrees. hydrogen as
is
kcalml-1 at the (1 -- If
atom
the
which
is
located
NH hydrogen.
-
HP/&31G*
11.96
kJ m&-l).
geometries
has
been
been shown that in both cases the barrier for the rotation of the CNH group is larger than for the inversion. 5. SEMIRIGID BENDER CALCULATIONS
The semirigid bender program which we described in a previous publication (12) is based on the model of Bunker and co-workers (13, 5) and its extension by Szalay (14). It allows the calcufation of vibration-rotation spectra of molecules with a single arbitrary lake-amplitude motion without any symmetry restrictions. To our knowledge the inversion splitting in ketenimine of ca. 66 KHz or 2.2 X lOA cm-’ is the smallest energy difference until now fitted with the semirigid bender model, and it was necessary to check whether the integration of the large-amplitude wave equation was performed with the required accuracy. Energies were calculated with the Numerov-Cooley algorithm (15) in which the energy was varied until the computed correction to it was smaller than an arbitrarily chosen limit. A value of lo-” cm-’ was chosen as the convergence criterion which ensured that derivatives for the least-squares procedure could be calculated to about two significant digits for the inversion splitting Av. For checking purposes AV was also calculated using the WKB approximation (8). With the reduced mass P = &I), explicitly depending on the inversion angle p, the potential
ROTATION-INVERSION
273
SPECTRUM
V = V(p) and the energy of the O+ state E, we numerically integrated between the classical turning points ltpo to obtain the value A where A = exp
[2p(I’ - E)]“2dp
.
With v. as the 1+-O- frequency Au is represented by Au = vo/(* - A2). Agreement of better than 10% was obtained from both methods confirming the correctness of the Numerov-Cooley integration. The following input data have been used for the fit: the observed splitting of the 9 iT8-10o,,o transition of H2CCNH and the infrared frequencies (1 --O+) for H2CCNH (at 1001.3 cm-‘) and D2CCND (at 798.5 cm-‘). The infrared frequencies resulted from matrix experiments and might therefore be slightly shifted compared to the gas phase frequencies. The potential was chosen to be qua&c with a quadratic barrier and the barrier height and position of the minima were fitted. As Table II shows there is a K-i dependence of the splitting of the microwave lines. In order to properly account for the factors leading to this effect, which is discussed below in detail, we directly fitted the observed splitting as the difference in frequency of 0+-O- intersystem lines. The alternative procedure of taking it to be twice the splitting of the pure inversion levels, Of and O-, assumes the rotational constants to have the same values for the two levels. Our previous investigations into molecules with amino inversion had shown that semirigidity had to be taken into account to explain all experimental data, i.e., inversion frequencies and vibrational satellite shifts. For cyanamide (22), we had found that ab initio predictions at the MP3/6-31G ** level yielded quite reliable estimates of the parameters which determine the pathway during the inversion. They differed by less than 10% from the experimentally obtained values. Therefore we applied the same method here as well. It was necessary to obtain reasonable values for all geometrical parameters as a function of the inversion parameter p (which in our case is the CNH angle). This was done by interpolation between the ab initio optimized C2” structure and C’, structure. Depending on the symmetry of the change of the parameters with respect to p, we either interpolated linearly or quadratically. We explored the effect of semirigidity in ketenimine in a number of calculations: the molecule inverted rigidly, with the remaining parameters frozen at the optimized C’, structure or semirigidly with the MO pathway parameters. In the semirigid bender fits we also varied the relative weighting of the O--O+ inversion and l--O+ infrared frequencies as well as the actual value of the observed inversion doubling in order to assess how strongly the inversion potential depended on the’input data. The results of the above-mentioned calculations are presented in Table V. When semirigidity is neglected the fit gets markedly worse. In particular the inversion splitting is not fitted as well as with inclusion of semirigidity and the value for the equilibrium angle pes is relatively far out from the ab initio prediction. In cyanamide pq from MO calculations and experiment agree to better than one-half degree. The semirigid bender fit shows that the inversion splitting is a very sensitive function of both pe4 and barrier height. Both parameters are determined without correlation (coefficient 0.146) and with only small standard deviations. Comparison of models 3
274
RODLER ET AL. TABLE V Results of the (~~i)~~d
Li*c=c=NH splitting 91,s - 100,lC
of (kHz)
132(I)
obs.-ealcH,C-C=xK
1--o*
125(l) #
-38 (&f
10o1‘3f1.0)
l--o+(cla
-21.3
790*5(1*0)
-1)
4
3
132(l)
132(l)
-3
0
1001.3(1.0)
-28.2
&J.-C&Z. D*C=C=ND
2
I
Model
Bender C~c~atio~s(‘~
1001*3el.25) -21.3
798.5(1.0)
798.X1.0)
28.4
28.4
[email protected](0.25)
5
132 110 I00f.3
21.3
-33.1
798.5(0.25)
798.5
26.4
85.0
ohs.-cslc.
37.3
(cm-‘)
4508(608)
4697( 102)
4686(101)
4682(!83)
4686
119.5(53)
115,3(6)
If5.4(6)
I&4(12)
115.4
Barrier pa,<“)
Models:
1 2,3,4 5
rigid semlrlgfd r&id
bender
Fit
bender bender
with
ah ioitio
fully
optimized
C, bond leogths
and angles.
fits,
as I with
potential
OP 3.
and 4 shows that a well-balanced weighting is important to obtain the best fit for all frequencies, although there is not a great difference in the actual potentials. As final values we derived: barrier = 4700 + 200 cm-‘; pes = 115.4 + 0.6”. The rigid bender results should not be regarded as completely unreahstic, because frequencies of largely different order of magnitude are fitted to within 20%. With the final semirigid bender potential the inversion splitting is calculated too small by a factor of 6. This can be explained by inspecting the actual pathway: the nitrogen atom slowly moves in opposite direction to the imino hydrogen thus effectively decreasing the reduced mass. The WKB approximation shows that this increases the inversion splicing, which can also be seen by the numerical solution of the inversion wave equation. The value of In A is 18.9 for H,=C=C=NH and 26.2 for the N-deuterated ketenimine. This predicts the inversion splitting to be 0.03 kHz for the latter and makes it unfeasible to be observed by microwave spectroscopy. Table II shows that there is a small but definite decrease in the inversion splitting in higher K_ t leveis. The following effects coufd contribute: (if SfightIy different rotational constants in the 0” and O- state, (ii) and (iii) a J and K-r dependence of the inversion splitting. In the following discussion we shall use the axis label z along the heavy chain because we refer to the Eckart axis system. Also we use pXClzr and Z for the corresponding elements of the inverse of the inertia tensor and its inversion average. There is only a slight difference to the value A of the principal axis system. Similar to the inversion splitting itself the observed Kdependence can partially also be rationalized in the WKB approximation. During the inversion, which is much slower than the rotation, the molecule has tu accelerate in its rotation around the z axis because the rotational constant 2 increases by ea. 30% by going from the equi-
ROTATION-INVERSION
SPECTRUM
275
librium to the planar configuration. The term $K?, - prz cannot be neglected in the kinetic energy expression and changes the effective potential. The K-dependent energy EUKis approximately EVK = E,,+ fK?I(pzz), where the main contribution to the average of prz over the inversion wavefunction comes from near the equilibrium configuration. In the WKB approximation, one integrates over the region where pzz is the larger than (& and consequently the inversion splitting decreases with K. The same result is obtained from the numerical integration of the inversion wave equation and amounts to -2 kHz. There is a similar but smaller J-dependent effect which, however, is not calculated in our semirigid bender model. Slightly different effective rotational constants 2 in O+ and O- make another contribution: there is a decrease of AZ = -0.6 kHz from O+ and O-. If only rotation about the a axis is considered the change in the splitting is A = AvKz2- AI+,, + 4AZ. The resulting value of -4.4 kHz is at least qualitatively in agreement with the observation. There certainly will be higher order centrifugal effects because of the high-J value of the measured transitions, which we, however, cannot estimate in our model. Therefore we did not include the observed inversion splitting of the J = 28-27 transition in the fitting. 6. CONCLUSIONS
Ketenimine is the first compound in which the splitting of rotational transitions due to the inversion motion of an imino hydrogen has been observed. The energy difference of 66 kHz (2.2 10e6 cm-‘) between the ground and first excited state is one of the smallest ever observed and considerably smaller than most splittings due to the inversion of amino hydrogens. Ammonia (8), cyanamide (I2), isocyanamide (16) and even monochloramine (17) exhibit splittings which are several orders of magnitude larger. For methanimine, which can undergo an inversion similar to ketenimine, the inversion splitting could not be resolved. As both molecules have similar reduced masses for the inversion motion this indicates a higher barrier for methanimine. This is in qualitative agreement with ab initio calculations. The observed splitting for ketenimine in combination with infrared data made it possible to determine the potential barrier of 4700 f. 200 cm-’ (56.2 + 2.4 kJ mol-’ or 13.4 f 0.6 kcal mol-‘) and the CNH angle of 115.4 f 0.6” using the semirigid bender model. The ab initio molecular orbital calculations at the MP3 level were of substantial help in reliably predicting the rotational constants and consequently facilitating the search for rotational transitions. On the other hand, the prediction of the inversion barrier is significantly in error. The calculated barrier (6060 cm-’ at the MP3 level) is about 1400 cm-’ higher than the experimental value. At the Hartree-Fock level, where the electron correlation is not taken into account, the difference amounts to 700 cm-‘. Both barriers lead to splittings which are many orders of magnitude smaller than has been observed. This large discrepancy is quite surprising in light of similar calculations for related molecules. For cyanamide and &cyanamide, which are isoelectronic to ketenimine, the calculated barrier at the MP3 level was calculated to 467 and 2100 cm-’ (18) respectively. This compares favorably with the observed values of 504 (12) and 2070 cm-’ (16), respectively. Two possible explanations for the difference might be considered: First, deficiencies of the ab initio calculations in properly describing the electronic
RODLER
276
ET AL.
properties of this imine. Qualitatively speaking the hybridization of the nitrogen nucleus changes from sp2 to sp for imino inversions in contrast to the change from sp3 to sp2 for amino inversions. Due to the lack of experimental data no comparison between experimental and ab initio barriers for imino inversions have been possible so far. And second, the effective inversion potential, which is the zero-point average over all other vibrations except the inversion, might be appreciably different from the hypothetical vibrationless potential. Some indications have been found that the second point might contribute at least partially. According to the MO calculations the force constants for the CH2 wagging changes from 0.146 to 0.040 mdyn A/rad2 going from the r, to the C2, structure. But its quantitative influence cannot be assesed with confidence. ACKNOWLEDGMENTS Financial support by the ARCS is acknowledged. We are grateful to Robert Champion for helpful discussions and Kaoru Yamanouchi for measurements in the early stages of the project. M. Rodler also acknowledges the assistance of a Monash University Vice Chancellor’s Postdoctoral Fellowship.
RECEIVED:
October 3 1, 1985 REFERENCES
1. M. E. JACOXAND D. E. MILLIGAN,J. Amer. Chem. Sot. 85,278-282 (1963). 2. M. E. JACOX, Chem. Phys. 43, 157-172 (1979). 3. M. RODLER,R. D. BROWN,P. D. GODFREY, AND L. M. TACK, Chem. Phys. Lett. 110,447-45 I ( 1984). 4. L. M. JACKMAN,in “Dynamic Nuclear Magnetic Resonance Spectroscopy” (L. M. Jackman and F. A. Cotton, Eds.), pp. 244-249, Academic Press, New York, 1975. 5. P. R. BUNKERAND B. M. LANDSBERG,J. Mol. Spectrosc. 67, 374-385 (1977). 6. J. K. G. WATSON,in “Vibrational Spectra and Structure” (J. R. Durig, Ed.), Vol. 6, pp. l-89, Elsevier, Amsterdam, 1977. 7. P. R. BUNKER,“Molecular Symmetry and Spectroscopy,” Academic Press, New York, 1979. 8. C. H. TOWNESAND A. L. SCHAWLOW,“Microwave Spectroscopy,” pp. 300-307, McGraw-Hill, New York, 1955. 9. P. C. HARIHARANANDJ. A. POPLE, Theor. Chim. Acta 2t3,2 13-222 (1973). 10. J. A. POPLE,J. S. BINKLEY,AND R. SEEGER,Int. J. Quantum Chem. Symp. 10, l-19 (1976). Il. J. A. POPLE, K. RAGHAVACHARI,M. J. FRISCH,J. S. BINKLEY,AND P. V. R. SCHLEYER,J. Amer. Chem. Sot. 105, 6389-6398 (1983). 12. R. D. BROWN,P. D. GODFREY,AND B. KLEIB~MER,J. Mol. Spectrosc. 114,257-273 (1985). 13. J. T. HOUGEN,P. R. BUNKER,ANDJ. W. C. JOHNS,J. Mol. Spectrosc. 34, 136-172 (1970). 14. V. SZALAY,J. Mol. Spectrosc. 102, 13-32 (1982). 15. J. W. COOLEY,Math. Comp. 15, 363-374 (1961). 16. M. WINNEWISSER,J. Mol. Struct. 126, 41-66 (1985). 17. G. CAZZOLIAND D. G. LISTER,J. Mol. Spectrosc. 45,467-474 (1973). 18. M. RODLER,R. D. BROWN,AND P. D. GODFREY,unpublished results.
OF MOLECULAR
SPECTROSCOPY
(1986)
118,267-276
The Rotation-Inversion Spectrum of Ketenimine, H&=C=NH M. RODLER, R. D. BROWN, P. D. GODFREY, AND B. KLEIB~MER Chemistry Department, Monash University, Clayton, Victoria 3168, Australia High-resolution measurements of p&pe transitions of ketenimine in the 4- to 7-GHz region revealed a splitting of each line caused by the inversion motion of the imino hydrogen. The inversion splitting amounts to 66 kHz. Data from ab initio molecular orbital calculations for the changes of the geometrical parameters during the inversion motion have been used to carry out semirigid bender calculations. A barrier height of 4700 + 200 cm-’ and an equilibrium HNC angle of 115.4+ 0.6” have been derived. In addition, the microwave spectrum of the Ndeuterated species has been assigned. The inversion splitting could not be resolvedbut the quadrupole coupling of the deuterium nucleus has been observed. Attempts to detect the inversion splitting in methanimine, H,C=NH, have been unsuccessful, suggesting a higher barrier than in ketenimine. Q 1986 Academic Press, Inc. I. INTRODUCTION
Ketenimine (etheneimine, vinylideneamine) is a transient tautomer of acetonitrile. It was first generated in cryogenic matrices and spectroscopically identified by observing its infrared spectrum in 1963 (I). The study of isotopic species allowed a normal coordinate analysis of the totally symmetric A’ block by Jacox (2). Recently we succeeded in detecting ketenimine in the gas phase by measuring its microwave spectrum (3). Ketenimine is structurally similar to the isoelectronic allene (H2C=C=CH2) where the planes formed by the two CH2 groups lie perpendicular to each other. In the case of the imine one CH2 group is replaced by NH and the nitrogen lone pair. In principle the imino hydrogen can change its place with the lone pair in an inversion type motion: H
H
‘C=C=N-H H’
‘C=C=N.. H’
.H
or in a general case: H X=N
X=N’
‘H’ This is similar to the inversion motion of ammonia derivatives like cyanamide (N----t--NH2) or monochloramine (Cl-NH3 where the two hydrogen atoms attached to the nitrogen invert simultaneously: H
:H X-N:
X-N’ ‘H 267
*.H’ 0022-2852186 $3.00 Copyright 0
1986 by Academic Rcss. Inc.
All rights of reproduction in any form reserved
RODLER
268
ET AL.
But while the splitting of rotational lines due to this latter motion (which one might generally call amino inversion) has been observed in a number of cases, no such splitting has ever been reported for the former type (imino inversions). In the liquid phase however, inversions of imines have been studied for more than 20 years using NMR-techniques (4). But for experimental reasons the imino hydrogen has always been replaced by larger substituents. We now report the observation of the inversion splitting in the main isotopic species of ketenimine. These data together with the infrared data (2) were used to determine the potential function of the inversion motion applying the semirigid bender model introduced by Bunker and Landsberg (5). The parameters dete~ining the ~rni~~dity were transferred from ab initio calculations at the MP3/6-3 lG** level. The rotational spectrum of the isotopic species H&CND was also assigned. The inversion splitting could not be resolved. Instead the splitting of the lines due to the deuterium quadrupole coupling could be measured and the coupling constants determined. One of the simplest molecules which can perform an imino inversion is methanimine (methyleneimine). But in this case we have been unable to resolve the inversion splitting. 2. EXPERIMENTAL
DETAILS
Besides the two precursors reported in the previous publication (3), two other substances have been found to produce ketenimine: isoxazole and 1,2,3-triazole. Applying the same pressure in the cell they all produced lines of similar intensity. Isoxazole has some advantages owing to its considerably higher vapor pressure (leading to stronger but broader lines) and its commercial availability. Ketenimine-ND was generated by pyrolyzing 3-propionitrile-OD which was produced by an exchange reaction of the nitrile with excess 40 and sub~quent distillation. Aminoacetonit~le was used to generate methanimine. The vapors of the starting materials were pyrolyzed in a silica tube (2 cm inner diameter) which was heated to 1000-l 1OO’Cover a length of 30 cm with an electric furnace. The gases were pumped through the absorption cell at pressures of 0.05- 1 Pa. In the 12- to 60-GHz region a conventional microwave spectrometer was employed with 30-kHz Stark modulation and a cell with G-band dimensions. The microwave sources were phase-locked OK1 klystrons. In the 4- to 7-GHz range where all the highresolution work was done a 5-kHz Stark modulated instrument was used with a waveguide cell of L-band dimensions (16.5 by 8.255 cm). The microwave source was a Hewlett-Packard K03-8690A phase-locked backward-wave oscillator. In cases where the transitions could not be modulated sufficiently in the L-band cell, a cell of G-band size was used instead. The data were collected by a Varian V75 computer, the multiplets being repetitively scanned upward and downward at low pressures (0.05-0.2 Pa) and averaged. The resulting linewidth (full-width at half-maximum) was typically about 35-40 kHz. 3. .ANALYSIS
AND
ASSIGNMENT
OF THE MICROWAVE
SPECTRA
The microwave spectrum of the previously unknown N-deuterated ketenimine has been assigned in the same way as the parent compound (3). Seventeen transitions
ROTATION-INVERSION
269
SPECTRUM
TABLE I Observed Rotational Constants (in MHz) and Centrifugal Distortion Constant (in kHz) for Ketenimine-NH and -ND@’ HZC=ONa
A
163242.42(3)
201445.47(4)
B
9663.144(Z)
9032.951(Z)
C
9470.126(l)
8962.187(I)
233.1(3)
DJK
138.3(7) 10321.(31)
10128.(19)
DK
0.0172(Z)
-0.071(4)
dl
0.0152(l)
-0.004(Z)
d2
-0.085(2)
-0.19(Z)
“KJ
Numbers of
2.78(l)
3.032(6)
DJ
(a)
H2C=C=ND
the
in
parentheses
least
squares
represent
one
standard
deviation
fit.
have been measured. The derived rotational and centrifugal distortion constants are listed in Table I. They are defined according to Watson’s symmetric reduction in a I’ representation (6). Due to an incorrect assignment of the 192,17- 201,i9 transition of HzCCNH the constants given in the previous publication differ slightly from the values now reported. Measurements of additional lines led to the constants given in Table I for this isotopic species. Figure 1 shows the multiplet found for the 9i,s - 10o,10transition of the main isotopic species at 4930 MHz where the inversion- splitting could be observed. The three strongest lines represent the three quadrupole components of the transition from the vibrationally first excited state (O- or v = 1) to the ground state (O+ or v = 0),
I 4930.0
4930.
FREQUENCY
s
/MHz.
FIG. I. Observed quadrupole and inversion splitting of the 9,,8-10 0,10transition in ketenimine-NH. The assignmerit of the components is given in Table II.
270
RODLER ET AL. TABLE II Measured Transition Frequencies of H2CCNH and H2CCND in the 4- to 7-GHz Region H*C
K+i) +
J’(K.i,
9
(1,8>
l
J”(K_i,
$0
p*
K+i)
=
+ F”
9 + IO
fO,iCJ)
c =
NH
“I
+ “”
5+
+ o-
4929.902
6
+ 0+
4930.033
o+ + o-
4930,469
a-
o+
4930.600
o+ f
o-
49JU.535
o-
*
o+
4930.668
o+
f
o-
4254.625
o+ + o-
4254.740
a-
4255.080
Ftequency/Mu7.
SplittinK/kHz
I31
10
*
11
131
8f9
l
133
27(2,25)
+ 28
(1.27)
28
+ z,(a)
115
27
+ 28
*
u+
II? Q- + I?+
H*C
J’(K,i,
K+i)
+ J”(K_1”,K+i),
9(0,9)
*
8
Fi’
(I,71
-
F’
Fi(b)
St
c =
7
4255.
ND
+ F”(‘)
Frequency/MHz
Ef7
6442.582
9 + Sfdf I.0 + 9
9*8
I97
6442.627
10
l
9
6442.653
11
+
m(d)
6442.705
9*8
6443.239 6443.283
(a)
The
(b)
F1 = J FL
quadrupole
is
cmponents
+ IN, still
(cf
P = F1 +
fdf
The
IN being a good
ID,
quadrxxpole
F’ the
quantum
ID being
the
components
= J’
f
nuclear
1 + F”
= j”
f
1 could
not
be
resolved.
spin
quantum
number
of
the
nitrogen
spin
quantvm
numbet
of
the
deuterfum
nucleus;
number. nuclear F”
=F;
f
I-P”
= F;fl
could
not
be
nucleus.
resolved.
whereas the three weaker lines are due to the three components of the O+to O- transition. They each lie 132 kHz higher than in the former triplet and possess only one-third of the intensity. This separation leads to an energy difference between O+ and O- of 66 kHz. The intensity ratio of three to one is due to the different spin statistical weight of the two transitions. Since the inversion splitting is resolvable the appropriate symmetry group is C&(M) (7). In order to study the dependence of the observed splitting on the romtional energy we also measured the 272,2s +- 28~~ transition which also happens to lie in the G-band region, The energy difference of 117 kHz is slightly smaher in this case. Attempts to measure the splitting in higher f%equency ranges f&led
ROTATION-INVERSION SPECTRUM
271
due to increased Doppler broadening. But while all p&pe transitions showed an asymmetric line profile no such asymmetry could be observed for PO-type lines. The measured transition frequencies of the two multiplets and their assignments are listed in Table II. When the 90,9- 8,,, transition of ketenimine-ND was measured with high resolution a pattern very similar to that in Fig. 1 was obtained. But the splitting of the lines is caused by a different effect. Calculations using the WISB method (8) indicated that the inversion splitting for this isotope should be smaller than 1 kHz. The observed structure is due to the partially resolved deuterium quadrupole coupling which splits each component of the nitrogen quadrupole triplet into three lines. Two of them are not resolved. Table II lists the measured transition frequencies whereas in Table III the fitted quadrupole coupling constants are given for HzCCND as well as HzCCNH. Additional information from other transitions has also been used to determine the listed constants. Some measurements were carried out in an attempt to resolve the inversion splitting in methanimine (H&L%NH). Being the lowest lying &,-type Iine the 215,17-224,18transition at 4567.3 MHz was selected. Al~ou~ the full linewidth was less than 40 kHz no sign of a splitting was observed. Both quad~pole components showed a symmetric line profile. 4. AB INITIO MOLECULAR ORBITAL CALCULATIONS
Some information about the change of the geometrical parameters during the inversion motion was needed in order to carry out semirigid bender calculations. Thus ab initio calculations at different geometries have been performed using the 6-3 lG** basis set (9) which includes p and d-type polarization functions on the hydrogen and heavy atoms, respectively. To include the effect of electron correlation on the geometries and energies the M0ller-Ples~t ~~ur~tion theory carried to third order (MP3) was used (10). The core molecular orbitals were frozen. The GAUSSIAN 80 system of programs was employed. The optimized MP3 geometries for ketenimine and methanimine at the minima and saddle points are given in Table IV. Additional calculations have been performed to prove that the C,, structures indeed represent saddle points. In particular it has TABLE III ObservedNuclear Qua~~le
CouplingConsul H*C-C-NH
fin MHz) as Obtainedfrom a Least-SquaresFit I%$-C-ND
XB,(N)
0.030(46)
0.030(a)
XbbW
I .523(40)
1.601(28)
Xa,(0)
-0.011(31)
Xbb( Dt
-0.131(15)
fa)
Was not
fitted.
272
RODLER ET AL. TABLE IV Structures and Energies Obtained for Ketenimine and Methanimine from Ab Initio MP3/6-3 lG** Optimizations
Ketenimine Parameter(a)
c,-symmetry
Methanimine c.-synmetry
c7..-smetw
C?..-syrrrmetrY
CN
1.234
1.189
1.274
1.239
NH
1.017
0.986
1.020
0.985
CH
1.077
1.075
CC
1.315
1.328
1.089/1.085(b)
1.101
113.7
180.
109.7
180.
120.2
119.7
125.l/ll8.7(b)
123.2
174.6
180.
90.5
90.
-132.3207
-132.2931
(a)
Bond
(b)
The same
0.0
1140CLfe)
0.0
5410.
0.0
11040.
(e)
on
the
in value
side
-94.3050
6060.
lengths first
-94.3570
0.0
of
(c)
In Bartrees.
Cd)
In cm -1
(e)
The HF energy cafeuleted to
(1000
;;,
angles
refers
the
cm-l
in
to
double
= 2.859
differenc 10670 cm-*
the
bond
degrees. hydrogen as
is
kcalml-1 at the (1 -- If
atom
the
which
is
located
NH hydrogen.
-
HP/&31G*
11.96
kJ m&-l).
geometries
has
been
been shown that in both cases the barrier for the rotation of the CNH group is larger than for the inversion. 5. SEMIRIGID BENDER CALCULATIONS
The semirigid bender program which we described in a previous publication (12) is based on the model of Bunker and co-workers (13, 5) and its extension by Szalay (14). It allows the calcufation of vibration-rotation spectra of molecules with a single arbitrary lake-amplitude motion without any symmetry restrictions. To our knowledge the inversion splitting in ketenimine of ca. 66 KHz or 2.2 X lOA cm-’ is the smallest energy difference until now fitted with the semirigid bender model, and it was necessary to check whether the integration of the large-amplitude wave equation was performed with the required accuracy. Energies were calculated with the Numerov-Cooley algorithm (15) in which the energy was varied until the computed correction to it was smaller than an arbitrarily chosen limit. A value of lo-” cm-’ was chosen as the convergence criterion which ensured that derivatives for the least-squares procedure could be calculated to about two significant digits for the inversion splitting Av. For checking purposes AV was also calculated using the WKB approximation (8). With the reduced mass P = &I), explicitly depending on the inversion angle p, the potential
ROTATION-INVERSION
273
SPECTRUM
V = V(p) and the energy of the O+ state E, we numerically integrated between the classical turning points ltpo to obtain the value A where A = exp
[2p(I’ - E)]“2dp
.
With v. as the 1+-O- frequency Au is represented by Au = vo/(* - A2). Agreement of better than 10% was obtained from both methods confirming the correctness of the Numerov-Cooley integration. The following input data have been used for the fit: the observed splitting of the 9 iT8-10o,,o transition of H2CCNH and the infrared frequencies (1 --O+) for H2CCNH (at 1001.3 cm-‘) and D2CCND (at 798.5 cm-‘). The infrared frequencies resulted from matrix experiments and might therefore be slightly shifted compared to the gas phase frequencies. The potential was chosen to be qua&c with a quadratic barrier and the barrier height and position of the minima were fitted. As Table II shows there is a K-i dependence of the splitting of the microwave lines. In order to properly account for the factors leading to this effect, which is discussed below in detail, we directly fitted the observed splitting as the difference in frequency of 0+-O- intersystem lines. The alternative procedure of taking it to be twice the splitting of the pure inversion levels, Of and O-, assumes the rotational constants to have the same values for the two levels. Our previous investigations into molecules with amino inversion had shown that semirigidity had to be taken into account to explain all experimental data, i.e., inversion frequencies and vibrational satellite shifts. For cyanamide (22), we had found that ab initio predictions at the MP3/6-31G ** level yielded quite reliable estimates of the parameters which determine the pathway during the inversion. They differed by less than 10% from the experimentally obtained values. Therefore we applied the same method here as well. It was necessary to obtain reasonable values for all geometrical parameters as a function of the inversion parameter p (which in our case is the CNH angle). This was done by interpolation between the ab initio optimized C2” structure and C’, structure. Depending on the symmetry of the change of the parameters with respect to p, we either interpolated linearly or quadratically. We explored the effect of semirigidity in ketenimine in a number of calculations: the molecule inverted rigidly, with the remaining parameters frozen at the optimized C’, structure or semirigidly with the MO pathway parameters. In the semirigid bender fits we also varied the relative weighting of the O--O+ inversion and l--O+ infrared frequencies as well as the actual value of the observed inversion doubling in order to assess how strongly the inversion potential depended on the’input data. The results of the above-mentioned calculations are presented in Table V. When semirigidity is neglected the fit gets markedly worse. In particular the inversion splitting is not fitted as well as with inclusion of semirigidity and the value for the equilibrium angle pes is relatively far out from the ab initio prediction. In cyanamide pq from MO calculations and experiment agree to better than one-half degree. The semirigid bender fit shows that the inversion splitting is a very sensitive function of both pe4 and barrier height. Both parameters are determined without correlation (coefficient 0.146) and with only small standard deviations. Comparison of models 3
274
RODLER ET AL. TABLE V Results of the (~~i)~~d
Li*c=c=NH splitting 91,s - 100,lC
of (kHz)
132(I)
obs.-ealcH,C-C=xK
1--o*
125(l) #
-38 (&f
10o1‘3f1.0)
l--o+(cla
-21.3
790*5(1*0)
-1)
4
3
132(l)
132(l)
-3
0
1001.3(1.0)
-28.2
&J.-C&Z. D*C=C=ND
2
I
Model
Bender C~c~atio~s(‘~
1001*3el.25) -21.3
798.5(1.0)
798.X1.0)
28.4
28.4
[email protected](0.25)
5
132 110 I00f.3
21.3
-33.1
798.5(0.25)
798.5
26.4
85.0
ohs.-cslc.
37.3
(cm-‘)
4508(608)
4697( 102)
4686(101)
4682(!83)
4686
119.5(53)
115,3(6)
If5.4(6)
I&4(12)
115.4
Barrier pa,<“)
Models:
1 2,3,4 5
rigid semlrlgfd r&id
bender
Fit
bender bender
with
ah ioitio
fully
optimized
C, bond leogths
and angles.
fits,
as I with
potential
OP 3.
and 4 shows that a well-balanced weighting is important to obtain the best fit for all frequencies, although there is not a great difference in the actual potentials. As final values we derived: barrier = 4700 + 200 cm-‘; pes = 115.4 + 0.6”. The rigid bender results should not be regarded as completely unreahstic, because frequencies of largely different order of magnitude are fitted to within 20%. With the final semirigid bender potential the inversion splitting is calculated too small by a factor of 6. This can be explained by inspecting the actual pathway: the nitrogen atom slowly moves in opposite direction to the imino hydrogen thus effectively decreasing the reduced mass. The WKB approximation shows that this increases the inversion splicing, which can also be seen by the numerical solution of the inversion wave equation. The value of In A is 18.9 for H,=C=C=NH and 26.2 for the N-deuterated ketenimine. This predicts the inversion splitting to be 0.03 kHz for the latter and makes it unfeasible to be observed by microwave spectroscopy. Table II shows that there is a small but definite decrease in the inversion splitting in higher K_ t leveis. The following effects coufd contribute: (if SfightIy different rotational constants in the 0” and O- state, (ii) and (iii) a J and K-r dependence of the inversion splitting. In the following discussion we shall use the axis label z along the heavy chain because we refer to the Eckart axis system. Also we use pXClzr and Z for the corresponding elements of the inverse of the inertia tensor and its inversion average. There is only a slight difference to the value A of the principal axis system. Similar to the inversion splitting itself the observed Kdependence can partially also be rationalized in the WKB approximation. During the inversion, which is much slower than the rotation, the molecule has tu accelerate in its rotation around the z axis because the rotational constant 2 increases by ea. 30% by going from the equi-
ROTATION-INVERSION
SPECTRUM
275
librium to the planar configuration. The term $K?, - prz cannot be neglected in the kinetic energy expression and changes the effective potential. The K-dependent energy EUKis approximately EVK = E,,+ fK?I(pzz), where the main contribution to the average of prz over the inversion wavefunction comes from near the equilibrium configuration. In the WKB approximation, one integrates over the region where pzz is the larger than (& and consequently the inversion splitting decreases with K. The same result is obtained from the numerical integration of the inversion wave equation and amounts to -2 kHz. There is a similar but smaller J-dependent effect which, however, is not calculated in our semirigid bender model. Slightly different effective rotational constants 2 in O+ and O- make another contribution: there is a decrease of AZ = -0.6 kHz from O+ and O-. If only rotation about the a axis is considered the change in the splitting is A = AvKz2- AI+,, + 4AZ. The resulting value of -4.4 kHz is at least qualitatively in agreement with the observation. There certainly will be higher order centrifugal effects because of the high-J value of the measured transitions, which we, however, cannot estimate in our model. Therefore we did not include the observed inversion splitting of the J = 28-27 transition in the fitting. 6. CONCLUSIONS
Ketenimine is the first compound in which the splitting of rotational transitions due to the inversion motion of an imino hydrogen has been observed. The energy difference of 66 kHz (2.2 10e6 cm-‘) between the ground and first excited state is one of the smallest ever observed and considerably smaller than most splittings due to the inversion of amino hydrogens. Ammonia (8), cyanamide (I2), isocyanamide (16) and even monochloramine (17) exhibit splittings which are several orders of magnitude larger. For methanimine, which can undergo an inversion similar to ketenimine, the inversion splitting could not be resolved. As both molecules have similar reduced masses for the inversion motion this indicates a higher barrier for methanimine. This is in qualitative agreement with ab initio calculations. The observed splitting for ketenimine in combination with infrared data made it possible to determine the potential barrier of 4700 f. 200 cm-’ (56.2 + 2.4 kJ mol-’ or 13.4 f 0.6 kcal mol-‘) and the CNH angle of 115.4 f 0.6” using the semirigid bender model. The ab initio molecular orbital calculations at the MP3 level were of substantial help in reliably predicting the rotational constants and consequently facilitating the search for rotational transitions. On the other hand, the prediction of the inversion barrier is significantly in error. The calculated barrier (6060 cm-’ at the MP3 level) is about 1400 cm-’ higher than the experimental value. At the Hartree-Fock level, where the electron correlation is not taken into account, the difference amounts to 700 cm-‘. Both barriers lead to splittings which are many orders of magnitude smaller than has been observed. This large discrepancy is quite surprising in light of similar calculations for related molecules. For cyanamide and &cyanamide, which are isoelectronic to ketenimine, the calculated barrier at the MP3 level was calculated to 467 and 2100 cm-’ (18) respectively. This compares favorably with the observed values of 504 (12) and 2070 cm-’ (16), respectively. Two possible explanations for the difference might be considered: First, deficiencies of the ab initio calculations in properly describing the electronic
RODLER
276
ET AL.
properties of this imine. Qualitatively speaking the hybridization of the nitrogen nucleus changes from sp2 to sp for imino inversions in contrast to the change from sp3 to sp2 for amino inversions. Due to the lack of experimental data no comparison between experimental and ab initio barriers for imino inversions have been possible so far. And second, the effective inversion potential, which is the zero-point average over all other vibrations except the inversion, might be appreciably different from the hypothetical vibrationless potential. Some indications have been found that the second point might contribute at least partially. According to the MO calculations the force constants for the CH2 wagging changes from 0.146 to 0.040 mdyn A/rad2 going from the r, to the C2, structure. But its quantitative influence cannot be assesed with confidence. ACKNOWLEDGMENTS Financial support by the ARCS is acknowledged. We are grateful to Robert Champion for helpful discussions and Kaoru Yamanouchi for measurements in the early stages of the project. M. Rodler also acknowledges the assistance of a Monash University Vice Chancellor’s Postdoctoral Fellowship.
RECEIVED:
October 3 1, 1985 REFERENCES
1. M. E. JACOXAND D. E. MILLIGAN,J. Amer. Chem. Sot. 85,278-282 (1963). 2. M. E. JACOX, Chem. Phys. 43, 157-172 (1979). 3. M. RODLER,R. D. BROWN,P. D. GODFREY, AND L. M. TACK, Chem. Phys. Lett. 110,447-45 I ( 1984). 4. L. M. JACKMAN,in “Dynamic Nuclear Magnetic Resonance Spectroscopy” (L. M. Jackman and F. A. Cotton, Eds.), pp. 244-249, Academic Press, New York, 1975. 5. P. R. BUNKERAND B. M. LANDSBERG,J. Mol. Spectrosc. 67, 374-385 (1977). 6. J. K. G. WATSON,in “Vibrational Spectra and Structure” (J. R. Durig, Ed.), Vol. 6, pp. l-89, Elsevier, Amsterdam, 1977. 7. P. R. BUNKER,“Molecular Symmetry and Spectroscopy,” Academic Press, New York, 1979. 8. C. H. TOWNESAND A. L. SCHAWLOW,“Microwave Spectroscopy,” pp. 300-307, McGraw-Hill, New York, 1955. 9. P. C. HARIHARANANDJ. A. POPLE, Theor. Chim. Acta 2t3,2 13-222 (1973). 10. J. A. POPLE,J. S. BINKLEY,AND R. SEEGER,Int. J. Quantum Chem. Symp. 10, l-19 (1976). Il. J. A. POPLE, K. RAGHAVACHARI,M. J. FRISCH,J. S. BINKLEY,AND P. V. R. SCHLEYER,J. Amer. Chem. Sot. 105, 6389-6398 (1983). 12. R. D. BROWN,P. D. GODFREY,AND B. KLEIB~MER,J. Mol. Spectrosc. 114,257-273 (1985). 13. J. T. HOUGEN,P. R. BUNKER,ANDJ. W. C. JOHNS,J. Mol. Spectrosc. 34, 136-172 (1970). 14. V. SZALAY,J. Mol. Spectrosc. 102, 13-32 (1982). 15. J. W. COOLEY,Math. Comp. 15, 363-374 (1961). 16. M. WINNEWISSER,J. Mol. Struct. 126, 41-66 (1985). 17. G. CAZZOLIAND D. G. LISTER,J. Mol. Spectrosc. 45,467-474 (1973). 18. M. RODLER,R. D. BROWN,AND P. D. GODFREY,unpublished results.