Methyl isocyanate: An analysis of the low-J rotational spectrum using the quasi-symmetric top molecule approach

JOURNAL

OF MOLECULAR

SPECTROSCOPY

106,

12-2 1 ( 1984)

Methyl Isocyanate: An Analysis of the Low-J Rotational Spectrum Using the Quasi-symmetric Top Molecule Approach J. KOPUT’ Department of Chemistry, A. Mickiewicz University, Poznari, Poland

The low-J rotational spectrum of methyl isocyanate (CHINCO) has been analyzed in terms of the quasi-symmetric top molecule model, accounting explicitly for the large-amplitude CNC bending motion, and internal and overall rotation. An assignment of 25 J = 1 - 0 and 2 - 1 rotational transitions arising from the various CNC bending and torsional states is proposed. The molecule is found to be a nearly freely internally rotating quasi-symmetric top, with a barrier to linearity of the CNCO skeleton of 1049 cm-’ and an equilibrium CNC valence angle of 140.2”. I. INTRODUCTION

Molecules of the XH3NYZ type, such as methyl (l-3), silyl (d-12), and germyl (13-15) pseudohalides, undergo the two large-amplitude motions, namely the XNY bending motion and internal rotation of the XHs group. Although the rotational spectra of some pseudohalides, such as silyl(6, 7) and germyl(14, 15) isothiocyanates, can be described quite well in terms of the standard theory, special theoretical models are necessary in order to understand the molecular dynamics of most of the molecules in question. The two-dimensional anharmonic oscillator model, allowing for the largeamplitude XNY bending motion, has been developed by Duckett, Robiette, and Mills (5, 16). Recently, the quasi-symmetric top molecule model, describing explicitly both the large-amplitude motions, has been developed by Wierzbicki, Koput, and Kreglewski (I 7-20). Both models have been successfully applied in the analysis of the rotational spectrum of silyl isocyanate (5, 1 I, 12, 21). In the present paper the quasi-symmetric top molecule model is extended to account for a tilt of the XH3 group symmetry axis, and used to study the CNC bending-torsion-rotation energy levels of methyl isocyanate (CH3NCO). There has been little spectroscopic work done on the methyl isocyanate molecule. From microwave (I, 2) and electron diffraction (22) studies, the molecule was found to be an asymmetric top with the CNC valence angle of about 140” and a low barrier to internal rotation [49 f 3 (1) or 83 +- 5 cal/mol (2)]. Although several lines, corresponding to the transitions arising from the lowest torsional states, in the lowJ rotational spectrum were assigned, the spectrum could not be fitted by the usual semirigid internal rotation treatment (I, 2). The paper is divided into two parts. The quasi-symmetric top molecule model is ’ Present address: Physikalisch-Chemisches Ring 58, 6300 Giessen, West Germany. 0022-2852184 $3.00 Copyright Q 1984 by Academic Press. Inc. All rights of reproduction in any form reserved.

Institut, Justus-Liebig-Universitat

12

Giessen, Heinrich-Buff-

CH,NCO ASA QUASI-SYMMETRIC TOP

13

reviewed in SectionII, andthe resultsof calculationsof the CNCbending-torsionrotationenergylevelsof CH3NC0arepresentedin SectionIII. II.THE

MODEL

HAMILTONIAN

The vibration-torsion-rotation Hamiltonian for the CH3NC0 molecule is a slight modification of the Hamiltonian developed for a quasi-symmetric top molecule with two internal C,, rotors (17, 18). Since the exact Hamiltonian is too complicated to solve the corresponding Schriidinger equation directly, we consider the approximate Hamiltonian obtained from the exact one by putting all the small-amplitude vibrational coordinates and their conjugate momentum operators equal to zero. This approximate five-dimensional Hamiltonian describes explicitly the CNC bending motion, and internal and overall rotation of the molecule. The reference configuration of the atomic nuclei of the CH3NC0 molecule is defined by fixed bond lengths r%, &, r$, &!,, and an angle $, and by variable angles p, T, and 6; these quantities being depicted in Fig. 1. The angle p is the supplement of the CNC valence angle. The angle 7 is defined as the dihedral angle between the plane through the atoms C, ,N, and C3, and the plane including the CH3 group symmetry axis and the atom Ha. We assume that the CH3 group has Go point group symmetry, with the symmetry axis lying in the plane through the atoms C,, N, and C3, and being tilted from the CN bond by the angle 6. On the analogy of the nonrigid reference configuration model (20), the angle 6 is assumed to vary with the angle p so that 6 = 0 at p = 0. The NC0 chain is assumed to be linear. The molecule-fixed xyz-axis system is located so that its origin is at the center of mass of the reference configuration, the xz plane passes through the atoms CI, N, C3, and 0, and the z axis makes an angle E with the CN bond. The angle E is chosen so that the component of the angular momentum due to the large-amplitude CNC bending motion vanishes in the molecule-fixed axis system [see Eq. (4) of (to)]. Making use of this condition and the explicit expressions for the components of the position vectors aj(p, 7) [analogous to those given by Eqs. (1) of (20)], we determine the following equation for the derivative dc/dp:

I

0

FIG. I. The CH,NCO molecule. The numbering of atoms and location of the molecule-fixed system. The axis a is the CH3 group symmetry axis.

xyz-axis

14 f’ =

J. KOPUT d&p

=

(u3

+

2413cos p +

w148 cos

6 -

w34(

+ [wq + (1/2)u4]S’}/[u, +

1 + 6’) cos(p - 6) u3 +

+

0%

~3 =

m3ts83

u13

=

(ml

+

3m4wL -

+

-

rS3>’

3m4W

62)’

+

(ml

Y2 -

+

Cm2

+

m2

+

472)4!3

-

+

m3

3m4(d412

~4

=

(ml

~14

=

mdr?2

-

4!2)4?4

-

(m2

+

m3

w34

=

m3@3

-

4!3)4!4

-

(ml

+

m2h&!39!4

m2

+

m3

+

+

m2d2d3

m7)(d4)2

+

+

3m4@4 +

p,

-

a)],

(1)

m&i3

W2)m4(d4)2 -

d3J2

-

4!3)

+

-

d2><84

d4)

+

wd2@3

-

4!3)

d4J2

mdd24?4 +

+

m3d2VS3

-

2W34 COS(p

and where the quantities u and

m7)(d2>2

3m4)(d3)2

~4 =

+

+

22413 cos p

2W14 COS 6 -

where prime denotes the derivative with respect to w are defined as Ul =

w4 +

-

3m40?2

3m49Fi3C.84

-

-

d4)

m7W3

-

4?3)4?4. (2)

Here the constants p”, so, and

q”

are defined as

py4 =

ry4

sY4=

rT4 cos p”

P!J

rS3 +

=

472 =

[(ml

sin @

r% +

3m4H2llm

d3

=
+ wd3Ym

d4

= Um4sY4Ym,

and mi is the mass of the ith atom, and m atoms of the CH3NC0 molecule. The skeletal CNC bending-torsion-rotation (42) of (17)i

(3) is the sum of the masses of the seven Hamiltonian

HO,,, is given by [see Eq.

+ ; (~“)1’4{Jpp~p(~o)-“2[Jp(cL”>‘/“l> + ; CL!,J: + ; ,&(JxJ~ + Jr Jx)

+ ; &JzJr f Jr JA +

f’-O(P, T),

(4)

where all the symbols have the same meanings as in (17). The quantities &, ((Y,/3 = x, y, z, p, 7) are the components of the inverse of the 5 X 5 moment-of-

CH3NC0

AS A QUASI-SYMMETRIC

inertia I0 matrix, and the nonvanishing components

TOP

15

I!& as functions of p are given

by I!., = uI cos2 t + u3 cos2(p - E) + 2u13 cos E cos(p - c) + w4 cos2(c - 6) + 2w14 cos c cos(c - 6) - 2w34 cos(p - t) cos(c - 6) + (1/2)u4[sin2 E + sin2(E - S)] riY = U1+ 19,

=

uI

U3 +

2Ut3

COS p +

W4 +

2W14 COS 6 -

2W34 COS(p -

6)

sin’ c + u3 sin2(p - e) - 2~~~ sin c sin(p - t) t w4 sin2(c - 6)

t 2wf4 sin E sin(e - 6) t

I22 = -(1/2)u,

2W34

sin(p - E) sin(t - 6) + (1/2)u4[cos2 6 t cos2 (c - S)]

sin 2~ t (l/2)u3 sin 2(p - c) t u13 sin@ - 26) - (l/2)w4 sin 2(~ - 6)

t WI4sin(b - 2~) - w34sin@ + 6 - 2~) + (1/4)u4[sin 2~ t sin 2(~ - S)]

ZEP= z4,(Q2 + u3(1 - ~‘1~- 2u13 cos p (1 - 8)t’ + w~(E’- 6r)2+ 2w14cos 6 (E’ - 8’)~’ t 2W34 COS(p - 6)(t' - a')(1 - E')t (1/2)24&c' - 6')2- (E')'] z:, = u4

z:* =

-u4

cos(c

-

6),

(5)

where the quantities e’, U, and w are given by Eqs. (1) and (2), and the value of c at any value of p is determined by numerical integration of Eq. (1). The value of 6’ is determined from the explicit form of 6 as a function of p [see Eq. (1 I)]. The skeletal CNC bending-torsion-rotation energy levels can be determined by diagonalization of the H&, Hamiltonian matrix in the basis of wavefunctions 9 JMkmvb . Each of these wavefunctions is a product of a rotational symmetric top wavefunction [s,,k(O, 4)eikx], a torsional free internal rotor wavefunction [eim’], and a skeletal CNC bending wavefunction [&,,&P)]: (6)

The wavefunction 1C/k,&P)is a solution of the Schriidinger equation (I 3) of (20). The form of the HzMrHamiltonian implies that only the rotational quantum numbers J and M are good quantum numbers for the problem under consideration. Thus, the exact wavefunction !@I,~~ can be written as

where the constants c(S m, ub) are some unknown coefficients, and the sum goes over the rotational (k), free internal rotor (m) and CNC bending (Q) quantum numbers. ’ Hamiltonian matrix elements are given by Eqs. The explicit expressions for the Hsbtr (16) of (20). The numerical techniques that we use are the same as those described in (18).

16

J. KOPUT III. ANALYSIS OF THE MICROWAVE

SPECTRUM OF CH3NC0

The microwave spectrum of methyl isocyanate was investigated by Curl et al. (I) and by Lett and Flygare (2). Instead of a simple rotational spectrum, ,as would be expected for a rigid asymmetric top molecule, the authors observed a very complex spectrum consisting of rotational transitions arising from excited torsional and vibrational states. It was found that the spectrum could not be fitted by the usual semirigid internal rotation treatment (an asymmetric top molecule with a rigid methyl group attached to a rigid frame). Some of the k = 0 lines would be assigned, and these lines would be fitted only if a semiempirical correction accounting for the internal rotation-rotation interaction was used and a tilt of the methyl group symmetry axis was assumed (2). An extended model including the interaction of the CNC bending motion with internal and overall rotation failed entirely to give satisfactory results and to improve this fit. This led Lett and Flygare (2) to the conclusion that this simple five-dimensional model was not sufficient, and that an extensive vibrationrotation treatment was necessary. As will be shown below, the five-dimensional but quasi-symmetric top molecule model allows one to interpret quantitatively at least a part of the observed spectrum of methyl isocyanate. To be consistent with the work of Lett and Flygare (2) we carried out calculations of the CNC bending-torsion-rotation energy levels of CH3NCO with fixed values of the C=O, N=C, and C-H bond lengths and p” angle [see Table IX (Structure 1) of (2) and Table III below]. The skeletal CNC bending-torsional potential function VO(p,r) [see Eq. (4)] was expanded for each value of p as a Fourier series in the torsional coordinate 7 [cf. Eq. (26) of (17)]

The CNC bending potential function V&p) was chosen as quadratic plus a Lorentz hump, i.e., of the form V,(p)

=

- PZ12 $hp2 + -1 +Kap* = fp: w-CP2 + (8H -fp:)p*

’

(9)

where X, K, and a were some parameters. The second form (23) is preferred, in which pe is the equilibrium bending angle, H is the barrier height [i.e., I/,(O) - Voo(pe)], and fis the harmonic force constant at p = pe. The expansion coefficient V3(p), as well as the tilt angle a(p), was expanded as a Taylor series in the bending coordinate p V,(p) = vyp

+ v:*‘p2 + vI:3)p3 + 0 * *

(10)

and 6(p) = &(‘jp + 8mp2 + . . . >

(11)

where we assumed that both the functions vanished at p = 0, i.e., when the molecule took a configuration with the linear CNCO skeleton. It follows from symmetry requirements that for a CH3NCO-like molecule with a linear equilibrium configuration of the heavy-atom skeleton, the expansion coefficients V\3n*‘) and 8(2nr’),where n is

CH3NC0AS A QUASI-SYMMETRIC TOP an integer, are equal to zero. For methyl isocyanate this is not the case, and since in

preliminary calculations the expansion coefficientsYy)as well as Sci)were found to be strongly correlated, all terms other than the linear terms in the above expansions were neglected in further calculations. Energies of the rotational transitions were calculated using the selection rules derived in Ref. (20). The problems of symmetry of the molecule were also discussed in detail ibidem. The experimental data used in the calculations are all frequencies of the J = 1 +0, J = 2 - 1, k = 0 and of the pair of J = 2 - 1, k = +-1, m = 0 transitions quoted in the work of L&t and Flygare [see Tables VII and VIII of (2)]. In the initial stage we adopted the assignment made by these authors, and we fitted the pair of the k = +-1 transitions, all the k = 0 transitions arising from the ground CNC bending state, as well as the CNC bending fundamental (2). The six parameters per H, J; V:“, 6(l), and the C-N bond length were varied in a least-squares manner to improve this fit. These calculations and intensities of the rotationai transitions determined by Lett and Flygare (2) served as a guide to assign the rotational transitions arising from the excited CNC bending states. In the final calculations we fitted all the observed rotational transitions.* In the least-squares fitting, the frequencies of these transitions were given a unit weight. The observed frequencies and differences between the observed and calculated values are given in Table I. The calculations showed that the expansion of Eq. (7), when written in the symmetry-adapted basis set wavefunctions given by Eqs. ( 17) of Ref. (20) [see also Eqs. (13) of Ref. (Is)], converged very rapidly, with dominant expansion coefficients c(k, m, ub) being about 0.99. This explains that we can also use the quantum numbers k, m, and Q, to label the CNC bendingtorsion-rotation energy levels. The calculated energies of some lowest CNC bendingtorsion-rotation energy levels of CHjNCO are given in Table II. Each of the energy levels is labeled by the symmetry species A ,, AZ, or E, and by one of the pair of labels (vb, k, m) and (vb, -k, -m).3 The optimized values of the molecular parameters are given in the first column of Table III. To estimate the effect of the tilt angle 6, we carried out calculations with this angle fixed at zero. The optimized values obtained for the molecular parameters in these calculations are given in the second column of Table III. A comparison between the standard deviations of the two fits clearly indicates that the effect of a tilt of the CH3 group symmetry axis is important. Inclusion of the nonzero tilt results mainly in a considerable decrease in the differences between the calculated and observed frequencies for the pair of the J = 2 - 1, k = 5 1, m = 0 transitions, these differences being about 5 MHz in the calculations with the tilt angle 6 fixed at zero (cf. Table I). We may then expect that it would be also important to account for a variation of the other molecular parameters (the bond lengths and valence angles) with the bending angle p (20), as well as for a coupling between the CNC and NC0 bending motions (2). However, such a sophisticated model seems to be unnecessary at the present stage of the analysis. 2 The frequency of the CNC bending fundamental was excluded because it is not precise, (the known frequency of a weak, broad Raman band of liquid CH,NCO). ’ This also refers to all results quoted.

18

J. KOPUT TABLE I Comparison of the Observed and Calculated” Frequencies (in MHz) of the Rotational Transitions of CH3NC0 J=2

J=lcO o-c

Observed

o-c

8617.13

-0.41

17342.50

-0.37

8714.32

-0.42

17426.09

0.48

8712.16

-0.22

17424.73

-0.04

3

6721.19

-1.04

17444.10

-0.36

3

0722.65

0.05

17445.79

0.60

0

4

8737.23

0.06

17474.86

0.57

0

0

5

8755.17

0.02

17510.75

0.48

0

0

6

8775.17

-0.66

7551.10

-0.52

1

0

0

8670.33

0.21

7340.96

0.91

1

0

1

8705.27

-1.56

7409.29

-1.00

1

0

2

8710.48

0.52

1

0

3

8726.82

2.04

Observed

k

m

0

0

0

0

0

1

0

0

2

0

0

0

0

0

vb

7421.50

1.57

b

7452.84

3.31 b

1.70 b

1' 7452.84

1

0

3

0726.82

2

0

0

0660.52

0

1

0

17190.50

-0.30

0

1

0

17504.51

-0.12

a Calculated Table b

cl

using

III(Column

Tentative

c Transition

the molecular

b

parameters

given

in

Il.

assignment, not

2.63

c

-0.92

omitted

from

the fit,

see

text.

observed.

The results given in Table I show that all but two rotational transitions quoted by Lett and Flygare (2) can be assigned using the quasi-symmetric top molecular model. The two transitions, at 8726.82 and 17452.84 MHz, are in the correct position to be assigned to the (Q = 1, k = 0, m = 3) transitions but no characteristic splitting, as for the (0, 0, 3) transitions, has been observed (2). The two lines, at 17452.78 and 17453.66 MHz, were observed [see Table VIII of (2)], but these were assigned as components of the 14N quadrupole hyperfine structure of the transition at 17452.84 MHz. We also assigned some of the transitions observed by Curl et al. [while not quoted by Lett and Flygare (2)] [see Table I of (I)], for example, at 8796.5 MHz to (0, 0, 7), at 8747.6 MHz to (1, 0, 4), at 8692.3 MHz to (2, 0, l), at 175 10.4 MHz to (0, - 1, 3), and at 17489.5 MHz to (1, - 1, 3). The other transitions would be only tentatively assigned. In our view an unambiguous assignment would require further experimental and theoretical investigations; the new analysis of the rotational and vibrational spectra of CH,NCO has already begun (24). A few remarks shall be made about the barrier to internal rotation for CHXNCO and the related molecules. It is apparent from Eq. (8) that the usual definition of the barrier to internal rotation cannot be applied in the quasi-symmetric top molecule

19

CHJNCOAS A QUASI-SYMMETRIC TOP TABLEII CalculatedJ = 1 CNC Bending-Torsion-RotationEnergyLevels’(in cm-‘) of CH3NC0 A

vbk

0

AE

m

1

O-l 0

0

0

13

AE

km

Vb

0

4.15

0

0

3

61.17

0

IO

3

80.17

O-l

110

0

107.16

0

o

196.22

0

l3

3

0

110

Calculated Table

b energy

using

the molecular

III(Column

I).

to

95.38

equal

cm

-1

0.00

vbk

b

4.15 3

10

a

E

A2

1

above

O-l

1

0

61.17

m

0

01

80.46

o-1

107.16

0

0

191.34

0

12

196.22

o-1

parameters

the

0

0

0

14

5.13

1

8.71

7

18.95

2

26.51

2

36.33

4

115.34

4

141.77

55.75

175.46

o-1

5

I-1

1

196.49

IO

1

200.81

given

minimum

AE

186.71

in

of the potential

function.

model because the expansion coefficient V&) is a function of the bending coordinate p. Instead, we can define the effective barrier to internal rotation Vjff for a given (u,,, k, m) state as the expectation value

where &,&(P) is the skeletal CNC bending wavefunction [see Eq. (6)]. For the ground (0, 0, 0) state, @ is calculated to be 13.7 cm-‘, compared to the barrier to internal rotation of 17 cm-’ [49 f 3 cal/mol (I)] or 29 cm-’ [83 -t 5 cal/mol(2)] determined using the usual semirigid treatment. Although the effective barrier value is close to the barrier value determined by Curl et al. (I), it is apparent from a comparison of the observed and calculated splittings of the k = 0, m = +-3 transitions (see Table I) that the effective barrier to internal rotation is underestimated in the quasi-symmetric top molecular model. The calculations have shown that the effective barriers only slightly depend on the quantum numbers t)b, k, and m; for various CNC bendingtorsional-rotational states with 1](,= 0, 1, 2, and 3, the effective barriers Vjff differ from that for the ground state by about +I cm-‘. Similar remarks also apply to the tilt angle S(p), and we can define the effective tilt angle deffas aeff =

(~kmvb(P)ls(P)I1Lkm”~(~))

For the ground (0, 0, 0) state, &effis calculated to be 1.1’.

(13)

20

J. KOPUT TABLE

III

Values of the Molecular

Optimized

Parameters’

for CH,NCO II b

I

'C-N/

1.43421(

2

1.42657( 98)

y.J=C/ 2

c

1.207

1.207

rc.o/

c

1.171

1.171

61 c

1.091

1.091

109.5

109.5

39.817(83)

39.‘J12(98)

2

r.C_ff/ [3’/

deix

?,/

deg

=

H/ cm-' f/

mdyne

v(ll 3 / a-' 6"'/

deg

2 rad-' rad

-1

Std. deviation of the fit/ MHz

a Figures in units b

79)

in parentheses of the last

Calculations

c Held

fixed,

with see

the

1048.8(70)

1056.1(80)

0.2580(21)

0.2685(

20.0(431

10.6(56)

1.54(23)

0

0.78

1.87

are figure tilt

one

standard

21)

deviation

quoted. angle

6 fixed

at zero.

text.

IV. CONCLUSIONS

The calculations performed have shown that (a) the quasi-symmetric top molecular model accounting explicitly for the large-amplitude CNC bending motion, and internal and overall rotation is needed to account for the microwave spectrum of methyl isocyanate; (b) large centrifugal distortion effects observed in the microwave spectrum (I, 2) are mainly due to the strong CNC bending-internal rotation-overall rotation interaction; (c) the quasi-symmetric top molecular model allows one to interpret quantitatively the low-J rotational spectrum of methyl isocyanate that was not possible using the usual semirigid internal rotation treatment (I, 2); and (d) methyl isocyanate is an example of a nearly freely internally rotating XH3NYZ molecule with the highest barrier to linearity of the heavy-atom skeleton among the molecules investigated (I-15). ACKNOWLEDGMENT I wish to thank Dr. M. KrFglewski for the preprint of Ref. (19).

RECEIVED:

September 22, 1983

CH3NC0AS A QUASI-SYMMETRIC TOP

2 -1

REFERENCES F. CURL, JR., V. M. RAo, K. V. L. N. SASTRY, AND J. A. HODGESON,J. Chem. Phys. 39,3335 3340(1963). 2. R. G. LETTAND W. H. FLYGARE,J. Chem. Phys. 47,4730-4750 (1967).

1.R. 3. 4. 5. 6.

S. CFUDOCK, J. Mol. Spectrosc. 92, 170-183 (1982). M. C. L. GERRY,J. C. THOMPSON,AND T. M. SUGDEN,Nature (London) 211, 846-847 (1966). J. A. DUCKETT, A. G. ROBIETTE, AND I. M. MILLS,J. Mol. Spectrosc. 62, 34-52 (1976). K. F. DOSSELAND A. G. ROBIETTE,Z. Naturforsch.A 32, 462-472 (1977). 7. K. F. DOSSELANDD. H. SURER, Z. Naturforsch.A 32, 473-481 (1977). 8. J. R. DURIG, K. S. KALASINSKY,AND V. F. KALASINSKY,J. Chem. Phys. 69,918-923 (1978). 9. J. R. DURIG, K. S. KALASINSKY, AND V. F. KALASINSKY, J. Phys. Chem. 82,438-442 (1978). 10. S. CRAD~CKANDD. C. J. SKEA,J. Chem. Sot. Faraday Trans. 2 76, 860-871 (1980). Il. J. A. DUCKETT,A. G. ROBIETTE,AND M. C. L. GERRY,J. Mol. Spectrosc. 90, 374-393 (1981). 12. L. HALONENAND I. M. MILLS,J. Mol. Spectrosc. 98, 484-494 (1983). 13. J. R. DURIGANDJ. F. SULLIVAN,J. Mol. Struct. 56, 41-55 (1979). 14. J. R. DLJRIG,Y. S. LI, AND J. F. SULLIVAN,J. Chem. Phys. 71, 1041-1049 (1979). 15. J. F. SULLIVANANDJ. R. DURIG,J. Mol. Struct. 60, 37-42 (1980). 16. J. A. DUCKETT,A. G. ROBIETTE, AND I. M. MILLS,J. Mol. Spectrosc. 62, 19-33 (1976). 17. A. WIERZBICKI, J. KOPUT,AND M. KREGLEWSKI, J. Mol. Spectrosc. 99, 102-I 15 (1983). 18. J. KOPUTAND A. WIERZBICKI, J. Mol. Spectrosc. 99, 116-132 (1983). 19. M. KREGLEWSKI, .I. Mol. Spectrosc., in press. 20. J. KOPUT,J. Mol. Spectrosc. 104, 12-24 (1984). 21. M. KREGLEWSIU AND P. JENSEN,J. Mol. Spectrosc. 103, 312-320 (1984). 22. D. W. W. ANDERSON,D. W. H. RANKIN,AND A. ROBERTSON, J. Mol. Struct. 14, 385-396 (1972). 23. T. BARROW,R. N. DIXON, AND G. DUXBURY,Mol. Phys. 27, 1217-1234 (1974). 24. J. R. DURIG, private

communication.