Development of millimeter- and submillimeterwave spectroscopy and its application to isotopically-substituted nonpolar molecules, deuterated cubane and deuterated cyclobutanes

Journal of Molecular Structure, 190 (1988) 235-258 Elsevier Science Publishers B.V.. Amsterdam - Printed

235 in The Netherlands

DEVELOPMENT OF MILLIMETERAND SUBMILLIMETERWAVE SPECTROSCOPY AND ITS APPLICATION TO ISOTOPICALLY-SUBSTITUTED NONPOLAR MOLECULES, DEUTERATED CUBANE AND DEUTERATED CYCLOBUTANES”

EIZI HIROTA, The Institute ERNEST

YASUKI

END0

for Molecular

W. DELLA

and MASAHARU

FUJITAKE

Science, Okazaki 444 (Japan)

and PAUL E. PIGOU

School of Physical Sciences, The Flinders Australia 5042 (Australia)

University

of South Australia,

Bedford

Park, South

JAMES S. CHICKOS Department of Chemistry, University Louis, Missouri 63121-4499 (U.S.A.) (Received 8 February

of

Missouri-St.

Louis, 8001 Natural

Bridge Road, St.

1988)

ABSTRACT A spectroscopic method has been developed to observe rotational spectra of molecules in the millimeter- and submillimeter-wave regions. Advantages and disadvantages of the method are discussed and compared to those of Stark-modulation and Fourier-transform spectroscopy in the centimeter-wave region. As examples of the method’s applicability, the results for cubane-d and cis and trans cyclobutane-1,2-d, are presented. The transitions of J= 14t13 up to 26625 are observed for cubane-d, yielding the rotational and centrifugal distortion constants B,=3220.720 08 (85) and DJ,=O.OOO 180 99 (93) MHz; values in parentheses represent three standard deviations. Trans cyclobutane-1,2-d, is found to exist in an equatorial-equatorial and an axial-axial conformation, with only the b-dipole component being nonvanishing, as expected from previous results on the structure of cyclobutane. The observed spectra lead to the rotational constantsA= 794.3831(58),B=9 758.3272(56),andC=5782.6540(73)andA=9738.242(15), B = 9 693.452 (14)) and C= 6 048.564 (14) MHz, for the two forms, respectively; values in parentheses again represent three standard deviations. Cis cyclobutane-1,2-d, is expected to exist in two equivalent forms, axial-equatorial and equatorial-axial. The observed spectrum exhibits the effect of puckering. Preliminary values of the rotational constants are A =9 938.757 (47), B =9 577.008(47), and C=5 913.212(41) MHz. *Dedicated to the memory of Professor Walter Gordy.

0022-2860/88/$03.50

0 1988 Elsevier Science Publishers

B.V.

236 INTRODUCTION

It was as early as 1970 when the late Professor Walter Gordy and his coworkers [ 1 ] observed the J= 67e66 transition of carbonyl sulfide at $13 353.706 MHz. This was really a remarkable achievement, because generation, transmission, and detection of submillimeter-waves were all extremely difficult to realize at that time. They employed a special technique that relied on the nonlinear action of a tungsten whisker and silicon crystal point contact diode. Their technique involved some unique procedures that were difficult to reproduce in other laboratories. In fact, only a limited number of groups succeeded in generating such high frequency microwave radiation, and the majority of microwave spectrometers have been confined to the region lower than about 40 GHz. However, recent progress in designing and fabricating frequency multipliers makes it rather routine to work in frequency regions up to 400 GHz. We have recently constructed a microwave spectrometer with such frequency multipliers [ 21. The extension to the high frequency regions without causing any serious increase of conversion loss, has brought about a dramatic improvement in sensitivity. The present paper describes the performance of our spectrometer, paying special attention to its advantages and disadvantages in comparison to conventional Stark-modulation spectrometers and Fouriertransform spectrometers in the centimeter-wave region. MILLIMETER-

AND SUBMILLIMETER-WAVE

SPECTROSCOPY

The difficulties encountered in performing spectroscopy in millimeterand submillimeter-wave (mm- and submm-wave) regions lie primarily in generation, transmission, and detection of high-frequency microwave radiation. Recently high-efficiency frequency doublers, triplers, and quadruplers have become commercially available; for input in the range from 80 to 100 GHz, they provide output up to 400 GHz or so, with power sufficient for absorption spectroscopy. It is now routine to obtain a microwave source down to 0.75 mm. Short-wave radiation behaves similarly to the light, as it should do; it is fairly easy to transmit mm- and submm-waves through the space. It is therefore natural to choose a glass tube of an appropriate diameter as the absorption cell. It is not difficult to pass more than 50% of the input power through a freespace cell as long as 3 m, if both ends of the cell are shielded with appropriate lenses. Teflon is suitable for making such lenses. Unfortunately, it is not easy to apply a large electric field to such a cell. On the other hand, the cell may be subjected to a magnetic field of up to a few tenths of a Tesla without too much difficulty. It can also be cooled down to liquid nitrogen temperatures or warmed up to 1000 K or so, provided that a suitable material such as quartz tube is selected. A cylindrical glass tube is particularly suitable for studying chemically active molecules because the glass wall is relatively inactive and because

237

the sample, including reaction products, can be pumped out quickly [ 31. We have found that an InSb detector designed for far-infrared detection works for mm- and submm-waves as well; it may be used down to 40 or 30 GHz. This type of detector, although requiring cooling down to liquid helium temperature, is extremely easy to use; there are almost no components that require fine adjustments. The main advantage of mm- and submm-wave spectroscopy over cm-wave spectroscopy is the higher sensitivity. In the case of a diatomic molecule, the peak absorption coefficient (x,,, is proportional to a ,,ccVo3exp[-((h/4BkT)Vo

2],

where v. denotes the transition frequency and B the rotational absorption coefficient thus peaks at v. which is given by

[GB(kT/h)]* (uo)pealc=

constant.

The

(2)

Gordy and Cook [4] showed that am,, of carbon monoxide is largest at ;1 (wavelength of microwave) equal to 0.20 mm, i.e. ( vO)peak= 1500 GHz. Equation (2) shows that ( vO)peakis 474 GHz for a molecule with B ten times smaller than that of CO. It must be admitted that ( vO)peakwill be smaller for polyatomic molecules than for diatomic molecules; still, it is quite obvious that one can increase the effective sensitivity by working in the short wavelength region. Introduction of high-efficiency multipliers and a high-sensitivity InSb detector allows us to readily search for spectra over wide frequency regions. Various difficulties in operating the spectrometer and in data acquisition have been eliminated to a great extent by interfacing the spectrometer to a microcomputer. It is rather difficult to express the sensitivity of our spectrometer in a quantitative way. Our experience with the spectra of carbonyl sulfide has shown that roughly lo6 molecules crnm3 are needed to observe rotational spectra at 300 to 400 GHz. The high sensitivity thus achieved has permitted us to develop a time-resolved or kinetic method of microwave spectroscopy [ 51. The time resolution is about one microsecond (IUS), and is limited mainly by the signal-detecting system. We have applied this method to a few photochemical reactions induced by an excimer laser or by a mercury lamp with Hg sensitization, in order to elucidate the detailed mechanisms involved [ 5-81. Applications of this sort would be quite difficult or even impossible with cm-wave spectroscopy, simply because the sensitivity is too low. Fourier-transform spectroscopy may provide some time-dependent information. A Flygare-type spectrometer [9], for example, may give T,, i.e. the dephasing time, which corresponds roughly to the collision time. Additional time-dependent processes, if any, may contribute to the dampling oscillation of the absorption signal. However, it would not be easy to achieve the same time-resolution as with high-sensitivity mm- and submm-wave spectroscopy. Fourier-transform spectroscopy will be difficult to

238

extend into the high-frequency regions; microwave components such as switches are expensive or difficult to obtain. On the other hand, mm- and submm-wave spectroscopy suffers from several disadvantages, Stark effects are rather difficult, although not completely impossible, to measure [lo]. This is because the beam size in the cell is of the order of 3 to 4 cm in diameter, making it necessary to hold the Stark plates at a spacing well exceeding the beam size. As is well known, the Stark effect not only yields the dipole moment of the molecule, but also provides a clue to assignments. This is very unfortunate, because mm- and submm-wave spectroscopy detects normally only high-J transitions, which, in the absence of information from Stark effects, are often very difficult to assign. We have had to rely on the spectral pattern, as in the case of infrared spectroscopy for our assignments. However, the higher sensitivity and the wider frequency coverage of mm- and submm-wave spectroscopy make the assignment much easier than one might think based on experience with cm-wave spectroscopy. We have applied mm- and submm-wave spectroscopy for the structure elucidation of a number of transient molecules and molecular ions, as previously reported [3,11]. In view of the versatility of the method, other groups of molecules may be investigated as well, and the present paper describes the recent results of studies on two nonpolar molecules made slightly polar by isotopic substitution [ 121. CUBANE-d

The first molecule investigated was cubane-d. Cubane, i.e. pentacyclo [4.2.0.02,50.3,80.4,7]octane, is an interesting molecule because of its high symmetry, Oh. It was synthesized for the first time by Eaton and Cole [ 131 in 1964 and was immediately subjected to an X-ray study by Fleischer [ 141 to confirm octahedral symmetry. This study yielded two sets of bond distances: r(C-C)=1.553(3) and 1.549(3) A and r(C-H)=1.11(5) and l.Ol(5) A and three sets of bond angles: e(CCC) =89.3(3)“, 90.5(3)“, and 89.6(3)’ and B(CCH)=123(2)“, 127(2)“, and 126(a)“. The last angle is 125.3” in 0, symmetry. Della et al. [ 151 initiated spectroscopic studies of cubane in 1979; they observed and assigned the infrared and Raman spectra not only of the normal species, but also of the d, (C,,)) sym-d, (D3d), sym-d, (D3J, and da (0,) species, in solutions and in the solid state. Cole et al. [ 161 extended the infrared observation to the gas phase, using a Nicolet 7199 Fourier transform spectrom; eter with a resolution of 0.06 cm-l. They analyzed the rotational structure for the three bands of the normal species, Y,, at 852, vli at 1235, and vi0 at 2990 cm-l , to evaluate the rotational and centrifugal distortion constants. By using a sum rule for Coriolis coupling constants, they derived the rotational constant to be 0.1165 cm-l, which differed from the B value calculated from the X-ray

239

structure by +0.0009 cm-‘. The Raman spectra were also observed in the condensed phase. Pine et al. [ 171 applied infrared diode laser spectroscopy to the Y,, and v12 bands to derive the ground-state B,, constant and these were found to be 0.11183 (25) and 0.112 38 (16) cm-l, respectively. A weighted mean of these two values, B,, =0.1122 (2) cm-l, was then employed to calculate two Coriolis coupling constants, & = 0.224 (4) and &= - 0.200 (3)) which they compared with the values derived from a force field calculation, 0.224 and -0.201, respectively. By assuming r(C-H) to be 1.11 (2) A, they derived r(C-C) = 1.565 (4) A. Almenningen et al. [ 181 investigated the structure of cubane by electron diffraction and derived the parameters r(C-C) =1.575(l) A and r (C-H) = 1.110 (6) A. Theoretical calculations have also been carried out by several groups to estimate the structure parameters [ 19-221. It is interesting t,” note that values for r(C-H) are scattered in a range from 1.073 A to k.081 A, which is narrower than the range obtained for r (C-C ), 1.570 to 1.585 A. Experimental

details and analysis of the observed spectrum

A sample of cubane-d was synthesized at Flinders University according to the procedure reported by Della and Patney [ 231. The rotational spectrum was observed by a mm-wave spectrometer set up at the Institute for Molecular Science. A number of impurity lines interfered with the observation of cubaned lines. Most impurities seemed to have been adsorbed on the walls of the absorption cell and of peripherals. An appropriate molecular model predicted successive J+ 1 t J transitions to appear every 6737 MHz. The observation was carried out at - 20’ C, but most experiments were subsequently conducted at room temperature. The spectrum was searched from 140 GHz to 150.1 GHz. After several trials a line at 148 144.33 MHz was assigned to the J=23t22 transition. This assignment predicted the J=22t21 and 24t23 transitions to appear at 141 703 and 154 585 MHz, respectively, which were in turn observed at 141 704 and 154 585 MHz, respectively. Finally we observed 13 rotational transitions of J= 14t 13 up to 26~25, as listed in Table 1. The J= 14~13 transition is shown in Fig. la. The lineshape is symmetric for this line within experimental error, but becomes asymmetric as Jincreases; an example, the 5~24-23 transition, is shown in Fig. lb. These traces were obtained by modulating the klystron frequency with two square waves of 50 kHz, out of phase with each other by n/2, and by detecting the absorption signals with a lock-in amplifier operated at 100 kHz. It should be noted that the signal-to-noise ratio significantly improves in going from 90 GHz to 155 GHz. The asymmetry in lineshape observed for the J=24+23 transition is caused by unresolved K structure. Although no attempt was made to simulate the observed lineshape, it clearly indicated that the D, constant was negative. We tried to resolve the M structure of high-J transitions, but individual

240 TABLE

1

Observed transitions

of cubane-d

(in MHz)”

J’CJ”

Observedb

Observed - calculated

14+-13 15t14 16~15 17t16 18t17 19+-N 2oc19 21+-20 22-21 23t22 24+23 25e24 26-25

90 178.171(14) 96 619.157(34) 103 060.074(11) 109 500.929(11) 115 941.692(19) 122 382.410(14) 128 823.015 (27) 135 263.542(54) 141703.994( 19) 148 144.322(21) 154 584.540(U) 161024.695 (37) 167 464.756 (26)

- 0.005 - 0.002 - 0.003 0.003 - 0.009 0.013 0.003 0.002 0.019 0.006 -0.016 0.002 0.035

BO

3220.720 08 (85)’ 0.000 180 99(93)’

D JO

“Observed frequencies were weighted in proportion to the inverse squares of the measurement errors, and a,, was 0.0156 MHz. bValues in parentheses denote three standard deviations of the frequency measurements and apply to the last digits of the frequencies. ‘Values in parentheses denote three standard deviations and apply to the last digits of the constants.

(a) +v so 178

(b)

90 179

154 584

154585

(MHz)

(MHz)

Fig. 1. (a) J=14+13

and (b) J=24+23

transitions

of cubane-d.

components were too weak to record with a good signal-to-noise peak frequencies were simply fitted to the expression

v(J+ltJ)=2B,(J+1)-405,(J+1)3

ratio. The

(3)

241

to derive the B0 and DJO constants, which are included in the bottom of Table 1. A separate fit was made by including the &, term, but no substantial improvement was obtained. Discussion Because the cubane molecule is rigid, the correction to convert the B,, constant to an average rotational constant B, will be small, perhaps 1 or 2 MHz. Therefore, the observed& value was employed to get some information on the molecular structure. The moment of inertia Ib’ of cubane-d is given by I,‘=&

+ [3M(mn

-mu)/4{M+

where & denotes the moment

(mD +mH)}] of inertia

(R+2r/3t)2

of the parent molecule,

(4) C,Hs:

Ib =4mcRZ+4mH(R+2r/3f)2

(5) R and r stand for the C-C and C-H distances, respectively, and M, mc, mH, and mn for the masses of the entire parent molecule, the carbon, hydrogen, and deuterium atoms, respectively. The observed &, or I,,’ was used to derive a relation between R and r, which is indicated by the solid line designated as MW in Fig. 2. The &,, or & value reported by Pine et al. [ 171 is plotted in a similar way, as designated by IR, with the uncertainty. The results of the Xray [ 141 and the electron diffraction [ 181 studies are also included with the respective error limits. Some of the ab initio MO structures [ 19-221 are indicated by circles with a dot at the center. It is obvious that not all the results are compatible with each other. The electron diffraction data may often be subjected to an ambiguity in scale

Fig. 2. Structure parameters of cubane-d derived using experimental and ab initio MO methods: X-ray diffraction [ 141, electron diffraction [ 181, infrared spectroscopy [ 171, microwave spectroscopy [present study], and ab initio MO calculations [ 19-221.

242

factor, whereas the rotational constant fixes the overall dimension of the molecule very precisely. Therefore, the ratio r (C-H ) /r (C-C ) was fixed to the value attained by electron diffraction [ 181 and was combined with the B,, value determined in the present study to calculate the individual bond length as follows: r (C-C) = 1.5708 A and r( C-H) = 1.097 A. The uncertainties of the two lengths are related as dr (C-H) = - 5.68 dr (C-C). The present value of DJ, 0.180 99 (93) kHz may be favorably compared with the value 0.184 kHz which Robiette [ 241 calculated from “his” force field [ 171. Robiette also obtainedDJK to be - 0.032 kHz from the same field. The splitting between the K=J” and K= 0 components is then - 1.04 MHz even for the J=26+25 transition, in qualitative agreement with the observation. We made additional measurements on some high-J transitions, J= 50-49, 51-50,52-51,58-57, and 59-58, to detect the spectra of the 13C species in natural abundance. The sensitivity was high enough, but the presence of many weak lines made it difficult to establish assignments for the 13C species. In order to obtain additional information on the molecular structure, infrared spectroscopy might be used; the 1,3-dz or 1,4-dZ species may be goodcandidates from both spectroscopic and synthetic points of view. Finally, it may be mentioned that another set of symmetric-top like transitions were observed in the cubane system: J= 53-52 at 134 782.31, J= 56-55 at 142 408.20, J=57-56 at 144 950.06, J=58-57 at 147 491.79, J=59-58 at 150 033.49, J=60-59 at 152 575.12, and J=61-60 at 155 116.76 MHz. These transition frequencies were fitted to eqn. (3)) yielding the B and DJ constants to be 1271.7861 (33) and 0.000 045 35 (48) MHz, respectively, with three standard deviations in parentheses. We have so far been unable to identify the species responsible for these lines. CIS AND TRAMS CYCLOBUTANE-1,2-D2

Cyclobutane has attracted much attention, because it is one of the simplest molecules that executes the unique intramolecular motion of puckering. A number of infrared and Raman studies have been carried out to unveil the nature of the puckering motion. Lord and Stoicheff [25] observed the rotational Raman spectrum for both C,Hs and C4D, to determine the rotational constants in the ground state, from which they calculated the r (C-C) distance to be 1.558 (3 ) A and derived a relation between r (C-H ) and 0( HCH). Apparently, no information was obtained on the puckering. Lord and Nakagawa [ 261 carried out a normal coordinate analysis and deduced the molecular symmetry to be DZd based on the signs of the Coriolis coupling constants of the E, modes. Ueda and Shimanouchi [ 271 applied the ingenious idea of observing side bands (mainly difference bands) associated with the CH, symmetric stretching band vi9 at 2878.60 cm-l to calculate the puckering energy levels in the ground state,

243

from which they derived the potential barrier V at the planar configuration and the puckering angle 8 to be 448 cm-l and 34”) respectively. Stone and Mills [28] took into account couplings among the rotation, puckering, and vibration and applied the results to the v14 band of C,H, and C*D,. The V and 0 values thus obtained for C,H, in the ground state are 503 cm-l and 35”, respectively. Miller and Capwell [ 291 observed four and six Raman bands for C,H8 and C4D8, respectively, in the gas phase and determined V to be 518 (5) and 508 (8) cm-l for C4Hs and C4D8, respectively, and 8 to be 35’ for the both species. Miller et al. [ 301 extended the analysis of Lord and Nakagawa [ 261, confirming the vibrational assignments on a much firmer basis. Malloy and Lafferty [31] took into account the dependence of the effective mass of the puckering on its coordinate and discussed isotope effects on the puckering parameters. Recently Egawa et al. [32] reinvestigated cyclobutane by electron diffraction; they obtained much improved diffraction patterns, compared with those of previous studies, which they analyzed together with the ground state rotational constant of C4Hs derived from Fourier-transform infrared spectra of the v14 and vi6 bands. In the structure analysis they took into account the coupling of the puckering with the CH, rocking and determined the 19angle to be 27.5 ( 11) O and the potential barrier V to be 510 (2) and 504 (3 ) cm-l for C,H, and C4Ds, respectively. In order to get more detailed information on the puckering in cyclobutane, we decided to apply mm- and submm-wave spectroscopy to some deuterated cyclobutanes. The present paper describes preliminary results on the 1,2-d, cis and trans species. After we achieved rotational assignments, Vogelsanger et al. [33] started to investigate the cyclobutane-d and cyclobutane-1,1-d, species by pulsed microwave Fourier transform spectroscopy. Because of the limited coverage of frequency, their results are much less accurate than ours. Experimental

details and observed spectra

Samples of cis and trans cyclobutane-1,2-d, were synthesized at the University of Missouri by the procedures described in ref. 34. The rotational spectra TRANS h@

“Y ax-eq P

e
p@

CIS ‘a”

eq-eq y$,/,D

eq-ax

6’“”

e>o

Fig. 3. Schematic diagrams of cis and tram cyclobutane-1,2-d,.

244 TABLE

2

Observed transitions

of the trans cyclobutane-1,2-d,

Transition

equatorial-equatorial

form (in MHz)

Observed

Observed-

0.0018 0.0113 0.1650 -0.1375 0.0029 0.0044

J’,

K,‘,

Kc’

J”,

K,“,

Kc”

16, 16, 16, 16, 16, 16,

14, 13,

3 3 4 4 5 5

15, 15, 15, 15, 15, 15,

11, 12, 11, 10, 9, 1%

4 4 5 5 6 6

340 670.4423 340 646.3175

1 1 2 2

16, 16, 16, 16,

15, 14, 14, 13,

2 2 3 3

341667.3187 347 843.3342 351615.9683 352 509.6955

- 0.0586 - 0.0320 0.0272 0.0289

1 0 2

17, 17, 17,

17, 17,

0 1 1

350 294.6767 353 974.7823 342 540.6277

-0.0413 - 0.0034 -0.0022

2 3 3 4 4

18, 18, 18, 18, 18,

18,

1 2 2 3 3

354 944.6445 351024.7790 352 165.2685 343 509.8670 343 461.0065

-0.0222 0.0127 -0.0222 -0.0053 0.0099

5 5 6 6 7 7

1% 19, 19, 19, 1% 19,

16,

355 008.6813 355 009.9113

-0.0188 0.0252 - 0.0052 -0.0137

20, 20, 20, 2% 20, 20,

15, 14, 13, 14, 13,

17, 17, 17,

12, 13,

1% 11,

16,

17,

17, 15, 16

18, 18,

18, 18,

18,

17,

1% 1% 1% 1% 1%

17,

16, 17,

16, 15,

20, 20, 20, 20, 20, 20,

15,

21, 5% 21, 21, 21, 21,

14, 15, 14, 13,

2% 2% 2% 22, 22, 2%

1%

23, 23, 23, 23,

1%

16, 14, 15, 14, 13,

12, 13, 13,

1% 11, 10, 11, 11, 10, 11,

16, 17,

16, 15,

16, 15, 15, 14, 13, 14,

356 672.3260

347 015.0983

12,

10 10 11 11 12 12

21, 21, 21, 21, 21, 21,

1% 11, 1% 11, 10,

9 9 10 10 11 11

12 12 13 13

2% 22, 2% 22,

11, 1% 11, 10,

11 11 12 12

13,

348 674.1843

339 028.9905

0.0151

358 563.2055

0.0194

350 580.0403

0.0177

342 598.4273

0.0046

354 150.5103 346 170.5327 338 190.6195 357 722.8357 349 743.6123

-0.0319 0.0027 -0.0103 0.0159 -0.0122

calculated”

245 TABLE

2 (continued)

Transition

Observed

J’,

Kc’,

KC’

J”,

K,“,

Kc”

23, 23,

10, 9,

14 14

2% 22,

9, 10,

13 13

24, 24, 24, 24,

8, 9, 10, 9,

16 16 15 15

23, 23, 23, 23,

9, 8, 9, 10,

15 15 14 14

25, 25, 25, 25, 25,

8, 9, 8,

17 17 18 18 19 19

24, 24, 24, 24, 24, 24,

9, 8,

16 16 17 17 18 18

20 20 21 21

25, 25, 25, 25,

22 22 23 23 24 24

26, 26, 26, 26, 26, 26,

24 24 25 25 26 26

27, 27, 27, 27, 27, 27,

5, 4, 3, 4, 3,

2% 2% 28, 2% 28, 2%

3,

2, 2, 1, 1, 0,

26 26 27 27 28 28

2% 2% 29, 2%

1, 2, 1, 0,

28 28 29 29

7,

6,

25,

7,

26, 26, 26, 26,

6, 7,

6, 5,

27,

6,

27,

5, 4, 5, 4, 3,

27, 27, 27, 27, 28,

28, 28, 28, 28, 28,

4, 5, 4, 3,

2, 3,

2% 2% 29, 2% 2% 2%

2, 0, 1,

27 27 28 28 29 29

30, 30, 30, 30,

2, 1, 0, 1,

29 29 30 30

2, 3, 1,

“Standard

deviation

7, 8, 7,

6, 7,

6, 5,

6, 5,

6, 5, 4, 3, 4,

2,

19 19 20 20 21 21 22 22 23 23 23 23 24 24 25 25

of the fit is 0.032 MHz.

Observed-calculated”

341764.2920

0.0035

345 338.1112

0.0171

353 317.1047

- 0.0046

356 890.6585

0.0072

348 911.8012

0.0248

340 932.3980

0.0028

352 485.1247

0.0154

344 505,6175

0.0186

356 057.8510

- 0.0330

348 078.0982

- 0.0029

340 097.5078

-0.0162

359 629.8953

- 0.0044

351649.6995

- 0.0045

343 668.5907

-0.0171

355 220.2078

-0.0041

347 238.4522

- 0.0064

339 255.6308

- 0.0036

358 789.4197

-0.0107

350 806.9247

0.0420

246 TABLE

3

Molecular

constants of the tram

Constant A B C 4 A JK AK 4 &

.

cyclobutane-1,2-d,

Observed

Calculated

9 794.3831 (58) 9 758.3272 (56) 5 782.6540 (73)

9 792.123 9 757.131 5 746.838

0.002 830 0.000 599 0.000 907 0.000 747 0.001887

equatorial-equatorial

form (in MHz)”

2 (67) (11) 6 (70) 8 (20) 7 (31)

“Values in parentheses denote three standard deviations and apply to the last digits of the constants. A prolate representation was used for the centrifugal terms.

were recorded by the mm- and submm-wave spectrometer at the Institute for Molecular Science. The measurements were carried out with a sample pressure of about 40 mtorr maintained at around - 60’ C. Figure 3 shows schematic diagrams of the cis and tram forms projected on a plane made by the four carbon atoms when the molecules are not puckered. As shown, at the equilibrium puckering angles, the tram form exists in two nonequivalent forms, i.e. either in an axial-axial (ax-ax) form or in an equatorialequatorial (eq-eq) form. The molecule always maintains Cz symmetry. Because the C, axis coincides with the b-axis, only b-type transitions are expected to be observed for both the ax-ax and eq-eq forms. If the dipole moment is proportional to the sum of the unit vectors located on the C-D bonds, it is 1.166 and 0.425 for eq-eq and ax-ax, respectively. Therefore, the ax-ax spectra will be weaker than the eq-eq spectra by a factor of 0.13. On the other hand, the cis form is transformed by puckering between two equivalent forms, ax-eq and eq-ax, as shown in Fig. 3. It should be noticed that the principal axes a and b are suddenly rotated by nearly + 45 ’ or - 45 ’ when the molecule is slightly puckered from the “planar” configuration. As a result, one of the “in-plane” dipole moment components changes sign upon puckering. This component will coincide approximately with the b-component. The other “in-plane” component and the “out-of-plane” component, which correspond roughly to the a- and c-components, respectively, are symmetric with respect to puckering. A rigid-rotor calculation gives the three components, ,uu,, ,LQ,,and ,u,, to be 0.86,0.38, and 1.48, where again the dipole moment is assumed to be parallel to the sum of the unit vectors on the C-D bonds. Searching for spectral lines of the tram eq-eq form was started in 300 to 400 GHz region. It was noticed that b-type transitions with dJ= + 1 and dK(K= Kc) = + 1 appeared around the frequencies given by

247 TABLE 4 Observed transitions

of the truns cyclobutane-1,2-dz

form (in MHz)

Observed

Observed-

1 2 1

348 795.7343 351351.8722 357 152.6805 341942.7923

- 0.0579 -0.0113 0.0066 -0.0097

0. 1 2 3 3

368 361 350 343 343

395.9583 712.3008 072.9357 561.2189 450.3323

0.0348 0.0182 0.0179 0.0346 - 0.0096

362 363 355 355

864.8145 016.8792 539.1217 542.7860

0.0913 0.0931 0.0225 0.0433

Transition

J’,

axial-axial

K,‘,

Kc’

J”,

K,“,

Kc”

17, 17,

0

18,

18,

18, 18, 18,

18, 17, 17,

1 0 1 2

17, 17, 17, 17,

16, 16,

19, 19, 19, 19, 19,

19, 18, 16, 16, 15,

1 2 3 4 4

1%

18,

18,

17, 17, 15,

20, 20, 20, 20,

16, 17, 15, 16,

4 4 5 5

19, 1% 1% 19,

16, 16, 15,

3 3 4 4

20, 20, 20, 20,

14, 15, 14, 13,

6 6 7 7

1% 1% 1% 19,

15, 14, 13, 14,

5 5 6 6

348 189.2220

21, 21, 21, 21, 21, 21,

13, 14, 12, 13, 12, 11,

8 8 9 9 10 10

20, 20, 20, 20, 20, 20,

14, 13, 13,

7 7 8 8 9 9

352 931.2510

-0.0156

345 599.7573

-0.0040

338 269.2665

0.0041

22, 22, 22, 22, 22, 22,

12, 13, 11, 12, 10, 11,

10 10 11 11 12 12

21, 21, 21, 21, 21, 5%

357 681.1252

0.0328

11, 11, 10,

9 9 10 10 11 11

350 351.3700

0.0218

23, 23, 23, 23, 23 23

10, 11, 10, 9, 8 8

13 13 14 14 15 15

2% 2% 2% 2%

11, 10, 9 10, 9 8

12 12 13 13 14 14

355 103.0957

0.0138

347 773.5107

- 0.0028

340 443.4628

-0.0195

24, 24, 24, 24, 24, 24,

10, 9, 8, 9, 8, 7,

15 15 16 16 17 17

23, 23, 23, 23, 23, 23,

9, 10, 9,

14 14 15 15 16 16

1% 1% 1%

22 22

16, 17,

12, 11,

12, 13,

12, 12,

8, 7, 8,

340 851.1712

343 021.6623

359 853.9470

-0.1240 -0.1595 0.0048 0.0049

-0.0129

0.0228

352 523.9577

-0.1161

345 193.5645

- 0.0047

calculated”

248 TABLE

4 (continued)

Transition J’,

K,‘,

Kc’

J”,

K,“,

Kc”

25, 25, 25, 25, 25, 25,

7, 8, 6, 7, 6, 5,

18 18 19 19 20 20

24, 24, 24, 24, 24, 24,

8,

17 17 18 18 19 19

26,

5,

6,

26, 26, 26, 26,

4, 5, 4, 3,

21 21 22 22 23 23

25, 25, 25, 25, 25, 25,

6,

26,

27, 27, 27, 27, 27, 27,

4, 5, 4, 3, 2, 3,

23 23 24 24 25 25

26, 26, 26, 26, 26, 26,

5, 4, 3, 4, 3,

27, 27, 27, 27, 27, 27,

3,

28, 28,

28,

2,

28,

3,

28, 28, 28, 2%

2, 1, 0, 1,

26 26 27 27 28 28

2% 2%

0, 1,

29 29

“Standard

deviation

7, 7,

6, 5,

6, 5, 5, 4, 3, 4,

2, 2,

1, 2,

1, 0, 1, 0,

20 20 21 21 22 22 22 22 23 23 24 24 25 25 26 26 27 27 28 28

Observed

Observed - calculated”

357 272.8372

- 0.0297

349 941.6145

- 0.0232

342 609.5110

0.0068

354 687.2913

- 0.0039

347 354.1115

0.0472

340 019.7172

0.0141

359 430.1777

0.0116

352 095.6455

0.0225

344 759.8820

0.0709

356 833.8587

0.0432

349 496.3663

0.0235

342 157.4277

0.0424

354 228.7888

-0.1482

of the fit is 0.054 MHz.

v(J,K)=(A+B)(J+1)+[2C-(A+B)](K+1/2), and that the separation between Y(J+ 1, K+2) and u(J,K) was approximately equal to 4C- (A +B), which was estimated to be about 3572 MHz using an appropriate model. Two series were readily found by a graphical plot of the observed spectral lines; the first series included three lines observed at 328 544, 332 116, and 335 686 MHz, which were assigned to J,K=26,23+-25,22, 27,25+26,24, and 28,27+27,26, respectively, and also three lines were observed for the second series at 329 379, 332 952, and 336 525 MHz assigned, respectively, to J,K=24,1&+-23,17, 25,20+24,19, and 26,22+25,21. Other series then followed, and finally 47 lines were assigned as listed in Table 2.

249

TABLE

5

Molecular constants of the trans Constant

cyclobutane-1,2-d,

Observed

Calculated

9 738.242 (15) 9 693.452 (14) 6 048.564 (14)

9 742.254 9 697.868 6 013.026

0.003 0.000 0.000 0.000 0.002

314 453 274 333 540

axial-axial

form (in MHz)”

(14) (25) (20) 8 (50) 1 (95)

“See footnote a of Table 3.

T

331.5

Fig. 4. J= 17~16 transitions

GHz

of cis cyclobutane-1,2-dz.

The values of K, are indicated.

Table 3 shows the rotational and centrifugal distortion constants derived from the observed lines by the least-squares method. The fitting was made using a prolate-rotor representation. As mentioned earlier, the ax-ax form was expected to show spectra weaker than those of the eq-eq form by a factor of 0.133, making the former quite difficult to detect. However, careful observation of the spectra revealed the presence of the ax-ax form. The nuclear spin statistical weight, 276 and 300, respectively, for the ee,oo and eo,oe rotational levels, was clearly observed for closely-spaced K doublets such as 1915,5c 18,,,d and 1914,5t 18,,,d. As shown in Table 4, the observed lines were assigned and analyzed to obtain the rotational and centrifugal distortion constants listed in Table 5. The cis form was more difficult to detect than the trans form. Impurities remaining in the absorption cell interfered with the observation of cyclobutane lines. However, most of them could be eliminated by comparing the spectrum observed for the cis sample with that for the tram sample. Then the K-structure of c-type R-branch transitions showed up clearly, as exemplified by the

250 TABLE

6

Splittings

observed for the c-type J= 17+16 transition

Transition” J’,

K,‘,

17,16 17,15 17,14 17,13 17,12 17,ll 17,lO 17,9 17,8 17,7 17,12, 17,11, 17,5 17, 14, 17,13, 17,3 17, 16, 17, 15, 17, 1 17,0

I$’

6 6 4 4 2 2

Doublet splitting J”,

K,“,

16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,

16 15 14 13 12 11 10 9 8 7 11, 10, 5 13, 12, 3 15, 14, 1 0

of cis cyclobutane-1,1-d, K-type splitting Observedb

K,”

4 4 2 2

5.2127 5.3860 0.00 7.9470 10.4932 0.00 4.6358 9.0798 0.00 2.1986

Calculated

0.00 oioo 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.3980 0.7682 0.9890 1.2328 1.6144 2.1474 2.8659 3.8239 6 6

(in MHz)

0.05 1.39 27.3379 322.3478

27.35 324.34

1744.5071

1744.41

3290.9498

3290.90

3161.2290

3161.23

2522.0036

2522.13

“K-type doubling was not resolved for K=16 to 8; J, Kc are indicated. The K=7, 5, 3, and 1 transitions appeared as doublets, and the splitting was primarily ascribed to K-splitting except for K= 7. bSeparation between the two doublets for the even-K transitions.

J= 17-16 transition reproduced in Fig. 4. As shown, the K( =K,) = 16 and 15 lines did not show any splittings, whereas the K= 14 line was observed as a barely resolved doublet. The splitting steadily increased as K decreased. For K=7, the K-type splitting becomes of measurable magnitude, i.e. 1.39 MHz, which may be compared with the observed splitting 3.82 MHz. The K= 6 transition was observed as a quartet, or a pair of doublets; the doublet splitting was 5.24 and 5.39 MHz and the separation between the centers of the doublets was 27.34 MHz, in good agreement with the calculated K-type splitting 27.35 MHz. The K = 5,3, and 1 transitions behaved similarly to the K = 7 transitions, namely they were doublets. The doublet splitting agreed with the calculated K-type splitting for K= 3 and 1, but differed from the latter by 2 MHz for K= 5. The even K transitions were similar to the K= 6 transition; the separation between the two doublets agreed with the calculated K-type splitting for K=4 and 2. All the splittings observed are listed in Table 6. The K components of the J= 18t17 and 19t18 transitions also exhibited similar splittings.

251 TABLE

7

Observed transitions

of cis cyclobutane-1,2-d,

(in MHz)

Transition

J',

_ K,',

“c-type” 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18,

Observed

1, 2, 2, 3, 3, 4, 4, 5, 5,

6, ‘3, 7, 7,

8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15,

16, 16, 17, 17,

2,

18,

3, 3, 4, 4, 5, 5,

18, 18,

6, 6,

18,

7,

18, 18, 18,

Kc'

J",

K,", Kc"

16 16 15 15 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0

16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 1‘5, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,

0, 1, 1, 2, 2,

16 16 15 15 14 14 13 13 12 12

17, 17, 17, 17, 17, 17, 17, 17, 17, 17,

3, 3, 4, 4, 5, 5,

‘3, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11,

12, 12, 13, 13, 14, 14, 15, 15,

16, 16, 1, 2, 2, 3, 3, 4, 4, 5, 5,

6,

16 16 15 15 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 16 16 15 15 14 14 13 13 12 12

331570.9248

Observed-

0.0178

1

331553.4910

I

331533.9585

0.0010

I-

331511.4531

0.0061

i

331484.7887

- 0.0002

1

331452.2114

- 0.0102

1

331411.0255

0.0008

1

331356.7945

I

331281.9793 331170.6418 331174.4657 330 984.9058 331012.2437 330 520.7642 330 843.1120 329 293.3949 331037.9020 328 890.5542 332 181.5040 331069.9439 334 231.1729 334 081.0932 336 603.0968 336 597.4930

-0.0131

- 0.0044 - 0.0055 0.0063 -0.0413 - 1.2081 1.2211 0.0012 - 0.0058 0.9708 - 1.0240 - 0.0539 0.0406 -0.0143 0.0440 0.0263 0.0270 0.0559 -0.0748 0.0080

I

351052.6867

0.0148

t

351032.7903

- 0.0014

1

351010.3114

-0.0035

1

350 984.2623

- 0.0036

350 953.2223

-0.0135

calculated

252 TABLE

7 (continued)

Transition

J’, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 1% 1% 1% 1% 19, 1% 19, 1% 19, 1% 1% 19, 19, 1% 19, 19, 19, 1% 1%

K,‘,

Kc’

J”,

7,

11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0

17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17,

18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 11 10 10 9 9

18, 18, 18, 18, 18, 18, 18, 18,

8, 8,

9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15,

16, 16, 17, 17,

18, 18,

1, 2, 2, 3, 3, 4, 4, 5, 5,

6, 6, 7, 7,

8, 8,

9, 9, 10, 10, 11,

1%

18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,

6, 7, 7,

8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15,

16, 16, 17, 17, 0, 1, 1,

2, 2, 3, 3, 4, 4, 5, 5,

6, 6, 7, 7,

8, 8, 9, 9, 10,

11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 11 10 10 9 9

Observed

Observed-calculated”

350 915.1218

- 0.0030

350 866.6886

0.0044

350 581.1252 350 585.4692 350 347.9763 350 398.9095 349 729.6302 350 242.2327 348 374.0153 350 572.3113 348 421.6818 351916.5822 351025.7151 354 071.7439 353 972.4747 356 459.3698 356 456.2429

- 0.0196 - 0.0229 0.0445 - 0.0734 - 0.6815 0.6678 - 0.0098 0.0029 0.4043 - 0.4342 - 0.0488 0.0469 0.0427 0.0602 0.0700 0.0245 0.0477 -0.1803 0.0921

370 569.5582

0.0195

370 550.9285

0.0120

370 530.6025

0.0041

350 802.6216 350 713.8872

370 507.9838

-0.0071

370 482.2714

- 0.0054

370 452.3013

- 0.0048

370 416.4066

- 0.0093

370 372.0996

- 0.0253

370 315.5771 370 240.5110

- 0.0066 - 0.0068 -0.0074 -0.0162

253 TABLE

7 (continued) Observed

Transition

Observed-calculated”

J’,

IL’,

Kc’

J”,

K,“,

Kc”

19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19,

r1, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19,

8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0

18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,

10, 11, 11, 1% 12,

370 136.0342

18, 18,

8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0

“a-type” 20, 13, 20, 14,

7 7

1% 19,

13, 14,

6 6

340 707.712b

21, 21, 21, 21,

12, 13, 13, 14,

9 9 8 8

20, 20, 2% 20,

12, 13, 13, 14,

8 8 7 7

344 461.6703

22, 22, 22, 22, 22, 22,

10, 11, 11, 12, 12, 13,

12 12 11 11 10 10

21, 21, 21, 21, 21, 21,

340 765.9455

13,

11 11 10 10 9 9

23, 23, 23, 23,

9, 10, 10, 11,

14 14 13 13

22, 22, 2% 22,

9, 10, 10, 11,

13 13 12 12

344 875.8674

-0.0126

352 568.2738

-0.0220

24, 24, 24, 24, 24, 24,

7, 8, 8, 9, 9, 10,

17 17 16 16 15 15

23, 23, 23, 23, 23, 23,

7,

8, 8, 9, 9, 10,

16 16 15 15 14 14

341319.9385

0.0063

349 000.2543

0.0002

356 683.6085

- 0.0047

25, 25,

6, 7,

19 19

24, 24,

7,

18 18

345 452.7794

0.0074

13, 13, 14, 14, 15, 15,

16, 16, 17, 17,

10, 11, 11,

12, 1%

6,

369 979.1230 369 983.4223 369 683.9837 369 774.7538 368 874.3790 369 649.2797 367 495.9445 370 140.3040 368 063.0983 371678.0352 370 995.1987 373 916.7225 373 852.1943 376 313.1410 376 312.4456

0.1304 -0.1448 0.8901 -0.9319 -0.0016 - 0.0048 0.0843 -0.1626 -0.0541 0.0533 0.0353 0.0778 0.0854 0.0440 0.0733 - 0.6898 0.6334

- 0.4952 0.4946

352 316.1785b

348 479.1255 356 220.3258

- 0.0069 - 0.0068 - 0.0007 0.0017 - 0.0588 0.0232

254 TABLE 7 (continued) Transition

Observed

Observed-calculated”

-0.0041

J’,

K,‘,

Kc’

CT”, K,“,

Kc”

25, 25,

7; 8,

18 18

24, 24,

7, 8,

17 17

353130.6020

26, 26, 26, 26, 26, 26,

4, 5, 5, 6, 6, 7,

22 22 21 21 20 20

25, 25, 25, 25, 25, 25,

4, 5, 5, 6, 6, 7,

21 21 20 20 19 19

341909.4853

0.0115

349 586.4094

0.0082

27, 27, 27, 27,

3, 4, 4, 5,

24 24 23 23

26, 26, 26, 26,

3, 4, 4, 5,

23 23 22 22

346042.4399

0.0108

353719.5849

0.0065

28, 2% 28, 2% 28, 28,

1, 2, 2, 3, 3, 4,

27 27 26 26 25 25

27, 27, 27, 27, 27, 27,

1, 2, 2, 3, 3, 4,

26 26 25 25 24 24

342495.0118

0.0055

350173.7881

0.0155

357851.5454

0.0031

2% 2% 2% 29,

0, 1, 1, 2,

29 29 28 28

28, 2% 28, 28,

0, 1, 1, 2,

28 28 27 27

346623.1932

30, 30,

0, 1,

30 30

2% 2%

0, 1,

29 29

358429.9725

357263.2085

354303.0819

-0.0004

-0.0112 0.0039 -0.0220

“Standard deviation of the fit is 0.257 MHz. bNot included in the fit.

The transitions which showed splittings in addition to K-type splittings were included in the least-squares fit by assigning the average frequencies of the doublets to their frequencies. The result of this fit was then employed to predict transitions which were induced by the second symmetric component of the dipole moment, i.e. the “a-type” component. Some twenty-four transitions were identified by a graphical method. All of these transitions except two consisted of unresolved K-type doubling components. For transitions for which the Ktype doubling was resolved, such as 2113,8~2013,7 and 2114,8~2014,7, the average frequencies agreed approximately with those predicted by the least-squares result on “c-type” transitions, but the splittings showed sizable discrepancies from the calculated values. The assigned “u-type” lines were about 0.23 times as intense as the “c-type” lines, to be compared with the square 0.34 of the ,LLJ

255 TABLE

8

Molecular

constants of cis cyclobutane-1,2-dz

Constant

observed

Calculated

A B C

9938.757 (47) 9577.008 (47) 5913.212 (41)

9942.401 9574.855 5877.520

.

0.003 -0.003 0.005 0.000 0.000

4 AJK AK 4J SK

(in MHz)”

294 (56) 02 (21) 56 (12) 707 (23) 823 (36)

“See footnote a of Table 3.

,u~ratio, as mentioned earlier. A search was also made for “b-type” transitions, i.e. transitions between symmetric and antisymmetric levels, but no definite assignments have been obtained. All the assigned transitions are listed in Table 7 and Table 8 gives molecular constants derived by applying a conventional asymmetric-top analysis to the observed spectra. Discussion The trans form always maintains C, symmetry during the puckering motion, and the C, axis coincides with the b axis. Therefore, the rotational and rotational-puckering transitions are induced by the following dipole-moment matrix elements: < eq-eq,R

I rub @Zb

I w-e@

> =


I rub

I eq-eq)


I %b

I R’

> 7

(ax-ax,RI~Ub~ZbIax-ax,R’)=(ax-axI~ubIax-ax)(RI~ZbJR’),

(w-e@ I pb

%b

I ax-=@ > = (w-w I iub

I ax-ax

(6a)

(6b) > CR

I @Zb IR’ >,

(6~)

where dizb denotes a direction cosine and R and R’ stand for rotational states. The matrix element (eq-eq I ,&, I ax-ax), that determines the strength of the rotational-puckering transition, may not be much smaller than the pure rotational counterparts, (eq-eq I ,&, I eq-eq) and (ax-ax I,& I ax-ax), because the dipole moment depends strongly on the puckering coordinate. We have searched for rotational-puckering transitions of the tram form, but without success. This failure is probably ascribed to poor overlap of the eq-eq and ax-ax wavefunctions. As shown in Tables 2 and 4, the rotational spectra of both the eq-eq and ax-ax forms behave normally; no indication of perturbations which could be ascribed to resonances caused by puckering were detected. There were, however, a few transitions for which the fit was somewhat worse than the experi-

mental errors; 20,6+19,5, 24,16+23,15, and 29,29+28,28 of the ax-ax form are such examples. The rotational energy levels of the cis form are likely to depend critically on puckering. As mentioned earlier (see Fig. 3), when the molecule is slightly puckered from a “planar” configuration shown at the center, the a and b principal axes suddenly rotate by about + 45’) resulting in a large internal angular momentum. The A and B rotational constants are nearly equal at the “planar” configuration, but increase and decrease, respectively, as the molecule puckers. It is therefore more appropriate to require the angular momentum induced about the “out-of-plane” axis, which nearly coincides with the c axis, to vanish, rather than to use the principal axis system. There are two “in-plane” axes, one of which, together with the “out-of-plane” axis, defines the symmetry plane, and the other of which is thus perpendicular to the symmetry plane. The former and the latter are close to the a- and b-axes, respectively, but not exactly. They are referred to as x: and y, whereas the “out-of-plane” axis is called z. The asymmetry of the molecule is then divided into two parts: [ (B, B,,)/2] (J, ‘- Jy “) and (R,/2) (J,J, + J,J,.). The former term (referred to as the dB term) connects puckering states of the same symmetry, whereas the latter term called the R term has matrix elements only between puckering states of different symmetry. As a result, the [ ] Fz= + 1) & ] k= - 1) ] /2 i levels of the symmetric state will mix with the [ ] k= + 1) f ] k= - 1) ] /2 t levels of the antisymmetric state to a considerable extent. This fact will make the structure of the K= odd matrices quite different from that of the K= even matrices, and may account for the absence and presence of additional splittings observed for K= odd and K= even transitions, respectively. The observed rotational constants are compared in Tables 3,5, and 8 with those calculated from an assumed set of structure parameters, that are taken from ref. 32, i.e., r (C-C) = 1.552A, r (C-H) = 1.093& 13(HCH) = 106.4’, the dihedral angle between two C3 planes = 27.9 ‘, and the tilt angle of CH, = 6.2 O. These structure parameters result in a B constant for C4Hs of 10 673.97 MHz, which is (l/O.999 366) times the observed value 10 667.2 (27) MHz [ 321. The calculated rotational constants were thus scaled by multiplying by 0.999 366. The agreement between the observed and calculated values are satisfactory for the A and B constants; the discrepancies are within 5 MHz. In contrast with these, the discrepancies in the calculated C constants are an order of magnitude larger; the deviation (talc - obs) is - 35.816, - 35.538, and - 35.692 MHz for trans eq-eq, tram ax-ax, and cis, respectively. These data suggest that the structure parameters mentioned above need to be revised. In this respect, it should be noted that no C constants have been determined spectroscopically in the past. However, attention should also be paid to the fact that the C constant is more sensitive to the puckering coordinate than the A andB constants by a factor of 1.6 to 5.9.

257 CONCLUSION

The present paper demonstrates the potential of mm- and submm-wave spectroscopy by reporting results obtained for two systems, i.e. two non-polar molecules made slightly polar by isotopic substitution. Although these molecules have very small dipole moments and thus give very weak rotational spectra, the present method is sensitive enough to detect such weak transitions. The sensitivity of this method exceeds that of Fourier-transform spectroscopy in the cm-wave region. Because of their simple structure and ease of operation, mm- and submm-wave spectrometers can be applied to many problems including structural studies of free radicals and molecular ions and studies of chemical reaction mechanisms. The method may also be combined with spectroscopic methods in other wavelength regions. An example of the combination of this technique with a pulsed dye laser was recently reported [35]. Sub-Doppler information can be obtained by this technique. ACKNOWLEDGMENT

One of the authors (E.H.) thanks Alan G. Robiette for supplying him with the calculated values of DJ and DJKof cubane-d and for suggesting a way to estimate the structure of cubane. Calculations in the present study were carried out at the Computer Center of the Institute for Molecular Science. Partial support from the National Science Foundation (CHE-84-05386 to JSC ) is also greatly acknowledged.

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