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Microwave investigation and the ring puckering potential function of 3-methylthietan
JOURNAL OF MOLECULAR SPECTROSCOPY
127,450-463 (1988)
Microwave Investigation and the Ring Puckering Potential Function of 3-Methylthietan W. CAMINATI,*~-~$ A. C. FANTONI,*+~ R. MEYER,* R. A. SHAW,~ T. L. SMITHSON,~’AND H. WIESER~I *LXpartimento di Chimica Fisica ed Inorganica dell’ Universiia ‘, Kale Risorgimento 4, 40126 Bologna, Italy; tlstituto di Spettroscopia Molecolare de1 C.N.R.. Via de’ Castagnoli I, 40136 Bologna. Italy; $Laboratoriumfir Physikalische Chemie, Eidgeniissische Technische Hochschule Universitiitsstrasse 22, CH-8092 Zurich. Switzerland; $Departmento de Fisica, Universidad National de La Plats, C.C. 67, 1900 La Plata, Republic ofArgentina; YDepartment of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N IN4; and ‘IDREV, 2459 Blvd. Pie XI Nerd, C.P. 8800, Courcellette, Quebec, Canada GOA IRO
Themicrowave spectrum of 3-methylthietan wasinvestigated in the frequency range 26.5-40 GHz. The rotational spectra were measured for the ground state, five puckering states (including the lowest state of the second conformer), and two methyl torsion excited states. The conformer with the methyl group in the equatorial orientation (the ground state, up = 0) is more stable than the axial counterpart (u,, = 1) by 100(17) cm-’ (1.2(2) k.J/mol). The electric dipole moment was determined for both conformers by measuring the Stark effect on several transitions. A V, barrier of 1470(30) cm-’ (17.6(4) kJ/mol) was obtained for the internal rotation of the axial methyl group from the A-E doubling of several rotational transitions in the first torsional excited state. Earlier far-infrared assignments were revised on the basis of microwave intensity measurements. The flexible model approach was used to reproduce the spacings between puckering levels simultaneously with the variation of the rotational constants with puckering excitation, allowing some structural relaxation accompanying the ring deformation. Comparisons are made with the results obtained when an asymmetric one-dimensional puckering Hamiltonian is used. Q 1988 AcademicPm% Inc.
INTRODUCTION
The ring puckering vibration of 3-methylthietan has been investigated recently by far-infrared Fourier transform spectroscopy (I). A barrier to inversion similar to that of thietan (2) has been obtained from the spacings of the vibrational levels. The existence of two conformers as shown in Fig. 1 has been inferred, but it has not been possible to predict which of them was the more stable. In order to determine the conformational preference, confirm the potential function, and investigate the structural relaxation related to the ring motion, we decided to analyze the rotational spectrum which, in addition to the rotation constants in the ground state, would supply also their variations in the puckering excited states. Our method of choice was the flexible model (3) with which it has been possible to obtain the related information for problems with two asymmetric minima in the potential surface, as, for example, in the case of lactonitrile (4). We further hoped to investigate the internal rotation of the methyl group which, as a result of the splitting of the A-E torsional levels when the V, barrier has suitable 0022-2852/88 $3.00 copyrightQ 1988 by Aademic
Rc.s, Inc. All rightsof reprodunion in any form -ed.
450
MICROWAVE
INVESTIGATION
OF 3-METHYLTHIETAN
451
Jig__&i& Axial
Equotoriol
s
RG. 1. Conformations of 3-methylthietan, indicating also the angles (Yand 8 subject to structural relaxation.
magnitude, should lead to a doubling of the rotational transitions (5). In favorable cases when using the flexible model, the A-E doubling measured for the vibrational satellites belonging to motions other than the methyl torsion has been useful for obtaining information about the coupling between the two vibrations (6-10). EXPERIMENTAL
DETAILS
The compound was synthesized in the same way as described previously (I). The microwave spectra were recorded in the frequency range 26.5-40 GHz with a computer-controlled spectrometer consisting mainly of Hewlett-Packard components (I I). The frequency measurements are believed to be accurate to better than 0.1 MHz. The temperature of the cell was kept constant at about -30°C. The radiofrequencymicrowave double-resonance technique (rfmwdr) (12) was used for assigning the first transitions. Intensity measurements were made following the recommendations of Esbitt and Wilson (13). New far-infrared assignments were made from spectra that were recorded previously (I) and stored on computer discs. RESULTS AND DISCUSSION
Assignment ctfthe Microwuve Spectrum The structure of the parent thietan molecule, as obtained by electron diffraction (14), was used for the first trial calculation of the rotational transitions of both the axial and the equatorial conformers of the 3-methyl derivative, taking advantage also of the positions of the two potential minima of thietan evaluated previously (15). Calculated Ray’s asymmetry parameters were in the range -0.78 to -0.84 for both conformations, suggesting that it should be possible to observe ,uaR-type bands. Indeed, such bands were found for the axial and equatorial conformers and for their vibrational satellites in the low-resolution spectra. By pumping the 431-432, 440-44,, 532-533, 54,&, 633-634, and 642-643 doublets at radiofrequencies in the range 2-120 MHz, the first transitions that were assigned were the K doublets 53-43, 54-44, 63-53, and 6454 for the axial and 63-53, 73-63, and 74-64 for the equatorial structure. Other transitions were then measured with the conventional Stark modulation technique. Several putQtype transitions were located for the axial conformer, whereas none could be found for the equatorial conformer due to its lower pLcvalue (see the section concerning the dipole moments below). A number of rotational transitions were assigned for several additional puckering excited states, namely for up = 2 to 4 and 6, u, the puckering
452
CAMINATI ET AL.
quantum number (where D, = 0 and 1 correspond to the equatorial ground state and the lowest axial state, respectively), as well as for the first excited state of the methyl torsion in both conformations. The splitting expected as a result of the A-E doubling was observed for some jamQ-type transitions in the first torsional excited state of only the axial methyl group. The measured line frequencies are listed in Tables I and II, grouped into “equatorial” (up = 0, 2, 4, and 6) and “axial” (up = 1 and 3) satellites, respectively. The transition frequencies were fitted separately for each vibrational state with Watson’s Hamiltonian in the A reduction (16). Strong interactions between the puckering states give rise to unusually large values for the centrifugal distortion constants, whereas for the first methyl torsion excited states their values are very close to those of their corresponding states without torsional excitation. The best-fitting rotational and quartic centrifugal distortion constants are listed in Table III. Dipole Moments The displacements of some Stark lobes have been measured as a function of the applied electric field for several transitions. All lobes showed a second-order Stark effect. The cell was calibrated with the 3 * 2 line of OCS (p = 0.71521 D (17)). The TABLE I Measured Line Frequencies (in MHz) of the “Equatorial” Satellites of 3-Methylthietan J'(K;,K;)
+ J"(K;,K;)
6(0. 6(1, 611.
6) 6) 51 -
5(0, 5(1, 5(1.
51 5) 41
6(2, 6(3;
5) 4) 4) -
5i2; 5(2, 5(3,
4j 31 3)
6(3, 6(4. 6i4; 6(5, 7(0, 7(1, 7(1, 7(2, 7(2, 7(3, 7(3, 7(4, 7(4, 7(5. 7(6,
31 31 Pj 2) 7) 7) 6) 6) 5) 5) 41 4) 3) 3) 2)
5(3, 5(4. 5i4; 5(5, 6(0, 60, 6(1, 6(2, 6(2, 6(3, 6(3, 6(4. 6(4. 6(5, 6(6,
2) 2) li 1) 6) 6) 51 5) 4) 4) 3) 3) 2) 2) 1)
6(2,
-
ll(l,lO)12(1,11)13(1,12)15t2.13)16(2,14)19C3.16)20(3;17)24C4.20)25(4,21)Std.
dev.
ll(1.11) 12(1.12) 130.13) 15t2.14) 16t2.15) 19(3,17) 20(3;18) 24t4.21) 25(4,22)
VP = 0
30685.16 29899.17 32763.66 31426.87 32288.22 31670.85 31722.47 31638.86 31639.99 31615.16 35510.92 34805.96 38093.49 36597.29 37888.66 36974.24 37088.68 36938.25 36941.48 36901.35 36881.28 29602.39 33994.63 38359.90 30323.16 35207.79 28540.94 33769.30 30199.13 35869.05 0.07
of fit
a "me? the quantum orientation.
(g-s.)
number
for
the
torsion
VP = 2
30830.53 30056.27 32926.37 31589.65 32471.71 31839.93 31894.31 31807.82 31809.12 31783.75 35676.70 34987.64 38279.04 36785.23
VP = 4
vp = 6
31331.46 32551.94 30589.90 31877.07 33444.96 34599.89 32125.01 33346.07 33041.47 34268.26 33614.06 32453.55 33679.28 32372.47 33588.69 32373.88 33590.42 33570.68 36253.24 37686.21 ;;f%;.;; 37107.23
37402:76 38827.99 38765.82 37813.69 37946.07 39381.29 37791.83 37139.58 37795.80 39181.99 37098.36 39170.92 37078.15
38104.32 37171.67 37292.34 37136.13
0.08 of the methyl
in the
la
30639.42 29852.66
32700.42 31370.50 32219.14 31610.86 31660.57 31578.99 31580.21 35460.61 34752.80 38022.18 36532.51 37806.16 36903.94 37015.58 36868.03 36871.22 36831.60 36812.08
0.16
0.23 group
"me =
equatorial
0.12
MICROWAVE INVESTIGATION
OF 3-METHYLTHIETAN
TABLE II Measured Line Frequencies (in MHz) for the “Axial” Satellites of 3-Methylthietan J'(K' K') + J"(K;,K;) a, c
4c 4( 5( 51 5t 51
4. 4, 0, 1, 1, 2.
1) 0) 51 5) 4) 4)
-
6(
0: 6i - 5io: si
6( 4: 3; -
4(3, 413. 4(0. 411, 4(1, 412.
1) 2) 4) 4) 3) 31
5i4: 2i
VP = 1
29866.03 29874.71 29640.41 29052.49 31033.88 30104.88 30631.23 30252.75 30278.60 29818.96 29854.06 35336.39 34802.34 37143.25 36074.00 36936.08 36323.96 36391.96 36297.49 29724.49 36299.29 29829.31 36214.07 29550.67 29810.75 38343.75 38351.25 29253.02 29817.75 38276.51 38299.01 28776.50 29880.71 38172.23 38230.60 28061.84 30044.08 38013.12 38148.25 27059.62 30367.55 37773.40 38059.12 30927.25 37416.95 37977.51 31816.12 36896.11 37926.90 33138.03 36154.30 37942.43 35000.09 35132.15
VP = 3
"ma = la
28821.66 28185.99 30291.03 29299.44 29844.51 29447.75 29473.68 29418.90
29663.27 29081.30 31029.59 30115.32 30627.32 30258.95 30284.11 30238.61
34344.73 33761.83 36250.87 35107.65 36003.16 35361.22 35429.42 35325.03
35369.19 34838.15 37140.97 36087.85 36927.82 36331.10 36396.36 36305.05
35326.88
36306.96 36282.41 29415.28 29664.97
32038.05 32605.34
31541.07 32652.68
30798.41 32798.83
0.09
29883.20
33646.97 37264.36 34521.81 37743.50 35836.60 36050.32 37752.23 35066.22 37869.14
37497.24 33779.64 38383.07 32069.73 38954.16 30006.17 27625.59 38260.54 35804.50 32993.59 29894.22 38349.07 34820.79 31064.04 27186.69 35599.64 31271.46 35448.44 34496.11 29366.50 Std. de". of fit
29127.79 29670.20 38092.35 38114.04 28667.25 29120.74 37991.75 38047.18
38156.28 32105.35 38691.51 27778.43 38369.86 35991.57 33257.42 30228.58 38743.77 35303.53 31620.81 36339.23 32077.17 36467.79
0.13
0.12
nsnber for the torsion of the methyl group a "ma *the quantum in the axial orientation.
453
454
CAMINATI ET AL. TABLE III Rotational and Centrifugal Distortion Constants of 3-Methylthietan”
10,Olb
ll,OIC
(2,O)
(3.0)d
(4.0)
(6.01
(O,l)
(l-1)
A/MHz
9207.50(3)
7291.86(21
9077.0(51
7609.0(B)
8780.0(13)
8X1.5(10)
9229.317)
7271.61(Z)
B/MHz
2872.005(91
3217.53(l)
2886.54(l)
3149.6212)
2931.16(4)
3022.38(3)
2865.61(2)
3215.02(Z)
C/MHz
2385.994(g)
2816.09(l)
2399.14(l)
2723.37(2)
2445.3114)
2557.79(3)
2382.6312)
2820.36(21
dJ/kHz
0.44(10)
AJK/kHz
-0.83(U)
1.98118) -11.4015)
0.471111 -2.79(15)
-4.5(3) 83.7(71
1.1313) -130.7(81
6.7(3)
0.3306)
-71.47(34)
-1.17(22)
2.26(24) -11.40(9)
k/kHz
o.oe
24.5(3)
o.oe
o.oe
o.oe
0. oe
24.2(61
dJ/kHz
0.077l16)
-0.26112)
O.Oe
o.oe
o.oe
o.oe
o.oe
-0.258(5)
dJKlkHz
o.oe
3.612)
o.oe
7(2)
o.oe
o.oe
o.oe
2.813)
std. dev. MHz
0.073
0.087
0.082
0.127
0.234
0.161
0.124
0.119
no. of lines JIM E&m'
f
-330133)
30
74
21
26
18
16
21
49
25
49
7
14
7
7
7
42
1021121
113(15)
69l15)g
219(20)
286(301
213(201
a The energy levels are labeled with the notation 1~p.v~). vp,the puckering quantum number, Vm,the methyl flutier. b Equatorial conformation (ground state). ' Lowest state of the axial conformer. d A sextic centriPc;al distortion constant. HJK = 7.3(6) Hz, was required for a satisfactory fit. e Fixed. f Vibrational energy relative to the ground state. as obtained 9 Relative to (1.0). that is,to the lowest axial state.
by relative
intenrlty
239(20)9 torslon
quantum
measurements.
transitions, Stark coefficients (Z8), and the resulting dipole moment components listed for both conformers in Table IV.
are
Methyl Group Internal Rotation for the Axial Conformer The A-E splitting resulting from the methyl internal rotation was observed for seven Q-type transitions in the first torsional excited state of the axial methyl group by recording the absorption lines at very low pressure (1 to 2 pm of Hg). The observed splittings, listed in Table V, were fitted with the IAM method (19) in the high barrier approximation of the program developed by Woods (20). The vibrational splitting between the rotationless A-E states, & = EE - EA, was free to vary without restriction. The parameters p and /3 in Woods’ formulation (20), representing respectively the relative size of the top and one of the two angles of orientation of the top axis, were allowed to vary within a confidence interval of 20% of the values calculated from the structure while, since the methyl group lies in the molecular (ac) plane, the second orientation parameter y was held fixed (to 1.571 rad = 7r/2). The quantities so determined, including I’, and F, are also given in Table V. Conformational Equilibrium From the values of the pn dipole moment components, and of the measured peak intensities (I) and half-widths (Au) for pa-type lines close in frequency and similar for the two conformers, the energy difference between the rotationless equatorial and axial states, AEO,O= EO,O(ax)- EO,O(eq),can be obtained from the formula (21)
MICROWAVE INVESTIGATION
455
OF 3-METHYLTHIETAN
TABLE IV Stark Coefficients (Hz cm’/V*) and Dipole Moment Components (D) of 3-Methylthietan Equatorial
Axial
conformer
conformer Av/AEz
Av/AE2 J’(K;,K;)
f J”(K;.K;l
625-524
726-62s
obs .
IHI
J'(K' K') + J"(K" K"1 a' c a' c
ohs.-talc.
I"1
ohs.
ohs.-talc.
1
3.83
0.29
1
-0.31
-0.01
2
15.06
0.22
2
0.66
-0.01
3
33.33
-0.34
3
2.36
0.06
1
0.89
0.01
2
3.59
0.01
5,s40,
625-524
1
2.65
2
10.59
0.11 -0.01
3
8.09
0.01
3
24.05
0.02
4
14.20
-0.16
4
42.50
-0.32
52r-423
p,
1
15.58
0.62
2
60.98
0.48
,L~ = 1.766(5)
= 2.04017)
pb = oa
pb = oa
pc = 0.16(21
pc = 0.88119)
et = 2.04619)
u.
= 1.974181
TABLE V Methyl Group Internal Rotation of the Axial Conformer of 3-Methylthietan Measured
splittings
J*(K;,K;)
+
J”(K;,K;)
24(6,19) 25(6,20) 30(7,24) 31(7,251 3618.29) 37(8,30) 42(9,34)
-
Calculated
A,IMHz F/GHz Vi/kJ mol-' fl/rad ylrad
obs.
talc.
24(5,19)
0.10
25(5,20) 30(6,24) 31(6,25) 36(7,29) 37(7,30) 42t8.341
0.14 0.14 0.17 0.21 0.20 0.34
0.128 0.137 0.174 0.182 0.221 0.226 0.266
parameters
2.07 (24) 162.0b 17.6(4) o.o344(19)a 0.394C181" 1.571
a Allowed to vary within a confidence interval of 20% of the values calculated from the structure. b From the structure. ' Fixed.
456
CAMINATI
ET AL.
where g, y, and v are the degeneracy, and linestrength, and the transition frequency, respectively. The corresponding value for A,!& is lOO(17) cm-’ ( 1.2(2) kJ/mol). Flexible Model A simultaneous interpretation of both infrared and microwave data by a common model was attempted by the flexible model approach (3). The data calculated in this scheme are the energy levels and wavefunctions for overall angular momentum quantum numbers J = 0 and J = 1 and yield transition frequencies between vibrational levels as well as the effective rotational constants associated with different vibrational states. The model allows one to define the dynamic path of motion by including structural relaxations depending on a leading coordinate and to adjust the respective parameters along with those of the potential function to the observed data. For the ring puckering motion of 3-methylthietan the angle T (see Fig. 1) was chosen as the independent variable. This coordinate is zero at the planar configuration of the ring and negative for the equatorial conformation. Since the potential energy increases to very large values as the angle 7 approaches 180” or - 180”, a power expansion was considered appropriate for the potential function, V((7)= AE(T/270) + B( 1 - (7/7iJ)z)2.
(2)
In the symmetric case (AE = 0) the parameters p and 7. represent the barrier to inversion and the absolute equilibrium angle, respectively. These properties are modified, however, by the asymmetry term with the parameter AE approximating the energy difference between the two potential energy minima. In order to reproduce the variations of the rotational constants upon excitation of the puckering motion, structural relaxations were assumed for the CCC angle (Ywithin the ring and for the angle 0 between the bisector of (Yand the C-C bond involving the methyl group (Fig. 1). The dependence of CYon 7 was assumed as (Y(T)= cxo+ A~,(T/To) + Aa,( 1 - (r/~>~)
(3)
with three parameters related to the values at 7 = +T~ near the potential energy minima and to the value for a planar ring frame. Only two parameters were chosen for the second skeletal angle 8, e(7) = B. + A&(T/T~).
(4)
Bondlengths were considered to remain sufficiently rigid to be assumed constant. Also valence angles and twisting angles involving hydrogen atoms were assumed constant since relaxation of such coordinates should displace only small masses and thus have relatively little influence on the rotational constants. By constraints, the valence angles within the ring, however, vary with T and CY.In the model, the planes of the CH2 group were kept perpendicular to the adjacent CCS planes and the HCH angle bisectors remained in line with the respective CCS angle bisectors. Methyl and methylene group angles, as well as the HCC angle involving the methyl carbon and the single hydrogen, were assumed to be 109.47“. The length 1.095 A was chosen for all C-H bonds. The bondlengths of the ring frame, r(C-C) = 1.549 A and r(C-S) = 1.847 A, were assumed to be the same as those obtained from electron diffraction for thietan
MICROWAVE
INVESTIGATION
OF 3-METHYLTHIETAN
457
(14) while the C-CH3 bondlength for the methyl group was adjusted as another model parameter. As a consequence of the curvilinearity of the puckering motion, the coefficient gr’(7) of the kinetic energy (3) varied with 7 and went through a maximum near 7 = -25”. Calculations with preliminary parameter values were made to adjust the range and the numerical resolution of the variables, in order to ensure convergence (3) of the results. The range -60” =G7 < 60”, resolved into 41 equidistant mesh points, was found to be adequate. From the calculated effective rotational constants A, B, and C for a particular vibrational state the second moments of the apparent molecular mass distribution were derived as M,,=(h/16a2)(-l/A+
l/B+ l/C), etc.
(5)
When adjusting model parameters it is often preferable to consider these second moments since their shifts AM,, associated with vibrational excitation reflect changes in molecular extension along the respective principal axes. These shifts are easier to visualize than the corresponding changes of the rotational constants. Some additional information from the calculated vibrational states was obtained by estimating relative intensities of infrared absorptions. Assuming a relevant component of the dipole moment perpendicular to the CCC plane of the ring and linear in the coordinate T, relative intensities
for transitions from a lower state 1to an upper state u were obtained from the calculated wavefunctions and the relative Boltzmann populations p(E) = exp(-E/kT). The first attempts to fit the measured vibrational spectrum and the microwave data led to inconsistencies with the transition frequencies between the lowest vibrational levels assigned to the strong infrared absorption peaks in the region 90-l 15 cm-‘. This region differs from that at lower frequencies in that the absorptions are considerably broader than the Av = +l lines for v, > 3 below 90 cm-‘. The rotational structure for the transitions involving the states v, = 0, 1, 2, 3 seems to be more complicated. This is probably due to the fact that the changes in rotational constants among these lower levels are particularly large. Therefore the respective absorption peaks need not be very close to the vibrational transition frequencies. The calculated relative intensities suggested that the first vibrational transition within the equatorial well be assigned to the strong absorption with peaks at 110.30 and 115.08 cm-‘, while the transition from the lowest equatorial to the lowest axial level was predicted to be too weak to be observed. When the frequency of the latter transition was assumed above that of the former, serious contradictions emerged with the observed rotational constants for the lowest three states. Thus the sequence for the lowest energy levels, namely vi, = 0 for the equatorial ground state, vp = 1 for the lowest axial state, and v,, = 2 for the first excited equatorial state, was corroborated by the microwave data. Admitting uncertainties due to still unknown rotational bandshapes, the weight of the measured frequencies in the range 90-l 15 cm-’ was reduced in the adjustment of the model parameters, thus allowing for larger deviations between calculated and assigned frequencies in this region. The results of these model calculations are collected in Table VI, and the potential function is shown with vibrational states in Fig. 2. The calculated
458
CAMINATI ET AL. TABLE VI Flexible Model Results for the Ring Puckering Motion in 3-Methylthietan Puckering
energy separations/cm-' observed far-i@
calculated
microwave
flex. model
;y:;;:;:
110.30b
6905)' 219(2O)C 51.35 286(30)' 40.62 52.73 57.62 62.50 66.71 70.49 74.13 77.10 so.og 83.5
Shifts !-
3
observed
calculated
y
3
-32.98 0.48 13.94 -1.42 0.26 0.53 26.79 0.40 11.13
-32.80 0.62 13.83 -1.24 0.12 0.50 27.29 0.43 11.43
4
a b c a b
-5.68 0.54 2.13
: b c
-14.63’ 0.41c 5.88’
b c a b : b c
Rotational
conformer
6
calculated -5.94 0.12 2.41 -18.15 0.11 7.50 -16.17 -0.26 6.63
observed
axial conformer
(v = 0)
calculated
A0 9207.50
9209.37
80 CO
2871.52 2386.93
2872.00 2385.99
Flexible
5
observed
constants/MHz
equatorial
81 Cl
(v = 1) calculated
observed
Al
7291.86 3217.53 2816.09
7290.24 3218.47 2814.83
model parameters
'c /" E?cn+
25.96(24) 235.9(151
aoI0 Aql”
AE/cm-’
109.7 (30)
AUJ eo/”
1.5040(31)
r(C-CH,)/A
be1 f”
Stationary
points of potential equatorial
V/Calr/O a/" W"
90.15 109.65 95.50 202.50 51.22 293.41 39.70 53.13 57.50 62.56 66.79 70.65 74.19 77.49 80.57 83.48
of second moments MggWMgg(0)/~A2
1
la
2
one-dim."
100.29 113.49 92.18 209.10 51.06 300.52 40.37 53.10 57.61 62.53 66.67 70.43 73.88 77.07 80.06 82.86
minimum
-55.6115) -26.68(25) 94.61(24) 131.99(56)
95.19(21) 0.51112) 0.96(39) 129.55(45) -2.37
(36)
function top of barrier '";.:;W; 96:18(44) 129.41(45)
a See text and Table VII. b Used with lower weight in adjustment of parameters. c Not used in adjustment of parameters.
axial minimum 54.0(15) 25.17(25) 95.74(24) 127.25(56)
MICROWAVE
INVESTIGATION
!
8
0 _i
i
OF
459
3-METHYLTHIETAN
I
14 :
13 12
I
11
~Y+_a_nnhll lo,,,,,,
6
8
7
6
v,_-_-_
4
_
8
-
9
/-
7
10
; E, sz
6 6
3
2 I:-:
5
5
4
:
0
1
i~I~l~l~,,l,i -40
x
_v -
3
2 -1
0 -60
-._,-_,-_
OJL -20
0 -
20
40
60
I’I’I’I’I’I’I
-60
-40
0
-20 -
TP-
20
40
60
rp-
FIG. 2. Ring puckering potential function with energy levels (left) and wavefunctions ylthietan, as determined by the flexible model.
(right) for 3-meth-
infrared spectrum is compared with the experimental one in Fig. 3. The model does not yield any appreciable intensity for the 1-O transition at 100.29 cm-’ as a result of the localization of the respective states in different wells. For the same reason, a very small transition moment should still be obtained when the expansion of the dipole moment is taken to higher orders. This argument does not apply, however, to the double-quantum transitions 9-7 through 13- 11 near and above 120 cm-‘. The respective observed absorptions are considerably larger than expected from Eq. (6) and may well indicate significant higher order terms in the expansion of the dipole
30
44
58
72
100 114 86 WAVEN UMBERS
128
142
156
FIG. 3. Far-infrared spectrum of 3-methyhhietan (I). Bars indicate calculated transitions with approximate relative intensities derived from the flexible model. The units for the abscissa are centimeters-‘.
460
CAMINATI
ET AL.
moment. In the potential function, higher order contributions were tentatively introduced by including a term proportional to (T/T~)(1 - (T/TO)‘) and a term of the type (~/r,,)~( 1 - (T/TO)~)~.The respective parameters turned out to be insignificant as their values were in the order of only a few centimeters-’ with standard errors larger or similar. Reevaluation of the Far-Infrared Spectrum The intensities of the microwave lines arising from rotational transitions in the puckering excited states indicate that the earlier far-infrared analysis is incorrect (I). The comparable essential information which would have provided details of the transitions below the inversion barrier was not available from the far-infrared spectra. Therefore, using the microwave data as a guide, the puckering separations were recalculated with the one-dimensional “rigid” Hamiltonian employed previously (I). The reduced mass in the kinetic energy was held fixed as before, and the quadratic, cubic, and quartic potential function constants varied to best fit the assigned infrared absorption bands. The results are compared with the flexible model in Table VI and with the previous values in Table VII. In order to achieve reasonable agreement with the microwave data, it is necessary to know confidently the assignment of at least two transitions below the inversion barrier. In terms of their effect upon the potential function and the likelihood of finding them in the far-infrared spectrum, we chose either the 1-O or the 2-O transition plus the 5-4 transition. The proper choice of one from the 1-0/2-O pair critically affects the separation between the energy minima which in turn determines the relative intensity of the two transitions. As before, the absorption at 110.30 cm-’ was taken as the most appropriate candidate. The calculated 5-4 separation then varied from 35 to 55 cm-’ depending on the use of either 1-O or 2-O. The most reasonable agreement with the microwave intensity measurements was obtained when in addition to the transitions from 7-6 upward, 2-O was assigned to the 110.30 cm-’ absorption and 5-4 together with 7-6 to the apparent doublet with an average peak intensity at 52.04 cm-‘. The results of that fit are listed under calculation I in Table VII. For calculation II, one minor change and one additional assignment were incorporated. The 5-4 and 7-6 transitions evidently are close in energy which suggests that they could be assigned separately to the two components of the doublet. This was done for calculation II, although the possibility that one of the two peaks arises from the 7-6 transition in an excited state of another low-energy vibration cannot be excluded. The 6-5 separation appears to be relatively insensitive to the inclusion of the 5-4 transition, hovering near 40 cm-‘, suggesting that the weak absorption at 40.62 cm-’ could be assigned accordingly. The effects of these two additions are minor. It is worth mentioning that the fit of the far-infrared data reflected in Table VII is not unique. A second solution using transitions the same as those for calculation I is possible with a standard deviation of 0.50 cm-‘, giving an inversion barrier of 275.6 cm-’ and a second well depth of 116.8 cm-‘. In this case, the intensity formerly in 2-O has shifted to 1-O calculated at 106.65 cm-‘. From the point of view of the farinfrared spectrum, therefore, the two solutions would be indistinguishable, since the band origin of either transition may be appreciably different from the band maximum. The agreement between the results of the flexible model and the “rigid” Hamiltonian
MICROWAVE INVESTIGATION
461
OF 3-METHYLTHIETAN
TABLE VII Observed and Calculated Puckering Transitions and Potential Function Constants for 3-Methylthietan Transitiona "u + "1
Previousb
Revised
111.05
1 :
0 1
4 5 6 7 8 9 10 11 12 13 14
: 4 5 6 7 8 9 10 11 12 13
52.34 57.62 62.50 66.71 70.49 74.12 77.10 79.99
2 3
0 1
95.54
45 ;
: 4
0 9 10 11 12 13
: 7 8 9 10 11
51.35 40.62 52.73 57.62 62.50 66.71 70.49 74.13 77.10 80.00 110.30
Std. dev. of obs./caf'
Second well depth/cm-' Equ.-ax. energy diff./cml
previousb
110.27 96.37 93.71 68.40 90.70 91.61 110.03 119.41 128.71 136.89 144.32 151.18
157.17 95.58 85.00
Previous
I 91.20 19.08 77.29 16.42 51.98 38.14 52.89 57.14 62.27 66.51 70.38 73.94 77.24 80.33
111.04 46.13 49.45 35.55 38.69 44.09 52.25 57.70 62.45 66.64 70.43 73.92 77.17 80.21
119.52 128.71 136.60 144.68 151.27
Potential function parameters e
Calc. Rel. 1nt.d
Calculated/car'c
Observed/car'
-I
II
lql
90.15 19.51 76.00 16.86 51.22 39.70 53.13 57.50 62.56 66.79 70.65 74.19 77.49 80.57 109.65 95.50 92.85 68.07 90.91 92.82 110.63 120.06 129.35 137.43 144.84 151.68
lq21
Iq'l
0.000 0.000 0.041 0.15 0.60 0.79 1.00 0.94 0.84 0.71 0.58 0.46 0.35 0.26
0.000 0.000 0.028 0.001 0.082 0.000 0.008 0.005 0.005 0.004 0.003 0.003 0.002 0.001
0.000 0.000 0.025 0.022 0.19 0.18 0.30 0.31 0.31 0.29 0.26 0.22 0.18 0.15
0.73 0.43 0.72 0.22 0.16 0.000 0.003 0.001 0.001 0.000 0.000 0 .ooo
1.00 0.39 0.77 0.26 0.51 0.43 0.55 0.51 0.46 0.40 0.33 0.27
1 .oo 0.27 0.67 0.062 0.17 0.002 0.018 0.011 0.011 0.009 0.007 0.006
-II
0.15 -31.81
0.42 -34.31(27)
0.50 -34.02(29)
1.683 1.205 310.7 144.3 166.4
0.9318076) 1.245/8) 289.9 193.8 96.13
0.9352(197) 1.247(9) 285.1 190.0 95.11
i Quantum number labels for the upper (u) and leer (1) puckering energy levels. See ref.(l). ",Transitions that are underlined were included in the least-squaresfitting process. Contributions to the relative intensities for Calc. II calculated according to Iq"J = cu)q"ln>, e q the dimensionless coordinate, corrected for the Boltzman factor. Calculated with a one-Gwnsional Hamiltonian with the potential function V(q) = [V2/(mr)Iq2+ [Vs/(mr) ]q3 + [V,/(mr)*Iq4 , q the dimensionless puckering coordinate. Fixed parameters: reduced mass m = 100.0 u, harmonic oscillator frequency v = 100.0 earl, y = 4n*cv/h = 296.60 u-l nnr2, 80 harmonic oscillator basis functions.
is pleasing in all respects, including the calculated transitions and their relative intensities and the essential features of the potential function. The barrier height, second well depth, and energy difference between minima calculated with the rigid Hamiltonian (Table VII) compare to 293.1, 183.5, and 109.6 cm-‘, respectively, with the flexible model. The discrepancies between the transitions below the barrier, evident in Table VI, can be ascribed to the effects of the relaxation of the ring angles accompanying the puckering motion for which the flexible model compensates.
462
CAMINATI ET AL. CONCLUSIONS
The microwave spectrum of 3-methylthietan was analyzed, assigning rotational transitions for the ground state and for four excited states of ring puckering and two of methyl torsion. Utilizing this data together with the puckering energy separations derived from the far-infrared spectra, the flexible model (3) was used to determine three potential function parameters, three structural parameters, and three parameters expressing structural relaxation accompanying ring puckering. In this manner it was possible to reproduce the spacing between the energy levels of the puckering and methyl torsion vibrations and the variations of the rotational constants upon vibrational excitation and conformational change. While the majority of assignments of the farinfrared spectrum reported earlier (I) were confirmed, one crucial reassignment and one additional assignment, necessary to comply with microwave intensity measurements, altered the previously determined asymmetric potential function significantly. The combined analysis yields the following structural information for 3-methylthietan. The methyl group adopts the equatorial orientation in the lowest energy conformation. The axial conformer is higher in energy by lOO(17) cm-’ (1.2(2) kJ/mol) as evaluated from the rotational transitions. The potential energy minima of the two conformers are separated by 95 or 110 cm-’ with an inversion barrier of 285 or 293 cm-’ as determined, respectively, by fitting the far-infrared absorptions with an asymmetric potential function in a “rigid” one-dimensional puckering Hamiltonian or by the combined analysis of the microwave and far-infrared data with the flexible model. The puckering angles are 26.7“ and 25.2”, respectively, for the equatorial and axial conformers. The angle 6’between the C-CH3 bond and the ring CCC plane (see Fig. 1) is larger in the equatorial form by almost 5” than in the axial form. This might be surprising as CH3 - - - S repulsion should be expected to lead to a larger angle in the axial form. The present result given at the end of Table VI suggests a larger effect due to the repulsion between the methyl group and methylenic hydrogen atoms, which should favor a larger angle 0 in the equatorial form. Possibly the same type of interaction is also the cause for an apparent enhancement of methyl torsional barriers observed in the present and in related ring molecules (22, 23). The barrier hindering the internal rotation of the methyl group was determined as 1470(30) cm-’ (17.6(4) kJ/mol) for the axial conformer. Unfortunately, this high value precluded the measurement of the A-E doubling in excited puckering states, which could have been useful for investigating kinetic and potential energy coupling between the two motions, as was possible in other cases (6-10). ACKNOWLEDGMENTS Professor A. Trombetti, Director of the Istituto di Spettroscopia Molecolare de1 C.N.R., kindly allowed us to use the microwave spectrometers. ACF acknowledges the award of a fellowship from the Consejo National de Investigaciones Cientificas Y Tecnicas (CONICET) of Argentina. HW gratefully acknowledges financial support via an Operating Grant from the Natural Sciences and Engineering Research Council of Canada (NSERC). W. Caminati thanks Professor A. Bauder for having given him the opportunity to work in his group. RECEIVED:
July 7, 1987
MICROWAVE
INVESTIGATION
OF 3-METHYLTHIETAN
463
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. IO. II. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
R. A. SHAW, T. L. SMITHSON, ANDH. WIESER,J. Mol. Struct. 102, 199-202 (1983). H. WIESER,J. A. DUCKE’IT, AND R. A. KYDD, J. Mol. Spectrosc. 51, 115-122 (1974). R. MEYER, J. Mol. Spectrosc. 76, 266-300 (1979). W. CAMINATI, R. MEYER, M. OLDANI, AND F. SCAPPINI,J. Chem. Phys. 83,3729-3737 (1985). See, for example, C. C. LIN AND J. D. SWALEN, Rev. Mod. Physics 31,841-892 (1959). W. CAMINATI AND R. MEYER, J. Mol. Spectrosc. 90, 303-3 14 (198 I). A. BAUDERAND R. MEYER, J. Mol. Spectrosc. 94, 136-149 (1982). R. MEYER, T.-K. HA, M. OLDANI,AND W. CAMINATI, J. Chem. Phys. 86, 1848 (1987). W. CAMINATI AND A. C. FANTONI, Chem. Phys. 105,59-67 (1986). W. CAMINATI, R. MEYER, AND Z. SMITH, Chem. Phys. 110,67-82 (1986). G. CAZZOLI, A. DAL BORGO,D. G. LISTER, AND D. DAMIANI, J. Mol. Spectrosc. 95,43-50 (1982). F. J. WODARCZYK AND E. B. WILSON, J. Mol. Spectrosc. 37,445-463 (1971). A. S. ESBITTAND E. B. WILSON, JR., Rev. Sci. Instrum. 34,901-907 (1963). K. KARAKIDA AND K. KUCHITSU,Bull. Chem. Sot. Japan 48, 1691 ( 1975). (a) D. 0. HARRIS, Diss. Abstr. 26,3648 (1966); (b) D. 0. HARRIS, H. W. HARRINGTON, A. C. LUNTZ, AND W. D. GWINN, J. Chem. Phys. 44,3467-3480 (1966). J. K. G. WATSON, .J.Chem. Phys. 46, 1935-1949 (1967). J. S. MUENTER, J. Chem. Phys. 48,4544-4547 (1968). S. GOLDEN AND E. G. WILSON, JR., J. Chem. Phys. 16,669-685 (1948). K. T. HECHT AND D. M. DENNISON,J. Chem. Phys. 26,31-47 (1957). R. C. WOODS, J. Mol. Spectrosc. 21,4-24 (1966). C. H. TOWNESAND A. L. SCHAWLOW,“Microwave Spectroscopy,” McGraw-Hill. New York, 1956. W. CAMINATI AND F. S~APPINI, J. Mol. Spectrosc. 117, 184-194 (1986). J. L. ALONSO, E. GONZALES,W. CAMINATI, AND B. VELINO, J. Mol. Spectrosc. 122, 247-258 (1987).
127,450-463 (1988)
Microwave Investigation and the Ring Puckering Potential Function of 3-Methylthietan W. CAMINATI,*~-~$ A. C. FANTONI,*+~ R. MEYER,* R. A. SHAW,~ T. L. SMITHSON,~’AND H. WIESER~I *LXpartimento di Chimica Fisica ed Inorganica dell’ Universiia ‘, Kale Risorgimento 4, 40126 Bologna, Italy; tlstituto di Spettroscopia Molecolare de1 C.N.R.. Via de’ Castagnoli I, 40136 Bologna. Italy; $Laboratoriumfir Physikalische Chemie, Eidgeniissische Technische Hochschule Universitiitsstrasse 22, CH-8092 Zurich. Switzerland; $Departmento de Fisica, Universidad National de La Plats, C.C. 67, 1900 La Plata, Republic ofArgentina; YDepartment of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N IN4; and ‘IDREV, 2459 Blvd. Pie XI Nerd, C.P. 8800, Courcellette, Quebec, Canada GOA IRO
Themicrowave spectrum of 3-methylthietan wasinvestigated in the frequency range 26.5-40 GHz. The rotational spectra were measured for the ground state, five puckering states (including the lowest state of the second conformer), and two methyl torsion excited states. The conformer with the methyl group in the equatorial orientation (the ground state, up = 0) is more stable than the axial counterpart (u,, = 1) by 100(17) cm-’ (1.2(2) k.J/mol). The electric dipole moment was determined for both conformers by measuring the Stark effect on several transitions. A V, barrier of 1470(30) cm-’ (17.6(4) kJ/mol) was obtained for the internal rotation of the axial methyl group from the A-E doubling of several rotational transitions in the first torsional excited state. Earlier far-infrared assignments were revised on the basis of microwave intensity measurements. The flexible model approach was used to reproduce the spacings between puckering levels simultaneously with the variation of the rotational constants with puckering excitation, allowing some structural relaxation accompanying the ring deformation. Comparisons are made with the results obtained when an asymmetric one-dimensional puckering Hamiltonian is used. Q 1988 AcademicPm% Inc.
INTRODUCTION
The ring puckering vibration of 3-methylthietan has been investigated recently by far-infrared Fourier transform spectroscopy (I). A barrier to inversion similar to that of thietan (2) has been obtained from the spacings of the vibrational levels. The existence of two conformers as shown in Fig. 1 has been inferred, but it has not been possible to predict which of them was the more stable. In order to determine the conformational preference, confirm the potential function, and investigate the structural relaxation related to the ring motion, we decided to analyze the rotational spectrum which, in addition to the rotation constants in the ground state, would supply also their variations in the puckering excited states. Our method of choice was the flexible model (3) with which it has been possible to obtain the related information for problems with two asymmetric minima in the potential surface, as, for example, in the case of lactonitrile (4). We further hoped to investigate the internal rotation of the methyl group which, as a result of the splitting of the A-E torsional levels when the V, barrier has suitable 0022-2852/88 $3.00 copyrightQ 1988 by Aademic
Rc.s, Inc. All rightsof reprodunion in any form -ed.
450
MICROWAVE
INVESTIGATION
OF 3-METHYLTHIETAN
451
Jig__&i& Axial
Equotoriol
s
RG. 1. Conformations of 3-methylthietan, indicating also the angles (Yand 8 subject to structural relaxation.
magnitude, should lead to a doubling of the rotational transitions (5). In favorable cases when using the flexible model, the A-E doubling measured for the vibrational satellites belonging to motions other than the methyl torsion has been useful for obtaining information about the coupling between the two vibrations (6-10). EXPERIMENTAL
DETAILS
The compound was synthesized in the same way as described previously (I). The microwave spectra were recorded in the frequency range 26.5-40 GHz with a computer-controlled spectrometer consisting mainly of Hewlett-Packard components (I I). The frequency measurements are believed to be accurate to better than 0.1 MHz. The temperature of the cell was kept constant at about -30°C. The radiofrequencymicrowave double-resonance technique (rfmwdr) (12) was used for assigning the first transitions. Intensity measurements were made following the recommendations of Esbitt and Wilson (13). New far-infrared assignments were made from spectra that were recorded previously (I) and stored on computer discs. RESULTS AND DISCUSSION
Assignment ctfthe Microwuve Spectrum The structure of the parent thietan molecule, as obtained by electron diffraction (14), was used for the first trial calculation of the rotational transitions of both the axial and the equatorial conformers of the 3-methyl derivative, taking advantage also of the positions of the two potential minima of thietan evaluated previously (15). Calculated Ray’s asymmetry parameters were in the range -0.78 to -0.84 for both conformations, suggesting that it should be possible to observe ,uaR-type bands. Indeed, such bands were found for the axial and equatorial conformers and for their vibrational satellites in the low-resolution spectra. By pumping the 431-432, 440-44,, 532-533, 54,&, 633-634, and 642-643 doublets at radiofrequencies in the range 2-120 MHz, the first transitions that were assigned were the K doublets 53-43, 54-44, 63-53, and 6454 for the axial and 63-53, 73-63, and 74-64 for the equatorial structure. Other transitions were then measured with the conventional Stark modulation technique. Several putQtype transitions were located for the axial conformer, whereas none could be found for the equatorial conformer due to its lower pLcvalue (see the section concerning the dipole moments below). A number of rotational transitions were assigned for several additional puckering excited states, namely for up = 2 to 4 and 6, u, the puckering
452
CAMINATI ET AL.
quantum number (where D, = 0 and 1 correspond to the equatorial ground state and the lowest axial state, respectively), as well as for the first excited state of the methyl torsion in both conformations. The splitting expected as a result of the A-E doubling was observed for some jamQ-type transitions in the first torsional excited state of only the axial methyl group. The measured line frequencies are listed in Tables I and II, grouped into “equatorial” (up = 0, 2, 4, and 6) and “axial” (up = 1 and 3) satellites, respectively. The transition frequencies were fitted separately for each vibrational state with Watson’s Hamiltonian in the A reduction (16). Strong interactions between the puckering states give rise to unusually large values for the centrifugal distortion constants, whereas for the first methyl torsion excited states their values are very close to those of their corresponding states without torsional excitation. The best-fitting rotational and quartic centrifugal distortion constants are listed in Table III. Dipole Moments The displacements of some Stark lobes have been measured as a function of the applied electric field for several transitions. All lobes showed a second-order Stark effect. The cell was calibrated with the 3 * 2 line of OCS (p = 0.71521 D (17)). The TABLE I Measured Line Frequencies (in MHz) of the “Equatorial” Satellites of 3-Methylthietan J'(K;,K;)
+ J"(K;,K;)
6(0. 6(1, 611.
6) 6) 51 -
5(0, 5(1, 5(1.
51 5) 41
6(2, 6(3;
5) 4) 4) -
5i2; 5(2, 5(3,
4j 31 3)
6(3, 6(4. 6i4; 6(5, 7(0, 7(1, 7(1, 7(2, 7(2, 7(3, 7(3, 7(4, 7(4, 7(5. 7(6,
31 31 Pj 2) 7) 7) 6) 6) 5) 5) 41 4) 3) 3) 2)
5(3, 5(4. 5i4; 5(5, 6(0, 60, 6(1, 6(2, 6(2, 6(3, 6(3, 6(4. 6(4. 6(5, 6(6,
2) 2) li 1) 6) 6) 51 5) 4) 4) 3) 3) 2) 2) 1)
6(2,
-
ll(l,lO)12(1,11)13(1,12)15t2.13)16(2,14)19C3.16)20(3;17)24C4.20)25(4,21)Std.
dev.
ll(1.11) 12(1.12) 130.13) 15t2.14) 16t2.15) 19(3,17) 20(3;18) 24t4.21) 25(4,22)
VP = 0
30685.16 29899.17 32763.66 31426.87 32288.22 31670.85 31722.47 31638.86 31639.99 31615.16 35510.92 34805.96 38093.49 36597.29 37888.66 36974.24 37088.68 36938.25 36941.48 36901.35 36881.28 29602.39 33994.63 38359.90 30323.16 35207.79 28540.94 33769.30 30199.13 35869.05 0.07
of fit
a "me? the quantum orientation.
(g-s.)
number
for
the
torsion
VP = 2
30830.53 30056.27 32926.37 31589.65 32471.71 31839.93 31894.31 31807.82 31809.12 31783.75 35676.70 34987.64 38279.04 36785.23
VP = 4
vp = 6
31331.46 32551.94 30589.90 31877.07 33444.96 34599.89 32125.01 33346.07 33041.47 34268.26 33614.06 32453.55 33679.28 32372.47 33588.69 32373.88 33590.42 33570.68 36253.24 37686.21 ;;f%;.;; 37107.23
37402:76 38827.99 38765.82 37813.69 37946.07 39381.29 37791.83 37139.58 37795.80 39181.99 37098.36 39170.92 37078.15
38104.32 37171.67 37292.34 37136.13
0.08 of the methyl
in the
la
30639.42 29852.66
32700.42 31370.50 32219.14 31610.86 31660.57 31578.99 31580.21 35460.61 34752.80 38022.18 36532.51 37806.16 36903.94 37015.58 36868.03 36871.22 36831.60 36812.08
0.16
0.23 group
"me =
equatorial
0.12
MICROWAVE INVESTIGATION
OF 3-METHYLTHIETAN
TABLE II Measured Line Frequencies (in MHz) for the “Axial” Satellites of 3-Methylthietan J'(K' K') + J"(K;,K;) a, c
4c 4( 5( 51 5t 51
4. 4, 0, 1, 1, 2.
1) 0) 51 5) 4) 4)
-
6(
0: 6i - 5io: si
6( 4: 3; -
4(3, 413. 4(0. 411, 4(1, 412.
1) 2) 4) 4) 3) 31
5i4: 2i
VP = 1
29866.03 29874.71 29640.41 29052.49 31033.88 30104.88 30631.23 30252.75 30278.60 29818.96 29854.06 35336.39 34802.34 37143.25 36074.00 36936.08 36323.96 36391.96 36297.49 29724.49 36299.29 29829.31 36214.07 29550.67 29810.75 38343.75 38351.25 29253.02 29817.75 38276.51 38299.01 28776.50 29880.71 38172.23 38230.60 28061.84 30044.08 38013.12 38148.25 27059.62 30367.55 37773.40 38059.12 30927.25 37416.95 37977.51 31816.12 36896.11 37926.90 33138.03 36154.30 37942.43 35000.09 35132.15
VP = 3
"ma = la
28821.66 28185.99 30291.03 29299.44 29844.51 29447.75 29473.68 29418.90
29663.27 29081.30 31029.59 30115.32 30627.32 30258.95 30284.11 30238.61
34344.73 33761.83 36250.87 35107.65 36003.16 35361.22 35429.42 35325.03
35369.19 34838.15 37140.97 36087.85 36927.82 36331.10 36396.36 36305.05
35326.88
36306.96 36282.41 29415.28 29664.97
32038.05 32605.34
31541.07 32652.68
30798.41 32798.83
0.09
29883.20
33646.97 37264.36 34521.81 37743.50 35836.60 36050.32 37752.23 35066.22 37869.14
37497.24 33779.64 38383.07 32069.73 38954.16 30006.17 27625.59 38260.54 35804.50 32993.59 29894.22 38349.07 34820.79 31064.04 27186.69 35599.64 31271.46 35448.44 34496.11 29366.50 Std. de". of fit
29127.79 29670.20 38092.35 38114.04 28667.25 29120.74 37991.75 38047.18
38156.28 32105.35 38691.51 27778.43 38369.86 35991.57 33257.42 30228.58 38743.77 35303.53 31620.81 36339.23 32077.17 36467.79
0.13
0.12
nsnber for the torsion of the methyl group a "ma *the quantum in the axial orientation.
453
454
CAMINATI ET AL. TABLE III Rotational and Centrifugal Distortion Constants of 3-Methylthietan”
10,Olb
ll,OIC
(2,O)
(3.0)d
(4.0)
(6.01
(O,l)
(l-1)
A/MHz
9207.50(3)
7291.86(21
9077.0(51
7609.0(B)
8780.0(13)
8X1.5(10)
9229.317)
7271.61(Z)
B/MHz
2872.005(91
3217.53(l)
2886.54(l)
3149.6212)
2931.16(4)
3022.38(3)
2865.61(2)
3215.02(Z)
C/MHz
2385.994(g)
2816.09(l)
2399.14(l)
2723.37(2)
2445.3114)
2557.79(3)
2382.6312)
2820.36(21
dJ/kHz
0.44(10)
AJK/kHz
-0.83(U)
1.98118) -11.4015)
0.471111 -2.79(15)
-4.5(3) 83.7(71
1.1313) -130.7(81
6.7(3)
0.3306)
-71.47(34)
-1.17(22)
2.26(24) -11.40(9)
k/kHz
o.oe
24.5(3)
o.oe
o.oe
o.oe
0. oe
24.2(61
dJ/kHz
0.077l16)
-0.26112)
O.Oe
o.oe
o.oe
o.oe
o.oe
-0.258(5)
dJKlkHz
o.oe
3.612)
o.oe
7(2)
o.oe
o.oe
o.oe
2.813)
std. dev. MHz
0.073
0.087
0.082
0.127
0.234
0.161
0.124
0.119
no. of lines JIM E&m'
f
-330133)
30
74
21
26
18
16
21
49
25
49
7
14
7
7
7
42
1021121
113(15)
69l15)g
219(20)
286(301
213(201
a The energy levels are labeled with the notation 1~p.v~). vp,the puckering quantum number, Vm,the methyl flutier. b Equatorial conformation (ground state). ' Lowest state of the axial conformer. d A sextic centriPc;al distortion constant. HJK = 7.3(6) Hz, was required for a satisfactory fit. e Fixed. f Vibrational energy relative to the ground state. as obtained 9 Relative to (1.0). that is,to the lowest axial state.
by relative
intenrlty
239(20)9 torslon
quantum
measurements.
transitions, Stark coefficients (Z8), and the resulting dipole moment components listed for both conformers in Table IV.
are
Methyl Group Internal Rotation for the Axial Conformer The A-E splitting resulting from the methyl internal rotation was observed for seven Q-type transitions in the first torsional excited state of the axial methyl group by recording the absorption lines at very low pressure (1 to 2 pm of Hg). The observed splittings, listed in Table V, were fitted with the IAM method (19) in the high barrier approximation of the program developed by Woods (20). The vibrational splitting between the rotationless A-E states, & = EE - EA, was free to vary without restriction. The parameters p and /3 in Woods’ formulation (20), representing respectively the relative size of the top and one of the two angles of orientation of the top axis, were allowed to vary within a confidence interval of 20% of the values calculated from the structure while, since the methyl group lies in the molecular (ac) plane, the second orientation parameter y was held fixed (to 1.571 rad = 7r/2). The quantities so determined, including I’, and F, are also given in Table V. Conformational Equilibrium From the values of the pn dipole moment components, and of the measured peak intensities (I) and half-widths (Au) for pa-type lines close in frequency and similar for the two conformers, the energy difference between the rotationless equatorial and axial states, AEO,O= EO,O(ax)- EO,O(eq),can be obtained from the formula (21)
MICROWAVE INVESTIGATION
455
OF 3-METHYLTHIETAN
TABLE IV Stark Coefficients (Hz cm’/V*) and Dipole Moment Components (D) of 3-Methylthietan Equatorial
Axial
conformer
conformer Av/AEz
Av/AE2 J’(K;,K;)
f J”(K;.K;l
625-524
726-62s
obs .
IHI
J'(K' K') + J"(K" K"1 a' c a' c
ohs.-talc.
I"1
ohs.
ohs.-talc.
1
3.83
0.29
1
-0.31
-0.01
2
15.06
0.22
2
0.66
-0.01
3
33.33
-0.34
3
2.36
0.06
1
0.89
0.01
2
3.59
0.01
5,s40,
625-524
1
2.65
2
10.59
0.11 -0.01
3
8.09
0.01
3
24.05
0.02
4
14.20
-0.16
4
42.50
-0.32
52r-423
p,
1
15.58
0.62
2
60.98
0.48
,L~ = 1.766(5)
= 2.04017)
pb = oa
pb = oa
pc = 0.16(21
pc = 0.88119)
et = 2.04619)
u.
= 1.974181
TABLE V Methyl Group Internal Rotation of the Axial Conformer of 3-Methylthietan Measured
splittings
J*(K;,K;)
+
J”(K;,K;)
24(6,19) 25(6,20) 30(7,24) 31(7,251 3618.29) 37(8,30) 42(9,34)
-
Calculated
A,IMHz F/GHz Vi/kJ mol-' fl/rad ylrad
obs.
talc.
24(5,19)
0.10
25(5,20) 30(6,24) 31(6,25) 36(7,29) 37(7,30) 42t8.341
0.14 0.14 0.17 0.21 0.20 0.34
0.128 0.137 0.174 0.182 0.221 0.226 0.266
parameters
2.07 (24) 162.0b 17.6(4) o.o344(19)a 0.394C181" 1.571
a Allowed to vary within a confidence interval of 20% of the values calculated from the structure. b From the structure. ' Fixed.
456
CAMINATI
ET AL.
where g, y, and v are the degeneracy, and linestrength, and the transition frequency, respectively. The corresponding value for A,!& is lOO(17) cm-’ ( 1.2(2) kJ/mol). Flexible Model A simultaneous interpretation of both infrared and microwave data by a common model was attempted by the flexible model approach (3). The data calculated in this scheme are the energy levels and wavefunctions for overall angular momentum quantum numbers J = 0 and J = 1 and yield transition frequencies between vibrational levels as well as the effective rotational constants associated with different vibrational states. The model allows one to define the dynamic path of motion by including structural relaxations depending on a leading coordinate and to adjust the respective parameters along with those of the potential function to the observed data. For the ring puckering motion of 3-methylthietan the angle T (see Fig. 1) was chosen as the independent variable. This coordinate is zero at the planar configuration of the ring and negative for the equatorial conformation. Since the potential energy increases to very large values as the angle 7 approaches 180” or - 180”, a power expansion was considered appropriate for the potential function, V((7)= AE(T/270) + B( 1 - (7/7iJ)z)2.
(2)
In the symmetric case (AE = 0) the parameters p and 7. represent the barrier to inversion and the absolute equilibrium angle, respectively. These properties are modified, however, by the asymmetry term with the parameter AE approximating the energy difference between the two potential energy minima. In order to reproduce the variations of the rotational constants upon excitation of the puckering motion, structural relaxations were assumed for the CCC angle (Ywithin the ring and for the angle 0 between the bisector of (Yand the C-C bond involving the methyl group (Fig. 1). The dependence of CYon 7 was assumed as (Y(T)= cxo+ A~,(T/To) + Aa,( 1 - (r/~>~)
(3)
with three parameters related to the values at 7 = +T~ near the potential energy minima and to the value for a planar ring frame. Only two parameters were chosen for the second skeletal angle 8, e(7) = B. + A&(T/T~).
(4)
Bondlengths were considered to remain sufficiently rigid to be assumed constant. Also valence angles and twisting angles involving hydrogen atoms were assumed constant since relaxation of such coordinates should displace only small masses and thus have relatively little influence on the rotational constants. By constraints, the valence angles within the ring, however, vary with T and CY.In the model, the planes of the CH2 group were kept perpendicular to the adjacent CCS planes and the HCH angle bisectors remained in line with the respective CCS angle bisectors. Methyl and methylene group angles, as well as the HCC angle involving the methyl carbon and the single hydrogen, were assumed to be 109.47“. The length 1.095 A was chosen for all C-H bonds. The bondlengths of the ring frame, r(C-C) = 1.549 A and r(C-S) = 1.847 A, were assumed to be the same as those obtained from electron diffraction for thietan
MICROWAVE
INVESTIGATION
OF 3-METHYLTHIETAN
457
(14) while the C-CH3 bondlength for the methyl group was adjusted as another model parameter. As a consequence of the curvilinearity of the puckering motion, the coefficient gr’(7) of the kinetic energy (3) varied with 7 and went through a maximum near 7 = -25”. Calculations with preliminary parameter values were made to adjust the range and the numerical resolution of the variables, in order to ensure convergence (3) of the results. The range -60” =G7 < 60”, resolved into 41 equidistant mesh points, was found to be adequate. From the calculated effective rotational constants A, B, and C for a particular vibrational state the second moments of the apparent molecular mass distribution were derived as M,,=(h/16a2)(-l/A+
l/B+ l/C), etc.
(5)
When adjusting model parameters it is often preferable to consider these second moments since their shifts AM,, associated with vibrational excitation reflect changes in molecular extension along the respective principal axes. These shifts are easier to visualize than the corresponding changes of the rotational constants. Some additional information from the calculated vibrational states was obtained by estimating relative intensities of infrared absorptions. Assuming a relevant component of the dipole moment perpendicular to the CCC plane of the ring and linear in the coordinate T, relative intensities
for transitions from a lower state 1to an upper state u were obtained from the calculated wavefunctions and the relative Boltzmann populations p(E) = exp(-E/kT). The first attempts to fit the measured vibrational spectrum and the microwave data led to inconsistencies with the transition frequencies between the lowest vibrational levels assigned to the strong infrared absorption peaks in the region 90-l 15 cm-‘. This region differs from that at lower frequencies in that the absorptions are considerably broader than the Av = +l lines for v, > 3 below 90 cm-‘. The rotational structure for the transitions involving the states v, = 0, 1, 2, 3 seems to be more complicated. This is probably due to the fact that the changes in rotational constants among these lower levels are particularly large. Therefore the respective absorption peaks need not be very close to the vibrational transition frequencies. The calculated relative intensities suggested that the first vibrational transition within the equatorial well be assigned to the strong absorption with peaks at 110.30 and 115.08 cm-‘, while the transition from the lowest equatorial to the lowest axial level was predicted to be too weak to be observed. When the frequency of the latter transition was assumed above that of the former, serious contradictions emerged with the observed rotational constants for the lowest three states. Thus the sequence for the lowest energy levels, namely vi, = 0 for the equatorial ground state, vp = 1 for the lowest axial state, and v,, = 2 for the first excited equatorial state, was corroborated by the microwave data. Admitting uncertainties due to still unknown rotational bandshapes, the weight of the measured frequencies in the range 90-l 15 cm-’ was reduced in the adjustment of the model parameters, thus allowing for larger deviations between calculated and assigned frequencies in this region. The results of these model calculations are collected in Table VI, and the potential function is shown with vibrational states in Fig. 2. The calculated
458
CAMINATI ET AL. TABLE VI Flexible Model Results for the Ring Puckering Motion in 3-Methylthietan Puckering
energy separations/cm-' observed far-i@
calculated
microwave
flex. model
;y:;;:;:
110.30b
6905)' 219(2O)C 51.35 286(30)' 40.62 52.73 57.62 62.50 66.71 70.49 74.13 77.10 so.og 83.5
Shifts !-
3
observed
calculated
y
3
-32.98 0.48 13.94 -1.42 0.26 0.53 26.79 0.40 11.13
-32.80 0.62 13.83 -1.24 0.12 0.50 27.29 0.43 11.43
4
a b c a b
-5.68 0.54 2.13
: b c
-14.63’ 0.41c 5.88’
b c a b : b c
Rotational
conformer
6
calculated -5.94 0.12 2.41 -18.15 0.11 7.50 -16.17 -0.26 6.63
observed
axial conformer
(v = 0)
calculated
A0 9207.50
9209.37
80 CO
2871.52 2386.93
2872.00 2385.99
Flexible
5
observed
constants/MHz
equatorial
81 Cl
(v = 1) calculated
observed
Al
7291.86 3217.53 2816.09
7290.24 3218.47 2814.83
model parameters
'c /" E?cn+
25.96(24) 235.9(151
aoI0 Aql”
AE/cm-’
109.7 (30)
AUJ eo/”
1.5040(31)
r(C-CH,)/A
be1 f”
Stationary
points of potential equatorial
V/Calr/O a/" W"
90.15 109.65 95.50 202.50 51.22 293.41 39.70 53.13 57.50 62.56 66.79 70.65 74.19 77.49 80.57 83.48
of second moments MggWMgg(0)/~A2
1
la
2
one-dim."
100.29 113.49 92.18 209.10 51.06 300.52 40.37 53.10 57.61 62.53 66.67 70.43 73.88 77.07 80.06 82.86
minimum
-55.6115) -26.68(25) 94.61(24) 131.99(56)
95.19(21) 0.51112) 0.96(39) 129.55(45) -2.37
(36)
function top of barrier '";.:;W; 96:18(44) 129.41(45)
a See text and Table VII. b Used with lower weight in adjustment of parameters. c Not used in adjustment of parameters.
axial minimum 54.0(15) 25.17(25) 95.74(24) 127.25(56)
MICROWAVE
INVESTIGATION
!
8
0 _i
i
OF
459
3-METHYLTHIETAN
I
14 :
13 12
I
11
~Y+_a_nnhll lo,,,,,,
6
8
7
6
v,_-_-_
4
_
8
-
9
/-
7
10
; E, sz
6 6
3
2 I:-:
5
5
4
:
0
1
i~I~l~l~,,l,i -40
x
_v -
3
2 -1
0 -60
-._,-_,-_
OJL -20
0 -
20
40
60
I’I’I’I’I’I’I
-60
-40
0
-20 -
TP-
20
40
60
rp-
FIG. 2. Ring puckering potential function with energy levels (left) and wavefunctions ylthietan, as determined by the flexible model.
(right) for 3-meth-
infrared spectrum is compared with the experimental one in Fig. 3. The model does not yield any appreciable intensity for the 1-O transition at 100.29 cm-’ as a result of the localization of the respective states in different wells. For the same reason, a very small transition moment should still be obtained when the expansion of the dipole moment is taken to higher orders. This argument does not apply, however, to the double-quantum transitions 9-7 through 13- 11 near and above 120 cm-‘. The respective observed absorptions are considerably larger than expected from Eq. (6) and may well indicate significant higher order terms in the expansion of the dipole
30
44
58
72
100 114 86 WAVEN UMBERS
128
142
156
FIG. 3. Far-infrared spectrum of 3-methyhhietan (I). Bars indicate calculated transitions with approximate relative intensities derived from the flexible model. The units for the abscissa are centimeters-‘.
460
CAMINATI
ET AL.
moment. In the potential function, higher order contributions were tentatively introduced by including a term proportional to (T/T~)(1 - (T/TO)‘) and a term of the type (~/r,,)~( 1 - (T/TO)~)~.The respective parameters turned out to be insignificant as their values were in the order of only a few centimeters-’ with standard errors larger or similar. Reevaluation of the Far-Infrared Spectrum The intensities of the microwave lines arising from rotational transitions in the puckering excited states indicate that the earlier far-infrared analysis is incorrect (I). The comparable essential information which would have provided details of the transitions below the inversion barrier was not available from the far-infrared spectra. Therefore, using the microwave data as a guide, the puckering separations were recalculated with the one-dimensional “rigid” Hamiltonian employed previously (I). The reduced mass in the kinetic energy was held fixed as before, and the quadratic, cubic, and quartic potential function constants varied to best fit the assigned infrared absorption bands. The results are compared with the flexible model in Table VI and with the previous values in Table VII. In order to achieve reasonable agreement with the microwave data, it is necessary to know confidently the assignment of at least two transitions below the inversion barrier. In terms of their effect upon the potential function and the likelihood of finding them in the far-infrared spectrum, we chose either the 1-O or the 2-O transition plus the 5-4 transition. The proper choice of one from the 1-0/2-O pair critically affects the separation between the energy minima which in turn determines the relative intensity of the two transitions. As before, the absorption at 110.30 cm-’ was taken as the most appropriate candidate. The calculated 5-4 separation then varied from 35 to 55 cm-’ depending on the use of either 1-O or 2-O. The most reasonable agreement with the microwave intensity measurements was obtained when in addition to the transitions from 7-6 upward, 2-O was assigned to the 110.30 cm-’ absorption and 5-4 together with 7-6 to the apparent doublet with an average peak intensity at 52.04 cm-‘. The results of that fit are listed under calculation I in Table VII. For calculation II, one minor change and one additional assignment were incorporated. The 5-4 and 7-6 transitions evidently are close in energy which suggests that they could be assigned separately to the two components of the doublet. This was done for calculation II, although the possibility that one of the two peaks arises from the 7-6 transition in an excited state of another low-energy vibration cannot be excluded. The 6-5 separation appears to be relatively insensitive to the inclusion of the 5-4 transition, hovering near 40 cm-‘, suggesting that the weak absorption at 40.62 cm-’ could be assigned accordingly. The effects of these two additions are minor. It is worth mentioning that the fit of the far-infrared data reflected in Table VII is not unique. A second solution using transitions the same as those for calculation I is possible with a standard deviation of 0.50 cm-‘, giving an inversion barrier of 275.6 cm-’ and a second well depth of 116.8 cm-‘. In this case, the intensity formerly in 2-O has shifted to 1-O calculated at 106.65 cm-‘. From the point of view of the farinfrared spectrum, therefore, the two solutions would be indistinguishable, since the band origin of either transition may be appreciably different from the band maximum. The agreement between the results of the flexible model and the “rigid” Hamiltonian
MICROWAVE INVESTIGATION
461
OF 3-METHYLTHIETAN
TABLE VII Observed and Calculated Puckering Transitions and Potential Function Constants for 3-Methylthietan Transitiona "u + "1
Previousb
Revised
111.05
1 :
0 1
4 5 6 7 8 9 10 11 12 13 14
: 4 5 6 7 8 9 10 11 12 13
52.34 57.62 62.50 66.71 70.49 74.12 77.10 79.99
2 3
0 1
95.54
45 ;
: 4
0 9 10 11 12 13
: 7 8 9 10 11
51.35 40.62 52.73 57.62 62.50 66.71 70.49 74.13 77.10 80.00 110.30
Std. dev. of obs./caf'
Second well depth/cm-' Equ.-ax. energy diff./cml
previousb
110.27 96.37 93.71 68.40 90.70 91.61 110.03 119.41 128.71 136.89 144.32 151.18
157.17 95.58 85.00
Previous
I 91.20 19.08 77.29 16.42 51.98 38.14 52.89 57.14 62.27 66.51 70.38 73.94 77.24 80.33
111.04 46.13 49.45 35.55 38.69 44.09 52.25 57.70 62.45 66.64 70.43 73.92 77.17 80.21
119.52 128.71 136.60 144.68 151.27
Potential function parameters e
Calc. Rel. 1nt.d
Calculated/car'c
Observed/car'
-I
II
lql
90.15 19.51 76.00 16.86 51.22 39.70 53.13 57.50 62.56 66.79 70.65 74.19 77.49 80.57 109.65 95.50 92.85 68.07 90.91 92.82 110.63 120.06 129.35 137.43 144.84 151.68
lq21
Iq'l
0.000 0.000 0.041 0.15 0.60 0.79 1.00 0.94 0.84 0.71 0.58 0.46 0.35 0.26
0.000 0.000 0.028 0.001 0.082 0.000 0.008 0.005 0.005 0.004 0.003 0.003 0.002 0.001
0.000 0.000 0.025 0.022 0.19 0.18 0.30 0.31 0.31 0.29 0.26 0.22 0.18 0.15
0.73 0.43 0.72 0.22 0.16 0.000 0.003 0.001 0.001 0.000 0.000 0 .ooo
1.00 0.39 0.77 0.26 0.51 0.43 0.55 0.51 0.46 0.40 0.33 0.27
1 .oo 0.27 0.67 0.062 0.17 0.002 0.018 0.011 0.011 0.009 0.007 0.006
-II
0.15 -31.81
0.42 -34.31(27)
0.50 -34.02(29)
1.683 1.205 310.7 144.3 166.4
0.9318076) 1.245/8) 289.9 193.8 96.13
0.9352(197) 1.247(9) 285.1 190.0 95.11
i Quantum number labels for the upper (u) and leer (1) puckering energy levels. See ref.(l). ",Transitions that are underlined were included in the least-squaresfitting process. Contributions to the relative intensities for Calc. II calculated according to Iq"J = cu)q"ln>, e q the dimensionless coordinate, corrected for the Boltzman factor. Calculated with a one-Gwnsional Hamiltonian with the potential function V(q) = [V2/(mr)Iq2+ [Vs/(mr) ]q3 + [V,/(mr)*Iq4 , q the dimensionless puckering coordinate. Fixed parameters: reduced mass m = 100.0 u, harmonic oscillator frequency v = 100.0 earl, y = 4n*cv/h = 296.60 u-l nnr2, 80 harmonic oscillator basis functions.
is pleasing in all respects, including the calculated transitions and their relative intensities and the essential features of the potential function. The barrier height, second well depth, and energy difference between minima calculated with the rigid Hamiltonian (Table VII) compare to 293.1, 183.5, and 109.6 cm-‘, respectively, with the flexible model. The discrepancies between the transitions below the barrier, evident in Table VI, can be ascribed to the effects of the relaxation of the ring angles accompanying the puckering motion for which the flexible model compensates.
462
CAMINATI ET AL. CONCLUSIONS
The microwave spectrum of 3-methylthietan was analyzed, assigning rotational transitions for the ground state and for four excited states of ring puckering and two of methyl torsion. Utilizing this data together with the puckering energy separations derived from the far-infrared spectra, the flexible model (3) was used to determine three potential function parameters, three structural parameters, and three parameters expressing structural relaxation accompanying ring puckering. In this manner it was possible to reproduce the spacing between the energy levels of the puckering and methyl torsion vibrations and the variations of the rotational constants upon vibrational excitation and conformational change. While the majority of assignments of the farinfrared spectrum reported earlier (I) were confirmed, one crucial reassignment and one additional assignment, necessary to comply with microwave intensity measurements, altered the previously determined asymmetric potential function significantly. The combined analysis yields the following structural information for 3-methylthietan. The methyl group adopts the equatorial orientation in the lowest energy conformation. The axial conformer is higher in energy by lOO(17) cm-’ (1.2(2) kJ/mol) as evaluated from the rotational transitions. The potential energy minima of the two conformers are separated by 95 or 110 cm-’ with an inversion barrier of 285 or 293 cm-’ as determined, respectively, by fitting the far-infrared absorptions with an asymmetric potential function in a “rigid” one-dimensional puckering Hamiltonian or by the combined analysis of the microwave and far-infrared data with the flexible model. The puckering angles are 26.7“ and 25.2”, respectively, for the equatorial and axial conformers. The angle 6’between the C-CH3 bond and the ring CCC plane (see Fig. 1) is larger in the equatorial form by almost 5” than in the axial form. This might be surprising as CH3 - - - S repulsion should be expected to lead to a larger angle in the axial form. The present result given at the end of Table VI suggests a larger effect due to the repulsion between the methyl group and methylenic hydrogen atoms, which should favor a larger angle 0 in the equatorial form. Possibly the same type of interaction is also the cause for an apparent enhancement of methyl torsional barriers observed in the present and in related ring molecules (22, 23). The barrier hindering the internal rotation of the methyl group was determined as 1470(30) cm-’ (17.6(4) kJ/mol) for the axial conformer. Unfortunately, this high value precluded the measurement of the A-E doubling in excited puckering states, which could have been useful for investigating kinetic and potential energy coupling between the two motions, as was possible in other cases (6-10). ACKNOWLEDGMENTS Professor A. Trombetti, Director of the Istituto di Spettroscopia Molecolare de1 C.N.R., kindly allowed us to use the microwave spectrometers. ACF acknowledges the award of a fellowship from the Consejo National de Investigaciones Cientificas Y Tecnicas (CONICET) of Argentina. HW gratefully acknowledges financial support via an Operating Grant from the Natural Sciences and Engineering Research Council of Canada (NSERC). W. Caminati thanks Professor A. Bauder for having given him the opportunity to work in his group. RECEIVED:
July 7, 1987
MICROWAVE
INVESTIGATION
OF 3-METHYLTHIETAN
463
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