The Journal of Physical Chemistty, Vol. 83, No. 1 I, 1979
Microwave Spectrum of 3-Methyl-1-butene
studies of the coordination chemistry of GOase-Cu(I1) with CN- and F-12 and will be used to study the effect of modifying protein residues near the Cu(I1) site.
1427
(8) M. Eisenstadt and H. L. Friedman, J. Chem. Phys., 48, 4445 (1968). (9) G. Navon, R. G. Shulman, B. J. Wyluda, and T. Yamane, J. Mol. Blol., 51, 15 (1970). (10) A. S.Mildvan, J. S.Leigh, and M. Cohn, Biochemistry, 6, 1805 (1967). (1 1) J. M. Guo, C. Chang, N. C. Li, and K. T. Douglas, Biochemistry, 17, 432 (1978). (12) B. J. Marwedel, Ph.D. Thesis, State University of New York at Buffalo, 1978. (13) R. D. Bereman and D. J. Kosman, J . Am. Chem. Soc., 99, 7322 (1977). (14) L. D. Kwiatkowski, L. Siconolfi, R. E. Weiner, R. S. Giordano, R. D.
Acknowledgment. B. J. Marwedel gratefully acknowledges fellowships from the Allied Chemical Corporation and from the Graduate School, SUNY/Buffalo. We thank the National Science Foundation for support of this research (Grant No. BMS73-01248-A01) and for some of the NMR instrumentation used (Grant No. CHE 7506183-A02 to the Department of Chemistry, SUNY / Buffalo). We also thank our colleagues in the Bioinorganic Graduate Research Group for stimulating and helpful discussions.
Bereman, M. J. Ettinger, and D. J. Kosman, Arch. Biochem. Biophys., 182, 712 (1977). (15) D. J. Kosman, M. J. Ettinger, R. E. Weiner, and E. J. Massaro, Arch. Biochem. Siophys., 165,456 (1974). (16) H. G. Hertz, G. Keller, and H. Versmoid, Ser. Bunsenges. fhys. Chem., 73, 549 (1969). (17) H. P. Carr and E. M. Purcell, Phys. Rev., 94, 630 (1954). (18) S.Meiboom and D. Gill, Rev. Sci. Instrum., 29, 688 (1958). (19)A. Abragam in "Principles of Nuclear Magnetism", Oxford University Press, New York, N.Y., 1961,pp 289-312. (20) R. J. Kurland and B. R. McGarvey, J . Mag. Reson., 2, 286 (1970). (21) R. A. Dwek, "Nuclear Magnetic Resonance in Biochemistry, Applications to Enzyme Systems", Oxford University Press, New York, N.Y., 1973,Chapters 9 and 10. (22) N. Bloembergen and L. 0. Morgan, J . Chem. fhys., 34, 842 (1961). (23) B. P. Gaber, R. D. Brown, S. H. Koenig, and J. A. Fee, Siochlm. Siophys. Acta, 271, l(1972). (24) S.H. Koenig and R. D. Brown, Ann. N. Y. Acad. Sci., 222, 752 (1973). (25) Reference 19,pp 315-316. (26)The relaxation rates exhibit an approximately linear increase with for C, GOase concentration, C,, for C, less than about 7 X greater than M the dependence is nonlinear. Relaxation rates at the three frequencies are taken here to correspond to C, = 3 x 10-5 M. (27) R. R. Jesse and R. Hoppe, Z. Anorg. Allg. Chem., 428, 83 (1977).
References and Notes (1) D. Amaral, F. Kelly-Falcoz, and B. Horecker, Methods Enzymol., 9, 87 (1966). (2) G. A. Hamilton, J. DeJersey, and D. K. Adolf in "Oxidases and Related Redox Systems", Vol. 1, T. E. King, H. S.Mason, and M. Morrison, Ed., University Park Press, Baltimore, Md, 1973,pp 103-124. (3) R. D. Bereman, M. J. Ettinger, D. J. Kosman, and R. J. Kurland, Adv. Chem., 162, 263 (1977). (4) T. Vannegard in "Biological Applications of Electron Spin Resonance", H. M. Swartz, J. R. Bolton, and D. C. Borey, Ed., Wley-Interscience, New York, N.Y., 1972,pp 411-447. (5) B. J. Marwedel, R. J. Kurland, D. J. Kosman, and M. J. Ettinger, Biochem. Biophys. Res. Commun., 63, 773 (1975). (6) B. R. McGarvey and R. J. Kurland in "NMR of Paramagnetic Molecules", G. N. LaMar, W. de W. Horrocks, Jr., and R. H. Holm, Ed., Academic Press, New York, N.Y., 1973,pp 564-565. (7) R. G. Shulman arid K. Knox, J. Chem. fhys., 42, 813 (1965).
Microwave Splectrum, Internal Rotation, and Dipole Moments of 3-Methyl-I-butene' R. PI. Creswell, M. Pagitsas, P. Shoja-Chaghervand, and R. H. Schwendernan*+ Department of Chemistry, Michlgan State University, East Lansing, Michigan 48824 (Received November 20, 1978) Publication costs assisted by the National Science Foundation
Microwave rotational spectra have been assigned for species of 3-methyl-1-butene in which the vinyl group is trans and gauche to the isopropyl group. Rotational transitions have also been assigned in the first three excited states of the torsional motion of the vinyl group in the trans conformer and in the first two excited states of the corresponding torsional mode of the gauche species. From relative intensity measurements the torsional excitation energies have been estimated to be 90 f 10 and 104 f 10 cm-l for the trans and gauche species, respectively. The gauche-trans energy difference has been estimated to be 130 f 20 cm-l. The excitation energies and energy difference have been used to estimate the torsional potential constants. By analysis of Stark effects the dipole moments have been determined to be for the trans conformer pa = 0.312 f 0.003 D, p b =: 0 (assumed),p, = 0.071 f 0.042 D, and p~ = 0.320 f 0.010 D. For the gauche conformer they are pa = 0.367 f 0.004 D, pb 0, pc = 0.154 f 0.006 D, and p~ = 0.398 f 0.004 D.
Introduction During the past several years there has been considerable interest in the characterization and comparison of the potential functiions for the internal rotation of groups attached to the cyclopropane ring, to the ethylene oxide ring, and to the isopropyl group. Among the molecules in this class are those in which the attached atom is a double-bonded carbon atom such as the carbon atom in an aldehyde or vinyl group. The internal rotation in these molecules is of interest because of the possibility of conjugation between the attached group and the cyclopropyl or ethylene oxide ring. The corresponding molecules in which the same group is attached to an isopropyl group have been studied for comparison. The earliest comparison of this type followed the determination by
electron diffraction of the structures of cyclopropanecarboxaldehyde' and isopropyl~arboxaldehyde.~It was shown that isopropylcarboxaldehyde occurs in conformations with the CO bond eclipsing either a CC bond or a CH bond in the isopropyl group. These conformations are consistent with those found in CH3COX compounds4 and most RCH2COX molecule^.^ By contrast, cyclopropylcarboxaldehyde was found2 to occur as an almost 50:50 mixture of conformers with the oxygen atom cis and trans to the ring, and this result was later confirmed by microwave spectroscopya6 Since that time cyclopropylcarboxylic acid ~ h l o r i d e ,cyclopropyl ~,~ methyl ketone,'^^ and cyclopropylcarboxylic acid fluoridelo have all been shown to occur with cis and trans conformers, and therefore have a torsional potential which is dominated
0022-3654/79/2083-1427$01.00/00 1979 American Chemical Society
1428
The Journal of Physical Chemistry, Vol. 83,
No. 11, 1979
Creswell et al.
TABLE I : Comparison of Observed and Calculated Frequenciesa of Assigned Transitions in trans-3-Methyl-1-butene transition
u= 0
v= 1
u= 2
v=3
413 312 5,s 4"4 514 41, 51, 414 5,, 4,, 5,, 4,, b3, 4,, 5,, + 4,, 541 440 5,, 4,, 606 50, 61, 514 61, 51, 624 + 5*3 6,, 5,, 633 53, 634 -+ 533 64, 54, 643 54, 651 530 652 55,
26535.23(0.01)b 29679.94(- 0.01)
26624.02( 0.03) 297 07.48(0.00) 32992.71(- 0.07) 29075.52(- 0.01) 331 26.58( 0.01 ) 31291.37(0.02) 32055.08( 0.00) 31848.46( 0.00) 31807.66(- 0.03) 31801.75( 0.03) 35122.38(0.02) 39127.38(0.03) 34700.91(-0.01)
26712.90(- 0.02) 29734.00(- 0.01) 3309 1.02(0.02) 291 07.78( 0.00) 33261.57(0.01) 31367.23( 0.01) 32163.86( 0.00) 31944.81(- 0.01) 31904.44(- 0.03) 31898.04(0.04) 35146.86(0.00) 39224.55(0.00) 34734.13( 0.00)
26802.21(- 0.01) 29759.49(- 0.01) 33189.15(0.02) 291 39.36(0.00) 33398.00(- 0.02) 31443.15(0.00) 32 274.09 (0.01) 32041.91(0.02) 32002.04(- 0.02) 31995.07( 0.03) 35170.25(0.01) 39320.81(-0.01) 34766.37(0.00)
37344.00(-0.01) 38769.10(0.01) 38247.42(0.00) 38265.70(-0.01) 38239.24(0.00) 38143.60(- 0.05) 38143.20(0.04)
37427.09( 0.00) 38913.74( 0.00) 38362.02(- 0.03) 38386.19(- 0.02 ) 38357.53(0.01) 38258.55(- 0.03) 38258.06( 0.03)
37509.95(- 0.01) 39060.72(0.01) 38477.44( 0.01) 38507.90(- 0.02) 38476.86(0.02) 38374.34(- 0.05) 38373.82(0.04)
+
+ -
+
+-
+
+ -
-+
+
+ -
+
+
+ -
+
+
+
+
+-
29042.59(0.01) 32992.60(0.00) 31215.37(0.01) 31947.35( 0.00) 31752.54(-0.01) 31711.42(- 0.04) 31706.00( 0.04) 35096.88( 0.01) 39029.03(- 0.01) 34666.80(- 0.01) 39894.36(0.01) 37 260.57( 0.01) 38626.20( 0.00) 381 33.16( 0.00) 38146.03(- 0.01) 38121.61(- 0.01) 38029.23(- 0.06) 38028.91(0.07)
a All frequencies are in MHz. Estimated experimental uncertainty is I0.02 MHz. Observed minus calculated frequencies are in parentheses. Calculated frequencies based on the rotational constants in Table 111.
by a cos 2a term. On the other hand, an electron diffraction investigation of vinylcyclopropane'l was interpreted in terms of species with the vinyl group trans to the ring and rotated approximately 120' from the trans configuration. A microwave study12 confirmed only the trans conformer; no transitions from a second conformer were found. In the present work the microwave spectrum of 3-methyl-1-butene was studied and transitions were assigned to species with the vinyl group eclipsing the CH bond of the isopropyl group (referred to here as the "trans" configuration) and with the vinyl group rotated approximately 1200 from the trans configuration (the ''gauche" The = 0+ 1torsional excitation energies and the ground state energy difference of the two species have been evaluated by relative intensity measurements and used to estimate the first four coefficients in the torsional potential function.
Experimental Section The sample was obtained from the Chemical Samples Co., Columbus, Ohio, and used without further purification. The spectra were taken in the 18-40-GHz region with a Hewlett-Packard 8460 A MRR spectrometer. The J = 2 1 and 3 2 transitions in OCS (yD = 0.7152 DI3) were used to calibrate the effective electric field spacing of the sample cell for Stark effect measurements. Relative intensity measurements were made by recording pairs of transitions a t constant crystal current under conditions of low microwave power.14 For many of the transitions the peak intensities were measured and compared a t several pressures and Stark fields. All of the intensity measurements were made with the sample cell surrounded by dry ice. The temperature of the cell a t several points was measured by taping a Pt resistance thermometer to the cell walls. The temperature was taken to be the mean of the measured values (204 K).
- -
Microwave Spectrum The microwave spectrum of 3-methyl-1-butene in the 18-40-GHz region is relatively sparse with transitions of moderate intensity. The a-type transitions belonging to two species were easily identified by their frequencies and Stark effects. No b or c type transitions could be assigned for either species, presumably due to the small P b or y, components of the dipole moment. The two species were
Lcf
HLcA
/
H \
\H
Figure 1. Diagram of an approximate projection of trans-3-methylI-butene in its ac plane of symmetry. The angle a measures internal rotation about the indicated CC bond.
assigned to trans and gauche conformers on the basis of a comparison of their moments of inertia to those calculated for assumed structures. The structural parameters were transferred from values determined for propane15 and propylene.16 Figure 1 is a projection of trans-3-methyl1-butene in its ac plane of symmetry. The transitions for each of the species were accompanied by a single intense series of satellite lines which have been assigned to rotational transitions in the excited states of the torsional motion of the vinyl group relative to the isopropyl group. Precise frequency measurements were made for states up to u = 3 for the trans species, and up to u = 2 for the gauche conformer. The frequencies of the transitions for u = 0-3 for the trans species were fit to a Hamiltonian which contained fourth power angular momentum terms in the form described by Wats0n.l' Without the centrifugal distortion terms deviations between observed and calculated frequencies were as large as several megahertz. By contrast, the transitions for the gauche species were well represented by rigid rotor theory. Comparisons of the observed and calculated frequencies are shown in Tables I and I1 and the resulting rotational constants and derived moments of inertia are given in Tables I11 and IV.
Dipole Moment The Stark effects of several transitions for both transand gauche-3-methyl-1-butene were studied in order to determine dipole moments for the two species. In each case the observed slopes of plots of the frequencies vs. the
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
Microwave Spectrum of 3-Methyl-1-butene
1429
TABLE 11: Comparison of Observed and Calculated Frequenciesn of Assigned Transitions in gauche-3-Methyl-1-butene u= 0
v = l
28762.00( 0.14)b 28711.64( 0.17) 27 02 0.9 8( 0.17 ) 27674.28(0.11) 27524.00(0.13) 3117 2.26( 0.10) 35402.81(- 0.04) 30714.61(0.17) 36307.39(-0.03) 33524.21( 0.04) 34947.13(- 0.05) 34451.64(- 0.06) 34449.67(- 0.20) 34428.64(-0.15) 36831.20(- 0.08) 36584.74(- 0.04) 39876.56(- 0.19)
28766.47( 0.14) 287 14.60( 0.18) 27033.91(0.22) 27682.96(0.07) 27533.84(0.15) 31202.96(0.11) 35411.97(- 0.03) 30746.67(0.18) 36309.40(- 0.03) 33541.87(0.03) 34955.68(- 0.06) 34463.78(- 0.03) 34461.54(- 0.20) 34440.68(- 0.16) 3687 0.59(- 0.09 ) 36624.67(- 0.04) 39899.88(- 0.22)
transition
u= 2
28766.47(0.22) 27042.20(0.17) 27686.31( 0.13) 27538.55(0.15) 31229.7 1(0.09 ) 35416.17(-0.07) 30774.07(0.21) 36304.14(0.03) 335 54.17 (0.06) 34956.94(- 0.02) 34469.56(-0.04) 34466.89(- 0.18) 34446.25(- 0.17) 36905.07(- 0.12) 36659.16(- 0.02) 39917.12(-0.24)
Observed minus calculated frea All frequencies are in MHz. Estimated experimental uncertainty is i 0.02 MHz. quencies are in parentheses. Calculated frequencies are based on the rotational constants in Table IV. TABLE 111: Rotatioinal Constants, Moments of Inertia, and Second Moments for trans-3-Methyl-1-butene ~
parameter
~
u= 0
u= 1
v= 2
u= 3
7 536.335( 350)' 3550.987(24) 2741.614(26)
7536.561(368) 3567.316(30) 2742.475(30)
7536.938(256) 3583.788( 21) 2743.243( 22)
7536.950(250) 3600.419(22) 2743.938(22)
_ I -
A/MMz B/MHz C/MHz
Ialu
A2
Ib/u 8'
Iclu ' 4 2 PaalU A 2
A,' Pcclu A Pbb/U
Aj/kHZ AjK/kHz AK/kHZ bj/kHZ 6K/kHZ a
67.0586b 142.3199 184.3352
67.0566 141.6684 184.2773
67.0532 141.0172 184.2258
67.053 1 140.3659 184.1791
129.7983 54.5370 12.5217 0.6(2) 20.4(6) -26.8(944) 0.2(2) 8.5(54)
129.4446 54.8328 12.2239 0.5(2) 21.4(8) -43.2( 1030) 0.2(2) 6.4(66)
129.0949 55.1309 11.9223 0.6( 1) 22.2(6) -13.5(683) 0.2(1) (46)
128.7460 55.4332 11.6200 0.8(2) 22.9(7) 5.1(638)
Values in parentheses are two times the standard deviations.
TABLE IV: Rotational Constants, Moments of Inertia, and Second Moments for gauche-3-Methyl-1-butene parameter A/MHz BIMHz C/MHz
u= 0
u= 1
Assumed conversion factor is 505376 MH2.u A , . TABLE V: Stark Coefficients and Dipole Moments for trans-3-Methyl-1-butene
u= 2
7294.39(48)a 7280.47(50) 7268.91(56) 3914.90(2) 3913.03(3) 3916.06(2) 2879.23(2) 2883.36( 2) 2887.03(2)
Ib/u .kz I& A 2
69.2828b 129.0521 175.5245
69.4153 129.0903 175.2730
69.5257 129.1522 175.0507
Paa/u A 2 Pbb/u A 2 P c c / uA 2
117.6469 57.8776 11.4052
117.4740 57.7990 11.6163
117.3386 57.7121 11.8136
Ia/U A 2
0.1(1) 12.3(47)
4,, 422 62,
GZ4
a Values in parentheses are two times the standard deviations. b Assumed conversion factor is 505376 MH2.u 8 2 .
square of the field were fit by least squares to expressions which contained the squares of the components of the dipole moment as adjustable parameters. In addition, in each case the result was that Wb2 was found to be negative. For the trans species this is presumably because & = 0 by symmetry and the negative value of Fb2 was a result of experimental error. In the gauche species, however, it is expected that Wb # 0, and therefore the negative value of Yb2 is taken to mean that & , is very small. Thus, for each species the fitting of the Stark slopes was repeated with the assumption that y b = 0. The results of the fittings, including comparisons of observed and calculated Stark slopes, are shown in Tables V and VI. The dipole moments for the trans conformer are pa = 0.312 f 0.003 D,
+ -
+
+
+ -
322
s2, 524
1.09 1.10 4.16 4.16b - 1.04 - 1.05 -4.08 -4.08b 0.083 0.086 0.196 0.197 0.353 0.353 0.556 0.553 -0.080 -0.083 -0.182 -0.183 -0.318 -0.322 - 0.509 -0.500 = 0.312 ?: 0.003 D fib = 0 (assumed) p c = 0.071 c 0.042 D p~ = 0.320 t 0.010 D 1 2 1 2 2 3 4 5 2 3 4 5
a Units are MHz/(V/cm)2. These slopes were calculated from frequencies obtained by direct diagonalization of the energy matrix. The other slopes were obtained by second-order perturbation.
(assumed), pc = 0.071 f 0.042 D, and p~ = 0.320 f 0.010 D; for the gauche conformer they are y, = 0.367 f 0.004 D, pb 0, pc = 0.154 f 0.006 D, and p~ = 0.398
&=0
0.004 D. The total dipole moments of several compounds that contain a vinyl group were recently compared.12 If the present species are included in that comparison, it is found f
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The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
Creswell et al.
TABLE VI: Stark Coefficients and Dipole Moments for gauche-3-Methyl-1-butene transition 4 ~ 3
52,
523
f -
+
+-
3 ~ 3
423
422
M
(dvl de2)obsda
(dvl de2)calcda~b
2 3 1 2 3 4
0.305 0.314 0.746 0.742 1.509 1.515 0.878 0.852 0.383 0.378 0.088 0.094 2 -0.336 -0.350 3 -0.773 - 0.783 p a = 0.367 ? 0.004 D Pb p c = 0.154 i
U 60
wb
that the total dipole moments of the two conformers of 3-methyl-1-butene are closer to that of propylene (0.364 D)lS and methylallene (0.401 D)19 than to trans-vinylcyclopropane (0.498 D).12 I n t e r n a l Rotation Relative intensity measurements were made on several transitions in the ground and first excited torsional states of both species of 3-methyl-1-butene with the sample cooled in dry ice. Analysis of the relative intensities led to the following estimates of energy differences: E(t,u=l) - E(t,u=O)= ut = 90 f 10 cm-l, E(g,u=l) - E(g,u=O) = w g = 104 f 10 cm-l, and E(g,u=O) - E(t,u=O)= AE,, = 130 f 20 cm-l. As is usual with microwave intensity measurements, the uncertainty estimates for these numbers are based on the internal consistency of the intensity ratios. The excitation energies for the trans and gauche species were derived from relative intensity measurements on nine and eight transitions, respectively, whereas nine pairs of transitions were studied to obtain AEgt. The three energy differences together with an estimate of the equilibrium torsional angle for the gauche configuration may be used to estimate the first four potential constants in a Fourier expansion of the torsional potential energy, V
v = C(Vn/2)(1 n
-
cos ncy)
180
Figure 2. Plot of the variation of calculated values of A - A,, B - Bo, and C - Co with torsional angle a for 3-methyl-1-butene. Here, A o , Bo, and C, are constants for the trans configuration calculated for an assumed structure. The vertical scale is in MHz. The crosses mark the experimental values of A , - A,, B, - B,, and C, - C,.
0.006 D
Calculated with
I20
Q
/.LT= 0.398 t 0.004 D a Units are MHz/(V/cm)*. assumed to be zero.
A
0
(1)
In this equation cy is the torsional angle, which is assumed to be zero in the trans configuration, and the V, are the potential constants. Unfortunately, the determination of the equilibrium angle for the gauche configuration offered even more uncertainty than usual. If reasonable values of bond distances and angles are transferred from the known structures of propane and propylene and adjusted slightly, it is possible to compute moments of inertia and rotational constants which agree with those in Table I11 for the trans species. If then the rotational constants are calculated as a function of a , the plot shown in Figure 2 is obtained. The experimental rotational constants for the gauche conformer are indicated in the plot. It is evident that all one can say is that the equilibrium value of a is near 120". The fact that the three rotational constants for the gauche species do not indicate the same equilibrium angle is evidence for either some poor assumptions in the assumed structure for the trans species or a correlation between a and some other internal coordinate. We tried varying the two C-C-C angles and the C-C=C angle to improve the consistency of the predicted a for the gauche species. By adjusting cy and any two of the mentioned angles, the conclusion is always the same: the angles
increase and the torsional angle increases to greater than 120". This result is most simply interpreted by assuming that as the vinyl group rotates from the trans to the gauche configuration, a steric hindrance causes the molecule to open up. We changed each of the possible CC distances by 0.01 A and repeated the above calculation without changing the conclusion. The problem then is that if only the torsional angle is changed, the predicted torsional angle for the gauche conformer is less than 120° ( 1 1 2 O is the best compromise). On the other hand if the CCC angles are allowed to vary, the predicted gauche torsional angle is 122-125". As a result of this uncertainty, we kept the torsional angle at 120" and included a &5O uncertainty in this angle in the reported uncertainty in the torsional potential constants. To derive estimates of the torsional potential constants we followed the procedure of Quade and LinZ0in which the angle cy is assumed to be the only internal degree of freedom. The resulting kinetic energy expression may be written
2T = o + I w or
T = P+FP In these equations the transpose of the column matrix w is defined as w+ = (w,w,w,&)
and the transpose of the corresponding momentum matrix as
P+ = (P,P,P,P) The wg and Pg are components of the molecular velocity and angular momentum about the g axis, respectively, and p is the momentum conjugate to cy. The matrix F is the inverse of the matrix I/2. After substitution into the usual expression for the Hamiltonianz1 % = I-1/4p+FIl/ZPI-1/4+ V in which I is the determinant of I, and simplification, it is found thatz2 % = CCFggJ'gPgi g g'
+ C(PgFg, + Fg,Pg)P + PF,G + g
V'+
v
In this expression Fgg8,F,,, and Fa, are appropriately defined components of the 4 X 4 matrix F, V is the torsional potential energy, and V' is a multiplicative operator which remains from the evaluation of the quantum-me-
Microwave Spectrum of 3-Methyl-1-butene TABLE VII: Parameters Related to the Internal Torsion of the Vinyl Group in 3-Methyl-1-butenea F , = 1 . 6 7 8 cm-' w t = 90 t 10 cm-' w g = 104 F 1 0 cm-' F , = 0.022 cm-' F , = - 0 . 1 0 2 cm-' AEgt = I30 + 20 cm-' V,= 300 c 100 cm-' ( 0 . 8 6 i. 0.30 kcal/mol) V, = - 50 i. 100 cm-' (- 0.14 F 0.30 kcal/mol) V, = 750 + 7 5 (em-' (2.14 + 0.21 kcal/mol) V, = -100 i 5 0 cm-' (-0.29 + 0.15 kcal/mol) a
The Journal of Physical Chemistry,
Fourier expansion of V'leads to terms which simply add to the corresponding terms of V and lead to slightly altered values of the V,. The first three terms of the Hamiltonian lead, after application of perturbation theory, to an effective Hamiltonian for a rigid rotator with centrifugal distortion, from which the usual rotational energy levels are obtained. The last three terms of the Hamiltonian make up the torsional energy operator, as follows € 1 =~ PF,$ + in which the Fourier components of B are the sums of the V, and the corresponding components of V'. To obtain the torsional energy levels from H T we have used expressions given by IQuade and LinZ0and by Knopp and QuadeZ3for the moments of inertia as a function of torsional angle for a molecule with a planar top (here the CH=CHz group) attached to a frame with a plane of symmetry (here the (CH,),CH group). The moment of inertia matrix I was iinverted at 10" intervals from 0 to 180" and the resulting values of F,, were fit to a Fourier series of the form
Fa, = F,,"
-t Feu(')COS a
+ Fa,(') COS 2a
With the Fa,(,) given in Table VI1 the computed Fa, agree with those obtained by inversion of I to within 0.5% across the entire range of C Y . The torsional energies were obtained by direct diagonalization of a truncated matrix for HT. The basis functions used weire normalized even and odd linear combinations of the free-rotor functions, exp(ima). Twenty basis functions were found to give the lowest few levels to sufficient accuracy. The trans and gauche levels were identified by examination of the angular dependence of the squares of the wave functions. The potential constants were adjusted in this calculation to match the four pieces of information in Table VII. The effects of varying the input parameters on the calculated energies were analyzed to obtain rough estimates of the uncertainties in the derived potential constants. The results of all of this calculation were somewhat predictable. The torsional potential function is predominantly threefold with contributions from the other terms being considerably smaller than from the V , term. The V , obtained arle given in Table VI1 and a plot of the potential function is, shown in Figure 3. A final point concerns the possible splittings in the spectra of the gauche form arising from tunneling through the gauche-gauche barrier. No splittings were seen in the spectra up through u = 2. It is possible that there is a slight broadening of the u = 2 lines, but this is not certain. Of course, the greatest effect should be seen in b-type
1431
'A
I
-
2-
V/kcol /tnd
"a
-
/
/ ' 0
/ :
\
I_
See text for the definitions of the parameters
chanical kinetic energy operator after separating out the Pgand p dependent terms. It is found that
Vol. 83, No. 11, 1979
O
I
1
I
o 1
-
1482
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
J.
ring is difficult. The corresponding 1,2-epoxy-3-butene does not appear to have been studied by either electron diffraction or microwave spectroscopy. An electron diffraction study of vinylcyclopropane" was interpreted to favor a mixture of 3 parts trans to 1 part gauche a t 293 K, which would correspond to a 6.5:l ratio at 204 K. Here, trans refers to the vinyl group trans to the ring and the gauche conformer is rotated -120' from trans. A microwave investigationI2 failed to uncover transitions belonging to another species. Also, as indicated in the Introduction, a number of related cyclopropyl derivatives have shown trans-cis conformers rather than trans-gauche. However, if accepted, the electron diffraction results predict a gauche-trans energy difference of approximately 1 kcal/mol, which is larger than the 0.37 kcal/mol difference determined for 3-methyl-1-butene, The corresponding aldehyde compounds can be intercompared because all three compounds have been studied. An electron diffraction study of 2-methylpropanal (isopropyl~arboxaldehyde)~ showed that 10% of the molecules have the oxygen atom trans to the isopropyl group (aldehyde hydrogen trans to isopropyl hydrogen) and -90% of the molecules are gauche conformers (at 266 K). Electron diffraction2 and microwave6 studies of cyclopropanecarboxaldehyde predict an approximately 50-50 mixture ( 4 5 7 ~ ~ 5 5 % of )species containing the oxygen atom cis and trans to the ring. Thus, the predominantly threefold potential in the isopropyl compound becomes a predominantly twofold potential when the methyl carbons are joined to form a cyclopropane ring. Finally, in a microwave study of gly~idaldehyde,~~ only species with the aldehyde oxygen approximately trans to the ring were found. It was concluded that any other species, if present, occur with considerably lower concentration. Thus, in the aldehyde compounds there is an increase in the relative stability of the trans species in going from isopropyl to cyclopropyl to ethylene oxide group. A corresponding increase in the relative stability of the trans species occurs for the vinyl compounds in going from the isopropyl to the
F. Stevens, R.
F. Curl, and P.
S.Engel
cyclopropyl group. Comparison of the two groups of molecules shows that the relative stability of the trans species is greater in the vinyl compounds than in the aldehydes. We do not a t present have a consistent interpretation of these interesting results.
Acknowledgment. One of the authors (R.H.S.) acknowledges with gratitude his introduction to the field of microwave spectroscopy and the subject of internal rotation in the laboratory of Professor E. B. Wilson. References and Notes The research in this paper was supported in part by grants from the National Science Foundation. L. S. Bartell and J. P. Guiliory, J . Chem. fhys., 43, 647 (1965). J. P. Guillory and L. S. Bartell, J . Chem. fhys., 43, 654 (1965). (a) R. W. Kilb, C. C. Lin, and E. B. Wilson, Jr., J . Chem. fhys., 26, 1695 (1957); (b) L. Pierce and L. C. Krisher, ibid., 31, 875 (1959); (c) K. M. Sinnott, ibid., 34, 851 (1961); (d) L. C. Krisher and E. B. Wilson, Jr., ibid., 31, 882 (1959). S. S. Butcher and E. B. Wilson, Jr., J. Chem. fhys., 40, 1671 (1964). H. N. Volltrauer and R. H. Schwendeman, J . Chem. fhys., 54, 260 (1971). L. S. Bartell, J. P. Guillory, and A. T. Parks, J . fhys. Chem., 69, 3043 (1965). K. P. R. Nair and J. E. Boggs, J . Mol. Struct., 33, 45 (1976). P. L. Lee and R. H. Schwendeman, J. Mol. Spectrosc., 41, 84 (1972). H. N. Volltrauer and R. H. Schwendeman, J . Chem. fhys., 54, 268 (1971). A. de Meijere and W. Luttke, Tetrahedron, 25, 2047 (1969). E. G. Codding and R. H. Schwendeman, J . Mol. Spectrosc., 49, 226 (1974). J. S. Muenter, J . Chem. fhys., 48, 4544 (1968). A. S. Esbiti and E. B. Wilson, Jr., Rev. Sci. Insfrum., 34, 901 (1963). D. R. Lide, Jr., J. Chem. fhys., 33, 1514 (1960). D. R. Lide, Jr., and D. Christensen, J. Chem. fhys., 35, 1374 (1961). J. K. G. Watson, J . Chem. fhys., 48, 4517 (1968). D. R. Lide, Jr., and D. E. Mann, J . Chem. fhys., 27, 868 (1957). D. R. Lide, Jr., and D. E. Mann, J . Chem. fhys., 27, 874 (1957). C. R. Quade and C. C. Lin, J . Chem. fhys., 38, 540 (1963). E. B. Wilson, Jr., and J. B. Howard, J . Chem. Phys., 4, 260 (1936); E. E. Wilson, Jr., J. C. Decius, and P. C. Cross, "Molecular Vibrations", McGraw-Hill, New York, 1955. J. V. Knopp and C. R. Quade, J . Chem. fhys., 53, 1 (1970). J. V. Knopp and C. R. Quade, J . Chem. Phys., 48, 3317 (1968). S. Kondo, E. Hirota, and Y. Morino, J. Mol. Spectrosc.,28, 471 (1968). R. A. Creswell, P. J. Manor, R. A. Assink, and R. H. Schwendeman, J . Mol. Spectrosc., 64, 365 (1977).
N
Microwave Spectrum, Structure, Dipole Moment, and Internal Rotation of cis -Azomet hane James F. Stevens, Jr., R. F. Curl, Jr.,*
and Paul S. Engel"
Chemistry Department, Rice University, Houston, Texas 7700 7 (Received November 10, 1978) Publication costs assisted by the National Science Foundation
The microwave spectra of the ground state of cis-azomethane and of the ground and first excited torsional state of cis-azomethane-d6have been observed and analyzed (for the excited torsional state, Q-branch assignment only). Values for r(C-N) and LCNN of 1.48A and 119.3",respectively, are obtained from the rotational constants of these two isotopic species and an assumed r(N=N) of 1.254 A. Analysis, neglecting possible top-top coupling, of the internal rotation splittings observed in the ground state transitions of the h6 species gives a barrier of 1320 cal/mol, with the uncertainty determined by the inadequacy of the model. This internal rotation analysis also gives an outward tilt of the methyl groups of 6.7 3O. The dipole moment has been determined by measurement of the Stark effect to be 3.27 h 0.1 D.
*
Azodkanes (R-N=N-R) exist as two geometric isomers, of which the trans is by far more common. The usual syntheses of azoalkanes provide exclusively the trans isomer; moreover, this isomer is of lower energy content than cis. The only exceptional compound, difluorodiimide, is more stable in the cis configuration.2 Perfluoroazo0022-3654/79/2083-1432$01 .OO/O
methane was originally thought to exist in the cis form, but more recent work casts considerable doubt upon this concl~sion.~ Both experimental4 and theoretical5 results suggest that, for unhindered azoalkanes, the cis isomer lies about 8 kcal mol-' higher in energy than trans. Although photochemical isomerization of aromatic azo compounds
0 1979 American
Chemical Society
