The Journal of Physical Chemistry, Vol. 83, No. 22, 1979 2879
Torsional Spectra of Molecules with Two Internal C3" Rotors
(7) R. E. Penn and J. E. Boggs, J. Mol. Spectrosc., 47, 340 (1973). (8) H. Wolff and G. Gamer, Spectrochim. Acta, Part A, 28, 2121 (1972). (9) 0. Gamer and H. Wolff, Spectrochim. Acta, Part A , 29, 129 (1973). (10) B. M. Harney and F. A. Miller, Appl. Spectrosc., 24, 291 (1970). (11) J. E. Wollrab and V. W. Laurie, J. Chem. Phys., 48, 5058 (1968). (12) Y. S. Li, private communication. (13) M. Hayashi and K. Kuwada, J. Mol. Struct., 28, 147 (1975). (14) H. Imaishi and M. Hayashi, J . Sci. Hiroshima Univ., Ser. A , 38, 21 (1974). (15) J. R. Durig and Y. S. Li, J. Chem. Phys., 63,4110 (1975).
References and Notes (1) P. Groner and J. R. Durig, J . Chem. Phys., 66, 1856 (1977). (2) J. R. Durig, M. 0. Griffin, and P. Groner, J . Phys. Chem., 61, 554 (1977). (3) J. R. Durig, P. Groner, and M. G. Griffin, J . Chem. Phys., 66, 3061 (1977). (4) J. R. Durig and D. A. C. Compton, J. Phys. Chem., 83, 265 (1979). (5) J. R. Durig and D. A. C. Compton, J. Chem. Phys., 89, 4713 (1978). (6) J. R. Durig, D. A. C. Compton, and M. R. Jalliian, J. Phys. Chem., 83, 511 (1979).
Analysis of Torsional Spectra of Molecules with Two Internal C g vRotors. 16.+ Infrared and Raman Spectra, Vibrational Assignment, Methyl Torsional Potential Function, and Gas Phase Thermodynamic Functions of 2,3-Dimethylbuta-I ,3-diene J. R. Durlg" and D. A. C. Compton Department of Chemistry, University of South Carolina, Columbia, South Carolina 29208 (Received March 18, 1979) Publication costs assisted by the University of South Carolina
The vibrational spectra of gaseous, liquid, and solid 2,3-dimethylbuta-1,3-diene have been investigated between 4000 and 50 cm-', and a complete vibrational assignment is proposed. No spectral evidence was found for the presence of any high-energy conformer. Two series of bands in the far-infrared spectrum of the gaseous phase have been assigned to transitions involving the methyl torsional modes; the higher frequency series near 400 cm-l is due to difference bands of the Raman active methyl torsion and a higher frequency mode. The methyl torsional potential function has been calculated, leading to a value of 4.27 kcal/mol for the effective barrier height to internal rotation, and the reasons for this relatively large barrier have been discussed. Values for the gas phase thermodynamicfunctions have been calculated over a range of temperatures by using these data.
Introduction From studies on a number of compounds which have two internal C3usymmetric rotors on a common atom, such as dimethyl ether,l it has been shown that the two torsional fundamental modes are strongly coupled and that the resulting torsional vibrations can only be satisfactorily explained by using a two-dimensional treatment of the torsional potential function. These studies have recently been extended to compounds where the methyl tops are separated by one bond length, such as for n-butaneS2From the results it was shown that the methyl torsional vibrations are also coupled for this molecule. An interesting consequence of separating the methyl tops by one bond length is that an asymmetric torsion (around this new bond) is present, which not only gives rise to conformers of different energy but also was found to interact with the methyl torsional modes in ethyl methyl ether3 and nbutane.2 Both of these compounds exist as a mixture of low energy s-trans and high-energy gauche conformers. In both cases the methyl torsional barrier of the gauche conformer was observed to be higher than that of the s-trans conformer; this was attributed to steric hindrance between the methyl rotors in the gauche conformer. The molecule 2,3-dimethylbuta-l,3-diene has two methyl rotors separated by one bond length, but in this case each methyl rotor is also joined to an unsaturated carbon. The most stable conformer has been established as s-trans by an electron diffraction s t ~ d y This . ~ is in agreement with earlier vibrational and rotational studies from which it was 'For part 15 see J. Phys. Chem., previous article in this issue. 0022-365417912083-2879$01 .OOlO
concluded that the structure must be C 2 h due to the lack of coincidence between the infrared and Raman spectra6 as well as the lack of a microwave spectrum! In a number of studies including measurement of the dipole moment7 and a variable temperature8 study of the vibrational spectrum it has been postulated that a significant concentration of the high-energy conformer is present at room temperature. However, no evidence has been given for the structure of this high-energy form which may be s-cis like or skewed buta-1,3-dieneg and 2-methylbuta-1,3-dienel0 out-of-plane by methyl group interactions to a gauche conformation. The published vibrational spectra on 2,3-dimethylbuta-l,&diene have not contained enough data for a full assignment of all the fundamental modes. Harris and Witkowskill assigned bands to the low-frequency fundamentals in a number of conjugated compounds by using their far-infrared spectrum of the gaseous phase and previous Raman data8 for liquid 2,3-dimethylbuta-1,3diene, but they had no Raman depolarization data to aid their assignment. A full assignment was later attempted by Tarasova and Sverdlov,12who performed normal coordinate calculations to assign the available spectral data, but they were hampered by poor data, much of which was recorded before 1960 and did not include the infrared spectrum of the gaseous compound. Consequently, a number of modes were not observed, notably the torsions. In a recent spectroscopic studylo of 2-methylbuta-1,3diene, methyl torsions due to both the s-trans and highenergy s-cis conformers were observed, and the barrier to internal rotation of the s-trans methyl torsion was cal0 1979 American Chemical Society
2880
The Journal of Physical Chemistry, Vol. 83, No. 22, 1979
I
I I
J. R. Durlg and D. A. C. Compton 1
I
I
1 I
I
I
I
I
1
I
I I
I
3000
2500
2000
1500
1000
500
I
I
1
I I
I
I
I
WAVENUMBER (CMS)
Figure 2. Infrared spectra of 2,Wimethylbuta-1&diene between 3200 and 300 cm-': (A) gas at 20 torr pressure and (B) solid condensed onto a cold window. I
1
C
1 l ~ ,
,!' 11
1
-
-.
+3000
i
I1
d
-
-_
i
~
111
I b
I
1500 1000 500 WAVENUMBER (CW1)
Figure 1. Raman spectra of 2,3dimethylbuta-l,3diene between 3200 and 50 cm-': (A) gas, (B)liquid, and (C) solid.
culated to be higher than that of the s-cis conformer. This difference was attributedlO to steric hindrance in the strans conformer and resulted in a larger concentration of the s-cis conformer than was calculated for buta-l,&diene where this steric hindrance was absent. The dimethyl compound should therefore have an interesting torsional potential function due to this steric hindrance which would probably be present in the high-energy conformer as well as in the s-trans conformer. This study was therefore undertaken in order to examine the evidence for the presence of the high-energy conformer, complete the vibrational assignment, and characterize the torsional potential functions of 2,3-dimethylbuta-l,3-diene. Experimental Section
2,3-Dimethylbuta-1,3-diene(99%) was obtained from Chemical Samples, Co., Columbus, Ohio, and was purified with a low-temperature sublimation column. Traces of water were removed by using activated molecular sieves. Raman spectra were recorded by using a Cary Model 82 spectrophotometer equipped with a Spectra Physics 171 argon ion laser tuned to the 514.5-nm line. Gaseous samples were held in standard Cary multipass cells at the vapor pressure of approximately 135 torr. Spectra were recorded by using 2 W of laser power at the sample and spectral bandwidths between 2 and 5 cm-l. Liquid samples sealed in capillary tubes were examined at various temperatures ranging from room temperature to just above the freezing point with a Harney-Miller13 apparatus. Solid samples were examined by freezing the low temperature liquid slowly with careful annealing. Typical experimental conditions for the spectra of the liquid and solid were 500-mW laser power and 4-cm-l spectral bandwidth. Spectra of gaseous, liquid, and solid samples between 3200 and 50 cm-l are shown in Figure 1. Mid-infrared spectra of gaseous and solid samples were recorded by using a Perkin-Elmer 621 spectrophotometer between 4000 and 300 cm-l. Gaseous samples were ex-
400
300 200 WAVENUMBER (CM-l)
100
Figure 3. Far-infrared spectrum of gaseous 2,3dlmethylbuta-l,Wiene between 450 and 50 cm-' recorded by using (A) I-m pathlength and 135-torr sample pressure, and (B) 12-cm pathlength and 50-torr pressure. The arrows point to spectral artifacts.
amined over a range of pressures in a 10-cm cell fitted with CsI windows. Solid samples were prepared by condensing the vapor onto a CsI plate maintained at 20 K by using a Cryogenic Technology, Inc. Spectrim cryostat equipped with a Lake Shore Cryotronics Model DTL-500 highprecision temperature controller, and the samples were annealed carefully. Spectra of gaseous and solid samples between 3200 and 250 cm-l are shown in Figure 2. Spectra of the liquid and solid samples were also recorded by using a Perkin-Elmer 580 spectrophotometer. Liquid samples were held in a Specac variable-temperature accessory equipped with KBr windows, and examined over a range of temperatures from room temperature to the freezing point. Samples were frozen and carefully annealed to give the best spectrum of the solid. Far-infrared spectra of gaseous samples were recorded by using a Digilab FTS-15B Fourier transform interferometer fitted with a 6.25-pm mylar beam splitter. The samples at several pressures up to the ambient vapor pressure were held in 12-cm or 1-m pathlength cells fitted with polyethylene windows. Interferograms for both the sample and empty reference cell were recorded 3000 times, averaged, and transformed by using a boxcar apodization function to give 0.5-cm-l resolution. The spectrum between 450 and 50 cm-l is shown in Figure 3. Results Close examination of the spectra of gaseous, liquid, and solid 2,3-dimethylbuta-1,3-diene showed no significant differences which could be attributed to the presence of a high-energy conformer. In particular, only one very weak
Torsional Spectra of Molecules with Two Internal CBvRotors
band present in the fluid phases disappeared on freezing even though the spectra of the solid were annealed carefully. It was therefore concluded that no spectroscopic evidence could be found for the existence of a high-energy conformer. Vibrational Assignments. The established C 2 h structure4 of 2,3-dimethylbuta-1,3-diene has important consequences for the assignment of the spectra of the molecule. As a planar molecule the vibrational modes can be classified as either in-plane or out-of-plane (denoted here as ip and op, respectively); furthermore, the centrosymmetric structure results in application of the rule of mutual exclusion between the infrared and Raman active fundamentals. The 42 normal modes span the following representations: 14 A, (Raman, polarized, ip), 8 A, (infrared, C type band contour, op) 7 B (Raman, depolarized, op), and 13 B, (infrared, A/B hykrid band contour, ip). The tentative assignment given in Tables I and I1 has been made by using the newly recorded spectral data on gaseous, liquid, and solid samples of 2,3-dimethylbuta1,3-diene,with depolarization and band contour data from the gas phase. In such a large molecule, it is not possible to assign these frequencies accurately to specific modes without a full normal coordinate treatment so the vibrational descriptions offered can only be considered as approximate. Assignment of the modes was based on the previously reported assignments on buta-1,3-diene1°and 2-methylbuta-l,3-diene,1° along with consideration of the previously reported assignments for the dimethyl compound.11J2 A, Modes. The region of the Raman spectrum between 2900 and 3110 cm-l is very complex due to the large number of hydrogens present in the molecule, so the assignment of C-H stretching vibrations was carried out on the basis of band intensity and the assumption that those hydrogens on an unsaturated carbon could give rise to bands above 3000 cm-l. The band of medium intensity at 3096 cm-l in the liquid was assigned to the asymmetric CH2stretch. Although it was observed to be depolarized, this vibration was observed at the same frequency in and the penbuta-1,3-diene,1° 2-methylbuta-1,3-diene,1° ta-1,3-dienes14 and was observed to be polarized in the spectrum of cis-penta-1,3-diene. The methyl group vibrations are similar in frequency to those of 2-methylbuta-1,3-diene,1° and the strongest Raman line has been assigned to the symmetric CH3 stretch. The region between 1300 and 1500 cm-l is also complex and was expected to show the methyl group deformation vibrations and also the CH2scissors. The strongest Raman line in this region in the gaseous and liquid phases was observed to be polarized and was assigned to the =CH2 scissoring mode. On solidification, two sharp, strong lines were observed close together in this region which indicated that the B symmetric deformation had a similar frequency. T i e asymmetric and symmetric methyl deformations were assigned to the bands at 1471 and 1385 cm-l, respectively, which are the normal frequencies for these modes. Difficulty was encountered in assigning the C-C stretch as well as the methyl and CH2 rocking modes since these modes are expected to interact strongly. Previous experience with the assignments of buta-1,3-diene1°and its monomethyl derivatives1°J4has shown that the frequencies of these modes are quite variable. On the basis of their intensities, the bands at 1025 and 726 cm-l have been assigned as the symmetric =C-C= and C-CH, stretches, respectively, even though these frequencies are much lower
The Journal of Physlcal Chemlstty, Vol. 83,No. 22, 1979 2881
than those observed for the corresponding vibrations in similar compounds. The CH2 rock was assigned to the weak band at 970 cm-l which is close to the 985-cm-l frequency observed for this motion in butadiene.1° The methyl rock was more difficult to locate and was finally assigned to the weak band at 1341 cm-l, although this frequency was higher than observed in similar compounds. It is possible that the strong band at 1025 cm-l and the weak band at 1341 cm-l could be reversed in assignment, but the stretch is more likely to be the stronger band. Harris and Witkowskill assigned the two A skeletal bending vibrations to bands at 405 and 552 cm-5 and the B, bending modes to bands at 496 and 727 cm-l. Examination of Table I shows that these assignments must be reversed in order to explain the depolarization results. Also their assumption that only two A, modes would be observed below 850 cm-' was also probably optimistic because the 726-cm-l band has been previously assigned12 to a C-CH3 stretch which is at an unexpectedly low frequency. The two A bending modes have been assigned by Tarasova and bverdlov12to the band of medium intensity at 491 cm-l and the weak, broad band at 256 cm-' and there is no reason to alter this assignment. A, and B, Modes. These vibrations were easily observed as C type bands in the infrared spectrum of the gas (A,) and as depolarized Raman bands (B,). The modes occurring above 800 cm-l are pairs of similar vibrations and were observed to have similar frequencies. The only noteworthy point is that the band contour of the vi7 band was better described as A type; however, there were no other similar bands observed to compare this with, and no other C type bands in this region to assign this mode to. The A, bends were observed as sharp C type bands at 656 and 327 cm-' but the corresponding B, modes were not as well defined because of their depolarized nature. Previous1y,12the broad band near 400 cm-l was assigned to one of these B bends, while the other was assigned to a band at 689 cm-g . We did not observe the latter band, and have assigned the band at 553 cm-l in the liquid phase to this mode, even though this band is not observed in the gas. The out-of-plane torsions will be discussed later in a separate section. B, Modes. Assignment of these modes was simplified by comparison with the Ak modes, because the A, and B, modes have similar descriptions except for the =C-C= stretch (4).The B, modes above 950 cm-l all have similar frequencies to their 4 counterparts except for the methyl rock which is assigned to the weak band at 1075 cm-l, much lower than the 1341-cm-l band. The C-CH3 stretch B, is assigned to a band of medium intensity observed in the spectrum of the solid at 920 cm-l, which is hidden by the very strong =CH2 wag (A,) in the fluid phases. This frequency is very different from the 726-cm-' band of A, symmetry and it is likely therefore that the C-CH3 stretch (A,) and methyl rock are interacting more strongly than the B, modes which have similar frequencies in related compo~nds.~~J~ The low-frequency bends (B,) are also similar in frequency to their counterparts of A, symmetry. Harris and Witkowskill noted that a number of conjugated compounds all have an in-plane bend between 200 and 300 cm-l, but that the buta-l,&dienes this mode is very weak and could not be observed in the dimethyl compound. On this basis, the very weak band at 272 cm-l in the gaseous phase has been assigned to the ~ 4 vibration. 2 The corresponding modes in buta-1,3-diene and 2-methylbuta1,&diene were observedlOJ1as weak bands at 300 and 288
2882
J. R. Durig and D. A.
The Journal of Physical Chemistry, Vol. 83, No. 22, 1979
C. Compton
TABLE I: Observed Vibrational Spectrum of 2,3-Dimethylbuta-l,3-diene Raman infrared gas cm-1 re1 into
liquid
--cm-l re1 inta ---
3109
m, br, d p
3096 m , d p
3065 3049 3019 3011 2991 2983 2968 2953
vw w,p w,sh,p s, p w,sh,p m,p w,sh,dp w,p
3055 3044
2930 2908 2876
vs, p w,p w,p
2916 2900 2863
1655
w,sh,p
1653
1633
vs, p
1 6 3 1 vs, p
1480 1471
vw w
1447 1414 1385
w
1341 1309
1025 970
726
s
3056 3038 3011 3008 2984 2974 2947
vw
vs,p vw,sh w,p
2916
vs
2863
vw
w,sh,p
1656
w
1628
vs
1586
vw
1473
w
vw,p w,sh,p
3010 s , p 2974 m , d p 2950 w , d p
1468 w , p
w w, sh m m m s
s
w w vw
1339 w , p 1312 v w , p
1342 1325
w w
w,p
m,p vw, br
495 491 487
vw, sh, d p m,p vw,sh,dp
w,dp
1022 s , p 964
m,p
729 m , p 657 w , p 551 w , d p
1025 970
732 673 556
w
vw,dp
139 125 107
vw,p vw,p vw,p
cm-' re1 inta cm-l re1 inta
s, A
3094
m
3093
3011
vw
3012
w
3012 W
2984 2961
vs,A s,C
2976 2951
s
2973 S 2943 S
2932
m
2908
w
2929 2915 2895
1800 m
s
1794
m,B
1790
m
1640
vw,sh
1635
vw
1605
s,B
1600 s
1457 1447
w,A s,C
1386 1377 1250 1205 1183 1075
m W
w, sh
1600 S 1585 w, sh
1450 s 1442 w , s h
1454 vw, sh 1448 S 1435 w, sh
s,A m,B
1384 m , s h 1374 s
1388 S 1374 S
w vw,sh m,C w,br
1272 1210 1181 1089 1036
w w m vw w
1250 1220 1186 1109 1039
w, br
1000 w
vw m w w
w,B
998
w
897 894 754
vw,sh vs,C vw
915 895 757
w,sh
vw
920 m 895 vs 725 vw
657
w,C
660
m
663
562
vw
553
w
M
Bu
Bu 43
m vw w
AU Ag
998
w
assignment
m
s
m
Bu
Au A, AU
B, '14
493
m,dp
497
m
A, v21
403
w,dp
403
225
vw,dp
234
w,A w, A
470
m
471 468 463 41OC 400
vw w,C vw, br
420 403
vw vw
368 328
vw, br m,sh
365
w,sh
327 325
m,C w,sh
327
m
324
w,sh
322
w,sh
272
vw,A
470 m
375
vw
338 s
+
v42
hot band of 4 7 1 cm-' hot band of 4 7 1 cm-'
-
'19
B, AU
hot band of 327 cm-a 313 271
vw
w
221 vw
w,C
'7.9
hot band of 327 cm-'
vw 215c
+
% I
'I9
w
330 vw,dp
256
solid
3104
m
1412 1403 1384
s,p
liquid
cm-1 re1 into cm-1 re1 in@ 3094
1440 w , d p 1408 s , d p 1378 m , p
s
654
392
solid
220
Bu
A%
Au
vw 2 + 0 ( 2 x Au) 3-1 4-2
91 78
s
45
vs
w,sh 70
vw,br
lattice mode lattice mode AU lattice mode
Torsional
Spectra of Molecules with Two Internal CSvRotors
The Journal of Physical Chemistry, Vol. 83, No. 22, 7979 2883
Footnotes t o Table I : a Abbreviations used: s, strong; m, medium; w, weak; v, very; p, polarized; dp, depolarized; sh, shoulder; br, broad, A, E, and C refer t o gaseous phase band contours in the gaseous phase. For more detailed analysis of the complex absorptions in the far-infrared spectrum of the gaseous phase between 430 and 405 and 215 and 190 cm-' see Table 111. TABLE 11: Frequencies (cm-' ) and Approximate Descriptions for the Fundamental Modes of 2,3-Dimethylbuta-1,3.diene approximate description
freq, cm-'
Ag asymmetric =CH, stretch symmetric =CH, stretch asymmetric CH, stretch symmetric CH, stretch symmetric C=C stretch asymmetric CH, deformation symmetric =CH2 scissor symmetric CH, deformation symmetric CH, rock =C-C= stretch symmetric =CH, rock symmetric C-CH3 stretch symmetric bend symmetric bend
3109 3011 2983 2930 1633 1471 1414 1385 1341 1025 970 726 491 2 56
AU
asymmetric CH, stretch asymmetric CH, deformation asymmetric CH, rock asymmetric = CH, wag asymmetric bend asymmetric bend asymmetric CH, torsion =C-C= torsion
B,
symmetric CH3 stretch symmetric CH3 rock symmetric CH, deformation =CH, twist symmetric bend symmetric bend symmetric methyl torsion
2961 1447 1183 894 657 327 21 5 7 3a 2968 1447 1414 895 551b 392 247a
BU
asymmetric =CH, stretch symmetric =CH, stretch asymmetric CH, stretch symmetric CH, stretch asymmetric C=C stretch asymmetric CH, deformation asymmetric = CH, scissor symmetric CH, deformation asymmetric CH, rock asymmetric =CH, rock asymmetric C-CH, stretch asymmetric bend asymmetric bend
3104 3011 2984 2932& 1605 1457 1386 1377 1075 998 897 471 27 2
Fundamental frequency calculated from torsional over tone or difference band. b Liquid phase frequency.
cm-l, respectively, and the bends in the dimethyl compound should be at lower frequencies. The assignment of the Raman mode to the broad band in the gaseous phase a t 256 cm-l can only be tentative since the nearest band in the liquid phase is at 225 cm-l which indicates a substantial shift in frequency between the phases. However, good evidence is found for the assignment of the 256- and 272-cm-' bands as fundamentals since pairs of bands in the 1650- and 490-cm-l region can be assigned as combination bands involving these two modes. Torsional Modes Asymmetric =C-C= Torsion. An earlier attemptll to locate the asymmetric torsion failed which would indicate that this mode is very weak. Fateley et al.15 predicted a
frequency of approximately 80 cm-l for this mode, and close examination of the far-infrared spectrum of the gas in this region (Figure 3) revealed a very weak, broad, and featureless absorption centered at 70 cm-'. The shape of this band is not C type as expected, but it closely resembles the band corresponding to the similar motion in strans-n-butanea2 It must be stressed that the observed value of 70 cm-l is in the region of absorption of the polyethylene windows which results in low sensitivity in this part of the spectrum. The low-frequency Raman spectrum of the gas was more revealing. A broad polarized band was observed between about 160 and 90 cm-l, and when the spectrum was scanned more slowly at 2-cm-l bandwidth very weak Q branches were observed at 139,125, and 107 cm-l. These bands decreased in intensity with decreasing frequency, and they were assigned as two-quantum transitions of the asymmetric torsion. Methyl Torsions. The presence of two methyl groups gives rise to two methyl torsional motions, the A, and B, modes which are asymmetric and symmetric to the inversion center, respectively. In a recent study of n-butane2 it was observed that the infrared active mode was the lower frequency torsional series. Since both molecules belong to the same point group, it was expected that the infrared active methyl torsions of 2,3-dimethylbuta-l,&dienewould also be the lower frequency series. The internal Hamiltonian for a C2h molecule with equivalent tops has previously been derived' as where V(70,Tl) = '/2[V30(l - COS 370) + V60(l - COS 670) + v 0 3 ( 1 - COS 371) + vo&l- COS 671) f V,,(cos 3~~cos 3~~- 1) + V3,'sin 3~~sin 3711 In the above expression the following restrictions apply for the C2hcase: V30 = Vo3, v 6 0 = Vos, and g44 = g55. The high barrier torsional levels, (vu), have been shown1 to split into four sublevels according to rOOuluz ylo rlh e y12q where ul is + or - for u even or odd, respectively, and u2 is also + or - for u even or odd, respectively. D is the limiting vibrational quantum number of the infrared active mode. I'oouluz is a one-dimensional representation, and rlZUz are two-dimensional, and Pois fourfold degenerate. The symmetry selection rules for the coupled methyl torsional transitions of 2,3-dimethylbuta-1,3-dieneare presented in Table 111. Examination of this table shows that the one-quantum transitions belong to the A, (lowfrequency series) and B, modes, whereas the two-quantum transitions of both series occur as A, active bands. Transitions "vertically" up the well, such as 11 00, belong to the B, representation. The kinetic coefficients,g"A, etc., used in the calculations were derived from the molecular structure proposed by Aten et al.; on the basis of their electron diffraction study. These values are given in Table V. The A, torsion was assigned to the series of bands observed in the spectrum of the gaseous phase at 214.5 cm-l and falling to lower frequencies. The B, mode was not observed directly in accord with our observations on s-trans-n-butane2 where no one-quantum transitions due +-
2884
The Journal of Physical Chemistry, Vol. 83, No. 22, 7979
J. R. Durig and D. A.
C.Compton
TABLE 111: Selection Rules for the Methyl Torsional Transitions ( u , ' u , ' + u , u 2 )of 2,3-Dimethylbuta-1,3-dieneU species operator Raman infrared
A,
(COS
3T0 f COS 3T1) polarized inactive
-
~'ooulu2
r l "+.+
~ 0 0 0 , 0 ,
y10
AU (sin 3~~ + sin 3r1) inactive C-type yOOU,+
l-10
c-.)
1~000~-
yl"
yllol
H yll'Jl
r1IuI H
ylz0,
H r1*02
r12t
rlz-
B,
(sin 3~~ -- sin 3r1) depolarized inactive yOO+U,
-
BU (cos 3~~ - cos 37,) inactive AIB hybrid
roo-0,
roo+-
--
roo-roo-+
ylo ylQ y l l + +.+ y l l -
y l o w p10
r l * O z w r1202
rlZ+
rll+
yllr12-
0 , is t or - when u , is even or odd, respectively, whereas u 2 is + or - when u , is even or odd, respectively. Transitions involving the I?'' or rI1sublevels are weakly active where the column head says "inactive". These selection rules are valid for any C*h molecule which has the C, axis identical with the C principal axis and two coupled methyl torsional modes.
TABLE IV: Observed Far-Infrared Frequencies (in cm- ) Assigned to the Methyl Torsional Transitions of 2,3-Dimethylbuta- 1.3-diene derived freq obsd re1 for B obsd freq int" mode% assignment calcd 407.8 m 248.9 excited state transition 409.9 vs 246.8 01 + 00 1.8 411.3 m 245.4 excited state transition 413.2 W 243.5 excited state transition 415.2 S 241.5 excited state transition 418.1 m 238.6 excited state transition 419.5 m 237.2 excited state transition 428.8 W 231.9 excited state transition 214.5 vs 10 +- 00 4.3
211.8 209.8 208.7 207.1 205.6 202.6 199.7 196.6 193.0 180.7 179.4 178.2 173.2
S
20 10 30 + 20 40 + 30 50 +- 40 21 + 11 11 +- 01 12 + 02
0.5 -1.4 - 0.6 -3.1 0.4 - 3.7 - 0.9
excited state transition excited state transition excited state transition 02 01
- 3.6
+-
m W
vw W
m W
vw vw
vw vw
vw vw
229.2 230.5 231.7 236.7
+-
a Abbreviations used: vs, very strong; s, strong; m, medium; w, weak; vw, very weak. b The frequencies for the u Z 9B, methyl torsion were calculated by using a frequency of 656.7 cm-' for u I O .
to the methyl torsions were observed in the Raman spectrum. Most methyl torsions are weak in the Raman effect and presumably the symmetric modes in C 2 h molecules have a minimal effect on the polarizability tensor. In the infrared spectrum of the gaseous phase near 410 cm-l, a number of relatively weak, sharp bands were observed as a complex pattern, as shown in Figure 3. The strongest band was observed at 409.9 cm-l, and an apparent series of bands was observed at progressively higher frequencies. These bands are listed in Table IV. These bands cannot be assigned to a fundamental mode of strans-2,3-dimethylbuta-1,3-diene, because the corresponding very weak band in the spectrum of the liquid phase was not observed in the spectrum of the solid phase, even though attempts were made to locate it. It is possible that these bands in the fluid phases are due to the presence of the high-energy conformer; indeed, such bands are most commonly observed in the low-frequency region where the frequencies of these modes differ sufficiently in the highand low-energy conformers to enable resolution of these bands. However, no other bands observed in the spectrum of the liquid phase disappeared on freezing. Thus, another explanation for the band near 410 cm-' may be that the band arises from a difference combination of two e-trans
fundamentals. The possible combinations which result in an infrared active band are either A, or B, with either A, or B . The considerable amount of fine structure on the band at 409.9 cm-l in the gaseous phase indicates that a significant interaction is occurring between one or both of the fundamental modes concerned and the asymmetric torsion at 73 cm-l. Examination of the fundamental modes listed in Table I1 showed that none of the previously assigned modes led to a difference band with a frequency of 410 cm-l, unless the unobserved symmetric methyl torsion, ~29,was involved. In this case the difference band could be assigned as u19 - uZ9, which has A, - B, = B, symmetry, involving two out-of-plane motions of the methyl groups. A search was made for further weak bands which could be assigned to complex vibrations involving uZ9, in order to increase the confidence in this assignment. Observation of the u19 - ua difference band should also lead to observation of the u19 + uZ9 sum band at 657 + 247 = 904 cm-l, or slightly lower frequency. Unfortunately, the very strong asymmetric CH2wag, u18, was observed at 894 cm-'; this band with its envelope swamped the region where the weak combination band would be expected. This region was scanned at low vapor pressure, and a weak Q branch was observed at 897 cm-l. The absence of any fine structure near this band indicated that the weak band was not due to the expected combination; it has instead been assigned to the C-CH, stretch (B,) which is readily observed as a medium-intensity band in the solid phase at 920 cm-l. It was concluded that any weak combination mode was hidden under the intense CH2 wag. However, supportive evidence for the assignment of uZ9 from the difference band at 410 cm-l came from careful examination of the Raman spectrum of the gaseous phase. Depolarization measurements on the A, symmetric bend at 491 cm-l revealed very weak depolarized bands at slightly higher and lower frequency than the strongly polarized A fundamental. These weak bands could only be assigned as equivalent combinations involving a methyl torsion and low-frequency bend, ~ 1 +4 vZ9 (Ag + B, = Bg)and u21 + V42 (A, B, = B,). On this basis the ua fundamental has been assigned a frequency of 246.8 cm-l; however, the lack of any direct observation of this mode must mean that this assignment is tentative. A further search for two-quantum transitions was made in the Raman spectrum of the gaseous phase, but unfortunately no bands were observed which could be assigned to these transitions. Also, attempts were made to reassign the infrared bands near 410 cm-l to the B, transitions, but these attempts proved futile as no potential function could be calculated which explained the data. The observed A, transitions and the observed difference bands assigned to u19 - uZ9 are listed in Table IV. The notation used for the torsional transitions follows that used previous1y.l Initial calculations were made by using the strongest band in the A, series as the 10 00 transition and 246.8
+
-
Torslonal Spectra of Molecules with Two Internal CSvRotors
TABLE V: Potential Coefficients and Their Dispersions Calculated for Methyl Torsions of 2,3-Dimethylbuta-l,3-diene, Kinetic Coefficients Used, and Standard Deviation of the Fit (All Values Are in cm-') coeff value dispersn -__.
'30=
1494.8 - 96.8 - 170.4 10.561 -0.2769 3.0
30'
vv",= V", *a.7*
g44= g55
g4 U
24.8 11.5 15.7
The Journal of Physical Chemistry, Vol. 83, No. 22, 1979 2885
TABLE VI: Calculated Values (J K-' mol-') for the Gaseous Phase Thermodynamic Functions of 2,3-Dimethylbuta-l,3-diene -(Go -
~ T,K
273.15 298.15 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0
(ye-
H," )IT H" )IT -258.6 265.0 265.5 289.6 312.0 333.3 353.5 372.8 391.3 409.0
70.9 75.2 75.5 92.6 109.0 124.3 138.3 151.1 162.8 173.5
S"
329.6 340.3 341.1 382.2 421.0 457.6 491.8 524.0 554.1 582.5
117.9 126.5 127.1 159.9 188.5 212.3 232.2 249.0 263.4 275.8
dimethylbuta-1,3-dieneare shown in Figure 4. Transitions up the left-hand side of the diagram and those parallel to them arise from the A, mode, whereas those up the right-hand side are from the B, mode. It can be seen that sufficient transitions have been observed to calculate the energy levels up to the 50 level, which has an energy 1275 cm-l above the potential minimum. This level is 220 cm-l below the calculated barrier, and the 50 40 transition shows no splitting between symmetry blocks, even though a l-cm-l splitting was predicted. The absence of this splitting may be due to the poor fit leading to an ill-defined potential function, in which case the barrier must be even higher than calculated.
-
0 ' Figure 4. Energy level diagram for the methyl torsions of 2,3-dimethylbuta-I,3diene. The numbers to the right of each energy level denote the llmltlng vibrational quantum numbers (vij). Broken arrows represent the A, symmetry torsional transitions observed directly and the solid arrows represent the B, symmetry transitions calculated from the difference bands, u l g - vZg.
-
cm-' for the B, 01 00 fundamental. The A, band showed a clear series of higher transitions to progressively lower frequency which were added into the fit successively 10, 30 20, etc. transitions. These bands as the 20 could be fit adequately by using the coefficients V30 = Vo3, V,, = V,, and V331only, although the convergent nature of the A, series did not allow a close fit indicating some perturbation of the potential function. These initial calculations predicted other bands of reasonable intensity which were readily observed. The important "cross transition", 11 01, was predicted to have an intensity approximately equal to the 30 20 transition and so was assigned to the band at 202.6 cm-l. The second B transition was calculated to have a frequency of 240 cm-l; hence the second difference band was predicted at approximately 657 - (247 + 240) = 170 cm-l. A very weak band was observed at 173 cm-l with a series of excited bands to higher frequency, similar in spacing to those near the 410-cm-l band. This band was therefore assigned to the second difference, u19 - vZ9, and led to a value of 236.7 cm-' for the 02 +- 00 transition. The observation of this second difference band increases the confidence in the assignment of uZ9. These two transitions were added into the fit, and further calculations led to the assignment of two more weak bands. I t became apparent at this point that the coefficient V3,was insignificant in the fit, and so in the final calculations this coefficient was held at zero. The final results for the potential coefficients are given in Table V, with their dispersions and the standard deviation of the fit, u. The barrier height to internal rotation of the methyl because the cosine-cosine tops is given simply by Vm = VO3, coupling term, Vs3,was found to be insignificant. The barrier height, f dispersion, is therefore 1495 f 25 cm-l or 4.27 f 0.07 kcal/mol. The calculated methyl torsional energy levels of 2,3-
- -
-
+-
Thermodynamic Functions No values for the gas phase thermodynamic functions have been reported, and so of 2,3-dimethylbuta-1,3-diene calculation of these functions by normal statistical methods has been performed by using the complete vibrational assignment proposed in Table 11. The principal moments of inertia I,, Ib,and I, were calculated to be 103.74,156.10, and 253.28 amu A2, respectively, using the molecular structure proposed by Aten et al.4 All vibrations were assumed to be harmonic oscillators except the two methyl torsions. The contributions to the functions for the methyl torsions were calculated by assuming each torsion to be a separate vibration with a barrier height of 4.274 kcal/mol and a reduced moment of inertia of 3.195 amu A2. The thermodynamic contributions were taken from the tables where Qf is the internal rotational of V3/RTagainst l/Qf partition function.16J7 The final values for the thermodynamic functions over a range of temperatures are given in Table VI. The accuracy of the values given in Table VI is hard to assess, but the following points must be kept in mind. These calculations involve the normal rigid rotor ideal gas assumptions, such as neglect of vibration-rotation, vibration-vibration interactions, vibrational anharmonicity, and excited electronic states. The major sources of error for this molecule will arise from the coupling between the methyl tops (which has been partially accounted for in the barrier height calculations) and the asymmetric torsional potential function. Results of studies on the thermodynamic functions of a number of conjugated compoundsloJe which existed as a mixture of conformers have shown that the presence of only a small amount of high-energy conformer gives a significant increase in the values of thermodynamic functions, as a result of the mixing of conformers. However, the concentration of the high-energy conformer of 2,3-dimethylbuta-1,3-dieneis probably very small and so the increases should be minimal. The values presented in Table VI are expected to be accurate to f 2 J / K mol at the lower temperatures, but less accurate at the higher temperatures where the increased concentration
2886
The Journal of Physical Chemisfty, Vol. 83, No. 22, 1979
of high-energy conformer and nonideality will lead to larger errors. Conclusions The vibrational spectrum of 2,3-dimethylbuta-1,3-diene varies little between the three phases which indicates either that only one conformer is present in the fluid phases at room temperature, or that the amount of high-energy conformer present is very low and cannot be detected by spectroscopic methods. The latter conclusion is the more likely, and points to a similar situation to that of buta1,3-diene where neither microwave spectroscopy6 nor a conventional vibrational studylo gave evidence for the presence of the high-energy form. The first spectral evidence for the s-cis conformer of buta-1,3-diene was obtained by a study of the Raman overtonesg of the asymmetric torsions in the gaseous phase; it had been hoped that similar results would be obtained in the present study but no bands due to the high-energy conformer overtones were observed. This meant therefore that either the amount of high-energy conformer was very low, or that the proximity of the exciting line hindered the observation of any bands present. In a recent theoretical study of a number of conjugated polyenes,lg using a molecular mechanics model, it was calculated that the high-energy conformer of 2,3-dimethylbuta-1,3-diene is gauche, and that the enthalpy difference between conformers is 780 cal/mol. The results of the present study strongly indicate that AH is much higher than this value and is probably comparable to, or higher than, the value of 2.5 kcal/mol obtained experimentally for buta-1,3-dieneq The assignment of the vibrational spectrum presented in Table I1 shows that the s-trans C% structure was adequate to explain the spectrum. In general, the rule of mutual exclusion was obeyed, although some weak coincidences were noted. An interesting result was that the in-plane vibrations fall into pairs of 4 and B, modes with similar frequencies, and combination modes were observed for both vibrations (in a pair) in a number of cases. This result was important in that the observation of very weak combination bands at 495 and 487 cm-l in the Raman spectrum (equivalent combinations of the lowest frequency in-plane bend and methyl torsions) added weight to the assignment of the B, methyl torsion from the difference band at 410 cm-l. The barrier height calculated for the internal rotation of the methyl groups, 4.27 kcal/mol, is very high for methyl groups attached to a double bond. The barriers for the methyl rotation in propenez0 and s-trans-2-methylbuta-1,3-diene1° were calculated to be 1.95 and 2.71 kcal/mol, respectively, which indicates that the effect of eclipsing the methyl group by a vinyl group in the diene raises the barrier by nearly 0.8 kcal/mol. In a microwave study of l-butene21lines were assigned to both the s-cis and gauche conformers, and the barriers to methyl rotation were calculated to be 3.99 and 3.16 kcal/mol, respectively. The methyl group of 1-butene is eclipsed by the vinyl group only in the s-cis conformer, and so again the effect of this eclipsing is to raise the barrier by 0.8 kcal/mol, which yields a value similar to the 4.27 kcal/mol calculated for 2,3-dimethylbuta-1,3-diene. On the basis of straightforward addition, the presence of a second methyl
J. R. Durig and D. A. C. Compton
group by a vinyl group in 2,3-buta-1,3-diene should therefore increase the barrier (assuming both methyl tops have coupled torsional motions) to approximately 3.5 kcal/mol. The observed barrier is somewhat higher than this, and may be rationalized by the small structural distortion present in 2-methylbuta-1,3-diene which arises from enlargement of the skeletal bond angles in order to move the methyl and vinyl groups from each other and minimize steric interactions. The 2,3-dimethyl compound is not able to minimize these interactions in the same manner. Indeed, evidence was put forward previouslylO for the presence of steric hindrance in s-trans-2-methylbuta-1,3-diene because the s-cis conformer was found to have a slightly lower methyl rotational barrier, due to the unhindered orientation of its methyl group. The relatively high barriers calculated for the 2-methylas compared to propene,20 and 2,3-dimethylbuta-l,3-dienes, probably arise from a nonbonded attraction between the T cloud of the vinyl group and the methyl hydrogen orbitals, which has been observed for s-cis-methyl vinyl ether.z2 In fact, the similarity between these compounds is quite striking; they are all planar vinyl compounds and the methyl groups are situated on electron rich centers eclipsing a vinyl group. Evidence for such a nonbonded interaction can be found in the spectra of both methyl where in both vinyl ether” and 2,3-dimethylbuta-l,3-diene, cases the methyl torsions were observed to converge on moving to higher transitions, instead of diverging as normally found with unperturbed potential functions. Acknowledgment. The Perkin-Elmer 580 spectra were recorded at the Polytechnic of Wales and we are grateful to the Head of the Department of Science, Dr. W. 0. George, for allowing the spectra to be published here. The authors also gratefully acknowledge the financial support given this study by the National Science Foundation by Grant CHE-76-23542. References and Notes (1) P. Groner and J. R. Durig, J . Chem. Phys., 88, 1856 (1977). (2)J. R. Durlg and D. A. C. Compton, J. Phys. Chem., 83, 265 (1979). (3) J. R. Durig and D. A. C. Compton, J. Chem. Phys.,89, 4713 (1978). (4)C. F. Aten, L. Hedberg, and K. Hedberg, J. Am. Chem. Soc., 90, 2483 (1968). (5) G. J. Szasz and N. Sheppard, Trans. Faraday Soc., 49,358 (1953). (6) D. R. Llde and M. Jen, J . Chem. Phys., 40, 252 (1984). (7) A. P. Atshulier, J. Phys. Chem., 57, 538 (1953). (8) M. I. Batuev, A. S. Onishchenko, A. D. Matveeva, and N. 1. Aronova, Dokl. Akad. Nauk. SSSR, 132, 581 (1960). (9) L. A. Carrelra, J . Chem. Phys., 62, 3851 (1975). (10) D. A. C. Compton, W. 0. George, and W. F. Maddams, J . Chem. Soc., Perkin Trans. 2 , 1866 (1976). (11) R. K. Harris and R. E. Witkowski, Specfrochim.Acta, 20,1651 (1964). (12) N. V. Tarasova and L. M. Sverdlov, Russ. J. Phys. Chem., 42,842 (1968). (13) 8 . M. Harney and F. A. Miller, Appl. Spectrosc., 24,291 (1970). (14) D. A. C. Compton, W. 0. George, and W. F. Maddams, J . Chem. Soc., Perkin Trans. 2 , 1311 (1977). (15) W. G. Fateiey, R. K. Harris, F. A. Miller, and R. E. Witkowskl, Spectrochim. Acta, 21, 231 (1965). (16) G. N. Lewis and M. Randall, “Thermodynamics”, revised by K. S. Pitzer and L. Brewer, McGraw-Hili, New York, 1961. (17) D. R. Stuii, E. F. Westrum, and G. C. Slnke, ”Chemical Thermodynamics of Organic Compounds”, Wiiey, New York, 1969. (18) D. A. C. Compton, J . Chem. Soc., Perkin Trans. 2 , 1307 (1977). (IS) J. C. Tal and N. L. Aillnger, J . Am. Chem. Soc., Q8,7928 (1978). (20) C. E. Souter and J. L. Wood, J . Chem. Phys., 52, 674 (1970). (21) S. Kondo, E. Mota, and Y. Morino. J. W .Spectrosc., 28,471(1968). (22) J. R. Durig and D. A. C. Compton, J . Chem. phys., 89, 2028 (1978).
