Torsional transitions and barrier to internal rotation of 1,2-butadiene

Spectrochiraica Acta, Vol. 45A, No. 4, pp. 479 485, 1989.

0584 8539/89 $3.00+0.00 ~) 1989 Pergamon Press plc

Printed in Great Britain.

Torsional transitions and barrier to internal rotation of 1,2-butadiene STEPHEN BELL,* GAMIL A. GUIRGISt~ and JAMES R. DURIGt *Department of Chemistry, University of Dundee, Dundee DD1 4HN, Scotland, U.K.; and tDepartment of Chemistry, University of South Carolina, Columbia, SC 29208, U.S.A. (Received 25 Auaust 1988; accepted 9 November 1988)

-The far i.r. spectrum of 1,2-butadiene (methyl allene) has been recorded in the gas phase from 370 to 40 cm- t with a resolution of 0.1 cm- I. The methyl torsional fundamental has been observed for the first time at 154.3 cm-~, along with some accompanying torsional hot bands. From these data the barrier to internal rotation has been calculated to be 556 cm- 1 (1.59 kcal/mol). Detailed K-structure has also been observed for both A-A and E-E torsional transitions and considered in the analysis. SCF calculations have been made for the structure and energies of conformers, so that both kinetic and potential constants for internal rotation have been obtained. The a' skeletal fundamental is observed at 201.8 cm-t as a much stronger band than the torsional mode, and the a" skeletal fundamental gives rise to an even stronger band at 319.8 cm- 2. Abstract

INTRODUCTION

EXPERIMENTAL

Very little spectroscopic work has been done on 1,2butadiene (methyl allene). The microwave spectrum [1] of the normal species only has been studied in the 16-33 G H z region, where most of the lines show splittings due to internal rotation. Hence, most of the parameters of the structure given have been assumed with only the C C C angle and perhaps C C distances fitted. To interpret the splittings, a value for I~ of 3.103 a.m.u. A 2 has been assumed from the analysis of propene [2-l, and the fitted value of the barrier V3 is 556 c m - 1 with no evidence that V6 is other than zero. N o high-resolution study of the i.r. spectrum of methyl allene has been made, but a few low-resolution studies have been made and most of the fundamentals have been observed and assigned from i.r. and Raman spectra [3-5]. Low frequency fundamentals have been observed down to 210 c m - 1 but the torsional fundamental has not previously been observed. In this series of studies, the far i.r. spectrum of propene [6] was obtained at a resolution of 0.1 c m - ~. Its torsional fundamental is observed with a central peak at 188.05 c m - t. It exhibits extensive rotational K-structure which was analyzed and provided useful information about rotational-torsional coupling. The fitted value of V3 is 693.7 c m - ~ for propene. The structure of methyl allene should allow interesting comparisons with propene. F r o m the microwave value of V3 for methyl allene, we would expect a lower torsional fundamental frequency for methyl allene and greater interaction of rotation and torsion. The far i,r. spectrum is obtained under the same conditions as for propene.

The sample of methyl allene was obtained from a commercial source and purified using a low temperature and low pressure sublimation column. The far i.r. spectrum of the gas from 370 to 40 cm - t was obtained with a Nicolet model 8000 spectrometer equipped with a vacuum bench and liquid helium cooled Ge bolometer detector. Mylar beamsplitters of 6.25 and 12.5 #m were used and the gas was contained in a 1 m multiple-reflection cell with polyethylene windows. The ab initio SCF calculations were made with the TEXAS program [7] and geometry optimization was carried out by an implementation of the BFGS quasi-Newton method in the MINIT program [8]. Calculations were made with the small split-valence 3-21G basis [9], but in view of very short C=C distances the larger split-valence 6-31 G basis I-10] was also tried. Because the optimized C=C bond lengths were still short, the HUZ1NAGA-DUNNINGdouble-zeta basis [11, 12] had to be used, as for propene [6].

:~Present address: Research Department, Mobay Corporation, Dyes and Pigments Division, P.O. Box 10288, Charleston, SC 29411, U.S.A.

RESULTS AND ANALYSIS The far i.r. spectrum of methyl allene is shown in Fig. 1. A very strong band is observed with a central spike at 320 c m - t which was previously assigned [4] as the out-of-plane carbon-skeleton bending vibration. The other strong feature is a B-type band centered about 200 c m - t but with a maximum at about 210cm -1 which was the measurement previously reported [3]. This is assigned as v15, an in-plane carbon-skeleton bending vibration of A' symmetry. However, on the low-frequency side of this band are a large number of sharp features, the stronger ones being assigned as the central peaks of three or four Ctype bands all involving the torsional vibration. The peak at 154.3 c m - 1 is assigned as the torsional fundamental and the A - A and E - E components of the 2,-- 1 transitions are resolved. Only the measurements of these stronger peaks are given in Table 1. The weaker features are interpreted as K-sub-band structure associated with the main peaks and their measurements are given and discussed below.

479

480

STEPHEN BELL et al.

"' I pl' "ll,

I

I

350

I

IT'It

I

250

i

150

W,a,V[NUMnER {¢m-1) Fig. 1. Far i.r. spectrum of gaseous methyl allene from 370 to 100 cm- 1 with water reference above.

Table 1. Torsional transitions of methyl allene with assignments and fitted constants (in cm-1) Transition I*--0A E 2.-- 1E A 3 ~ 2A E F

Main peaks obs. calc. 154.296 141.070 138.983

V3

V6

154.273 154.092 141.420 138.693 134.95 116.05 555.93 - 16.97

Fitted origins* obs. calc. 154.33 154.04 141.070 138.983

154.290 154.109 141.420 138.691 134.94 111.03 6.1589 555.88 - 16.90

* From Table 6. Torsional transitions

The microwave values [1] of the internal rotation kinetic constant, F, and the potential barrier, V3, are given in Table 2. This value of F is used in fitting the three main torsional peaks given in Table 1 and values of both V3 and V6 are obtained. The value of V3 is in very good agreement with the value obtained from the microwave spectrum. However, it was shown [6] that there is a very large variation of V 3 with F for molecules like propene but a much smaller variation of V6. The value of I~ used here is transferred from a value obtained for propene [2] on the assumption that It = la + / b - Ic. Due to the neglect of inertial defect the value of It should be larger and a value of 3.17 a.m.u. /~2 was chosen in the analysis of the far i.r. spectra of propene [6] and the 2-halopropenes [13]. The corresponding values of F and the fitted potential constants V3 and V6 are given in Table 2, along with other values of F used in forming the graphs in Fig. 2. The

variation of V3 with F is very similar to that found for propene [6]. Ab initio calculations The value of F used above is still determined from an assumed structure [1] and it would be helpful to determine a better structure. In particular, it seemed worthwhile to check the equality of the C = C bond lengths, the linearity of the C = C = C chain, and the equality or otherwise of the methyl C H bonds [14-1. The geometry of methyl allene was optimized using the ab initio SCF method with the assumption that the CH 3 and C H 2 groups are symmetric with respect to the skeletal plane. When a methyl H eclipses the C = C = C chain, the arrangement which is shown in Fig. 3, is called cis in Table 3. F o r the split-valence 321G basis [9], the results are given for both the cis and trans conformations in Table 3. The C = C bond lengths are indeed almost equal but they are rather short relative to the value assumed in analyzing the microwave spectrum [1-1. Apart from the methyl group itself, the structure changes very little on rotation of the methyl group. It was expected that the 631 G basis would improve on the short C = C bonds, but the structure is almost unchanged as shown in Table 3. With the D Z basis, there is again almost no difference in most of the structural parameters but the C = C lengths are nearer to expectations. The methyl C H bond lengths differ systematically by 0.0035 ~ in the cis configuration. Optimizations were also made in two basis sets with the methyl C H lengths and H C H angles constrained to equality, since that is the model most readily used for analysis of the far i.r. spectrum. Values of the reduced moment of

Rotation-torsion in 1,2-butadiene

481

Table 2. Variation of fitted potential energy constants with kinetic constant F* R.m.s.

I~ Microwave fitt F from microwave

F

3.103 3.103 3.170

V3

6.307 6.307 6.158951: 6.0 6.5

556.0 550.4 555.9 562.5 542.7

-

V6

dev.

19.08 16.97 14.66 21.80

0.45 0.26 0.09 0.71

* Moments in a.m.u..~2, kinetic and potential constants in cm- 1. tRef. [1]. ~Calculated using structure by LIDE and MANN [1, 2] except for methyl group.

V3 560

V6

V3

550

• -10

cases, the agreement with the experimental values is very good, with the larger basis sets which utilize the semi-rigid model being particularly close. In the cases where a symmetric methyl has been used, a value of V6 has also been obtained by ab initio calculations. V6 is seen to be small and positive. The larger and negative experimental value must therefore be mainly due to neglecting the interaction of the torsion with other vibrations in the usual fitting model used. Rotational structure

540

-20

61o

61s F

Fig. 2. Variation of V3 and V6 with the kinetic parameter F (all units are cm- 1).

/ I-~

C1~C2

H

C3

Hs

Fig. 3. Structure of 1,2-butadiene with atom numbering used in Table 3.

On both sides of the main torsional peaks, whose measurements are given in Table 1, there is a considerable a m o u n t of detailed structure. As for propene I-6] and 2-bromo and 2-iodopropene 1-13], rotational subbands with AK = + 1 (R form) and AK = - 1 (P form) are easily identified, i.e. the band has the appearance of a perpendicular band of a symmetric top, except for the central peak which is due to asymmetry. From the sub-band intensities, it is deduced that these belong to the 1A ~-0A torsional transition, but among these subbands are weaker ones. Some of these can be arranged into another set of R and P sub-bands, which may belong to the IE,--OE torsional transition. Measurements of both of these sets of sub-bands are given in Table 5. Both A-A and E-E sub-bands have been assigned in the far i.r. spectrum of acetaldehyde [15]. The measurements of all these sub-bands have been fitted as in the previous cases, with a symmetric top model, and the constants from the least-squares fit are given in Table 6. For an approximately prolate symmetric top, the constants B= (B + C)/2 and ,4 = A - / ~ are used in the formula F(J, K)=BJ(J + 1 ) + A K 2 - D r K 4.

inertia, It, and the kinetic constant for internal rotation calculated for all of these ab initio structures are given in Table 4. All the values of I, are small and about 3.1 a.m.u./~2 due to the systematically short CH bond lengths obtained at this ab initio calculation level. Making an empirical correction to the methyl CH lengths of +0.01 It, gives I, values of approximately 3.17 a.m.u. ,~2, which is the value used in propene [6-1 and discussed above. Values of the barrier parameter V3 obtained by ab initio calculations for each of the basis sets employed and for various models are also given in Table 4. In all

For the A-A sub-bands, the fits in Table 6 are given for both a rigid rotor model ( D k = D ~ = 0 ) and nonrigid, but because of correlation a third fit is also given with .4" fixed at the microwave value. For all of these fits AA = A ' - A " is fairly consistent at - 0 . 0 1 5 cm-1, and this change is even larger than in propene [6]. This large A.4 is at least partially due to torsional-rotational interaction. The appropriate equation for the energy showing K dependence was given by LIN and SWALEN [16] (Eqn 3-31a). Since it is assumed that the sub-band features are not J dependent (Q peaks), the J part is omitted. However, since a

482

STEPHEN BELL et al.

Table 3. Optimized geometries* of 1,2-butadiene for ab initio calculations with various basis sets 3-21G Microwave't C1C2 C2C3 C3C4 C 1H C3H C4Hs C4Ha C 1C2C3§ C2C3C4 HC1C2 HC3C2 HsC4C3

1.33 1.33 1.48 1.07 1.07 1.09 180 123 120 120 111.84

HaC4C3

HsC4Ha HaC4Ha Ha tor. CH3 tiltll CH2 tilt¶ - ( E + 154)**

107 -120 0 0

cis

1.2932 1.2922 1.5172 1.0744 1.0763 1.0817 1.0852 179.92 124.02 121.43 118.99 110.88 110.42 108.60 107.83 120.42 0.26 -0.02 0.041475

3-21G Me(C3)

3-21G

6-31G

DZ

trans

cis

cis

1.2932 1.2925 1.5173 1.5242 1.0745 1.0755 1.0840 1.0824 1.0835 179.89 124.03 123.79 121.45 118.66 110.86 110.30 110.43 110.89 108.35 108.15 -108.35 120.09 60.21 0.29 0.41 -0.03 -0.02 0.041461 0.039096

1.2957 1.2955 1.5062 1.0733 1.0762 1.0810 1.0844 179.84 124.88 121.62 118.50 111.31 110.78 108.22 107.38 120.47 0.30 -0.09 0.844245

1.3106 1.3090 1.5159 1.0750 1.0772 1.0816 1.0851 179.94 124.97 121.34 118.18 111.35 110.45 108.42 107.64 120.52 0.55 -0.08 0.856078

DZ Me(C3):~

1.5160 1.0840 --

111.35 110.45 108.16 120.19 0.60 -0.08 0.856064

* Bond lengths in ~, angles in degrees. tRef. [1]. :~Optimization made with CH 3 constrained to be C3; parameters same as previous column except where given. §The C=C=C chain is very slightly bent towards the methyl group. IIMethyl tilt defined as angle between C4C3 and normal to H 3 plane. ¶This parameter is out-of-plane angle of C2 from C1HH plane; the negative value means that Hs are bent away from methyl group. **SCF energy for ab initio calculations, in Hartrees.

Table 4. Ab initio potential and kinetic energy constants* for methyl internal rotation in methyl allene Basis and modelt Experimental far infrared 3-21G semi-rigid 3-21G full optimization 3-21G C 3 constraint 6-31G semi-rigid DZ semi-rigid DZ C 3 constraint

V3

V6

I~

F

555.88 541.68 522.13 529.99 551.96 557.15 535.44

- 16.90

3.17 3.1141 -3.1140 3.0940 3.1064 3.1064

6.1589 6.3046 -6.3048 6.3700 6.3488 6.3490

+0.24 -~-1.65

* V3, V6 and F in cm- 1, 1, in a.m.u./~2. t Semi-rigid means that in the model used, the energy of the trans conformer is obtained with the geometry of the cis; full optimization means that the energy of the optimized trans conformer is used to obtain the barrier.

non-rigid model is used in some fits, a K 4 term is included in the following: E ( K , v, ~) = .4K 2 - D x K 4 2nn + F n=0 a~"v)cos T (pK -~).

The Fourier series can be expanded to any order (n = 2 is sufficient in this case) and, for a = 0 , each cosine series can be easily expanded to fourth order. The reduced barrier height parameter, s = 4 V3/9F, has the value 40.1 for methyl allene, which is not greatly different from that for propene (s = 43.4). Taking Fourier coefficients from the table of HAYASHI and PIERCE [17], the contributions to the coefficients of

t h e K 2 and K 4 terms have been calculated for both the

torsional ground and excited states. The calculated contribution to the effective A,4 is - 0 . 0 0 7 1 cm -1. Hence, the observed difference of effective ,4 constants is partially explained by torsional-rotational interaction, but other rotational interactions cannot be negligible. F o r the 320 c m - 1 b a n d of methyl allene involving transition in the out-of-plane skeletal bending m o d e where there can be no torsional-rotational interaction, A/i happens to be negligible, but for the corresponding b a n d of 1-butyne, A,4 is significant ( - 0 . 0 0 6 c m - 1). It is tempting to assign the weaker series of subb a n d Q peaks to the 1E *- 0E torsional transition. F o r = 1 energy levels, the Fourier series can be e x p a n d e d

Rotation-torsion in 1,2-butadiene

483

Table 5. Measurements and assignments of K sub-bands of methyl allene torsional band Main sub-band peaks Second sub-band series

A-A

AK=-I k

v

k

--16 --15 --14 --13 -12 -ll -10 -9 -8 -7 -6 - 5 --4 --3 --2

120.779 123.006 125.302 127.541 129.765 131.988 134.216 136.503 138.652 140.783 142.997 145.178 147.283 149.306 151.311

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

AK= +1 v 161.093 162.871 164.697 166.470 168.220 170.064 171.762 173.406 175.031 176.745 178.269 179.897 181.401 182.918 184.472

k

AK= - 1 v

--12 --11 --10 -9 -8 -7 -6 -5 -4 -3 -2

128.229 130.699 133.069 135.448 137.774 140.066 142.394 144.5" 146.835 149.0" 150.949

k

AK= +1 v

3 4 5 6 7 8 9 10 11 12

160.87" 162.579 164.296 166.033 167.723 169.356 171.001 172.553 174.045 175.496

*Omitted from least-squares fit.

Table 6. Band origins and rotational constants by least-squares fits of K structure of the torsional and v23 fundamentals v0

.4"

A'

D~/106

Dk/106

tr*

Torsional band

Experimental'~ A-A Structure Rigid rotor fit Non-rigid rotor fit Second series Rigid rotor fit Non-rigid rotor fit

154.296

0.99387

154.26(3) 154.33(2) 154.31(2)

0.9894(8) 0.9982(11) 0.99387~

0.9758(8) 0.9827(10) 0.9790(4)

29(3) 17(2)

21(3) 12(2)

0.088 0.044 0.056

154.01 (2) 154.04(2)

1.0079 (6) 1.0106(15)

0.9860(5) 0.9876(13)

16(8)

8(6)

0.037 0.035

320.2 319.83(1) 319.83(1) 318.89(1) 318.89(2)

0.99387 0.9985(6) 0.99387, 0.9968(7) 0.99387,

0.9991(6) 0.9942(2) 0.9972(8) 0.9942(5)

30(2) 14(2) 23(3) 12(2)

29(3) 10(2) 19(4) 7(3)

0.019 0.036 0.022 0.031

Skeletal band

Experimental'f Main series Second series

*Standard deviation; standard errors in parentheses. tMeasurement of central peak in far i.r., rotational constants from microwave in symmetric-top notation /i =0.13558 cm - t and ,4=A-/~. :~Fixed parameter.

as for the tr = 0 transitions above, but since the argument of the cosine is a difference in terms, both sine and cosines involving K are needed and both odd and even powers of K are obtained. F o r transitions between energy levels, a signed quantum number k is required (with the convention used here, k is negative for the P form and positive for the R form with Ak = + 1 for both) and because of odd powers in trk, two distinct series of K sub-bands are obtained. The torsional-rotational contribution to the quadratic term is calculated by the tabulated Fourier coefficients to be + 0.0036 c m - 1, which is smaller and of opposite sign to the fitted constants of the second series of subbands in Table 6. Also, the E - E series are calculated as

not being split much from the A - A series until k is about + 6, and for o = + 1 the R form deviates more than the P form and for a = - 1 the P form deviates more than the R form. There is, therefore, some doubt about assigning the weaker sub-bands to the E - E torsional transition. However, there must be other rotational interaction contributions to Ati and the fitted origin of the observed sub-band series lies very close to the position calculated for 1E ~ 0E from the torsional constants in Table 1. The fitted origins in methyl allene are, therefore, assumed to give good values of the torsional transition wavenumbers for both the A - A and the E - E transitions. For the rigid symmetric-top and the

484

STEPHEN BELLet al.

non-rigid symmetric-top fits, the difference between the two 1 ,--0 transitions is fairly consistent. Since measurements of both the A - A and E - E components of the 1 ~ 0 torsional transition are, thus, available, all of the observed torsional transitions have been refitted and the fitted constants are given on the right hand side of Table 1; there is little difference from simply fitting the main peaks. Using the value of A,4 obtained from the symmetrictop fit above and the rotational constants from the microwave spectrum [1], an asymmetric-top simulated band envelope of a C-type band is shown in Fig. 4 to be like the A - A structure of the main far i.r. torsional band. Due to the omission of the frequency factor the low frequency end of the simulated envelope is too strong. L o w frequency skeletal vibrations

The torsional peaks described above are adjacent to the much stronger v 1~ B-type band. Some attempt was made to fit a rotational envelope to this band, but it proved difficult with a rigid asymmetric-top program to generate the sub-band structure on the low-fre-

quency side without also obtaining a similar structure on the high-frequency side. Also, sequence bands in vl~ and/or %4 make all the sub-bands broad. However, the deep valley between the two absorbance peaks is easily generated by a computer program and is close to the origin. The observed valley is taken as an accurate measurement of the vibrational wavenumber and is 201.8 cm;- 1. If the band at 320 c m - 1 is correctly assigned [5] as the a" skeletal frequency %3, it should be a C-type band. It shows K sub-band structure like the torsional fundamental with two clear series (Fig. 5). For the stronger series, 25 sub-bands have been fitted as if it was a perpendicular transition of a prolate symmetric top and the fitted constants are given in Table 6. A weaker series of sub-bands lie between the stronger ones and the origin fitted is 1 c m - 1 lower than for the stronger series. The two fitted origins correspond to two central peaks of C-type bands; the weaker one being a hot sequence band on the stronger. The overall appearance of the band is of a hybrid band rather than a pure C-type band, but the in-plane skeletal bending vibration has been assigned to the 201.8 cm-1 band which shows only B-type character. The previous assignments must therefore be accepted. All the lowfrequency fundamentals of methyl allene are now

I

i 350

i

l 300

WAVENUMBER

i

(cm -1)

Fig. 5. Details of the 320 cm- 1 band. Table 7. Low frequency vibrational fundamentals of methyl allene l 180

l 150 WAVENUMBER

l 120 (cm "1)

Fig. 4. K structure of torsional bands of methyl allene with simulated C-type band: (A) water reference, (B) observed spectrum, and (C) calculated envelope.

Assignment v15 %2 %3 V24

7'(C=C=C) z(CH2) 7"(C=C=C) r(CH3)

Refs [4, 5] This study a' a" a" a"

210 523 322

201.8 -319.8 154.3

Rotation-torsion in 1,2-butadiene k n o w n a n d those below 600 c m - 1 are presented in Table 7.

REFERENCES

[1] D. R. LIDE and D. E. MANN, J. chem. Phys. 27, 874 (1957). [2] D. R. LIDE and D. E. MANN, J. chem. Phys. 27, 868 (1957). [3] R.S. RASMUSSENand R. R. BRATrAIN,J. chem. Phys. 15, 131 (1947). [4] G. J. SZASZ,J. S. MCCARTNEVand D. H. RANK, J. Am. chem. Soc. 69, 3150 (1947). [5] M. G. BORISOV and L. M. SVERDLOV, Opt. Spectrosc. 24, 37 (1968). [6] J. R. DURIG, G. A. GUIRGISand S. BELL, J. phys. Chem., in press.

485

[7] P. PULAY, Theor. chim. Acta 50, 299 (1979). [8] S. BELL and J. S. CRIGHTON, J. chem. Phys. 80, 2464 (1984). [9] J. S. BINKLEV, J. A. POPLE and W. J. HEHRE, J. Am. chem. Soc. 102, 939 (1980). [10] W.J. HEHRE, R. DITCHFIELD and J. A. POPLE, J. chem. Phys. 56, 2257 (1972). [11] S. HUZlNAGA,J. chem. Phys. 42, 1293 (1965). [12] T. H. DUNNINO, J. chem. Phys. 53, 2823 (1970). [13] S. BELL, G. A. Gumois, A. R. FANNING and J. R. DURIG, J. molec. Struct. 178, 63 (1988). [14] D. C. MCKEAN, J. molec. Struct. 113, 251 (1984). [15] H. HOLLENSTEINand F. WINTHER, J. molec. Spectrosc. 71, 118 (1978). [-16] C. C. LIN and J. D. SWALEN, Rev. mod. Phys. 31, 841 (1959). [17] M. HAYASHI and L. PIERCE, Tables for the Internal Rotation Problem. University of Notre Dame, IN, U.S.A.