The Journal ot Physical Chemistry, Vol. 83, No. 2, 1979 265
Torsional Spectra of +Butane
Analysis of Torsional Spectra of Molecules with Two Internal CsvRotors. 12.1a Low Frequency Vibrational Spectra, Methyl Torsional Potential Function, and Internal Rotation of n-Butane J. R. Durig" and D. A. C. Compton Depadrnent of Chemistry, University of South Carolina, Columbia, South Carolina 2:?208 (Received July 24, 1978)
Publication costs assisted by the Unlverslty of South Carollna
The vibrational spectrum of gaseous n-butane has been investigated below 500 cm-'. A vibrational assignment for the observed bands in this region has been given for both s-trans and the high-energy gauche conformers. The asymmetric potential function has been calculated from three observed transitions, leading to a value of the enthalpy difference between the conformers of 0.89 kcal/mol and a gauche dihedral angle of 62". The values of the potential coefficients were Vl = 418 f 6 cm-' (1.19 kcal/mol); V3= 639 f 67 cm-' (1.83 kcal/mol); V , = 136 f 23 cm-' (0.40 kcal/mol). Bands have been assigned to the methyl torsions of both conformers and from these assignments the barriers to internal rotation of the methyl groups for both the s-trans and gauche conformers have been calculated to be 3.21 f 0.01 and 4.30 f 0.03 kcal/mol, respectively.
Introduction Butane is an important compound from both the theoretical and industrial viewpoints, and yet the spectroscopic data on this compound is incomplete in the lowfrequency region for a number of reasons. The main problem has been that hydrocarbons in general have small dipole nnoments and so some vibrations involving relatively small changes in dipole moment are very weak in the infrared spectrum. s-trans-Butane itself has no permanent dipole moment due to its C2h centrosymmetric structure and hence shows no microwave spectrum; low-frequency vibrations can often be calculated from the analysis of the splitting of the rotational lines caused by the internal rotation or from the relative intensities of the vibrationally excited states, The rule of mutual exclusion holds for C2h molecules and so complete vibrational data can only be obtained by observing both the Raman and infrared spectra. Theoretically, n-butane is an interesting compound because it is the simplest alkane with a possible equilibrium between low- and high-energy conformers and also because the two methyl rotors may have coupled torsional vibrations like propaneIb even though the tops are separated by a bond length. As yet no experimental values for the torsional frequencies of butane have been reported, and although evidence has been presented that the high-energy conformer is observable at room temperatures, no evidence has been put forward for the structure of this high-energy form. Early spectroscopic studies2concluded that butane exists predominantly in the s-trans conformer because there were no observable coincidences between the infrared and Raman spectra of the solid phase. In the liquid phase extra bands were observed in the Raman spectrum which were assigned to the high-energy conformer, and the extra enthalpy of this conformer was calculated2 to be 770 f 90 cal/mol Electron diffraction ~ t u d i e s ~ upheld - ~ the conclusion that the s-trans conformer was predominant near room temperature. The latest of these studies5 allowed for shrinkage corrections due to the vibrational modes of the molecule and these workers calculated the molecular structure of the s-trans conformer. The concentration and dihedral angle of the high-energy gauche conformer were also calculated5 and found to be 46.5 f 9% and 64.9 f 6O, respectively. A large number of estimates for the barriers to internal rotation and enthalpy difference between conformers of 0022-3654/79/2083-0265$01 .OO/O
butane have been made by spectroscopic, thermodynamic, ultrasonic relaxation, and theoretical calculations. Those values published before 1975 have been tabulated and referenced in a thermodynamic study by Chen, Wilhloit, and Zwolinski,Gwho selected values for the gaseous gauche dihedral angle, s-trans methyl barrier height, and AH of 62.3', 3.3, and 0.76 kcal/mol, respectively. The most recent estimate for the enthalpy difference between conformers in gaseous butane7 was made by measuring the temperature dependence of the relative intensity of pairs of Raman bands at 432/421 and 842/833 cm-', leading to values for AH OF 976 f 43 and 942 f 98 cal/mol, respectively. These estimates were substantially higher than previous values which ranged from 400 to 800 cal/mol.6 However, a subsequent study on the Raman spectrum of the liquid and solid phases and normal coordinate analysis of the results8 indicated that the 421-cm-' gaseous band was probably not due to the gauche conformer because it was absent in the low-temperature spectrum of the liquid; hence the estimate of 976 cal/mo17 for AH cannot be used. Recent studies in this laboratory on compounds with two Cs0tops on a common atom such as dimethyl etherg and propanelb have shown that these molecules have strongly coupled torsional modes. Similar studies on compouinds where the symmetric tops are separated by a bond length, ethyl methyl etherlo and ethyl methyl sulfide," indicated that these compounds also had coupled methyl torsional motions because their spectra could not be analyzed on the basis of independent rotors. There is evidence which suggests that the gauche conformer of ethyl methyl e t h d 0 suffers steric hindrance between the two methyl tops, hut that the sulfide'' shows no steric hindrance. gauche-nButane may well show steric hindrance similar to ethyl methyl ether because the two molecules are isoelectronic. In an attempt to complete the low-frequency vibrational data and characterize the torsional potential functions of n-butane, this study was undertaken. Experimental Section
Research grade n-butane (99.99%) was purchased from Matheson Gas Co. and used without further purification, except that tracer; of water were removed using sodium hydride. Far-infrared spectra between 500 and 40 cm-' were obtained by using a Digilab FTS-15B Fourier transform interferometer. The spectra were recorded using a 1-m pathlength cell filled to a pressure of 1atm. Interferograms 0 1979 American Chernical Society
266
The Journal of Physical Chemistry, Vol. 83, No. 2, 1979
J. R. Durig and D. A. C. Compton
TABLE I: Observed Vibrational Spectrum of n-Butane below 500 cm-' and Proposed Assignment Raman"
infrared
cm- '
re1 intC
491 471 454
w, br vw w, br
431
vs
428
w, sh
420 406 318
S
vw m
255 245
vw vw
cm'
'
440.5 437.4 434.0
w, sh m m
429.2
vs
422.0
mw
318d 26 2d
20 + 00 methyl torsion 30 +- 1 0 methyl torsion 2nd hot band R branch 1st hot band 6 C-C-6-C Q, 6 C-C-C-C 1st hot band P branch combination band 0 2 +- 00 methyl torsion
"I:
c-c-c-c s c-c-c-c
a bU a
vw vw
1 0 +- 00 methyl torsion 20 +- 10 methyl torsion hot bandof 206.3 hot band of 206.3 01 +- 00 methyl torsion hot band of 199.6 02 + 01 methyl torsion hot band of 192.5 11 10 methyl torsion 0 3 +- 0 2 methyl torsion 12 + 11 methyl torsion 1 +- 0 skeletal torsion 1t +- O-t skeletal torsion 2-t + 1 i skeletal torsion
W
a,
W W
vw vw
f-
W
vw
a, a
W
0.5 -0.5
-0.3
6
vw mw
obsd calcd
assignment
ag
211.2 209.1 206.3 202.0 199.6 196.8 194.9 192.5 185.3 121e 116 107
re1 intC conformerb
-1.0 1.0 -0.1 -0.2
0.0 0.5 0.0 1.3 -0.9 0.3
vw All Raman bands were observed to be strongly polarized. g = gauche, t = s-trans. w = weak, m = medium, s = strong, v = very, sh = shoulder, br = broad. Center of B type band. e Band center of broad featureless absorption. TABLE 11: Predicted Prouerties of the Exuected Fundamental Modes of n-Butane below 500 cm-' s-trans
mode
symmetry
symmetric bend asymmetric bend symmetric methyl torsion asymmetric methyl torsion CH,-CH, torsion
ag bU b, a, a,
Raman polarization
gauche
ir contour
symmetry
Raman polarization
AIB a C C
a b a b a
P dP P dp P
P dP a
ir contour B A/C B A/C B
a Coupling between the methyl torsions results in the possiblity of weak transitions being observed here, contrary to the mutual exclusion principle.
for both the sample and empty reference cell were recorded 4000 times, averaged, and transformed using a boxcar apodization function to give an effective resolution of 0.5 cm-l. No peaks were observed below 100 cm-l and so a 6.25-pm mylar beamsplitter was sufficient. The complete spectral data are given in Table I and the listed frequencies are expected to be accurate to f0.5 cm-' for sharp bands and *2 cm-I for B type bands. Raman spectra were recorded by using a Cary Model 82 spectrophotometer equipped with a Spectra Physics argon ion laser tuned to the 514.5-nm line. Samples were examined in the standard Cary multipass gas cells at 1 atm pressure. The laser power at the sample was 3 W, and the resolution used varied from 1 cm-l for the strong bands between 400 and 440 cm-l, to 4 cm-* to study very weak bands. The frequencies listed in Table I are expected to be accurate to fl cm-l for strong lines and *2 cm-' for other lines.
Results The predominant s-trans conformer of n-butane has C2h symmetry whereas the expected high-energy gauche conformer has C2 symmetry. Previous normal coordinate
caleulationsl2 have shown that both conformers should have two skeletal bends and three torsions observable in the spectrum below 500 cm-l. The expected vibrations with their spectral behavior are given in Table 11. The s-trans bends have previously been assigned to the strong polarized Raman band near 430 cm-l (aJ12 and a very weak broad band at 215 cm-' (b,).13 The torsional frequencies have been estimated12at 225 and 194 cm-' for the b, and a, methyl torsions and 100 cm-l for the asymmetric torsion. The corresponding gauche modes have been calculated12 at 315 and 440 cm-l for the a and b bends, 196 cm-l for both methyl torsions, and 100 cm-l for the asymmetric torsion. The gauche bends have previously been assigned2v7 to the Raman bands at 325 and 421 cm-l, which on the basis of Snyder's normal coordinate calculations12should belong to the a and b representations and be polarized and depolarized, respectively. We observed all of the Raman bands below 500 cm-' to be strongly polarized. This upholds the assignment of the gauche a mode, but the 421-cm-' band cannot therefore be the bend of b symmetry of the gauche conformer. This gives weight to the previous argument8 that the 421-cm-' band is due to a combination band or hot band of the
The Journal of Physical Chemistry, Vol. 83, No. 2, 1979 267
Torsional Spectra of n-Butane
s-trans conformer. The far-infrared spectrum of gaseous n-butane shows only one relatively strong band at 429 cm-l. This band had an A type band contour with two hot bands on the high-frequency side and was assigned to the gauche asymmetric bend. No other bend of either conformer should show this band contour and it is close to the calculated frequency.12 Two very weak B type bands were observed at 318 and 262 cm-l; the higher frequency band coincides with the Raman band assigned to the gauche symmetric bend while the lower one was very close to the frequency of 270 cm-l predicted by Snyder12for the s-trans asymmetric bend and so it has been assigned to that mode. Hence these bending modes of n-butane have now all been tentatively assigned. CHz-CH2 Torsions. The s-trans and gauche CH2-CH, torsions have been predicted12 to be very close together a t approximately 100 cm-l. Observation of two Raman bands a t 116 and 107 cm-' which were strongly polarized can only be due to the gauche conformer, as the s-trans torsion would show depolarized Raman bands for this mode. This is the first spectral evidence for the structure of the high-energy conformer of butane. The s-trans torsion was expected to show sharp Q branches in the infrared spectrum because of its expected C type band contour, but the broad weak band centered at 121 cm-l showed no fine structure. However, the observation of this band at slightly higher frequency than the gauche torsion means it is probably due to the s-trans torsional motion. The observed band shape may be due to an abundance of hot bands which leads to an ill-defined band contour. Using the limited torsional data available, an attempt to calculate the torsional potential function was made by using the s-trans structure calculated from the electron diffraction5 data. The reduced rotational constant was calculated as a function of the dihedral angle, a Fa = Fo CF, cos ia
+
1
The values of F, used were Fo = 1.629, F, = -0.105, Fz = 0.0668, F3 = -0.0146, F4= 0.0042, and F5 = -0.0011, The observed frequencies were then fitted to a potential function of the type v = 1/22CV1(1- cos ia) Previous calculations on the potential functions of ethyl methyl etherlo and ethyl methyl sulfidell have shown that the only coefficients likely to be significant in n-butane are VI, L73, and v6, so these potential coefficients were used to fit the observed frequencies. An assumed value of AH, the enthalpy difference between the lowest energy levels of the gauche and s-trans potential wells, was used as a forbidden transition and given a low weighting in order to fit four transitions with the three variables. The resulting potential function calculated had values for the potential coefficients (fdispersions) of Vl = 418 f 6 cm-' (1.19 f 0.02 kcal/mol), V3 = 639 f 67 cm-l (1.83 f 0.19 kcal/mol), and v6 = 136 f 23 cm-' (0.40 f 0.07 kcal/mol). The calculated value of AH was 310 cm-l (0.886 kcal/mol); however, it is not possible to estimate the error on AH. The calculated potential function showed minima a t 0 and 118' (dihedral angle of 62') representing the s-trans and gauche conformers, respectively, and barriers to the s-trans/gauche, gauche/s-trans, and gauche/gauche interconversions of 769,458, and 746 cm-' (2.20,1.31, and 2.13 kcal/mol), respectively. Methyl Torsions. A number of bands were observed which could be assigned to the methyl torsions. A pair of very weak polarized Raman bands a t 255 and 245 cm-l
-1
230 (CMl) 180 Figure 1. Far-infrared spectrum of gaseous butane between 230 and 180 cm-', recorded using 1 atm pressure at I-m pathlength. Interpolation was performed on this spectrum, inserting three extra points between each existing adjacent pair of data points. The transmittance ranges from 85 to 100%. could only be assiigned to the gauche a mode, whereas the weak series of infrared bands, shown in Figure 1, coulcl be assigned as the asymmetric methyl torsion of either comformer on the basis of the band contours given in Table 11. The potential function governing the internal rotations of two coupled methyl groups has been set up previously by Groner and D ~ r i g gauche-n-Butane .~ has Cz symmetry and so can be labeledgas a C3"T-C2F-C3,T or C2(e)system, where the e indicates equivalent tops; similarly s-transn-butane is a Czh(e) system. The internal rotational Hamiltonian has been derivedg as
HI = 1/2[g4?302+ g 4 5 ~+ ~g 5~5 ~l l ?+
V(ro,rl)
For the C2(e) system V(ro,rl)is expressed as
V(ra,rl)= 1/2[v30(1 - COS 370) + v60(1- COS 670) + Vl,, sin 670 + VO3(l- cos 3 ~ +~VO6(l ) - cos 67J + Vb6 sin 6 ~ + 1 V3,(cos 3~~ cos 3~~ - 1) + V;, sin 3r0 sin 3~~ + Vf53sin 3~~ cos 3~~ + Vff53cos 3~~ sin 3r1 + ...I The following restxictions apply for the above expressions in the Cz(e) case: g44
= g55
V30 = Vo3
V6o
= Vo,
Vl,o = Vbl;
Vff33= v 3 3
These restrictions also apply for the Czh(e) system, but additional restrictions are vio := = v'$3= V"' 33 = 0 The s-trans stiructure calculated from the electron diffraction study5 was used to calculate the kinetic coefficients, g44,etc. for both conformers; for the gauche conformer a value of 62' was used for the dihedral angle, as deduced from ithe asymmetric potential function. The polarized Raman bands a t 255 and 245 cm-l are assigned as gauche methyl torsions. Initial calculations for the gauche conformer using V,, = Vo3 only indicated that the two torsional fundamental transitions, 10 00 and 01 00, may be observed close together because of the small value of g45used. On this basis the infrared bands observed near 200 cm-' were too low in frequency to be gauche methyl torsions and so were assigned to the s-trans conformer. Hence it was not possible to fully characterize the gauche methyl torsional potential function, and so only V,, = Vo3 were used to fit the two observed bands whereas all other coefficients were held to zero. The resulting barrier height calculated (with dispersion) was 1503 f 11 cm-' (4,30 f 0.03 kcal/mol).
-
-
268
The Journal of Physical Chemistry, Vol. 83, No. 2, 1979
J. R. Durig and D. A. C. Compton
TABLE 111: P o t e n t i a l C o e f f i c i e n t s C a l c u l a t e d for t h e M e t h v l T o r s i o n s of s-trans-n-Butane in c m - ' coefficient v 3 , '60
= =
v 0 3 '06
V,, (V3,,t V,,/2)- V,, g45 = g 5 5
value
dispersion
1069.5 -26.3 -53.9 1123.9
7.8 1.8 9.0 4.5
12.014 -1.761 0.26
The bands near 200 cm-l in the infrared spectrum were confirmed to be a series because a very weak peak was observed a t 406 cm-l in the Raman spectrum (206.3 + 199.6 = 405.9) which was assigned to the 02 00 two quantum transition. This indicates that the peaks at 206.3, 199.6, and 192.5 cm-l formed the basic series and the other bands in this region are hot bands due to the asymmetric torsion. Similar hot bands were observed near the methyl torsional transitions of ethyl methyl ether.1° The potential function for the s-trans conformer was obtained by using the Au = 2 Raman transition at 406 cm-l and the three infrared bands at 206.3,199.6,and 192.5 cm-l which were assigned to the single quantum transitions 01 00, 02 01, and 03 02, respectively. Initial calculations using V30, v60, and V,, potential coefficients indicated that the 20 00 and 30 10 transitions should be observed in the Raman spectrum near 470 and 454 cm-l and that infrared bands due to the 11 10 and 12 11 transitions should be observed near 195 and 185 cm-l, respectively. All of these bands were observed and so they were included in the assignment, although the Raman band a t 454 cm-l was weighted lower than the other transitions because its broad nature did not allow an accurate frequency measurement. The torsional energy levels (w)split into four sublevels according to
-
- -
-
-
-
-
-
rooe Po rll e r12 All of these symmetry blocks were examined in order to determine if any splitting might be expected in the higher energy levels. A small amount of splitting was calculated, but the 1'1° block adequately represented all transitions and so was used for the final iterations. Eight transitions were used to calculate the final fit, and the resulting potential coefficients with dispersions are listed in Table 111, along with the kinetic coefficients used and standard deviation of the fit. The V i 3 term was found to be insignificant and so was held to zero for the final calculations. The resulting fit calculates the b, methyl torsion 10 00 transition at 239 cm-'. The barrier height can be obtainedg from 1/2(V30+ Vo3) - V3,and has a lower dispersion than either V30 or V3,because of the high correlation between these two coefficients.
-
Conclusion The approximate asymmetric potential function calculated from the limited torsional data indicates that the enthalpy difference between the s-trans and high-energy
gauche conformers is 310 cm-l (886 cal/mol), although it is not possible to give any estimate for the accuracy of this value. This result is in agreement with the previous reliable value' of 942 f 98 cal/mol for the gaseous phase, although higher than previous estimatese for the liquid phase. The calculated barriers, however, may not be accurate quantitatively because only the lower torsional transitions were observed, especially as previous estimates6 gave higher barriers. The resulting dihedral angle for the gauche conformer of 62O agrees well with the previous estimate from electron diffraction studies, 65 f 6O, and is the same as that selected for the thermodynamic study? The barrier heights to internal rotation of the methyl groups were calculated to be 1124 f 5 and 1503 f 11 cm-l (3211 f 13 and 4296 f 31 cal/mol), respectively, for the s-trans and gauche conformers. The s-trans value is a little smaller than previous estimates6 of 3.3-3.4 kcal/mol for the barrier in n-butane, and is also slightly lower than the value obtained for propanelb (3.26 kcal/mol). The barrier calculated for gauche-butane is 1.1kcal/mol higher than the s-trans barrier, which is probably due to steric hindrance between the gauche methyl groups. A similar effect was noted for ethyl methyl etherlo where the gauche C-CH, barrier was 0.9 kcal/mol higher than the s-trans barrier. A search was made for transitions in the microwave spectrum which could be attributed to the rotational spectrum of gauche n-butane. The 26.5-40.0-GHz frequency region was scanned using a Hewlett Packard 8460A MRR spectrometer. The sample was held in a conventional Stark cell at pressures between 50 and 100 pm and the spectrum recorded with the sample cooled to dry ice temperature as well as room temperature. Stark fields ranging from 0 to 1000 V were applied to the sample and the region scanned at high sensitivity. No transitions were observed which could be attributed to a spectrum of nbutane. Thus, it is concluded that the dipole moment of gauche-n-butane is quite small. Acknowledgment. The authors gratefully acknowledge the financial support of this study by the National Aeronautics and Space Administration by Grant NGL-41002-003. References and Notes (1) (a) For part XI, see J . Chem. fhys., in press. (b) J. R. Durig, P. Groner, and M. G. Griffin, bid., 66, 3061 (1977). (2) G. J. Szasz, N. Sheppard, and D. H. Rank, J . Chem. fhys., 16, 704 (1948). (3) K. Kuchitsu, Bull. Chem. SOC. Jpn., 39, 748 (1959). (4) R. A. Bonham and L. S. Bartell, J. Am. Chem. Soc., 81, 3491 (1959). (5) W. F. Bradford, S. Fitzwater, and L. S.Barteil, J . Mol. Struct., 38, 185 (1977). (6) S. S. Chen, R. C. Wilholt, and 8.J. Zwolinski, J. Phys. Chem. Ref. Data. 4. 859 (1975). (7) A: L.'Verma, W,F. Murphy, and H. J. Bernstein, J . Chem. fhys., 60, 1540 (1974). (8) I. Harada, H. Takeuchi, M. Sakakibara, H. Matsuura, and T. Shimanouchi, Bull. Chem. SOC. J m . , 50, 102 (1977). (9) P. Groner and J. R. Durig, J . &em. fhys., 66, 1856 (1977). (10) J. R. Durig and D. A. C. Compton, d . Chem. fhys., in press. (11) J. R. Durig, D. A. C. Compton, and M. R. Jalilian, J. fhys. Chem., submitted for publication. (12) R. G. Snyder, J . Chem. fhys., 47, 1316 (1967). (13) D. M. Gates, J . Chem. fhys., 17, 393 (1949).
