Torslonal Spectra of Molecules with Two Internal
The Journal of Physical Chemistry, Vol. 83, No. 22, 1979 2873
C S vRotors
Analysis of Torsional Spectra of Molecules with Two Internal CaVRotors. 15.+ Low-Frequency Vibrational Spectra, Methyl Torsional Potential Functions, and Molecular Structure of Ethylmethylamine J. R. Durig" and D. A. C. Compton Department of Chemistty, University of South Carolina, Columbia, South Carollna 29208 (Recelved March 15, 1979) Publicatlon costs asslsted by the Unlverslty of South Carollna
The infrared spectrum of gaseous ethylmethylamine and the Raman spectrum of gaseous, liquid, and solid ethylmethylamine have been investigated below 500 and 530 cm-', respectively. Bands present in the spectra of the fluid phases which disappear upon solidification of the sample have been assigned to high-energy conformers. From an analysis of the fine structure on a band present in the infrared spectrum of the gaseous compound it has been shown that the most stable conformer has the s-trans form. Using rotational constants derived previously by microwave spectroscopy, we have calculated a partial molecular structure for the s-trans conformer. Bands due to the low-frequencybending modes of all conformers have been assigned, but it was not possible to obtain the asymmetric potential function. A number of bands have been assigned to the methyl torsional transitions of both the s-trans and gauche conformers, and torsional potential functions have been calculated and from these it is apparent that the two methyl tops have coupled motions. The barriers to internal rotation have been calculated as 3.30 and 3.12 kcal/mol for the e-trans C-CH3 and N-CH, rotors, respectively, whereas the corresponding gauche barriers are significantlyhigher (3.84 and 3.27 kcal/mol). The higher gauche barriers are discussed in terms of steric hindrance which is absent in the s-trans conformer,
Introd uc tion From studies on a number of compounds which have two internal Csusymmetry rotors on a common atom, such as dimethyl ether,l dimethylamine: and propane? it has been shown that the two torsional fundamental modes in each molecule are strongly coupled. The resulting torsional transitions could only be satisfactorily explained by using a two-dimensional treatment of the torsional potential function. Similar studies on compounds where the methyl rotors are not on a common atom, but are separated by a bond length, such as n-butane: ethyl methyl ether: and ethyl methyl sulfide: have also given resulh which indicate that the methyl torsional modes are coupled in these molecules. An interesting consequence of separating the methyl rotors by one bond length is that an asymmetric torsion (around this new bond) is present, which not only gives rise to conformers of dissimilar potential energy, but also may interact with the methyl torsional potential functions as observed for n-butane4 and ethyl methyl ethera6 Both of these compounds exist as a mixture of low-energy s-trans and high-energy gauche conformers, but the relative stability of these conformers was found to be reversed in the case of ethyl methyl sulfide: where no such interaction between the asymmetric and methyl torsional potential functions was noted. Therefore, the extent of this interaction may depend on the conformation of the compound in which the more favorable is the s-trans. The conformational situation in ethylmethylamine, shown in Figure 1,is more complicated than that for the ether and other similar compounds studied previously because of the amino inversion present in this compound, The s-trans conformer, I, has now lost its molecular planarity and exists as an equilibrium between two rapidly interconverting mirror image conformers. There are also two nonequivalent gauche forms, I1 and 111, both of which can exist as a pair of mirror images. However, amino inversion in the gauche form does not lead to the mirror image of the same gauche form. This resulh in the unusual 'For part 14, see J. Chem. Phys., 70, 5747 (1979). 0022-365417912083-2873$0 1.OO/O
case of two gauche conformers where both the amino inversion and internal rotation about the CH2-NH bond can result in transforming one gauche conformer into one of the mirror images of the other gauche conformer. The overall situation in this molecule is therefore best considered to be three nonequivalent conformers, I, 11, and 111, each having a pair of mirror images with equal statistical weights. The presence of the s-trans conformer of ethylmethylamine has been demonstrated by microwave spectro~copy.~The c-dipole rotational lines of this near-prolate conformer were easily located as strong doublets split by about 2 GHz due to the amino inversion. However, no information was obtained about the barriers to internal rotation, and efforts to assign bands to the gauche conformers proved fruitless. On these bases the assumption was made that the gauche conformers were at least 1 kcal/mol higher in energy than the s-trans form. This assumption is in reasonable agreement with a study of diethylamine*in which a variable temperature study of the N-H stretching region was reported. The low-energy conformer of diethylamine was assigned as the trans-trans, and the two equivalent trans-gauche forms were found to be higher in energy (from relative intensity measurements) by 710 cal/mol. However, the lack of assignment of the microwave rotational lines of the gauche forms of ethylmethylamine cannot, by itself, be considered conclusive evidence that the s-trans conformer is more stable. The only vibrational spectrum of ethylmethylamine reportedgrefers to limited regions of the infrared spectrum. Two N-H stretching bands were observed, indicating significant concentrations of at least two conformers of ethylmethylamine. This study was undertaken with the hope that the torsional potential functions of ethylmethylamine could be characterized and the amount of coupling between the methyl tops evaluated. Experimental Section Ethylmethylamine was obtained from Fluka A.G. and further purified with a low-temperature sublimation 0 1979 American Chemical Society
2874
The Journal of Physical Chetnistty, Vol. 83,No. 22, 1979
J. R. Durig and D. A. C. Compton I
H
CH,
II
I
Ill
CH,NHCH&Hs Flgure 1. The s-trans conformer, I, and gauche conformers, I1 and 111, of ethylmethylamine viewed along the N-C bond. I
I
I
I
I
I
I
I
I
I
450
500
I
400
WAVENUMBER (CM-')
I
Figure 3. Raman spectrum of gaseous ethylmethylamine between 525 and 375 crn-' recorded with 500-torr pressure. Scan A was recorded with a spectral bandwidth of 3 cm-I, B and C were recorded with 2-cm-' spectral bandwidth.
300
200
100
WAVE NUMBER (CMml) Figure 2. Far-infrared spectrum of gaseous ethylmethylamine between 380 and 80 cm-' recorded with 500-torr pressure and 0.25-cm-' resolution. Interfering bands due to traces of water vapor were removed by computer subtraction.
column. Samples were stored over activated 3 A molecular sieves in order to remove water. Far-infrared spectra of gaseous samples between 500 and 40 cm-' were recorded with a Digilab FTS-15B Fourier transform interferometer equipped with either a 6.25 or 12.5 pm Mylar beam splitter. The samples were held over activated molecular sieves in 12-cm cells fitted with polyethylene windows at several pressures up to its vapor pressure at ambient temperature. Interferograms for both the sample and the empty reference cell were taken 2500 times, averaged and transformed by using a boxcar apodization function. The effective resolution was 0.25 cm-l. The resulting spectra showed traces of water vapor even though efforts were made to exclude all water. The strongest band assigned to water was, however, weaker in intensity than the strongest methyl torsional transitions observed, and so the spectrum of water was removed from the sample spectrum by computer subtraction. The spectral data below 500 cm-l are given in Table I, and the tabulated frequencies are expected to be accurate to at least 0.5 cm-l. The region of the spectrum between 380 and 80 cm-l is shown in Figure 2. 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 examined in standard Cary multipass cells with sample vapor pressures of -500 torr. The laser power at the sample was 2 W, and spectra were recorded by using spectral bandwidths of 1-3 cm-l. The observed transitions below 530 cm-l are given in Table I, and the frequencies are expected to be accurate to 1 2 cm-l. The portions of the spectrum between 525 and 375 cm-l and between 270 and 180 cm-l are shown in Figures 3 and 4, respectively. Liquid samples were sealed in capillary tubes and examined at room temperature and just above the freezing temperature by using a Harney-Millerlo apparatus. Solid samples were examined by freezing the low-temperature liquid slowly, followed by annealing the sample. Typical experimental conditions used for recording the spectra of
I / 250
200
WAVE NUMBER (CM-') Flgure 4. Raman spectrum of gaseous ethylmethylamine between 270 and 180 cm-' recorded with 500-torr pressure and 3-cm-' spectral bandwidth.
the liquid and solid samples were 600-mW laser power and 4-cm-l spectral bandwidth.
Results The vibrational spectral data of ethylmethylamine below 530 cm-', listed in Table I, show too many bending vibrations to be assigned on the basis of a single conformer. In a previous study of the N-H stretching region of the two bands infrared spectrum of gaseous eth~lmethylamine~ were reported at 3350 and 3375 cm-l, which indicated the presence of at least two conformers. In fact, three nonequivalent conformers can be postulated for this molecule, s-trans and two different gauche forms as shown in Figure 1. The vibrational spectra of the two gauche conformers may not differ markedly, but the s-trans conformer is likely to show a different spectrum because of the anti configuration of the bulky methyl groups. In order to correctly assign the observed bending modes of ethylmethylamine in the low-frequency region, a study was made of the Raman spectra of the liquid and solid samples. Bands in the liquid were observed at 283,345, and 362 cm-' (all very weak) and at 458 cm-' (strong), with the 345-cm-l band being a shoulder on the 362-cm-l band. Bands at 173,194, and 292 cm-l (all very weak) and at 466 cm-l (strong) were observed in the spectrum of the solid. On this basis the bands in the liquid at 345 and 362 cm-l have been assigned to the bending vibrations of the high-energy conformers, and hence the complicated region of the infrared spectrum of gaseous ethylmethylamine between 370 and 320 cm-l is probably all due to these high-energy conformers. Considerable fine structure was observed on the B-type band at 275 cm-' in the infrared spectrum of the gas and the observed Q branches are listed in Table 11. This band
The Journal of Physlcal Chemistry, Vol. 83, No. 22, 1979 2875
Torsional Spectra of Molecules with Two Internal C a vRotors
TABLE I: Observed Vibrational Spectrum of Gaseous Ethylmethylamine below 530 cm-’ and Proposed Assignment Raman cm-
infrared
re1 intb
510 506 493 488 481 474 459 456 452 432 423 406 363
cm-I
obsd - calcd, re1 intb
conformef
assignment,a v,’~,’ V,V,
t t t t t t t t
excited state of 506 cm-’ 02 + 00 excited state of 488 cm-I 03 01 excited state of 474 cm-I 12- 10 excited state of 456 cm-I 11 00 6 CCNC 21 10 20 00 30- 10 6 CCNC hot band of 362.0 cm-I 6 CCNC 6 CCNC hot band of 337.8 cm-I hot band of 337.8 cm-’ 6 CCNC hot band of 333.5 cm-I hot band of 333.5 cm-, 6 CCNCd 01 + 00 01 00 11 1 0 02 01 10 00 10 00 20 10 20 +- 1 0 11 + 01 30 20 30 +- 20 21 11 asymmetric torsion asymmetric torsion
vw W
vw W
vw W W
mw vs vw mw
447.2
355 336
w, sh m
330
w, sh
362.0 358.4 354.0 337.8 336.1 335.0 333.5 331.6 327.9 275.0 256.9
W W W
g, g,
W
vw m, B vw
249 244 237 217
W
k!
W
g g g
W
W
206
vw
115
mw
t
W
t
W
200.9 197.8
vw vw
189.9 125
m
t g t t g t t g
W
195
t
215.6 207.1
-
W
- 0.6
-0.2 - 0.2 0.1
+-
g,
m
-0.2
+-
t g,
277
0.2
+-
vs, A
w, c vw vw m, A
0.4
+
t t
W
m
cm“
+
- 0.2
--
0.1 -0.1 0.0 0.6 0.4 - 0.9 - 1.1 1.4 -O.le 0.6 - 0.6
+-
+-
+-
+-
+-
Abbreviations used: s, strong; m, meda All numbered assignments, e.g., 20 00, refer to methyl torsional transitions. Abbreviations used: t, s-trans; g, ium; w, weak; v, very; sh, shoulder; A and C are infrared gaseous phase band contours. and g,, gauche. Center of B type band showing considerable fine structure. e Refers to the rolsymmetry block,
corresponds to the bands at 277 and 283 cm-’ in the Raman spectrum of the gaseous and solid phases, respectively, and thus it can only be assigned to the lowenergy conformer. In order to assign a structure to the low-energy conformer, an analysis of the fine structure present on this band was carried out by calculation of the rotational constants from the observed spacings between the subbands. The rotational energy levels of a near prolate rotor can be written as
E, = BJ(J + 1) + ( A - B ) P For a Q branch transition, AJ = 0 and AK = 0, fl, but differing vibrational amplitudes give rise to the rotational constants, A and B, having slightly different values for the various vibrational levels. Thus, A” and A’ denote the constant in the ground and first excited states, respectively. It can be shown that when AK = $1 RQK
= AEf’r = YO
+ ( A ’ - B? + 2(A’- B?K + [ ( A ’ - B? - ( A ” - B’31P
and when AK = -1 ’ Q K = A E , = v ~ + (A’-B?-2(A’-B?K+
[ ( A ’ - B’) - ( A ” - B ” ) ] P To cancel the K2 term, a plot of RQK - ’QK vs. K can be made to give a slope of 4(A’- B?. Then a plot of RQK + pQK vs. Ei“L gives an intercept of 2[v0 + (A’- B?] and a slope
TABLE 11: Observed Rotational Fine Structure on the 275.0-cm- ' Vibrational Transition of Ethylmethylamine with the Assi ned K Quantum Numbers and Data Used in the Plots of Q K - ’QK Vs. K and P Q +~ R Q Vs. ~ K2 (All Frequencies Are in cm“ )
d
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
273.0 271.6 270.2 268.9 267.7 266.3 265.0 263.6 262.2 261.1 260.0 259.1 258.1 256.9 256.0 255.0
278.8 280.3 281.9 283.8 285.3 281.0 288.8 290.5 292.4 294.2 296.2 298.0 299.9 301.9 304.0 306.0 308.0 310.0 312.0
5.8 8.7 11.7 14.9 17.6 20.7 23.8 26.9 30.2 33.1 36.2 38.9 41.8 45.0 48.0 51.0
551.8 551.9 552.1 552.7 553.0 553.3 553.8 554.1 554.6 555.3 556.2 557.1 558.0 558.8 560.0 561.0
of 2 [ ( A ’ - B? - ( A ” - B’?]. In Table I1 are listed the rotational subbands with their assigned K values with the values of RQK - ’QK and RQK + p Q K utilized. The plot of RQK- ’QK vs. K gave a straight line through the intercept
2878
The Journal of Physical Chemistry, Vol. 83, No. 22, 1979
TABLE 111: Calculated Structure for s-transEthylmethylamine with the Skeletal Atom Notation C, CNC, bond lengths, A
c,-c,
C,-N C, -N C,-H C,-H C,-H N-H
1.525 1.466 1.466 1.091 1.095 1.090 1.022
bond angles, deg C , W V C , HC,C, HC2CI HNC, HC,N
110.6 112.2 109.7 112.9 108.8 110.0
TABLE IV: Comparison between Experimental Values for the Molecular Rotational Constants and Amino Hydrogen Substitution Coordinates of Ethylmethylamine, and Values Calculated by Using the Structural Parameters Listed in Table I11 exptl calcd Rotational Constants of s-trans-Ethylmethylamine-do (MHz) A 25936 26060 B 3919.8 3918.6
c
3668.2
3669.5
Rotational Constants of s-trans-Ethylmethylamine-d, (MHz) A 23768 23860 B 3904.3 3902.6 C
3627.5
3630.8
Substitution Coordinates of Amino Hydrogen (A ) a 0.373 0.434 b C
1.168 0.660
1.150 0.707
with a slope of 3.00 cm-l. This gave a value for (A’- B? of 0.750 cm-’. The second plot, RQK ’QK vs. P, gave another straight line with an intercept of 551.7 cm-l and slope of 0.032 cm-l, leading to values of vo and (A”- B’? of 275.1 and 0.734 cm-l, respectively. The observed value of vo, 275.0 cm-’, is the same within the experimental error limits, and the value of 0.734 cm-l calculated for (A”- B’? is exactly the same value as that obtained by using the s-trans rotational constants calculated from the microwave study. The significant differences between (A’- B? and (A”- B’? are to be expected from such a low-frequency,large-amplitude mode. By using the structural parameters of ethylmethylamine listed in Table 111, we calculated the rotational constants of the two gauche conformers by altering the CCNC dihedral angle from 180 to +60 and -60’. Both gauche conformers had values for (A”- B’? of approximately 0.3 cm-l, which is not in agreement with the experimental value of 0.734 cm-l. From these results it was concluded that the low-energy conformer of ethylmethylamine is s-trans, as proposed by the investigators7of the microwave spectrum. Molecular Structure. The microwave spectra of strans-ethylmethylamine-do and -dl have previously been assigned: leading to rotational constants for each isotope and also substitution coordinates for the amino hydrogen. These data are listed in Table IV. A structure for the molecule was not calculated, however, because of the small number of isotopes studied and the large number of structural parameters in this molecule. In order to calculate barriers to internal rotation in the present work it was necessary to use the best structural parameters, which were calculated from initial values taken from the results of microwave studies on the two related compounds, dimethylaminell and ethylamine.12 The initial values of the structural parameters used are listed in Table 111, except
+
J. R. Durig and D. A.
C. Compton
that the initial value of the CCN bond angle taken from ethylamine12was 114.80O. From these molecular structural parameters one predicts values which are too low for the B and C rotational constants and a value for the A rotational constant which is too high. It was assumed that the structural parameters of the heavy atoms in the dimethylamine moiety of ethylmethylamine would not appreciably change with addition of the methyl group, but that the CCN angle would be significantly altered from the value found in ethylamine. Therefore this angle was altered, by using a least-squares iterative procedure, to fit the observed rotational constants of both isotopes of ethylmethylamine. The resulting value, listed in Table 111, is 110.6’. As can be seen from Table IV, this structural change yields values for the rotational constants and substitution coordinates which agree well with the experimental data, and so no further optimization of the structural parameters was performed. It should be noted that the resulting value of 110.6’ is similar to the values of the corresponding CCX angles of 108.1 and 109.1’ found in s-trans-ethyl methyl ether13and s-trans-ethyl methyl sulfide,l* respectively. Asymmetric CH2-N Torsion. I t had been hoped that the asymmetric CH2-N torsional mode would be observed in the infrared spectrum of the gaseous phase as a number of sharp Q branches which could be assigned to the torsional transitions of the respective conformers. This would allow for the calculation of the asymmetric torsional potential function of this molecule. The band in the infrared spectrum of the gaseous compound observed around 125 cm-1 was assigned to this mode, because in the previous studies on b ~ t a n e ethyl ,~ methyl ether? and ethyl methyl sulfides the corresponding modes were observed at 121,115, and 91 cm-’, respectively. The observed band was relatively broad and it ranged between approximately 135 and 105 cm-l, and did not show any Q branches. In the Raman spectrum a single, weak, polarized line was observed at 115 cm-’. This latter band was assigned to both gauche conformers as it was apparently at a lower frequency than the infrared band; however, this assignment must be considered tentative. The lack of sufficient data for the asymmetric torsion of this molecule did not allow the calculation of the potential function. Methyl Torsions. A number of weak Q branches were observed, in both the infrared and Raman spectra of the gaseous compound, which could be assigned to the methyl torsional transitions. The infrared spectrum, shown in Figure 2, exhibits several weak, sharp bands at 215.6 cm-I and at lower frequencies. The bands at 215.6, 207.1, and 197.8 cm-l were assigned to the same series of transitions 01 00,02 01, and 03 02 since the two-quantum transitions were observed in the Raman spectrum (see Figure 3) at 423 cm-l (215.6 3 207.1 = 422.7) and 406 cm-l (207.1 197.8 = 404.9). Other two-quantum transitions were observed on the high frequency side of the 452-cm-l bending vibration, but no series of one-quantum transitions was found which correspond to these lines. The Raman spectrum of gaseous ethylmethylamine also showed a weak region of scattering between 250 and 190 cm-’, and by scanning this region with the highest sensitivity available and with a 2-cm-‘ spectral bandwidth, a number of weak Q branches were resolved. This region is shown in Figure 4, and the observed Q branches fall into two regions, i.e., between 250 and 235 cm-l and from 217 cm-’ to lower frequency. These two groups of lines were assigned to the high- and low-frequency series of the methyl torsions of both gauche conformers of ethyl-
-
+
+
+
Torsional Spectra of Molecules with Two Internal
c3"Rotors
The Journal of Physical Chemistry, Vol. 83, No. 22, 1979 2077
1200-
TABLE V : Potential Coefficients Calculated for the Methyl Torsions of Ethylmethylamine with Dispersionsa s-trans gaucheb coeff
value
dispersn
value
1183.8 13.0 1122.3 11.2 -7.1 3.6 30.4 13.1 2.5 -13.6 3.3 1153.4 8.3 1091.9 12.591 - 2.044 12.694 0.69
V30
30' 60'
v 33
v3 3'
V,, - V 3 , Vo3-- SIT,, g44 g4 U
1343.4 1142.9 -22.1
dispersn
'E 0
Y
tiU Y 5
-106.6 12.8 1343.4 7.5 1142.9 11.8 11.10 - 0.0364 11.16 0.97
u is the standard deviation of the frequency fit. All values are in cm-'. The kinetic coefficients, g44,etc., a
for the gauche conformers are given as an average value.
methylamine, since experience has shown that the gauche conformers often show stronger scattering in the Raman spectrum than absorption in the infrared spectrum, e.g., ethylamine15and n - b ~ t a n e .No ~ splitting of the torsions due to the two different gauche conformers was observed. The two-quantum transitions observed in the Raman spectrum and the infrared one-quantum transitions were all assigned to the low-energy s-trans conformer on the basis of their relative intensities. We are reasonably confident of our assignment of the various observed torsional transitions; however, it is possible that the s-trans and gauche torsional assignments could be reversed since both molecules have C1 symmetry and it is not possible to use depolarization measurements to aid in the assignments. The internal rotational Hamiltonian for the two C3,, rotors for a C1 symmetry molecule has already been given by Groner and Durig,l and the notations used follow those given previously. Both conformers of ethylmethylamine can be labeled as C3,(T) - Cl(F)- C3,,(T)or Cl(n) systems, where T = top, F = frame, and the bar, or n, indicates that the tops are not equivalent. The Hamiltonian can be written as with
V(70,rl)
in standard form as
V(ro,rl) = f/Z[v30(1 - cos 3 ~ 4- ~v60(l ) - cos 670) + v64 sin 670 VO3(l- cos 3r1) VO&l- cos 671) VOd sin 671 + V3,(cos 3r0 cos 3~~- 1) + V33/ sin 3~~sin 3~~ V33/' sin 3r0 cos 3r1 V33/11cos 3r0 sin 3r1]
+
+
+
c h
7.5 11.8 6.5
+
+
0
'
Figure 5. Energy level diagram for the methyl torsions of s-transethylmethylamine. Observed transitions are shown as solid lines (two-quantum transitions) and dashed lines (one-quantum transitions).
frequency series, two-quantum transitions 02 00 and 03 01 at 506 and 488 cm-l, respectively, and the lower frequency series, one-quantum transitions 10 00 and 20 + 10 at 215.6 and 207.1 cm-l, respectively. These transitions could be fit adequately by using only the coefficients V30, Vo3, and V3% From the results it was indicated that the very weak bands at 474, 256.9, 200.9,197.8, and 189.9 cm-l were due to the 21 10,Ol- 0 0 , l l - 01,30 20, and 21 11 transitions, respectively. The 11 00 transition was also predicted to show a band at approximately 457 cm-'with intensity greater than either the 02 00 or 20 00 transitions. The very strong bending mode at 452 cm-' was recorded with 1and 2 cm-' spectral bandwidths and lower sensitivity, as shown in Figure 3C, and a medium weak shoulder at 456 cm-' was resolved. This band did not appear in the infrared spectrum and did not form part of a series of excited state bending 00 transitions; therefore, it was assigned to the 11 transition as predicted. These observed transitions were then included in the calculations. At this point the intensities of all possible transitions up to the 04 energy level (see Figure 5) were calculated in all symmetry blocks. Most of the assigned transitions were best reproduced by the frequencies from the Posymmetry block, and they were thus assigned to this block. The 30 20 transition was predicted to split into two bands separated by approximately 0.8 cm-' with and I'lo transitions at higher frequency than the the roo P,P2,and YO1 transitions. This predicted splitting should have been observed with the 0.25-cm-' resolution used to record the infrared spectrum; therefore, either the very weak band at 200.9 cm-', previously assigned to the 11 01 transition, is the higher frequency 30 20 transition or the splitting was not resolved. The latter argument is preferred since the assignment of the 200.9 cm-l band to 20 transitions would mean a splitting the higher 30 between the symmetry blocks of 3.1 cm-l which is much larger than predicted. The 197.8-cm-l band was therefore reassigned to the 30 20 transition in the YO1 block. Further calculations with these data gave the final results listed in Table V. The coefficients Vso, v64, V,,' V,3: and V33111 were all found to be insignificant and so were held to zero in the final calculations. The resulting potential function is shown in Figure 5 and, by examination, one finds that the function should be reasonably well determined by the observed transitions. The analysis of the gauche methyl torsions, assigned to the Raman bands shown in Figure 4, was simpler because of the smaller number of observed transitions. In the first assignment it was assumed that the three highest fre-
-
+
+
-
+
+
- -
+
-
+ -
+
No restrictions are placed on any of the above terms in the Cl(n) system. The kinetic coefficients g4, g56,and d5 were calculated by using the structural parameters presented in Table I11 with dihedral angles of 180 and 60' for the s-trans and gauche conformers, respectively, and they are given in Table V. For the general Cl(n) case each transition is ninefold degenerate,l and the energy levels fall into five discrete symmetry blocks labeled I?',' I'll, P2, Po,and YO1. Initial calculations were made by using the roosymmetry block, as experience has shown that the transitions in the lower portion of the well do not split significantly. Calculations on the s-trans potential function were started by using values for V,, and Vo3 of 1139 and 1052 cm-', respectively, from the methyl barrier heights calculated previously for propane3 and dimethylamine.2 The four transitions which were used initially were the higher
+
+
2078
The Journal of Physical Chemistry, Val. 83, No. 22, 1979
- - -
-
quency bands at 249, 244, and 237 cm-’ were the transitions 01 00,02 10, and 03 02, and that the lowest frequency bands at 217, 206, and 195 cm-l made up the series 10 00,20 10, and 30 20. This assignment could be fit by using the coefficients V30, VO3,V,, and V33, but the dispersions were poor and the barriers unacceptably large and, most importantly, the 03 02 transition was predicted to be so weak as to be unobservable relative to the other bands. However, these calculations indicated that the 11 10 transition should have reasonable intensity and be observed at a slightly lower frequency than the 01 00 transition. This is similar to the corresponding assignment for gauche ethyl methyl sulfide! Reassignment of the 249,244, and 237-cm-l bands 00, 11 10, and 02 01 transitions, reto the 01 spectively, resulted in a much more reasonable potential function with lower dispersions and qualitatively correct relative intensities. The results of the final calculations are given in Table V. Addition of the coefficient V3, improved the frequency fit, but the resulting dispersion was larger than the value of the coefficient. The reason for this large dispersion was the paucity of observed transitions and this did not allow for an accurate determination of V33;however, the value of this coefficient is possibly in the range of -50 and -100 cm-’.
-
-
+-
-
+-
Conclusions A number of bands present in the low-frequencyRaman spectrum of the fluid phases of ethylmethylamine have been observed to disappear on sample solidification. These results have been taken as good evidence for the presence of high-energy conformers for this compound, and support the results of a previous study of the N-H stretching region of the gaseous phase where two bands were observed and assigned to two conformer^.^ The bending mode of ethylmethylamine, observed as a B-type band in the infrared spectrum of the gaseous phase, corresponds to the Raman lines at 277 and 283 cm-l in the spectra of the gaseous and solid phases, respectively. Analysis of the rotational fine structure on this band has shown that the most stable conformer of ethylmethylamine is s-trans, since the observed splitting between the rotational subbands was inconsistent with the predicted values from the assumed gauche structures. A molecular structure has been calculated for the s-trans conformer by using the results from previous microwave studies on ethylmethylamine,’ dimethylamine,ll and ethylamine,12 these structural parameters are presented in Table 111. Bands near 120 cm-’ in both the infrared and Raman spectra of the gaseous phase have been assigned to the asymmetric torsions of both conformers. Unfortunately these bands were observed as broad featureless bands with the infrared band devoid of the expected Q branches. Therefore accurate values for the torsional frequencies could not be measured, and the potential function could not be calculated. The reasons for the unresolved nature of these bands are not clear, but the following factors may well be involved. Similar s-trans molecules previously studied have had higher symmetry (C, or Cw point groups) than ethylmethylamine. Thus, the asymmetric torsions of the other s-trans conformers have all been “out-ofplane” modes with pure C-type band contours. In the case of s-trans-ethylmethylaminethe heavy atom skeleton is nearly in the plane of the two prinicpal moments of inertia, A and B, but the dipole moment (which is due primarily to the electron density of the lone pair) is no longer perpendicular to the C axis. This means that the “outof-plane” modes no longer have a dipole moment change along the C axis, and they now have hybrid band contours
J. R. Durig and D. A.
C.Cornpton
with predominantly AIB shape. It is possible that the amino inversion will also complicate the torsional motions significantly, either by splitting the torsional energy levels or by the similar nature of the conformational change and inversion in this molecule, as discussed in the Introduction. The methyl torsional barriers in the s-trans conformer have coupled torsional transitions, as shown by the observation of transitions involving the 11,21, and 12 levels which would not occur for uncoupled tops and by the dependence of the fit on the coefficients, V,’, the sineaine coupling term, and V33,the cosine-cosine coupling term. However, even though the tops are coupled, they retain some independent character and have different barrier heights. The barriers for the C-CH3 and N-CH3 tops can be calculated’ from (V, - V,) and (Vo3- V=), respectively, and in general have lower dispersions than V30 or Vo3 and V,, because these coefficients are highly correlated. The values given with dispersions in Table V for these barriers are 1153 f 3 and 1092 f 8 cm-l (3.298 f 0.009 and 3.122 f 0.023 kcal/mol) for the C-CH3 and N-CH3 tops, respectively. These values are only slightly higher than the corresponding barriers of 1139 and 1052 cm-l which were calculated previously for propane3 and dimethylamine,2 respectively. The calculated barriers for the gauche conformer of ethylmethylamine are significantly higher than for their s-trans counterparts, and have values of 1343 i 8 and 1143 f 12 cm-l (3.841 f 0.021 and 3.268 f 0.034 kcal/mol), respectively. The increase in the N-CH3 barrier is quite small, 51 cm-l, but the increase in the C-CH3 barrier, 190 cm-l, is substantial. These increases agree with the previously calculated values for n-butane4and ethyl methyl ether? and can be attributed to steric hindrance between the tops in the gauche conformer. The larger increase in the C-CH3 barrier relative to the N-CH3 barrier agrees with the results in ethyl methyl ether6 where the O-CH3 barrier was increased by 30 cm-l in the gauche conformer, but the C-CH3 barrier was increased by 316 cm-l. It was noted6 that the C-CH3 top environment is markedly different between the two conformers, but that the O-CH3 environment does not change appreciably, and a similar trend is observed in ethylmethylamine. Close examination of the Raman spectrum between 530 and 450 cm-l showed four very weak bands at 510,493,481, and 459 cm-l, which have not been previously discussed. These bands are 4, 5, 7, and 3 cm-l higher in frequency than the bands at 506,488,474, and 456 cm-l, respectively, which have been assigned as s-trans methyl torsions, and thus these higher frequency lines have been assigned to these same methyl transitions where the molecules are in the first excited state of the asymmetric torsion. Similar excited state transitions have been observed in the spectra of s-trans-n-butane4and s-trans-ethyl methyl ether,6 but not for the corresponding gauche conformers of ethyl methyl sulfide.6 Thus, it is possible that the necessary interaction between the asymmetric and methyl torsional potential functions only occurs in the s-trans conformer. However, it must be pointed out that the very weak bands at 493 and 481 cm-l could be assigned to the two-quantum transitions of the gauche conformer, 02 00 (249 + 244 = 493 cm-’) and 03 01 (244 237 = 481 cm-l), but this necessitates an assignment which leads to an unacceptable potential function, as discussed earlier, and leaves the other weak bands unassigned.
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+
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Acknowledgment. The authors gratefully acknowledge the financial support given this study by the National Aeronautics and Space Administration by Grant NGL41-002-003.
The Journal of Physical Chemistry, Vol. 83, No. 22, 1979 2879
Torsional Spectra of Molecules with Two Internal C3" Rotors
R. E. Penn and J. E. Boggs, J. Mol. Spectrosc., 47, 340 (1973). H. Wolff and G. Gamer, Spectrochim. Acta, Part A, 28, 2121 (1972). 0. Gamer and H. Wolff, Spectrochim. Acta, Part A , 29, 129 (1973). B. M. Harney and F. A. Miller, Appl. Spectrosc., 24, 291 (1970). J. E. Wollrab and V. W. Laurie, J. Chem. Phys., 48, 5058 (1968). Y. S. Li, private communication. M. Hayashi and K. Kuwada, J. Mol. Struct., 28, 147 (1975). 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).
(7) (8) (9) (10) (11) (12) (13) (14)
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
