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Infrared spectra and internal rotation in propane, isobutane and neopentane
Spectrochimica Acta, Vol. 25A,pp. 1759to 1766.PergamonPress1969.Printedin NorthernIreland
I&wed
spectra and internal rotation in propane, isobutane and neopentane
S. WEISS* and G. E. LEROI~ Frick Chemical Laboratory, Princeton University, Princeton, New Jersey, 08540 (Received 16
Jarauaw 1969)
Ab&&--The infrared spectra of propane, isobutane and neopentane were recorded at high path-length x pressure conditions between 200 and 800 cm-l. A large number of combination bends were observed and assigned, and values for the torsional frequencies of isobutane and neopentane were derived from the combination bands. Potential barriers to internal rotation were calculated from the torsional frequencies and are compared with other results available from the literature. INTR~DTJOTI~N
recent precise determination, from the infrared spectrum, of the barrier to internal rotation in ethane [l] led us to reinvestigate some other simple hydrocarbons having CH, tops. Propane is the only one of the molecules considered here for which a reliable determination of the barrier is available. This was obtained from an analysis of the splitting of rotational levels in the microwave spectrum [Z] assuming a sinusoidal hindering potential and taking into account top-top interaction. An alternate treatment of the microwave data [3] gives a slightly modified barrier, and recent theoretical calculations [3, 41 give results consistent with experiment. The barrier in isobutane was determined, with relatively large uncertainty, from the microwave spectrum by the imprecise intensity method [5]. In this case a harmonic potential with top-top interaction was assumed. Recently the cold neutron inelastic scattering technique has been applied to this problem. Of the molecules discussed here, results are available so far only for neopentane [6]. Such determinations, however, are not yet very precise. A previous attempt to directly observe the infrared torsional spectrum of propane and isobutane failed, [7] even though both molecules have symmetry-allowed torsional transitions. For neopentane the analogous transitions are infrared (and Raman) forbidden. Thermodynamic barrier determinations, assuming a sinusoidal potential and no top-top interaction, are available for all three molecules [S]. THE
* Present address: Department of Physical Chemistry, Nuclear Research Centre-Negev, Israel Atomic Energy Commission, Beer Sheva, Israel. t Present address: Department of Chemistry, Michigan State University, East Lansing, Michigan 48823. [l] S. WEISS and G. E. LEROI, J. Chem. Phye. 48, 962 (1968). [2] E. HIROTA, C. MATS-A and Y. MORINO, Bull. Chem. Sot. Japan 40, 1124 (1967). [3] J. R. HOYLAND, J. Chem. Phys. 49, 1908 (1968). [4] J. R. HOYLAND, J. Am. Chem. Sot. 90,2227 (1968). [5] D. R. LIDE and D. E. MANN, J. Chem. Phys. 29,914 (1958). [6] D. M. GRANT,K. A. STRONU and R. M. BRUGGER, Phye. Rev. Lett. 20, 983 (1968); see also J. J. RUSH, J. Chem. Phys. 46, 2285 (1967). [7] W. G. FATELEY and F. A. MILLER, Spectrochim. Acta 18, 977 (1961). [8] K. S. PITZER, Discussions Faraday Sot. 10, 66 (1951). 1759
1760
S. WEISS and G. E.
However, such determinations uncertainties. This situation thus clearly will make comparison possible, molecules. We present here isobutane and neopentane, conditions.
LEROI
are rather indirect
and subject
to relatively
large
calls for a uniform theoretical treatment [9], which and for more experimental results on these important the results of an infrared investigation of propane, conducted under high pressure-long path length EXPERIMENTAL
All spectra were recorded on a Beckman IR-12 spectrophotometer operating in double beam mode and recording ln I,,/1 directly. Gases were contained in a Beckman multiple reflection cell, the optical length of which could be varied in steps between 10 cm and 10 m. The cell was equipped with cesium iodide windows, and a simple evacuated cell with similar windows was placed in the reference beam. Sample pressures varied between 1 and 6 atm. Resolution was about 1.5-2 cm-l in the spectral region covered. The frequency calibration of the instrument was checked against known atmospheric absorptions ; the accuracy of the reported frequencies is approximately f 1 cm-i. All the experiments reported in this paper were carried out at room temperature. The hydrocarbons were obtained from the Phillips Petroleum Co. and were of the following stated purities : propane- 99.99% (ether and propylene the most likely impurities) ; isobutane- 99.99% (n-butane the most likely impurity); neopentane99.97% (n-butane the most likely impurity). The gases were used without additional purification except for being passed through a column packed with & in. “Linde” Type 3A molecular sieves when transferred between the cylinders and the folded path cell. RESULTS AND DISCUSSION The spectra obtained are reproduced in Fig. 1, and the positions of the band maxima and possible assignments are listed in Table 1. The relatively large number of bands obtained is due to the high path-length x pressure conditions (significantly greater than used in the previous study [7]) which made even weak bands observable. While it is well known that the “infrared active” torsional transitions of propane and isobutane must be extremely weak [7], it is important to note that, unlike ethane [l], in no case were torsional transitions intensified sufficiently through interaction with other vibrations to be observed directly. (The absorption at 264 cm-l in propane corresponds closely to the frequency expected for the i.r.-active B, component of the torsional fundamental, but cannot be thus assigned with certainty.) The same negative results were also obtained for n-butane and CH,CF,, which were also studied in this investigation, but in less detail [lo]. This may be understood if it is assumed [9] There has been a great deal of recent effort in this area. The results have been summarized (for the example of ethane) by SOMERS et al., who introduce a promising method utilizing bond-orbital wave functions. See 0. J. SOVERS, C. W. KERN,R. M. PITZERand M. KARPLUS, J. Chem. Phy8.49,2592 (1968). [lo] We have extended the region covered for the infrared spectrum of 1 ,l,l trifluoroethane to (See H. S. GUTOWSKY and H. B. LEVINE,J. Chem. phy8.18, 1297 (1950).) The 200 cm-l. primary new feature below 300 cm-l was a peak at 237 cm-l, which is assigned as
v5 -
v12*
1761
Infrared spectra and intmnal rot&ion in propane, isobutane and neopentane
KH314C I Sctm.,
I
I
III
860
!
820 840
780 600
I’
I
740 760
I
700 720
I
!
660 680
I
!
620 640
I
!
III
580 600
!
540 560
500 520
I
IIll
460 480
!
420 440
380 400
I
!
340 360
I’
II
300 320
!
260 280
IOm
I
220 240
200
cm-’
Fig. 1. Infrared spectra of (CHs)&X,,
(CH,),CH,
(CH&C
(In I,/1 vs. frequency).
Table 1. Observed infrared frequencies and their assignments Observed frequencies Compound (cm-“)
(CH,)&Hs*
256 264 460 468 634 541 661 661 620 628 643
(C&f&Et
244 247 263 351 366 384 422 432 447 476 482 490 600 628 639 677
Ae8igmnents B, torsion (1) 1378 - 922 = 466 1338 - 869 = 469 2 X 369271= 467 748216~ 632 P branch 2 x 271= 642 922 - 369 = 663 R branch 1064 - 2 x 216 = 622 369 +
271 = 640
961 - 433 - 280 = 248 913 - 433 - 226 = 266 P branch E fundamental R brsnch P brsnoh A, fundamental R branch (981) - 280 - 226 = (476) 1189432 - 280= 477 913 - 431= 482 432 + 280 - 226 = 487 2 x 432366= 498 P branch 1189 - 366 - 280 = 643 1330 - 786 = 634 432 + 366 - 226 = 673
Compound
G%)&t
Observed frequencies (cm-l) 336
406 416 428 467 480 498 620 626 647
691 604 616 663 687 689 733
140 743 749 334
Assignments 336 + 282 - 282 (E fundamental; normally infrtrted inaotwe) P branch F, fundamental R branoh 416 $ 282 - 230 = 468 R branch 2 x 416336 = 497 416 + 335 - 230 = 621 Ii branch 733 + 230 - 416 = 647 2 x 416282= 660 2 x 282 = 664 (981) - 416 = (666) 923 - 336 = 588 2 x 416 - 230 = 602 282 + 336 = 617 (1036) - 416 = (619) 733 + 335 - 416 = 652 1263 - 2 X 282 = 689 R branch 733 + 282 - 282 (A, fundsmental; normally infrared inaotive) 923 + 230 - 416 = 737 1263 - 230 - 282 = 741 336 $ 416 = 761 2 x 416 = 832 1263 - 416 = 837
l Frequencies used for fundamentals (exoept for torsions) are from J. N. GAYmS, JR. and W. T. KING, S~ectrochim. Acta $31, 543 (1966). Torsional frequencies are from Ref. [2]. t Frequencies used for fundamentals am from R. a. EYNDIGBand J. H. B~~~aarscmnn~~~, Specrrochim. Acfu 21,169 (1966); frequencies in parentheses were derived by these authors from en assumed force field.
S. WEISS and G. E. LEROI
1762
that Coriolis interaction through rotation about the C-C axis is responsible for the appearance of the torsional spectrum in ethane [ 1, 111. None of the molecules discussed here have moments of inertia about the C-C axis nearly as low as that of ethane, so that intensification by this mechanism would be much less likely. In the absence of direct observation or microwave splitting results the torsional frequencies can still be estimated from combination bands. This method led to quite reliable results for ethane [12]. It should be pointed out, however, that this method suffers in addition to its well known uncertainties, also from ambiguities in assignment. This situation becomes more serious with increasing number of fundamentals and when working under conditions which make very weak bands observable. Under such circumstances a large number of combination bands involving the torsional vibrations must be available before the torsional frequencies can be determined with any confidence. We consider this situation as having been realized in our experiments only for isobutane and neopentane. Each of the hydrocarbons considered here has two torsional normal modes, one of which may be degenerate (see Appendix for details). The frequency difference between the two normal modes is due partly to the different reduced moments of inertia which apply, and partly to top-top interaction terms in the potential energy (which are particularly important for isobutane and neopentane). The reduced moments of inertia may be calculated without difficulty once a molecular structure is assumed; however, this is not so with regard to the potential energy of the top-top interaction. When the potential energy is expanded in an n-dimensional Fourier series (n = number of tops) it is immediately apparent that, even when terms in 64 and higher are dropped (4 = internal rotation angle), the number of remaining interaction terms is quite large (2 for propane, 4 for isobutane, 7 for neopentane). Clearly the experimental data are insufficient for the determination of a large number of parameters. Also the mathematical complexity of the problem is considerable ; it has been solved, so far, only for propane [2-4, 13, 141. The simplified treatment of this problem proposed by LIDE and MANN for C,, molecules [15] (isobutane) can be readily extended to the rest of our hydrocarbons. The details are given in the Appendix. In this approach the potential energy is again expanded in an n-dimensional Fourier series and all terms in 64 and higher are dropped. The remaining terms are then expanded in a Taylor series about the equilibrium position and only the quadratic (harmonic) terms retained. All top-top interaction terms which shift both torsional frequencies in the same direction are added to the simple top potential and the coefficients are represented by one constant ; all interaction terms which contribute to the splitting of the torsional frequencies are added and their coefficients are represented by another constant. The first constant is taken as a measure of the barrier to internal rotation (vide infra) and the second as a measure of the top-top interaction. The assumption of a harmonic potential represents, of course, an approximation and causes a shift (decrease) in the [Ill [12] [13] [14] [15]
D. D. K. L. D.
F. EUUERS, JR., J. Chem. Phys. 48, 1393 (1968). R. LIDE, J. Chem. Phys. 29, 1426 (1958). D. MUELLERand H. G. ANDRESEN, J. Chem. Phys. 27, 1800 (1962). PIERCE, J. Chem. Phys. 34, 498 (1961). R. LIDE and D. E. MANN, J. Chem. Phya. 28, 572 (1958).
-
1024 cm-1 2928 cal/moIe
1501 cm-r 4921 callmole
-137 cm-l 1499 cm-r 4286 caljmole-392 caljmole
23O(A,) 0 282(F,) 0
5.40&) 0 54OWJ 8
(CH,),C
-
6030 cal/mole$ $
1504 cm-r 4300 calfmole
1260 cm-l 3620 Gal/mole
1367 cm-l$ -160 cm-r$ 3910 cal~moIe-457 oallmoie
1189 cm-l 3400 cal/mole
1163 cm-l t -60 cm-l t 3325 cal/mole-170 oal/mole
962 cm-r 2750 callmole
Barrier heights and top-top interaction terms a~ailabIe from the literature t t Top--top Barrier interaction height
* Ref. [l]. t Ref. [2] and references quoted therein, $ Ref. [5]. Our results agree with theirs and serve to decrease their large experimental uncertainties ( f20 cm-l). 0 This work. The CH, structure and C-C distance were assumed to be the same as in isobutane. ** Calculated with the aid of D. R. Hers~hbach’s Tables for the Internal Rotation Problem, Dept. of Chemistry, IIarvard University. The barrier height is Vs of the potential function 2 V = Vs( 1 - cos 3+). Vs was calculated for each torsional mode and then averaged. tt Exoept where noted, these are thermodynamic determinations, from Ref. [7]. (The value given in Pitzer’s Table 2 for the ethane barrier is the mean of the barriers determined thermodynamically and spectroscopically.) 2% Ref. [S].
1425 cm-l 4074 caI~moIe
- 160 cm-r 1367 cm+ 3900 caI/mole467 oalfmole
22Wz)S 28O(B)S
538(-4,)$ 570(E) $
(C%),CR
1107 cm--l 3336 oal/mole
(CHa)*CHz
897 cm-r 2505 cal/mole 1030 cm-l -99 cm-1 2945 oal/mole-283 cal/mole
2WQt
5*57(-J&)t 7.2l(Wt
CD,CD,*
Barrier height assuming sinusoidal potential and no top-top interaction* *
interaction terms
271VMt
208(&J)*
5357(A,,)*
Compound
Torsional frequentties (experimental) (cm-l)
Reciprocal reduced moment of inertia (cm-l)
Barrier height and top-top interaction term assuming harmonic potential Barrier Top-top height@K) interaction
Table 2. Torsional frequencies, barrier heights and top-top
1764
S. WEISS
and 0.
E. LEROI
calculated potential barrier relative to that calculated with the full Fourier series (neglecting terms in 64 and higher, but without Taylor expansion and truncation). The comparisons which are possible for ethane and propane suggest, however, that the shifts would be quite similar for all the molecules considered here, so that comparisons are still valid.* The torsional frequencies and the parameters of the potential function calculated from them are collected in Table 2. The frequencies for propane are from Ref. [2] ; those for isobutane and neopentane were fitted to best explain the observed oombination bands. The results for isobutane agree with those of LIDE and M&N [5] and serve to reduce their experimental uncertainty. The agreement with the neutron inelastic scattering results for neopentane [6] is fair, the discrepancy being comparable to that found for ethane [ 161. Results for C&D, (which was chosen rather than C,H,, since it has a moment of inertia more similar to those of the other molecules treated here) are included for comparison. For all three molecules the term providing a measure for the barrier height (K-see Appendix) is much larger than the one which indicates the magnitude of the top-top interaction (L-see Appendix). If it were not for various top-top coupling terms K would be directly proportional to the barrier height of a simple sinusoidal one dimensional potential function of the kind used for single top molecules. It has been suggested [15] that the fact that K > L may be taken to indicate that all toptop coupling terms in these molecules are small compared to the barrier height (in the above sense). This would then mean that the barrier as seen by a particular CH, group is only weakly dependent on the positions of the other CH, groups and that barrier heights as measured by K (*K-see Appendix) can be compared with barrier heights of single top molecules. The sequence of barrier heights is as expected, and so is that of the negative (indicating repulsion) top-top interaction terms. The small difference in top-top interaction between isobutane and neopentane is insignificant. Acknowledgment-This
work was supported in part by the U.S. Office of Naval Research.
APPENDIX Notation 4i V P IOH, I,,
Iv,
I,
angle of internal rotation of the i-th top. potential energy. reduced moment of inertia. moment of inertia of CH, group about its axis of rotation. moments of inertia about the 2, y, z axis, respectively.
1. Propane Propane (C,,) has two nondegenerate torsional modes of species A, and B,. active, infrared inactive; B, is infrared and Raman active.
A, is
R-an
* The assumption of a harmonic potential for C,D, causes a decrease in the potential barrier calculated from the torsional frequency of 12.5 ‘A. Likewise the harmonic potential barrier for propane is 13 % lower than that obtained assuming a sinusoidal potential (top-top interaction being taken into account in both calculations). If the sinusoidal barrier for C,D, were 1500 cm-l (as for neopentane) the corresponding harmonic barrier would be only 9.4% lower. [16] K. A. STRONQ and R. M. BRUWER,
J. Chem. Phy&
47,421 (1967).
Infrared spectra and internal rotation in propane, isobutane and neopentane
1766
Expanding the potential function in a two-dimensional Fourier series, dropping symmetry forbidden terms (those in which the sum of exponents of sine functions is odd) and terms in w, and higher, we obtain: 2V = VO -
V,(cos 34, + CO83&)
-
V, CO83+, 00s 34, +
V, sin 3+, sin 34,.
(1)
Expanding in a Taylor series and retaining quadratic terms only (the constant term VO does not affect torsional frequencies; there are no linear terms or terms where the sum of exponents is 3) we have: 2V = K&a
+ &2) + 2L&’
(2)
where K = Q(V, Applying
+
the orthogonal transformation =I
V,);
(3)
L = ;v,.
1 =
$2
($1
+
#J2)
(4) 1 x2
=
T2
WI
-
+2)
we obtain: 2v
= (K + L)X12 + (K
(5)
- L)X22,
from which the frequencies of the normal modes are obtained as: YA* = [W_4,(K
+
LJ11’2
YB* =
-
L)]“2.
[2FB,(K
(6)
Here
FAa = A2/21ca,[l
-
(2Ics,/I,)
cos2 a/2]
FBg = f2/21cs,[1
-
(2Icx,/I,)
sin2 a/2]
(7)
where a is the CCC angle, the z axis coincides with the symmetry axis, and the y axis is perpendicular to the z axis and lies in the CCC plane and passes through the center of gravity. 2. Isobutane Isobutane (C,,) has one nondegenerate torsional mode of species A, and one doubly degenerate mode of species E. A, is infrared and Raman inactive; E is infrared and Raman active. The final results of LIDE and MANN’s derivation [14] (in slightly different notation) are included here for completeness. The potential energy, expanded in a three dimensional Fourier series, is: 2V
= V,
-
V, J&os 3+5 -
V, 2 co8 3+* co8 3+, + V, x sin 3#i sin 3+,
i
i>i -
i>3
V, cos 3+, COB3+, cos 3& + V,
In this case K = Z(V,
+ 2v,
+
V,);
1
i#j#k
L = S(Vb +
COB3+f sin 3+, sin 3&. Vd),
(8)
(3)
and the frequencies of the torsional modes are given by: V
A2= P&K
V
k=
[2Fz(K
+ 2LH”2 -
(10)
L)]“2,
where
FAI = A2/21csg[l FB = h2/21cx,[1 -
(3Ics,/I,) (3IcsJ2IJ
cos2 a] sin2 a]
(11)
1766
S. WEISS
and G. E. LEROI
and tc is the angle between a top axis and the molecular symmetry coincides, and the x axis is perpendicular to the z axis and through
axis with which the z axis the center of gravity.
3. Neopentane Neopentane (Td) has one nondegenerate torsional mode of species A, and one triply generate mode of species E;. Both are infrared and Raman forbidden. Expanding the potential function in a four dimensional series we obtain:
2V = V, -
V, 2 cos 3+i i
V,
2
V, 2 cos 3j+ cos 3+j + V, 2 sin 3+d sin 39$ i>j
i>j
cos 3& cos 34j cos 3& +
Vd
+
Expanding
V@ co9
co9 3& sin 3f#j sin 3fjk
2
(12)
i#j#k
ififk
-
de-
395, CO83$b, CO83& cos 3954+ T’,
T’, sin 39, sin 34s sin 3+s sin 3+4.
as before in a Taylor
1
cos 3& cos 3+, sin 3& sin 3+,
i#j#k#Z
series we have: 21’ = K L: $i” + 2L 2 +i& i>j i
(13)
where
K = ;(VS Applying
the orthogonal
+ 3V,
+ 3V, + V,);
L =%(V,
+ 3v,
-t v,,.
(14)
transformation:
we obtain: 211 = (K + 3L)X12 The frequencies
of the normal
+ (K - L)(X22 + XS2 + X42).
(16)
modes are: Vd2 = [2P(K
+ 3L)]1’2
[2P(K
- L)]1’2,
(17) Vp1
=
where B,=
F*a
= Fpl
= A2/2&ss
and 0: is the CCC angle and I is the moment
[
1 -
(4&,/I)
co92 ;
of inertia of the molecule.
1
(181
I&wed
spectra and internal rotation in propane, isobutane and neopentane
S. WEISS* and G. E. LEROI~ Frick Chemical Laboratory, Princeton University, Princeton, New Jersey, 08540 (Received 16
Jarauaw 1969)
Ab&&--The infrared spectra of propane, isobutane and neopentane were recorded at high path-length x pressure conditions between 200 and 800 cm-l. A large number of combination bends were observed and assigned, and values for the torsional frequencies of isobutane and neopentane were derived from the combination bands. Potential barriers to internal rotation were calculated from the torsional frequencies and are compared with other results available from the literature. INTR~DTJOTI~N
recent precise determination, from the infrared spectrum, of the barrier to internal rotation in ethane [l] led us to reinvestigate some other simple hydrocarbons having CH, tops. Propane is the only one of the molecules considered here for which a reliable determination of the barrier is available. This was obtained from an analysis of the splitting of rotational levels in the microwave spectrum [Z] assuming a sinusoidal hindering potential and taking into account top-top interaction. An alternate treatment of the microwave data [3] gives a slightly modified barrier, and recent theoretical calculations [3, 41 give results consistent with experiment. The barrier in isobutane was determined, with relatively large uncertainty, from the microwave spectrum by the imprecise intensity method [5]. In this case a harmonic potential with top-top interaction was assumed. Recently the cold neutron inelastic scattering technique has been applied to this problem. Of the molecules discussed here, results are available so far only for neopentane [6]. Such determinations, however, are not yet very precise. A previous attempt to directly observe the infrared torsional spectrum of propane and isobutane failed, [7] even though both molecules have symmetry-allowed torsional transitions. For neopentane the analogous transitions are infrared (and Raman) forbidden. Thermodynamic barrier determinations, assuming a sinusoidal potential and no top-top interaction, are available for all three molecules [S]. THE
* Present address: Department of Physical Chemistry, Nuclear Research Centre-Negev, Israel Atomic Energy Commission, Beer Sheva, Israel. t Present address: Department of Chemistry, Michigan State University, East Lansing, Michigan 48823. [l] S. WEISS and G. E. LEROI, J. Chem. Phye. 48, 962 (1968). [2] E. HIROTA, C. MATS-A and Y. MORINO, Bull. Chem. Sot. Japan 40, 1124 (1967). [3] J. R. HOYLAND, J. Chem. Phys. 49, 1908 (1968). [4] J. R. HOYLAND, J. Am. Chem. Sot. 90,2227 (1968). [5] D. R. LIDE and D. E. MANN, J. Chem. Phys. 29,914 (1958). [6] D. M. GRANT,K. A. STRONU and R. M. BRUGGER, Phye. Rev. Lett. 20, 983 (1968); see also J. J. RUSH, J. Chem. Phys. 46, 2285 (1967). [7] W. G. FATELEY and F. A. MILLER, Spectrochim. Acta 18, 977 (1961). [8] K. S. PITZER, Discussions Faraday Sot. 10, 66 (1951). 1759
1760
S. WEISS and G. E.
However, such determinations uncertainties. This situation thus clearly will make comparison possible, molecules. We present here isobutane and neopentane, conditions.
LEROI
are rather indirect
and subject
to relatively
large
calls for a uniform theoretical treatment [9], which and for more experimental results on these important the results of an infrared investigation of propane, conducted under high pressure-long path length EXPERIMENTAL
All spectra were recorded on a Beckman IR-12 spectrophotometer operating in double beam mode and recording ln I,,/1 directly. Gases were contained in a Beckman multiple reflection cell, the optical length of which could be varied in steps between 10 cm and 10 m. The cell was equipped with cesium iodide windows, and a simple evacuated cell with similar windows was placed in the reference beam. Sample pressures varied between 1 and 6 atm. Resolution was about 1.5-2 cm-l in the spectral region covered. The frequency calibration of the instrument was checked against known atmospheric absorptions ; the accuracy of the reported frequencies is approximately f 1 cm-i. All the experiments reported in this paper were carried out at room temperature. The hydrocarbons were obtained from the Phillips Petroleum Co. and were of the following stated purities : propane- 99.99% (ether and propylene the most likely impurities) ; isobutane- 99.99% (n-butane the most likely impurity); neopentane99.97% (n-butane the most likely impurity). The gases were used without additional purification except for being passed through a column packed with & in. “Linde” Type 3A molecular sieves when transferred between the cylinders and the folded path cell. RESULTS AND DISCUSSION The spectra obtained are reproduced in Fig. 1, and the positions of the band maxima and possible assignments are listed in Table 1. The relatively large number of bands obtained is due to the high path-length x pressure conditions (significantly greater than used in the previous study [7]) which made even weak bands observable. While it is well known that the “infrared active” torsional transitions of propane and isobutane must be extremely weak [7], it is important to note that, unlike ethane [l], in no case were torsional transitions intensified sufficiently through interaction with other vibrations to be observed directly. (The absorption at 264 cm-l in propane corresponds closely to the frequency expected for the i.r.-active B, component of the torsional fundamental, but cannot be thus assigned with certainty.) The same negative results were also obtained for n-butane and CH,CF,, which were also studied in this investigation, but in less detail [lo]. This may be understood if it is assumed [9] There has been a great deal of recent effort in this area. The results have been summarized (for the example of ethane) by SOMERS et al., who introduce a promising method utilizing bond-orbital wave functions. See 0. J. SOVERS, C. W. KERN,R. M. PITZERand M. KARPLUS, J. Chem. Phy8.49,2592 (1968). [lo] We have extended the region covered for the infrared spectrum of 1 ,l,l trifluoroethane to (See H. S. GUTOWSKY and H. B. LEVINE,J. Chem. phy8.18, 1297 (1950).) The 200 cm-l. primary new feature below 300 cm-l was a peak at 237 cm-l, which is assigned as
v5 -
v12*
1761
Infrared spectra and intmnal rot&ion in propane, isobutane and neopentane
KH314C I Sctm.,
I
I
III
860
!
820 840
780 600
I’
I
740 760
I
700 720
I
!
660 680
I
!
620 640
I
!
III
580 600
!
540 560
500 520
I
IIll
460 480
!
420 440
380 400
I
!
340 360
I’
II
300 320
!
260 280
IOm
I
220 240
200
cm-’
Fig. 1. Infrared spectra of (CHs)&X,,
(CH,),CH,
(CH&C
(In I,/1 vs. frequency).
Table 1. Observed infrared frequencies and their assignments Observed frequencies Compound (cm-“)
(CH,)&Hs*
256 264 460 468 634 541 661 661 620 628 643
(C&f&Et
244 247 263 351 366 384 422 432 447 476 482 490 600 628 639 677
Ae8igmnents B, torsion (1) 1378 - 922 = 466 1338 - 869 = 469 2 X 369271= 467 748216~ 632 P branch 2 x 271= 642 922 - 369 = 663 R branch 1064 - 2 x 216 = 622 369 +
271 = 640
961 - 433 - 280 = 248 913 - 433 - 226 = 266 P branch E fundamental R brsnch P brsnoh A, fundamental R branch (981) - 280 - 226 = (476) 1189432 - 280= 477 913 - 431= 482 432 + 280 - 226 = 487 2 x 432366= 498 P branch 1189 - 366 - 280 = 643 1330 - 786 = 634 432 + 366 - 226 = 673
Compound
G%)&t
Observed frequencies (cm-l) 336
406 416 428 467 480 498 620 626 647
691 604 616 663 687 689 733
140 743 749 334
Assignments 336 + 282 - 282 (E fundamental; normally infrtrted inaotwe) P branch F, fundamental R branoh 416 $ 282 - 230 = 468 R branch 2 x 416336 = 497 416 + 335 - 230 = 621 Ii branch 733 + 230 - 416 = 647 2 x 416282= 660 2 x 282 = 664 (981) - 416 = (666) 923 - 336 = 588 2 x 416 - 230 = 602 282 + 336 = 617 (1036) - 416 = (619) 733 + 335 - 416 = 652 1263 - 2 X 282 = 689 R branch 733 + 282 - 282 (A, fundsmental; normally infrared inaotive) 923 + 230 - 416 = 737 1263 - 230 - 282 = 741 336 $ 416 = 761 2 x 416 = 832 1263 - 416 = 837
l Frequencies used for fundamentals (exoept for torsions) are from J. N. GAYmS, JR. and W. T. KING, S~ectrochim. Acta $31, 543 (1966). Torsional frequencies are from Ref. [2]. t Frequencies used for fundamentals am from R. a. EYNDIGBand J. H. B~~~aarscmnn~~~, Specrrochim. Acfu 21,169 (1966); frequencies in parentheses were derived by these authors from en assumed force field.
S. WEISS and G. E. LEROI
1762
that Coriolis interaction through rotation about the C-C axis is responsible for the appearance of the torsional spectrum in ethane [ 1, 111. None of the molecules discussed here have moments of inertia about the C-C axis nearly as low as that of ethane, so that intensification by this mechanism would be much less likely. In the absence of direct observation or microwave splitting results the torsional frequencies can still be estimated from combination bands. This method led to quite reliable results for ethane [12]. It should be pointed out, however, that this method suffers in addition to its well known uncertainties, also from ambiguities in assignment. This situation becomes more serious with increasing number of fundamentals and when working under conditions which make very weak bands observable. Under such circumstances a large number of combination bands involving the torsional vibrations must be available before the torsional frequencies can be determined with any confidence. We consider this situation as having been realized in our experiments only for isobutane and neopentane. Each of the hydrocarbons considered here has two torsional normal modes, one of which may be degenerate (see Appendix for details). The frequency difference between the two normal modes is due partly to the different reduced moments of inertia which apply, and partly to top-top interaction terms in the potential energy (which are particularly important for isobutane and neopentane). The reduced moments of inertia may be calculated without difficulty once a molecular structure is assumed; however, this is not so with regard to the potential energy of the top-top interaction. When the potential energy is expanded in an n-dimensional Fourier series (n = number of tops) it is immediately apparent that, even when terms in 64 and higher are dropped (4 = internal rotation angle), the number of remaining interaction terms is quite large (2 for propane, 4 for isobutane, 7 for neopentane). Clearly the experimental data are insufficient for the determination of a large number of parameters. Also the mathematical complexity of the problem is considerable ; it has been solved, so far, only for propane [2-4, 13, 141. The simplified treatment of this problem proposed by LIDE and MANN for C,, molecules [15] (isobutane) can be readily extended to the rest of our hydrocarbons. The details are given in the Appendix. In this approach the potential energy is again expanded in an n-dimensional Fourier series and all terms in 64 and higher are dropped. The remaining terms are then expanded in a Taylor series about the equilibrium position and only the quadratic (harmonic) terms retained. All top-top interaction terms which shift both torsional frequencies in the same direction are added to the simple top potential and the coefficients are represented by one constant ; all interaction terms which contribute to the splitting of the torsional frequencies are added and their coefficients are represented by another constant. The first constant is taken as a measure of the barrier to internal rotation (vide infra) and the second as a measure of the top-top interaction. The assumption of a harmonic potential represents, of course, an approximation and causes a shift (decrease) in the [Ill [12] [13] [14] [15]
D. D. K. L. D.
F. EUUERS, JR., J. Chem. Phys. 48, 1393 (1968). R. LIDE, J. Chem. Phys. 29, 1426 (1958). D. MUELLERand H. G. ANDRESEN, J. Chem. Phys. 27, 1800 (1962). PIERCE, J. Chem. Phys. 34, 498 (1961). R. LIDE and D. E. MANN, J. Chem. Phya. 28, 572 (1958).
-
1024 cm-1 2928 cal/moIe
1501 cm-r 4921 callmole
-137 cm-l 1499 cm-r 4286 caljmole-392 caljmole
23O(A,) 0 282(F,) 0
5.40&) 0 54OWJ 8
(CH,),C
-
6030 cal/mole$ $
1504 cm-r 4300 calfmole
1260 cm-l 3620 Gal/mole
1367 cm-l$ -160 cm-r$ 3910 cal~moIe-457 oallmoie
1189 cm-l 3400 cal/mole
1163 cm-l t -60 cm-l t 3325 cal/mole-170 oal/mole
962 cm-r 2750 callmole
Barrier heights and top-top interaction terms a~ailabIe from the literature t t Top--top Barrier interaction height
* Ref. [l]. t Ref. [2] and references quoted therein, $ Ref. [5]. Our results agree with theirs and serve to decrease their large experimental uncertainties ( f20 cm-l). 0 This work. The CH, structure and C-C distance were assumed to be the same as in isobutane. ** Calculated with the aid of D. R. Hers~hbach’s Tables for the Internal Rotation Problem, Dept. of Chemistry, IIarvard University. The barrier height is Vs of the potential function 2 V = Vs( 1 - cos 3+). Vs was calculated for each torsional mode and then averaged. tt Exoept where noted, these are thermodynamic determinations, from Ref. [7]. (The value given in Pitzer’s Table 2 for the ethane barrier is the mean of the barriers determined thermodynamically and spectroscopically.) 2% Ref. [S].
1425 cm-l 4074 caI~moIe
- 160 cm-r 1367 cm+ 3900 caI/mole467 oalfmole
22Wz)S 28O(B)S
538(-4,)$ 570(E) $
(C%),CR
1107 cm--l 3336 oal/mole
(CHa)*CHz
897 cm-r 2505 cal/mole 1030 cm-l -99 cm-1 2945 oal/mole-283 cal/mole
2WQt
5*57(-J&)t 7.2l(Wt
CD,CD,*
Barrier height assuming sinusoidal potential and no top-top interaction* *
interaction terms
271VMt
208(&J)*
5357(A,,)*
Compound
Torsional frequentties (experimental) (cm-l)
Reciprocal reduced moment of inertia (cm-l)
Barrier height and top-top interaction term assuming harmonic potential Barrier Top-top height@K) interaction
Table 2. Torsional frequencies, barrier heights and top-top
1764
S. WEISS
and 0.
E. LEROI
calculated potential barrier relative to that calculated with the full Fourier series (neglecting terms in 64 and higher, but without Taylor expansion and truncation). The comparisons which are possible for ethane and propane suggest, however, that the shifts would be quite similar for all the molecules considered here, so that comparisons are still valid.* The torsional frequencies and the parameters of the potential function calculated from them are collected in Table 2. The frequencies for propane are from Ref. [2] ; those for isobutane and neopentane were fitted to best explain the observed oombination bands. The results for isobutane agree with those of LIDE and M&N [5] and serve to reduce their experimental uncertainty. The agreement with the neutron inelastic scattering results for neopentane [6] is fair, the discrepancy being comparable to that found for ethane [ 161. Results for C&D, (which was chosen rather than C,H,, since it has a moment of inertia more similar to those of the other molecules treated here) are included for comparison. For all three molecules the term providing a measure for the barrier height (K-see Appendix) is much larger than the one which indicates the magnitude of the top-top interaction (L-see Appendix). If it were not for various top-top coupling terms K would be directly proportional to the barrier height of a simple sinusoidal one dimensional potential function of the kind used for single top molecules. It has been suggested [15] that the fact that K > L may be taken to indicate that all toptop coupling terms in these molecules are small compared to the barrier height (in the above sense). This would then mean that the barrier as seen by a particular CH, group is only weakly dependent on the positions of the other CH, groups and that barrier heights as measured by K (*K-see Appendix) can be compared with barrier heights of single top molecules. The sequence of barrier heights is as expected, and so is that of the negative (indicating repulsion) top-top interaction terms. The small difference in top-top interaction between isobutane and neopentane is insignificant. Acknowledgment-This
work was supported in part by the U.S. Office of Naval Research.
APPENDIX Notation 4i V P IOH, I,,
Iv,
I,
angle of internal rotation of the i-th top. potential energy. reduced moment of inertia. moment of inertia of CH, group about its axis of rotation. moments of inertia about the 2, y, z axis, respectively.
1. Propane Propane (C,,) has two nondegenerate torsional modes of species A, and B,. active, infrared inactive; B, is infrared and Raman active.
A, is
R-an
* The assumption of a harmonic potential for C,D, causes a decrease in the potential barrier calculated from the torsional frequency of 12.5 ‘A. Likewise the harmonic potential barrier for propane is 13 % lower than that obtained assuming a sinusoidal potential (top-top interaction being taken into account in both calculations). If the sinusoidal barrier for C,D, were 1500 cm-l (as for neopentane) the corresponding harmonic barrier would be only 9.4% lower. [16] K. A. STRONQ and R. M. BRUWER,
J. Chem. Phy&
47,421 (1967).
Infrared spectra and internal rotation in propane, isobutane and neopentane
1766
Expanding the potential function in a two-dimensional Fourier series, dropping symmetry forbidden terms (those in which the sum of exponents of sine functions is odd) and terms in w, and higher, we obtain: 2V = VO -
V,(cos 34, + CO83&)
-
V, CO83+, 00s 34, +
V, sin 3+, sin 34,.
(1)
Expanding in a Taylor series and retaining quadratic terms only (the constant term VO does not affect torsional frequencies; there are no linear terms or terms where the sum of exponents is 3) we have: 2V = K&a
+ &2) + 2L&’
(2)
where K = Q(V, Applying
+
the orthogonal transformation =I
V,);
(3)
L = ;v,.
1 =
$2
($1
+
#J2)
(4) 1 x2
=
T2
WI
-
+2)
we obtain: 2v
= (K + L)X12 + (K
(5)
- L)X22,
from which the frequencies of the normal modes are obtained as: YA* = [W_4,(K
+
LJ11’2
YB* =
-
L)]“2.
[2FB,(K
(6)
Here
FAa = A2/21ca,[l
-
(2Ics,/I,)
cos2 a/2]
FBg = f2/21cs,[1
-
(2Icx,/I,)
sin2 a/2]
(7)
where a is the CCC angle, the z axis coincides with the symmetry axis, and the y axis is perpendicular to the z axis and lies in the CCC plane and passes through the center of gravity. 2. Isobutane Isobutane (C,,) has one nondegenerate torsional mode of species A, and one doubly degenerate mode of species E. A, is infrared and Raman inactive; E is infrared and Raman active. The final results of LIDE and MANN’s derivation [14] (in slightly different notation) are included here for completeness. The potential energy, expanded in a three dimensional Fourier series, is: 2V
= V,
-
V, J&os 3+5 -
V, 2 co8 3+* co8 3+, + V, x sin 3#i sin 3+,
i
i>i -
i>3
V, cos 3+, COB3+, cos 3& + V,
In this case K = Z(V,
+ 2v,
+
V,);
1
i#j#k
L = S(Vb +
COB3+f sin 3+, sin 3&. Vd),
(8)
(3)
and the frequencies of the torsional modes are given by: V
A2= P&K
V
k=
[2Fz(K
+ 2LH”2 -
(10)
L)]“2,
where
FAI = A2/21csg[l FB = h2/21cx,[1 -
(3Ics,/I,) (3IcsJ2IJ
cos2 a] sin2 a]
(11)
1766
S. WEISS
and G. E. LEROI
and tc is the angle between a top axis and the molecular symmetry coincides, and the x axis is perpendicular to the z axis and through
axis with which the z axis the center of gravity.
3. Neopentane Neopentane (Td) has one nondegenerate torsional mode of species A, and one triply generate mode of species E;. Both are infrared and Raman forbidden. Expanding the potential function in a four dimensional series we obtain:
2V = V, -
V, 2 cos 3+i i
V,
2
V, 2 cos 3j+ cos 3+j + V, 2 sin 3+d sin 39$ i>j
i>j
cos 3& cos 34j cos 3& +
Vd
+
Expanding
V@ co9
co9 3& sin 3f#j sin 3fjk
2
(12)
i#j#k
ififk
-
de-
395, CO83$b, CO83& cos 3954+ T’,
T’, sin 39, sin 34s sin 3+s sin 3+4.
as before in a Taylor
1
cos 3& cos 3+, sin 3& sin 3+,
i#j#k#Z
series we have: 21’ = K L: $i” + 2L 2 +i& i>j i
(13)
where
K = ;(VS Applying
the orthogonal
+ 3V,
+ 3V, + V,);
L =%(V,
+ 3v,
-t v,,.
(14)
transformation:
we obtain: 211 = (K + 3L)X12 The frequencies
of the normal
+ (K - L)(X22 + XS2 + X42).
(16)
modes are: Vd2 = [2P(K
+ 3L)]1’2
[2P(K
- L)]1’2,
(17) Vp1
=
where B,=
F*a
= Fpl
= A2/2&ss
and 0: is the CCC angle and I is the moment
[
1 -
(4&,/I)
co92 ;
of inertia of the molecule.
1
(181