J. Phys. Chem. 1989, 93, 3487-3491 is just one example of the use of pressure to determine the relationship between the bulk and molecular properties of a material. Acknowledgment. This work was supported in part by the Materials Science Division, Department of Energy, under contract
3487
DE-AC02-76ER01198. Registry No. 1, 10081-39-7;2, 15753-54-5;3, 86581-38-6; methanol, 67-56-1; ethanol, 64-17-5; 2-propano1,67-63-0;poly(styrene), 9003-53-6: poly(methy1 methacrylate), 901 1- 14-7.
Torsional Spectrum and ab Initlo Calculations for Propene J. R. Durig,* G. A. Guirgis,+ Department of Chemistry, University of South Carolina, Columbia, South Carolina 29208
and Stephen Bell* Department of Chemistry, University of Dundee, Dundee DDl 4”. In Final Form: November 21, 1988)
Scotland, UK (Received: July 22, 1987;
The far-infrared spectrum of propene, CH2CHCH3,has been recorded in the gas phase with a resolution of 0.10 cm-l from 370 to 80 cm-I. The methyl torsional fundamental with at least two accompanying hot bands has been observed and the barrier to internal rotation has been calculated. Detailed K structure is also measured and used in the analysis. A two-quantum transition has been observed in the Raman spectrum of the gas. A systematic comparison is made between propene and acetaldehyde,both for the far-infrared spectrum and for the interpretation of the torsional kinetic and potential energy parameters. For the chosen value of the kinetic parameter F = 7.1007 cm-l, the potential constants V3 = 693.7 crn-l and V, = -14.0 cm-I fit four observed transitions well. The calculated value V3= 649.4 cm-’ obtained by ab initio methods is in fair agreement 6 is much smaller than the experimental one. with experimental values but the calculated value of v
Introduction The torsional spectrum of propene has been studied previously but not as extensively as that of the similar molecule, acetaldehyde. Torsional frequencies of propene were measured by Fateley and Miller’ as part of their thorough, elegant study of the far-infrared spectra of many molecules with hindered methyl rotors. They observed three bands but only the two stronger, higher frequencies were interpreted and used to determine V, and V,. This spectrum has been reexamined a few and the third band was not observed. The spectrum by Moller et aL2 was recorded at the higher resolution and some K structure associated with the main torsional band was partially resolved. Since the far-infrared spectrum of propene has not been studied after the commercial availability of high-resolution Fourier transform interferometers, a new study is timely and worthwhile. This is particularly true in view of the similarity of this molecule with acetaldehyde and the more recent far-infrared spectral study of Hollenstein and Winther5 where detailed rotational fine structure was reported. In order to interpret a torsional spectrum it is usually necessary to use data from the microwave spectrum. Lide and Mann6 used the microwave spectra of normal propene and one isotopic species to determine the structure of the carbon skeleton and from the splittings of the lines to obtain a torsional potential barrier. A complete r, structure was determined by Lide and Christensen7 from the spectra of seven isotopic species. Doubly deuterium substituted species have been synthesized and their microwave spectra measured by Hirota and Morino.6 A very thorough study of the internal rotation in propene has been made by Hirota9 by the measurement of rotational line splittings in two excited torsional states as well as the ground state. Although some microwave data are used to interpret far-infrared torsional frequencies, potential energy constants found in this way often do not agree well with potential constants found from the microwave data alone.3 In fact, only a value of V, was obtained from the microwave data in the past since a value for ‘Permanent address: Analytical Research Laboratory, Dyes and Pigments Division, Mobay Corporation, Bushy Park Plant, Charleston, SC 2941 1.
0022-3654/89/2093-3487$01 .50/0
V6 can only be determined with additional observations for excited torsional states either in the microwave or far-infrared spectrum. The reduced torsional barrier (s = 4V3/9f;3 may be transferred from microwave work and used in the analysis of the far infrared,’ but with a least-squares computer program like Woods’,1os is not usually a fitting parameter now. Since the reduced internal rotation constant F is a structural parameter, it can be derived directly from the geometrical structure of the molecule as determined from a microwave study. Such a semirigid F does not take into consideration the zero-point vibrations of the molecule, inertial defect contributions, and the large-amplitude motion of the torsional mode i t ~ e l f . ~However, a microwave value of F obtained by least-squares fit of I , and other (torsional and rotational) parameters to microwave frequencies and splittings may be rather different from the F obtained from structure. Hirota9 used a value for the moment of the internal top, I,, from the structural parameters determined by Lide and Christensen.’ The other four or five parameters, including the direction cosines of the top axis, were determined by a fitting procedure and hence a value of F was obtained. It turns out that this is in very close agreement with the value obtained from the structure directly. Hirota’s values of F a r e nearly constant for the v Z I= 0, 1, and 2 torsional levels and thus might be taken to confirm the usual semirigid assumptions. For acetaldehyde, a wide range of values of F have been derived from the microwave spectra and employed in the calculations of the potential c ~ n s t a n t s . l l - ~Although ~ the models and approx(1) Fateley, W. G.; Miller, F. A. Spectrochim. Acta 1963, 19, 611.
(2) Moller, K. D.; DeMeo, A. R.; Smith, D. R.; London, L. H. J. Chem. Phys. 1967, 47, 2609. (3) Souter, C. E.; Wood, J. L. J. Chem. Phys. 1970, 52, 674. (4) Tuazon, E. C.; Manocha, A. S.; Fateley, W. G.Chem. Phys. Lett. 1973, 23, 63. ( 5 ) Hollenstein, H.; Winther, F. J. Mol. Spectrosc. 1978, 71, 118. (6) Lfde, D. R.; Mann, D. E. J. Chem. Phys. 1957, 27, 868. (7) Lide, D. R.; Christensen, D. J. Chem. Phys. 1961, 35, 1374. (8) Hirota, E.; Morino, Y . J. Chem. Phys. 1966, 45, 2326. (9) Hirota, E. J. Chem. Phys. 1966 45, 1984. (10) Woods, R. C. J. Mol. Spectrosc. 1966, 21, 4; 1967, 22, 49.
0 1989 American Chemical Society
3488 The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 imations used in obtaining geometrical structures there is reasonable agreement among the values of F obtained from these structures directly. However, much lower values have been obtained from fitting microwave splittings.'"" A much lower value is obtained by fitting far-infrared frequencies only.5 Since the kinetic energy constant for internal rotation may be transferred from the microwave spectrum, only potential energy constants V3and v6 are obtained by fitting torsional transitions in the far infrared. A barrier height obtained in this way may be preferable in view of the high relative precision of torsional transitions obtained by a high-resolution Fourier transform interferometer, and in view of the fact that such transitions span much more of the potential well than rotational transition in u = 0. When fitting the torsional transitions of acetaldehyde, the values of V3 obtained with different values of F are remarkably constant, so long as v6 is included in the least-squares fit. With the precision now available in far-infrared spectroscopy, pure torsional transitions should be fitted together with torsional-rotational splittings to simultaneously determine all the kinetic and potential energy constants and a computer program able to make such fits would be timely. In the far-infrared spectrum of acetaldehyde, the strong peaks have been assigned by Hollenstein and Winthe$ as A-A transitions, but none as E-E transitions. They argue that no E-E transitions have been properly assigned in any molecule of this type. However, the central peak in one of these bands is due to asymmetry and is not a single Q branch. Due to the molecule being a nearly prolate but asymmetric top, a C-type band has the appearance of a perpendicular ( A K = f l ) symmetric-top band with K subbands on each side with approximately constant spacing apart from a central peak due to asymmetry of 2A - ( B 0, and missing or weak low K subbands. Since much of the K subband structure to each side of the central peak in the acetaldehyde spectrum is interpreted as belonging to the E-E transitions, there seems no reason why asymmetry would not cause a central peak. In the interpretation of the far-infrared spectrum of propene and 2-fluoropropene,18possible assignments of the peaks include E-E transitions. There have been a considerable number of ab initio studies of propene, but only a few give an optimized geometric structure or enough energies to obtain torsional potential constant^.^^-^^ However, these calculations use only small basis sets; the STO-3G basis gives barriers about 200 cm-' too small,'9*20and split valence bases 4-31G2' and 4-21GZ2give barriers of about 630 cm-I.
+
Experimental and Theoretical Methods The propene sample was obtained from a commercial source and purified by sublimation on a low-temperature vacuum fractionation column. All handling of the sample was accomplished by using high-vacuum techniques to minimize sample contamination by air and water. A higher resolution (0.12 or 0.06 crn-') far-infrared spectra of all samples in the gas phase were recorded from 370 to 80 cm-I on a Nicolet Model 8000 interferometer equipped with a vacuum
( I I ) Kilb, R. W.; Lin, C. C.; Wilson, E. B. J. Chem. Phys. 1957.26, 1695. (12) Iijima, T.; Tsuchiya, S. J . Mol. Spectrosc. 1972, 44, 88. ( 1 3) Nesberger, P.; Bauder, A.; Giinthard, H. H. Chem. Phys. 1973, I ,
418. (14) Bauder, A.; Giinthard, H. H. J . Mol. Spectrosc. 1976, 60, 290. (15) Quade, C. R. J . Chem. Phys. 1980. 73, 2107. (16) Crighton, J. S.; Bell, S . J . Mol. Spectrosc. 1985, 112, 315. (17) Liang, W.; Baker, J. G.; Herbst, E.; Booker, R. A,; DeLucia, F. C. J . Mol. Spectrosc. 1986, 120, 298. (18) Bell, S.; Guirgis, G. A.; Fanning, A. R.; Durig, J. R., J . Mol. Slruct. 1988, 178, 63.
(19) Whangbo, H.-H.; Schlegel, H. B.; Wolfe, S . J . Am. Chem. Soc. 1977, 99, 1296.
( 2 0 ) Bernardi, F.; Robb, M. A.; Tonachini, G.Chem. Phys. Lett. 1979, 66. . ~195. ... ,
(21) Hehre, W. J.; Pople, J. A.; Devaquet, A. J . P. J . Am. Chem. SOC. 1977, 98, 664. (22) Schafer, L.; Van Alsenoy, C.; Scarsdale, J. N. J . Mol. Struct.: THEOCHEM 1982, 3, 349.
Durig et al.
I
C
250
190 WAVENUMBER
130
(cm-')
Figure 1. Far-infrared spectrum of gaseous propene from 240 to 115 cm-I: (A) water reference, (B) observed absorption, and (C) calculated asymmetric-top envelope. TABLE I: Torsional Transitions of Propene with Assignments and Fitted Potential Energy Constants' A only A + E transition
uOM
1 +- 0 (A) 1 0 (E) 2 +- 1 (E) 2 1 (A) 3 2 (A) 3 2 (E) 2 +- 0 (E) 2 - 0 (A)
188.05
+ -
171.24
+ -
F V3 MWC v3 v6
358" 7.1007 686.7
v,ldb 187.83 187.70 173.10 171.03 162.37 143.90 360.81 358.80
uowc
vcaldb
188.05
188.14 188.00 171.70 169.39 160.52 140.19 359.70 357.53
171.24 169.67 160.25? 358"
a b initio
7.1007
7.1007
7.2677
708.5 -21.2
693.7 -14.0
649.4 0.3
"In cm-'. bCalculated from the potential constants in same column. An alternative assignment. "From Raman spectrum. Reference 9.
bench and a liquid helium cooled germanium bolometer containing a wedged sapphire filter and polyethylene windows. A 12.5- or 6.25-pm Mylar beamsplitter was employed and every sample was contained in a 1-m cell. Raman spectra were recorded with a Cary Model 82 spectrophotometer by using the 5 1 4 5 - A excitation line f r o m either a Spectra-Physics Model 171 argon ion laser or a Coherent Radiation Model CR-8 argon ion laser where the maximum power available at the sample was 4 W. The spectra of the vapor phase were recorded by utilizing the standard Cary multipass accessories. The ab initio S C F calculations were made with the TEXAS program23and geometry optimization was carried out by a BFGS quasi-Newton optimization method implemented in the MINIT program.24 In view of the good agreement between the experimental barrier heights in acetaldehyde and acetone and ab initio barriersZ5sz6 calculated by using the Huzinaga-Dunning double-l (23) Pulay, P. Theor. Chim. Acta 1979, 50, 299. (24) Bell, S.; Crighton, J. S . J . Chem. Phys. 1984, 80, 2464.
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3489
Torsional Spectrum for Propene TABLE II: Experimental and ab Initio Structural Parameters for Propene
parameter" ClC2
exptb
ab initio staggeredC
eclipsed'
1.3344 1.5169 125.02 CIC2C3 1.0760 HICI 122.06 HlClC2 1.0742 H2CI 121.46 H2CIC2 1.0765 H3C2 116.47 H3C2C3 1.0829 HsC3 1.OS46 H*C3 11 1.09 H~C3C2 11 1.23 W3C2 HsC3C2CI 0.00 0.00 180.00 HaC3C2Cl 121.34 120.56 59.99 HsC3Ht 109.04 108.23 107.74 W3Ht 106.12 107.29 107.64 methyl tilt/ 0.18 0.47 0.12 SCF energy/Eh -1 17.039682 -117.036787 c2c3
1.3360 1.5012 124.26 1.0914 120.51 1.0808 121.54 1.0896 116.70 1.0846 1.0979 111.20 110.65
1.3342 1.5091 125.38 1.0755 121.93 1.0743 121.53 1.0776 115.79 1.083 1 1.0859 111.49 110.73
eclipsedd 1.3342 1.5092 125.39 1.0754 121.94 1.0742 121.53 1.0775 115.78 1.0850
I
1 I
111.49 111.72 0.00 120.17 107.92 0.51 -117.039666
OTwo elements for a bond length (in A), 3 or 4 elements for an angle (in degrees). bCalculated from the Cartesian coordinates of ref 7. cFull optimization in C, symmetry, methyl group not C3. "Methyl group constrained to be C3, CH lengths and HCH angles same. CTheseangles are redundant but given for comparison purposes. /The methyl axis is tilted away from the CI atom.
(DZ) basis set,27s28the geometries and energies for propene reported here were obtained for this basis only.
Results and Assignments The far-infrared spectrum of propene is shown in Figure 1 and the measurements of the main peaks are given in Table I. The stronger bands in the far infrared are interpreted as torsional transitions, but there are also other peaks which are probably hot bands involving sequences in other low-frequency vibration^.^^ A very weak band observed at 358 cm-' in the Raman spectrum is O(A) torsional transition. also assigned in Table I as the 2 The notation for the kinetic and potential energy constants for internal rotation in a molecule such as propene is given with the Schrodinger equation written as
Ha
Hs
2950
H3
3000
H1
';12
3050
V C H (cm-')
Figure 2. Correlation of CH bond lengths (ab initio 0 and experimental 0)with isolated CH stretching frequencies. The straight line is drawn with the slope of McKean's empirical correlation (ref 31).
\
/
+-
Figure 3. Structure of propene showing atom numbering. E$(T)
where F is the reduced rotational constant obtained from the moments of inertia by the equations F = h2/8a2Z, I, = Zr(l - Z q Z r / Z i ) i
Xi is the direction cosine between the internal rotor axis and the ith principal axis, and I, is the moment of inertia of the internal top about its symmetry axis. In order to interpret the torsional transitions and calculate potential energy parameters that fit the frequency, a value of the kinetic energy constant F is required. From the experimental r, geometric structure of Lide and Christensen' given in Table I1 a value for F of 7.1043 cm-l is obtained if their Cartesian coordinates are used directly, and even if the methyl group is made symmetric (equal C H lengths and HCH angles) but tilted slightly (25) Crighton, J. S.; Bell, S . J . Mol. Spectrosc. 1985, 112, 285. (26) Crighton, J. S.; Bell, S . J . Mol. Spectrosc. 1986, 118, 383. (27) Huzinaga, S . J . Chem. Phys. 1965, 42, 1293. (28) Dunning, T. H. J . Chem. Phys. 1970, 53, 2823. (29) Silvi, B.; Labarbe, P.; Perchard, J. P. Spectrochim. Acra 1973, 29A, 263.
as in their structure, one obtains a value of 7.0979 cm-'. However, one might question these values in view of the rather dissimilar methyl C H distances (1.0846 and 1.0979 A).. From isolated C-H stretching f r e q u e n ~ i e sand ~ ~ the slope of the empirical plot by McKean3' of the C-H lengths versus these frequencies, the C-H, and C-Ha lengths should differ by only 0.0029 A. Figure 2 shows the r, values of all the C-H lengths in propene plotted against the isolated frequencies and also shows a straight line with the slope from McKean's plot. The numbering of the atoms is given in Figure 3. The optimum geometry of propene as obtained by ab initio calculation is also shown in Table 11. Results are shown for the structure fully optimized in C, symmetry in both eclipsed and staggered configurations, and for the eclipsed configuration with the methyl group kept symmetric. The latter structure was used in the calculation of potential energy constants to be consistent with the semirigid internal rotation model used in fitting the torsional data. The methyl CH distances from the eclipsed, fully optimized geometry differ by 0.0028 A in agreement with the prediction based on isolated frequencies. All the C-H lengths are plotted against isolated stretching frequencies in Figure 2 and are seen to lie very close to the slope of the McKean plot.31 Plots of this kind have been made by using ab initio results of this quality (30) McKean, D. C. Spectrochim. Acta 1975, 31A, 861. (31) McKean, D. C. J . Mol. S t r u t . 1984, 113, 251.
3490
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989
TABLE 111: Variation of V , and V r with Kinetic Constant P
source of F
F
rms devb ref
v3
V,
7.1043 7.0979 7:1007 7.2677 6.8 6.5
709.59 709.85 709.73 703.11 722.53 736.42
-21.23 -21.12 -21.17 -24.01 -15.95 -10.51
7.1043 7.0979 7.1007 7.2677 6.7259 6.5
693.28 693.65 693.52 686.26 710.76 721.93
-14.25 -14.21 -14.25 -16.74 -8.28 -4.49
0.31 0.30 0.30 0.46 0.00 0.15
7 7 9
-27.37 -20.83 -20.85 -19.76 -19.74 -16.47 -9.98 -0.81
0.07 0.03 0.03 0.00 0.00 0.08 0.20 0.36
12 11
Propene
-
2 torsional transitions, A A only
M W structure M W sym CH, M W fit
SCF structure
7 7 9
7.8588 7.7728 7.7739 7.7148 7.7133 7.5372 7.2 6.751
SCF structure M W structure FIR fit M W fit FIR
415.04 415.71 415.70 416.12 416.15 417.44 419.91 422.95
13
17 5
All quantities in cm-I. Root-mean-squaredeviation of calculated torsional frequencies from observed. "6
v3
710
700
590
\
p i o p e r,P
~
65
70
F
acetaldfhyde
1
75
7.0
161.OS3 163.687 166.282 168.877 171.490 174.IO8 176.616 179.145
-1 1 -10 -9 -8 -6 -5
Acetaldehyde
M W fit M W structure
TABLE IV: Measurements and Assignments of K Subbands of Propene P form R form k ulcm-' k ulcm-' -13 155.764 3 196.586 -1 2 4 158.386 198.983
-7
3 torsional transitions,
A-A,E-E M W structure M W sym CH3 M W fit SCF structure FIR fit
Durig et al.
F
Figure 4. Variation of V, and V6 with kinetic energy parameter r (all in cm-I) for propene and acetaldehyde.
for a number of saturated hydrocarbon^.^^ The reduced internal rotation constant, F,for this structure is 7.2671 cm-I, while the value obtained for the constrained symmetric C H 3 structure is 7.2677 cm-I. These values are larger than those obtained from the experimental structure, but it is well-known that the ab initio rap, lengths, which should be compared with re lengths, are systematically shorter than ro length^.^' Least-squares fits to the torsional transition frequencies have been made for two different assignments over a range of values of F including the experimental and ab initio values discussed, and the resulting potential parameters V3and V6 are given in Table 111. Similar calculations have been made by Tuazon et al.4 but they were interested in the V6/V3 ratio. The variation of V3and V6 with F is shown in Figure 4 for the second of the possible assignments. This shows the sensitivity of the barrier height to change in F. One should notice the near linearity of this plot. For comparison purposes, a similar series of least-squares fits have been made to the torsional frequencies of acetaldehyde, ( 3 2 ) Aljibury, A . L.; Snyder, R. G.; Straws, H. L.; Raghavachari, K. J . Chem. Phys. 1986,84, 6872.
-P
5 6 7 8 9 IO 11 12 13 14 15
201.408 203.835 206.242 208.650 210.998 213.341 215.696 218.039 220.334 222.612 224.852
especially because of the wide variation of the experimentally determined values of F. The torsional frequenciesSused are vIqA), u + ~ ( E ) , vZ-l(A). The values of F obtained directly from the three structures are not greatly different: Kilb et a1.I' 7.7728; Iijima and Tsuchiyai2 7.6273 (r,) or 7.7444 ( r z / r e ) and ; Nosberger et aI.l3 7.7148 crn-'. An exact fit to the torsional frequencies is given with F = 7.7133 cm-l. The potential parameters obtained for acetaldehyde are also given in Table I11 and the variations of these with F a r e shown in Figure 4. It is clear that the fitted V6 has approximately the same dependence on F (72-80% change in V6 for 10% change in F) for both acetaldehyde and propene. However, the fitted V3is not very sensitive to the value of F for acetaldehyde (1.4% change in V3 for 10% change in F), while for propene V3shows much greater dependence on F (4.7% change in V3 for 10% change in F). A possible explanation of this difference is that acetaldehyde has a low barrier to internal rotation while the barrier in propene is almost 2 times larger. For a low-barrier case, this means that, although there may be a wide variation in experimental F values, the barrier does not have a large uncertainty. The obverse of this is that, for a low barrier, the torsional motion is rather floppy and a large difference is expected between an F calculated directly from a structure and one obtained by a model that includes corrections for inertial defect and large-amplitude motion. In the higher barrier case, for a more rigid torsional motion, the values of F calculated from structure only is not much different from that allowing for dynamic correction. The dynamic value of F (7.1007 cm-') obtained by Hirota9 seems too near to the structural F, but it is the value chosen for the final fits given for propene in Table I . Fitting only the two strongest peaks at 188.05 and 171.24 cm-I as u~...+(~) and Y ~ ~to determine ~ ( ~ ) V3and V6 gives a value of V6 larger than in acetaldehyde and much larger than expected in view of the argument about the higher barrier. The values of V6 obtained from ab initio SCF energies by using the semirigid model are usually very small and positive.I6 In acetaldehyde, QuadeIs has estimated that the dynamic contribution to V6 should be -3 to -6 cm-I. An alternative assignment of the 171.24-cm-I peak as v2c1(E) and a slightly weaker peak at 169.67 cm-I as u ~ - ~ as ( ~by) Tuazon et al.4 gives an excellent fit. This has two advantages: the magnitude of V6 is more reasonable, and the value of V3is closer to the microwave value. It has been argued by Hollenstein and Winther5 that this assignment of an E E transition is incorrect. However, the nuclear spin statistical weight factor for C H roups is the same for E E transitions as for A A transitions5 6 and they ought to have the same total intensity. Also, the E E bands may be affected by asymmetry in a similar manner to A-A bands. The SCF value of the barrier weight obtained with the DZ basis and given in Table I is low in comparison with experiment, but much closer than with the smaller STO-3G and 4-3 1G Clearly polarization functions are needed to describe properly the electron density in the double bond. Rotational Structure. Propene is an approximate prolate symmetric top and each Au = 1 torsional transition gives rise to
-
-
- -
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3491
Torsional Spectrum for Propene TABLE V: Rotational Constants for Propene from Least-Squares Fitting method/model
wn
d‘
2’’
Dx”/106 Dy‘/106
a
~~
FIR peak/MW rigid-rotor fit non-rigid-rotor fit
188.046 1.2529 187.958 1.2484 1.2415 187.940 1.2473 1.2411
-6.1
-2.7
0.024 0.022
a C-type band very like a perpendicular band of a symmetric top, but with a central peak due to asymmetry. On each side of the main peak at 188 cm-I in the far-infrared spectrum of propene, there are several Q spikes belonging to K subbands. The measurements of these are given in Table IV. From the microwave s p e ~ t r u mthe , ~ asymmetry parameter is K = -0.9386, and the rotational constants in symmetric top notation are
B = (B + C)/2 = 0.2909,
A = A - B = 1.2529 cm-I
where the rotational energy formula, allowing for some centrifugal distortion, is written as
Af? - D,K4
F(J,K) = BJ(J 4- 1)
It is convenient for least-squares fitting to use a signed quantum number k = f K in order to write the AK = +1 form with positive k and the AK = -1 form with negative k.33 It is assumed that AB is approximately zero, but it is obvious from the nonequal spacing of Q spikes that is not zero. A least-squares fit of 22 subband Q spikes gives a very close fit with standard deviation of 0.02 cm-’, when the A constant for the excited torsional uZ1 = 1 state is different from that of the ground state. The fitted parameters are given in Table V. Including distortion constants in the fit gives a slightly lower standard deviation. The differences AA = A’- A”are -0.0069 and -0.0062 cm-] in the two fits and are significantly different from zero. may in part be due to torsional-rotaThis large value of tional interaction. In the internal axis method, the energy levels are given by m
E(K,u,u) = A@
- D,K4
21rn + Fn=O x a , ( V )COS - (pK - a) 3
where the J part is omitted from equation (3-31a) of Lin and S ~ a l e nas , ~it~is assumed that the fitted subband features are not J dependent. For propene, with a reduced barrier parameter, s of value 43.4, the Fourier series needs to be expanded to only n = 2. Assuming that the K structure fitted is for CI = 0, the cosine series is easily expanded to fourth order. From tabulated Fourier coefficient^,^^ the contributions due to torsional-rotational interaction to the coefficients of f? and K4 have been calculated for the torsional ground and excited states. The calculated contributions to the effective is -0.013 cm-’, which is of the same sign as the observed difference of effective A constants. As the theoretical value is much greater in magnitude than the observed (33) Bell, S.;McNee, E. R. Chem. Phys. Lett. 1984, 1 1 1 , 105. (34) Lin, C. C.; Swalen, J. D. Reu. Mod. Phys. 1959, 31, 857. (35) Hayashi, M.; Pierce, L. Tables for the Internal Rotation Problem, University of Notre Dame, Notre Dame, Indiana.
a,
effective there must be other significant contributions for other rotational interactions. The appearance of this band has been simulated by a rigid-rotor asymmetric-top envelope which is shown with the experimental spectrum in Figure 1. The ground-state constants, A”, B”, and C”, used for this envelope are from Hirotag as are the excited-state B’and C’, but A was determined from the change in A obtained by the symmetric-top least-squares fit. In both the calculated envelope and the observed band, there is some obvious J structure toward the high-frequency end of the band. This has a spacing of 2 8 and is probably due to the in-phase overlap of R branches of a number of AK = +1 subbands. Agreement to this detail between the calculated envelope and the observed band confirms the near constancy of 8 and the change in d obtained by the symmetric-top analysis. Among the Q spikes fitted in the observed spectrum, there are a number of weaker features. Some of these may be due to the 1 O(E-E) transition, but they are clearly not so prominent as in the corresponding band of a~etaldehyde,~ and no E-E K structure has been fitted. Expanding the energy level equation for CI = f l results in terms in both odd and even powers of uK. When transitions are calculated, two distinct series of K subbands are obtained and from the tabulated Fourier coefficient^^^ these only split sufficiently to be resolved for K > 6. There are still two prominent peaks in the far-infrared spectrum not fitted as pure torsional transitions, nor as K subbands, which occur next to the main 1 0 peak at 189.10 cm-I and between the 2 1 peaks at 170.64 cm-I. In view of their intensities relative to the main peaks, these are probably due to sequences in the lowest in-plane vibration vI4, the CCC bend. There is also a band O(A) at 365.2 cm-’ which is not in agreement with the 2 transition seen in the Raman spectrum; it may be a difference band.
-
-
-
+-
Conc1usion The experimental structure of propene is not well determined: especially the various C-H bond lengths, as indicated by the a b initio structure which has been calculated. However, the internal rotation constant F obtained from the experimental structure is in close agreement with the dynamic value of F obtained by Hirota’ where the methyl internal rotation moment was assumed from the structure.’ It is also compatible with a value of F obtained from the ab initio geometry with empirically corrected C-H bond lengths. In spite of these structural uncertainties, Hirota’s value of F = 7.1007 cm-’ has been adopted for the least-squares fitting of three far-infrared torsional transitions and one Raman transition. The present best-fitted potential constants are V3 = 693.7 cm-I and V6 = -14.0 cm-’. Comparison with the 6 indicates that the large negative value’ of ab initio value of v the experimental V, is mostly due to vibrational-torsional interaction or some other perturbation. Acknowledgment. We gratefully acknowledge the financial support of this study by the National Science Foundation by Grant CHE-83-11279. S.B.is grateful for several helpful discussions with Dr. Peter Groner. Registry No. CH2CHCH,, 115-07-1.
