J. Phys. Chem. 1993, 97, 3994-4003
3994
Spectroscopy of C-H Stretching Vibrations of Gas-Phase Butenes: cis-2-Butene, trans-2-Butene, 2-Methyl-2-butene, and 2,3-Dimethyl-2-butene Carlos Manzanares I.,' Victor M. Blunt, and Jingping Peng Department of Chemistry, Baylor University, Waco. Texas 76798 Received: December 4. I992
The C-H fundamental and overtone spectra of gas-phase cis-Zbutene, trans-2-butene, 2-methyl-2-butene, and 2,3-dimethyl-2-butene were measured. Three main bands were observed for each overtone for cis- and trans2-butene and 2-methyl-2-butene that correspond to the out-of-plane C-H (a), the in-plane C-H (s), and the olefinic C-H (1) bonds. Two main bands were observed for 2,3-dimethyl-2-butene that correspond to C-H (a) and C-H (s) bonds. The highest energy absorption corresponds to the olefinic C-H (1) bond followed by the methyl in-plane C-H (s) and the methyl out-of-plane C-H (a) bonds, respectively. Computer decopvolution of the overtone absorptions was done to separate the bands corresponding to the different C-H bonds and to obtain information about the peak position, band profile, and line width of the absorption. Local mode harmonic frequencies and anharmonicities were calculated from the analysis of the spectra. Comparison was made with results obtained with infrared studies of partially deuterated cis- and trans-2-butene. The C-H fundamental local mode frequencies (we - 2wdX,)are very close to the corresponding isolated frequencies (visa) in trans-2butene. The agreement is also very good for cis-2-butene except in the values of the methyl C-H (s) bond. The calculated dissociation enegy indicates that the olefinic C-H (1) and the in-plane methyl C-H (s) bonds are stronger in cis-Zbutene than those in the trans-2-butene. The out-of-plane methyl C-H (a) bonds are very similar in strength in both compounds, By use of the fifth overtone peak absorption, isolated frequencies (vim) and bond lengths (rCHo) are predicted for 2-methyl-2-butene and 2,3-dimethyl-2-butene.
Introduction The gas phase overtone spectroscopy of C-H bonds of the molecules cis-2-butene, trans-Zbutene, 2-methyl-2-butene, and 2,3-dimethyl-2-butenewas first studied by Fang and Swofford.1 They reported specta for a mixture of cis- and trans-2-butene around Au = 4-6 from which harmonic frequencies and anharmonicities were calculated. The spectra around Av = 6 of 2-methyl-2-butene and 2,3-dimethyl-2-butene were presented, but the spectroscopicconsants were not calculated. They showed that for all the molecules two peaks were observed that correspond to the in-plane C-H (s) and out-of-plane C-H (a) bonds of the methyl groups shown in Figure 1. At each overtone, the C-H (a) is the lowest energy transition followed by the C-H (8). The olefinic C-H (1) is the highest energy transition. Qualitatively they showed an energy splitting between C-H (s) and C-H (a) bonds that appears to depend on the number of methyl groups attached to the central C - C bond and that increases as the number of methyl groups increases around thedouble bond. Wong and MooreZreported the Av = 6 spectrum of cis-2-butene with a tentative assignment for the C-H (5) transition. Liquid phase C-H overtones have been reported for 2,3-dimethyl-2-butene3,4 and 2-methyl-2-butene.4 Isolated C-H stretching frequencies in the fundamental have been measured from 11 isotopomers of cisand truns-2-butenesa5Infrared and Raman techniques were used to show that the olefinic C-H (1) and methyl C-H (s) bonds are stronger in the cis compound than those in the trans compound. Many studies of fundamental vibrational levels of butenes have been published and they include infrared and Raman studies of cis- and t r a n s - 2 - b ~ t e n e , ~2-methyl-2-but~ne,~-~~ -~~ and 2,3dimethyl-2-b~tene~~-~~J~*l~ in gas, liquid, and solid phases. Complete normal coordinate analysis studies are available for ~is-2-butenel9-24~2~ and trans-2-butene.*C-27 Partial studies of normal coordinate analysis of 2-methyl-2-b~tene2~~28 and 2,3-dimethyl-2-buteneZ7-z9 have been obtained. Skeletal vibrations have been studied for cis- and tr~ns-2-butene3~and 2-methyl2-butene.3' Studies of torsional modes from 350 to 33 cm-1have been published for cis- and t r ~ n s - 2 - b u t e n e ,2-methyl-2~~~~~ 0022-3654/93/2097-3994$04.00/0
cis-2-Butene
2-Methyl-Z.butene
trans-2-Butene
2,3-Dlmethyl-2.butene
Figure 1. Molecular structurea of cis-2-butene,tram-2-butene, 2-methyl2-butene, and 2,3-dimcthyl-2-buteneshowing the olefinic C-H (l), inplane C-H (s), and out-of-plane C-H (a) bonds.
butene,33 and 2,3-dimcthyl-2-buten~.~~ A low temperature infrared study of cis- and trans-2-butene in an argon matrix" has been published. The rotational constants of cis-2-butene have been obtained by microwave ~tudies.3~ From the vibrational transitions observed in deuterated samples,s it was concluded that the C-H (s), C-H (a), and C-H (1) bonds in cis-2-butene are different in strength from the corresponding C-H bonds in trans-2-butene. In this paper, an overtone study of pure samples of cis-butene, trans-butene, 2-methyl-2-butene, and 2,3-dimethyl-2-butene was done to determine the correct local mode spectroscopicconstants of the different C-H bonds in all molecules and to properly assign the C-H transitions at several levels of excitation. To this end, absorptions correspondingto Av = 1-6 of the nonequivalent C-H stretching modes have been obtained for the four molecules. Absorptions in the Av = 5 and 6 regions were obtained using 0 1993 American Chemical Society
Spectroscopy of C-H Stretching Vibrations
The Journal of Physical Chemistry, Vol. 97,No. 16, 1993 3995
cis-2-Butene
j
1.6 7
1.28
cis-2-Butene
AV-1
0'16
0.13
3
1
A
Av-2
3 0.96 9 0.64 0.32
-/ trans-2-Butene AV- 1
1 1
O.l3 0.1
0.03
trans-2-Butene AV-2
I
4
2650
2750
2850 2950 3050 Wavenumber (cm .' )
3150
3250
Figure 2. Absorption spectra of the fundamental (Ao = 1) C-H stretch region of cis- and trans-2-butene. The cell path length was 10 cm. The sample pressure was 50 and 52 Torr, respectively.
intracavitycontinuouswave dye laser excitationand photoacoustic detection. Absorptions in the Av = 1-4 regions were obtained using Fourier transform infrared and near-infrared techniques. Computer deconvolution of the overtone bands around Av = 3-6 has been performed. The magnitude of the separation between the C-H (s) and the C-H (a) bonds of the methyl groups of the four molecules was determined for all the levels studied. Peak positions, overtone assignments, and line widths of the bands are reported. These results are interpreted in terms of a local mode description of vibrational overtones from which local mode harmonic frequencies and anharmonicities have been calculated.
Experimental Section The fundamental spectra of the molecules were recorded in a 10-cm gas cell with a Mattson Fourier transform spectrophotometer operating in the range from 400 to 4000 cm-I at instrumental resolution of 2 cm-I. Spectra of the overtones with Av = 2-4 in the range 5000 to 12 000 cm-I were obtained with the same Fourier transform spectrophotometer, using a PbSe detector, a tungsten light source, and a quartz beam splitter at instrumental resolution of 8 cm-1. For Av = 1-2 the cell path length was 10 cm. In the region of the overtones with Av = 3-4, a variable path length mini gas cell equipped with KBr windows was used. Path lengths between 3.3 and 6.6 m were selected. In some cases averages of up to 10 000 scans were necessary to improve the signal-to-noise ratios. Gas-phase laser photoacoustic spectra were obtained for the Av = 5 and 6 C-H stretching vibrations using a cell mounted within the cavity of a continuous wave dye laser (Coherent 59901) with high reflectance optics, pumped with an argon-ion laser (Laser Ionics 554A). The acoustic cell is 1 cm in diameter and 20 cmlong, made of Pyrex tubing with quartz windows mounted at Brewster's angle. The photoacoustic signal is detected by a Knowles BT1759 electret microphone mounted at the midpoint
5350
\
J
o , , , , , , ,
0
n
5500
5650
I
I
,
,
I
,
5950 Wavenumber (cm.') 5800
I
I
I
6100
I
,
,
6250
Figure 3. Absorption spectra of the first overtone (Au = 2) C-H stretch region of cis- and tram-2-butene. The cell path length was 10 cm and the sample pressure was 292 and 300 Torr, respectively. The spectra are the average of 500 scans.
of the cell. The ion laser is modulated by a mechanical chopper at a frequency of 100 Hz. Signals from the microphone are amplified and processed by an Ithaco (3962A) lock-in amplifier. The intracavity dye laser power is monitored with a photodiode which detects a reflection off the Brewster angle window of the cell. Thissignal is fed to'another Ithaco (3962A) lock-in amplifier. Normalization of the phbtoacoustic spectra is achieved by obtaining the ratio of the output signals from both lock-in amplifiers. Wavelength tuning (1.O cm-I band width) of the dye laser is accomplished with a birefringent filter driven by a stepper motor. A microcomputer systemcontrolsthedye laser wavelength scan and digitizes and stores the normalized signals for further analysis. Absolute calibration of the laser lines was achieved by obtaining the optogalvanic spectra of hollow cathode lamps filled with argon (700-800 nm) or neon (600-700 nm). The tuning ranges of the laser dyes are as follows: Pyridine 2 (13000-14500 cm-1) and Rhodamine 610 (14800-1 6500 cm-I). All experiments were performed at 20 f 2 "C. The samples, cis-2-butene (95%), trans-2-butene (99+%), 2-methyl-2-butene (99+%), and 2,3dimethyl-2-butene (99+%) were purchased from Aldrich and further purified by freeze-pumpthaw cycles before use. Results The spectra shown in Figures 2 through 7 are for the fundamental and overtone transitions (Av = 1-6) of the C-H stretching vibrationsof cis-2-buteneand tram-Zbutene. Figures 8 through 13 show the C-H stretching fundamental and overtone regions (Av = 1-6) for 2-methyl-2-butene and 2,3-dimethyl-2butene. For all the molecules, the experimental conditions of pressure, cell path length, and averaged number of scans are indicated in the figures. The absorption bands corresponding to the overtones with Av = 3-6 were digitized and deconvoluted to obtain the position of the peaks and the full width at half maximum
Manzanares I. et al.
3996 The Journal of Physical Chemistry, Vol. 97,No. 16, 1993 1.2
cis-2-Butene AV-3
0.1
0.96
0.08
0.02
0‘12
]
d
trans-2-Butene AV-3
1 -
0.06
25:
,
0.04
cis-2-Butene AV-4
-
trans-2-Butene Av-4
g 0.9
o ! 7850
I
!
8050
I
,
8250
I
I
8450
I
I
j
8650
,
8850
,
, 9050
(cm-‘) Figure 4. Experimental and deconvoluted absorption spectra of the second overtone (b= 3) C-H stretch region of cis- and tram-2-butene. The cell path length, sample pressure, and number of scans were 6.6 m, 377 Torr, and 10 000 scans for cis-2-butene and 3.0 m, 717 Torr, and 1000 scans for tram-2-butene.
10500
10700
10900
(fwhm) of the absorptions. Deconvolution of the absorption bands was performed with programs developed by Jones and Pitha modified to run in a VAX computer. The spectra were fit by the computer program to a sum of Lorentzians plus a constant background. The discrepancy between the calculated and experimental spectra was minimized with the program. The calculated spectra were then plotted with the experimental spectra. A visual comparison was made to ensure the quality of the fit. The experimental and deconvoluted spectra around the C-H region of the overtone (Au = 3-6) of cis- and trans-2-butene are shown in Figure 4-7 and for 2-methyl-2-butene and 2,3-dimethyl2-butene in Figures 1&13. Tables I and IV present the fundamental frequencies and assignments to be used to assign local mode-normal mode combinationbands around the overtone regions of the 2-butenes. In Tables 11,111, V, and VI the peak positions, assignments for deconvoluted local mode bands, and line widths (fwhm) are summarized for cis-Zbutene, trans-2butene, 2-methyl-2-butene,and 2,3-dimethyl-2-butene, respectively. BirgeSponer plots of theolefinic C-H (l), in-plane C-H (s), and out-of-planeC-H (a) are presented in Figure 14 for cisand rrans-2-butene and in Figure 15 for 2-methyl-2-buteneand 2.3-dimethyl-2-butene. Table VI1 presents the local mode vibrational frequencies, anharmonicities, and the calculated dissociation energies for each C-H bond in the molecules.
Discussion A. Vibrational Assignments. & and b.are2-Butene. The fundamental frequencies obtained from infrared and Raman studies and the normal coordinate analysis have been reported for cis- and trans-2-butene in the gas phase.5.2’ Assuming C, symmetry for cis-2-butene,the 30 vibrational frequenciescan be divided into groups of symmetry 10Al + 6A2 5B1 + 9B2. For
+
11100
11300
11500
11700
Wavenumber (r”’ )
Wavenumber
Figure 5. Experimental and deconvoluted absorption spectra of the third overtone ( b= 4) C-H stretch region of cis- and tram-2-butene. The cell path length, sample pressure, and averaged number of scans were the same as for Figure 4.
trans-Zbutene, assuming C2h symmetry, the vibrational representationis 10A, + 5B, 6A, + 9B,. Thevibrational frequencies and assignments for both molecules are shown in Table I. This information will be used to assign local mode-normal mode combination bands that occur in the C-H spectra. Figure 2 shows the absorption spectra of the fundamental C-H stretch region of cis- and trans-2-butene. All the prominent peaks agree with the gas phase absorptions reported in the literat~re.~ The spectra shown in Figure 3 are in the C-H absorption region. Both, cis and trans compoundsshow three prominent peaks that are assigned in order of increasing energy as the out-of-plane (ua), in-plane (us),and olefinic (u0l) C-H bonds. In Tables I1and 111,comparison is made of the experimentalfrequencies with the calculated local mode frequencies obtained from the Birgdponer plot to be discussed later. For Au = 2 the bands represent a transition between normal mode and local mode; in this case, u0l behaves like a local mode because the experimental and calculated frequencies are close but us and ua behave like normal modes because the separation in energy between experimental and calculated frequencies is larger. In Figure 4, the experimental and deconvoluted spectra around the Au = 3 C-H region are shown that present three main absorption bands in addition to low intensity absorptionsthat are assigned to local modenormal mode combination bands. The spectrum for the cis compound shows main bands at 8385,8490, and 8670 cm-I assigned as 3ua, 3us, and 3u01, respectively, and a smaller band at 8292 cm-I tentatively assigned to 2vs + 2U7 where u7 = 1260 cm-l is a fundamental in-plane deformation of the olefinic C-H bond (Si(CH)). The band at 8589 cm-’ is assigned to the combination 2ua + u2 in which uz is the symmetric CH3 stretch. The trans compound shows main transitions at 8389,8498, and 8593 cm-1 assigned as 3uB,jus, and 3u01. There are also transitions at 8308 cm-1 assigned as 2us + 2u27 and at 8436 cm-I assigned as 2ua 2u6. These two last assignments are typical of overtone local
+
+
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 3991
Spectroscopy of C-H Stretching Vibrations
cis-2-Butene AV-6
cis-2-Eutene
a
9 1
7.2
Trans-%Butene AV-5
j
12900
8
13200
trans-2-Butene AV-6
10
13500
13800
14100
$
A
15100
14400
15400
15700
16000
16300
16600
Wavenumber (cm.' 1
Wavenumber (Cm-')
Figure 6. Experimental photoacoustic absorption and deconvoluted spectra of the fourth overtone (A0 = 5 ) C-H stretch region of cis- and trans-2-butene. The sample pressures were 29 and 15 Torr, respectively.
Figure 7. Experimental photoacoustic absorption and deconvoluted spectra of the fifth overtone (Au = 6) C-H stretch region of cis- and trans-2-butene. Thesample pressures were 194 and 229 Torr, respectively.
mode-normal mode combination bands in the sense that they involve the first overtone of a CH3deformation (bs,,(CH3)). The band at 8703 ~ m could - ~ be any of the combinations 2us + VI6 or 2us UII. The spectra around Av = 4 are shown in Figure 5 for cis- and trans-Zbutene. A pattern develops in which the olefinic (u0l), in-plane (us), and out-of-plane (u,) absorptions are well-defined in trans-2-butene but the in-plane (us) absorption is not so welldefined for cis-2-butene. This is also the case for transitions around Av = 5 and 6 shown in Figures 6 and 7, and it is the main reason why the assignment given for us at Av = 6 in ref 2 was tentative. In the present paper the assignment was made based on the Birge-Sponer plot to be discussed later. The local modenormal mode combination bands of cis-2-butene around Av = 4 involve the first overtone (2u7)of the C-H in-plane deformation (bi(CH)). The band at 10 876 cm-1 is assigned as 3u, 2u7 and at 11 034cm-I assignedas3us+ 2u7. Thebandsat 10 930,11099, and 11 314 cm-i correspond to u,, us,and u0l, respectively. The spectrum of trans-2-butene around Au = 4 presents three main bands that are easily identified as u, = 10 945 cm-I, us = 11 064 cm-1, and u , ~= 11 226 cm-1 . A combination band at 10 919 cm-1 is tentatively assigned as 3U01+ 2u8 because the arithmetic sum (10 877 cm-1) is the closest in energy. The spectra around Av = 5 shown in Figure 6 were obtained by laser acoustic methods. For cis-2-butenethe spectrum shows a complex set of absorption bands in contrast with the spectrum of trans-2-butene in the same region, where only three peaks are expected and obtained. The two main absorption peaks of the spectrum of cis-2-buteneare readily assigned as ua = 13 361 cm-I and uol = 13 836 cm-I. The assignment of the us = 13 548 cm-' peak could only be made after deconvolution, by means of the BirgeSponer plot. Other bands in the Av = 5, cis-2-butene spectrum correspond to local mode combinations with the first overtone of a CH3 rocking vibration (4u,l + 2 u 4 , with an inplane CH deformation (4u, + 2u7), and a symmetric CH3
deformation (4u, 2~27). The Av = 6 overtone spectrum of cis-2-butenepresents three main peaks and a combination band which are listed on Table 11. As in the case of Au = 5, the assignment of the us= 15 9 14 cm-I peak could only be made after deconvolution, by means of the BirgeSponer plot. In ref 2, this transition which was listed at 15 952 cm-i was not assigned. The main transitions in the Av = 6 spectrum of trans-2-butene are easy to assign and are shown in Figure 7 and presented on Table 111. The only uncertainties in this case are with respect to the origin of the combination bands. The band at 15 445 cm-I is assigned as 5u, 2u28 or 5u, + 2~19,which are very close in energy. The same can be said about the combinations5u01 + 2u13 and 5u01 2u18to describe the absorption at 15 640 cm-I. 2-Methyl-Zbutene and 2,3-Dimethyl-2-butene. A complete normal coordinate analysis of the two molecules has not been made. Because of this, a detailed analysis of the overtone combination bands cannot be presented and the assignments made for all combination bands are tentative. The molecule 2-methyl2-butene belongs to the symmetry group C, with 39 vibrational modes subdivided into 24A' 15A'', both of which are allowed in both the Raman and infrared spectra. A partial list of fundamental assignments has been obtained from IR and Raman bands16 below 1700 cm-I, a normal coordinate analysisz7of the transitions with symmetry A", and a study of torsional modes.3z The results are summarized in Table IV. The molecule 2,3dimethyl-2-butene belongs to the symmetry group with 48 vibrational modes subdivided into the symmetry groups 8A, + 7B1, 5B2, 4B3, 5BI, 5A, + 7Bz, + 7B3,. The partial list of assignments presented in Table IV is from ref 27. Some of the frequencies listed in Table IV are used to assign combination bands around the overtone absorptions. Figure 8 shows the spectra of the fundamental C-H absorption for the two molecules. The main peaks are listed in Table IV. Figures 9 through 13 present the spectra of the overtones with Av = 2 through 6. Tables V and VI present the experimental and calculated frequencies of
+
+
+
+
+
+
+
+
+
+
Manzanares I. et al.
3998 The Journal of Physical Chemistry, Vol. 97,No. 14, 1993 0'09
0.07
2.3-Dimethyl-2-butene AV- 1
0.04
A
A
1;
8
l L z L L
0.36 0 2650
2750
2850
2950
3050
3150
3250
Wavenumber (Cm .' ) Figure 8. Absorption spectra of the fundamental (Au = 1) C-H stretch region of 2-methyl-2-butene and 2,3-dimethyl-2-butene. The cell path length was 1Ocm. The sample pressures were 26 and 25 Torr, respectively.
the C-H overtones. The calculated frequencies of the main overtones are obtained from the Birge-Sponer plots tobediscussed later. The combination bands are calculated with the reported fundamentalsand overtone transitions for 2-methyl-2-buteneand 2,3-dimethyl-2-butene. The assignments of the three peaks for 2-methyl-2-butene(Au = 2) in Figure 9 correspond to C-H (1) with the largest intensity and frequency, C-H (s) with intermediate intensity and frequency, and C-H (a) with the lowest intensity and frequency. Of the four absorptionsin the spectrum of 2,3-dimethyl-2-butenein Figure 9, the ones at 5718 and 5862 cm-I are assigned to 2ua and 2us, respectively. There is a drastic change in intensities beginning with the spectra shown in Figures 10 through 13. The C-H (a) absorption band is very easy to assign in all the spectra with Au = 3-6 because it has the largest intensity and appears at low frequencies. Table V for 2-methyl2-butene shows that the majority of combination bands includes a first overtone of an asymmetric rocking motion of a methyl group (2pas(CH3)),whose frequency is indicated in parentheses in the table. Combinations with torsional modesarealsoindicated in Table V. Table VI shows some of the combination bands obtained for 2,3-dimethyl-2-butene. In Figures 10 and 11, the spectra are very easy to assign because there are a few combination bands. The acoustic spectra shown in Figure 12 (Au = 5) show more combination bands, particularly around the strong C-H (a) absorption. In the case of 2,3-dimethyl-2-butene,Table VI shows the assignments as combinations of symmetric and asymmetric rocking motions of methyl groups. B. Harmonic Frequencies and Anhanaonicities. The local mode absorptionscan be fitted to the equation for the transition energy for a one-dimensional anharmonic oscillator35
AE = (we - wexe)u- wex, u2
(1) where weis the harmonicfrequency and o~~is the anharmonicity. From the values of we - w g e and wcxc, the dissociation energy
0.02 0.03
O
2-Methyl-2-butene
]
Av-2
A
1
2,3-Dimethyi-2-butene
1
/
A
AV-2
1
5350
i\
A
,
,
,
5500
,
,
,
5650
,
,
,
,
5800
I
l
5950
I
I
1
6100
I
,
I
6250
Wavenumber (cm-I)
Figure 9. Absorption spectra of the first overtone (Au = 2) C-H stretch region of 2-methyl-2-b~teneand 2,3-dimethyl-2-butene. The cell path length was 10 cm and the sample pressures were 200 and 115 Torr, respectively. The spectra are the average of 500 scans.
(A&,,)
is calculated with the equation
"ax = (we - wexcJ2/4(wexe) (2) where A&,, is measured from the u = 0 level. In Figures 14 and 15, Birge-Sponer plotsof A E / u versus u are shown. Three straight lines are obtained for the correspondingoscillatorsC-H ( 1) (upper line), C-H (s) (intermediate line), and C-H (a) (lower line) of the molecules cis-Zbutene, trans-2-butene, and 2-methyl-2butene. The two straight lines corresponding to the C-H (s) and C-H (a) oscillators of 2,3-dimethyl-2-butene are shown in Figure 15. The values of we and w d e obtained from the BirgeSponer plots and AE,,, from equation are presented in Table VII. In Figure 14, the C-H isolated frequencies measured by McKean et aL5are shown (Av = 1) for cis and trans-2-butene. Those frequencies are shown only for comparison and were not included in the fit. The results in Table VI1 show that for the C-H (1) oscillator the local mode frequency we - cogeis larger for cis-2-buteneand very similar for trans-Zbutene and 2-methyl2-butene. The anharmonicities of the C-H (1) oscillator are essentially equal for the three molecules and the dissociation energies decrease in the order cis > trans > 2-methyl. The compounds trans-Zbutene and 2,3-dimethyl-2-butene in Figures 14 and 15 show approximatelyparallel lines in the BirgeSponer plots. In cis-Zbutene, the lines corresponding to C-H (s) and C-H (a) are not parallel and have separation that is smaller at u = 0 compared with the separation at u = 6. In 2-methyl-2butene, the separation between the C-H (s) and C-H (a) lines clearly increases as a function of the quantum number. It is possible that a gradual interaction develops between the C-H (s) bond overtone and another level resulting in a shift of the overtone as a function of the vibrational quantum number. C. Methyl Interactions with T Electrons. Studies of fundamental transitions in partially deuteratedcompounds and overtone
Spectroscopy of C-H Stretching Vibrations 2-Methyl-2-butene AV-3
1.04
z3
0.78
E
0.52
0.26
{
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 3999
TABLE I: Fundamental Vibrational Frequencies (cm-1) Used for the Overtone Assignments of cis- and tram2-Buten@
i\ II
cis-2-butene AIY I
-
~2 ~3 ~4
u5 Y6
UT
1 ug ~9
0.48
i
II
3038 2935 2870 1660
trans-2-butene A , Y I 3009 ~2 2973 ~3 2869 u4 1682
1445 1406 1260
u5
986 870
ug
v6
~7
~9
1444 1385 1306 1142 863
UIO 291 A ~ V I 2953 I ~ 1 2 1447 Y I ~ 1043
UIO 500 B , u ~ I 2950 vi2 1442 Vi3 1043
Vi4
871
745
VIS
396
Vi5
195
105 VIS
2975 1445
U I ~
1016
~ 2 0
675
Y21
100
BI ~
7850
8050
8250
8450
8650
8850
9050
1 7
Wavenumber (cm" )
Figure 10. Experimental and deconvoluted absorption spectra of the second overtone (a0= 3) C-H stretch region of 2-methyl-2-butene and 2,3-dimethyl-2-butcne. Thecell pathIength,sampleprcssure, and number of scans were 4.2 m, 375 Torr, and 5000 scans for 2-methyl-2-butene and 6.6 m, 105 Torr, and 10 000 scans for 2,3-dimethyl-2-butene.
absorptions of molecules with methyl groups attached to a double bond have shown that the out-of-plane C-H (a) bonds are always weaker than thein-planeC-H (9) bonds. Theexplanation favored in the studies of partially deuterated cis- and trans-2-butenes is that there is a valence bond electron pair repulsion interaction between the x electrons and the C-H (a) bonding pairs. This view is supported by dipole moment calculations in propene36 which show that thedipolemoment is largely due toa polarization of the a bond away from the methyl group. The same interaction between the x electrons and the C-H (a) bonds described in terms of molecular orbital calculations37 is called hyperconjugation. The interaction described before is responsible by the weakening of the C-H (a) bond with respect to the C-H (s) bond and its effect increases when the number of methyl groups increases. In this investigation, it isconfirmed that the magnitude of the difference in strength between the C-H (s) and C-H (a) bonds increases. In Table VII, the magnitude of the difference in dissociation energies between the C-H (s) and C-H (a) is 2307,2900,3241,and4146cm-l for tram-2-butene, cis-2-butene, 2-methyl-2-butene, and 2,3-dimethyl-2-butene, respectively. D. Isolated C-H Stretching Frequencies. Because of the good correlation between the fifth overtone transition energies and the isolated frequencies measured by McKean,38 it is possible to calculate the isolated C-H stretching frequencies from the empirical formula of Wong and Moore2 u,,.&cm-')
= (-3716
* 45) + (6.62 f o.09)uCHis0
(3) Taking the fifth overtone frequencies from Tables 11,111,V, and VI, the isolated frequenciescan be calculated. The experimental values of UCH" for cis- and trans-2-butene have been obtained by McKean5 and are presented in Table VII, where, for comparison,the calculated isolated frequencies obtained from eq 3 are also presented. There is good agreement between the two
B2~22 3023 ~ 2 3 2949 ~ 2 4 2876 ~ 2 5 1462 ~ 2 6 1445
u21 195 BUu22 3027 ~ 2 3 2974 ~ 2 4 2874 ~ 2 5 1468 Y26 1382
~ 2 8
1383 1135
~ 2 9
976
Y29
978
Y ~ O
570
~30
260
~ 2 7
~ 2 7 ~ 2 8
1303 1061
Key: sym = symmetric,as = asymmetric,v = stretch, 6 =deformation, p = rocking, o = out of plane, i = in plane, T = torsion. The vibrational
frequencies are from refs 5 and 21.
for cis- and trans-2-butene for all three types of C-H bonds. Also for comparison with the Y C H ~ ~ O , the local mode fundamental frequencies oc- 2wgc are presented for each oscillator. Many other molecules2 have shown excellent agreement between the experimental U C H and ~ ~ ~the calculated value from eq 3. On the basis of this, the isolated frequencies for 2-methyl-2-butene and 2,3-dimethyl-2-butenewere calculated from eq 3 and are presented in Table VII. A calculation of the C-H bond lengths in the ground state (v = 0) can be made using the correlation formula proposed by M ~ K e a n ~ ~
rCHo(A) = 1.402 - (1.035 x 1t)-4)uCHiSo (cm-I) (4) The calculated rCHo values for 2-methyl-2-butene and 2,3dimethyl-2-butene are presented in Table VIII. The ucHiSo values were calculated with eq 3 and the fifth overtone frequencies of 2-methyl-2-butene (Table V) and 2,3-dimethyl-2-butene (Table VI). The U C H ~ S O values were used to calculate the rCHo with eq 4. Also the rCHO given by McKean for cis- and trans-2-butene are presented in Table VII. The results of A ~ c H O in Table VII, show that there is an increase in the strength of the C-H (s) with respect to the C-H (a) in the order trans < cis < 2-methyl < 2,3-dimethyl.
Manzanares I. et al.
4000 The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 2-Methyl-2-butene
0.05
0.04
14
2,3-Dimethyl-2-butene AV-4
lo
1
2.3-Dimethyl-2-butene AV-5
j
10250
10550
10850
11150
11450
12850
11750
Wavenumber (Cm.’ )
Figure 11. Experimental and deconvoluted absorption spectra of the third overtone (Au = 4) C-H stretch region of 2-methyl-2-butene and 2,3-dimethyl-2-butene. The cell path length, sample pressure, and averaged number of scans were the same as for Figure 10.
E. Line Widths. The lineshape of the overtone transitions of gas phase molecules is explained in terms of inhomogeneous and homogeneous contributions. The inhomogeneous broadening of the bands in the result of rotational transitions along with contributions from superimposed hot bands, combination bands, and difference bands. Homogeneous broadening is due to dephasing and vibrational energy redistribution. Dephasing models predict a general increase in overtone line widths with increasing vibrational quantum number.39 This is obviously not the case in the present study as shown in Tables 11,111, V, and VI. There is general agreement that the onset of vibrational energy redistribution occurs at low energies (Au = 1,2) and the overtone line widths have in general a predominant contribution that is homogeneous in origin. Large overtone line widths in some molecules are explained by assuming that in the statistical limit, the density of states is so large that the excited state couples directly with a very large number of final states that are in resonance with it.40 Even though the density of states is very large for high overtones of polyatomic molecules, the statistical mechanism cannot explain the line widths of the absorption bands in many molecule^.^^^^ It is possible to explain the line width of some molecules coupling the excited state to a local density of resonances rather than the full density of states. According to this, vibrational relaxation takes place through a sequence of many intermediate off-resonant transitions until the appropriate high density of quasi-resonant states is reached. The dynamics of the energy transfer is dictated by the intermediate off-resonant transitions. A detailed analysis of resonances is not presented in this investigation but the changes in line width with vibrational quantum number for cis- and trans-2-butene, 2-methyl-2-butene, and 2,3-dimethyl-2-butene suggest a mechanism of intermediate receptor states which are coupled with the initial excited state and connect with the full density of excited states. In cis-2-
13050
13250
13450
13650
13850
14050
Wavenumber (cm ” )
Figure 12. Experimental photoacoustic absorption and deconvoluted spectra of the fourth overtone (Au = 5) C-H stretch region of 2-methyl2-butene and 2,3-dimethyl-2-butene. The sample pressures were 19 and 15 Torr, respectively.
TABLE II: Observed and Calculated Peak Position, C-H Transition Assignments, and Line Widths in the Overtone Spectra of ci42-Butene
. ,
oeak wsition Icm-l) observed calculated L
Av
1
5 721 5 782 5 899 8 264 8 389 8 494 8 586 8 668 10 905 10 930 11 010 11 086 11 316 13 266 13 342 13 450 13 559 13 696 13 844 15 626 15 788 15 912 16 251
5 561 5 744 5 894 8 292 8 385 8 490 8 589 8 670 10 876 10 930 11 034 11 099 11 314 13 252 13 361 13 463 13 548 13 651 13 836 15 611 15 729 15 914 16 258
I:-.. 1111G
assignment 2va 2% 2voi 2v, + 2v7 3va 3vs 2v, v2 3vol 3va 2v, 4va 3vs 2Y7 4vs 4vol 4v0i + 2V29 5va 4v, + 2v, 5vs 4ua 2v27 5vo1 6va 5v0i + 2~29 6vs 6~01
+
+
+
+
widths (cm-I)
67 61 124 96 77 180 62 61 234 133 144 114 82 128 108 118 179 113 462 113
butene, the C-H (s) band shows large fluctuations in the magnitude of its line width, having at Av = 3, 4, 5, and 6 the values 124, 234, 128, and 462 cm-I, respectively. It is possible that at levels with Av = 4 and 6, resonance could be established with one or two combination bands of the C-H (a) and the olefinic C-H (1) bonds. For example, the band whose maximum is at us= 15 9 14cm-l has a line width of 462 cm-l ;resonant interactions with the levels 5u, 2u7 = 15 881 cm-I and 5U01 + 2u13= 15 922
+
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 4001
Spectroscopy of C-H Stretching Vibrations
TABLE IV Partial List of Fundamental Vibrational Frequencies (cm-I) Used for the Overtone Assignments of 2-Methyl-2-butene and 2,3-Dimethyl-2-butene
2-Methyl-2-butene AV-6
2.3-dimethyl-2-butene a
A,
2920 2869 1676
Bzg
2920 1458 1072 410 (139) 2915 1446 1060 311 ( 142) 2990 2860 1446 1370 1167 896 410
1
g
2.3-Dimethyl-2-butene AV-6
BI,
A
B3"
14700
15000
15300
15900
15600
16200
16500
1 Figure 13. Experimental photoacoustic absorption and deconvoluted spectra of the fifth overtone (Au = 6) C-H stretch region of 2-methyl2-butene and 2,3-dimethyl-2-butene. The sample pressures were 252 and 98 Torr, respectively. Wavenumber (cm
TABLE III: Observed and Calculated Peak Position, C-H Transition Assignments, and Lme Widths in the Overtone Spectra of tmw-2-Butene
2
peak position (cm-I) observed calculated 5 663 5 748 5 872 8 308 8 389 8 436 8 498 8 593 8 703
3
4
10 919 10 945 11 064 11 226 13 333 13 522 13 706 15 445
5 6
15 640 15 787 15 899 16 114
5 722 5 782 5 850 8 354 8 392 8 433 8 489 8 594 8 698 8 698 10 877 10 934 11 075 11 218 13 348 13 539 13 722 15 455 15 448 15 634 15 792 15 790 15 880 16 105
assignment 2~a 2VS 2Vol 2Us 2127 3ua 2ua + 2U6 3us 3Vol 2% + V I 6 2VS + V I I 3v01 2vs 4va 4vs 4vol 5ua 5us 5vol 5ua + 2u28 5 U s + 2U19 6va 5Vol + 2vlS
+
+
5VOl
+ 2ws
6~s
6~01
line widths (cm-1)
35 54 71 55 62 67 96 47 75 82 123 74 130 85 152 181 148 117
cm-1 could explain this increase. The modes with frequency u7 and ~ 1 correspond 3 to 6i(CH) andp(CH3),respectively. Similarly, at Av = 4 the band at 11 099 cm-1 could interact with the level 3u, 2u27 = 11 151 cm-1 to increase its line width to 234 cm-I. The mode with frequency 1127 corresponds to 6,,,(CHs). The line width of the C-H (a) band increases from 61 to 179 cm-I as a function of the quantum number. The line width of C-H (1) bands increases at Av = 4 but remains approximately constant
+
A'
1681 1453 1389 138 1 1336 1222 1107 1042 953 808 768
A"
2973 2967 1463 1453 1453 1111 1073 805 434 257 (148) (145) (142)
u(C=C) 6,,(CH3) 6svm(CH3) 8,;,(CH3) 6,(C=CH) p(CH3) p(CH3) p(CH3) u(C-C)
Key: sym = symmetric, as = asymmetric, u = stretch,b = deformation, = rocking, T = torsion. Numbers in parentheses are calculated frequencies. Frequencies for 2,3-dimethyl-2-butene are from ref 27. Frequencies for 2-methyl-2-butene are from refs 16, 27, and 32.
p
0
Au
uaS(CH3) ~sym(CH3) u(C=C)
2-methyl-2-butene
TABLE V Observed and Calculated Peak Position, C-H Transition Assignments, and Lme Widths in the Overtone Spectra of 2-Methyl-2-butene Au 2 3
4
5
6
peak position (cm-I) observed calculated 5 645 5 729 5 867 8 284 8 358 8 481 8 614 10812 10 896 11 000 11 075 11 201 13 181 13 268 13 327 13 447 13 524 13 595 13 721 15 560 15 657 15 769 15 964 16 125
assignment'
line widths (cm-1)
5 703 5 762 5 855 8 301 8 363 8 479 8 606 10 836 10 896 11 021 11 085 11 225 13 149 13 275 13 302 13 423 13 541 13 582 13 727 15 580 15 669 15 795 15 969 16 108
53 55 120 116 246 64 47 79 265 154 91 93 79 122 61 179 165 104 329 227 129
The number in parentheses is the vibrational frequency.
below 133 cm-I. The molecule trans-Zbutene presents small changes in line width for all three oscillators generally increasing from 50 to 150 cm-I approximately. For 2-methyl-2-butene, beginning with similar line widths at Av = 3, the line width of the C-H (1) for Av = 3-6 passes through a minimum (120,79, 61, and 227 cm-I), simultaneously, the line width of the C-H (s) oscillator passes through a maximum (1 16,265, 179, 129 cm-I). The line width of the C-H (a) band increases from 5 5 to 165cm-i asa functionofthequantumnumber. In thecaseof2,3-dimethyl2-butene, the C-H (s) band has large line widths and their
Manzanares I. et al.
4002 The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 2-Methyl-2-butene
cis-2-Butene 3100
7
2500
!
3100
1
1
3100
7
2500
I 2,3-Dimethyl-2-butene
trans-2-Butene 3100 7
3000
-
2900
'
2800
8>
-
-z5
3000
-
2900
-
2800
-
r
W
a 2700 -
2700
2600
2600 2500
2500
I
0
1
2
3
4
5
6
magnitude fluctuates going from Au = 3 to 6 (140,244,143, and 265 cm-I); the C-H (a) bands also fluctuate but the magnitude of the changes is smaller, and as with the other molecules the magnitude is between 50 and 150 cm-I. Summarizing for the four molecules, the C-H (a) bands show steady increase in line width with quantum number but seem to be unaffected by the change in number of methyl groups. The line width of the C-H (s) bands seems to begreatly affected by the substitution, showing small fluctuations in magnitude in trans-Zbutene, strong fluctuations in magnitude in cis-Zbutene, small oscillations in 2-methyl-2-butene, and large fluctuations in 2,3-dimethyl-2butene. The magnitude of the line width of the olefinic C-H (1) seems to be large only in 2-methyl-2-butene and shows small increases or constant value in cis- and trans-2-butene. These results are in agreement with the results obtained by Baylor and Weitz45for out-of-planeC-H and in-plane C-H bonds of propene and cis-propene-1,2-d2, where the out-of-plane C-H band increases from 50 to 180 cm-1 (Au = 3-6).
1
2
3
4
5
6
7
Quantum number (v)
Figure IS. BirgeSponer plot for different C-H osciiiators of 2-methyl2-butene and 2,3-dimethyl-2-butene. For 2-methyl-Z-butene, the upper straight linecorresponds to theolefinicC-H (1) bond, the middlestraight line corresponds to the in-plane C-H (s) bonds, and the lower straight line corresponds to out-of-plane C-H (a) bonds. The two lines shown for 2,3-dimethyl-2-butene correspond to the in-plane (upper line) and out-of-plane (lower line) C-H bonds.
TABLE M: Observed and Calculated Peak Position,C-H Transition Assignments, and Line Width in tbe Overtone Spectra of 2,3-Mmethyl-2-butene Av
peak position (cm-I) observed calculated
assignment" ~
2
3
4
5
Conclusions The spectra of C-H fundamentals and overtones of cis-2butene, trans-2-butene, 2-methyl-2-butene, and 2,3-dimethyl2-butene have been investigated using intracavity photoacoustic spectroscopy and Fourier transform infrared and near-infrared techniques. Three types of vibrational transitions are identified for C-H absorptions of cis- and trans-Zbutene and 2-methyl2-buteneand two types for 2,3-dimethyl-2-butene: (a) transitions that correspond to olefinic C-H (1) bonds; (b) transitions that correspond to the in-plane C-H (s) bonds; (c) transitions that correspond to the out-of-plane C-H (a) bonds. cis- and trans-
I
0
7
Quantum number (v) Figure 14. BirgeSponer plots for different C-H oscillators of cis- and trow-2-butene. Upper straight line in each case corresponds to olefinic C-H (1) bonds. Middle straight line in eachcase corresponds to in-plane C-H (s) bonds. Lower straight line in each case corresponds to outA, 0) shown for comparison of-plane C-H (a) bonds. The points (0, at u = 1 were not included in the linear fit and correspond to the isolated C-H frequencies reported in ref 5.
-
6
5642 5718 5862 5 927 8287 8 343 8 433 8 553 8638 10 700 10866 11 008 11 220 13 159 13 244 13284 13 386 13 500 13741 15077 15485 15 572 15 703 15 933 16141
5698 5874
line widths (cm-1)
~~
~
2va 2v,
8 348 8 458 8 578 8623 10 696 10867 10 972 11 248 13 200 13 278 13254 13 364 13 554 13747 15076 15509 15 618
3va 2va + 26,,,(CH3) (1370) 2 ~ a+ ~sym(CH3)(2860) 3u, 3vS 2psym(CH3)(1029) 4ua 3va 2psym(CH3)(1 167) 4v, 4va + 2psym(CH3)(1167) (1029) 4v, + 2psym(CH~) 5va 4 ~+ s 2pas(CH3) (1072) 4vS+ 2psym(CH3)(1 167) 5v, 5va+2v(C-C) 6va 5va + 2psYm(CH3)(1167)
16122
5vs + 2~as(CH3)(1072) 6v,
+ +
79 51 149 96 140 167 88 206 244 195 119 62 118 289 143 171 152 198 329 399 265
The number in parentheses is the vibrational frequency.
2-Butene show fundamental and overtone C-H spectra that are different and characteristic of each isomer. The harmonic frequencies and anharmonicitiesof the pure isomers were obtained
Spectroscopy of C-H Stretching Vibrations
The Journal of Physical Chemistry, Vol. 97,No. 16, 1993 4003
TABLE VII: Vibrational Local-Mode Frequencies (we o x ) , Anhamodcity Constants ( o x ) ,Isolated Frequencies (vCHiSO), and Dissociation E nergies ( A L X )of C-H Stretch Bonds C-H (1)
C-H (s)
C-H (a)
(A).
3070 f 3 3010 3015 3017 -60.2 f 0.7 39140 1.089 (8)
301 1 f 6 2951 2969 2965 -60 f 1 37776 1.094 (5)
2988 f 7 2924 2926 2920 -64 f 2 34876 1.098 (9)
(A).
3045 f 6 2985 2989 2995 -60fl 38633 1.092 (4)
3013 f 9 2952 2958 2963 -61f2 37206 1.095 (6)
2989 f 6 2925 2928 2924 -64f 1 34899 1.098 (7)
3 0 4 9 f 12 2988 2997 -61 f 3 38100 1.091 (6)
2991 f 6 2936 2973 -59f 1 37907 1.094 (1)
2979f9 2915 2912 -64f2 34666 1.100 (3)
3062f 13 3000 2999.5 -62f3 37806 1.091 (4)
2981 f 11 2915 2900 -66f2 33660 1.101 ( 5 )
A
cis-2-butene
- wcxc (cm-1) - 2wcxe(cm-I) YCH"O (cm-l). Y C H ' * O (cm-')* wCxc(cm-I) AEma (cm-9
W,
w,
rCHo
frans-2-butene wc - wexe (cm-I) w, - 2w,x, (cm-1) VC#O (cm-1). VCHI'O (cm-I)b wCxc(cm-I) AEma (cm-') rCHo
2-methyl-2-butene wc - wCxc(cm-I) we - 2w,x, (cm-1) YcHI'O (cm-l)b wCxc(cm-I) A E m d x (cm-') rCHo
(A)'
2,3-dimethyl-2-butene w, - wexe (cm-1) w, - 2wexe(cm-I) V C H (cm-')b ~ ~ wcxC(cm-1) u m a a (cm-9 rCHo
(A).
23 27 43 45 2900 -0.004 24 27 30 39 2307 -0.003 12 21 61 3241 -0.006 81 85 99 4146 -0.010
a uCHlsO and rCHo for cis- and trans-2-butene from ref 5 . calculated fromeq 4. rcHOcalculated from eq 5. A =difference between C-H (s) and C-H (a). '
in the present investigation. The overtone transitions of the inplane C-H (s) bond of cis-2-butene have been assigned, in particular, the fifth overtone transition that could not be assigned by Wong and Moore appears at 15 914 cm-'. The local mode fundamental frequencies (w, - 2wexe)of cis- and tram-Zbutene are very close in magnitude to the isolated frequencies Y C H ~ ~ O obtained from the infrared spectra of partially deuterated compounds. A correlation between the fifth overtone frequencies and the isolated frequencies was used to predict the values for 2-methyl-2-buteneand 2,3-dimethyl-2-buteneUThe calculated energy difference (A) between the dissociation energies of the C-H (s) and C-H (a) bonds indicates that A increases in the order trans < cis < 2-methyl < 2,3-dimethyl-2-buteneS The line widths of the out-of-plane bonds C-H (a) show modest increase as a function of the vibrational quantum number and are not affected by the methyl substitution. The line widths of the inplane bonds C-H (s) are a function of the methyl substitution and the vibrational quantum level excited. cis-2-butene and 2,3dimethyl-2-butene show the largest fluctuations in line widths going from Au = 3 to 6. Changes in line width are consistent with intramolecular energy redistribution of the initially prepared state through intermediate receptor states which in turn connect with the full density of states.
Acknowledgment. This work was supported by the Robert A. Welch foundation under Grant No. AA-1173. We acknowledge the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. This study was also supported in part by funds from the Baylor Universitv Research Committee and the Bavlor Universitv Sabbatick Committee of the College of Arts a i d Sciences.
-
References and Notes (1) Fang, H. L.; Swofford, R. L. Appl. Opt. 1982,21, 55. (2) Wong, J. S.; Moore, C. B. J . Chem. Phys. 1982, 77, 603. (3) Nakagaki, R.; Hanazaki, I. Chem. Phys. Left. 1981,83,512. (4) Fang, H. L.; Compton, D. A. C. J. Phys. Chem. 1988,92,7185. (5) McKean, D. C.; Mackenzie, M. W.; Morrison, A. R.; Lavalley, J. C.; Janin, A.; Fawcett, V.; Edwards, H. G. M. Specfrochim.Acta 1985,41A, 435. (6) Gershinowitz, H.; Wilson, E. B. J. Chem. Phys. 1938,6, 247. (7) Richards, C. M.; Nielsen, J. R. J . Opt. SOC.Am. 1950,40, 442. (8) Creitz, E. C.; Smith, F. A. J. Res. Nail. Bur. Stand. 1949,43,365. (9) Rasmussen, R. S.; Brattain, R. R. J . Chem. Phys. 1947,15, 120. (10) Fox, J. J.; Martin, A. E. Proc. R . SOC.1940,A175, 208. (11) Thompson, H. W.; Torkington, P. Proc. R . SOC.1945,A184, 3. (12) Sheppard, N.; Sutherland, G. B. B. M. Proc. R . SOC.1949,A196, 195. (13) Sheppard, N.; Simpson, D. M. Q.Rev. (London) 1952,6, 1. (14) Sverdlov, L. M. Dokl. Akad. Nauk SSSR 1957,112,706. f 151 Sverdlov. L. M. Fir. Sborn. L'uov Vniu. 1957.3. 278. (16j Scott, D.'W.; Waddington, G.;Smith, J. C.; Huffman, H. M. J . Am. Chem. SOC.1949,71, 2767. (17) Kimmel, H. S.;Snyder, W. H. J . Mol. Sfruct. 1969,4, 473. (18) Scott,D. W.;Finke,H.L.;McCullough,J.P.;Gross,M.E.;Messerly, J. F.: Pennineton. R. E.: Waddinaton. G. J . Am. Chem. SOC.1955. 77.4993. (19) Lev&, I. W.; Pearce, R-A. R. J. Mol. Spectrosc. 1974,49,91. (20) Kilpatrick, J. E.; Pitzer, K.S. J . Res. Natl.Bur.Sfand.1947,34191. (21) Zakharieva-Pencheva, 0.; Farster, H. Vibraf.Spectrosc. 1992,2, 227. (22) Schei, S. H. Acta Chem. Scand. 1984,A38, 377. (23) Ermer, 0.;Lifson, S . J . Mol. Spectrosc. 1974,51, 261. (24) Aston, J. G.;Szasz,G.; Woolley, H. W.; Brickwedde, F. G.J. Chem. Phys. 1946,14, 67. (25) Levin, I. W.; Pearce, A. R.; Harris, W. C. J . Chem. Phys. 1973,59, 3048. (26) Nagel, B.; Handschuh, P.; Fruwert, J.; Geiseler, G. Z . Phys. Chem. 1984,265,474. (27) Handschuh, P.; Nagel, B.; Fruwert, J. Z . Chem. 1984,24, 199. (28) Sverdlov, L. M. Opt. Spekfrosk. 1956,1, 152. (29) Shimanouchi, T.; Abe, Y.; Alaki, Y. Polym. J . 1971,2, 199. (30) Shimanouchi, T.; Abe, Y. J . Polym. Sci., Parr A-2 1968,6,1419. (31) Durig, J. R.; Hudson, S.D.; Natter, W. J. J . Chem. Phys. 1979,70, 5141. (32) Durig, J. R.; Hawley, C. W.; Bragin, J. J . Chem. Phys. 1972,57, 1426. (33) Barnes, A. J.; Howells, J. D. R. J . Chem. Soc., Faraday Trans. 2 1973,69,532. (34) Kondo, S.;Sakurai, Y.; Hirota, E.; Morino, Y. J . Mol. Spectrosc. 1970,34,231. (35) Herzberg, G. Infrared and Raman Spectra; Van Nostrand: New York. 1945. (36) Radom, L.; Lathan, W. A.; Hehre, W. J.; Pople, J. A. J . Am. Chem. SOC.1971,93, 5339. (37) Mulliken, R. S.;Rieke, C. A.; Brown, W. G. J . Am.Chem. SOC.1941, 63, 41. (38) McKean, D. C. Chem. Soc. Rev. 1978,7, 399. (39) Mukamel, S.; Islampour, R. Chem. Phys. Lett. 1984,108, 161. (40) Freed, K. F.; Nitzan, A. J . Chem. Phys. 1980,73, 4765. (41) Sibert, E. L., 111; Hynes, J. T.; Reinhardt, W. P. J . Chem. Phys. 1984,81, 1135. (42) Sibert, E. L., 111; Reinhardt, W. P.; Hynes, J. T. J . Chem. Phys. 1984,81,1115. (43) Sibert, E. L., 111; Reinhardt, W. P.; Hynes, J. T. Chem. Phys. Left. 1982,92,455. (44) Stannard, P. R.; Gelbart, W. M. J . Phys. Chem. 1981,85, 3592. (45) Baylor, L. C.; Weitz, E. J . Phys. Chem. 1990, 94,6209. ~
