J. Pkys. Ckem. 1987, 91, 3959-3969 at the MP2 level is of similar magnitude irrespective of the basis set employed, as shown above, the currently best theoretical value of the AG(G-T) (and M ( G - T ) as well) can be estimated as -0.6 to -0.7 kcal/mol: a combination of the lowest hECs(G-T) value given by Radom et al. (-0.14kcal/mol from the HF/D106++** c a l ~ u l a t i o nwith ) ~ ~ our electron correlation correction (-0.4to -0.5 kcal/mol) and thermal correction (AUthermo - ThS(G-T): -0.05 kcal/mol). This currently best estimate can and will be further improved by explicit consideration of the effect of internal rotation on the partition functions.52 (46) (a) Dunning, T. H. J . Chem. Phys. 1970,53,2823. (b) Dunning, T. H. J. Chem. Phys. 1971,55,716. (c) Dunning, T. H.; Hay, P. J. In "Methods of Electronic Structure Theory", Modern Theoretical Chemistry, Vol. 3 , Schaefer 111, H. F., Ed.; Plenum: New York, 1977; pp 1-27. (47) Even the H F level calculation with Dunning basis sets such as D95V**, D95**, D106** etc. gives a negative value for O ( G T ) (see ref 29 for the notations of these basis sets). Radom et al., however, did not include the calculated total energies in their table in ref 29. We traced their calculations and found that the Dunning basis set gives a lower total energy than that arrived at by a Pople basis set of similar size. It follows that the Dunning series are better, at least, for 1,2-difluoroethane.
3959
Thus, there is much room for refinement of the present calculations. This is also true for the corresponding experimental values. They should converge into one common value for a given state within experimental errors. Therefore, further investigation by both theoretical and experimental approaches is necessary to settle the debate on the A H ( G T ) and AG(GT) values concerning the gauche effect in 1,2-difluoroethane. We are trying to determine the population ratio in the unperturbed state directly by gas-phase high-resolution N M R s p e c t r o ~ c o p y . ~ The ~ - ~ ~preliminary 'H and I9FN M R results indicate that AG(G-T) could be about -0.8 kcal/mol.5' Registry No. F(CH2)*F, 624-72-6. (48) Hirano, T.; Miyajima, T.; Kato, K.; Sato, H. J . Chem. SOC.,Chem. Commun. 1984,935. (49) Miyajima, T.; Hirano, T.; Sato, H. J . Mol. Struct. 1984, 125, 97. (50) Hirano, T.; Miyajima, T. J . Mol. Struct. 1985, 126, 141. (51) Hirano, T.; Nonoyama, S.;Miyajima, T.; Kurita, Y.; Kawamura, T.; Sato, H. J. Chem. SOC.,Chem. Commun. 1986, 606. (52) In the present calculations, internal rotation is treated as one of the harmonic vibration modes.
Spectroscopy of High Vibrational Levels in Pyramidal Molecules: C-H Stretching Overtones of N(CH,),, P(CH3),, and As(CH,), Carlos Manzanares I,*+ N. L. S. Yamasaki, and Eric Weitz* Department of Chemistry, Northwestern University, Euanston, Illinois 60201 (Received: December 9, 1986)
Photoacoustic spectra of the overtones of the C-H stretches of N(CH3)3,P(CH3),, and A s ( C H ~ in ) ~the gas phase are reported. The observed spectral features are assigned on the basis of the local-mode model. Two bands are observed for each overtone which are assigned to nonequivalent methyl C-H bonds. The higher energy absorption band in each overtone region (AD = 5 , 6, and 7) is assigned to the out-of-plane methyl C-H bonds while the lower energy absorption band is assigned to the in-plane C-H bond. Deconvolution of the overtone bands for Au(C-H) = 5, 6, and 7 provides additional information with respect to peak position, profile, and line width of the overtone absorptions. Local-mode harmonic frequencies (oc) and anharmonicities (w&J are obtained from an analysis of the spectra. Data suggest that the major factor contributing to the width of P(CH3), and As(CH,), overtone absorptions is the rotational envelope of the molecule while line widths obtained for N(CH3)3indicate there is also a major contribution to the width from homogeneous broadening.
Introduction Early work on vibrational overtones was performed in the photographic infrared using standard spectroscopic techniques.' The availability of tunable pulsed and continuous wave laser systems in the visible region of the electromagnetic spectrum combined with sensitive detection techniques such as photoacoustic spectroscopy and thermal l e n ~ i n ghave ~ , ~ contributed to a resurgence in the study of vibrational overtones. Studies of highly excited vibrational states of polyatomic molecules have provided information that is relevant to many areas of chemistry including molecular ~ t r u c t u r e , ~intramolecular -~ dynamics,lGI7 selective laser-induced vibrational p h o t o ~ h e m i s t r y , ~and ~ ~ 'local-mode ~ theories.2G22 In this paper we report on the overtone spectra of the molecules trimethylamine, phosphine, and arsine, which are all members of the homologous series, M(CH3)3. Trimethylamine, phosphine, and arsine have been characterized by microwave spectroscopy and electron d i f f r a ~ t i o n . * ~They - ~ ~ are symmetric rotors which exhibit internal rotation with barriers to rotation between 1.5 and 4.4 kcal mol-'. Their vibrational spectra have been studied by infrared and Raman spectroscopy resulting in the assignment of vibrational f ~ n d a m e n t a l s . ~ ' ~In~ addition, overtones of the C-H 'Current address, Department of Chemistry, Hope College, Holland, MI 49423.
0022-3654/87/2091-3959$01.50/0
stretches (Au = 4,5, 6) of N(CH,), have been previously studied by using photoacoustic spectroscopy.' In this work, absorptions (1) Herzberg, G. Infrared and Raman Spectra; Van Nostrand New York, 1945. (2) Pao, Y. H. Optoacoustic Spectroscopy and Detection; Academic: New York, 1977. Klinger, D. S. Ultrasensitive Laser Spectroscopy; Academic: New York, 1983. (3) West, G. A,; Barret, J. J.; Siebert, D. R.; Reddy, K. V. Rev. Sci. Instrum. 1983,54,797. Long, M. E.; Swofford, R. L.; Albrecht, A. L. Science 1976, 191, 183. Stella, G.; Gelfand, J.; Smith, W. H. Chem. Phys. Lett. 1976, 39, 146. (4) Greenlay, W. R. A.; Henry, B. R. J. Chem. Phys. 1973, 69, 8. ( 5 ) Wong, J. S.;Moore, C. B. J . Chem. Phys. 1982, 77, 603. (6) Fang, H. L.; Swofford, R. L.; McDevitt, M.; Anderson, A. B. J . Phys. Chem. 1985.89, 225. (7) Fang, H. L.; Meister, D. M.; Swofford, R. L. J . Phys. Ckem. 1984, 88, 410. ( 8 ) Fang, H. L.; Swofford, R. L.; Compton, D. A. C. Chem. Phys. Lett. 1984, 108, 539. (9) Fang, H. L.; Meister, D. M.; Swofford, R. L. J . Phys. Chem. 1984, 88, 405. (10) Reddy, K. V.; Heller, D. F.; Berry, M. J. J . Chem. Phys. 1982, 76, 2814. (11) Bray, R. G.; Berry, M. J. J . Chem. Phys. 1979, 71, 4909. (12) Siebert, E. L.; Reinhardt, W. P.; Hynes, J. T. J. Chem. Phys. 1984, 81, 1115. (13) Siebert, E. L.; Reinhardt, W. P.; Hynes, J. T. Chem. Phys. Lett. 1982, 92, 455. (14) Henry, B. R.; Greenlay, W. R. A. J . Chem. Phys. 1980, 72, 5516. (15) Henry, B. R.; Mohammadi, M. A. Chem. Phys. Lett. 1980, 75,99.
0 1987 American Chemical Society
Manzanares et al.
3960 The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 corresponding to AG = 1-7 of the C-H stretching modes have been obtained for N(CH3), and Au = 1, 2, and 5-7 for P(CH,), and As(CH,), where Au = 1-4 have been obtained via standard infrared techniques. Absorptions in the Au = 5, 6, and 7 regions were obtained by using intracavity C W dye laser excitation and photoacoustic detection. Computer deconvolution of the highenergy overtone bands has been performed. Peak positions and absorption cross sections are reported. These results are interpreted in terms of a local-mode description of vibrational overtones from which local-mode harmonic frequencies (we) and anharmonicities (w,x,) have been calculated. An important aspect of the local-mode picture is that structurally and conformationally nonequivalent C-H oscillators show distinct transition f r e q ~ e n c i e s . ~For - ~ example, studies of C-H overtones have shown that for normal alkanes and several branched alkanes each overtone band is principally composed of peaks corresponding to the different C-H oscillators in the molecule; CH,, CHI, or CH.4 The energies of the C-H absorptions have been found to occur in the order methylene < methyl < aryl olefin < acetylenic-the same order as the bond dissociation energies and frequencies of the respective C-H fundamentals.s,6 If a methyl group is in a conformationally anisotropic environment it has been shown that the IR spectra consist of distinct bands for each nonequivalent C-H bond. The presence of a central heteroatom such as N , 0, or S has been shown to produce an anisotropic environment. Each nonequivalent absorption is a t a different frequency where the magnitude of the frequency shifts are a consequence of the "trans effect".w3 For heteroatoms with a lone pair of electrons, such as N or 0, it has been suggested that there is a donation of electron density from the lone pair into an antibonding orbital of a trans C-H bond. This effect, known as the trans effect, induces a weakening of the trans C-H bond. This behavior has been observed for the overtones of N(CH,)3:7 Since the compounds reported on in this paper all contain central heteroatoms and barriers to rotation of the methyl groups which vary from I .5 to 4.4 kcal/mol, nonequivalence of the hydrogens in the absorbing methyl group would be anticipated. In fact, the structural and conformational studies of N(CH3)3and P(CH,), by IR and microwave spectroscopy have confirmed the nonequivalence of C-H This nonequivalence comes about due to the large difference in time scales for infrared absorption vs. rotation of the methyl group. As expected, we observe
-
(16) Henry, B. R.; Mohammadi, M. A.; Hanazaki, I.; Nakagaki, R. J . Phys. Chem. 1983.87, 4827. (17) Manzanares, C.; Yamasaki, N. L. S.; Weitz, E.; Knudtson, J. T. Chem. Phys. Lett. 1985, 117, 477. (18) Reddy, K. V.; Berry, M. J. Chem. Phys. Lett. 1977,52, 111; Chem. Phys. Left. 1979, 56, 223; Faraday Discuss. 1979, 67, 188. (19) Crim, F. F. Annu. Reo. Phys. Chem. 1984, 35, 657. (20) Mecke, R. Z . Phys. Chem. 1932, 817, 1 Z . Phys. 1936, 99, 217. Mecke, R.; Ziegler, R. 2. Phys. 1936, 101, 405. (21) Henry, B. R. Acc. Chem. Res. 1977, 10, 207. (22) Halonen, L.; Child, M. S. Mol. Phys. 1982, 46, 235. (23) Beagley, B.; Medwid, A. R. J . Mol. Sfrucf.1977, 38, 229. (24) Beagley, B.; Hewitt, T. G. Trans. Faraday SOC.1968, 64, 2561. (25) Lide, D. R.; Mann, D. E. J . Chem. Phys. 1958, 28, 572. (26) Lide, D. R.; Mann, D. E. J . Chem. Phys. 1958, 29, 914. (27) Lide, D. R. Spectrochim. Acfa 1959, 473. (28) Bartell, L. S.; Brockway, L. 0. J . Chem. Phys. 1960, 32, 512. (29) Gayles, J. N. Specfrochim. Acta 1967, 23A, 1521. (30) Barcelo, J. R.; Bellanato, J. Spectrochim. Acta 1956, 8, 27. (31) Bauer, S . H.; Blander, M. J . Mol. Specfrosc. 1959, 3, 132. (32) Halmann, M. Specfrochim.Acta 1960, 16, 407. (33) Rojhantalab, H.; Nibler, J. W.; Wilkins, C. J. Spectrochim. Acta 1976, 32A, 519. (34) Park, P. J.; Hendra, P. J. Spectrochim. Acra 1968, 24A, 2081. (35) Rosenbaum, E. J.; Rubin, D. J.; Sandberg, C. R. J . Chem. Phys. 1940, 8, 366. (36) Bouquet, G.; Bigorgne, M. Spectrochim. Acta 1967, 23, 1231. (37) McKean, D. C.; McQuillan, G. P. J . Mol. Sfruct. 1978, 49, 275. (38) Wollrab, J. E.; Laurie, V. W. J . Chem. Phys. 1969, 51, 1580. (39) Bryan, P. S.; Kuczkowski, R. L. J . Chem. Phys. 1971, 55, 3049. (40) McKean, D. C. Chem. SOC.Reo. 1978, 7 , 399 and references therein. (41) Bellamy, L. J. Mayo, D. W. J . Phys. Chem. 1976, 80, 1276. (42) Bellamy, L. J. Appl. Spectrosc. 1979, 33, 439. (43) Bellamy, L. J. The Infrared Spectra of Complex Molecules, Vol. 2, Aduances in Infrared Group Frequencies, 2nd ed.; Chapman and Hall: New York. 1980.
two sets of chemically nonequivalent hydrogens for each member of the M(CH,), series. One absorption corresponds to the two hydrogens out of the plane established by the heteroatom, the C atom of the absorbing methyl group, and the other H atom, while the other absorption is due to the H atom in this plane and trans to the lone pair of the heteroatom. The positions of these absorptions are reported and discussed. Another aspect of our study relates to overtone line widths. Overtone absorptions typically have rather large line widths relative to those of the fundamental. Attempts have been made to interpret line widths of highly vibrationally excited states of polyatomic molecules in terms of intramolecular energy-transfer processes. For example, the overtone spectra of benzene exhibit broad homogeneous line shapes that have been interpreted as corresponding to subpicosecond intramolecular vibrational energy redistribution p r o c e s ~ e s . ~However, ~ * ~ relatively narrow line widths have been obtained from room temperature studies of neopentane and for the tetramethyl compounds of silicon, germanium, and tin.I4-l7 Rather narrow line widths are also observed for the M(CH3), series of compounds with overtone line widths for P(CH,), and As(CH,), being quite similar to those of their respective fundamental line widths while the N(CH3)3 overtone line width is typically a few times the fundamental line width. The ramifications of the observed line widths in terms of broadening mechanisms and implications for intramolecular energy transfer will be discussed further.
Experimental Section A detailed description of the experimental system has been previously provided." Briefly, laser photoacoustic spectra were obtained for the Au = 5, 6, and 7 C-H stretching vibrations using a cell mounted within the cavity of a Kr+ pumped (3000K) CW dye laser (CR-599-01) with high reflectance optics. The photoacoustic cell is 1 cm diameter and 20 cm long, made of Pyrex tubing with quartz windows mounted at Brewster's angle. The photoacoustic signal is detected by a Knowles BT1759 electret microphone attached to a flange mounted at the midpoint of the cell. The ion laser pump beam is modulated by a mechanical chopper at a frequency of 125 Hz. Wavelength tuning (-0.5 cm-] bandwidth) of the dye laser is accomplished with a stepper-motor-driven birefringent filter. The stepper motor is controlled by a microprocessor. Dye laser wavelengths were obtained with a calibrated JY HR320 monochromator. Signals from the microphone are amplified and processed by an Ithaco lock-in amplifier, Model 291A. The laser output is monitored with a photoiodide which detects a reflection off of the Brewster angle window of the in-cavity cell. This signal is fed to a P.A.R. Model 128A lock-in amplifier. Normalization of the photoacoustic spectra is achieved by ratioing the output signals from both lock-in amplifiers. The normalized signal is then displayed on a strip chart recorder. The tuning ranges of the laser dyes are as follows: LD 700 pumped by all red lines of the Kr+ laser (1 2 000-14 000 cm-I), Rhodamine 610 (14 800-16 500 cm-I), and Rhodamine 560 pumped by the blue green lines of the Kr+ ion laser (1 7 O W 1 8 600 cm-I). In each case a high reflectance (>99.7%) dye laser output coupler is used to increase intracavity laser power. Spectra of the C-H stretching fundamentals were obtained with a Nicolet 7 199 Fourier transform infrared spectrophotometer and a 0.10-m cell. Spectra for Au = 2-4 were obtained with a Perkin Elmer Model 330 IR-UV-vis spectrophotometer. Trimethylamine, anhydrous, 99% purity, was purchased from Aldrich; trimethylphosphine, 99% pure from Alfa; and trimethylamine, 99% pure, from Chemicals Procurement Laboratories, Inc. These samples were degassed by freeze-pump-thaw cycles before use. All experiments were performed at 21 2 OC.
*
Results The spectra shown in Figure 1 are for the fundamental transitions of the C-H stretching vibration of N(CH,),, P(CH3),, and As(CH,),. These spectra were obtained by using 4 Torr of gas. Figure 2 shows spectra for the three molecules in the region of
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 3961
Spectra of N(CH,),, P(CH3),, and As(CH3), 100
c
~
TABLE 11: Observed Peak Position, C-H Transition Assignments, and Peak Cross Sections in the Fundamental and Overtone Spectra of P(CHA quantum no. peak position, peak cross section, (Av) cm-I assignment pm2/moiecule
NICH,),
1 2
3" 4" 5
6 7
2 829.5 2 899.6 2 959.7 5 512.7 5691.5 5 760.4 5 882.4 8 313 8 436 10854 11 034 13 276 13 320 13 444 13 528 13615 13 732 15606 15 896 17785 18 144 18 187
-2-2
J.J
21.2 37.5 1.5 X lo-' 1.3 X lo-' 3"b 3va 4yb
4va 5ub
5u, - torsion 4ub 2v17 5ua 4u, 2Y1,
+ + 5u, + torsion
6yb
3.6 x 10-4
6Va 7yb
6Yb 7ua
1.7 x 10-3
+ 2U17
'Calculated by using eq 2 and the parameters we and w p e listed in Table V for P(CH3),. TABLE 111: Observed Peak Position, C-H Transition Assignments, and Peak Cross Sections in the Fundamental and Overtone Spectra of A 4 W h quantum no. peak position, peak cross section,
Oo0
'
2600
2700
do0
2900 30b0 WAVENUMBERS (cm-')
3/00
:
Figure 1. Absorption spectra of the fundamental (Av = 1) C-H stretch region of N(CH3)3,P(CH&, and A s ( C H ~ ) ~The . path length was 10 cm and the pressure, in each case, was 4 Torr. TABLE I: Observed Peak Position, C-H Transition Assignments, and Peak Cross Sections in the Fundamental and Overtone Spectra of N(CHaL quantum no. peak position peak cross section, (AD)
cm-l
1
2 773.2 2821.6 2 962.8 5 720.8 5 798.8 5 948.8 8 460 8 500 8 587 I O 240 11 038 12485 13 439 13 493 13 767 14 575 15811 15981
2
3 4 5
6
7
16 535.0 18 000 18 100
assignment"
pm2/molecule
(AD)
cm-'
1
2822.1 2912.1 2 980.2 5 640.2 5 780.4 5917.2 8 388 8, 502 10968 11 108 13 434 13 514 13 595 13718 15781 15817 15 947 16048 18042 18 232
2
3" 4" 5
6
61.7 50.4 32.3 7 1.3 X IO-'
2ua
pm2/molecule 1.8 12.9 14.3 1.4 X lo-' 1.2 x 10-1
yb
3va 4yb
4ua 4vb 5va ?
+ 2Y4
3.9 x 10-3
6yb
6ua - T 6ua 6Yb T
+
3.1 x 10-4
7ub
7v,
'Calculated by using eq 2 and the parameters we and w,xe listed in
3ua 2ua
assignment
Table V for As(CH,),.
+ y14
+ y13
4Vbb 4va 5u: 4ua 2UI9 5ua 5ua + ~ 2 2 6u: 6 ua 5ua 2UI8 6ub + u4 7u: 7ua 6ua 2~19
+
+
2.3 x 10-3 1.3
x 10-4
+
frequency corresponding to C-Ha type bond. ub frequency corresponding to C-Hb type bond. *Experimentalvalues from ref 7. Y,
the first overtone of the C-H stretching vibration. These spectra were obtained by using a 0.10-m cell with gas pressures of 121
Torr for N(CH,),, 122 Torr for P(CH,),, and 125 Torr for As(CH3),. Spectra of the second ( u = 3) and third ( u = 4) overtones of the C-H stretch of N(CH,), were obtained by using a Wilks variable path length cell. In each case the pressure was 420 Torr. The path length was 2.25 m for u = 3 and 6.75 m for u = 4. Figure 3 depicts the fourth overtone spectra ( u = 5) in the C-H stretching region for N((CH,),, P(CH,),, and As(CH,),. These spectra were obtained via intracavity dye laser photoacoustic spectroscopy. Gas pressures were 10, 11, and 12 Torr, respectively. Figure 4 displays the fifth overtone spectra (u = 6) of the C-H stretching region. Gas pressures were 120 Torr for N(CH,),, 122 Torr for P(CH,),, and 116 Torr for As(CH,),. Figure 5 shows the sixth overtone spectra (u = 7) in the region of the C-H stretch. Gas pressures were 400, 260, and 200 Torr for N(CH,),, P(CH,),, and As(CH3),, respectively. In Tables I, 11, and I11 the peak positions, assignments for selected transitions, and peak absorption cross sections are sum-
3962
Manzanares et al.
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 I
r
0700
I
I
N(CH,),
I 0525
1 I
0350
-
PICHJ,
n
,0175
t
---
13000
13400
I 3800
Wavenumbers
Figure 3. Photoacoustic absorption spectra of the fourth overtone (Au = 5 ) C-H stretch region of N(CH3),. P(CHo)3,and As(CH3),. The solid
lines are the experimental bands, the dot-dashed lines are the computer deconvolution fits, and dashed lines are the individual Lorentzian bands. The pressure was 10, 11, and 12 Torr, respectively.
0000 5400
5600
5000
6000
6200
WAV ENU M BE R S ( c m-0
Figure 2. Absorption spectra of the first overtone (Au = 2) C-H stretch region of N(CH,),, P(CH3),, and As(CH3),. The path length was 10 cm and the pressure was 121, 122, and 125 Torr, respectively.
marized for N(CH,),, P(CH3)3,and As(CH3),. The peak absorption cross sections for quantum levels 5 and 6 were determined by the use of an internal standard of known cross section and the equationlo u
= uoVP,/VoP
(1)
where P is the pressure of the sample, V the normalized signal intensity (arbitrary units), and u the absorption cross section in
units of pm2/molecule. The subscript (0) identifies the internal standard molecule. The v = 5 absorption cross section of N(CH3)3r P(CH3)3,and As(CH3), was determined relative to the v = 5 cross section of ethylene (CzH4); uo = 1.85 X lo4 pm2/molecule. The u = 6 C-H absorption cross section was determined relative to the v = 6 cross section of ethylene; uo = 3.02 X pm2/molecule. The uo values of ethylene for v = 5 and 6 were previously determined.19 No background signal was observed for an empty cell in the region of absorption for any of the molecules studied. Deconvolution. Since the observed spectra were, in general, a composite of peaks due to different transitions, the peaks were separated into individual bands via a deconvolution program. Deconvolution was performed with programs developed by Jones and Pitha44modified to run on a VAX computer. The spectra were digitized with an Apple computer graphics tablet. These data were fed to the computer along with the number of peaks to be used in the analysis, a set of approximate absorbances, peak positions, and bandwidths. Each individual peak was fitted with a Lorentzian band shape defined by the maximum peak absorbance, the frequency of the maximum, the full width at halfmaximum (fwhm), and the base-line constant which is used to represent background absorbance. The program then uses a nonlinear least-squares method to optimize the fit of a generated spectrum to the data. A visual comparison of experimental and calculated band envelopes was used to determine the best match between generated spectra and experimental data. The results of this deconvolution procedure are depicted in Figures 3, 4, and 5. ~~
(44) Jones, R. N.; Pitha, J. Natl. Res. Counc. Can.Bull. 1968,N12.
Spectra of N(CH3)3, P(CH3),, and As(CH3),
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 3963
PICH,).
+
I 15200
tI AdCH,),
15600
16000 Wave nu m b e r s
Figure 4. Photoacoustic absorption spectra of the fifth overtone (Au = 6) C-H stretch region of N(CH3),, P(CH3)3,and A S ( C H ~ )The ~ . solid
lines are the experimental bands, the dot-dashed lines are the computer deconvolution fits, and the dashed lines are the individual Lorentzian bands. The pressure was 120, 122, and 116 Torr, respectively.
17400
17800
18200
Wavenumbers Figure 5. Photoacousticabsorption spectra of the sixth overtone (Au = 7 ) C-H stretch region of N(CH3),, P(CH,),, and AS(CH,)~.The solid
lines are the experimental bands, the dot-dashed lines are the computer deconvolution fits, and the dashed lines are the individual Lorentzian bands. The pressure was 400, 260, and 200 Torr, respectively.
Discussion As(CH3), it appears that the intensity of the Au = 2 peaks around the fundamental absorption has reversed with respect to the Au A . Vibrational Assignments. The fundamental frequencies for the infrared active modes of N(CH3)3have been r e p ~ r t e d . ~ ~ , ~=~ 1 peaks. Overtone spectra were obtained for N(CH3), in the regions of The assignments have been made based on both gas and solid the C-H absorptions for Au = 3 and 4. Although they are not phase (-190 "C) studies of the infrared spectra of trimethylamine and its deuteriated analogues. Figure 1 depicts the infrared shown in the figures, their frequencies are given in Table I. In spectrum of the methylamine from 2600 to 3200 cm-'. According the region of each overtone, two strong absorptions are observed to the assignment of G a y l e ~ ?the ~ prominent peaks at 2963,2822, with an intensity ratio of approximately 2:l. Absorptions of this and 2773 cm-' correspond to the vI2, ~ 1 3 ,and ~ 1 C-H 4 stretching type have been previously observed and have been assigned to the two sets of conformationally nonequivalent C-H stretches in this modes of E symmetry. Transitions at 2950 and 2872 cm-' are assigned as the v 1 and v2 C-H stretching modes of AI symmetry. molecule.' As previously stated, the two sets correspond to (1) the H atom in the plane of the C and N atoms, which is typically Absorption bands are also shown in Figure 1 for P(CH3),. The band centered at 2960 cm-' corresponds to an overlap of the vl, at lower frequency and (2)the H atoms above and below this plane v12, and vi3 C-H asymmetric stretching The band which are typically the higher frequency of the two absorptions. These absorptions have been designated as Hb and Ha, respectively. centered at 2900 cm-I corresponds to an overlap of the C-H stretches vZ1and vi4 (symmetric), and the band around 2830 cm-' The frequencies of these absorptions are influenced by the now has been assigned as being due to overtone absorption^.^^-^^ well-known trans effect4"-", where the C-H bond trans to a lone Similar assignments are made for As(CH,)~(Figure 1). The band pair of a first-row heteroatom is weakened by donation of charge into an antibonding orbital of the C-H bond trans to the lone pair. around 2980 cm-' is assigned to absorption of the asymmetric C-H Higher overtones of the Ha and Hb absorptions have been pre; band around 2912 an-'is assigned stretching modes vl, u I 2 ,~ 1 3 the to the vZ1 and ~ 1 symmetric viously observed by Swofford7 for N(CH3), and fundamentals of 4 C-H stretches and the band around these absorptions have been observed by McKean3' in N(CH3), 2822 cm-I has been assigned as due to overtone absorption^.^^ The spectra shown in Figure 2 are in the C-H absorption region and P(CH,),. for Au = 2. For the Av = 2 region it is difficult to make a clear Though there has been some discussion in the literature reassignment of absorption bands since this spectrum represents a garding the magnitude of the trans effect for heteroatoms heavier transition between normal-mode and local-mode behavior. than those in the first row, McKean ascribes the observed However, it is interesting to note that the band at 5977 cm-' for 35-cm-I splitting between the Ha and Hb absorptions in P(CH,), N(CH3), is higher in frequency than twice the frequency of any to the trans effect.37 As will be discussed in more detail, we observe of the strong absorptions in the fundamental region. In addition, splitting between the Ha and Hb absorptions in As(CH,),. These splittings are certainly due to the conformational nonequivalence the N(CH3), Au = 2 spectrum has been reduced in complexity of the H atoms in the methyl groups of this compound. Based compared to the fundamental absorption. For P(CH,), add
-
3964 The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 TABLE I V Fundamental Frequencies (cm-I) Used for the Overtone Assignments of N(CH3)3, P(CH3), and A S ( C H ~ ) ~ molecule
N(CH3)3
assignment u17
VI8
VI9 y22
P(CH313
y17
torsion
As(CHd3
y4
VI7
torsion
freauencv
ref
1444 1273 1183 269 1298 208 1263 1242 280
29 29 29 29 32, 33 32, 33 34 34 34, 35
on McKean's assignment for P(CH3)3we feel this splitting is also significantly influenced by a heavy atom trans effect resulting from interaction of the As lone pair with the antibonding orbitals of the C-H bond of the trans H atom. These absorptions are reported in Tables I, 11, and I11 for the molecules N, P, and A s ( C H ~ ) ~ , respectively. In addition to the C-H stretching normal-mode fundamentals given in Tables I, 11, and I11 for N(CH3),, P(CH3),, and As(CH3)3,Table IV lists a number of other normal-mode fundamentals. These fundamentals are used to establish tentative assignments for the combination bands given in Tables I, 11, and 111. One problem in assigning the weaker bands observed in the photoacoustic spectra of these compounds is that there is often disagreement in the literature on the assignment and, in some cases, the position of f ~ n d a m e n t a l s . ~ ~ - ~ ~ Even though experimental spectra were not obtained for P(CH3)3and A s ( C H ~ )in~the C-H regions of Av = 3 and 4, calculated values of the frequencies for these modes are presented. These calculated frequencies were obtained by using eq 2 and appropriate parameters from Table V. Frequencies for Av = 4 are necessary to assign potential local-mode-normal-mode combination bands that appear in the Au = 5 C-H stretching region. The Au = 5 spectra are shown in Figure 3. Only the region around the C-Ha absorption is shown for N(CH3)3. Deconvolution of this region indicates that it is likely that there are three transitions that make up the experimental band envelope. The main transition corresponds to the C-Ha absorption at 13493 cm-' and it is indicated as 5ua in Table I. The absorption due to C-Hb was not obtained in the present work since it is outside of the range over which our dye laser was scanned. It was taken as being at 12485 cm-' from ref 7. The most likely assignment for the absorption band at 13 767.2 cm-' is a local-mode-normal-mode combination between the local-mode 5ua and the torsional mode vz2. The arithmetic sum of the frequencies of the two modes is 13 762 cm-l. The corresponding transitions 5Ua-U22, expected around 13 224 cm-', may not be observed because it would fall under and be obscured by the larger absorption which is centered at 13 439 cm-I. A possible alternative assignment for this abu18 with an arsorption is a combination band involving ithmetic sum of 13 758 cm-I. No clear assignment can be made for the absorption band at 13439 cm-I. The most likely possibility is to assign the absorption to 4ua 2vl9, where the arithmetic sum of the absorption frequencies would place this transition at 13 404 cm-I, already somewhat lower in frequency than the observed absorption even without taking into account anharmonic interactions in the ~ 1 mode 9 or between this mode and 4ua. The P(CH3), spectrum shown in Figure 3 (for Av = 5) exhibits bands at 13 528 and 13 276 cm-' which are assigned to the C-Ha (5ua) and C-Hb (5Vb) absorptions, respectively. Other transitions in this region, at 13 732 and 13 320 cm-I, are assigned as 5ua f 7' where is a torsional mode at approximately 208 cm-1.33 It is tempting to assign absorptions a t 13 615 and 13 444 cm-I to 5ua T~ where 72 would have a frequency of approximately 85 cm-'. However, there is no precedent in the literature for a torsional mode in this compound a t this low a frequency. A possible alternative assignment for the absorption at 13 615 cm-' is to a band corresponding to 4ua 2uI7with an arithmetic sum of frequencies of 13 630 cm-I. Similarly, the absorption at 13 444 cm-' could be assigned to the combination band 4ub + 2v17with an arithmetic sum of frequencies of 13 450 cm-I.
+
+
*
+
Manzanares et al. TABLE V Vibrational Local-Mode (we - w & ~ ) and Isolated (yak) Frequencies, Anharmonicity Constant ope, and Dissociation Energy AEmx of C-H Stretch Bonds" C-Ha C-Hb A 3011 f 4 2948 2952 -63 f 1 35976.7 1.0965
2826 f 8 2760 2799 -66 f 2 3025 1.O 1.1123
2974 f 8 2920 2954 -54 f 2 40947.6 1.0962
2939 f 10 2882 2919 -57 f 3 37884.7 1.0999
2977 f 14 2924 2970b -53 f 3 41804.4 1.0946
2958 f 7 2904 2945b -54 f 1 40508.2 1.0972
185 188 153 5726 -0.01 58
35 38 35 3063 -0.0037 19 20 25 1296 -0.002 6
a YCHiso for N(CH3)3and P(CH3).,from ref 37. U C H for ~ ~ As(CHp), ~ calculated from eq 4. r°CHcalculated from eq 5. A = difference between C-Ha and C-Hb vibrational constants. bCalculated by using eq 4.
Although the two absorptions at 13 276 and 13 320 cm-' are very close in energy and are overlapped in the spectrum, there is justification for assigning the lower frequency transition to 5Yb and the upper to a difference band involving 5ua. As shown in Figure 6, the Birge-Sponer plot obtained by using the 13 276-cm-' absorption gives a straight line for C-Hb for P(CH,), which is parallel to the C-Ha line. The difference in the intercept for the two lines is 35 cm-'. If the 13 320-cm-' absorption were to be assigned to 5%, the line for the C-Hb absorptions in Figure 6 would no longer be parallel to the C-Ha line and would have a very similar intercept. This behavior would be contrary to what is expected for nonequivalent C-H bonds. The Av = 5 spectra for A s ( C H ~ )(Figure ~ 3) depicts three strong absorptions at 13595, 13514, and 13434 cm-I. A weaker absorption is also observed at 13718 cm-'.The absorptions at 13 595 and 13 434 cm-' are assigned to the C-Ha and C-Hb transitions, respectively. Assignment of these transitions to C-Ha and C-Hb absorptions is also necessary to obtain parallel Birge-Sponer plots for these transitions. The strong absorption at 13 514 cm-' is assigned to the 4ub 2u4 combination band where u4 is a bending mode. The arithmetic sum of the frequencies for this band would be approximately 13 514 cm-'. The anomalous intensity for this transition is attributed to Fermi resonance between the combination band and the adjacent C-H stretches. The weaker transition at 13 718 cm-' could be assigned to either 4ua 2u4 or 5Vb + 7. Neither assignment is, however, completely satisfactory. In the former case, the observed transition is at a higher frequency than expected by the sum of frequencies of the component transitions, and in the latter case, the observed frequency is somewhat higher in energy than could be achieved from the reported frequencies of torsional modes for A s ( C H , ) ~ . ~ ~ , ~ ~ The C-H absorptions for Av = 6 are shown in Figure 4 with the frequencies of the observed absorptions reported in Tables 1-111. In the spectral region shown in Figure 4, N(CH3)3displays a single strong absorption at 15811 cm-' with a weak, broad shoulder at approximately 15 98 1 cm-I. The strong absorption at 15 81 1 cm-' is assigned as the 6ua transition. 6ubis outside the range of the region scanned. Its frequency was taken from ref 7 and is reported in Table I. The broad absorption at 15 98 1 cm-l is most likely due to 6ub u,, (arithmetic sum at 16019 cm-I) and/or the 5u, 2u18mode (arithmetic sum at approximately 16040 ~ m - l ) .For ~ ~either of these cases, the respective combi-
+
+
+
+
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 3965
Spectra of N(CH3)3, P(CH3)3, and A s ( C H ~ ) ~ TRIMETHYLAMINE
3'00r
7
*H-l-+-t+-l--
noisy to allow for reliable assignments. The Av = 6 spectrum for As(CH3), similarly exhibits two major peaks at 15 947 and 15781 cm-I. These peaks are assigned as the C-Ha and C-Hb absorptions, respectively. Another absorption at 15 817 cm-' appears as a shoulder on the C-Hb absorption. Other smaller peaks which do not significantly exceed noise levels are also observd in this spectrum. It would not be unreasonable to assign the peaks at 15 817 and 16 048 cm-' to combination or , ~ a torsional mode at approximately difference bands of 6 ~ ,with 280 cm-1.34,35This would result in 6ua - T and 6ub T being assigned to these transitions. 68, + T would be outside the range scanned while 6ub- T may be too weak to observe. Alternatively the band at 16 048 cm-' could be due to or have a contribution from the Sua + 2u17 combination band with an arithmetic sum of 16089 cm-l. The former assignment is preferred since it simultaneously explains two observed bands. However, due to the small signal/noise level of these transitions, these assignments should be considered as tentative. The Av = 7 absorption for N(CH3), is a broad asymmetric band which is composed of a major absorption at 18 000 cm-' which is assigned as the 7ua absorption with a shoulder at approximately 18 100 cm-I. There is also a broad absorption at lower frequency than the major peak. The 7vb absorption is at 16 535 cm-'? outside the range of frequencies that were scanned in these experiments. The absorption at 18 100 cm-' is most likely due to a combination band involving two quanta of the C H 3 rocking mode (~19)with 6ua. This would have an arithmetic sum frequency of 18 177 cm-1.29 The corresponding combination band with 6ub would be outside the range of scanned frequencies. The broad shoulder to lower frequency could be due to 7ua - T where the torsional mode would be at 269 cm-' and/or to combination bands involving u = 6.29 The spectrum for v = 7 of P(CH3), exhibits two major absorptions where the higher frequency absorption appears as an asymmetric band with a shoulder to lower frequency. The two major absorptions at 18 187 and 17 785 cm-' are assigned as 7ua and 7 4 , respectively. The shoulder on the 18 187 cm-' absorption centered at 18 144 cm-' is at a frequency such that it could be due to a combination band involving 6ub + 2u17 (arithmetic sum = 18 203 cm-'). The 6ua 2u17 band would be outside the range scanned but might not be seen because of the lack of Fermi resonance with a u = 7 absorption. The weak absorptions between the two major peaks are of magnitude that is comparable to noise levels and thus no attempt has been made to assign them to specific transitions. The broad shoulder to lower frequency of the 7% mode could be due to combination bands involving the overtone of a methyl rocking mode and 6ub which is enhanced by Fermi resonance with 7vb. The corresponding combination band with 6ua would sit directly under the 7Yb absorption. Assignment of the u = 7 absorptions for As(CH,), is straightforward with only two peaks being observed at 18 042 and 18 232 cm-I. These peaks are assigned to the 7 v b and 7ua absorptions, respectively. B. Harmonic Frequencies and Anharmonicities. The localmode absorptions can be fitted to the equation for the transition energy for a one-dimensional anharmonic oscillator
+
\. \.
2500-
2300:: , , ,
\
i
,\;
-
t c
\
+
t 1
t
~~OO.--LLLLLYJ 0
1
,
2
,
I
3
, ,
I\
---
4 5 QUANTUM NUMBER 111
6
7
6
9
Figure 6. Birge-Sponer plots for different C-H oscillators of N(CH3)3, . straight line in each case corresponds P(CH3)3,and A s ( C H ~ ) ~Upper to C-Ha bonds (C-H bonds out of the molecular symmetry plane containing C-X and Hb with X = N, P, or As). Lower straight line in each case corresponds to C-H, bond (C-H bonds in the molecular symmetry plane). The points on the ordinate (W) correspond to the isolated C-H frequencies reported by McKean in ref 40.
nation bands with the other C-H stretching absorption would fall out of the region scanned in these experiments. The Av = 6 spectrum for P(CH3), exhibits two strong peaks on a somewhat noisy background. The two peaks, at 15 605 and 15 896 cm-', are assigned as Av = 6 of the C-Hb and C-Ha absorptions, respectively. The remainder of the spectrum was too
AEv = (w, - W,X,)U - wsx,u2 (2) where W, is the harmonic frequency and w & ~is the anharmonicity. From the values of W, - W,X, and w,x,, an upper limit on the dissociation energy of the anharmonic oscillator is given by the equation (3) where AE,,, is measured from the v = 0 level. In Figure 6, a Birge-Sponer plot of AE,/v vs. v is given for the molecules N(CH,),, P(CH3)3,and As(CH3),. Two straight lines are given for each molecule corresponding to the two different C-H stretching oscillators. The values of W, - W,X, and obtained from the Birge-Sponer plot and AE,,, from eq 3 are presented in Table V. As found in a previous study' of N(CH3),, the
3966 The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 anharmonicities for the C-Ha and C-Hb bonds are equal within experimental error. In our case, the anharmonicities for both types of oscillators are larger for N(CH3), than for P(CH3), and As(CH,), which in turn are approximately equal. The upper line in Figure 6 for each molecule corresponds to the fundamental and overtone transitions of the out of plane methyl C-H bonds. The lower line for each molecule corresponds to the fundamental and overtone transitions of the C-H bonds in the molecular symmetry plane. The results show good linear fits for the two conformations. The points for u = 5 of the As(CH3), Birge-Sponer plot are slightly off the line (see Figure 6), presumably due to the Fermi resonance found for As(CH,), at this level, as discussed in the previous section. C. The Trans Effect. One of the questions that exists in the literature regarding the trans effect is whether it is important for heteroatoms beyond the first row.37,41-43 McKean has shown that the effect is large for heteroatoms in the first row (0,N) and a smaller effect is shown for elements of the second (P,S). In overtone studies, the trans effect has been observed for compounds containing methyl groups and N, 0, and S heteroatom^.^ Though the trans effect was originally recognized for systems involving heteroatoms, it has now been generalized to other systems as well.45 The present experiments show that the trans effect can also be important for third-row heteroatoms such as As. The effect is smaller than that observed for P(CH3), and follows the order N > P > As. In discussing the trans effect it must be realized that commonly the term trans effect has been used both to refer to the existence of an anisotropic environment which can lead to conformationally nonequivalent C-H stretches and to the result of this conformational nonequivalence: a change in vibrational frequencies of the conformationally nonequivalent C-H stretches. These two uses of the term, trans effect, are not synonymous. One involves considerations of the anisotropy of the environment, while the other involves dynamical factors such as the time scale of the spectroscopic process and the coupling between the environment and the vibrations under study. Since the current situation involves conformational nonequivalence of H atoms in a methyl group, we will refer to that situation specifically but the general principles of the trans effect are not limited to methyl For a methyl group, any adjacent (or even nearby) atom or group of atoms that produces an anisotropic distribution of electrons can result in a conformationally nonequivalent environment for the methyl C-H bonds. If the time scale of the spectroscopic process probing this environment is sufficiently rapid to observe the existence of different conformations, then the existence of these different conformations will, in general, lead to a frequency shift in the absorption spectrum. Infrared spectroscopy is a very rapid time scale spectroscopic process and, as seen in this work on the M(CH3)3 compounds, is sensitive to nonequivalent environments even when there is a very modest barrier to rotation. In fact, Fang et al. have shown that the trans effect can manifest itself in the infrared even when there is free rotation of the moiety of interest.45 The next aspect of the trans effect involves the magnitude of the frequency difference between the C-H stretches in diffferent environments. This is clearly related to the coupling of the anisotropic electron distribution with the orbitals of the methyl group. In fact, the name trans effect comes from the fact that the change in frequency of the C-H stretches was deduced to arrive from donation of electron density from the lone pair of a heteroatom to the antibonding orbital of the trans H atom. When we ask whether the trans effect occurs for a specific heteroatom, the two components of the effect should be separated. For As, it is clear that the lone pair of the As coupled with the barrier to rotation will cause an anisotropic environment for the methyl groups in As(CH,),. The remaining question involves the magnitude of the effect. McKean ascribes the observed splitting of C-H stretches (45) Fang, H. L.; Swofford, R. L.; McDevitt, M.; Anderson, A. B. J . Phys. Chem. 1985, 89, 225. (46) Townes, C. H.; Schawlow, A. L. Microwave Spectroscopy; McCraw-Hill: New York, 1955.
Manzanares et al. in P(CH3), to the trans effect.37 This splitting is considerably smaller than the splitting observed in N(CH,), and of similar magnitude to that observed for As(CH3),. Given that the lone pair on the heteroatoms is the major source of anisotropy and that the splitting in P(CH,), is due to donation of electron density from the lone pair, one is forced to conclude that a similar effect occurs for the As compound. The difference in magnitude of the effect between the amine vs. the phosphine and arsine compounds is then due to the differences in coupling between the heteroatom and the methyl groups which is likely to be due to the change in heteroatom-carbon bond distance which follows the same trend as the magnitude of splitting of the C-H stretches. D. Isolated CH Stretching Frequencies. Figure 6 contains the Birge-Sponer plots for the three molecules under study. McKean has measured the isolated C-H stretching frequency v~~~~~ for N(CH3), and P(CH3),. These frequencies are also presented in the figure so that the values of the isolated C-H stretching frequencies can be conveniently compared to the fundamental frequency, we- 2wge, which is obtained from the slope and intercept of the AE/v vs. u plot. These data are also presented in Table V. The expected values for vCHW can also be calculated from the empirical formula of Wong and Moore.5 v,=6
(cm-') = (-3716 f 45)
+ (6.62 & 0.09)~cH"~ (4)
Taking the fifth overtone frequencies (vu=& from Tables I, 11, and 111, the expected values for the isolated CH frequencies can be calculated. For N(CH3), the calculated vCHIa from eq 4 are 2950 cm-' (C-Ha) and 2763 cm-' (C-Hb). The experimental values of ~~~l~~ are 2952 cm-' (C-Ha) and 2799 cm-' (C-H,). There is good agreement with C-Ha but not as good agreement for C-Hb. The same calculation for P(CHJ3 shows 2963 cm-' (C-Ha) and 2919 cm-' (C-Hb) in better agreement with the experimental vCHW values of 2954 cm-' (C-Ha) and 2919 cm-I (C-H,). Many other moleculesS show excellent agreement with experimental values when eq 4 and the fifth overtone frequencies are used. Based on this, the calculated isolated frequencies for As(CH,), are 2970 cm-' for C-Ha bonds and 2945 cm-' for C-Hb bonds. These values are shown in Table V. It has been shown that the energy levels of high C-H vibrational overtones (Au = 3-8) of aromatic and aliphatic hydrocarbons can be adequately described in terms of a one-dimensional Morse o ~ c i l l a t o r . ~ ~ ~ -This * ~ ' ~should - ' ~ also be valid for the system currently under consideration. Thus, Birge-Sponer plots for the three molecules of interest were constructed and are shown in Figure 6. From the Birge-Sponer plots the intercepts, we- @ae, and the slopes, -w$le, are used to calculate the fundamental frequencies, w e - 2wexe,which are presented in Table V. Interestingly, the fundamental frequencies are always smaller than the isolated frequencies, vCHW. The best agreement occurs for the C-H, bond of N(CH3), where the two values are within experimental error. A possible source for the differences observed for the C-Hb bond of N(CH3), and both C-H bonds of P(CH3), (recall that the uCHW frequencies for As(CH3), are calculated) may simply be due to the fact that the u = 3 and u = 4 points for these compounds were not available. Since the lower frequency points tend to be above the Birge-Sponer line formed by the higher overtone points, inclusion of the u = 3 and u = 4 points could be expected to increase the value for we - w,xe somewhat which would lead to better agreement between we - 2w,xe and vCHIS0. Other sources of the disagreement between we - 2w$x, and uCHW could be due to Fermi resonance between the C-H stretching modes and the overtone of the bends or due to interactions between the methyl groups of the molecules. However, the mass of the central atoms in the M(CH3), compounds affects the frequency of the bending modes, lowering their frequency significantly as the mass of the central atoms increases. Thus it is highly unlikely that Fermi resonance could be the cause of the observed disagreement in all cases. A calculation of the C-H bond lengths in the ground state ( u = 0) can be made using the empirical formula proposed by M ~ K e a n : ~ ' r'CH
= 1.402 - (1.035
X
10-4)vCH1S0 (cm-')
(5)
The calculated r°CHvalues are presented in Table V. Note that
Spectra of N(CH,),, P(CHJ3, and A s ( C H ~ ) ~ TABLE VI: Rotational Constants (BmCo),Internuclear Distances ( r ) ,Bond Angles ( a ) ,Barriers to Internal Rotation (V), and Line Widths for Parallel and Perpendicular Bands for N(CH&, P(CH3),, and As(CHd$
c;,cm-1
0.17 0.12 dC-M). A 1.458 f 0.002 1.844 f 0.003 a(C-M-C), deg 109 c99 18.4 10.9 V,kJ.mo1-l
0.11 1.979 f 0.01 96 6.3-10.5
Parallel Bands 9.66 x 10-39 16.48 x 10-39 -0.4138 1.4809 32.4
14.75 x 10-39 23.35 x 10-39 -0.3684 1.4719 26.1
17.51 x 10-39 25.47 x 10-39 -0.3125 1.4622 23.8
Perpendicular Bands 0.0374 -0.4138 0.776 24.1
0.0303 -0.3684 0.819 2016
0.0278 -0.3 125 0.864 19.9
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 3967 TABLE VII: Line Widths (cm-I) of Overtone Spectra for C-H Transition
Au
assignment
N(CH3):,
5
v(C-H,) U(C-Hb) u(C-H,)
101 f 3
6
(47) Edgell, W. F.; Moyniham, R. E. J . Chem. Phys. 1966, 45, 1205. (48) Gerhard, S. L.; Dennison, D. M. Phys.-Reu. 1933, 43, 197.
39f3 39 f 3 37 f 3 45f3 40f 3 170f4
163 f 4
v(C-Hb) 7
v(C-H,) u(C-Hb)
129 f 4
AS(CH~)~ 48f3 31f3 39 f 3 37f3 34f 3 61f4
two classes. In one class (parallel transitions) the electric moment oscillates parallel to the symmetry axis, in the other class (perpendicular transitions) the electric moment oscillates perpendicular to the symmetry axis. The selection rules for the parallel bands are AJ = O,f 1 and AK = 0. For perpendicular bands, AJ = O,f 1 and AK = f l . From the theoretical calculation of Gerhard and Dennison@the separation between the maxima of the R (positive) and P (negative) branches in parallel bands is Av(P,R) = S(8)
Molecular constants from ref 25-27. parallel with the increase in the C-M bond length (Table VI) there is a decrease in the flCHbond length. However, the increase in C-M bond length is significantly larger than the decrease in C-H bond length. This increase in C-M bond distance would be expected to lead to less interaction among the CH3groups. Thus no clear explanation can be given at this time for the observed frequency shifts between we - 2wexeand U C H ~ ~ O . The results presented in Table V for N(CH3)3,P(CH3)3, and As(CH& give validity to the assumption that differences in frequencies derived from overtone data can be useful in estimating the separation in energy between nonequivalent C H bonds within a methyl group of a molecule. The differences in local-mode frequencies (we - upe)obtained for C-H, and C-Hb bonds (see Table V) are 185, 35, and 19 cm-’ for N(CH3)3,P(CH3)3,and A s ( C H ~ )respectively. ~, The same diffefences between C-Ha and C-Hb bonds with the uCHiso frequencies obtained by McKean40 are 153 and 35 cm-l for N(CH3)3 and P(CH3)3, respectively. When vCHiso values calculated from eq 4 are used, the differences are 187, 44, and 25 cm-’ for N(CH3)3,P(CH&, and As(CHJ3, respectively. The differences with uCHiso calculated from eq 4 tend to be higher than McKean’s experimental results. If the localmode frequencies, w, - uex0 are used, the general trend N > P > As is followed and there is good quantitative agreement with the differences from vCHiso for P(CHJ3 and As(CH& but not for N(CH3)3. One possible reason for the discrepancy in N(CH3), could be that the C-Hb overtone data for this molecule were taken from ref 7 and both the C-Ha and C-Hb data were not obtained under the same experimental conditions. E . Line Widths. Contributions to the line shape of the overtone transitions have two basic origins. Inhomogeneous broadening of a transition is due to the width of the rotational envelope of a vibrational transition along with contributions from superimposed hot bands, combination bands, and difference bands. Homogeneous broadening for vibrational overtones is principally the result of one of two mechanisms: (1) vibrational energy relaxation or (2) vibrational dephasing. The contributions of each of these broadening mechanisms to the observed spectra will now be discussed. 1 . Inhomogeneous Broadening. An important component of the overtone line width in the molecules N(CH3),, P(CH&, and A S ( C H ~is) ~the width of the rotational envelope.46 Calculations were made to obtain an estimate of the effect of the rotational band contour on the overtone line width. A substantial aid in analyzing the situation is found in the work of Edgell and Moynihan4’ and the earlier work of Gerhard and Denni~on.~*In symmetric top molecules vibrational transitions are divided into
fwhm P(CH3)3
[ 5]”2-! A
The separation function S(8) is given by the following empirical formula which is accurate to within -0.5% for all values of 8 log S = 0.721/(8
+ 4)’.13
(7)
where @ = -I B- I IC
The calculated values of ,B, S(,B),and Au(P,R) for parallel bands of the symmetric tops N(CH&, P(CH&, and As(CH,), are given in Table VI. For perpendicular bands, Av(P,R) is obtained by using the numerical calculations of Edgell and M ~ y n i h a n . ~In ’ this case, the assumption is made that the Coriolis coupling constant ( l ) is zero. The separation between the maxima of the R and P branches is then
(9) where Bo is the rotational constant given in Table VI and CT’= hcBo/kT. The model uses a parameter X which is a reduced frequency with the center of the band at X = 0. The parameter X , is the magnitude of X at the maximum of the R branch. The position of the maximum of the P branch is (-X,,,). Calculated values of X , for different 8 values are presented in ref 47. For 5 = 0, X m can be expressed as the following polynomial:
X, = 0.975 - 0.03248 - 1.24p2
(10)
Using this equation with the calculated 8 values for the three molecules gave X , values for N(CH3)3,P(CH3)3,and A s ( C H ~ ) ~ . and X , and the calculated Av(P,R) for the The values of 8, d2, perpendicular bands are presented in Table VI. Of course, these calculations make the assumption that the rotational constants for the upper level are the same as those for the ground state. Obviously this is not true, especially for higher overtones. The calculation also assumes that the Coriolis coupling constant is equal to zero which is obviously an approximation. A calculation for the perpendicular band line widths assuming that the Coriolis coupling constant has the extreme value F = -1 increases the calculated line widths modestly to 37, 30, and 28 cm-I for N(CH3)3, P(CH3)3,and A s ( C H ~ ) respectively. ~, In the absence of detailed data regarding the magnitude of the rotational constants and Coriolis coupling constants in higher vibrational states, this calculation will at least serve as an indicator of expected rotational bandwidths for the overtones of the M(CH3)3compounds. The fwhm of the bands assigned to C-H transitions in As(CH3)3, P(CH,),, and N(CH& are reported in Table VII. The fundamental absorption spectrum of A s ( C H ~ shown )~ in Figure
3968 The Journal of Physical Chemistry, Vol. 91, No. 15, 1987
Manzanares et al.
1 gives a separation between the P and R branches (-25 cm-' It is apparent that the line widths for P(CH,), and As(CH,), are for the band at 2980 cm-' and -20 cm-' for the band at 2912 comparable in magnitude to what would be expected due merely cm-I) which is in good agreement with the calculated widths for to the width of the rotational envelope (except where Fermi resonant interactions occur) and are generally significantly narrower parallel and/or perpendicular bands. For the Au = 5 C-Ha transition the fwhm is 48 cm-' and decreases to 39 cm-' for Ac than the corresponding overtones of N(CH,),. = 6 and to 34 cm-I for Au = 7. These values are close to the The question is then, why do molecules with similar geometries exhibit very different line widths? As was discussed before, even estimated line width for perpendicular and parallel bands. The C-Hb transition of As(CH,), has a fwhm of 31 cm-' for Au = though the geometry of the molecules is very similar, there are significant differences in the M-C and C-H bond distances (M 5. The fwhm increases to 37 cm-' for Au = 6 and 61 cm-l for Au = 7 suggesting that the Au = 7 transition may be somewhat = N, P, As) among the molecules. Tables V and VI list the C-H broadened by interaction with another state. and M-C bond distances for the three molecules. If, as expected, a longer M-C bond coupled with a slightly shorter C-H bond The fundamental absorption spectrum of P(CH3), (see Figure 1) gives a separation between the maxima of the P and R branches distance implies weaker interactions between methyl groups,40the of -29 cm-' for the band a t 2960 and -26 cm-' for the band change in bond distances for As(CH3), and P(CH,), compared at 2899 cm-I. The line widths of the overtones of the C-Ha with N(CH,), could be implicated in the significant difference absorptions are approximately constant (37-40) cm-' for tranin line width observed for As(CH,), and P(CH3), vs. N(CH,),. sitions with Au = 5 , 6, and 7 and are close to the expected values At the same time, since the bond distances in As(CH,), and P(CH,), are similar, this correlation could explain the similarities based on rotational widths. The C-Hb transitions of P(CH,), have between the overtones of P(CH,), and As(CH,),. line widths which increase from 39 cm-' at Au = 5 to 45 cm-I for Au = 6 and 170 cm-I for Au = 7 suggesting a resonance with Of course these changes in bond distance also correlate with other level(s) for Au = 7. a change in mass of the central atom. A similar correlation of Thus the estimated line widths for the two molecules P(CH3), line width with mass of the central atom was observed in the study and As(CH,), are generally similar in magnitude to what is of overtone transitions of M(CH,)4 compound^.'^ Unfortunately experimentally observed. The exceptions are for the Au = 7 C-Hb since changes in mass and bond length in the M(CH3), and M(CH3)4series are linked, it is not possible to isolate one effect transitions of P(CH3), and As(CH,), where broadening may be due to a resonance with other states. However, experimental line vs. the other. However, it is interesting to note that As(CH,)~ widths obtained for the C-Ha transitions of N(CH,), are always and P(CH,), have very similar overtone line widths (except where at least 3 times larger than the estimated values for the rotational a resonance occurs) and they have very similar M - C bond lengths envelopes. The line widths (see Table VII) are observed to be while there is a considerable change in mass of the central atom. 101 cm-' for Au = 5, 163 cm-l for Au = 6, and 129 cm-' for Au For the specific molecules presented in this paper, there are = 7. Thus, for N(CH3), it is not possible to explain the experno theoretical calculations of the effect of heavy central atoms on intramolecular vibrational energy redistribution. However, imental line widths as being dominated merely by the width of there has been considerable attention paid to the possibility of the rotational envelopes. 2. Homogeneous Broadening. As indicated previously two basic slow energy randomization caused by a heavy central atom in other molecules. Experiments by Rogers et a1.53,54have studied the processes account for the homogeneous broadening of the overtone absorptions: dephasing and energy redistribution. Dephasing is reactions of F atoms with both tetraallyltin and tetraallylgermanium. The measured rate of formation of fluoroethylene due to the effects of the randomly fluctuating motions within a is approximately lo3 times larger than that calculated from molecule and involves loss of phase coherence with or without RRKM theory. Their conclusion was the heavy central atom energy redistribution. Pure dephasing models for overtone line inhibits the intramolecular flow of vibrational energy which is then shapes have been developed and applied to deuteriated benzene.49 confined to one side chain of the molecule. However, Rabinovitch Dephasing predicts a general increase in overtone line widths with and co-workers5' studied the unimolecular dissociation of chemincreasing vibrational quantum number. This trend is not apparent ically activated 4-(trimethyllead)-2-butyl and 5-(trimethyltin)in the present work (see Table VII). 2-pentyl radicals. Heavy atom inhibition of energy randomization A variety of theories related to energy redistribution have been was not observed. Motivated by these experimental studies, Lopez developed and many have been applied in an attempt to explain used classical trajectory calculations to model vibrational energy redistribution in b e n ~ e n e . ' ~For~ example, ' ~ ~ ~ ~ ~ ~ and energy flow in a linear chain, C-C-C-Sn-C-C-C. Considerable Stannard and GelbartSopropose that in benzene there is efficient inhibition toward energy transfer through the heavy mass was coupling of the initially prepared local-mode state v ) to a comcalculated to occur when the initial energy deposited in one portion bination state with u - 1 quanta in a local C-H oscillator and the of the molecule was large. When the mass of S n is decreased by remaining energy in lower frequency modes. If all modes were a factor of 2 the inhibition disappears. Swamy and HaseS8in directly involved in the decay of the initially prepared overtone another quasi-classical trajectory study of energy redistribution the measured line widths would be expected to grow with u folin tetraallyltin and carbon compounds find that (1) the energy lowing a sharp increase in the vibrational state density. This is introduced in one C=C bond of the tetraallyl molecule does not observed experimentally for benzene. Thus, in their model, remain localized in the originally excited allyl group; (2) no it is proposed that a subset of the normal modes of the molecule difference in the rate of energy randomization is observed if Sn interact strongly with the C-H local mode. Heller and Mukamel" is replaced by C in the tetraallyl tin without changing the Hampropose off-resonance coupling of the initially prepared pure iltonian but energy redistribution is modestly faster for a Hamlocal-mode overtone state uvCH,5 ) to local-mode combination states iltonian modeled for tetraallyl carbon. of the form ( v - 1)vCH, [) corresponding to different local-mode The theoretical calculations discussed above do not include the states and identical skeletal states 5 ) . Siebert, Reinhardt, and hydrogen atoms and their associated high-frequency stretching H y n e ~ , ' *in ~ 'a~ related model, propose a strong coupling between and bending motions. As Swamy and Hase point it is the C-H stretch (vCH) and the C C H in-plane wag (vB) vibration possible that resonant energy-transfer channels are not adequately of the benzene molecule. For example, for the overtone (6uCH) in benzene, a coupling is proposed with the state (SUCH, he). represented as a result of this simplification. (5vCH), in turn, could be coupled to (4vCH,2vB) and so on. It is difficult to rationalize the overtone line widths in the (53) Rogers, P.; Montague, D. C.; Frank, J. P.; Tyler, S. C.; Rowland, F. M(CH3), compounds under study as arising from a single cause. (49) Mukamel, S.; Islampour, R . Chem. Phys. Lett. 1984, 108, 161. (50) Stannard, P. R.; Gelbart, W. M. J . Phys. Chem. 1981, 85, 3592. (51) Heller, D. F.; Mukamel, S. J . Chem. Phys. 1979, 70, 463. (52) Sage, M. L.; Jortner, J. Chem. Phys. Let?. 1979, 62, 451.
S . Chem. Phys. Lett. 1982, 89, 9. (54) Rogers, P.; Selco, J.; Rowland, F. S. Chem. Phys. Leu. 1983, 97, 313. (55) Lopez, V.; Marcus, R. A. Chem. Phys. Lett. 1982, 93, 232. (56) Marcus, R. A. Faraday Discuss. Chem. SOC.1983, 75, 103. (57) Wrigley, S. P.; Oswald, D. A,; Rabinovitch, 9. S. Chem. Phys. Lett. 1984, 104, 521. (58) Swamy, K. N.; Hase, W. L. J . Chem. Phys. 1985, 82. 123.
J . Phys. Chem. 1987, 91, 3969-3974
3969
Without detailed calculations or further experimental work it is not possible to say with certainty that the N(CH3)3line widths are dominated by homogeneous broadening. However, it seems unlikely that the line widths obtained for N(CH3), are entirely due to inhomogeneous broadening. The line widths are far larger than those estimated from ground-state rotational constants and are larger than line widths for As(CH,)~and P(CH3)3which do correlate well with estimates based on ground-state rotational constants. Thus it is more likely that observed line widths obtained for P(CH3)3and As(CH3), are largely inhomogeneous in origin with perhaps some homogeneous contribution (especially where resonances are expected). The predominance of inhomogeneous broadened line widths for P(CH3), and As(CH3), could be confirmed (or denied) by measurements of line widths as a function of temperature to determine if the changes in rotational contours are consistent with changes in rotational populations.
lecular symmetry plane containing the C, M, and H b atoms ( M = N, P, or As); (b) transitions which correspond to C-Hb bond absorptions; these transitions involve C-H bonds in the molecular symmetry plane and are at lower energy than the C-H, absorptions; and (c) combination bands corresponding to local-modenormal-mode transitions. Overtone studies of N(CH,),, P(CH,),, and As(CH3), indicate that the trans effect, involving lone pairs of electrons, previously found in compounds with elements in the first and second row, also operates in the molecule As(CH,),, which contains a third-row heteroatom. It appears that the overtone line widths of P(CH3), and As(CH,), can be explained principally via inhomogeneous mechanisms. For N(CH3)3the overtone line widths have a significant component due to homogeneous broadening. This change in the broadening mechanism appears to correlate with the M-C bond length in the M(CH3), compounds.
Conclusions
Acknowledgment. We gratefully thank Dr. R. N. Jones and his collaborators from the National Research Council of Canada for the computer programs used in the deconvolution of the spectra. This work was supported by the National Science Foundation under grants CHE82-06976 and CHE85-06957. Registry No. N(CH3),, 75-50-3; P(CH,),, 594-09-2; As(CH,),,
The spectra of C-H overtones of N(CH3),, P(CH3),, and A s ( C H ~ have ) ~ been investigated by using intracavity photoacoustic spectroscopy and standard infrared techniques. Three. types of vibrational transitions are identified for C-H absorptions of these molecules: (a) transitions which correspond to C-Ha bond absorptions; these transitions involve C-H bonds out of the mo-
593-88-4.
Electron-Donating Ablllty of Ethyl and Ethenyl Groups from Core-Electron Spectroscopy and ab Initio Theory. A Study of CH3CH,X and CH,CHX (X = F, CI, Br, I ) M. R. F. Siggel:* G. S. Nolan: L. J. Saethre,**T. D. Thomas,*+ and L. Ungiert Department of Chemistry, Oregon State University, Corvallis. Oregon 97331, and Department of Chemistry, Institute of Mathematical and Physical Sciences, University of Tromsca, N-9001 Tromso, Norway (Received: December 29, 1986)
Core-ionization energies and Auger kinetic energies of fluorine, chlorine, bromine, and iodine in haloethane and haloethene have been used to study the factors that affect the relative ability of ethane and ethene to accept charge at a substituent site. The difference in this ability between the two types of molecules is due almost entirely to the difference in the initial-state charge distribution and almost not at all to differences in the valence-electron rearrangement that accompanies addition of charge to the substituent (in this case, by core ionization). Ab initio calculationsgive results that agree with the experimentally measured quantities and with the interpretation. In the initial state the charge on the halogen is calculated to be less negative in haloethene than in haloethane; both A and u electrons are involved in this charge difference. The contribution to final-state relaxation in haloethene from polarization of the carbon-arbon T bond is approximately matched in haloethane by polarization of the additional carbon-hydrogen u bond in the a position. Hence, the relaxation energies are nearly the same in the two molecules.
Introduction Such fundamental chemical properties as acidity, basicity, ionization energy, strength of hydrogen bonding, and rates of acidand base-catalyzed reactions depend on the ablity of a molecule to accept charge at a particular site. Traditionally, these properties have been understood in terms of field and resonance effects, which can, in turn, be related to various u parameters.' During the past 15 years, however, emphasis has shifted to the role played by initial-state charge distribution and final-state charge rearrangement in determining these properties.2-8 The effects of charge distribution and rearrangement can be measured experimentally by comparison of core-ionization energies with either Auger kinetic energies6-'s9 or gas-phase Such techniques have been used recently to measure the influence of initial-state charge distribution and final-state charge rear+ Oregon State University. 'University of Tromse.
0022-3654/87/2091-3969$01 .50/0
rangement on the relative electron-donating ability of aliphatic and aromatic rings' and on the relative acidities of organic acids (1) (a) Johnson, C. D. The Hammett Equation; Cambridge University Press: Cambridge, 1973. (b) J a m , H. H. Chem. Rev. 1953, 53, 191. (2) (a) Brauman, J. I.; Blair, L. K. J. Am. Chem. SOC.1970, 92, 5986. (b) Brauman, J. I.; Blair, L. K. J . Am. Chem. SOC.1971.93, 3911. (c) Brauman, J. I.; Riveros, J. M.; Blair, L. K. J . Am. Chem. SOC.1971, 93, 3914. (d) Yamdagni, R.; Kebarle, P. J . Am. Chem. SOC.1973,95,4050. (e) Hiraoka, K.; Yamdagni, R.; Kebarle, P. J . Am. Chem. SOC.1973, 95, 6833. (3) (a) Kollman, P. A.; Allen, L. C. Theor. Chim. Acta 1970, 18, 399. (b) Morokuma, K. J . Chem. Phys. 1971, 55, 1236. ( c ) Dreyfus, M.; Pullman, A. Theor. Chim. Acta 1970,19, 20. (d) Kollman, P. A. Modern Theoretical Chemistry; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977; Vol. 4, pp 109-151. (e) Davis, D. W.; Singh, U. C.; Kollman, P. A. J . Mol. Struct. 1983, 10.5, 99. (f) Davis, D. W. J . Mol. Struct. 1985, 127, 337. (4) (a) Martin, R. L.; Shirley, D. A. J . Am. Chem. SOC.1974, 96, 5299. (b) Davis, D. W.; Rabalais, J. W. J . Am. Chem. SOC.1974, 96, 5305. (c) Davis, D. W.; Shirley, D. A. J . Am. Chem. SOC.1976, 98, 7898. (d) Davis, D. W.; Shirley, D. A. J . Electron Spectrosc. Relat. Phenom. 1974, 3, 137. (5) Smith, S. R.; Thomas, T. D. J . Am. Chem. SOC.1978, 100, 5459.
0 1987 American Chemical Society
