J . Phys. Chem. 1989, 93, 4733-4741 yields Na*( 32P) only through nonadiabatic curve crossings. Conclusion We have measured the relative excitation function for the four-center reaction F2 Na2 F N a F Na*(32P) between 5.8 and 15.5 kcal/mol of collision energy. This function rises sharply a t first and then levels off, suggesting the presence of a barrier to the reaction yielding Na*(32P) atoms. The cross section increases by about a factor of 7.5 in this energy range. The onset of reaction indicates a barrier of about 4 kcal/mol. We cannot, however, rule out the possibility that the rise in cross section comes from increasing probability of a nonadiabatic curve crossing leading to Na*(32P). We have compared this Fz + N a z excitation function to that for the production of the 32P state of sodium in the related
+
-+
+
+
-
4733
+
three-center reaction, F Na2 NaF Na*(32P). The three-center process is found to have a greater reactive cross section than the four-center reaction yielding Na*. In addition the cross section for the three-center reaction increases at an even greater rate than does that for the four-center reaction, rising by a factor of -30 between 4.7 and 12.8 kcal/mol. Acknowledgment. D.F.T. thanks the Natural Sciences and Engineering Research Council of Canada (NSERC) for the award of a postgraduate scholarship and the University of Toronto for the award of a University of Toronto Open Scholarship. We are indebted to the Natural Sciences and Engineering Research Council of Canada (NSERC) for support of this research. Registry No.
Fz,7782-41-4; Naz, 25681-79-2.
Spectroscopy of C-H Stretching Overtones in Dimethylacetylene, Dimethylcadmium, and Dimethylmercury Carlos Manzanares I.,*,+N. L. S. Yamasaki, and Eric Weitz* Department of Chemistry, Northwestern University, Evanston, Illinois 60208 (Received: October 26, 1988; In Final Form: January 18. 1989)
The overtone spectra of a number of C-H stretching vibrations of dimethylacetylene, dimethylcadmium,and dimethylmercury were obtained by using intracavity dye laser photoacoustic spectroscopy. Transitions corresponding to the Ao = 5, 6 , and 7 overtones of the C-H stretch are assigned by using the local-modemodel. In addition, a number of local-mode-normal-mode combination bands have been identified. Local-mode harmonic frequencies (we) and anharmonicities (upe)are obtained from Birge-Sponer plots. The line widths of the pure local-mode transitions are analyzed in terms of possible resonances with local-mode-normal-mode combination bands. Line widths in this series of compounds are compared to line widths in the M(CH3)4and M(CH& series.
introduction rotation in molecules of the type CH3-M-CH3,35-37 with the available evidence pointing to a linear C-M-C structure with the The study of vibrational overtones of small molecules in the photographic infrared was a very important source of information (1) Herzberg, G. Infrared and Raman Spectra; Van Nmtrand: New York, about molecular structure and interactions among vibrational 1945. modes.' Recent studies of overtones have made use of photoa(2) Pao, Y. H. Optoacousric Spectroscopy and Detection; Academic Press: coustic spectroscopy and thermal lensing techniques2" Due to New York, 1977. Klinger, D. S. Ultrasensitive Laser Spectroscopy; Academic Press: New York, 1983. the high sensitivity of the photoacoustic detection technique and (3) West, G. A.; Barret, J. J.; Siebext, D. R.; Reddy, K. V. Reu. Sci. the power of new laser sources, the study of high vibrational Instrum. 1983,54,797. Long, M. E.; Swofford, R. L.; Albrecht, A. L. Science overtones has provided a new source of information about mo1976, 191, 183. Stella, G.; Gelfand, J.; Smith, W. H.Chem. Phys. Lett. 1976, 39, 146. lecular s t r u ~ t u r e , " ~intramolecular dynamics,l0-I7 selective la(4) Greenlay, W. R. A.; Henry, B. R. J . Chem. Phys. 1973, 69, 8. ser-induced vibrational photo~hemistry,'**'~ and local-mode the(5) Wong, J. S.; Moore, C. B. J . Chem. Phys. 1982, 77, 603. ories.2h22 (6) Fang, H. L.; Swofford, R. L.; McDevitt, M.; Anderson, A. B. J . Phys. In this paper we report on the overtone spectra of the molecules Chem. 1985,89, 225. (7) Fang, H. L.; Meister, D. M.; Swofford, R. L.J . Phys. Chem. 1984, dimethylacetylene, dimethylcadmium, and dimethylmercury, 88, 410. which are members of a homologous series M(CH3)zwhere the (8) Fang, H. L.; Swofford, R. L.; Compton, D. A. C. Chem. Phys. Lett. lightest member of the series is M = C2. 1984, 108, 539. The overtone spectra of the compounds Cz(CH3)2,Cd(CH3)2, (9) Fang, H. L.; Meister, D. M.; Swofford, R. L. J . Phys. Chem. 1984. and Hg(CH3)2were obtained in the gas phase for Av = 5,6, and 88, 405. (10) Reddy, K. V.; Heller, D. F.; Berry, M. J. J . Chem. Phys. 1982, 76, 7 (except Av = 7 for Cd(CH,),) by intracavity laser excitation 2814. and photoacoustic detection. Standard spectroscopic techniques (11) Bray, R. G.; Berry, M. J. J . Chem. Phys. 1979, 71, 4909. were used to obtain spectra of the fundamentals and lower ov(12) Sibert, E. L.; Reinhardt, W. P.;Hynes, J. T. J. Chem. Phys. 1984, 81, 1115. ertones. The observed peaks are assigned and absorption cross (13) Sibert, E. L.; Reinhardt, W. P.;Hynes. J. T. Chem. Phys. Lett. 1982, sections for Av = 5 , 6 have been obtained. 92, 455. The determination of the vibrational frequencies of the C2(C(14) Henry, B. R.; Greenlay, W. R. A. J. Chem. Phys. 1980, 72, 5516. H3)2, Cd(CH3)z,and Hg(CH3)2molecules has been the subject (15) Henry, B. R.; Mohammadi, M. A. Chem. Phys. Lett. 1980, 75,99. of studies using standard infrared and Raman t e ~ h n i q u e s . ~ ~ - ~ O (16) Henry, B. R.; Mohammadi, M. A.; Hanazaki, I.; Nakagaki, R. J . Phys. Chem. 1983,87,4827. Structural studies have been made using rotational Raman (17) Manzanares I., C.; Yamasaki, N. L. S.; Weitz, E.; Knudtson, J. T. ~ p e c t r o s c o p and y ~ ~gas-phase ~~~ electron d i f f r a ~ t i o n . ~A~ number *~~ Chem. Phys. Lett. 1985, 117, 477. of investigators have considered the problem of free internal (18) Reddy, K. V.;Berry, M. J. Chem. Phys. Lett. 1977.52, 111; Chem. 'Permanent address: Department of Chemistry, Baylor University, Waco,
TX 76798.
0022-365418912093-4733$01 SO10
Phys. Lett. 1979, 56, 223; Faraday Discuss. Chem. Soc. 1979, 67, 188. (19) Crim, F. F. Annu. Rev. Phys. Chem. 1984, 35, 657. (20) Mecke, R. 2.Phys. Chem. 1932, B17, 1; Z Phys. 1936, 99, 217. Mecke, R.; Ziegeler, R. 2.Phys. 1936, 101, 405.
0 1989 American Chemical Society
4734
The Journal of Physical Chemistry, Vol. 93, No. 12, 1989
methyl groups free to rotate about the M-C bond.3' However, experimental difficulties have prevented the direct determination of the C-H internuclear distances and the H-C-H angles of the methyl group^.^'-^^ McKean and c o - w o r k e r ~have ~ ~ , ~studied ~ the C-H fundamental spectra of the nearly fully deuterated compounds (CHD2)M(CD3) (M = Cd and Hg) and ( C H D 2 ) C ~ C ( C H D zto) obtain the isolated C-H stretching fundamental frequencies (vCHiSO). By deuteration, the lone C-H stretch is decoupled from the C-D stretching vibrations as well as from the first overtones of the bends. It has been shown by M ~ K e a n 'that ~ for many different molecules the vCHiso frequencies correlate well with C-H bond lengths in the ground state. A separate correlation between the vCHh and the H-C-H angles has also been found for CH3groups of compounds in which internal rotation is essentially free. The vCHh values have been used for the prediction of C-H bond lengths and H-C-H angles of the deuterated molecules (CHD,)M(CD,), with M = Cd and Hg. For undeuterated molecules Wong and MooreS have found that the fifth overtone transition energies of C-H stretches show an excellent correlation with isolated C-H stretching frequencies. The same correlation for overtone frequencies with vCHh has been found by Hayward and Henry39in the case of fourth overtone frequencies. It is then possible to obtain the isolated frequencies from overtone data of the normal molecules, CH3-M-CH3, and use the correlation fit obtained by McKean to investigate the internuclear distances and angles of the methyl groups in these molecules. This illustrates one of the advantages of the overtone technique; structural information can be obtained without a dependence on deuterated samples that are often not readily available. In previous investigations of permethylated molecules with a variable mass central atom, relatively narrow line widths were obtained from room temperature studies of overtones of tetramethylsilicon, -germanium, and -tin.17 Narrow line widths were also generally observed for the M(CH3)3 series40 ( M = P, As) with overtone line widths usually being quite similar to those of their respective fundamental line widths. In this paper we will also consider the line widths of the overtones of the molecules dimethylacetylene, -cadmium, and -mercury, which are all molecules with similar linear backbones and similar rotational constants. Thus overtone line widths would not be expected to be significantly affected by changes in the width of the rotational envelope. Results for this series will be compared with results for the other two series of compounds we have studied, M(CH3)3 and M(CH3)4.17,40
Experimental Section The dye laser intracavity photoacoustic apparatus has been Laser photoacoustic techniques were described in earlier employed to obtain spectra for the b = $ 6 , and 7 C-H stretching (21) Henry, B. R. Acc. Chem. Res. 1977, 10, 207. (22) Halonen, L.; Child, M. S.Mol. Phys. 1982, 46, 235. (23) McKean, D. C.; McQuillan, G.P.; Thompson, D. W. Spectrochim. Acta 1980, 36, 1009. (24) Koops, Th.; Visser, T.; Smit, W. M.; Brandsma, L.; Verkruijsse, H. D. J . Mol. Sfruct. 1983, 100, 95. (25) Butler, I. S.;Newbury, M. L. Spectrochim. Acta 1980, 36A, 453. (26) Butler, I. S.; Newbury, M. L. Spectrochim. Acta 1977, 33A, 669. (27) Durig, J. R.; Brown, S.C. J . Mol. Specrrosc. 1973, 45, 338. (28) Bakke, A. M. W. J . Mol. Spectrosc. 1972, 41, 1 . (29) Kendall, R. F. Spectrochim. Acta 1968, ZIA, 1839. (30) Crawford, Jr. B. L. J. Chem. Phys. 1939, 7, 5 5 5 . (31) Rao, K. S.;Stoicheff, B. P.; Turner, R. Can. J. Phys. 1960,38,1516. (32) Callomon, J. H.; Stoicheff, B. P. Can. J. Phys. 1957, 35, 373. (33) Allen, P. W.; Sutton, R. E. Acta Crystallogr. 1950, 3, 46. (34) Kashimabara, K.; Komaka, S.;Ijima, T.; Kumura, M. Bull. Chem. SOC.Jpn. 1973, 46, 407. (35) Longuet-Higgins, H. C. Mol. Phys. 1963, 6 , 445. (36) Hougen, J. T. Can. J . Phys. 1964, 42, 1920. (37) Bunker, P. R. J . Chem. Phys. 1967,47, 718. (38) McKean, D. C. Chem. SOC.Rev. 1978, 7 , 399. (39) Hayward, R. J.; Henry, B. R. Chem. Phys. 1976, 12, 387. (40) Manzanares I., C.; Yamasaki, N . L. S.; Weitz, E. J . Phys. Chem. 1987, 91, 3959.
Manzanares I. et al. vibrations. The tuning ranges of the laser dyes were as follows: LD 700 (12000-14000 cm-') pumped by all red lines of a Kr+ ion laser; Rhodamine B (14 8000-16 500 cm-') and Rhodamine 1 10 (1 7 000-1 8 600 cm-') pumped by the blue green lines of the Kr+ ion laser. In each case a high reflectance (>99.7%)dye laser output coupler was used to increase intracavity laser power. The pump laser beam was mechanically chopped at 125 Hz, the frequency being chosen to optimize the photoacoustic response of the cell. The modulated photoacoustic signal was detected by a microphone (Knowles BT1759) inside the 20-cm in-cavity cell just above the path of the laser beam. Signals from the microphone were amplified and fed to an Ithaco, Model 391A, lock-in amplifier. The laser power was monitored with a photodiode which detected a reflection from the Brewster's angle window of the in-cavity cell. The diode output was monitored by a P.A.R., Model 128A, lock-in amplifier. Normalization of the photoacoustic spectra was achieved by taking the ratio of the output signals from both lock-in amplifiers. The normalized spectrum was displayed on a strip-chart recorder. Dimethylacetylene (C2(CH3),), 99%, was obtained from Aldrich, and dimethylmercury (Hg(CH,),), 98%,from Alfa Products. Both were used without further purification. Dimethylcadmium (Cd(CH3),) was obtained from Chemical Procurement Laboratories. It was found that normally colorless Cd(CH3)zdecomposes in the sample bottle as indicated by coloration of the sample. Thus, before use, Cd(CH3), was purified by freeze-pump-thaw cycles until the sample was transparent and the IR spectrum showed no evidence of impurities. Although the Cd(CH3)2did not decompose in the photoacoustic cell when the Av = 5 and 6 spectra were taken, it was not possible to obtain the Av = 7 spectrum, presumably due to decomposition of the sample in the cell. Fundamental spectra were obtained with a Nicolet 7199 FT-IR and a 10 cm path length cell. Transitions with Av = 2, 3, and 4 of CZ(CH3)2were obtained with a Perkin Elmer 330 spectrophotometer and a Wilks variable path length cell. Fundamental spectra were obtained with a Nicolet 7199 IT-IR and a 10 cm path length cell. Transitions with Av = 2, 3, and 4 of Cz(CH3)2were obtained with a Perkin Elmer 330 spectrophotometer and a Wilks variable path length cell. Results The vapor-phase fundamental spectra in the C-H stretch region of Cz(CH3)zrCd(CH3)zand Hg(CH3)2are presented in Figure 1 . The pressure was approximately 3.3 Torr for C2(CH3)z,3.9 Torr for Hg(CH3),, and 4.1 Torr for Cd(CH3),. Transitions around the C-H stretch region with Av = 2,3, and 4 for Cz(CH3)z (not shown) were also obtained. For all of these overtones, the sample pressure was 200 Torr and the path lengths were 6.75 m for Av = 4 and 0.75 m for Av = 2 and 3. Av = 2, 3 , and 4 transitions for the dimethylmetal compounds were not obtainable because of the low vapor pressures of these compounds. Figure 2 presents the gas-phase photoacoustic spectra for each of the compounds in the C-H stretch region for Av = 5 . The pressure was 12 Torr for C2(CH3)2,1 1 Torr for Cd(CH3)z, and 9.9 Torr for Hg(CH3),. Figure 3 presents the gas-phase photoacoustic spectra of Cz(CH3)2(1 10.8 Torr), Cd(CH3), (9 Torr), and Hg(CH3)z (9 Torr) in the C-H stretch region for Av = 6. Figure 4 presents the gas-phase photoacoustic spectra for C2(CH3)2(400 Torr) and Hg(CH3)2(36 Torr) in the CH stretch region for Av = 7 . The ordinates of the spectra are shown in arbitrary units corresponding to the relative intensity of the normalized photoacoustic signal. The observed positions of the various absorptions are listed in Table I. The absolute absorption cross sections for the gas-phase molecules are also listed in Table I for the Av = 5 and 6 transitions. These values were determined by the use of an internal standard of known cross section and the equationz0 rJ
= uovPo/vJJ
where P is the pressure in Torr, V the normalized signal intensity (arbitrary units), and r~ the absorption cross section in pmz/ molecule. The subscripts (0) identify the internal standard
The Journal of Physical Chemistry, Vol. 93, No. 12, 1989 4135
C-H Overtones of C2(CH3)2,Cd(CH3)2,and Hg(CH3)2
180
157
I
065 3312
3221
3130
I
1
1
3099
2940
2057
2766
2675
I
I
2504
2493
I
, 13800
I3600
I3400
flr
201! I76
v-1 v 0
6 9 51
151
4 D
126
101
076
I
051 3239
3173
3107
3041
2975
2909
2043
2777
2711
2645
2690
i 2627
236
220
20 4
I86
1401 3266
,
3195
1
3124
,
3053
I
2902
2911
I
I
2040
2769
Wovenumbers
Figure 1. Absorption spectra of the fundamental (Au = 1) C-H stretch region of C2(CH3)z,Cd(CH3)z,and Hg(CH3)2.The path length was 10 cm and the pressures were 3.3, 4.1, and 3.9 Torr, respectively.
molecule. The Av = 5 and 6 cross sections were determined relative to ethylene, which has reported16-'* values of uo = 1.85 X 10-4 pm2/molecuIe (Au = 5) and uo = 3.02 X IW5pm2/molecule (Av = 6). Methane, usually chosen as an internal standard, was not employed in this study because it has spectral features that overlap the absorptions of the dimethyl molecules.
Discussion A . Assignments. Fundamental frequencies for the I R and Raman modes of C2(CH3)2,Cd(CH3)2,and Hg(CH3)2molecules have been previously reported.2*" Table I1 lists the normal-mode fundamentals of the three molecules. The IR spectra of the C H fundamentals of the three molecules (see Figure 1) are unusual due to characteristic fine structure on the high-energy side of the CH stretching vibration region with a separation between lines of approximately 10 cm-'. This structure is attributed to free
1
1
13eoo
1
136W
13400
Wovenumbers
Figure 2. Photoacoustic absorption spectra of the fourth overtone (Au = 5) C-H stretch region of C2(CH3)z,Cd(CH3),, and HD(CH,)~.The pressures were 12, 1 1, and 9.9 Torr, respectively.
internal rotation of the methyl groups2' Overtones corresponding to transitions with Av = 2, 3, and 4 for C2(CH3)*are listed in Table I. Strong bands in the Au(CH) = 2 region were assigned as 2vCH= 5781 cm-I and v6 2v10= 5814 cm-', where the arithmetic sum for the latter transition, which does not include anharmonicity, is 5838 cm-'. The absorption at 5906 cm-' is best assigned as v6 ~ 1 3 arithmetic , sum = 5897 cm-'. A single absorption band was obtained in the Av = 3 region at 8443 cm-' which is assigned as 3vCH. Similarly a single transition was observed in the Av = 4 region at 11 043 cm-I
+
+
4736 The Journal of Physical Chemistry, Vol. 93, No. 12, 1989
Manzanares I. et al.
h
16CCO
15800
15600
15400
8 41 0 0
"c0 0
,
18200 1
,
l8ooO 1
1
17800 1
,
17600 1
n
z
t
n
a
u 16400
l62W
16CCO
15800
15600
18400
18200
18000
17800
17600
Wavenumbers
Figure 4. Photoacoustic absorption spectra of the sixth overtone (Au = 7 ) C-H stretch region of C2(CH3),and Hg(CH,),. The pressures were 400 and 36 Torr, respectively.
Wavenumbers
Figure 3. Photoacoustic absorption spectra of the fifth overtone (Au = 6 ) C-H stretch region of C2(CH3),, Cd(CH,),, and Hg(CH3),. The pressures were 110.8, 9, and 9 Torr, respectively.
and is assigned as 4UCH. As previously stated, spectra of the lower overtones of Cd(CH3)2and Hg(CH3)2could not be observed in these studies. In Figure 2 transitions in the region of the Au = 5 overtones of the CH local mode are presented. The energies and assignments of the transitions are also given in Table I. Assignments of the absorptions due to the pure overtone transitions are relatively straightforward for all compounds from Au = 5 to Au = 7. Assignments for the minor peaks that appear in regions near the
pure overtone transitions are in some cases unusual relative to assignments for the other compounds with central metal atoms and with respect to similar assignments for hydrocarbons. In many cases the best assignments appear to involve combinations bands of three modes rather than the more usual binary combination bands or combination bands involving an overtone of a local mode and an overtone of a normal mode. In some cases small absorbances may be due to impurities. However, this is unlikely to be the source of all or even most of the observed minor peaks. Whether the differences in assignments in these systems represent a fundamental difference in the Hamiltonians of the systems under consideration is beyond the scope of this study; however, this would be an interesting topic for theoretical consideration. For C2(CH3)2the Au = 5 local mode, SUCH, is at 1 3 544 cm-I. A small band at 1 3 442 cm-I could be assigned to any or all of the combinations 4uCH u7 + v l 5with an arithmetic sum of 1 3 4 5 3 cm-', 4uCH + u3 + u I I with an arithmetic sum of 1 3 462 cm-', or 4uCH + u2 u I 2 with an arithmetic sum of 1 3 4 7 1 cm-'. In ref 24 the u7 + u I s and u3 + uI1 normal-mode combinations are reported as having the same frequency, 2 4 1 5 cm-'. Thus both combinations would be expected at a similar position when combined with 4VCH. Raman and IR studies in the region of the
+
+
The Journal of Physical Chemistry, Vol. 93, No. 12, 1989 4737
C-H Overtones of C,(CH,),, Cd(CH3),, and Hg(CH3)2
TABLE I: Transition Energies, Harmonic Frequencies, Anharmonicity Constants, and Absolute Cross Sections (Av = 5 and 6) for Cas-Phase M(CH,)z Molecules
c2 ( freq, cm-' u=2 u=3 u=4 0-5
Cd(CHd2
3)2
assignt
freq, cm-'
WCHA assignt
5781 5814 5906 8443 11043 13345 13442
5"CH - V I 1
0-7
15750 15843
SUCH+ 2381 cm-'
15848 15862 15883 15966
18000
%H
+
SUCH 2416 cm-l 6YCH
+ "I1
"CH
assignt
13392 13477 13509 13520 13541 13550 13569
13544
u=6
freq, cm-l
13578 13598 13693 15868 15922 15932 15946 16057 18033 18082
SUCH
- Y1l
4vCH+ 2377 cm-l
I
18093 18228 we - w & ~ , cm-'
@ac, cm-' u(v=5), pm2/
molecule u(u=6), pm2/ molecule
3010 h 9 62 f 2 (1.9 i 0.2)
X
lo-'
(8.3 i 0.9)
(1.1 f 0.3)
X
lo4
(7.4
X
VI
Y2
"3 Y.4
&'5
y6 "1
Y8
"9 VI0 VI 1 Y1 2
"I3 y14
Y15
C2(CH3)2a 2935 2235 1381 696 2936 1380 1153 2976 1451 1038 193 2961 1447 1030
Cd(CH3),b
Hg(CH3)2b
2927 1158 (1127) 473 (459)
2927 1198 (1182) 518
2923 1155 536 2980 1318 (1324) 705 (700) 120 2859 1427 634
2913 1193 540 2985 1397 780 161 2874 1442 699
*
lo4
0.7) x 10-5
TABLE II: Fundamental Frequencies (em-') Used for the Overtone Assignments for C2(CH3)2,Cd(CH3)2, and H I ( C H ~ ) ~ assignt
3027 h 25 63 h 4 (1.8 0.2) x 10-3
OFrom ref 1, 24, 29, 25, and 30. bFrom ref 26 and 27. In Parentheses, value given in ref 27.
f ~ n d a m e n t a lof ~ ~the , ~ u2 ~ (CEC) vibration at 2235 cm-I have shown that there is a Fermi resonance between the u2 mode and the overtone, 2u8 at 2313 cm-', where u8 (C-C) is at 1143 cm-'. Thus the overtone 2u8, expected around 2286 cm-', is displaced to a higher frequency. The small absorption shown in Figure 2 for C2(CH3)2at 13 345 cm-' is thus most likely assignable as the local-mode-normal-mode combination band 4vCH + 2us, whose arithmetic sum is 13 356 cm-'. The fourth overtone spectrum for Cd(CH3)2is shown in Figure 2. For Cd(CH3)2,5uCHis at 13 467 cm-'. Assignment for combination bands in the Av = 5 region for both Cd(CH+ and Hg(CH3), have more uncertainty than similar assignments in other spectral regions since the position of the Av = 4 C-H stretch absorption is not known directly from spectroscopic data. Using the transition energies for Av = 1, 5 , and 6 of Cd(CH3), (2923, 13 467, and 15 862 cm-l, respectively) and the Birge-Sponer
(1.1 h 0.9)
X
lo4
-
equation (see next section), it is estimated that the energy of the transition with Av = 4 is approximately 4VCH 11 019 cm-'. This value was used for the assignments in the Av = 5 CH region of Cd(CH3)2presented in Table I. However, some assignments still present problems. It is difficult to find even a ternary combination band that could be assigned to the absorption at 13 437 cm-'. It is possible to find a combination band involving 4vCH and three other modes that could be assigned to this absorption. However, this high-order combination band appears unlikely and it is most likely that the absorption at 13437 cm-' arises from interactions between modes which shift their positions from the arithmetic sum. As such, we choose to leave this absorption unassigned. From the value in parentheses in Table I1 for the frequencies of u2 and u9 of Cd(CH3)Z the arithmetic sum for the combination band 4VCH uz u9 is 13 470 cm-', and a strong absorption at 13 457 cm-l is assigned to this combination band. The transition assigned as 4h-H v6 u9 has an arithmetic sum of -13498 cm-' and the absorption at 13 495 cm-' is assigned to this transition. There are small absorptions on either side of the main band at 13 335 and 13 586 cm-'. They are most likely due to 5vCHf ull, combinations of the local-mode SUCH with the torsional mode u l I = 120 cm-l. The fourth overtone spectrum for Hg(CH3), is also presented in Figure 2. The SUCH absorption is at 13 550 cm-'. In this case, a value of 4VCH r 11 100 cm-' is obtained from the Birge-Sponer parameters of Hg(CH3), (see next section). There are a series of small absorptions at 13 477, 13 495, 13 509, 13 520, and 13 541 cm-'. It is likely that most if not all of these absorptions are due to combination bands involving 4vCH and overtones and combinations of v2 and V6. Due to the uncertainty in the position of 4uCH it seems inappropriate to provide any more specific information as to likely assignments of individual absorptions in this spectral region. At higher frequencies than SueH,the absorptions around 13 569 and 13 578 cm-' could be the result of interactions between 4YCH 2u7 + u9 = 13 577 cm-I and 4VCH + 2u3 + ~ 1 =3 13 578 cm-l which result in one appearing at lower energy and the other at a higher energy. On either side of the SUCH transition, there
+ + +
-
+
+
4738 The Journal of Physical Chemistry, Vol. 93, No. 12, 1989 3100
!
Manzanares I. et al. is at 18 000 cm-' and it is assigned as 7vCH. The spectrum of Hg(CH3), shows the main peak 7vCH at 18 093 cm-'. An absorption at 18 033 cm-' is assigned as 6vCH+ ug v14 (arithmetic sum at 18 028 cm-'). Another absorption at 18 082 cm-I could be attributed to combinations 6ucH+ vg + vl0 (sum = 18 109 cm-I) or 6vcH + u 1 3 + uI4 (sum = 18073 cm-'). The small band at around 18 228 cm-I is assigned as the combination band 7vCH
A
+
+
Y11.
B. Local-Mode Parameters. The transition energy describing the excitation of a pure local-mode overtone is given by the Birge-Sponer e q ~ a t i o n ' ~ ~ ~ ~ 2500
L 0
1
2
3
4
5
6
7
8
Vibrational Level (v)
7
I
B
;z
3000 29001
25001 0
,
1
1
1
2
3
, 4
'
5
6
, 7
J
8
Vibrational Level (v)
Figure 5. Birge-Sponer plots for the C-H overtones of C2(CH3)2(A) and Hg(CH3)2(B). For comparison, the isolated frequencies ucHw ( 0 )are taken from ref 23 and presented in the plot.
are small absorptions at 13 392 and 13 693 cm-I that are most likely due to the combination bands SUCH f v l l with v I 1 = 161 cm-]. The ho(CH) = 6 region is presented in Figure 3. For C2(CH3),, the 6vCHis assigned with the help of the Birge-Sponer plot (see Figure 5) as 15 843 cm-I. The strong shoulder of this band at 15 750 cm-I is assignable as a local-mode-normal-mode combi+ u2 with arithmetic sum of 15779 cm-I. The strength nation of this absorption is most likely the result of a resonant interaction with 6vCH. The Au(CH) = 6 region of Cd(CH3), exhibits the 6vcH absorption at 15 862 cm-]. The best assignment for the absorption at 15 848 cm-' is SUCH u6 v7 vl0. The absorption at 15 883 cm-' is best assigned as 5vCH + v3 + v7 + ~ 1 3 . However, due to the a priori unlikelihood of these high-order combination bands, these assignments should be considered preliminary and tentative. The small band at 15966 cm-l is assigned to the combination band 6vCH + v11. The Au(CH) = 6 region of Hg(CH3)2 in Figure 3 shows the 6vCHpeak at 15 932 cm-l. The peak at 15 922 cm-I is assigned as 5vCH + 2u6, whose arithmetic sum is 15936 cm-I. On the high-energy side of 6vCH,the absorption at 15 946 cm-' could be either or both of the combinations SUCH 2v2 (arithmetic sum at 15946 cm-I) or 5VCH v 2 v6 (arithmetic sum at 15 941 cm-I) or even 2v6. The small absorption at 16057 cm-' is most likely the combination 6vCH+ v l l . This completes assignment of the absorptions in this region except for the absorption at 15 868 cm-I. This absorption is 2318 cm-I above SUCH. There is no combination band involving 5uCH and one or two other modes that, assuming plausible values for anharmonic terms, will yield an absorption at this frequency. There are combination bands involving SUCH and three other modes that are possible. However, assignments involving this large number of modes are necessarily subject to uncertainties and other possible interactions could also generate this absorption. Therefore, it is probably best to say that this absorption is currently left unassigned. The spectra in the Au(CH) = 7 region are shown in Figure 4 for C2(CH3), and Hg(CH3),. The main transition for C2(CH3)2
+ + +
+
+ +
+
AE = (we - w $ ~ ) u - w $ ~ v ~
(2) where we is the harmonic frequency and w g e is the anharmonicity. A plot of (AE/u) versus u was obtained for C2(CH3)2and Hg(CH3)2 by using the assignments for nVCH in Table I. The results are shown in Figure 5. The harmonic frequencies and anharmonicities are presented in Table I for C2(CH3)2and Hg(CH3),. Since only two overtones were obtained for Cd(CH3)2, no Birge-Sponer parameters are presented for this compound. However, since we and ascare within experimental error of each other for the members of the series with the heaviest and lightest central moiety, we and w,xe for Cd(CH3)2would be expected to be of similar magnitude to what was measured for C2(CH3), and Hg(CH3)2. C. Isolated Frequencies, Bond Distances, and Bond Angles. The isolated frequencies, vCHiS0, of the monohydride compounds analogous to C2(CH3),, Cd(CH3),, and Hg(CH3), have been reported by M c K e a n , ) ~as ~ ~2950, 2948, and 2954 cm-I, respectively. For this determination McKean used the compounds M(CHD2)(CD3) with M = Cd and Hg. The C H isolated frequency of the acetylenic compound was determined38 by using C,(CHD2),. Isolated frequencies can be compared with fundamental frequencies w, - 2w$, derived from the overtone data of the present experiment. For C2(CH3), and Hg(CH3),, the fundamental frequencies are 2948 and 2964 cm-'; both agree with McKean's values within the experimental margin of error of approximately *IO cm-I. Isolated frequencies can also be calculated for the compounds C2(CH3),, Cd(CH3)2,and Hg(CH3), by using the correlation obtained by Wong and Moores involving the fifth overtone frequency and the isolated frequencies of the fundamental. This empirical correlation function is (cm-') = (-3710 f 45)
+ (6.67 f 0.09)VCH'"
(3) Using the fifth overtone frequencies (v,=6) from Table I, the calculated values for vCHiso are 2954, 2958.5, and 2967.5 cm-I for C2(CH3),, Cd(CH3),, and Hg(CH3),, respectively. The difference between the uCHLS0calculated and experimental is 4 cm-I for C2(CH3),, 10 cm-I for Cd(CH,),, and 14 cm-I for Hg(CH,),. A calculation of the C-H bond lengths in the ground state ( u = 0) can be made using the empirical correlation function proposed by McKean.)* V,=6
rCHo (A) = 1.402 - (1.035 x 10-4)VCHi" ("I)
(4) From the experimental v~~~~~values, the C-H bond lengths are 1.097 X and 1.096 X cm for C2(CH3),, 1.097 X Cd(CH3),, and Hg(CH3),, respectively. The same calculation using the vCHLSOfrom fifth overtone data gives rCHo 1.096 X cm (C2(CH3),), 1.096 X cm (Cd(CH3),), and 1.095 X cm (Hg(CH,),). The difference between the two calculations is thus no more than 0.0010 X cm for any molecule. The empirical correlation function, as proposed by McKean, between v~~~~~ and the H C H angles for methyl groups is38 CYHCHO = 0 . 0 4 7 1 ~ c H' ~31.1 ~ (5) From the experimental uCHiso values, the H C H angles are 107.8' for C2(CH3),, 107.8O for Cd(CH3),, and 108' for Hg(CH3),. The same calculation using the vCHisofrom fifth overtone data gives 108' (C2(CH3),), 108.2' (Cd(CH,),), and 108.7' (Hg(CH3),). The good agreement between these two determinations again illustrates the utility of overtone spectroscopy for obtaining
C-H Overtones of C2(CH3)2,Cd(CH3)2,and Hg(CH3)z structural information on molecules. D. Line Widths. Contributions to the line width of overtone transitions of gas-phase molecules have two basic origins: (1) inhomogeneous broadening, which includes the width of the rotational envelope, and superimposed hot bands, combination bands and difference bands; (2) homogeneous broadening, whose main contribution in gases is from vibrational energy relaxation and/or dephasing. 1 . Inhomogeneous Broadening. Calculations to estimate the width of the rotational envelope can be performed considering the molecules M(CH3)2as linear molecules and neglecting the small moment of inertia perpendicular to the molecular axis. For linear molecules the estimated separation of the two maxima of the P and R branches of a fundamental transition4' A F ( P , R ) is 2.3583 (BoT)1/2with Bo in cm-' and T i n kelvin degrees. Using T = 293 K and Bo = 0.1 122, 0.1 140, and 0.1 162 cm-I, respectively, the AvmaX(P,R) are 13.5, 13.6, and 13.8 cm-' for C2(CH3)2,Cd(CH3)2, and Hg(CH3)2,respectively. These spacings are comparable to what is observed in the fundamental spectra of these molecules (see Figure 1). For example, the experimental values for Av-(P,R) for the v5 fundamental of Cd(CH3)2is approximately 10 cm-I. These calculations, of course, also make the assumption that the rotational constants for the upper levels (v = 5 , 6 , 7 ) are the same as those for the ground state. Obviously this is not true, especially for higher overtones. However, this calculation will at least serve as an indicator of expected rotational line widths for the overtones of the M(CH3)2molecules. From these calculations, it is apparent that the calculated rotational widths for all of the molecules are comparable. Experimentally the observed line width for the higher overtones of C2(CH3)2significantly exceeds that for both Cd(CH3)2and Hg(CH3)2,which are comparable in magnitude. In each case the observed line width is also significantly greater than the calculated rotational bandwidth. Nevertheless, the higher overtones in both Cd(CH3)2 and Hg(CH,), are significantly narrower than the corresponding overtones of C2(CH3)2. Possible reasons for this behavior will be discussed. 2. Homogeneous Broadening. When overtone line widths are observed that are significantly larger than the expected inhomogeneous width of a transition, the line widths are often ascribed to homogeneous broadening. Different dynamical models have been proposed for interpreting and calculating the line widths for the overtone states of a variety of molecular system^.'^*^^^^ All seek to relate the observed line widths of overtones to intramolecular vibrational relaxation processes. For example, Sage and J ~ r t n e have r ~ ~ developed a phenomenological random coupling model, in which interactions between the excited C-H oscillator and ring modes in benzene provide the main contribution to the overtone line widths. Sibert, Reinhart, and Hynes12have presented a model for benzene in which a 2: 1 Fermi resonance between the first overtone of HCC bend and a C H stretch is important in the relaxation of C H overtone states. This model was applied to the higher C H overtones and appeared to have predictive ability with regard to the observed line widths in benzene and its deuterated analogues. Recently, significantly narrower line widths than previously observed for the lower benzene overtones have been observed in a study performed in a supersonicjet!' Reddy, Heller, and Berrylo have assumed that interactions between C H oscillators play a key role leading to the broad overtone line shape. For benzene, Hase and c o - w ~ r k e r shave ~ ~ , calculated ~~ that there is a decrease in the H C C bending frequency upon excitation of a C H stretch. This could affect the 2:l Fermi resonance condition for relaxation of the excited overtone. In saturated alkyl com~ ~ there i ~ ~is an anharmonic 2:l pounds it has been f o ~ n d that (41) Herzberg, G.Spectra of Diatomic Molecules, 2nd ed.; Van Nostrand New York, 1950; p 127. (42) Sage, M. L.; Jortner, J. Chem. Phys. Lett. 1979, 62, 451. (43) Lu, D. H.; Hase, W. L.; Wolf, R. J. J . Chem. Phys. 1986,85,4422. (44) Swamy, K. N.; Hase, W. L. J . Chem. Phys. 1986, 84, 361. (45) Baggott, J. E.; Chuang, M. C.; Zare, R. N.; Dubal, H. R.; Quack, M.J . Chem. Phvs. 1985, 82, 1186. (46) Dubal, H. R.; Quack, M. J . Chem. Phys. 1984, 81, 3779. (47) Page, R. H.; Shen, Y. R.; Lee, Y. T. Phys. Rev. Lett. 1987.59, 1293. Page, R. H.; Shen, Y. R.; Lee, Y. T. J . Chem. Phys. 1988,88,4621.
The Journal of Physical Chemistry, Vol. 93, No. 12, 1989 4139 interaction that tightly couples the C H stretching and bending modes, which can lead to efficient energy transfer and thus line broadening. Hofmann et al. have shown that other high-amplitude motions can be important in the relaxation of C-H stretches, especially in less symmetric systems than benzene.48 3. Experimental Line Widths. The line widths of a few hundred cm-I typically observed in benzene and saturated alkyl compounds are similar to the line widths found for C2(CH3)2Av = 6 and 7. In contrast, the Cd(CH3)2and Hg(CH3)2compounds have significantly narrower line widths, in all cases less than 80 cm-l. Possible factors behind these differences will now be considered. In C2(CH3)2,the C H spectra in the Au = 3 and 4 region (not shown) consist of single narrow bands with line widths of approximately 45 cm-'. The line width increases to approximately 60 cm-' for the transition around Av = 5. For absorptions with Au = 6 and 7 (see Figures 2-4), the width is more than 200 cm-l. As indicated in the previous section, in a variety of previous studies, increases in line widths have been explained by interactions between the overtone under study and combination bands generally involving the next lowest overtone. In particular, in hydrocarbons, resonances often exist between the nth C-H stretch and the combination band of the ( n - 1)th C-H stretch and the first overtone of the methyl bending mode. Changes in line width in C2(CH3)2could certainly result from similar types of interactions. Possible resonances are indicated in Table I. Line widths for the Av = 5 and Av = 6 transitions of Cd(CH3)2 are 65 and 55 cm-I, respectively. Potential resonances exist between the 5vCH transition at 13 467 cm-' and the combination bands 4VCH V2 V9 and ~ V C H ~ , 5 Vg at 13 457 and 13 495 cm-", respectively. The width of the Av = 5 transition in Hg(CH3)2 is approximately 35 cm-' and increases to 68 cm-' for Av = 6 and 77 cm-I for Av = 7. Interactions are possible at Au = 6 between the transition 6vcH at 15 932 cm-' and the combination bands 5vCH + 2v2 at 15 946 cm-' and possibly 5VCH + 2v6 and/or v2 + V6. At hu = 7 an interaction is possible between 7VCH at 18 093 cm-' and the combination bands 6vCH 4- v9 + vlo or 6vCH + vI3 + vI4 calculated at 18 109 and 18073 cm-', respectively. Yet these interactions, which are similar to interactions present in C2(CH3)2, do not lead to nearly as extensive line broadening as in Cz(CH3)2. Of course this assumes that the larger line widths observed in C2(CH3)2are due to energy-transfer processes. As will be discussed in more detail in the following section, similar differences in line width between the lightest members and heavier members of a homologous series have been observed for M(CH3)4and M(CH3)3compounds. In each case the change in line width is not due to differences in B values, since the B values do not change significantly for any of the members of a series. It is also difficult to correlate the change with the density of overlapping hot bands available. In fact, since the heavier members of the series have lower frequency vibrations, hot bands would tend to be more important in the heavier members of the series than in the lighter members. Thus inhomogeneous broadening does not appear to have a dominant effect on the relative line widths in these compounds. Therefore, we are left to consider how processes that affect homogeneous broadening could change from one member of a series to another. As has been shown in a study of the behavior of the C-H stretching overtones of p r ~ p y n e the , ~ ~existence of a resonance is a necessary but not sufficient condition for rapid intramolecular energy transfer and a corresponding effect on the line width of an overtone. To have a significant effect there must also be good coupling between the modes in question. In propyne, it has been shown that the triple bond inhibits coupling between the acetylenic C-H stretch and potential resonant interactions involving vibrational motions of other parts of the molecule. This leads to a small matrix element connecting the states involved and the resonance has little effect on energy transfer out of the initially excited acetylenic C-H overtone. It is certainly possible that the dif-
+ +
+ +
(48) Hofmann, P.; Gerber, R. B.; Ratner, M. A,; Baylor, L. C.; Weitz, E. J . Chem. Phys. 1988,88, 7434.
4740
The Journal of Physical Chemistry, Vol. 93, No. 12, 1989
Manzanares 1. et al.
TABLE 111: Summary of Data for M(CH,),, M(CH3)3, and M(CH,)* Compounds"
molecule C(CH,), SiiCHyj4 Ge(CH3), Sn(CH3)4 N(CH3)S
rMxH3, 1.54 1.88 1.98 2.14 1.46
cm
central atom mass 12.01 28.09 72.59 118.69 14.00
exptl fwhm, cm-' rC-H, lo-'
cm
1.098 1.098 1.096 1.095
C-H, 1.0965
Av(P,R),~cm-' 23 18 17 16 34.4 (11) 24.1 (I)
Av = 5 58.5 29 35.5 26.7 101
Au = 6 115.5 46.5, 42.0 34.5 36.9 163
Av = 7 160 37 32 33 129
C-Hb 1.1123
P(CHd3
1.84
30.97
C-H, 1.0962
26.1 (11) 20.6 ( I )
C-Hb
39
37
40
39
45
170
48
39
34
31
37
61
1.0999
As(CH313
1.98
74.92
C-H, C-Hb
23.8 (11) 19.9 ('i)
1.0972 1.096 1.096 1.095
13.6 13.7 13.9
1.0946 CZ(CH3)2 Cd(CH3)2
1.46 2.11 2.09
(24.02) 112.41 200.59
-
62 -65 -35
-
200 -55 68
-230
-77 Hg(CH3)2 'Experimental data for M(CH& compounds is from ref 17 and for M(CH3), compounds from ref 40. bRotational envelope, calculated.
ferences in observed line widths for the compounds currently under study could be due to differences in coupling in the individual compounds which tend to affect intramolecular energy transfer. Such a possibility and the likely physical basis for this effect will now be considered. 4 . Geometry and Heavy Atom Effect. It is interesting to note that there appears to be a correlation between line width and mass in the M(CH,)2 system and the other systems that have been studied which have central metal atoms: M(CH3), and M(CH,), compounds. The line width at a given local-mode overtone level generally decreases as one goes from the lightest member of the series to heavier members of the series. Though the correlation appears to be between line width and mass it is important to realize that generally as the mass of the central atom increases, the M-CH3 bond distance also increases. Thus, if line widths are influenced by methyl group interactions, this could also be the source of the change in line width in these systems. In the M(CH3)2series there is a significant change in the mass of the central atoms, increasing from 24.02 g mol-' for the C2 group to 112.41 g mol-' for Cd and 200.59 g mol-' for Hg. However, it is interesting to note that, although the mass of the central atom(s) increases steadily throughout the series, the line widths of the overtones do not change significantly in going from Cd to Hg. This suggests that line widths are influenced by factors other than or in addition to the central atom mass. In this discussion it should be kept in mind that, as previously stated, the molecules dimethylacetylene, -cadmium, and -mercury are all molecules with very similar rotational constant^.^'^^^ As indicated above, one of the factors that could influence line widths is methyl group interactions. The M-CH, bond lengths in the heavier compounds are quite similar, while the C-CH, bond length in dimethylacetylene is significantly shorter. The bond distances are 1.46 X 10-8, 2.1 1 X 1OF8, and 2.09 X 10-8 cm for C2(CH3)2rCd(CH3)2,and Hg(CH3)2,respectively. The corresponding length for the triple bond in the C2group is 1.21 X cm. It is possible that these increased intramolecular distances (perhaps in combination with the increase mass of the central atom) are a major factor affecting the intramolecular coupling of the methyl groups. It is also possible that, after a given intramolecular distance, or a given mass, is reached, further increases will not greatly affect the degree of interactions between different methyl groups. E . Comparison with M(CH,), and M(CH3)3Molecules. The line widths for C-H overtones of the series of molecules M(CH,), (M = C, Si, Ge, Sn), M(CH,), (M = N , P, As), and M(CH3)2 ( M = C2, Cd, Hg) are presented in Table 111. Table 111 also contains the central atom-methyl group internuclear distances (rMCH,)and the atomic weight of the central atom. Included is the C-H internuclear distance (rC-H) of the
methyl groups. Table I11 also contains an estimated separation of the maxima of the P and R branches Avmax(P,R)of the fundamental transitions of these molecules. A summary of the behavior of line widths in these series is now provided. 1. M(CH,), Compounds. The M-C bond lengths increase considerably with increasing mass of the central atom M = C, Si, Ge, Sn. At the same time, the C-H bond distances in the methyl groups decrease in the same order, though the change in the C-H bond distance is small relative to the change in the M-CH3 bond distance. Line widths of the rotational envelope are calculated for a spherical top molecule by using ground-state rotational constants. The prediction of the calculations is that the rotational line widths decrease in the order C > Si > Ge > Sn, but the values for the rotational line widths are very close to each other. Experimental line widths for Av = 5, 6, and 7 show that the molecules Si(CH3)4,Ge(CH,),, and Sn(CH3)4exhibit values that are close to each other and there is a large contribution of the rotational envelope to the observed line width. For C(CH3), the line widths obtained are significantly larger than those predicted from the rotational envelope and also significantly larger than obtained for the other molecules in this series. 2. M(CH3),Compounds. The M - C bond lengths increase with increasing mass of the central atom M = N, P, As. Due to the trans effect there are two different types of C-H bonds in the methyl groups.40 The C-Ha and C-Hb bond distances in the methyl groups decrease in the order N > P > As. Line widths of the rotational envelope are calculated for a symmetric top molecule (oblate). The width of the parallel bands (11) and bands corresponding to transitions with AK perpendicular (I) = 0 and AK = f l , respectively, are presented. Details of the calculation are given in ref 40. The calculated rotational line widths follow the order N > P > As but are relatively close to each other. Experimental line widths for Av = 5, 6, and 7 show that the molecules P(CH3)3and As(CH3), have line widths that are close to each other with a large contribution from the rotational envelope (except for the C-Hb absorption at the v = 7 level of P(CH,),; the possible reasons for this relatively large line width are discussed in ref 40). The line widths for N(CH3), are significantly larger than for the -P and -As compounds and the contribution from the rotational envelope to the overall line width is considerably less important. The data on the three homologous series of compounds can be summarized as follows. The line widths of Si(CH3),, Ge(CH3),, and Sn(CH,), are comparable; the same can be said for the pairs P(CH3)3(except for the u = 7 C-Hb absorption) and As(CH3!, and for Cd(CH3)2and Hg(CH3)2. All of these compounds exhibit relatively narrow line widths in which the contribution from the rotational envelope is often greater than 50%. In each series, the lightest members, C(CH3),, N(CH3),, and C2(CH3)?,exhibit line
C-H Overtones of C2(CH3)*,Cd(CH3)2,and Hg(CH3)2 widths in which the contribution of the rotational envelope is comparatively small and intramolecular vibrational energy transfer is the probable cause of the larger line widths. In virtually all of the heavy atom centered compounds, combination bands are present that are in resonance with pure local modes at the levels of Au = 5-7. In some cases these resonances produce a change in line width, while in other cases these possible resonances do not produce obvious broadening of the overtone bands. However, for all of the compounds studied, the heavier members of the series generally have narrower line widths than the lighter members of the series. In all cases, in all series of molecules, it appears that the largest effect on the line width occurs in going from the carbon-centered compound to the next heavier member of the series. Beyond that there is relatively little change in the line width. Unfortunately, for the specific molecules presented in this paper, there are no theoretical calculations on the effect of heavy central atoms or changing methyl-methyl distances on intramolecular vibrational energy redistribution. However, experiments by Rogers et al.49*s0suggest the possibility of slow energy randomization caused by heavy central atoms in reactions of F atoms with tetraallyltin and tetraallylgermanium. In these experiments the rate of formation of fluoroethylene is approximately lo3 times larger than that calculated from RRKM theory. Their conclusion was that the heavy central atom inhibits the intramolecular flow of vibrational energy, which is then confined to one side chain of the molecule. Rabinovitch and co-workers5' studied the unimolecular dissociation of chemically activated 4-(trimethyllead)-2-butyl and 5-(trimethyltin)-2-pentyl radicals. However, heavy atom inhibition of energy randomization was not observed. Lopez and M a r c u ~used ~ ~ classical ? ~ ~ trajectory calculations to model energy flow in a linear chain, C-C-C-Sn-C-C-C. Inhibition toward energy transfer through the heavy atom was calculated to occur when the initial energy deposited in one portion of the molecule was large. When the mass of Sn is decreased by a factor of 2 the inhibition disappears. Swamy and Hases4 in another quasi-classical trajectory study of energy redistribution in tetraallyltin and carbon compounds find that (a) the energy introduced in one C=C bond of the tetraallyl molecule can remain localized in the originally excited allyl group, and (b) no difference in the rate of energy randomization is observed if Sn is replaced by C in the tetraallyltin without changing the Hamiltonian. Energy redistribution is modestly faster if the Hamiltonian for tetraallyl carbon is used. The theoretical calculations discussed above do not include the hydrogen atoms and their associated high-frequency stretching and bending motions. As Swamy and Hase point out, it is possible that resonant energy-transfer channels are not adequately represented as a result of this simplification. A conclusion that could be reached from these studies is that the mass of a central atom can affect intramolecular vibrational energy transfer, but the magnitude and relative importance of this effect versus other factors that can influence intramolecular energy transfer is still unquantified. For example, virtually nothing has been done to quantify the effect of methyl group interactions on intramolecular vibrational energy transfer. As has been pointed out in the previous sections, the most obvious correlation is between either central atom mass or M-CH3 distances and line widths. Unfortunately, in these systems it is not possible to isolate the effect of the mass of the central atom versus the M-CH3 internuclear distance, because the increase in the distance is linked to an increase in the mass of the central atom. However, it is interesting to note that in the case of Cd(CH3)2 and Hg(CH3)2the M-CH3 distance decreases from 2.1 1 X lo-* (49) Rogers, P.; Montague, D. C.; Frank, J. P.; Tyler, S. C.; Rowland, F. S. Chem. Phys. Lett. 1982, 89, 9. (50) Rogers, P.; Selco, J.; Rowland, F. S. Chem. Phys. Lett. 1983,97, 313. (51) Wrigley, S. P.; Oswald, D. A.; Rabinovitch, B. S. Chem. Phys. Lett. 1984, 104, 521. (52) Lopez, V.; Marcus, R. A. Chem. Phys. Lett. 1982, 93, 232. (53) Marcus, R. A. Faraday Discuss. Chem. SOC.1983, 75, 103. (54) Swamy, K. N.; Hase, W. L. J . Chem. Phys. 1985,82, 123. (55) Manzanares I., C.; Yamasaki, N. L. S.; Weitz, E. J . Phys. Chem. 1986, 90, 3953.
The Journal of Physical Chemistry, Vol. 93, No. 12, 1989 4741 to 2.09 X lo-* cm while the mass of the central atom increases considerably. In this case the line widths remain very similar. Similarly, in virtually all other cases, the change in M-CH3 distance more closely parallels the change in line width than does the change in mass of the central atom. However, intuitively, it is somewhat surprising that a change in M-CH3 bond length in a molecule in the M(CH3)2series, with a linear skeleton, would have such as large influence on line width. Unfortunately, the conclusion we finally reach is that without further theoretical work on these systems it is premature to assign changes in line width, and thus changes in the matrix elements, which dominate intramolecular energy transfer, to any single source. It is even simplistic to assume that the correlation between line width and either mass or M-CH3 distance should be linear. In fact it is possible that both parameters are important in determining the magnitude of the coupling matrix elements between various modes of these molecules. However, we believe it is fair to state that the preponderance of evidence indicates that a change in the magnitude of matrix elements that control the coupling behavior of the initially excited vibrational modes does occur in these systems. This leads to a change in overtone line width. This change parallels the change in mass of the central atom, but may not be directly linked to or solely dependent on the mass of the central atom. Clearly, theoretical calculations on the specific systems studied, similar to those performed on propyne$8 will be necessary to understand the experimental results relating to line-width variations obtained in the present study and in related studies.
Conclusions Overtone absorption spectra of the molecules C2(CH3)2,Cd(CH3)2, and H B ( C H , ) ~have been obtained. Absorptions have been assigned within the context of the local-mode description of vibrational overtones. A variety of local-mode-normal-mode combination bands have been observed and are assigned. An unusual feature of these assignments is that many of the assignments involved ternary combination bands. Birge-Sponer plots have been constructed for dimethylacetylene and dimethylmercury and harmonic frequencies and anharmonicities have been determined. This determination also allows one to infer these parameters for dimethylcadmium. Isolated frequencies have been determined for the compounds under study and correlate well with the isolated frequencies derived from studies of the analogous monohydrides. Absorption cross sections have been determined for the u = 5 and u = 6 absorptions of the compounds under study. As has been previously observed in a series of tetramethylmetal (M(CH3)4) and trimethylmetal (M(CH3)3)compounds, the line widths for the u = 5,6, and 7 overtones are largest for the lightest member of the series and are narrower and of similar magnitude for the heavier members of the series. The factors that could contribute to the change in line width in both the series under study and in the M(CH3)4and M(CH3) series are considered. From the existing data, it is concluded that the change in line width is linked to a change in the magnitude of the matrix elements governing intramolecular vibrational energy transfer out of the initially excited C-H overtone states. This change in matrix element correlates with a change in mass of the central atom. However, the change in mass of the central atom also correlates with a change in M-CH3 bond distance. Thus methyl group interactions could also be important in determining rates and pathways for intramolecular vibrational energy transfer. Since central atom mass and M-CH3 distance typically correlate, it is experimentally difficult to separate potential effects from each source. To further unravel the source of the observed line-width changes more theoretical work is needed and would be most useful if directed toward the specific compounds that have been studied experimentally. Acknowledgment. We thank the National Science Foundation for support of this work under N S F grants CHE85-06975 and CHE88-06020. Registry No. C2(CH3)2,503-17-3; Cd(CH&, 506-82-1; Hg(CH3)2, 593-74-8.
