Influence of methyl group deuteration on the rate of intramolecular vibrational energy relaxation

Joan E. Gambogi, Robert P. L'Esperance, Kevin K. Lehmann, Brooks H. Pate,a) and Giacinto Scoles Department of Chemistry, Princeton University, Princeton, New Jersey 08542

(Received 15 June 1992; accepted 25 September 1992)

The high resolution spectra of the fundamental and first overtone of the acetylenic C-H stretch in tert.-butylacetylene-d9 and (trimethylsilyl)acetylene-d9 have been measured using optothermal detection of a collimated molecular beam. IVR lifetimes determined from the homogeneously broadened Iineshapes are compared to those of their undeuterated analogues. It is found that for both molecules, at both levels of excitation, deuterating the methyl rotors results in an increased rate of IVR. The results indicate that the previously suggested methyl rotor effect, as an enhancer for IVR, plays a secondary role to increasing the number of low order resonances to which the C-H stretch can couple. Although the torsional modes are important for the molecules to exhibit statistical case IVR and contribute to the filled-in ho­mogeneous Iineshapes, the rate of energy relaxation seems to be dominated by the number of low order resonances.

INTRODUCTION

High resolution infrared spectroscopy of molecular beams has been recently used to study intramolecular vi­brational energy redistribution (IVR) following excitation of a hydride stretching mode in a number of medium to large molecules. 1 These studies have provided quantitative information about the mechanisms and strengths of the vibrational and rovibrational state couplings for individual molecules. Two main conclusions have been extracted from this work so far. First, the observed rates of IVR are often much slower than those observed in earlier work in which Franck-Condon active modes of excited electronic states are accessed2 or when high hydrogen overtones are excited.3 Since the observed rates are often comparable to gas phase collision rates for pressures near 1 atm, mode selective chemistry may still be possible upon hydrogen stretching excitation in spite of the presence of IVR. To date, mode specific enhancement of a bimolecular reaction rate following stretching excitation has been observed only for HOD, where IVR does not occur because of the small background density of states.4 IVR studies of larger mole­cules should help to identify other favorable molecules. The second general result is that IVR rates appear to show systematic changes when the molecule undergoes chemical modification.5 A major motivation for the current IVR work at Princeton is to extend our understanding of these trends with the long range goal of being able to design molecules to control IVR rates. The present paper exam­ines the effect of deuteration of the methyl groups in two trimethyl substituted acetylenes.

The series of trimethyl substituted acetylenes (CH3)3X-C==C-H(X=C, Si, and Sn), were previously studied in our laboratory and exceptionally long lifetimes, up to a few nanoseconds, were measured.5 It was found

that the lifetimes increase greatly as the central atom is made progressively heavier, despite the fact that the total density of vibrational states increases. One common feature in the structure of these three molecules is the presence of methyl rotors.

The influence of a hindered methyl rotor on IVR has received much experimental and theoretical attention.6-1O Most of the experimental results, especially the work of Stone and Parmenter, suggest that the methyl group acts as an IVR enhancer.6 This acceleration was attributed to re­pulsion in the van der Waals' radii of the methyl rotor hydrogens with the ring hydrogens leading to mixing of these states.9 We can apply their analysis to our series of trimethyl substituted molecules where there is a threefold, relatively high barrier ( 1434 cm -1 for tert.­butylacetylene). In the harmonic oscillator limit, the cou­pling between the torsions should scale as 6.q;n, where 6.q; is a displacement of the torsional mode, and n is some power that depends upon the order of the coupling. The matrix elements of this operator will scale as V-

n/2 or m-nI4• Therefore, as we increase the mass of the rotor, the coupling matrix elements should decrease at least slightly, leading to a decreased rate of IVR upon deuteration of the methyl groups. In a recent paper, Martens and Reinhardt lO

describe a strong anharmonic mixing of the internal rota­tion with other low frequency modes of the molecule. This results in a chaotically fluctuating bath that leads to relax­ation of higher frequency modes, much like multiphonon relaxation in crystals. Deuteration of the methyl group would then decrease the bandwidth of the bath and thus lower the relaxation rate, perhaps substantially.

Based upon these arguments, methyl deuteration in the (CH3hXC=CH molecules should lead to a measurable decrease in the IVR rate. To test this prediction, the high resolution spectra of 3,3-dimethylbutyne-d9 (tert.­butylacetylene-d9 ) and (trimethylsilyl) acetylene-d9 were

a}Current address: NIST, Molecular Physics Division, Gaithersburg, MD - ·~eas~r~d. The relaxation o(these molecules falls in the 20899 statistical limit, so the IVR lifetime can be directly ob-

1116 J. Chern. Phys. 98 (2), 15 January 1993 0021-9606/93/021116-7$06.00 © 1993 American Institute of PhYSics

Gambogi et al.: Methyl group deuteration 1117

tained from the observed Lorentzian linewidth of the spec­tral features, assuming that inhomogeneous effects are neg­ligible. In contrast to the theoretical predictions, the IVR rates obtained for the deuterated compounds were found to be substantially faster than those of the undeuterated iso­topomers. It is perhaps useful to add that when we began our experiments no unambiguous examination of the effect of methyl deuteration had been reported. Recent results by Paramenter and co-workers comparing para-fluorotoluene (pFf) to pFf-d3 showed the undeuterated compound to have a lifetime of 3.4 ps, while the deuterated pFf had a lifetime of 1.5 ps for the 3151 vibrational band. 11 The au­thors claim that this difference is within the error of their model, however, and conclude that deuteration has no ef­fect on IVR lifetimes for this molecule. While absolute lifetimes determined by the chemical timing technique are likely to show considerable uncertainties, it is not at all clear why the relative accuracy, when comparing two iso­topomers, should not be better than a factor of 2. The fact that the results of Parmenter and co-workers show a trend which is the same as the one reported here is likely to be significant.

EXPERIMENT

[4,4,4,4',4',4',4",4",4" _2 H91-3, 3-dimethyl-I-butyne (tert-Butylacetylene-d9) was synthesized by the method of Negishi, King, and Tourl2 from [1,1,1,4,4,4,4',4' ,4',4",4",4" _2 H 12]-3,3-dimethyl-butan-2-one (pinacolone-dI2 ). Pinacolone-dl2 was prepared by standard methods 13 from acetone-d6 (Cambridge Isotopes). Ethynyl tri-eH3]-methyl silane (trimethylsilylacetylene-d9 ) was synthesized by the method of Holmes and Sporikou 14 from ethynlymagne­sium chloride (Aldrich) and chloro tri-fH31-methylsilane (MSD isotopes).

Absorption spectra in the region of the VI and 2vI (the acetylenic hydrogen stretch) were observed using the method of optothermal spectroscopy in a cold, collimated molecular beam with the apparatus described in Ref. 5. A 1 % mixture of the sample gas in He is expanded through a 50 f.Lm diam. nozzle at a backing pressure of 5 atm. Two commercial color center lasers are used as· the source of infrared radiation. The first is a Burleigh FCL-20 color center laser pumped by 2 watts of the 647.1 nm line from Spectra-Physics model 171 Kr+ laser. In the acetylenic C-H region this yields 25 m W of single mode, continuous wave power. The second laser is a Burleigh FCL-120, pumped by 1.9 W of a Spectra-Physics 3460, continuous­wave Nd:YAG laser resulting in 150 mW of power at the acetylenic C-H first overtone region. The infrared radia­tion is crossed almost perpendicular to the beam through a multipass arrangement resulting in slightly Doppler broad­ened linewidths. The instrumental resolution of 8 and 16 MHz at 3 and 1.5 f.Lm, respectively, is much higher than the width of the observed features and can be neglected when determining the linewidths and thus the IVR rates from observed transitions.

WAVENUMBER (cm·!)

3329.10 . 3329.40

WAVENUMBER (em'!)

a) (CD3hCo.cH Q Branch

b) (CH3hCOOI Q Branch

3329.70

FIG. 1. The Q branches of the acetylenic C-H stretch fundamental for both (CD3hCC==CH (upper) and (CH3hCC==CH (lower) are plotted. The two Q branch features are fit to a single Lorentzian and the residuals of the fit are shown below each spectrum.

RESULTS

The Q-branch of the fundamental acetylenic C-H stretch for (CD3)3C-C==C-H (TBA-d9) and (CH3)3C­C==C-H (TBA) are shown in Fig. 1. For the deuterated compound the line shape is Lorentzian with a linewidth of 4 GHz which corresponds to an IVR lifetime of 40 ps. With such a broad linewidth, and the estimated rotational constant of 2.3 GHz, the rotational structure in the P and R branches are expected to be unresolved, and indeed no structure was observed. Because the line shape is symmet­ric and is accurately fit by a single Lorentzian we conclude that inhomogeneous contributions can be neglected. Broadening due to individual ro-vibrational transitions would produce an asymmetry on the low frequency side of the branch. The TBA Q-branch [Fig. l(b)] is in fact slightly asymmetric revealing a rotational inhomogeneous broadening of about 90 MHz. Since the rotational con­stants decrease upon deuteration, the inhomogeneous com­ponent of the deuterated compound is expected to be smaller. Therefore, for TBA-d9 the homogeneous linewidth dominates the spectrum. We also point out the presence of a 2.8 cm- I blueshift of the band origin upon deuteration (from 3329.4 cm -I for TBA to 3332.2 cm -I for TBA-d9 ).

Deuteration must result in a lowering of the vibrational

J. Chern. Phys., Vol. 98, No.2, 15 January 1993

1118 Garnbogi et al.: Methyl group deuteration

250

~ 200

N I

2-150

I f-a

~ 100 z :J o R Branch

¢ P Branch 50

0 1 2 3 4 5 6 7 8 9 10

J'

FIG. 2. Linewidths (fwhm) as a function of the upper state rotational quantum number, J, for the fundamental of (CD3)3SiC==CH.

harmonic frequencies (i.e., a redshift) and so this suggests a resonant interaction strong enough to shift the band or­igin a few cm- I .

The overtone region of TBA-d9 was scanned under the same conditions as the fundamental and no evidence of any absorption was found, indicating that the linewidth is so broad to place the peak height of the Q branch below' the noise level of our spectrometer. Based on signal-to-noise estimates, this corresponds to a lifetime in the overtone shorter than 20 ps.

The full spectrum of (CD3)3Si-C=C-H (TSA-d9 )

was measured from R (8) to P( 9). Each of the P and R branch features fits to a single Lorentzian. The linewidths obtained from these fits are plotted in Fig. 2 as a function of J', the rotational quantum number of the upper state. Contrary to the case of TSA,5 the linewidths appear to narrow slightly at higher J's. For the undeuterated silicon compound, the linewidths of the features in the fundamen­tal showed a slow but steady increase as a function of J, with a shoulder developing at the high frequency side. This was consistent with the expected increase in inhomoge­neous broadening from unresolved K structure and was not taken as evidence of a Coriolis coupling mechanism. Since the deuterated compound shows a slight decrease with J from about 215 MHz for R(1) to 170 MHz for R(8), we conclude that at least part of the linewidth is due to the anharmonic mixing of VI with a doorway state that detunes from near resonance with increasing J.

The spectra of the R(5) lines of the VI fundamental of TSA-d9 and TSA are compared in Fig. 3. For both mole­cules the linewidths are considerably narrower than those of the carbon analogues and corresponds to an IVR life­time of 850 ps for the deuterated silicon compound and 2000 ps for the undeuterated one. Table I gives the spec­troscopic constants determined in a fit to the observed line positions. The band origin for the silicon compound is only slightly redshifted (0.05 cm -I) upon deuteration.

In the overtone region of TSA-d9 the Q branch was observed at 6520 cm- I (Fig. 4). This absorption is asym­metric and the low energy side of the branch does not fit to a Lorentzian. (See Table II) However, for all of the trim-

I !

3313.20

WAVENUMBER (cm-1)

3313.24

WAVENDMBER(cm-l )

a) (CD3l3Sic.cH, R(5)

3313.14

b) (CH3l3SiOocri, R(5)

3313.28

FIG. 3. R(S) of the fundamental acetylenic C-H stretch of (CD3hSiC==CH (upper) and (CH3)3SiC==CH (lower) and their fits to a single Lorentzian.

ethyl substituted compounds measured previously,S it was found that obtaining the linewidth from the high energy half of the Q branch provided an excellent estimate (within 10%) of the linewidth of the individual rotational features of the spectrum. By fitting the high energy half of the line shape in Fig. 4, a lifetime of 140 ps was obtained. Contrary to TSA, the lifetime does not increase from the fundamen­tal to the overtone excitation for the deuterated silicon compound. The P and R branch features were observed for this molecule with a very low signal to noise ratio and provided no additional information. The broad weak fea­ture on the low frequency side of the Q branch is likely due to a hot band. The two sharp features near 6519.88 and 6519.92 cm- I are reproducible and it is very probable that they are the Q branches of resonantly coupled states. If these features were due to a chemical impurity or to hot bands, they would have also been seen in the V= 1 spec-

TABLE I. Measured spectroscopic constants (em-I) for the fundamen­tal of (CD3hSi-C==C-H."

Vo B" B' X11

3312.41202(66) 0.OS7223(32) 0.OS7 176(30)

-S2.4

"Reported uncertainties in the fit to the vibrational levels are 20'.

J. Chern. Phys., Vol. 98, No.2, 15 January 1993

Gambogi et al.: Methyl group deuteration 1119

6519.70

6520.00

a) (CD313SiC-CH, v=2 Q Branch

6519.90 6520.30

WAVENUMBER (cm'!)

6520.20 6520.40

WAVENUMBER (cm'!)

b) (CH313SiC=CH, v=2 Q Branch

6520.60

FIG. 4. The Q branches of the acetylenic C-H stretch overtone for (CDJ)3SiC"",CH (upper) and (CH3hSiC"",CH (lower) are plotted. Only the high energy half of the Q branch of (CD3) 3SiC"",CH is fit to a Lorentzian. The Q branch of (CH3)3SiC"",CH was not used to determine the IVR lifetime for this molecule but is shown for comparison.

trum. A very broad region was scanned for v = I and no evidence of other features was seen.

DISCUSSION

The fact that the IVR rate is increased upon deutera­tion is contrary to previous experimental observations and theoretical predictions. A gas phase FTIR study of the fundamental and first overtone of several carbonyl com­pounds suggested that deuteration of the methyl rotor re­duces the IVR rate'? In that study, a substantial simplifi­cation in the spectrum of acetyaldehyde was noted upon deuteration. However, at the low density of states for this molecule (3 states per cm -1 in the carbonyl overtone re­gion), IVR alone could not be responsible for the observed

TABLE II. IVR lifetimes obtained from the Lorentzian line shapes.

Molecule

(CH3hC-C"",C-HS

(CD3) 3C- C"",C-H (CH3)3Si-C"",C-Hs (CDJhSi-C"",C-H

v=l

200 40

2000 850

Lifetime (psec)

v=2

110 <20 4000 140

spectral congestion. The results probably reflect a changing hot band structure or the detuning of a single anharmonic resonance. Another study probed the fourth overtone of the O-H stretch in severai simple alcohols.8 Deuterating the alcohols resulted in spectra with sharpened band fea­tures. This was attributed possibly to a loss of vibrational congestion, however it could also indicate a change in the IVR rate since the energies were high enough for IVR to playa role.

To explain our results the theory of Moss et al., which explains the IVR enhancement as a result of overlap of the methyl hydrogens with the rest of the framework of the molecule, can be considered.9 This theory can mechanisti­cally account for the fact that a remote change in chemical structure (remote from the initially excited bond) may have such a large effect on the relaxation of the acetylenic chromophore. Increased overlap of van der Waals' radii leads to an increased IVR! rate which is consistent with the comparison between the carbon compound and its silicon analogue, since the C-CH 3 bonds are shorter than the Si­CH3 bonds. As mentioned earlier however, decreasing the methyl rotor torsional frequency (a consequence of deu­teration) should reduce the IVR rate and this is not con­sistent with our results.

Martens and Reinhardt have proposed an alternative expianatlon ofthemethyi rotOl~effect based on dividing'the molecule's multidimensional phase space into two sub­systems. IO The methyl rotor and other low frequency modes are included in the first subset and their dynamics is strongly chaotic leading to rapid energy redistribution. The second subset consists of the high frequency modes which do not couple to the methyl rotor directly due to a large energy mismatch. These modes are induced to relax by the low frequency modes producing a stochastic perturbation on the high frequency modes which leads to a diffusionlike relaxation. Evaluation of the IVR rate depends on the closeness of the torsional frequencies and the low fre­quency skeletal vibrations. For the substituted trimethyl acetylenes, as shown in Table III, the torsional modes are often in near resonance with a low frequency mode. The chaotic bath that Martens and Reinhardt describe could exist in these molecules however, as mentioned earlier, one would predict from this theory a reduction in the relax­ation rate upon deuteration.

As an alternative approach to the interpretation of the IVR lifetimes one can consider a tier model. This type of model treats the relaxation of the initial excitation as oc­curring through a set of sequential couplings to the back­ground states. The initial state first couples to a set of low order background states which subsequently couple to more background states, through low order anharmonic couplings. The process continues to fan out and drives the relaxation. This model of sequential couplings has proven

. _useful in the analysis of IVR for several polyatomic mole­cules. 15- 19 Sibert, Reinhardt, and Hynes have been able to describe quite well the overtone spectrum of benzene using a tier model. 15 In their calculations they found that the rate is only sensitive to the first (or first few) steps. Quack and co-workers have quantitatively modeled the C-H overtone

J. Chern. Phys., Vol. 98, No.2, 15 January 1993

1120 Garnbogi et al.: Methyl group deuteration

TABLE III. Nonnal modes of the trimethyl substituted acetylenes. spectrum of (CF3hCH, using the idea that efficient cou-

TBA20 TBA-d921 TSA22 TSA-dl2

pIing between the stretching and bending of the C-H group AI occurs predominantly through low order terms in the ex-

v..==C-H 3329" 3332" 3312" 3312" pansion of the potential. 16 This type of analysis has also

VasCH3 2977 2227 2966 2220 been used by Hutchinson and co-workers in calculating the

VsCH3 2889 2081 2900 2120 overtone spectra of simple hydrocarbons,17 propargyl alco-

vsC""'C 2107 2116 2037 2037b hollS and cyanoacteylene. 19

8asC-H 1475 1051 1420 1060 In Table III the fundamental frequencies for the four 8sC-H 1363 1028 1265 995 molecules discussed in this paper are listed. Neither IR nor v"x-c 1248 1210 654 530 Raman spectrum of TBA-d9 has been reported; the funda-v"x-c"",C 691 645 55] 515 mentals for this molecule (listed in Table III) were calcu-pC-H 885 740 860 745 lated by Crowder, using force constants adjusted to fit the 8"x-C3 382 319 218 185 observed fundamentals of TBA.20,21 The fundamental fre-

E quencies of TSA-d9 were obtained from those of TSA-dlO VasCH3 2978 2229 2966 2220 with minor adjustments.22 The low frequency torsional

VasCH3 2976 2221 2966 2220 modes have been reported only for TBA; the torsional

VsCH3 2889 2020 2900 2120 modes for the others are estimated from similar mole-8asCH3 1475 1054 1420 1030 cules.23 Density of states values were calculated by a direct 8asCH3 1456 1050 1420 1030 count for the fundamental and first overtone, treating all 8sCH3 1393 1016 1255 1003 modes as harmonic vibrations. Calculations carried out for va"x-c 1205 1189 700 562 the hydrogen compounds showed that treating the tor-PasCH3 1032 803 845 730 sional modes as uncoupled hindered rotors increased the PasCH3 930 755 765 583 density of A 1 symmetry vibrational states by a factor of 1.7. 8"",C-H 634 632 680 680b

A lifting of the torsional degeneracy is predicted to in-8."x-C3 542 493 236 202 crease the density of observed lines by as much as a factor pX-c"",c 362 308 132 115 of 24.24 Table IV summarizes the total density of states 8X-C"",C 182 181 350 322 calculations, the density of states with the torsional modes A2 excluded, and the number of low order resonances for each VasCH3 2974 2218 2967 2215

molecule in the harmonic approximation. It is evident from 8asCH3 1459 1048 1410 1034 pCH] 995 751 739 542 the calculated density of states without the torsional modes

that, at least for TBA and TBA-d9, the number of back-Torsions (estimated from.Ref. 23) ground states is too sparse to support "statistical" IVR. E 262 196 190 135 Some energy must flow into the torsional modes from the A2 202 144 190 135 initially excited C-H stretch.

"Taken from our spectra. The low order resonances, listed in Table IV, are for a bEstimated. 100 cm -I window around the acetylenic stretch fundamen-

TABLE IV. Density of states and low order resonances.

Fundamental C-H stretch

Total density of 4.9X102 2.8X103 1.0 X 104 1.0 X 105 AI states (fern-I)

Density of AI states without torsional Modes (fern-I) 50.0 1.7X 102 7.8X102 4.1 X 103

3rd order states' 24.0 34.0 15.0 6.0 4th order states 293.0 373.0 250.0 540.0 5th order states 1819.0 31523.0 1415.0 2932.0 IVR Rate (S-I) 5.0X109 25.0X109 0.5X109 1.2 X 109

Overtone C-H stretch

(CH3hC-C"",C-H (CD3)3C-C"",C-H (CH3)3Si-C"",C-H (CD3~Si-C"",C-H

Total Density of 6.2X105 7.6Xl06 2.9X107 6.0X108

Al States (fern-I)

3rd order states 24.0 30.0 24.0 51.0 4th order states 232.0 332.0 152.0 274.0 5th order states 1805.0 3189.0 2021.0 3408.0 IVR rate (S-I) 9.1 X 109 > 50.0X 109 O.25X109 7.1 X 109

"Total number of states in a 100 cm- I region around the C-H stretch.

J. Chern. Phys., Vol. 98, No.2, 15 January 1993

Gambogi et at.: Methyl group deuteration 1121

tal (and overtone). The size of the chosen window is rather arbitrary but has been chosen to reflect the size of the largest anharmonic matrix elements expected as well as neglected anharmonic shifts in the predicted energy levels. Third order states are those states coupled to the acetylenic stretch by a third order anharmonic term and correspond to removing one quantum of energy from the C-H stretch and replacing the energy into two of the lower lying nor­mal modes. Fourth order states have a total of three low frequency quanta and are coupled to the CH stretch in first order by a quartic anharmonic constant, or by cubic con­stants in second order.

Trying to base our explanation of the IVR dynamics on the number of resonances available without focusing on the strength of the couplings can only lead to qualitative results. Still, there are several pieces of evidence that im­plicate low order resonances. First, there is a rough corre­lation of the lifetimes with the number of low order reso­nances. The density of third and fourth order resonances is smaller for the Si compounds compared with the C species, as is found for the IVR rates. Looking at the change in density of states, going from hydrogen to deuterium spe­cies, we see that in three of the four cases, the density of both third and fourth order resonances increases as does the rate in all cases. The one exception is the fundamental of the Si species, where the density of third order reso­nances decreases by a factor of 2 upon deuteration, while that of the fourth order increases by a factor of 2.

When comparing the Si to the C compounds, the ob­served decrease in rate is significantly greater than the fall in density, suggesting that the average coupling matrix el­ement must decrease as well. In going from the fundamen­tal to the overtone in the C species, the density of levels hardly changes, but since one would expect the mean squared matrix element for a given resonance to scale lin­early with vibrational excitation in VI' the halving of the lifetime in the overtone is easily rationalized. On going from the fundamental to the overtone in both Si com­pounds we observe an increase in the number of third order and a decrease in the number of fourth order resonances. The 8.5 times increase in density of third order resonances for the overtone of the deuterated compound appears to dominate over the factor of 2 decrease in fourth order resonance, explaining the increased rate. For the hydrogen Si species, the changes in third and fourth order resonances from the fundamental to the overtone are of smaller and of similar size. Taking into account the expected increase in coupling matrix element with overtone excitation, the re­markable decrease in IVR rate on going from the funda­mental to the overtone of this molecule is not predicted.

In the comparison of the fundamental of the Si species before and after deuteration, it is interesting to note that the deuterium substitution effect is weaker here than for the C species or the overtone of the Si species. Also, as discussed in the results section, VI of the Si species shows evidence of a resonance interaction (as evidenced by the narrowing of the linewidth with J), and thus one of the third order states may be particularly close, despite the small density.

A second piece of evidence implicating the importance of low order resonances is the blue shift of the TBA-d9 band origin, which can only be explained by resonant cou­plings. Almost all of the low order resonances in the TBA­d9 window fall below the acetylenic C-H stretch. The ig­nored off diagonal anharmonicity will most likely not change this. A blue push is therefore expected. Lastly, there are the other two features in the overtone spectrum of TSA-d9• If they are, as it assumed, Q branches of reso­nantly coupled states, then this shows that some back­ground states are well defined and have a state identity making it proper to consider their couplings separately. These states appear to have dramatically different IVR rates, which demonstrates the difficulty in the tier model for quantitative interpretation since coupling out of the first tier can show large fluctuations (the tier model argu­ments assume an "average" coupling at each tier). A fur­ther indication that without a knowledge of coupling strengths predictions can be hazardous is provided by the fact that the recently measured fast IVR rate for (CF3hC­C=C-H does not agree with the calculated small number of low order resonances.25 On the other hand, the force constants for this molecule are very different and therefore any comparison with the hydrogen containing molecules may be invalid.

The evidence that the low order resonances are rele­vant to the dynamics gives a rationalization for the lack of success of the existing theories on methyl rotors to predict the increase in IVR rate upon deuteration. In the present series of molecules most of the low order resonances do not involve rotor excitation. According to the tier model these interactions only occur later in time. If the rate is largely determined by the initial coupling out of the C-H stretch, our results should be mainly independent of the methyl rotor properties.

Going beyond simple correlations to a full quantitative model which would include coupling strengths is a formi­dable task, but is being attempted by Stuchebrukhov.26

Quantitative predictions require estimations of size of cu­bic and quartic anharmonic force constants for large mol­ecules, for which there is little spectroscopic guidance. There is evidence that anharmonic constants calculated from ab initio methods are of good accuracy.27 Hopefully coupling matrix elements for larger molecules will be avail­able in the near future and thus allow for quantitative mod­els for predicting IVR lifetimes.

Note added in proof. Stuchebrukhov26 has made pre­dictions of the IVR lifetimes of these molecules which are in excellent agreement with our experimental results dis­cussed above.

ACKNOWLEDGMENTS

We would like to thank Professors Jeffrey Schwartz and Robert Pascal for advice on the synthesis of the deu­terated compounds; Professor Crowder for performing the normal coordinate calculations of tert.-butylacetylene-d9;

Professor Charles Parmenter and Dr. Alexi Stuchebrukhov for making their results available prior to publication. This work was supported by the National Science Foundation.

J. Chern. Phys., Vol. 98, No.2, 15 January 1993

1122 Gambogi et al.: Methyl group deuteration

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3528 (1986). 18K. T~ Marshall and J. S. Hutchinson, J. Phys. Chern. 91, 3219 (1987). 19J. S. Hutchinson, J. Chern. Phys. 82, 22 (1985). 20G. A. Crowder, Vib. Spectr. 1, 317 (1991). 21G. A. Crowder (private communication). 22V. S. Nikitin, M. V. Polyakova, 1. 1. Baburina, A. V. Belyakov, E. T.

Bogoradovskii, and V. S. Zavgorodnii, Spectrochim. Acta 46A, 1669 (1990).

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The density of observed lines is 24 times the density of Al states as opposed to 27 times because one of the irreducible representations of the molecular symmetry group G 162, 14, is separably 6-fold degenerate and thus has a density of only three times the'density of Al as opposed to the 6-fold degeneracy for the other I representations.

25 J. E. Gambogi, K. K. Lehmann, B. H. Pate, G. Scoles, and X. Yang, J. Chern. Phys. 98, 1748 (1993).

26 A. Stuchebrukhov (private communication). 27K. K. Lehmann, J. Chern. Phys. 96, 1636 (1992).

J. Chern. Phys., Vol. 98, No.2, 15 January 1993