Influence of methyl group deuteration
vibrational energy relaxation
Joan E. Gambogi, Robert P. L’Esperance,
and Giacinto Stoles
on the rate of intramolecular
Kevin K. Lehmann, Brooks H. Pate,a)
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-dg and ( trimethylsilyl)acetylene-dg
have been measured using
optothermal detection of a collimated molecular beam. IVR lifetimes determined from the
homogeneously broadened lineshapes 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 lineshapes, 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.’ 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.’ 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) ,X-G&!-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
-.
“k2urrent address: NIST, Molecular Physics Division, Gaithersburg, MD
20899
1116
J. Chem. Phys. 98 (2), 15 January 1993
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.“”
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.g We can apply their analysis to our series of
trimethyl substituted molecules where there is a threefold,
relatively
high
barrier
(1434
cm-’
for
tert.butylacetylene). In the harmonic oscillator limit, the coupling between the torsions should scale as Aqn, where Ag,
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-“‘~ or
m -“‘4 . 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”
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
( CH3)3XC=CH
molecules should lead to a measurable
decrease in the IVR rate. To test this prediction, the high
(tert.resolution
spectra of 3,3-dimethylbutyne-dg
butylacetylene-dg) and (trimethylsilyl)acetylene-dg
were
measured. The relaxation ofthese molecules falls in the
statistical limit, so the IVR lifetime can be directly ob-
0021-9606f 93/021116-7$06.00
0 1993 American Institute of Physics
Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp
1117
Gambogi et al.: Methyl group deuteration
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
(pl?T) to pm-d3 showed the undeuterated compound to
have a lifetime of 3.4 ps, while the deuterated pFT had a
lifetime of 1.5 ps for the 3’5l vibrational band.” 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 Kw3ccwH
Q Branch
G
Ii
WAVENUMBER
(cm-‘)
b)
(CH~)G%CH
Q Branch
t.
3329.10
[4,4,4,4’, 4’, 4’, 4”, 4”, 4”-2 Hg]-3, 3-dimethyl- 1-butyne
( tert-Butylacetylene-dg )
was
synthesized
by
the
Negishi,
King,
and
TourI
from
method
of
[l, 1, 1,4,4,4,4’,4’,4’,4N,4”,4”-2
HI,]-3,3-dimethyl-butan2-one ( pinacolone-d,,) . Pinacolone-d12 was prepared
by standard methods13 from acetone-& (Cambridge
Ethynyl
tri-[2H3]-methyl
silane
Isotopes).
( trimethylsilylacetylene-dg ) was synthesized by the
method of Holmes and Sporikou’4 from ethynlymagnesium chloride (Aldrich) and chloro tri-[2H3]-methylsilane
(MSD isotopes).
Absorption spectra in the region of the v1 and 2v1 (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 ,um 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 Krf laser. In the acetylenic
C-H region this yields 25 mW 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 pm, 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.
3332.50
3332.20
3331.90
.e#‘.
.
WAVENUMBER
I
3329.70
3329.40
@d)
FIG. 1. The Q branches of the acetylenic C-H stretch fundamental for
both (CD,),CC=CH
(upper) and (CH3)$C=CH
(lower) are plotted.
The two Q branch features are fit to a single Lorentzian and the residuals
of the tit are shown below each spectrum.
RESULTS
The Q-branch of the fundamental acetylenic C-H
stretch for (CD,)&!-C=C-H
(TBA-d,) and (CH,),CC=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. 1 (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-dg the homogeneous linewidth
dominates the spectrum. We also point out the presence of
a 2.8 cm-’ blueshift of the band origin upon deuteration
(from 3329.4 cm-’ for TBA to 3332.2 cm-’ for TBA-d,).
Deuteration must result in a lowering of the vibrational
J. Chem. Phys., Vol. 98, No. 2, 15 January 1993
Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp
1118
Gambogi et a/.: Methyl group deuteration
a) KTJah%%CH,
250 -
;;‘
200
s
-
150-
zz
R(5)
1
-
_.!zi
3
loo-
i
50-
O1
‘6
2
3
4
5
7
8~-
9
,
10
3313.06
3313.10
WAVENUMBER
J’
(cm-‘)
FIG. 2. Linewidths (fwhm) as a function of the upper state rotational
quantum number, J, for the fundamental of (CD,),SiC=CH.
harmonic frequencies (i.e., a redshift) and so this suggests
a resonant interaction strong enough to shift the band origin a few cm-‘.
The overtone region of TBA-d, 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)$i-CEC-H
(TSA-ds)
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,’ the linewidths appear to
narrow slightly at higher Ss. 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 y1 with a doorway state that detunes
from near resonance with increasing J.
The spectra of the R (5) lines of the y1 fundamental of
TSA-ds 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- ’) upon deuteration.
In the overtone region of TSA-d, the Q branch was
observed at 6520 cm-’ (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-
b) (CH%ii(=cH.
3313.20
RQ
3313.24
WAVFNUMBRR
(cd)
FIG. 3. R( 5) of the fundamental acetylenic C-H stretch of
(CD,),SiC!=CH
(upper) and (CH3)sSiC=CH (lower) and their fits to
a single Lorentzian.
ethyl substituted compounds measured previously,5 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
65 19.92 cm-’ 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 specTABLE I. Measured spectroscopic constants (cm-‘)
tal of (CDx)&C-CH.a
2,
B’
X11
for the fundamen-
3 312.412
0.057 02(66)
223(32)
0.057 176(30)
-52.4
aReported uncertainties in the fit to the vibrational levels are 2~.
J. Chem. Phys., Vol. 98, No. 2, 15 January 1993
Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp
a/.: Methyl group deuteration
Gambogi et
a) (CbkSicCH,
Q Branch
A
I
6519.70
6519.90
v=2
I
6520.10
WAVENUMBER
6520.30
(cm-l)
b) (CHMiGCH,
Q Branch
v=2
2
6520.00
6520.20
6520.40
WAVBNUMBER
6520.60
@m-‘1
FIG. 4. The Q branches of the acetylenic C-H stretch overtone for
(CD,),SiC=CH
(upper) and (CH3)$iC=CH
(lower) are plotted.
Only the high energy half of the Q branch of (CDs)$iC=CH
is fit to a
Lorentzian. The Q branch of (CH,)$iC=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= 1 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.7 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-’ in the carbonyl overtone region), IVR alone could not be responsible for the observed
TABLE
II. IVR lifetimes obtained from the Lorentzian line shapes.
Lifetime (psec)
Molecule
v=l
(CH, ) $-C&-H5
(CD,) 3C-C=C-H
(CHs),Si-CkC-H5
(CD,) ,Si-C=C-H
200
40
2cwo
850
v=2
110
<20
4oc0
140
1119
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 several simple alcohols8 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
play a role.
To explain our results the theory of Moss et aZ., 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.g 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-CH3 bonds are shorter than the SiCH, 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
explanation of the methyl rotor’effect ‘based on dividing-the
molecule’s multidimensional phase space into two subsystems.” 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.‘5-1g Sibert, Reinhardt, and Hynes have been able to
describe quite well the overtone spectrum of benzene using
a tier model. l5 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. Chem. Phys., Vol. 98, No. 2, 15 January 1993
Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp
Gambogi et a/.: Methyl group deuteration
1120
spectrum of (CF,),CH, using the idea that efficient coupling between the stretching and bending of the C-H group
occurs predominantly through low order terms in the expansion of the potential.r6 This type of analysis has also
been used by Hutchinson and co-workers in calculating the
overtone spectra of simple hydrocarbons,t7 propargyl alcohol’* and cyanoacteylene.”
In Table III the fundamental frequencies for the four
molecules discussed in this paper are listed. Neither IR nor
Raman spectrum of TBA-d9 has been reported; the fundamentals for this molecule (listed in Table III) were calculated by Crowder, using force constants adjusted to fit the
observed fundamentals of TBA.20921The fundamental frequencies of TSA-d9 were obtained from those of TSA-dr,
with minor adjustments.22 The low frequency torsional
modes have been reported only for TBA; the torsional
modes for the others are estimated from similar molecules.23 Density of states values were calculated by a direct
count for the fundamental and first overtone, treating all
modes as harmonic vibrations. Calculations carried out for
the hydrogen compounds showed that treating the torsional modes as uncoupled hindered rotors increased the
density of A1 symmetry vibrational states by a factor of 1.7.
A lifting of the torsional degeneracy is predicted to increase the density of observed lines by as much as a factor
of 24.24 Table IV summarizes the total density of states
calculations, the density of states with the torsional modes
excluded, and the number of low order resonances for each
molecule in the harmonic approximation. It is evident from
the calculated density of states without the torsional modes
that, at least for TBA and TBA-L-Z,, the number of background states is too sparse to support “statistical” IVR.
Some energy must flow into the torsional modes from the
initially excited C-H stretch.
The low order resonances, listed in Table IV, are for a
100 cm-’ window around the acetylenic stretch fundamen-
TABLE III. Normal modes of the trimethyl substituted acetylenes.
TBA=’ TBA-ds=’ TSA== TSA-d,==
Al
2977
2889
2107
1475
1363
1248
~691
885
382
3332”
2227
2081
2116
1051
1028
1210
645
740
319
3312’
2966
2900
2037
1420
1265
654
557
860
218
3312a
2220
2120
2037b
1060
995
530
515
745
185
2978
2976
2889
1475
1456
1393
1205
1032
930
634
542
362
182
2229
2221
2020
1054
1050
1016
1189
803
755
632
493
308
181
2966
2966
2900
1420
1420
1255
700
845
765
680
236
132
350
2220
2220
2120
1030
1030
1003
562
730
583
680b
202
115
322
2974
1459
995
2218
1048
751
2967
1410
739
2215
1034
542
262
202
196
144
190
190
135
135
v-C-H
GH3
GH3
V&EC
W-H
&C-H
v&C
v&cd2
PC-H
G-C,
E
47P3
4$-=3
VP,
bsCH3
WH3
WH3
V0SX-C
p&H3
P&H,
6=C-H
&.s--c3
px-c=c
8X-czc
A2
u&H3
&7sCH3
pCH3
Torsions (estimated from.Ref. 23)
E
A2
aTaken from our spectra.
bEstimated.
TABLE IV. Density of states and low order resonances.
Fundamental C-H stretch
(CH3)3C-C~GH
Total density of
4.9x102
A, states (/cm-‘)
Density of A, states without torsional
50.0
Modes (/cm-‘)
24.0
3rd order states=
293.0
4th order states
1819.0
5th order states
IVR Rate (s-r)
5.0x 109
(CH,),C-C=C-H
Total Density of
A, States (/cm-‘)
3rd order states
4th order states
5th order states
IVR rate (s-‘)
6.2 x 10’
24.0
232.0
1805.0
9.1x109
(CD3),C-C=C-H
(CH,),Si-C=C-H
1.7x 102
7.8X lo=
34.0
15.0
373.0
250.0
3623.0
1415.0
25.0~ lo9
0.5 x IO9
Overtone C-H stretch
(CD,) 3C-C=CH
(CH3)3Si-C=C-H
7.6x lo6
2.9 x 10’
30.0
332.0
3189.0
> 50.0x 109
aTotal number of states in a 100 cm-’ region around the GH
24.0
152.0
2021.0
0.25 X lo9
(CD,),%-C=C-H
.~
_
4.1x103
6.0
540.0
2932.0
1.2x 109
(CD3)$+C=C-H
6.0x lo8
~~
51.0
274.0
3408.0
7.1x109
stretch.
J. Chem. Phys., Vol. 98, No. 2, 15 January 1993
Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp
Gambogi et al.: Methyl group deuteration
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 yl, 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, v1 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.
1121
A second piece of evidence implicating the importance
of low order resonances is the blue shift of the TBA-d,
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 CH 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-d,. 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 (CF,) 3CC=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 proox 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. Chem. Phys., Vol. 98, No. 2, 15 January 1993
Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp
1122
Gambogi et al.: Methyl group deuteration
’ (a) A. M. deSouza, D. Kaur, and D. S. Perry, J. Chem. Phys. 88,4569
(1988); (b) A. McIlroy and D. J. Nesbitt, ibid. 92,2229 (1990); (c) B.
H. Pate, K. K. Lehmann, and G. Stoles, ibid. 95, 3891 ( 1991).
‘(a) C. S. Parmenter, .I. Phys. Chem. 86, 1735 (1982); (b) Faraday
Discuss. Chem. Sot. 75, 7 (1983); (c) R. E. Smalley, Ann. Rev. Phys.
Chem. 34, 129 (1983).
3 (a) H. R. Dubal and M. Quack, J. Chem. Phys. 81, 3779 (1984); (b)
K. K. Lehmann and S. L. Coy, J. Chem. Sot., Faraday Trans. 2 84,
1389 (1988).
4A. Sinha, M. C. Hsiao, and F. F. Crim, J. Chkm. Phys. 92,6333 (1990).
‘E. R. Th. Kerstel, K. K. Lehmann, T. F. Mentel, B. H. Pate, and G.
Stoles, J. Phys. Chem. 95, 8282 (1991).
‘C. S. Parmenter and B. M. Stone, J. Chem. Phys. 84, 4710 (1986).
‘V. A. Walters, S. D. Colson, D. L. Snavely, K. B. Wiberg, and B. M.
Jamison, J. Phys. Chem. 89, 3857 (1985).
8J. M. Jasinski, Chem. Phys. Lett. 109, 462 (1984).
9D. B. Moss, C. S. Parmenter, and G. E. Ewing, J. Chem. Phys. 86, 51
(1987).
“C. C. Martens and W. P. Reinhardt, J. Chem. Phys. 93, 5621 (1990).
‘ID. B. Moss, C. S. Parmenter, T. A. Peterson, C. J. Pursell, and 2. Zhao,
to appear in VIth International Symposium on Ultrafast Processes in
Spectroscopy, Bayreuth Germany (IOP, Bristol, United Kingdom)
1992.
12E-i. Negishi, A. 0. King, and J. M. Tour, Org. Syn. 64, 44 (1985).
I3 Vogel’s Elementaty Practical Organic Chemistry I, Preparations, edited
by B. V. Smith and N. M. Waldron (Longman, London, New York,
1980), pp. 214-215.
14A. B. Holmes and C. N. Sporikou, Org. Syn. 65, 61 (1987).
“E. L..Sibert III, W. P. Reinhardt, and J. T. Hynes, J. Chem. Phys. 81,
1115 (1984).
16J. E. Baggott, M.-C., Chuang, and R. N. Zare, H. R. Dubal, and M.
Quack, J. Chem. Phys. 82, 1186 ( 1985).
“J S Hutchinson, J. T. Hynes, and W. P. Reinhardt, J. Phys. Chem. 90,
3528 (1986).
“K. Ty Marshall and I. S. Hutchinson, J. Phys. Chem. 91, 3219 (1987).
I9J. S. Hutchinson, J. Chem. Phys. 82, 22 (1985).
“G. A. Crowder, Vib. Spectr. 1, 317 (1991).
” G. A. Crowder (private communication).
“V. S. Nikitin, M. V. Polyakova, I. I. Baburina, A. V. Belyakov, E. T.
Bogoradovskii, and V. S. Zavgorodnii, Spectrochim. Acta 46A, 1669
(1990).
23J. R. Durig, S. M. Craven, and J. Bragin, J. Chem. Phys. 53, 38 (1970).
“K. K. Lehmann and B. H. Pate, J. Mol. Spectrosc. 144, 443 (1990).
The density of observed lines is- 24 times the density of A, 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 A, as opposed to the
6-fold degeneracy for the other I representations.
25J. E. Gambogi, K. K. Lehmann, B. H. Pate, G. Stoles, and X. Yang, J.
Chem. Phys. 98, 1748 (1993).
26A. Stuchebrukhov (private communication).
“K. K. Lehmann, J. Chem. Phys. 96, 1636 (1992).
J. Chem. Phys., Vol. 98, No. 2, 15 January 1993
Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp