Deuterium isotope effects on the CH stretching overtone spectrum of toluene-α-d1

Article abstract of DOI:10.1021/jp981411t

The room-temperature vapor phase overtone spectrum of toluene-α-d₁ has been recorded in the CH stretching regions corresponding to Δυ_CH = 2-7. The vibrational overtone spectra are recorded by conventional near-infrared spectroscopy a

Full text of DOI:10.1021/jp981411t

J. Phys. Chem. A 1998, 102, 6095-6100
6095
Deuterium Isotope Effects on the CH Stretching Overtone Spectrum of Toluene-r-d1
Henrik G. Kjaergaard*
Department of Chemistry, UniVersity of Otago, P.O. Box 56, Dunedin, New Zealand
David M. Turnbull and Bryan R. Henry*
Department of Chemistry and Biochemistry, UniVersity of Guelph, Guelph, Ontario N1G 2W1, Canada
ReceiVed: March 6, 1998; In Final Form: May 14, 1998
The room-temperature vapor phase overtone spectrum of toluene-R-d1 has been recorded in the CH stretching
regions corresponding to ∆VCH ) 2-7. The vibrational overtone spectra are recorded by conventional near-
infrared spectroscopy and by intracavity titanium:sapphire and dye laser photoacoustic spectroscopy. Absolute
oscillator strengths are obtained from the conventional spectra, and relative oscillator strengths within a given
overtone, from both the conventional and photoacoustic spectra. The aryl region of the spectrum is nearly
identical to the aryl region of the spectrum of toluene-d0 and can be understood on the basis of two
nonequivalent aryl local modes. The methyl band differs markedly from the methyl band in toluene-d0 in
relative intensity, in line width, and in structure. We use an anharmonic oscillator local mode model and an
ab initio dipole moment function to calculate oscillator strengths for the aryl and methyl transitions. As was
the case for toluene-d0, these simple calculations show good agreement between observed and calculated
intensities both in absolute total intensities and for relative intensities between the two aryl groups and between
the aryl and methyl groups. We explain the differences between the methyl bands in the -R-d1 and -d0 spectra
on the basis of our intensity calculations and on the basis of coupling between CH and CD stretching vibrations
and methyl torsions.
Introduction
dependence of the dipole moment function must also be
incorporated. We have used such a model to account for the
In a previous paper,1 we have reported the overtone spectra
of toluene-d0 and toluene-d8 in the regions corresponding to
∆VCH ) 2-7 and ∆VCD ) 2-6. The aryl regions of the spectra
could be interpreted straightforwardly within the local mode
model.2,3 One peak was observed corresponding to aryl CH
bonds at the 2- and 6- positions (ortho) and one peak to the
aryl CH bonds at the 3-, 4-, and 5- positions (meta and para).
The assignment was in accord with ab initio calculations of the
relative bond lengths4 and with our calculations of relative
intensities.1 The methyl band has a much more complex
structure which we interpreted on the basis of interaction
between methyl CH stretching and methyl torsion.
We measured oscillator strengths of the two aryl peaks and
of the methyl band. We used an extension of our previous
model, which was based on the HCAO local mode approach5-8
and ab initio dipole moment functions,9-12 to calculate oscillator
strengths for the methyl and aryl transitions. The total CH
stretching intensity of the methyl band was obtained with a
simplified model which averaged over methyl torsion.
Toluene has a very low 6-fold barrier to methyl torsion.13
For molecules with a high barrier like propane and dimethyl
ether, the methyl overtone region consists of two peaks, one
associated with two out-of-plane CH bonds and one for the in-
plane CH bond of the methyl group.14,15 The resolution of these
peaks is in accord with their difference in bond lengths. Thus,
the torsion of the methyl group affects the CH bond lengths. It
will also have an effect on the dipole moment function for each
of the CH bonds. A full analysis of the methyl profile requires
consideration of coupling between stretching vibrations and
between the stretching vibrations and torsion. The torsional
methyl profiles in the overtone spectrum of 2,6-difluorotolu-
ene.16
In our work on toluene,1 we adopted a simpler approach. We
were interested in calculating the total methyl intensity and
comparing it to the calculated aryl intensity and to our
observations. We used a simple one-dimensional model that
neglected the harmonic coupling between the methyl CH bonds.
The variation of the dipole moment function with methyl torsion
was approximated by a simple functional form. Thus, we were
able to obtain the total intensity of the methyl group through
integration from 0 (in plane) to π/2 and normalization over the
torsional angle. Our calculated absolute intensities are in good
agreement with the observed CH and CD stretching overtone
intensities. Moreover comparison of relative intensities between
the two aryl transitions and between the aryl and methyl
transitions shows very good agreement between observation and
experiment.
An interesting feature of our previous work on toluene-d8
involved the appearance of impurity peaks due to the spectra
of molecules in which all but one hydrogen had been replaced
by deuterium. Although these molecules were present in very
low concentration, and the resultant overtone spectra had a low
signal-to-noise ratio, it appeared that the methyl spectral profile
was significantly altered. In other words, the methyl regions
of the overtone spectrum of a CHD2 group differed markedly
from the corresponding spectrum of a CH3 group.
In this work we investigate the effect of deuterium substitution
through a study of the overtone spectrum of toluene-R-d1, where
R refers to the methyl position. We again use our simple model
S1089-5639(98)01411-X CCC: $15.00 © 1998 American Chemical Society
Published on Web 07/07/1998

6096 J. Phys. Chem. A, Vol. 102, No. 30, 1998
Kjaergaard et al.
and average over the methyl group to calculate total and relative
intensities and compare the results to our measured values. We
make a detailed comparison between the overtone spectra of
toluene-d0 and toluene-R-d1, both for the aryl regions and for
the methyl regions. We use our intensity calculations and
coupling considerations to explain qualitatively the differences
between the methyl regions of the overtone spectra for these
two molecules.
regions ∆VCH )3-7, the aryl band could be deconvoluted into
two peaks. However deconvolution of the broad methyl band
leads to much larger uncertainties. From two to five peaks were
used in the methyl deconvolution, and the total methyl band
intensity is found as the sum of the areas of these deconvoluted
peaks. We estimate the error in the methyl area to be less than
20%, where a large part of the error arises from uncertainty in
the baseline.
Experimental Section
Theory and Calculations
Toluene-R-d1 was prepared by a method similar to that
described by Trevoy and Brown.17 A 5 g amount of lithium
aluminum deuteride (Aldrich, 98%) was added to 75 mL of
dimethyl ether under nitrogen. A 15 mL volume of benzyl
chloride (Aldrich) was added dropwise and the mixture was
refluxed for 3 h. The reaction was quenched with 5 mL of
D2O, 5 mL of 15% NaOH in D2O, and 15 mL of D2O. The
toluene-R-d1 was isolated through distillation, drying over 3 Å
molecular sieves, and several pump-freeze-pump-thaw cycles
on the vacuum line. The product was characterized with NMR,
near-IR, and GC/MS. The near-IR spectrum at ∆VCH ) 6
demonstrated the absence of dimethyl ether, as did GC/MS and
NMR. Both GC/MS and NMR demonstrated the absence of
benzyl chloride. Integration of the aryl and methyl peaks in
the NMR yielded an aryl:methyl ratio of 2.52, in agreement
with the expected ratio of 2.5 in toluene-R-d1. Our estimated
error in integration is ∼5%, and on this basis we believe the
purity of toluene-R-d1 to be >95%.
The theoretical models which we have used in the present
paper are similar to the models we used in our previous work
on toluene-d0.1 Thus only a brief outline is given here with
reference to recent papers for more details of the vibrational
model and the procedures used to obtain the dipole moment
functions.9,11,12 Within the Born-Oppenheimer approximation
the ab initio calculations for toluene-R-d1 and toluene-d0 will
be identical. Thus the previously optimized geometry and dipole
moment functions can be used for the present work on toluene-
R-d1.
The oscillator strength f of a transition from the ground
vibrational state g to an excited state e is given by18
2
feg ) 4.702 × 10-7[cm D-2]ν˜eg|bµeg|
(2)
where ν˜eg is the vibrational wavenumber of the transition and
bµeg is the transition dipole moment matrix element in Debye
(D).
The room-temperature vapor phase overtone spectrum of
toluene-R-d1 was recorded in the ∆VCH ) 2-4 regions by
conventional absorption spectroscopy and in the ∆VCH ) 4-7
regions by intracavity laser photoacoustic spectroscopy (ICL-
PAS). The conventional spectra were recorded with a Cary 5e
and a variable path length cell (see our previous work for
details1). The experimental absolute oscillator strength f of an
absorption band can be determined from these conventional
spectra and the equation18
Vibrational Model. The aryl CH bonds change very little
upon rotation of the methyl group.1 The three CHm,p bonds
(meta and para positions) have almost the same bond length as
have the two CHo bonds (ortho position). Thus we expect two
peaks in the aryl region of the overtone spectra of toluene-d0
and -R-d1. The coupling between the aryl CH oscillators will
be negligible as the aryl CH bonds are not attached to the same
carbon atom.12 We treat the aryl CH oscillators as five isolated
CH oscillators with one set of local mode parameters for the
two CHo oscillators and one set for the three CHm,p oscillators.
We use the local mode theory of anharmonic oscillators to
obtain vibrational wave functions and energies for each of the
CH oscillators. The Hamiltonian of an isolated CH oscillator
that is described as a Morse oscillator can be written as
T
pl
f ) 2.6935 × 10-9[K-1 Torr m cm]
A(ν˜) dν˜ (1)
∫
where T is the temperature, p is the pressure, l is the path length,
A is the absorbance, and ν˜ is the frequency in cm-1
.
Our version of ICL-PAS consists of an argon ion pumped
titanium:sapphire solid-state laser (∆VCH ) 4 and 5) or dye laser
(∆VCH ) 6 and 7), and details can be found in our previous
work.1,19,20 The spectrum in the ∆VCH ) 6 region was recorded
with the dye R6G. However the dye DCM gave a better signal-
to-noise ratio in the methyl region of the spectrum, and the DCM
spectrum was used in a comparison of the detailed methyl band
shape. The spectrum in region of ∆VCH )7 was recorded with
the dye Coumarin 6, and a small amount of argon buffer gas
(100 Torr) was added to the cell here and at ∆VCH ) 4 to
improve the photoacoustic signal. The laser power in the methyl
region at ∆VCH )7 is very low. We have used the aryl peak
positions in our analysis (vide infra); however, both the methyl
band shape and the comparison of methyl and aryl intensities
are subject to large uncertainties and have not been used.
Just as in our previous work,1 the overtone spectra were
decomposed into component peaks with a deconvolution
program within Spectra Calc.21 The spectra were deconvoluted
with a number of Lorentzian peaks and a linear baseline.
Uncertainty in the peak positions and areas obtained from the
aryl region of the spectrum are typically (5 cm-1 for peak
positions and less than 10% for relative intensities. In the
(H - E|0 j)/hc ) Vjω˜ j - (Vj2 + Vj)ω˜ jxj
(3)
where E|0 j is the energy of the vibrational ground state and ω˜ j
and ω˜ jxj are the local mode frequency and anharmonicity of
the CHj oscillator. The eigenstates of the Hamiltonian are
denoted by |Vj j, where Vj is the vibrational quantum number.
These eigenstates are thus Morse oscillator wave functions.
We have used the same axis system as in our previous work.1
The z-axis is along the CC bond around which the methyl group
rotates, the x-axis in the plane of the ring, and the y-axis
perpendicular to the plane. The torsional angle, θ, is defined
as the angle between one R-CH bond and the plane of the ring.
The calculated variation in the methyl CH bond length with
methyl torsion is about 3 mÅ at the HF/6-311+G(d,p) level.1
The parallel (||) CH bond has an ab initio calculated shorter
CH bond length, higher local mode frequency, and lower local
mode anharmonicity than the perpendicular ( ) CH bond. The
change in unscaled calculated frequency and anharmonicity is
about 40 and 1 cm-1 at the HF/6-311+G(d,p) level. The
intensity of a transition from the ground state to a vibrationally
excited state of a typical CH stretching oscillator changes less

CH Stretching Overtone Spectrum of Toluene-R-d1
J. Phys. Chem. A, Vol. 102, No. 30, 1998 6097
TABLE 1: Observed and Calculated Relative Intensities,
Observed Frequencies, and Peak Assignments for the CH
Stretching Overtone Spectra of Vapor Phase Toluene-r-d1
and Toluene-d0
TABLE 2: Local Mode Frequency and Anharmonicity of
a
the CH Stretching Modes in Vapor Phase Toluene-r-d1 and
a
Toluene-d0
toluene-R-d1
ω˜ b/cm-1
toluene-d0
toluene-R-d1
toluene-d0
ω˜ xb/cm-1
ω˜ c/cm-1
ω˜ xc/cm-1
b
c
d
e
e
ν˜a/cm-1
fobs
fcalc
fcalc
assignt
fobs
fcalc
CHo
3146 ( 2
3169 ( 3
3066 ( 7
3084 ( 9
3075
58.2 ( 0.3
58.9 ( 0.4
63.8 ( 1.1
61.5 ( 1.5
62.6
3144 ( 2
3170 ( 2
3053 ( 6
3068 ( 6
3060
57.9 ( 0.3
59.1 ( 0.4
62.6 ( 0.9
58.7 ( 0.9
60.6
(1.1)
(1.0)
(1.3)
1.10 1.09
1.00 1.00
1.96 1.97
|3
(1.4)
(1.0)
(1.4)
1.64
1. 0
1.97
CHm,p
R-CH
R-CH
R-CHav
r
8 740
8 806
|3
o
|3
m,p
0.89 (1.1) 1.06 1.03
1.0 (1.0)
1.5 (1.6)
|4
1.2 (1.4) 1.55
1.0 (1.0) 1.0
1.5 (2.1) 1.96
R
a Uncertainties are one standard deviation. b From a fit of the local
11 424
11 496
1.00 1.00
1.94 1.96
|4
o
mode frequencies in the ∆VCH ) 3-7 regions. c From ref 1.
|4
m,p
1.4
1.0
1.9
1.06 1.01
1.00 1.00
1.92 1.95
|5
1.6
1.0
1.8
1.51
1.0
1.95
R
functions defined according to eq 4. The low energy aryl peak
is calculated as the sum of two ortho CH oscillators (positions
2 and 6).
We have shown previously that the variation of the dipole
moment function of the methyl CH bond can to a good
approximation be written as1
13 979
14 075
|5
o
|5
m,p
0.8
1.0
2.1
1.11 1.03
1.00 1.00
1.90 1.95
|6
1.4
1.0
1.9
1.55
1.0
1.95
R
16 430
16 543
|6
0
|6
m,p
1.21 1.10
1.00 1.00
1.89 1.95
|7
1.6
1.0
2.5
1.65
1.0
1.95
R
18 766
18 895
1.0
1.6
|7
o
bµx ) a cos(θ)qi
(5)
(6)
(7)
|7
m,p
∑
i
a The methyl band is broad and complex, and no one frequency is
assigned to it. b Relative intensities within an overtone region; numbers
in parentheses are from Cary spectra. c Local mode calculations with
dipole moment from ref 1 and local mode parameters from Table 2.
d Calculated relative intensities from ref 1 except that the intensity for
i
bµy ) b sin(θ)qi
∑
i
i
|i is given as two-thirds the value for toluene-d0 in ref 1. e From ref
bµz ) (c + d cos(2θ))qi
a
∑
i
i
1.
i
than 10% with a 5% change in anharmonicity. Thus it seems
reasonable, for intensity purposes, to neglect the variation in
Morse potential with the methyl group rotation. We have also
neglected the coupling between the methyl CH oscillators. This
will have an effect in the ∆VCH ) 2 region where local mode
combination states can carry significant intensity that is obtained
both from vibrational coupling and mixed dipole moment terms
(vide infra).15 However, at higher overtones the local mode
combination states carry insignificant intensity. This approach
worked well for our recent toluene-d0 calculations. Thus we
treat the methyl group in toluene-R-d1 as two noncoupled CH
oscillators with an average Morse potential.
The coefficients a, b, c, and d are defined by the following:
ai ) bµix(|) bi ) bµiy( ) ci ) 1/2(bµiz(|) + bµiz( ))
di ) 1/2(bµiz(|) - bµiz( ))
where bµi(|) are the dipole expansion coefficients according to
eq 4 for a methyl CH bond in the parallel position and similarly
bµi( ) are the coefficients for a methyl CH bond in the
perpendicular position. Thus it is only necessary to calculate
two dipole moment grids, one each for the || and conformers,
to describe the dipole moment function of the rotating methyl
CH oscillator. The HF/6-311+G(d,p) calculated dipole moment
coefficients are given in Table 1 of ref 1.
The total intensity of a methyl CH oscillator can be found
by averaging over the methyl torsion. We do this by a simple
integration and normalization of the dipole components. Inte-
gration from 0 to π/2 and normalization (division by ∫π0/2 dθ )
π/2) of the four terms in eqs 5-7 gives 2/π for cos(θ), 2/π for
sin(θ), 1 for 1, and 0 for cos(2θ). (Our previous paper had a
typographical error in these integrals, but the correct values were
used in our calculations.1) To calculate the intensity of a rotating
methyl CH oscillator, the three Cartesian components, including
the integration and normalization factors, must be squared and
then summed and substituted into eq 2. We calculate the total
intensity of the partially deuterated methyl group CH2D as the
sum of two rotating average CH oscillators.
Dipole Moment Function. For an isolated CH oscillator,
we express the dipole moment function as a series expansion
in the internal CH displacement coordinate, q,
bµ(q) ) bµ qi
(4)
∑
i
i
where bµi is 1/i! times the ith order derivative of the dipole
moment function with respect to q. We limit the expansion in
eq 4 to fourth-order terms.11 The coefficients are determined
from ab initio calculated one-dimensional grids of the dipole
moment function as a function of q with standard numerical
differential techniques.22 To ensure a reasonable mapping and
to limit round off errors, seven points with a maximum
displacement of (0.3 Å in steps of 0.1 Å are calculated.11 All
grid points and optimized geometries are calculated at the
Hartree-Fock (HF) level with a 6-311+G(d,p) basis set, with
Gaussian 92.23 Previous work has suggested that this method
is adequate for absolute overtone intensities.24,25
Average dipole coefficients for the aryl CHo, CHm, and CHp
are given in Table 1 of ref 1. There is only a small variation
in dipole coefficients between the two CHo bonds. We have
calculated the intensity of the high energy aryl peak as the sum
of three CH oscillators (the 3-, 4-, and 5- positions) with the
local mode parameters from Table 2 and dipole moment
Results and Discussion
The room-temperature vapor phase overtone spectrum of
toluene-R-d1 in the CH stretching regions corresponding to ∆VCH
) 2-6 is shown in Figures 1-5. The figures also show the
overtone spectrum of toluene-d0 from our previous work1 and
is presented here for comparison. In the toluene-d0 spectrum,
the intensity of the high energy aryl peak maximum has been
scaled to match the corresponding peak in the toluene-R-d1
spectrum.

6098 J. Phys. Chem. A, Vol. 102, No. 30, 1998
Kjaergaard et al.
Figure 3. Room-temperature vapor phase overtone spectrum of
toluene-R-d1 (solid line) in the ∆VCH ) 4 region. The spectrum was
measured by ICL-PAS with a sample pressure of 17 Torr of toluene-
R-d1 and 100 Torr of argon buffer gas. The scaled spectrum of toluene-
d0 (dotted line) is taken from ref 1 (see text).
Figure 1. Room-temperature vapor phase overtone spectrum of
toluene-R-d1 (solid line) in the ∆VCH ) 2 region measured with a path
length of 11.25 m and a pressure of 17 Torr. The scaled spectrum of
toluene-d0 (dotted line) is taken from ref 1 (see text).
Figure 2. Room-temperature vapor phase overtone spectrum of
toluene-R-d1 (solid line) in the ∆VCH ) 3 region measured with a path
length of 11.25 m and a pressure of 17 Torr. The scaled spectrum of
toluene-d0 (dotted line) is taken from ref 1 (see text).
Figure 4. Room-temperature vapor phase overtone spectrum of the
toluene-R-d1 (solid line) in the ∆VCH ) 5 region. The spectrum was
measured by ICL-PAS with a sample pressure of 16 Torr. The scaled
spectrum of toluene-d0 (dotted line) is taken from ref 1 (see text).
The aryl regions of the toluene-R-d1 spectrum have been
decomposed into three peaks at ∆VCH ) 2 and two peaks at
∆VCH ) 3-7. In Table 1 we give the observed frequencies of
the two aryl peaks (∆VCH ) 3-7) as well as the relative areas
of the two aryl peaks and the methyl band.
conventional spectra (∆VCH ) 2-4). The total observed
overtone intensities in toluene-d0 are also given for comparison.1
The total overtone intensities calculated with the HF/6-311+G-
(d,p) dipole moment function are in good agreement with the
observed intensities. In Table 4 we compare the line widths of
the entire methyl and aryl bands for the different overtones in
the spectrum of toluene-R-d1. We also present the results for
The observed frequencies ν˜ of the local mode peaks have
been fitted to a two-parameter Morse oscillator expression
ν˜/V ) ω˜ - (V + 1)ω˜ x
(8)
1
toluene-d0 for comparison.
Perhaps the most striking feature in comparing the overtone
spectrum of toluene-R-d1 and toluene-d0 is that while the aryl
region of the spectrum is virtually identical, the methyl region
of the spectrum is significantly different. Inspection of Figures
1-5 shows identical aryl regions for ∆VCH ) 4-6 in Figures
3-5. In the construction of these figures, only the intensity of
the higher energy aryl peak was matched. No change was then
made in the relative intensity of the other peaks in the toluene-
d0 spectrum, nor was any attempt made to shift the wavenumber
position of the toluene-d0 spectrum.
to obtain values for the local mode frequency ω˜ and anharmo-
nicity ω˜ x for the different CH stretching oscillators. For the
aryl regions the procedure is straightforward and the local mode
parameters are given in Table 2. The very small uncertainties
in the aryl parameters indicate that the two-parameter fit is
excellent. For the CH stretching methyl region, we have fitted
peaks from the deconvolution that correspond to high- and low-
energy maxima in the broad unresolved methyl band. These
peaks do not represent pure local modes. However they do fit
reasonably well to eq 8, and we take the methyl CH oscillator
parameters to be the average of these two sets of values.
The observed and calculated absolute total oscillator strengths
are compared in Table 3 for those regions where we have
There are small changes in the low-energy side of the aryl
peak at ∆VCH ) 2 (Figure 1). These arise not from the aryl
peaks themselves but from differences in the methyl local mode

CH Stretching Overtone Spectrum of Toluene-R-d1
J. Phys. Chem. A, Vol. 102, No. 30, 1998 6099
TABLE 5: Observed and Calculated Aryl to Methyl
Intensity Ratios in the CH Stretching Overtone Spectra of
Vapor Phase Toluene-r-d1 and -d0
toluene-R-d1
obsa
(2.1)
2.8(2.3)
2.1
toluene-d0
obsc
(1.7)
2.1(2.1)
1.7
V
calcb
calcc
3
4
5
6
7
2.7
2.8
2.75
2.6
1.80
1.92
1.96
1.90
1.79
3.8
2.1
2.2
a Ratios in parentheses are from Cary spectra. b Local mode calcula-
tion from the parameters of Table 2 and the dipole moment function
of ref 1. c From ref 1.
toluene-d0.1 Moreover the aryl bandwidths in Table 4 are the
same as the toluene-d0 aryl bandwidths, with the exception of
∆VCH ) 7 where the uncertainty is much larger. Finally the
observed relative intensities of the ortho and meta/para peaks,
1:x, as given in Table 1, compare almost exactly to the values
for toluene-d0 (x ) 1.3, 1.5, 1.8, and 1.9 for ∆VCH ) 3-6).1
Any differences here probably relate to uncertainties in our
deconvolution procedure. In our calculations, we assume the
aryl vibrations are not coupled to the methyl vibrations, and
this approximation appears to be correct given the similarity in
the aryl overtones in toluene-R-d1 and toluene-d0.
Figure 5. Room-temperature vapor phase overtone spectrum of
toluene-R-d1 (solid line) in the ∆VCH ) 6 region. The spectrum was
measured by ICL-PAS with a sample pressure of 20 Torr. The scaled
spectrum of toluene-d0 (dotted line) is taken from ref 1 (see text).
TABLE 3: Observed and Calculated Total Oscillator
Strengths of the CH Stretching Regions in Vapor Phase
Toluene-r-d1
V
obs (toluene-R-d1) calca (toluene-R-d1) obsb (toluene-R-d0)
By contrast the methyl region of the overtone spectrum
changes significantly between the toluene-R-d1 and toluene-d0
spectra. The most obvious change is a decrease in the relative
intensity of the methyl as compared to the aryl spectral regions
from toluene-d0 to toluene-R-d1. The observed relative intensi-
ties for the methyl group in Table 1 are approximately two-
thirds of the values from the toluene-d0 spectrum. The decrease
in intensity also shows up in the absolute total oscillator
strengths given in Table 3. The calculated intensities change
very slightly because of the change in local mode parameters.
Apart from this small change due to the changed parameters,
on the basis of the Born-Oppenheimer approximation, we
expect the only change in intensity to come from a reduction
of one-third in the methyl intensity. Table 1 gives calculated
relative intensities based on our local mode model and the same
dipole moment as in the toluene-d0 calculation.1 We have also
given calculated relative intensities taken directly from our
toluene-d0 work with the toluene-d0 methyl intensities multiplied
by two-thirds. As expected the change in intensities due to the
small change in parameters is not significant. The relative
intensity between the two aryl CH stretching peaks is predicted
well by the anharmonic oscillator model and the HF/6-311+G-
(d,p) dipole moment function. The agreement occurs despite
the fact that these peaks overlap and thus make the deconvo-
lution procedure somewhat uncertain, especially for the lower
overtones.
A comparison of total aryl to total methyl intensities should
alleviate much of the problem associated with uncertainties in
deconvolution. Observed and calculated values for this ratio
are presented in Table 5 and compared to the corresponding
data for toluene-d0. Just as in the toluene-d0 case, the calculated
ratios are predicted to be approximately constant and agree
reasonably well with the observed ratios. Due to the inherently
lower intensity of the methyl region in toluene-R-d1, uncertain-
ties in total aryl to total methyl ratios are larger for toluene-R-
d1 than for toluene-d0. Note that in all cases the observed aryl
to methyl intensity ratio is larger in toluene-R-d1 in accord with
expectations.
1
2
3
4
5
3.1 × 10-5
4.7 × 10-7
6.2 × 10-8
3.6 × 10-9
4.7 × 10-7
5.7 × 10-8
6.2 × 10-9
7.8 × 10-10
5.6 × 10-7
6.7 × 10-8
4.0 × 10-9
a Calculated with the local mode parameters of Table 2 and the HF/
6-311+G(d,p) dipole moment function of ref 1. b From ref 1.
TABLE 4: Observed Spectral Widths of the Aryl and
Methyl Bands in the CH Stretching Overtone Spectra of
Toluene-r-d1 and -d0
a
methyl
toluene-R-d1
aryl
toluene-R-d1
b
b
V
toluene-d0
toluene-d0
3
4
5
6
7
156
221
290
434
493
156
187
248
406
471
120
142
182
196
220
126
147
184
195
198
a Fwhm bandwidths in cm-1 of the entire methyl or aryl band. b From
ref 1.
combination peaks that are predicted to appear in this area. In
the region of ∆VCH ) 2 in the spectrum of toluene-R-d1, the
peak |11 is predicted (eq 8) to lie at 5900 cm-1 on the basis of
the average values of the local mode parameters in Table 2.
The corresponding methyl local mode combinations in toluene-
d0 are the symmetrized combinations of the |110 , |101 , and
|011 states, and in zeroth order, these are predicted to start
about 20 cm-1 lower in energy than |11 on the basis of the
corresponding local mode parameters from ref 1. A very slight
shift on the low-energy side of the aryl peak at ∆VCH ) 3 (Figure
2) arises for the same reason. Local mode combination states
decrease in relative intensity compared to pure local mode states
(|V0 () with increasing V. This is why the aryl regions at ∆VCH
) 3 are only slightly changed from the toluene-d0 to the toluene-
R-d1 spectrum and are identical for higher overtones. At ∆VCH
) 3 the local mode combination states corresponding to |210 ,
|201 , etc., in toluene-d0 are expected at slightly lower energies
than the states corresponding to |21 and |12 in toluene-R-d1.
Not surprisingly the aryl local mode parameters in Table 2
are virtually identical to the corresponding parameters for
The other marked change between the -R-d1 and -d0 overtone
spectra is a change in the methyl profile. At ∆VCH ) 2 and 3

6100 J. Phys. Chem. A, Vol. 102, No. 30, 1998
Kjaergaard et al.
the methyl profiles are clearly different for -R-d1 and -d0.
Beginning at ∆VCH ) 4, the toluene-R-d1 methyl profile
broadens significantly and loses structure relative to the toluene-
d0 profile. This difference can be seen in Table 4, where the
methyl bandwidths are equal at ∆VCH ) 3 but are greater for
-R-d1 from ∆VCH ) 4-7.
of toluene-R-d1 in the regions corresponding to ∆VCH ) 2-7.
Oscillator strengths of the two aryl peaks and the methyl band
have been measured absolutely for ∆VCH ) 2-4 and relatively
for ∆VCH ) 2-6.
We have used a similar model to that used for our previous
work on toluene-d01 to calculate oscillator strengths of the CH
stretching aryl and methyl transitions. Just as in our previous
study,1 our calculated absolute total intensities are in good
agreement with the observed absolute CH stretching overtone
intensities. Similarly, observed relative intensities between the
two aryl transitions and between the aryl and methyl transitions
agree well with calculated relative intensities, particularly for
higher overtones.
A detailed comparison has been made between the spectrum
of toluene-R-d1 and the spectrum of toluene-d0. The aryl regions
of the spectrum are unchanged. In accord with expectations,
the methyl region of the spectrum decreases in relative intensity
for toluene-R-d1. Both the spectral bandwidth and the band
profile change for the methyl regions of toluene-R-d1. This
change is explained in terms of differences in coupling between
the CH/CD stretching vibrations and methyl torsion.
In our previous paper,1 we also presented the overtone
spectrum of toluene-d8, which was obtained from 99+ atom %
D toluene-d8 as well as from 100% toluene-d8. In the 99+%
sample we were able to observe the spectra of hydrogen
impurities from molecules with only one hydrogen atom. Such
a hydrogen impurity spectrum was observed in the regions of
∆VCH ) 3 and 4. Thus the methyl regions of these spectra
correspond to transitions involving the CD2H group as compared
to a CH2D group in toluene-R-d1. However if one compares
the profile at ∆VCH ) 3 and 4 of the hydrogen impurity spectra
with the methyl profiles for toluene-R-d1, they are very similar.
In our recent work on the overtone spectrum of 2,6-
difluorotoluene16 we were able to calculate the methyl profiles.
The model was based on a local mode treatment of the three
methyl CH stretching modes and a simple one-dimensional rigid
rotor for torsion. Interaction between torsion and stretching
occurs through angular-dependent terms involving both fre-
quency and anharmonicity. Angular-dependent terms were also
included in the dipole moment function. Because of coupling
between torsion and stretching, both in the Hamiltonian and
through the dipole moment function, a very large number of
transitions were predicted to carry intensity and to contribute
to the overall spectral profile.
Acknowledgment. B.R.H. is grateful to the University of
Otago for providing office facilities during a visit. Funding for
this research has been provided by the Natural Sciences and
Engineering Research Council of Canada and by the University
of Otago.
References and Notes
On the basis of this work16 we can provide a qualitative
explanation of the changes in methyl profile from -R-d1 to -d0
and of the similarity in the -R-d1 and -R-d2 (hydrogen impurity)
methyl profiles. The width of the methyl band is dependent
on the difference in energy of the methyl vibrational states at a
given overtone and the coupling between vibrational and
torsional states. As we noted in the toluene-d0 paper, the
predicted difference in methyl CH bond lengths as the methyl
group rotates is greater than the predicted difference in aryl CH
bond lengths. This factor would predict a greater width in the
methyl band relative to the aryl band. Moreover the methyl
bandwidth should increase more rapidly with increasing v than
the aryl bandwidth. Both of these characteristics are observed
in the spectra of -R-d1 and -d0.
(1) Kjaergaard, H. G.; Turnbull, D. M.; Henry, B. R. J. Phys. Chem.
1997, 101, 2589.
(2) Hayward, R. J.; Henry, B. R. J. Mol. Spectrosc. 1975, 57, 221.
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Torsional coupling is expected to increase methyl bandwidths
even further. However no coupling is expected between methyl
torsion and aryl CH stretching. In comparing the CH2D group
of -R-d1 to the CH3 group of toluene-d0, the spread in vibrational
frequencies will be slightly larger in the CH3 group due to a
greater spread in the energies of local mode combination states.
However, as we have noted previously, these combination states
carry very little intensity for ∆VCH g 3. The greater methyl
bandwidth implies greater torsional coupling in -R-d1 relative
to -d0. The presence of a deuterium atom increases the density
of CH or CD stretching vibrational states that carry intensity
from the ground state and couple to torsion. On this basis one
might expect that since both CH and CD oscillators are present
in toluene-R-d1 and toluene-R-d2, the methyl profiles in the
spectra of these two molecules would have common features
and would differ from the methyl profiles in the spectra of
toluene-d0 where only CH oscillators are present.
48, 86.
(14) Kjaergaard, H. G.; Yu, H.; Schattka, B. J.; Henry, B. R.; Tarr, A.
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(17) Trevoy, L. W.; Brown, W. G. J. Am. Chem. Soc. 1949, 71, 1675.
(18) Atkins, P. W. Molecular Quantum Mechanics, 2nd ed.; Oxford
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(21) Spectra Calc is a commercially available product from Galactic
Industries Corp. Marquardt’s nonlinear least-squares fitting algorithm is
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Numerical Recipes in C; Cambridge University: Cambridge, U.K., 1988.
(23) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.;
Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M.
A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley,
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Conclusion
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(25) Kjaergaard, H. G.; Daub, C. D.; Henry, B. R. Mol. Phys. 1997, 90,
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We have used conventional and intracavity laser photoacous-
tic spectroscopy to measure the vapor phase overtone spectrum