Rotational isomerism of acetic acid isolated in rare-gas matrices: Effect of medium and isotopic substitution on IR-induced isomerization quantum yield and cis→ trans tunneling rate

Article abstract of DOI:10.1063/1.1760733

The rotational isomerization of acetic acid was studied in Ar, Kr, and Xe matrices. Using resonant excitation of a number of modes in the 3500-7000 cm^-1 region, the light induced trans→cis reaction was promoted. The quantum yields for this process were also measured for various acetic acid isotopologues and matrix materials. For excitation of acetic acid at energies above the predicted isomerization energy barrier, it was found that the measured quantum yields were in average 2%-3%, one order of magnitude smaller that the corresponding values known for formic acid.

Full text of DOI:10.1063/1.1760733

Rotational isomerism of acetic acid isolated in rare-gas matrices: Effect of medium and
isotopic substitution on IR-induced isomerization quantum yield and cis→trans
tunneling rate
E. M. S. Maçôas, L. Khriachtchev, M. Pettersson, R. Fausto, and M. Räsänen
Citation: The Journal of Chemical Physics 121, 1331 (2004); doi: 10.1063/1.1760733
View online: http://dx.doi.org/10.1063/1.1760733
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/121/3?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 3
15 JULY 2004
Rotational isomerism of acetic acid isolated in rare-gas matrices:
Effect of medium and isotopic substitution on IR-induced isomerization
quantum yield and cis\trans tunneling rate
a)
E. M. S. Ma c¸ oˆ as
Department of Chemistry, University of Helsinki, P.O. Box 55, FIN-00014 Helsinki, Finland and
Department of Chemistry (CQC), University of Coimbra, P-3004-535 Coimbra, Portugal
L. Khriachtchev
Department of Chemistry, University of Helsinki, P.O. Box 55, FIN-00014 Helsinki, Finland
M. Petterssonb)
Department of Chemistry, University of Helsinki, P.O. Box 55, FIN-00014 Helsinki, Finland
R. Fausto
Department of Chemistry (CQC), University of Coimbra, P-3004-535 Coimbra, Portugal
M. R a¨ s a¨ nen
Department of Chemistry, University of Helsinki, P.O. Box 55, FIN-00014 Helsinki, Finland
͑
Received 5 April 2004; accepted 21 April 2004͒
Rotational isomerization of acetic acid (CH COOH) is studied in Ar, Kr, and Xe matrices. The
3
light-induced trans→cis reaction is promoted using resonant excitation of a number of modes in
Ϫ1
the 3500–7000 cm region, and the quantum yields for this process are measured for various acetic
acid isotopologues and matrix materials. For excitation of acetic acid at energies above the predicted
Ϫ1
isomerization energy barrier ͑у4400 cm ͒, the measured quantum yields are in average 2%–3%,
and this is one order of magnitude smaller than the corresponding values known for formic acid
͑
HCOOH͒. This difference is interpreted in terms of the presence of the methyl group in acetic acid,
which enhances energy relaxation channels competing with the rotational isomerization. This
picture is supported by the observed large effect of deuteration of the methyl group on the
photoisomerization quantum yield. The trans→cis reaction quantum yields are found to be similar
for Ar, Kr, and Xe matrices, suggesting similar energy relaxation processes for this molecule in the
various matrices. The IR-induced cis→trans process, studied for acetic acid deuterated in the
hydroxyl group, shows reliably larger quantum yields as compared with the trans→cis process.
For pumping of acetic acid at energies below the predicted isomerization barrier, the trans→cis
reaction quantum yields decrease strongly when the photon energy decreases, and tunneling is the
most probable mechanism for this process. For the cis→trans dark reaction, the observed
temperature and medium effects indicate the participation of the lattice phonons in the
tunneling-induced process. © 2004 American Institute of Physics. ͓DOI: 10.1063/1.1760733͔
I. INTRODUCTION
guest-guest energy transfer is reduced due to the low concen-
tration of the guest molecules. On the other hand, energy
relaxation may involve the transfer of excitation energy to
the vibrational modes of the lattice. This process can be
A large number of molecules have been found to un-
dergo rotational isomerization upon vibrational excitation of
the monomer isolated in low-temperature rare-gas
17
viewed as a phonon-assisted intramolecular vibrational en-
ergy relaxation ͑IVR͒, in which the lattice phonons act like a
thermal bath that compensates the energy differences be-
tween the relevant intramolecular vibrational states. The re-
laxation rates are then expected to be dependent on the num-
ber of phonons involved and on the temperature of the
1
–16
matrices.
In general, it is required that the excitation en-
ergy is transferred from the initially excited vibrational mode
to the reaction coordinate at energies higher than the reaction
3
barrier. However, it has been recently shown that isomeriza-
tion of the carboxylic group can take place due to tunneling
even when the excess energy is transferred to the reaction
coordinate ͑C-O torsion͒ below the reaction barrier.7
17
phonon bath. The IR-induced isomerization quantum yield
Isomerization is in competition with other possible en-
ergy relaxation channels. In low-temperature matrices, the
depends on the proportion of energy relaxation channels de-
positing energy into the reaction coordinate and the lifetimes
of the molecular states involved. In rare-gas matrices, those
factors are affected by the excitation energy, the host, and the
a͒Author to whom correspondence should be addressed. Email address:
emacoas@qui.uc.pt
1,11–13,17,18
nature of the excited mode.
b͒
Present address: Department of Chemistry, University of Jyv a¨ skyla, P.O.
Large quantum yields ͑20%–40%͒ were obtained for the
Box 35, FIN-40014, Finland.
0021-9606/2004/121(3)/1331/8/$22.00
1331
© 2004 American Institute of Physics
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1

1332
J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Ma c¸ oˆ as et al.
aids to evaluate the role of the methyl rotor in the dynamics
of vibrational energy relaxation.
In acetic and formic acids, the fast cis→trans conver-
sion by tunneling poses limitations to the detection of the
high energy conformers.6
,28,20
The tunneling rate of matrix
isolated cis-formic acid was shown to depend on the tem-
perature, the rare-gas host, and even the local environment
within the same host ͑matrix site͒.28 In that work, a qualita-
tive interpretation of the experimental results was attempted
on the basis of the relative position of the initial and final
states of tunneling. At least three solvation effects were
pointed out as influencing the tunneling dynamics, namely,
the changes in barrier height, nature of the states involved,
and energy gaps between the tunneling states. For the mo-
ment, the relative importance of those factors affecting tun-
neling is still not well understood. Computational simula-
tions and systematic experimental studies of tunneling in
different conformational systems, like acetic acid, are two
approaches that are likely to give valuable information on the
subject.
FIG. 1. Isomerization reaction of acetic acid. The trans→cis isomerization
can be induced by excitation of the 2␯OH mode of the trans conformer
isolated in rare-gas matrices, while the cis→trans process occurs in dark
Ϫ1
via tunneling. The trans→cis isomerization barrier of 4432 cm and the
Ϫ1
relative energy for the cis conformer of 1882.7 cm are calculated by
ab initio methods ͑Ref. 21͒.
In the present work, we study the rotational isomeriza-
tion of matrix-isolated acetic acid under resonant excitation
Ϫ1
in the 3500–7000 cm range and the cis→trans dark re-
IR-induced isomerization of formic acid ͑HCOOH͒ excited
at various modes above the energy barrier in Ar matrices.7
,19
action. The dependence of the trans→cis isomerization
quantum yield on the excited vibration, excitation energy,
and rare-gas host is evaluated. In addition, the effect of iso-
topic substitution on the isomerization efficiency is investi-
gated. For the hydroxyl deuterated isotopologues, the
isomerization quantum yields are obtained for both the
trans→cis and cis→trans processes. Finally, the medium
and temperature effects on the tunneling rates for the cis
This high efficiency was connected with the relatively large
energy gaps in the vibrational manifold of this molecule that
delay energy relaxation within the potential well of the ini-
tially excited conformer, allowing isomerization to take
1
9
place. Similarly, high quantum yields for isomerization
were estimated for the HONO molecule excited at the OH
1
stretching mode ͑␯OH͒ in Kr matrices. In contrast, very low
→
trans dark reaction are investigated and compared with
values were reported for CH FC͑F)vCH isolated in solid
2
2
Ϫ5
Ϫ2
11
the available data on formic acid.
Ar(10 %–10 %).
Acetic acid (CH COOH) has two stable structures that
3
II. EXPERIMENTAL DETAILS
are interconverted by rotation around the C-O bond, the cis
and trans conformers shown in Fig. 1. Only recently, the
higher energy cis conformer was detected experimentally, us-
ing excitation of the OH stretching overtone of the trans
conformer isolated in an Ar matrix.20 In that work, cis-acetic
acid was found to tunnel back to the ground conformational
state in dark even at temperatures as low as 8 K. According
to the ab initio calculations, the trans→cis energy barrier is
The gaseous samples were prepared by mixing acetic
acid ͑Sigma-Aldrich, Ͼ99%͒ or its isotopologues
(CD COOD and CH COOD, Sigma-Aldrich, 99.5%͒, de-
gassed by several freeze-pump-thaw cycles, with high purity
Ar, Kr, and Xe ͑AGA, Ͼ99.99͒ typically in the 1:2000 or
3
3
1:1000 proportions. The CD COOH form was obtained from
3
the fully deuterated form by exchange of deuterium with
Ϫ1
about 4400 cm and the cis form is higher in energy than
H O adsorbed on the inner surface of the sample container
2
Ϫ1 21
the trans form by about 1880 cm
.
For formic acid the
and the deposition line. The gaseous mixtures were deposited
onto a CsI substrate at 15–35 K ͑depending on the matrix
material͒ in a closed cycle helium cryostat ͑APD, DE 202A͒
and subsequently cooled down to 8 K. The IR absorption
Ϫ1
corresponding calculated values are ϳ4200 cm and ϳ1400
Ϫ1
cm for the trans→cis energy barrier and the relative en-
2
2
ergy of cis-formic acid, respectively. Importantly, acetic
acid differs from formic acid by the presence of a methyl
rotor, which has a low barrier for internal rotation ͑ϳ170
Ϫ1
spectra ͑7900–400 cm ͒ were measured with a Nicolet
SX-60 Fourier transform infrared ͑FTIR͒ spectrometer. A
liquid-nitrogen-cooled MCT detector and a Ge/KBr beam
splitter were used to record the mid-IR absorption spectra
Ϫ1
21
cm for the trans conformer͒. In the gas phase, the pres-
ence of low barrier internal rotations have been postulated to
be responsible for the decrease of the lifetime of excited
states associated with vibrations close to the center of flex-
Ϫ1
͑0.25–1.0 cm resolution͒, and a liquid nitrogen cooled
InSb detector and a quartz beam splitter were used to record
Ϫ1
ibility, due to the enhancement of the coupling of vibrational
the near-IR absorption spectra ͑0.5 cm resolution͒. Typi-
and internal rotational states.2
3–27
In the solid phase, the me-
cally 100–500 interferograms were coadded.
thyl rotor may also enhance couplings between the intramo-
lecular vibrational states and the phonon bath. Thus, the
comparison between the isomerization quantum yields for
formic and acetic acids in similar experimental conditions
Tunable pulsed IR radiation, provided by an optical
parametric oscillator ͑OPO Sunlite, Continuum, with IR ex-
tension͒ was used to produce cis-acetic acid via vibrational
excitation of trans-acetic acid. The pulse duration was ca. 5
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J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Isomerization of acetic acid in matrices
1333
TABLE I. Vibrational frequencies of trans-acetic acid in the 3500–7000 cmϪ1 region for acetic acid isolated in
solid Ar. The vibrational assignment is based on the observed fundamental modes for the molecule isolated in
solid Ar reported in Ref. 29. Symbols; ␯, stretching; ␦, bending; ␶, torsion; and ␥, rocking.
CH COOH
assignment
CH COOD
assignment
CD COOD
assignment
CD COOD
assignment
3
3
3
3
cmϪ1
cmϪ1
cmϪ1
cmϪ1
␯
␯
␯
␯
␯
␯
OH
3564 ␯OD
4096 ␯CH ϩ␯CO
4201 ␯HCH ϩ␯CO
4411 ␯HCH ϩ␦CH3
2629 ␯OH
3564
3941
3946
4041
OHϩ␥CvO
4215 ␯OHϩ␦COvO
3
OHϩ␶CO
4264
2
HCH ϩ␦CH
OHϩ␦COH
OHϩ␦CH3
4410 ␯OHϩ␥CvO
4396 ␯OHϩ␶COH
4464 ␯OHϩ␦CH3
5170 ␯OHϩ␯C-O
5148 ␯OHϩ␯CvO
2␯OH
2
3
2
4708 ␯ODϩ␯CvO
4173 ␯ODϩ␯CvO
4392
5168
4876 ␯HCH ϩ␦HCH
4710
2
2
2␯OD
4881 2␯OD
5335
6958
␯
2
OHϩ␯CvO
5351
6957
␯OH
ns, the spectral linewidth ϳ0.1 cmϪ1, and the repetition rate
0 Hz. The Burleigh WA-4500 wavemeter was used to con-
The absorption cross section is obtained using the measured
IR absorption at the excitation frequency, the known acetic
acid concentration, and the matrix thickness. We estimated
that the experimental error associated with the quantum yield
values is roughly 50%.
1
trol the OPO radiation frequency, providing an absolute ac-
Ϫ1
curacy better than 1 cm . The pumping beam was quasicol-
linear with the spectrometer beam allowing simultaneous
irradiation and recording of IR absorption spectra, and an
interference filter transmitting in the 3300–1100 cmϪ1 range
was attached to the detector to prevent its exposure to the
pumping radiation.
III. EXPERIMENTAL RESULTS
After deposition, the matrix-isolated acetic acid is found
in the most stable trans geometry. The vibrational modes of
For the CH COOH and CD COOH isotopologues, a
Ϫ1
3
3
trans-acetic acid observed in the 3500–7000 cm spectral
photoequilibrium of the trans and cis forms is established
under IR pumping of the trans conformers, as a result of the
interplay between cis-acetic acid photogeneration and its
depletion due to tunneling. At the equilibrium, the pumping
and tunneling rates are equal:
region for the monomer isolated in solid Ar are listed in
Table I, and the absorption wavenumbers in the mid-IR re-
20,29,30
gion can be found elsewhere.
The vibrational assign-
ments for the overtone and combination modes presented in
this table were based on the reported values for the funda-
mental modes and on the expected isotopic shifts.2 For the
molecule isolated in Kr and Xe matrices, the observed modes
0,29
k ͑␯͓͒trans-CH COOH͔ ϭk ͑T͓͒cis-CH COOH͔ .
p
3
eq
t
3
eq
͑1͒
Ϫ1
in the 3500–7000 cm range appear shifted to lower fre-
It follows that the averaged pumping rate k (␯) can be
p
quencies as compared with the values found in an Ar matrix,
as a consequence of the known matrix effect caused by
guest-host interactions. This effect is illustrated in Table II
where the bands observed in the Ar, Kr, and Xe matrices are
determined from the tunneling rate k (T), and the ratio of the
t
cis and trans photoequilibrium concentrations, as described
1
9
elsewhere. For these calculations, the bands corresponding
to the CH bending of trans-CH COOH, the CvO stretch-
3
3
listed for the CH COOH isotopologue.
3
ing of cis-CH COOH, the COH bending of
3
trans-CD COOH and the C-O stretching mode of
3
2
9
cis-CD COOH were used. Since deuteration of the hy-
3
TABLE II. Vibrational frequencies of trans-CH COOH in the 3500–7000
cm region in solid Ar, Kr, and Xe. The vibrational assignment is based on
the observed fundamental modes for the molecule isolated in solid Ar re-
ported in Ref. 29. The splitting of bands observed for Kr and Xe are due to
site effects. Symbols: ␯, stretching; ␦, bending; ␶, torsion, and ␥, rocking.
3
Ϫ1
droxyl group decreases the tunneling rate by orders of mag-
nitude, for the CH COOD and CD COOD species the pump-
3
3
ing rate coefficients were determined directly from the
pumping-induced changes in concentration of one of the
2
0
conformers. For these two isotopologues, the concentra-
tions were obtained from the integrated absorption of the
bands corresponding to the C-O stretches of the trans and cis
Assignment
Ar
Kr
Xe
␯
OH
3564
3552
3546
3538
3532
3528
4066
3551
2
9
forms. To avoid the influence of tunneling on the determi-
nation of the pumping rates, only the points obtained in the
first 10 min of irradiation were considered for the OD-
substituted species. Once the pumping rates are known, the
quantum yields of the rotamerization processes ␾(i) can be
extracted from the following equation:
3549
␯
OHϩ␥CvO
OHϩ␶CO
4096
4082
4079
␯
␯
4201
4411
4708
4876
5341
4190
4400
4694
4866
5326
4171
4403
4678
4846
5306
5303
6887
HCH ϩ␦CH3
2
␯OHϩ␦COH
␯
␯OHϩ␯CvO
OHϩ␦CH3
i
T
k ͑␯͒ϭ␾͑i͒␴ ͑␯͒I͑␯͒,
͑2͒
p
i
2
where ␴ (␯) ͑in cm ͒ is the absorption cross section of the
T
2␯OH
6957
6932
Ϫ1
Ϫ2
excited mode, I ͑in s cm ͒ is the photon intensity of the
pumping beam and i refers to the excited vibrational mode.
6881
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1334
J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Ma c¸ oˆ as et al.
FIG. 2. Difference IR absorption spectrum obtained by excitation of the
1
2
␯OH mode of the trans form. The bands at 3564 and 1779 cm belong to
Ϫ1
FIG. 3. Quantum yield for the IR-induced trans→cis isomerization of
the trans form of acetic acid, and the bands at 3623 and 1807 cm belong
to the cis form.
acetic acid ͓CH COOH in solid Ar ͑᭿͒, Kr ͑᭡͒; and Xe ͑૽͒; and
3
CD COOH ͑ꢀ͒, CH COOD ͑᭺͒, and CD COOD ͑᭹͒ in solid Ar͔. The
3
3
3
results for the trans→cis isomerization of formic acid in solid Ar are
shown for comparison ͑*͒. The error bar represents Ϯ50% of the estimated
quantum yields. The trans→cis isomerization barriers calculated for acetic
The trans→cis isomerization was induced by irradiat-
ing the sample at frequencies corresponding to some of the
Ϫ1
and formic acid are ϳ4400 and 4200 cm , respectively ͑Refs. 21, 22͒.
Ϫ1
most intense bands in the 3500–7000 cm spectral region.
In Fig. 2, the spectral changes induced in the regions of the
OH and CvO stretches by pumping at the ␯OH overtone
͑
2␯OH͒ of CH COOH are shown. The isomerization quan-
3
culated isomerization barrier ϳ0.025͒. On the other hand, the
tum yields estimated for several excited modes in various
matrices are listed in Table III and plotted in Fig. 3. For the
CH COOH isotopologue, the quantum yield is essentially
independent of the excited mode, when the excitation energy
is above the calculated isomerization barrier ͑ϳ4400 cm ͒.
quantum yields obtained for CD COOH ͑0.15 for 2␯OH, and
3
0
.085 for ␯OHϩ␯CvO͒ and CH COOD ͑0.0036 for 2␯OD͒
3
3
differ from each other and from the averaged values for
CH3COOH ͑ϳ0.025, see Fig. 3͒.
Ϫ1
The obtained quantum yields are about one order of magni-
tude smaller than the values measured for formic acid under
The concentration of the cis conformer is limited by the
low trans→cis isomerization quantum yield and by the
7
,19,31
20
similar experimental conditions ͑see Fig. 3͒.
below ϳ4400 cm , the quantum yield depends strongly on
At energies
cis→trans tunneling ͑Fig. 4͒. Therefore, the data con-
Ϫ1
cerning the photoinduced cis→trans process is much more
limited. For the OH-isotopologues, the cis→trans tunnel-
ing rate is fast ͑see Fig. 4͒,20 which practically prevents mea-
surement of the quantum yield for the cis→trans isomer-
ization process. However, in the case of the OD-
isotopologues the tunneling is much slower,20 and we could
follow the pumping kinetics while exciting the 2␯OD band
the excitation energy.
For CD COOD, the quantum yields obtained by excita-
3
tion of the 2␯OD and the ␯ODϩ␯CvO combination mode
were found to be 0.011 and 0.016, being similar to the values
for CH COOH ͑averaged value for pumping above the cal-
3
Ϫ1
of the cis form at Ϸ5258 cm , i.e., well above the predicted
TABLE III. Quantum yields for the IR-induced trans→cis isomerization
of acetic acid isolated in rare-gas matrices. The relative error has been
estimated as 50% of the quantum yield value.
cis→trans isomerization barrier. This enables estimation of
the quantum yields for the cis→trans isomerization in
CD COOD and CH COOD. In both cases, the quantum
Excited mode/Energy ͑cmϪ1
3
3
͒
Ar
Kr
yield was found to be reliably higher than that for the corre-
sponding trans→cis isomerization ͑by a factor of 40 for
CD COOD and by a factor of 3 for CH COOD).
a
CH COOH
3
b
b
b
Ϫ4
Ϫ3
Ϫ3
Ϫ3
Ϫ4
Ϫ3
Ϫ3
␯
␯
␯
␯
␯
␯
2
OH
3554
4090
4195
4406
4866
5326
6944
1.4 ϫ 10
2.6 ϫ 10
2.7 ϫ 10
3.0 ϫ 10
¯
1.5 ϫ 10
3.2 ϫ 10
8.4 ϫ 10
¯
3
3
OHϩ␥CvO
The effects of temperature and medium on the dark cis
→trans reaction of acetic acid were evaluated by following
the tunneling kinetics at various temperatures and in different
rare-gas matrices. The Arrhenius plots are shown in Fig. 4.
The tunneling rate is found to be similar in Ar and Kr ma-
trices, and it is enhanced by a factor of Ӎ5 in a Xe matrix.
The tunneling rate increases at higher temperatures. The data
for the temperature dependence in a Xe matrix is less accu-
rate because of the large tunneling rates. Deuteration of the
methyl group increases the tunneling rate. This is shown by
OHϩ␶CO
HCH ϩ␦CH
2
3
Ϫ2
Ϫ2
Ϫ2
OHϩ␦CH3
OHϩ␯CvO
␯OH
2.2 ϫ 10
2.9 ϫ 10
2.6 ϫ 10
¯
b
Ϫ2
2.2 ϫ 10
CH COOD
3
3.6 ϫ 10Ϫ3
2␯OD
5170
¯
CD COOH
3
Ϫ2
␯
2
OHϩ␯CvO
5335
6958
8.5 ϫ 10
1.5 ϫ 10
¯
Ϫ1
␯OH
¯
CD COOD
3
Ϫ2
␯
2
ODϩ␯CvO
4392
5168
1.6 ϫ 10
1.1 ϫ 10
¯
¯
Ϫ2
comparing the values measured for CD COOH and
␯OD
3
Ϫ2 Ϫ1
Ϫ6 Ϫ1
CD COOD (7.1ϫ10
s
and 1.1ϫ10
s
, respec-
3
a
The quantum yield determined for pumping at the 2␯OH mode of the mol-
tively͒ with those obtained for CH COOH and CH COOD
Ϫ2
3
3
ecule isolated in solid Xe is 3.5ϫ10
.
Ϫ2 Ϫ1
Ϫ7 Ϫ1
b
(2.1ϫ10
s
and 7.3ϫ10
s
, respectively͒, as mea-
Average value used for pumping acetic acid in the Ar and Kr matrices.
Symbols: ␯, stretching; ␦, bending; ␶, torsion; and ␥, rocking.
sured in solid Ar at 8 K.
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1

J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Isomerization of acetic acid in matrices
1335
trix materials ͑2.2%, 2.6%, and 3.5%, in Ar, Kr, and Xe,
respectively͒ increases slightly with the polarizability of the
rare gas as found previously for other compounds.3 How-
ever, the values here reported for the three matrices are still
within a possible experimental error. Therefore, the quantum
yield for acetic acid trans→cis isomerization is not
strongly affected by the rare-gas host; in particular, the acti-
vated relaxation channels and their efficiency seem to be
similar in various matrices.
,4
At excitation energies above the calculated isomerization
Ϫ1
barrier ͑Ͼ4400 cm ͒, the quantum yields for the trans
→
cis process in Ar and Kr matrices at 8 K show no differ-
ence for various modes ͑within the experimental error͒, the
obtained values being around 2%–3%. The energy above
which the quantum yield reaches a relatively stable value
Ϫ1
͑
4500 cm ͒ agrees with the computational barrier height,
which supports the theoretical estimation. The lack of evi-
dent mode specific effects on the quantum yield was also
reported for formic acid in solid Ar7
,19,31
For both molecules,
the range of excitation energies probed corresponds to the
discrete region of vibrational states and, thus, mode specific
effects are generally possible. We can speculate that the ob-
served lack of mode specificity in the isomerization quantum
yield is connected with a slow isomerization rate, allowing
effective randomization of the excitation energy between
various modes. The coupling of the intramolecular vibra-
tional states with the lattice possibly plays an important role
in this randomization process. It should be remembered that
the experiment probes the probability of becoming trapped in
either well, and after excitation the molecule may undergo
isomerization back and forth between the trans and cis forms
before cooling sufficiently to be trapped in either well. The
time between initial excitation and trapping may indeed be
long enough to allow extensive randomization of energy ir-
respective of the initially excited mode. Another possibility
is that all excited states decay essentially to a few common
low energy states with a dominant contribution to the energy
relaxation dynamics. The excitation energy introduced into
the molecule is still in the low density of states where such
bottleneck states could be found.
Deuteration of the methyl group increases the quantum
yield for the trans→cis isomerization from 2%–3% to
8
%–15%, as seen from comparison of the values obtained
for CH COOH and CD COOH. This difference shows that
the methyl group plays an important role in the isomerization
3
3
FIG. 4. Tunneling kinetics for the cis→trans isomerization of acetic acid
in rare-gas matrices: ͑a͒ time decay of the ␯CvO band of cis-CH COOH
3
dynamics. It may be that CH yields faster energy relaxation
3
in solid Ar at 8 K, ͑b͒ exponential fit of the integrated intensity of this band,
and ͑c͒ Arrhenius plots for the cis→trans tunneling rate. In plot ͑c͒, the
experimental data are fitted using an expression for a temperature dependent
rate constant ͓k(T)ϭk ϩk exp(ϪE /RT)͔, where k , k , and E are the
process than CD because its higher energy modes can par-
3
ticipate in lower-order couplings leading to a more efficient
nonreactive deactivation of the excited states.
Deuteration of the hydroxyl group decreases the quan-
tum yield by almost one order of magnitude ͑from 2%–3%
to 0.4%͒. This information is provided by the values ob-
0
1
a
0
1
a
parameters. The extracted activation energies (E ) are ͑57Ϯ4͒, ͑72Ϯ4͒, and
a
Ϫ1
͑
͑
͑
53Ϯ12͒ cm , the k values are ͑0.0223Ϯ0.0007͒, ͑0.0186Ϯ0.0002͒, and
0.104Ϯ0.005͒ s , and the k1 values are ͑0.40Ϯ0.07͒, ͑0.24Ϯ0.03͒, and
0
Ϫ1
Ϫ1
6Ϯ6͒ s for Ar, Kr, and Xe, respectively.
tained for the almost isoenergetic vibrations of CH COOH
3
Ϫ1
and CH COOD at Ϸ5250 cm . In the case of deuteration of
3
IV. DISCUSSION
the hydroxyl group, the reaction coordinate is directly af-
fected by the isotopic substitution, which decreases the fre-
quency of the ␶C-O mode. Therefore, at similar energies, the
␶C-O coordinate should be in a higher excited state in
CH COOD than in CH COOH. Thus, in CH COOH the
A. Quantum yield for the IR-induced isomerizations
For the 2␯OH mode ͑ϳ7000 cmϪ1͒ of the CH COOH
isotopologue, the quantum yield estimated for the three ma-
3
3
3
3
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1

1336
J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Ma c¸ oˆ as et al.
couplings between the ␶C-O and the excited states are ex-
However, this explanation is not supported by the fact that
the trans→cis quantum yields here reported are practically
insensitive to the excitation energy, as long as it is above the
calculated isomerization barrier. Furthermore, the barrier
height is the same for CD COOD and CH COOD, but the
pected to be of lower order than those in CH COOD, which
3
relatively increases the isomerization efficiency in
CH COOH.
3
Remarkably, no significant difference is observed be-
3
3
tween the isomerization quantum yields for CH COOH and
relative changes in quantum yield are quite different (␾c/t
Ϸ44 for CD3COOD and ␾c/tϷ3 for CH3COOD, where ␾c/t
denotes the ratio of the cis→trans and trans→cis quan-
tum yields͒. Accordingly, this factor does not seem to be the
dominant one in the studied system. A similar behavior was
also observed for HONO isolated in solid Kr (␾c/tϷ7),
where the isomerization barriers (Ei) for the direct and re-
verse processes are nearly identical (⌬Eiϭ130 cm ). For
the case of HONO, it has been suggested that kinetic or
potential couplings between the excited vibrations and nearly
resonant vibrational states could be responsible for the more
3
CD COOD. This observation is in agreement with the pre-
3
vious discussion. Indeed, in the perdeuterated isotopologue,
two opposite effects due to isotopic substitution in the me-
thyl group ͑increase in the quantum yield͒ and in the hy-
droxyl group ͑decrease in the quantum yield͒ seem to com-
pensate each other, leading to a minor net effect.
Ϫ1
1
Several modes with energies below the computed
isomerization barrier ͑e.g., pumping at Ϸ4200, 4100, and
Ϫ1
3
560 cm ͒ were also found to be active in promoting the
trans→cis process in acetic acid. In this case, a tunneling
mechanism is presumably involved. As shown in Fig. 3, for
these excitations, the quantum yield increases strongly with
the energy. A similar dependence of the quantum yield on the
excitation energy is observed for formic acid in solid Ar. The
effect was previously explained based on the delocalization
of the torsional wave functions between the cis and trans
efficient energy transfer from the excited states to the reac-
tion coordinate upon excitation of the cis isomer.3
2,33
These
factors may also be relevant for acetic acid.
B. Tunneling rate for the cis\trans dark reaction
7
potential wells.
As mentioned earlier, the cis→trans isomerization of
acetic acid is observed in dark. As it was discussed for the
analogous case of formic acid,28 the initial state in this dark
process is essentially the ground state of the cis conformer
and the final state is some excited vibrational level of the
trans conformer.20 From this excited state the energy relaxes
via a cascading process controlled by the energy gaps be-
tween intramolecular states and mode couplings. The ob-
served temperature dependence of the tunneling rate for the
cis→trans isomerization of acetic acid ͑see Fig. 4͒ indi-
cates participation of low energy quanta in the tunneling pro-
As seen in Fig. 3, the isomerization quantum yield is
about one order of magnitude higher for formic acid than for
acetic acid. As already mentioned, the presence of the methyl
group in acetic acid can enhance the coupling of intramo-
lecular vibrational states with each other and with lattice mo-
tion. Additionally, the low-frequency modes originated by
the methyl group are capable of participating in the energy
relaxation similar to the lattice phonon. Possibly these two
effects lead to an increase of the rate for intramolecular en-
ergy transfer and/or to an increase in the number of relax-
2
5
ation channels competing with isomerization. On the other
hand, large-amplitude vibrations such as ␶C-O and ␶C-C are
thought to be considerably anharmonic and, thus, strong cou-
pling between the two internal rotors of acetic acid may also
be operating. This is particularly important, since the methyl
motion has a lower frequency than ␶C-O and part of the
energy deposited into the reaction coordinate may also be
dissipated through the methyl motion without isomerization.
Another interesting observation is that the isomerization
quantum yield starts decreasing at energies lower by Ӎ500
cess, which compensates the energy mismatch between the
intramolecular levels involved in the process.1
7,18
The fitting
of the tunneling kinetics measured in the three studied ma-
trices with a temperature dependent rate of the type k(T)
ϭk ϩk exp(ϪE /RT) yields activation energies of 50–80
0
1
a
Ϫ1
cm ͑see Fig. 4͒. These activation energy values are consis-
tent with the participation of lattice phonon modes in the
tunneling process in the various hosts, where the Debye fre-
Ϫ1 34
quencies range from 40 to 70 cm
.
In addition, it should
be remembered that the methyl torsion ͑estimated below 100
Ϫ1
Ϫ1
cm for formic acid than for acetic acid, in qualitative
cm in the cis conformer͒ ͑Ref. 21͒ might also be involved
agreement with the predicted lower isomerization barrier for
formic acid. The difference between the energy barriers is
also experimentally supported by the large gap ͑roughly two
orders of magnitude͒ between isomerization yields for pump-
ing of formic and acetic acids at the OH-stretching modes.
The reverse, cis→trans photoinduced isomerization of
acetic acid was also investigated. In this case, excitation of
the 2␯OD mode of cis-CD COOD and cis-CH COOD was
in the mechanism.
For acetic acid, the cis→trans tunneling rate is larger
by at least one order of magnitude ͑for all hosts at 8 K͒ than
the tunneling rate observed for formic acid.28 The faster tun-
neling in acetic acid can be primarily connected to its pre-
dicted lower barrier for the cis→trans conversion as com-
pared with formic acid, the computed difference being ϳ300
Ϫ1 21,22
cm
.
Note that the increase in the cis→trans tunneling
3
3
found to be more efficient in promoting the isomerization
than the excitation of the same mode of the corresponding
trans conformers to promote the trans→cis conversion.
rate is quantitatively similar to the decrease in the trans
→cis isomerization quantum yield, discussed earlier. It fol-
lows that the faster tunneling rate for acetic acid can also be
a consequence of an efficient deactivation of the excited state
of the trans form by the low-energy states of the methyl
group.
The energy barrier for the cis→trans process was estimated
Ϫ1
to be Ϸ1880 cm
lower than for the trans→cis
2
1
conversion. Hence, this factor may partially contribute to
the observed difference in the isomerization quantum yields.
For acetic acid, the tunneling rate in solid Ar is some-
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J. Chem. Phys., Vol. 121, No. 3, 15 July 2004
Isomerization of acetic acid in matrices
1337
what higher than in solid Kr, while in solid Xe the rate is
faster than in those two matrices by a factor of ϳ5. A sig-
nificantly different matrix effect was observed for formic
sensitive to the excited vibrational mode and the rare-gas
host. The IR-induced cis→trans isomerization is more ef-
Ϫ1
ficient than the trans→cis process. Below 4400 cm , the
acid, where the tunneling rates increase in the order k
quantum yield for the trans→cis isomerization depends
strongly on the excitation energy, and this is probably due to
the participation of tunneling in the IR-induced mechanism.
͑2͒ Deuteration of the methyl group increases the
trans→cis isomerization quantum yield, while deuteration
of the hydroxyl group has the opposite effect. This behavior
is probably connected with the different orders of couplings
Ar
2
8
Ͼk Ͼk
.
This difference indicates a very specific de-
Kr
Xe
pendence of the tunneling rate on the solute-solvent interac-
tions in the studied systems. For formic acid, the dependence
of the tunneling rate with the matrix host was interpreted as
resulting from the interplay of three factors determined by
2
8
solvation effects. It was shown that the tunneling rate can
also be affected by the local environment within the same
between the excited modes. In the CD -isotopologues as
3
2
8
host. Practically, this means that any detailed interpretation
of the observed matrix effect is not realistic at the moment
due to the high complexity of the system. Particularly in
acetic acid, the lower energy vibrational modes of the methyl
group may participate in the tunneling mechanism, in addi-
tion to the phonon modes.
compared with the CH -isotopologues, the less efficient cou-
3
plings between the excited modes and the methyl torsion
seem to decrease the rate of deactivation of the excited
states, increasing the isomerization probability. In the OD-
isotopologues as compared with the OH-isotopologues, less
efficient couplings between the excited vibrational states and
the ␶CO mode could be responsible for a lower efficiency of
energy transfer to the reaction coordinate.
Some general ideas can be extracted from the compari-
son of the tunneling rates for different isotopologues in a
given matrix. As expected, the tunneling rate was found to
decrease by ca. four orders of magnitude upon substitution of
the tunneling particle ͑OH→OD͒ both for CH and CD con-
͑3͒ On average, the trans→cis isomerization quantum
yield is one order of magnitude smaller for acetic acid
7
,19
(CH COOH) than the values for formic acid ͑HCOOH͒.
3
3
3
taining isotopologues in Ar matrices.20 On the other hand, for
The presence of the low-barrier methyl rotor increases the
number of states coupled to the initially excited state, thus
probably increasing the number of accessible energy relax-
ation channels that deactivate the excited mode without
transferring energy to the reaction coordinate.
the CD COOH isotopologue, the tunneling rate in solid Ar at
3
Ϫ2 Ϫ1
8
K (7.1ϫ10
s
), is about three times faster than that
observed for CH COOH in the same experimental conditions
3
Ϫ2 Ϫ1
(
2.1ϫ10
s
). Similarly, the tunneling rate for the fully
Ϫ6 Ϫ1
deuterated species (1.1ϫ10
s
) is almost twice faster
͑4͒ For acetic acid, the cis→trans tunneling rates of
than for CH COOD (7.3ϫ10 sϪ1). These relative values
Ϫ7
the dark reaction follow the trend k ӷk Ͼk , which dif-
3
Xe
Ar
Kr
2
8
of tunneling rates can be correlated with an increased effi-
ciency in the energy dissipation within the trans well in the
acetic acid isotopologues bearing a deuterated methyl group.
The smaller energy quanta of the deuterated methyl group
can provide a better match with the small energy gap to be
overcome in the tunneling process. However, this interpreta-
tion is certainly an oversimplification, since the change of
the intramolecular vibrational structure occurring upon iso-
topic substitution may also change both the nature of the
states and order of coupling with the phonons involved in the
tunneling process.28
fers from the case of formic acid (k Ͼk Ͼk ). This
Ar Kr Xe
result indicates that the tunneling kinetics depends on spe-
cific solvation effects. The cis→trans tunneling rate is
larger for acetic acid than for formic acid by at least one
order of magnitude ͑at 8 K͒. This difference is presumably
connected with the lower isomerization barrier predicted for
acetic acid. In addition, this behavior can also be connected
with the low-frequency modes of the methyl group in acetic
acid increasing the efficiency of the energy relaxation within
the trans well.
ACKNOWLEDGMENTS
V. CONCLUSIONS
The Academy of Finland is thanked for financial sup-
port. E.M. and R.F. acknowledge the Portuguese Foundation
for Science and Technology ͑Ph.D. Grant No. SFRH/BD/
4863/2001 and POCTI/QUI/43366/2001͒.
Narrowband tunable IR radiation was used to excite se-
lectively various vibrational modes in the 3500–7000 cmϪ1
spectral region of monomeric acetic acid isolated in rare-gas
matrices. The isomerization quantum yields for both trans
1
→
cis and cis→trans processes were estimated, and the
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͑
1͒ Above the calculated isomerizaton barrier ͑ϳ4400
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