Tunneling chemical reactions in solid parahydrogen: A case of CD3+H2→CD3H+H at 5 K

Article abstract of DOI:10.1063/1.476152

Ultraviolet photolysis of CD₃I in solid parahydrogen at 5 K gives CD₃ radical, which decreases in a single exponential manner with a rate constant of (4.7±0.5)×10^-6 s^-1. Concomitantly, CD₃H is formed, which is accounted for by the quantum tunneling reaction CD₃+H₂→CD₃H+H. Under the same conditions. CH₃I yields CH₃ radical, but the corresponding reaction between CH₃ and H₂, expected to give CH₄+H, does not proceed measurably at 5 K. The difference between the two systems is attributed to the difference in the zero point energy change.

Full text of DOI:10.1063/1.476152

Tunneling chemical reactions in solid parahydrogen: A case of CD 3 +H 2 →CD 3 H+H
at 5 K
Takamasa Momose, Hiromichi Hoshina, Norihito Sogoshi, Hiroyuki Katsuki, Tomonari Wakabayashi, and
Tadamasa Shida
Citation: The Journal of Chemical Physics 108, 7334 (1998); doi: 10.1063/1.476152
View online: http://dx.doi.org/10.1063/1.476152
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 108, NUMBER 17
1 MAY 1998
Tunneling chemical reactions in solid parahydrogen: A case
of CD3؉H2˜CD3H؉H at 5 K
Takamasa Momose, Hiromichi Hoshina, Norihito Sogoshi, Hiroyuki Katsuki,
Tomonari Wakabayashi, and Tadamasa Shida
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
͑Received 15 December 1997; accepted 26 January 1998͒
Ultraviolet photolysis of CD3I in solid parahydrogen at 5 K gives CD3 radical, which decreases in
a single exponential manner with a rate constant of (4.7Ϯ0.5)ϫ10Ϫ6 Ϫ1. Concomitantly, CD3H is
s
formed, which is accounted for by the quantum tunneling reaction CD3ϩH2→CD3HϩH. Under the
same conditions, CH3I yields CH3 radical, but the corresponding reaction between CH3 and H2,
expected to give CH4ϩH, does not proceed measurably at 5 K. The difference between the two
systems is attributed to the difference in the zero point energy change. © 1998 American Institute
of Physics. ͓S0021-9606͑98͒00417-6͔
I. INTRODUCTION
surrounding hydrogen molecules, if the reaction is thermo-
dynamically allowed. In this paper, we have studied chemi-
cal reactions ͑I͒ and ͑II͒ between a methyl radical and a
hydrogen molecule:
Gas-phase chemical reactions at subambient tempera-
tures are current topics in connection with the modeling of
chemical and photochemical processes in the stratosphere as
well as in interstellar clouds.1,2 In particular, chemical reac-
tions of the type XϩH2→XHϩH are regarded as constitut-
ing major links in molecular processes in outer space be-
cause of the overwhelming abundance of hydrogen in the
universe. Until recently, X was considered to be a positive
ion as in the example CHϩϩH2→CH2ϩϩH. This is because
ion–molecule reactions proceed with temperature-
independent Langevin rate coefficients3 so that they can be
candidates for molecular evolution compatible with the en-
vironment in the outer space. However, as reviewed by
Herbst,1 reactions between neutral radicals and molecules
also appear surprisingly rapid at low temperatures. As one
such reaction, Herbst studied theoretically the reaction
C2HϩH2→C2H2ϩH, which has an activation energy as large
as Ϸ1000 cmϪ1, and showed that the rate constant increases
at temperatures below 50 K, reaching a value of 2.2
ϫ10Ϫ15 cm3 moleculeϪ1 sϪ1 at 10 K when the tunneling
contribution is included.4 Under the circumstances, an ex-
perimental investigation on the tunneling contribution to
chemical reactions between neutral molecules is desirable.
Numerous studies on the tunneling effect have been carried
out for reactions where the tunneling agent is an electron, a
proton, and a hydrogen atom, as is reviewed in textbooks.5–7
As for reactions at cryogenic temperatures, a typical example
of hydrogen atom transfer is of the type
RHϩ•CH3→•RϩCH4, which is studied by ESR
spectroscopy.8 In the present work, we are concerned with
reactions of the type XϩH2→XHϩH, with X being a neutral
species, as in the reaction studied by Herbst.
•CH3ϩH2→CH4ϩH,
•CD3ϩH2→CD3HϩH
͑I͒
͑II͒
The radicals were produced by the UV photolysis of methyl
iodide and its deuterated species as in ͑III͒:
CH3I/CD3Iϩh␯→•CH3 /•CD3ϩI in p-H2.
͑III͒
As a result, we have found that reaction ͑II͒ takes place at 5
K in solid p-H2, while reaction ͑I͒ does not measurably un-
der the same conditions. Since the activation energy of these
reactions is Ϸ3700 cmϪ1 ͑see below͒, thermal activation for
the reactions at 5 K is prohibitive. Therefore, the occurrence
of reaction ͑II͒ must be ascribed exclusively to quantum tun-
neling. To our knowledge, the present work provides the first
direct spectral evidence for an exclusive tunneling reaction
between neutral molecules.
II. EXPERIMENT
Normal hydrogen gas was converted to p-H2 which con-
tained about less than 0.01% residual orthohydrogen. The
converted gas was mixed with either CH3I or CD3I at room
temperatures. The concentration ratio of the iodides to p-H2
was typically 0.005%. The mixed gas was introduced into a
cylindrical copper cell of dimensions 5 to 10 cm long and 2
cm in diameter attached with BaF2 windows at both ends of
the cylinder. The temperature of the cell was kept at about
9.0 K during the introduction of the sample gas for some 1.5
h. Then, the temperature was slowly lowered to 5.1Ϯ0.2 K
and kept at the same temperature throughout the experiment.
A low pressure 20 W mercury lamp was used without filters
for the photolysis of the methyl iodides. The optical mea-
surement was performed using a Nicolet Magna 750 FTIR
spectrometer with a resolution of 0.25 cmϪ1 in combination
with a KBr beam splitter and a liquid N2 cooled MCT-
We have been using solid parahydrogen (p-H2) as a
matrix for matrix-isolation spectroscopy.9–15 By virtue of the
softness of the matrix, solid p-H2 is free from the cage ef-
fect, and unstable molecules such as free radicals can easily
be produced by photolysis in the matrix. The radicals thus
produced in the solid p-H2 are subjected to reactions with
0021-9606/98/108(17)/7334/5/$15.00
7334
© 1998 American Institute of Physics
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J. Chem. Phys., Vol. 108, No. 17, 1 May 1998
Momose et al.
7335
FIG. 1. Infrared absorption spectra of perdeuterated methyl iodide (CD3I) in
solid p-H2 at about 5 K in the spectral region of 2388Ϫ2407 cmϪ1. The
spectra are for the sample as deposited and recorded before UV irradiation
͑top͒, after a 4 h UV irradiation ͑middle͒, and after about 1.5 days in the
dark at about 5 K ͑bottom͒. The bottom spectrum has ϳ60% of the intensity
of the spectrum in the middle.
FIG. 3. The ␯ band of CD3H in solid p-H2 at about 5 K.
3a
doubly degenerate C–D stretching mode (␯3) of the CD3
radical by comparison with the reported band origin of the
radical at 2381 cmϪ1 in a Ne matrix16 and at 2381.088 cmϪ1
in the gas.17 The ␯ band extends over Ϸ2400–2330 cmϪ1
3
according to the gas phase study.17 The spectral structure of
CD3 in Figs. 2 and 3 is attributed to rotational structure sub-
jected to crystal field splitting.12–14 A detailed analysis of the
spectrum of the CD3 radical will be published separately.18
Due to the strong absorption of carbon dioxide, the peaks of
CD3 below 2388 cmϪ1 are not shown in Fig. 1. The peaks
attributed to CD3 diminish to about 60% after standing 1.5
͑HgCdTe͒ detector. For reference, the infrared spectra of
methane and methane-d3 dispersed in solid p-H2 were mea-
sured under the same conditions as those for the iodide sys-
tems. Further details of the experiment are given in our pre-
vious papers.9–15
III. RESULTS
days as shown in the bottom spectrum of Fig. 1. Figure 2
The experiment consists of a series of infrared absorp-
tion measurements of the CH3I/p-H2 and the CD3I/p-H2
systems before and after UV irradiation and after subsequent
standing in the dark at 5.1Ϯ0.2 K. Figures 1 and 2 show
representative portions of the spectra of the CD3I/p-H2 sys-
tem before UV irradiation ͑top͒, after a 4 h irradiation
͑middle͒, and after subsequent standing for about 1.5 days
͑bottom͒. A total of four runs of the experiment were carried
out to ascertain the reproducibility of the experimental re-
sults. The arrowed peaks at 2398.7, 2395.6, 2394.3, 2390.5,
and 2388.7 cmϪ1 in the middle spectrum are attributed to the
19
demonstrates that the absorption of CD3H ͑␯
͒ appears
3a
during the 1.5 days standing ͑the bottom spectrum͒. This
spectrum should be compared with Fig. 3, showing the ␯
3a
band of CD3H isolated in solid p-H2.20 One may notice a
slight difference in the intensity distribution between the ref-
erence spectrum in Fig. 3 and the bottom spectrum of Fig. 2.
This can be accounted for in terms of the slow relaxation of
the nuclear spin state of CD3H, in the same way as the pro-
totypical system CH4 /p-H2.12,14 Although not shown, other
19,20
absorptions of CD3H assigned to ␯3b , ␯2 , and ␯
also
4a
appeared in parallel with the absorption of ␯
.
3a
As for the CH3I/p-H2 system, the absorption of CH3
radical appeared upon the UV irradiation as a doublet at
3171.4/3170.6 cmϪ1 ͑strong͒, 1402.7/1401.6 cmϪ1 ͑strong͒,
and 2780.1/2779.3 cmϪ1 ͑weak͒, reproducing our previous
work.9 These absorptions are assigned to the crystal field
split doublet R(0) line of the doubly degenerate C–H
stretching (␯3), the doubly degenerate C–H bending (␯4),
and the overtone of ␯ of CH3, respectively.12 As in our
4
previous work, these absorptions of the methyl radical were
found not to diminish measurably at 5 K in the dark over a
period of a few days. The absence of the decrease of the CH3
radical in the dark is in remarkable contrast to the case of
CD3 radical shown in Fig. 1.
Figure 4 demonstrates the time dependence of the loga-
rithmic absorbance of CD3 at 2388.7 cmϪ1 during the stand-
ing in the dark. The tϭ0 point in Fig. 4 corresponds to the
sample after a 4 h UV irradiation ͑corresponding to the
middle spectrum of Fig. 1͒. Similarly, Fig. 5 demonstrates
the time dependence of the absorbance of CD3H at
FIG. 2. Infrared absorption spectra of perdeuterated methyl iodide (CD3I) in
solid p-H2 at about 5 K in the spectral region of 2978Ϫ3004 cmϪ1. The
spectra are for the sample as deposited and recorded before UV irradiation
͑top͒, after a 4 h UV irradiation ͑middle͒, and after about 1.5 days in the
dark at about 5 K ͑bottom͒.
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7336
J. Chem. Phys., Vol. 108, No. 17, 1 May 1998
Momose et al.
of the background absorption the accuracy of k and k is
Ј
only moderate, but k and k may be regarded as being equal
Ј
within the error, which is consistent with reaction ͑II͒ during
the dark period.
One might consider that the formation of CD3H in the
CD3I/p-H2 system is due to a reaction between CD3 and H
atoms, the latter being produced by some unknown reaction
in our system. Reactions of such migratory H atoms have
been discussed by Miyazaki et al.22 However, there seems
no mechanism to have migratory H atoms in our system,
which makes us consider the direct reaction between CD3
and H2. Moreover, if H atoms were produced by some over-
looked reaction, they would be produced plausibly in the
CH3I/p-H2 system also, and one would obtain CH4 by the
corresponding reaction of CH3ϩH→CH4, which is not sub-
stantiated in our experiment.
FIG. 4. The logarithmic intensity of CD3 as a function of time while stand-
ing at 5 K in the dark. The solid line is the theoretical curve of Eq. ͑1͒ with
kϭ(4.7Ϯ0.5)ϫ10Ϫ6 sϪ1
.
IV. DISCUSSION
Gas-phase reactions of the type XϩH2→XHϩH with X
being the isoelectronic series of F, OH, NH2, and CH3 have
been studied both experimentally and theoretically.23 In par-
ticular, the reaction CH3ϩH2→CH4ϩH and its deuterium
analogues have been intensively studied by Truhlar and his
co-workers because of their fundamental importance in hy-
drocarbon chemistry and because of the availability of ex-
2995 cmϪ1 in arbitrary units. In both figures the observed
peak height I was normalized relative to the intrinsic absorp-
tion of p-H2 at 2410.5384 cmϪ1 which is known to corre-
spond to the Jϭ6←0 transition.21 If we assume that reaction
͑II͒ occurred during the dark period, the temporal change of
the infrared absorption intensity of CD3, designated as
ICD (t), and that of CD3H, designated as ICD H(t), should be
3
3
perimental kinetic data over
a
wide range of
described by the following equations:
temperature.24–27 Deuterium isotope effects in the reaction
have also been investigated by Schatz et al.28 In these previ-
ous studies, focus was placed on normal ͑high temperature͒
chemistry and the contribution of the tunneling effect to the
reaction was treated rather secondarily because the major
part of the reaction is due to thermal processes.
ICD t͒ϭCeϪkt
,
͑1͒
͑2͒
͑
3
ICD H t͒ϭC 1ϪC eϪk t͒,
Ј
͑
͑
Ј
Љ
3
where C, C , and C are arbitrary constants. Equation ͑1͒ is
Ј
Љ
based on the consideration that the bimolecular reaction ͑II͒
is a statistical process to conform to an exponential decay.
In the present experiment carried out at about 5 K, the
occurrence of reaction ͑II͒ must be ascribed exclusively to
tunneling because the experimentally determined activation
energy for reactions ͑I͒ and ͑II͒ amounts to 10.9
Ϯ0.5 kcal/mol͑Х3700 cmϪ1).23
Quantum tunneling in chemical reactions has long at-
tracted chemists’ interest.5–7 The nonlinearity of the Arrhen-
ius plot of reaction rate constant versus the inverse of tem-
perature is taken customarily as an indication of the
involvement of tunneling. However, the nonlinearity itself
should not necessarily be attributed to tunneling because of
other possible causes such as the temperature dependent ef-
fect of solvent in the case of reactions in liquids and frozen
solvents. Therefore, convincing evidence for tunneling based
on the temperature dependence of reaction rate constants is
scarce29 and Siebrand stated that ‘‘it is difficult to prove that
a given reaction proceeds via tunneling.’’ 30
The parameters k and k represent the rate constants. The
Ј
decay of CD3 in Fig. 4 is fitted to Eq. ͑1͒ by the least squares
method to obtain kϭ(4.7Ϯ0.5)ϫ10Ϫ6 sϪ1 while the fitting
of the increase of CD3H in Fig. 5 to Eq. ͑2͒ gives the value
of k ϭ(4.1Ϯ0.5)ϫ10Ϫ6 Ϫ1. The best fitted curves are
s
Ј
drawn in Figs. 4 and 5. Due to the noise and the uncertainty
The present result demonstrated in Figs. 1–4 provides
spectral evidence for the occurrence of reaction ͑II͒, which
must proceed via tunneling at the low temperature of Ϸ5 K.
It is noted that the amplitude of the zero point vibration of
p-H2 molecule amounts to as much as Ϸ18% of the lattice
constant31 so that the overlap of the wave function of the
reacting p-H2 molecule with that of the radical is considered
to be essential for inducing the tunneling.
FIG. 5. The intensity of CD3H in arbitrary units as a function of time while
One may think that the iodine atom produced by the
photodissociation of the methyl iodides ͓reaction ͑III͔͒ plays
standing at 5 K in the dark. The solid line is the theoretical curve of Eq. ͑2͒
with k ϭ(4.1Ϯ0.5)ϫ10Ϫ6 sϪ1
.
Ј
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J. Chem. Phys., Vol. 108, No. 17, 1 May 1998
Momose et al.
7337
TABLE I. Zero point vibrational energies ͑ZPE͒ of reactions ͑I͒ and ͑II͒ in
units of kcal molϪ1
.
͑I͒
͑II͒
CH3ϩH2→CH4ϩH
CD3ϩH2→CD3HϩH
18.90
ZPE͑CD3͒
13.80
6.29
22.71
2.62
ZPE͑CH3͒
ZPE͑H2͒
ZPE͑CH4͒
⌬ZPEa
6.29
28.34
3.15
ZPE͑H2͒
ZPE͑CD3H͒
⌬ZPEa
a⌬ZPEϭZPE͑CH4 /CD3H͒–ZPE͑CH3 /CD3͒–ZPE͑H2͒.
some role in reactions ͑I͒ and ͑II͒. However, we can deny the
possibility as follows. The analysis of the rotation-vibration
spectra of CH3 and CD3 reveals that these radicals are rotat-
ing almost freely in a crystal field of D3h symmetry.12,18 The
conservation of the symmetry of the crystal surrounding the
radicals indicates that the iodine atom is separated enough
from the radicals not to disturb the energy levels of the radi-
cals. Since most of the excess energy of reaction ͑III͒ is
transferred to the radicals as translational energy,32,33 the
radical and the iodine atom are plausibly well separated in
the soft medium.
FIG. 6. An energy diagram for reactions ͑I͒ and ͑II͒. The horizontal lines at
the bottom and at the top correspond, respectively, to the energy levels
without and with the zero-point energies of the reactants and the products.
amplitude zero-point vibration of p-H2 favoring the overlap
of wave functions of the reacting hydrogen molecule and the
radical.
ACKNOWLEDGMENTS
The crux of the present work is the finding that reaction
͑II͒ takes place while reaction ͑I͒ does not under the same
experimental conditions. With such a clear-cut difference be-
tween the two systems, one may be inclined to call on such a
physical cause as the symmetry selection rules for reactants
and products consisting of several identical H ͑fermions͒ and
D ͑bosons͒.34 However, it is found that symmetry consider-
ations on the product of the rotational and the nuclear spin
states of the reactants and products do not lead to any restric-
tive selection rule. Since the usual isotope effect is kinetic
rather than thermodynamic and generally predicts slower rate
constants for deuterated systems, we seek a thermodynami-
cal cause as responsible for the apparently inverted isotope
effect in the present study.
The zero point vibrational energies ͑ZPE͒ pertaining to
reactions ͑I͒ and ͑II͒ and the difference defined as
⌬ZPEϭ⌺ZPE͑products͒Ϫ⌺ZPE͑reactants͒ are given in
Table I.35 The difference of the potential minima of reactants
and products is called here the reaction energy23 and is de-
noted as ⌬ER , while the sum of ⌬ER and ⌬ ZPE is called
the reaction enthalpy ⌬HR .23 Then, in so far as ⌬ER is as-
sumed to be common to reactions ͑I͒ and ͑II͒, reactions ͑I͒
The authors are grateful to Professor Yoshihiro Mizugai
and Dr. Kazumi Toriyama for their generous gift of
methane-d3 . They thank Professor Koichi Yamashita for his
helpful comment. The present work is partially supported by
the Grant-in-Aid for Scientific Research of the Ministry of
Education, Science, Culture, and Sports of Japan. T.M. ac-
knowledges the support from the Inamori Foundation and the
Asahi Glass Foundation.
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͓
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R
R
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attributed to the very subtle exothermicity and to the large
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J. Chem. Phys., Vol. 108, No. 17, 1 May 1998
Momose et al.
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