H/D isotope effects on formation and photodissociation of HKrCl in solid Kr

Article abstract of DOI:10.1063/1.1560635

The H/D isotope effects on formation and photodissociation of HKrCl in solid Kr were investigated. The formation kinetics of HKrCl and DKrCl reveals the isotope effect on thermally activated mobility of atomic hydrogen. Thus, the difference between the H and D mobilities allowed to show that a reaction of D atoms with HKrCl was taking place. Thus, the HKrCl and DKrCl photodecomposition rates were compared.

Full text of DOI:10.1063/1.1560635

H/D isotope effects on formation and photodissociation of HKrCl in solid Kr
Leonid Khriachtchev, Mia Saarelainen, Mika Pettersson, and Markku Räsänen
Citation: The Journal of Chemical Physics 118, 6403 (2003); doi: 10.1063/1.1560635
View online: http://dx.doi.org/10.1063/1.1560635
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 118, NUMBER 14
8 APRIL 2003
HÕD isotope effects on formation and photodissociation
of HKrCl in solid Kr
Leonid Khriachtchev,a) Mia Saarelainen, Mika Pettersson, and Markku R a¨ s a¨ nen
Laboratory of Physical Chemistry, P.O. Box 55, FIN-00014 University of Helsinki, Finland
͑
Received 19 November 2002; accepted 24 January 2003͒
The HCl ͑DCl͒/Kr matrixes were irradiated at 193 nm, which produced matrix-isolated H ͑D͒ and
Cl atoms as permanent photolysis products. The annealing-induced formation of HKrCl and DKrCl
was used as a measure of atomic hydrogen ͑H and D͒ mobility at various annealing temperatures
͑
from 24 to 30 K͒. The temperature dependencies of the HKrCl and DKrCl formation rates yield
ϳ64 and 68 meV for the corresponding activation energies estimating the isotope effect on atomic
hydrogen mobility in solid Kr ͑D slower than H͒. The difference in mobility of H and D atoms
allowed us to demonstrate a reaction between D atoms and HKrCl molecules, and the suggested
kinetic model is in good agreement with experiment. In addition, the H/D isotope effects on the
solid-state photodissociation of HCl and HKrCl are studied and discussed. © 2003 American
Institute of Physics. ͓DOI: 10.1063/1.1560635͔
I. INTRODUCTION
drogen atoms in a relaxed Xe lattice agreed reasonably with
experiment with respect to the isotopic effects but it under-
estimated the jump rate.
The family of HRgY molecules (Rgϭrare gas atom, Y
ϭelectronegative fragment͒ introduced in 1995 by the Hels-
inki group contains now 13 members ͑HXeI, HKrCl, HArF,
The annealing-induced formation of HRgY consumes a
large part of H atoms generated during photolysis of HY.1
Moreover, the experimental data reveal further reactions of
the HRgY molecules with mobile H atoms as demonstrated
for HXeH molecules in solid Xe.10 A simple kinetic model
including reactions of HRgY molecules with mobile H atoms
described the experimental observations. It was proposed
that these reactions limited the amounts of HXeH molecules
upon annealing and presumably resulted in formation of H2
molecules, hence the proposed reaction scheme formed a
buffering mechanism stabilizing the HXeH concentration in
solid Xe.
The HRgY molecules are known to decompose easily
while exposed to UV and, in some cases, to visible light,
which features the transition to electronically excited repul-
sive states. The wavelength dependence of the photodissocia-
tion efficiency was studied for matrix-isolated HKrCl, HArF,
1
–3
ϩ
Ϫ
etc.͒. These molecules show a charge transfer (HRg) Y
character, and they are easily detected due to very strong
absorption intensity of the H–Rg stretching vibration. The
HRgY molecules can be prepared in rare-gas matrixes using
photolysis of the HY precursor and subsequent thermal mo-
bilization of H atoms to promote their reactions with neutral
RgϩY centers. In some cases, the HRgY molecules ͑HKrCl,
HXeNCO, and HArF͒ were detected already during solid-
state photolysis of the HY precursor featuring a quite limited
light-induced travel distance of dissociating H atoms in rare-
2
,4,5
gas lattices.
This local formation of the HRgY intermedi-
ates in photolysis of HY in a rare-gas host was studied theo-
6
retically as well.
Thermally induced motion of atomic hydrogen in rare-
gas solids, in addition to the common interest, is of particular
importance for the formation of the HRgY molecules.
Eberlein and Creuzburg studied thermal mobility of atomic
hydrogen in Xe and Kr matrixes and extracted activation
energies of 123 and 66 meV, respectively. Vaskonen et al.
obtained considerably larger activation energy for H atom
thermal mobility in solid Kr ͑90–140 meV͒. No H/D iso-
tope effect was found in those two studies for hydrogen mo-
bility in solid Kr. We have recently suggested that the
diffusion-controlled formation of the HRgY molecules is a
productive approach to investigate accurately thermal mobil-
ity of atomic hydrogen in rare-gas solids, and the method has
been successfully employed for the case of HXeH and
HKrF, HXeOH, and HXeH molecules showing large differ-
7
3,5,11
ences between their photodissociation profiles.
However,
no clear H/D isotope effect on the solid-state photodissocia-
tion efficiency was found in those studies. Direct measure-
8
ments of UV absorption spectra were also performed for a
number of HRgY molecules.1
1–13
For HXeH, the measured
photodecomposition and absorption profiles are very
similar,13 which shows that this photodecomposition method
can be successfully applied to probe electronically excited
states of HRgY molecules.
9
HXeOH in solid Xe. That study definitely distinguished the
mobilities of atomic H and D isotopes in solid Xe featuring a
difference of ϳ4 meV between the corresponding activation
energies. The modeling of thermally activated jumps of hy-
In this work, we investigate H/D isotope effects on for-
mation and photodissociation of HKrCl in solid Kr. The for-
mation kinetics of HKrCl and DKrCl reveals the isotope ef-
fect on thermally activated mobility of atomic hydrogen. The
difference between the H and D mobilities allowed us to
a͒Electronic mail: Leonid.Khriachtchev@Helsinki.Fi
0021-9606/2003/118(14)/6403/8/$20.00
6403
© 2003 American Institute of Physics
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1

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J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Khriachtchev et al.
FIG. 1. IR absorption spectra of HCl and DCl in an as-deposited Kr matrix
the lower trace͒ and HKrCl and DKrCl prepared by irradiating the depos-
ited sample at 193 nm and consequent annealing at 30 K ͑the upper trace͒.
FIG. 2. Photolysis kinetics of the HCl and DCl precursors and the HKrCl
and DKrCl intermediate products. The data were obtained by integrating the
corresponding IR absorption bands in the same experiment with a HCl/
DCl/Kr sample ͑ϳ1:1:2000͒. The data for HKrCl and DKrCl are normalized
by the initial integrated absorptions of HCl and DCl, respectively, and mul-
tiplied by a factor of 2.5 for better presentation. The 193 nm photolysis was
͑
The IR absorption spectra were measured at 8 K.
2
show that a reaction of D atoms with HKrCl is taking place.
The HKrCl and DKrCl photodecomposition rates are com-
pared.
performed at 8 K, the pulse energy density being ϳ10 mJ/cm .
transfer absorption is observed for the present case of rela-
tively thick samples.17 The typical 193 nm photolysis kinet-
ics is presented in Fig. 2. The DCl photodissociation is
essentially slower, by a factor of ϳ2.0, as compared with
HCl. Both HKrCl and DKrCl are formed during photolysis,
and this evidences the locality of the primary photolysis
II. EXPERIMENT
The gaseous HCl ͑DCl͒/Kr mixtures were deposited onto
a CsI window. The deposition temperature was 20 K, the
deposition time was ϳ20 min, and the typical matrix thick-
ness was 50–100 ␮m. Efficient deuteration ͑up to 75%͒ was
achieved by passing the HCl/Kr gaseous mixture through a
tube with D SO droplets. The experiments were performed
5
event as discussed elsewhere for the case of HKrCl. In Fig.
2
, the HKrCl and DKrCl absorptions are normalized by the
initial amounts of HCl and DCl, respectively, which allows
their numerical comparison assuming the same H/D isotope
effect on the corresponding IR absorption intensities. It is
seen that HKrCl forms relatively more efficiently in the early
stage of irradiation whereas DKrCl is relatively more abun-
2
4
at temperatures down to 8 K provided by a closed-cycle cry-
ostat ͑DE-202A, APD͒. The infrared ͑IR͒ absorption spectra
Ϫ1
in the 4000 to 400 cm region were recorded with a Nicolet
6
0 SX FTIR spectrometer using resolution of 1 cmϪ1. In
ϩ
dant after long photolysis. As an additional product, KrHKr
order to decompose HCl and DCl molecules, the samples
were irradiated with an excimer laser ͑MPB, MSX-250͒ op-
erating at 193 nm. Typically, we used in photolysis up to
ϩ
18
and KrDKr ions appear after photolysis, but based on
their ab initio infrared intensities ͑MP2/aug-cc-pVTZ level͒
their concentration is negligible.5
4
2
ϳ10 pulses with a pulse energy density of ϳ10 mJ/cm .
Most of the experiments were performed using samples with
similar HCl/Kr ratios of ϳ1:1000. We decomposed HCl mol-
ecules to a similar level of ϳ0.3, which produced similar
concentrations for hydrogen atoms in various experiments.
The photodecomposition of HKrCl and DKrCl was done
with the second harmonic of tunable signal radiation of an
optical parametric oscillator ͑Continuum͒.
Upon annealing of a photolyzed sample at ϳ30 K, hy-
drogen atoms become mobile and HKrCl and DKrCl mol-
ecules form efficiently as monitored by the H–Kr and D–Kr
Ϫ1
stretching absorption bands at 1476 and 1106 cm , respec-
tively ͑see Fig. 1, the upper trace͒.19 The annealing-induced
formation of the products clearly depends on the annealing
temperature as demonstrated in Fig. 3͑a͒ for HKrCl obtained
in the HCl/Kr ͑deuterium-free͒ samples ͑matrix ratio
ϳ1:1000͒. The data points were normalized by the values
measured after additional annealing at 30 K, which saturated
processes caused by hydrogen mobility. In fact, the increase
of the matrix temperature by 1 K accelerated the growth of
the HKrCl concentration by a factor of 3–4. As shown in
III. EXPERIMENTAL RESULTS
The IR absorption spectrum of HCl and DCl in solid Kr
measured at 8 K is presented in Fig. 1 ͑the lower trace͒, and
it is in agreement with the literature data.1
4,15
The sample is
quite monomeric with respect to HCl and, in particular, com-
plexation with nitrogen is negligible. Upon irradiation at 193
Fig. 3͑a͒, the formation kinetics can be successfully fitted by
a
the stretched-exponential function 1Ϫexp(Ϫk t ) typically
0
nm, HCl and DCl decompose and the Kr Cl emission rises
with aϳ0.55. On one hand, the formation kinetics at a given
temperature is quite reproducible for various samples with
similar compositions. On the other hand, the formation rate
2
5
,16
around 355 nm.
For longer irradiation, clear features of
self-limited photolysis due to the rising Kr–Cl charge-
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J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Isotope effects of HKrCl in solid Kr
6405
FIG. 3. ͑a͒ Formation kinetics of HKrCl at various annealing temperatures
of photolyzed HCl/Kr matrixes ͑ϳ1:1000͒. The concentration values ob-
Ϫ1
tained by integrating the 1476 cm band of HKrCl are normalized by the
values obtained after additional annealing at 30 K. The lines are fits of the
a
experimental data by 1Ϫexp(Ϫk t ) with a ϳ0.55. ͑b͒ Characteristic for-
0
mation time ͑at the 0.63 level͒ and formation efficiency of HKrCl as a
function of the Kr/HCl ratio obtained upon annealing at 25 K. The formation
efficiency is defined as the ratio between the integrated absorption of result-
ing HKrCl and the integrated absorption of photolyzed HCl. The IR absorp-
tion spectra were measured at 8 K.
obviously slows down for less concentrated samples. Figure
3
͑b͒ shows a nearly linear dependence of the characteristic
FIG. 4. ͑a͒ Formation of HKrCl and DKrCl upon annealing at 26 K of a
photolyzed HCl/DCl/Kr matrix ͑ϳ1:1:2000͒. ͑b͒ Formation of HKrCl and
DKrCl upon annealing at 29 K. The first data point corresponds to annealing
during 1 min. Note the similar characteristic time of the DKrCl growth and
the HKrCl decay upon longer annealing. The HCl/DCl/Kr matrix
time of HKrCl formation on the initial Kr/HCl ratio obtained
at 25 K. The precursor concentration influences also the
HKrCl formation efficiency, which is defined as the ratio
between the integrated absorption of resulting HKrCl and the
integrated absorption of photolyzed HCl. This parameter was
quite similar for the 1:1000, 1:2000, and 1:5000 matrix ra-
tios, and it somewhat decreased for the HCl/Kr ratio of
͑
ϳ1:3:4000͒ was used. ͑c͒ Formation of HKrCl upon annealing at 27 K of a
photolyzed HCl/Kr ͑ϳ1:1000͒ and HCl/DCl/Kr ͑ϳ1:1:2000͒ matrixes. Note
that in the partially deuterated sample the HKrCl concentration decreases in
the final stage of annealing due to its destruction by reaction with D atoms.
Ϫ1
1
:500.
The concentrations are obtained by integrating the 1476 and 1106 cm
bands of HKrCl and DKrCl and then normalized by the values obtained
after additional annealing at 30 K. The IR absorption spectra were measured
at 8 K.
Figure 4͑a͒ compares the formation kinetics of HKrCl
and DKrCl at 26 K, the data being normalized by the values
measured after additional annealing at 30 K. The curves are
obtained in the same experiment with an initial HCl/DCl
concentration ratio of ϳ1. It is seen that the DKrCl forma-
tion during annealing is significantly slower than that of
HKrCl. HKrCl is formed upon H mobility and it grows at the
initial annealing stage whereas the DKrCl formation con-
trolled by D mobility is clearly delayed. In analogy with the
slightly decreases at the last stage of annealing while the
DKrCl concentration increases. This behavior can be demon-
strated more clearly using higher annealing temperatures ͓see
Fig. 4͑b͔͒. Importantly, the increase of the DKrCl concentra-
tion and the decrease of the HKrCl concentration occur in the
same time scale. Moreover, this decrease of the HKrCl con-
centration occurs only when D atoms are present in the ma-
trix. To illustrate this fact, Fig. 4͑c͒ presents the formation
kinetics of HKrCl in HCl/Kr and HCl/DCl/Kr matrixes upon
9
case of solid Xe, this experimental data can be qualitatively
explained by faster thermal motion of H atoms compared
with D atoms.
It is seen in Fig. 4͑a͒ that the HKrCl concentration
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6406
J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Khriachtchev et al.
composition in the HϩCl channel, and k2 describes the
HKrCl decomposition. It was measured by us earlier that
5
k /k ϳ1.4 for the 193 nm photolysis of HCl in solid Kr,
1
3
i.e., formation of the photolabile HKrCl intermediate is the
major channel for permanent solid-state dissociation of HCl
with excess energy of 1.8 eV. In particular, this model sug-
gests essentially short-range travel of the H atoms from the
parent cage in the primary photolysis event without essential
long-distance contribution. This conclusion on the locality of
the solid state photodissociation was verified by experiments
with very diluted matrixes ͑ϳ1:5000 and 1:15 000͒, and the
formation of the intermediate was at least as efficient as in
5
the more concentrated matrixes. As a relevant example dis-
cussed by Buck,21 photolabile HXeI intermediates were sup-
posed to be formed in Xe clusters via local photodissociation
of HI molecules irradiated at 243 nm.
The three-component model of local photolysis explains
the observed differences between the evolution of the HKrCl
and DKrCl isotopologues. The faster increase of HKrCl
compared with DKrCl seen in the beginning is a direct con-
sequence of the faster decomposition of HCl as compared
with DCl. The larger relative concentration of DKrCl after
long irradiation can be explained by its higher photostability
and the larger residual concentration of DCl. Based on the
initial stage of photolysis kinetics, the production of the
HKrCl and DKrCl intermediates is quite proportional ͑with
accuracy of 10%͒ to the decomposition of the HCl and DCl
precursors. Following Eq. ͑1͒ and taking into account that
k2Ͼk1ϩk3 , we see that our present data does not indicate
any large difference in solid-state photodissociation dynam-
ics of HKrCl and DKrCl, which is characterized by the
k1 /k3 ratios. The strongest isotope-induced distinctions in
photolysis kinetics occur at the HCl and DCl photodissocia-
tion step ͑cage exit controlled by k1ϩk3), and the branching
ratio between the short range and long range stabilization of
hydrogen atom seems to be rather similar for the H and D
forms. Thus, it can be tentatively concluded here that no
large isotope effect on the light-induced dynamics of H and
D atoms takes place for 193 nm photolysis of HCl and DCl
in solid Kr. A more precise numerical analysis is complicated
due to a number of parasitic processes. For instance, the
secondary Kr2Cl emission excited at 193 nm is capable of
contributing to decomposition of the unstable intermediates,
and this decomposition is somewhat different for HKrCl and
DKrCl ͑see Fig. 5͒. Furthermore, in the present experiments,
the photolysis kinetics is self-limited due to the rather high
concentrations of the absorbing Cl product and the rather
thick samples.17 More accurate data obtained with very di-
luted and thin matrixes is needed to detect a small isotope
effect on the k /k ratio and theoretical analysis seems to be
FIG. 5. Ratio of DKrCl and HKrCl photodecomposition rates in solid Kr at
K as a function of the photon energy. The line is a linear fit.
8
annealing at 27 K. Without D atoms, the HKrCl concentra-
tion smoothly increases. If D atoms are present in the matrix
͑in significant amounts͒, the shape of the HKrCl formation
kinetics changes remarkably, namely, the curve saturates
much quicker and finally the concentration even decreases
by ϳ10%. In analogy with similar findings for HXeH in
1
0
solid Xe, we explain the present decrease of the HKrCl
concentration in long annealing by reactions of HKrCl with
D atoms.
The HKrCl photodecomposition profile is known to have
5
maximum at ϳ280 nm. In the present work, the photodis-
sociation rates for HKrCl and DKrCl were compared. If both
species are present in the same matrix, this comparison can
be performed quite reliably even if the difference is rather
small. Clear distinctions in the solid-state photodissociation
rates for HKrCl and DKrCl were found, and the result is
presented in Fig. 5. Upon irradiation at longer wavelengths
͑Ͼ280 nm͒, DKrCl is more stable than HKrCl whereas the
situation becomes opposite at shorter wavelengths. The exci-
tation range in Fig. 5 is limited by 240 nm due to possible
artifacts caused by the secondary Kr Cl emission as dis-
2
cussed later.
IV. DISCUSSION
A. Photolysis-induced formation of HKrCl
The permanent photodecomposition of HCl in solid Kr
requires quite many absorption events due to the low cage
exit probability ͑ϳ5%͒.20 In the case of a successful cage
exit, either the HKrCl intermediate or the HϩCl pair is
formed. The HKrCl intermediate can be further decomposed
by light leading to the HϩCl final product. For the HKrCl
concentration, this model yields:5
1
3
valuable.
The observed difference in the HCl and DCl photodisso-
ciation rates should be commented. First, this effect can be
explained by isotope effect on photoabsorption cross-
sections. Cheng et al. measured HCl and DCl photoabsorp-
tion cross-sections for gas-phase HCl and DCl in the 120–
k1
͓
HKrCl͔ϰ
͓exp͑Ϫk t͒Ϫexp͑Ϫk tϪk t͔͒,
2 1 3
k Ϫk ϩk
3
1
2
͑1͒
22
Ϫ20
2
20 nm spectral region. The values of 8.37ϫ10
and
Ϫ20
2
where k is the rate constants of the HCl decomposition in
2.53ϫ10
cm were obtained at 193 nm for HCl and DCl,
1
the HKrCl channel, k is the rate constants of the HCl de-
respectively, i.e., they differ by a factor of 3.3. Our
3
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J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Isotope effects of HKrCl in solid Kr
6407
FIG. 7. Concentrations of H atoms and H2 and HKrCl molecules as a
function of the annealing time calculated using models ͑2͒–͑6͒. Initial con-
ditions: ͓H͔ ϭ͓Cl͔ ϭ1. Note that the H concentration is divided by 3.
FIG. 6. Natural logarithm of the characteristic formation time ͑in seconds͒
of HKrCl and DKrCl in solid Kr as a function of the reciprocal annealing
temperature. The data for HKrCl are obtained in experiments with HCl/Kr
samples and the data for DKrCl are from experiments with dominating DCl
precursor. As defined, the characteristic formation time corresponds to the
0
0
0
.63 level of the saturation HKrCl ͑DKrCl͒ concentration. The lines are
concentration of the precursors being similar in all experi-
ments. The two dependencies exhibit Arrhenius behavior
with activation energies of (64Ϯ4) and (68Ϯ6) meV for
the H and D forms, respectively, as obtained by their linear
fits. The extracted difference between the activation energies
for the HKrCl and DKrCl formation ͑4 meV͒ is somewhat
smaller than the possible error. However, the same value of
ϳ4 meV can be extracted if we a priori assume the same
pre-exponential factors (ϳe23 1/s) in the Arrhenius plots for
H and D, which makes this estimate quite confident.
The annealing induced formation of rare-gas molecules
allow thermal mobility of hydrogen atoms to be studied.9
This approach implies that the formation of the product oc-
curs at a similar time scale as the decrease of the H concen-
tration, and the characteristic times are proportional to the
jump time of H atoms in the lattice. This conclusion can be
illustrated using a kinetic scheme with the following solid-
state reactions:
linear fits yielding activation energies of (64Ϯ4) and (68Ϯ6) meV for the
H and D forms, respectively. The same difference value of ϳ4 meV can be
obtained if we
a
priori assume the same pre-exponential factors
2
3
(
ϳe 1/s) in the Arrhenius plots for H and D.
solid-phase measurements give a smaller ratio for the corre-
sponding photodecomposition rates ͑2.0͒. The distinction be-
tween the gas-phase and matrix ratios can be in principle due
to a matrix shift of the absorption cross-section contours.
Indeed, the gas-phase photoabsorption cross-sections of HCl
and DCl differ by a factor of 2 already at 185 nm.22 As the
second factor for the observed difference in the HCl and DCl
photodissociation rates, the exit probabilities for H and D
atoms might be different, however, we have neither experi-
mental nor theoretical basis to estimate its contribution.
B. Thermal mobility of H and D atoms
It is known that both annealing-induced decrease of the
H concentration and the formation of rare-gas molecules in
solid Xe slow down in time demonstrating a stretched-
HϩH→H2 ,
HϩKrϩCl→HKrCl,
HϩHKrCl→H ϩKrϩCl,
HϩHKrCl→HClϩKrϩH,
͑2͒
͑3͒
͑4͒
͑5͒
͑6͒
9
exponential shape of the corresponding curves. In addition
2
to the direct kinetic reasons for the deviation from a single-
exponential shape, the physical reasons contributing to this
behavior can be distribution of activation energies due to
structural inhomogeneity and change in the matrix lattice
HϩHCl→H ϩCl.
2
7
properties during annealing. In order to avoid problems with
These reactions are considered as fully controlled by diffu-
sion of H atoms and possessing the same reaction radius, kH
being the corresponding rate constant. The branching ratio
between reactions ͑4͒ and ͑5͒ is taken 1:1. A representative
computational result is given in Fig. 7. The simulations show
that the ratio of the characteristic formation time of HKrCl
molecules and the characteristic decay time of H atoms is
1.18, and it is independent of the initial HCl concentration
and of the annealing temperature. The curves for H and
HKrCl can be fitted by stretched exponents with aϭ0.78 and
0.83, respectively, and these values are also concentration-
finding the proper fitting function, the annealing-induced for-
mation of Xe-containing species was numerically described
using the characteristic time ␶ that corresponds to the 0.63
0
9
level of the saturation concentrations. In the present work,
we follow this approach.
Figure 6 presents the characteristic time ͑in seconds͒ for
the formation of HKrCl and DKrCl as a function of the an-
nealing temperature. The data for HKrCl are obtained in ex-
periments with HCl/Kr matrixes, and the data for DKrCl are
from experiments with the dominating DCl precursor, the
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6408
J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Khriachtchev et al.
independent. It should be emphasized that the stretching ef-
fect is introduced in this model purely by kinetic factors
without including any time dependence of the rate constant.
Taking into account the smaller experimental stretching pa-
rameter obtained for HKrCl formation ͑ϳ0.55͒, we suggest
some annealing-induced modification of matrix morphology
in the present experiments. According to models ͑2͒–͑6͒, the
characteristic time of the product formation is inversely pro-
portional to the initial H and Cl concentration, which is in
accord with the experimental data ͓see Fig. 3͑b͔͒. Of course,
this simple kinetic model yields no concentration depen-
dence of the formation efficiency. The experimentally ob-
served decrease on the HKrCl formation efficiency for more
concentrated samples should be explained by experimental
factor, such as a relative increase of various traps for H at-
oms due to improper lattice structure, HCl multimers, etc.
Some losses of H atoms during photolysis might become
important for the concentrated samples.
in the matrix upon annealing. A strong experimental evi-
dence for this image is a nearly linear dependence of the
HKrCl formation time on the initial Kr/HCl ratio shown in
Fig. 3͑b͒.
Thus, we claim that the formation kinetics of HKrCl and
DKrCl reflects differences in thermal mobility of H and D
atoms with activation energies of approximately 64 and 68
meV. When compared with the literature data on H atom
mobility, our data is in perfect agreement with the activation
7
energy of 66 meV obtained by Eberline and Creuzburg, but
it is considerably smaller than the value of 90–140 meV
8
extracted by Vaskonen et al. A computational model quali-
tatively explained the different mobility of H and D atoms in
solid Xe even though it did not provide numerically accurate
9
results. The model estimated energies in the relaxed inter-
stitial and transition-state configurations of H and D atoms in
solid Xe taking into account the zero-point energies. Analo-
gous calculations would qualitatively support the H/D iso-
tope effect on thermal mobility in solid Kr as well. However,
in the present work, we do not repeat those calculations for
solid Kr because we believe that a more advanced theoretical
approach is needed to reach adequate description.
The present results show the kinetic difference between
reactions promoted by mobility of H and D atoms ͑see Fig.
4͒. It should be emphasized once more that we connect this
difference in formation of HKrCl and DKrCl with slower
thermal motion of D atoms compared with H atoms, i.e.,
with a smaller rate of the elementary jumps for deuterium. In
this consideration, we essentially assume that the reaction
barriers for the formation of HRgY molecules can be ne-
glected at ϳ30 K. This assumption is experimentally veri-
fied. Indeed, HKrCl and HKrF show identical formation ki-
C. D¿HKrCl reaction
As assumed in kinetic models ͑2͒–͑6͒, the formed
HKrCl molecules can further react with hydrogen atoms.
This process can be tested using different thermal mobility of
H and D atoms. HKrCl molecules are formed quickly upon
H mobility. Motion of D atoms spreads into a longer time
scale, after formation of the main part of HKrCl molecules.
If HKrCl molecules react with D atoms, these kinetic distinc-
tions should lead to a decrease of the HKrCl concentration
upon selective mobilization of D atoms. This qualitative pic-
ture was analyzed using kinetic models ͑2͒–͑6͒ with added
analogous reactions for D atoms. We assumed k /k ϭ8 and
3
netics upon the long-range H atom mobility, which would
not be the case if the reaction activation energy were impor-
tant. The formation of HKrCN occurs at similar temperatures
even though the detailed data is not available.23 The forma-
tion of HArF molecules takes place in solid Ar at tempera-
2
tures below 20, which is known to promote H mobility in
8
solid Ar. A part of the HRgY products always form at tem-
peratures that do not allow global motion of H atoms. Fol-
lowing Ref. 24, we call this phenomenon local ͑short-range͒
atomic mobility, and it was studied in details for formation of
H
D
͓
D
͔0 ͓ ͔0
/ H ϭ3, which corresponded to the experimental con-
2
5
HXeI. The presence of low-temperature local formation of
these molecules does not allow essential HϩRgϩY reaction
barriers. Moreover, the formation of HXeCl and HXeBr in
solid Ne at 12 K supports the very low intrinsic formation
barriers of the HRgY molecules.26 Thus, we conclude that
these reactions are mainly diffusion-controlled.
ditions. A representative result of the calculations is shown in
Fig. 8. The HKrCl concentration increases quickly, reaches
the maximum, and finally decreases by about 10%, which is
in remarkable agreement with experiment ͑see Fig. 4͒. The
simultaneous presence of H and D atoms in the matrix
changes the shapes of the kinetic curves compared with the
previous ‘‘D-free’’ consideration: The stretching parameters
for the build up of the HKrCl and DKrCl concentrations
become different, 1.02 and 0.81, respectively. This trend was
found qualitatively for the experimental data presented in
Fig. 4. The good agreement between the experimental and
computational data strongly support the efficient DϩHKrCl
and, consequently, HϩHKrCl reactions. Similarly to the ex-
periment, the simulation shows that the HKrCl concentration
increases and the DKrCl concentration decreases in similar
time scales. The similarity in these time scales means that the
DϩHKrCl reaction barrier does not exceed much the activa-
tion energy for thermal mobility of D atoms, i.e., the reaction
can be considered as diffusion-controlled. These conclusions
are analogous to those done by us earlier for the HϩHXeH
reaction.10
The spatial distribution of H atoms produced by solid-
state photolysis of HCl deserves brief discussion. As shown
earlier, the primary UV photolysis of HCl in solid Kr is an
5
essentially local event. This locality means stabilization of
escaping H atoms at small distances ͑comparable with the
lattice parameter͒ from the parent cage. After the successful
escape, the H atom can react with some probability with the
parent Cl–Kr center resulting in the HKrCl molecule. The
formed rare-gas molecules can be photodecomposed effi-
ciently, making the distribution of H atoms more homoge-
neous taking into account the large excess energy upon 193
nm photodissociation of HKrCl ͑ϳ5 eV͒. Additionally, light-
induced motion of H atoms can be promoted by neutraliza-
ϩ
23
tion of (KrHKr) ions. As a result of this homogenization,
H atoms lose memory of the parent cage and globally diffuse
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J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Isotope effects of HKrCl in solid Kr
6409
DKrCl photodissociation because in this spectral region the
H form is less stable than the D form. In fact, we observed a
relative decrease of the HKrCl photostability at 230 and 193
nm, however, the proportion of the artificial contribution
from the secondary Kr Cl emission is unclear. In order to test
2
this idea further, we compared the HKrCl photodissociation
rates at 193 nm for matrixes with very different initial
HCl/Kr ratios ͑1:1000 and 1:15 000͒. In agreement with our
qualitative consideration, the HKrCl photodissociation was
essentially slower for the less concentrated sample.
It is seen in Fig. 9 that the solid-state DKrCl photodis-
Ϫ1
sociation contour is blue shifted by ϳ0.1 eV ͑ϳ800 cm
͒
with respect to the HKrCl photodissociation contour. An ob-
vious reason for this difference is the smaller zero point en-
ergy of DKrCl compared with that of HKrCl. However, the
direct gap between the zero point energies does not exceed
Ϫ1
3
00 cm suggesting that additional factors should exist. For
example, anharmonicity of the potential surface should lead
to the isotope effect of the same direction. Indeed, the typical
asymmetry of a potential surface with a steeper repulsive
wall should shift the photodissociation contour for DKrCl up
in energy compared with that of HKrCl. This additional shift
is an indirect consequence of the smaller zero point energy
for DKrCl. It is also possible that complex dynamical pro-
cesses of solid-state photodissociation can introduce some
additional difference between HKrCl and DKrCl. One can
speculate that the hydrogen atom ͑H or D͒ should escape the
interstitial site neighboring to the Kr–Cl center for perma-
nent decomposition of the molecule, and this process re-
quires larger excess energy for D atoms. Furthermore, a pos-
FIG. 8. Concentrations of H and D atoms and HKrCl and DKrCl molecules
as a function of the annealing time calculated using models ͑2͒–͑6͒. Initial
conditions: ͓H͔ ϭ0.25, ͓D͔ ϭ0.75, ͓Cl͔ ϭ1. The ratio between rate
constants of H and D mobility is 8. Note that the D concentration is
divided by 3.
0
0
0
D. Solid-state photodissociation
The results presented in Fig. 5 indicate a difference be-
tween photodissociation contours of HKrCl and DKrCl mol-
ecules in solid Kr. Based on the photodissociation data ob-
tained previously for HKrCl,5 we generated the
corresponding contour for DKrCl, and it is shown in Fig. 9.
The data points at 193 and 230 nm are omitted, and the
2
sible H/D isotope effect on the Cl ( P) spin–orbit branching
ratio ͑in analogy with photodissociation of HCl and DCl͒,27
reason for this disregard should be commented. The Kr Cl
2
emission is excited at wavelengths below 240 nm, and the
absorption maximum is at 222 nm. The Kr–Cl charge-
transfer cross-section is unknown to the best of our knowl-
edge, however, it is probably quite large. This secondary
emission locates in the 300–430 nm region, and it can pro-
duce artifacts in numerical comparison of the HKrCl and
might also contribute to the observed distinctions.
V. CONCLUSIONS
In this work, H/D isotope effects on formation and pho-
todissociation of HKrCl in solid Kr have been studied. We
can conclude the following:
͑i͒
The distinctions in the HKrCl and DKrCl formation
kinetics during 193 nm photolysis can be explained
by different photoabsorption cross-sections of HCl
and DCl. No difference for light-induced travel of H
and D atoms is claimed here.
͑ii͒
The kinetic difference in annealing-induced formation
of HKrCl and DKrCl molecules is due to the isotope
effect of global atomic hydrogen mobility in solid Kr,
similarly to the recently reported effect in solid Xe
͑
see Ref. 9͒. As an estimate, the activation energies
for thermal mobility of H and D atoms in solid Kr are
4 and 68 meV, respectively.
6
͑
iii͒ The different thermal mobility of H and D atoms al-
lowed us to demonstrate a reaction between D atoms
and HKrCl molecules. This reaction can be consid-
ered as diffusion-controlled. The experimental obser-
vations agree with the predictions of our simple ki-
netic model.
FIG. 9. Photodecomposition contours of HKrCl and DKrCl in solid Kr at 8
K. The data for HKrCl are from Ref. 5. The data for DKrCl are obtained
using the HKrCl photodecomposition contour and the fitting line in Fig. 5.
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1

6410
J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Khriachtchev et al.
͑
iv͒ The solid-state photodissociation contour for DKrCl
is blue shifted by ϳ0.1 eV as compared with that of
HKrCl. The smaller zero-point energy of the deuter-
ated species presumably contributes to this difference.
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