Temperature dependence and kinetic isotope effects for the OH + HBr reaction and H/D isotopic variants at low temperatures (53-135 K) measured using a pulsed supersonic laval nozzle flow reactor

Article abstract of DOI:10.1021/jp045540n

The reactions of OH + HBr and all isotopic variants have been measured in a pulsed supersonic Laval nozzle flow reactor between 53 and 135 K, using a pulsed DC discharge to create the radical species and laser induced fluorescence on the A ²∑ ←X ²π(v′ = 1 ←v″ = 0) transition. All reactions are found to possess an inverse temperature dependence, in accord with previous work, and are fit to the form k = A(T/298)^-n, with k₁ (OH + HBr) = (10.84 ±0.31) × 10^-12(T/298)^{(-0.67±0-02)} cm³/s, k₂ (OD + HBr) = (6.43 ±2.60) × 10^-12(T/298) ^(-1.19±026) cm³/s, k₃ (OH + DBr) = (5.89 ±1.93) × 10^-12(T/298)^(-0.76±22) cm³/s, and k₄ (OD + DBr) = (4.71 ±1.56) × 10^-12(T/298)^{(-1.09±0.21)} cm³/s. A global fit of k vs T over the temperature range 23-360 K, including the new OH + HBr data, yields k(T) = (1.06 ±0.02) × 10^-11(T/298) ^{(-0.90±0.11)} cm³/s, and (0.96 ±0.02) × 10^-11(T/298)(-0.90±0.03)exp(((-2.88±1.82K)/T) cm ³/s, in accord with previous fits. In addition, the primary and secondary kinetic isotope effects are found to be independent of temperature within experimental error over the range investigated and take on the value of (k_H/k_D)_AVG =1.64 for the primary effect and (k_H/k_D)_AVG =0.87 for the secondary effect. These results are discussed within the context of current experimental and theoretical work.

Full text of DOI:10.1021/jp045540n

J. Phys. Chem. A 2005, 109, 3893-3902
3893
Temperature Dependence and Kinetic Isotope Effects for the OH + HBr Reaction and H/D
Isotopic Variants at Low Temperatures (53-135 K) Measured Using a Pulsed Supersonic
Laval Nozzle Flow Reactor
Christopher Mullen and Mark A. Smith*
Department of Chemistry, UniVersity of Arizona, 1306 E. UniVersity Dr., Tucson, Arizona 85721
ReceiVed: September 30, 2004; In Final Form: February 17, 2005
The reactions of OH + HBr and all isotopic variants have been measured in a pulsed supersonic Laval nozzle
flow reactor between 53 and 135 K, using a pulsed DC discharge to create the radical species and laser
2
2
induced fluorescence on the A Σ r X Π (v′ ) 1 r v′′ ) 0) transition. All reactions are found to possess
-
n
an inverse temperature dependence, in accord with previous work, and are fit to the form k ) A(T/298) ,
-
12
(-0.67(0.02)
3
with k
1
(OH + HBr) ) (10.84 ( 0.31) × 10 (T/298)
cm /s, k
2
(OD + HBr) ) (6.43 ( 2.60) ×
(-0.76(0.22) 3
4
-
12
(-1.19(0.26)
3
-12
10
(T/298)
cm /s, k
3
(OH + DBr) ) (5.89 ( 1.93) × 10 (T/298)
cm /s, and k (OD +
-
12
(-1.09(0.21)
3
DBr) ) (4.71 ( 1.56) × 10 (T/298)
3-360 K, including the new OH + HBr data, yields k(T) ) (1.06 ( 0.02) × 10 (T/298)
and (0.96 ( 0.02) × 10 (T/298) exp cm /s, in accord with previous fits. In addition,
the primary and secondary kinetic isotope effects are found to be independent of temperature within
experimental error over the range investigated and take on the value of (k /k AVG ) 1.64 for the primary
effect and (k /k AVG ) 0.87 for the secondary effect. These results are discussed within the context of current
experimental and theoretical work.
cm /s. A global fit of k vs T over the temperature range
-
11
(-0.90(0.11)
3
2
cm /s,
-
11
(-0.90(0.03)
((-2.88(1.82 K)/T)
3
H
D
)
H
D
)
-
11
cm3 s . This study was motivated by earlier
-1 1
Introduction
× 10
measurements of k1 at temperatures of 298 and 1925 K, by
Takacs and Glass (298 K), Smith and Zellner (298 K), and
The reaction of OH + HBr f H2O + Br and the isotopic
variants has been studied both experimentally and theoretically
in the past by a number of different research groups.
2
3
4
Wilson et al. (1925 K), who found the rate to be (5.1 ( 1.0)
-
12
-12
-11
3
×
10 , (4.5 ( 1.0) × 10 , and 2.56 × 10
cm /s,
k1
respectively. Following these studies, additional measurements
near room temperature were also made using a variety of
OH + HBr 98 H2O + Br
(R1)
5
-8
techniques.
Sims et al. applied the pulsed laser photolysis-
k2
laser induced fluorescence technique to the ultra-cold gas-phase
environment created in the Cin e´ tique de R e´ action en Ecoulement
Supersonique Uniforme (CRESU) to study the reaction over
the temperature range of 23-295 K and found the inverse
OD + HBr
OH + DBr
98 HOD + Br
(R2)
(R3)
(R4)
k3
98 DOH + Br
9
temperature onset below 295 K. Atkinson et al. also studied
k4
OD + DBr 98 D2O + Br
the temperature dependence of the kinetics of R1 using a pulsed
supersonic Laval nozzle flow reactor over the temperature range
76-242 K and similarly found inverse temperature depen-
Motivation for doing so has been two-fold. First, the reaction
affects the Br partitioning in the middle to lower stratosphere
of earth’s atmosphere. Bromine has been implicated as a species
known to react with ozone creating BrO and O2, and therefore,
a rigorous understating of the reaction network surrounding Br
creation and destruction has been sought. In addition, the kinetics
of the reaction of OH with HBr has been experimentally found
to show a strong inverse temperature dependence below
approximately 200 K, i.e., temperatures pertinent to the upper
atmosphere and stratosphere. To date experiments on the OH
1
0
dence. The rate coefficient has been found to be pressure
1
,10,11
independent,
anism.
consistent with a bimolecular reaction mech-
More recently, a joint experimental effort was conducted
between the Rowe and Smith groups in Rennes and Tucson,
with the aim of reconciling the low-temperature data for the
OH + HBr reaction, and included new measurements between
8 and 224 K. The study produced temperature-dependent fits
12
4
to the available data between 23 and 416 K of
+
HBr system have been carried out in the temperature range
from 23 to 416 K. Ravishankara et al. conducted the first
temperature dependent study between 249 and 416 K using the
technique of laser flash photolysis-resonance fluorescence and
found the rate to be independent of temperature over the
temperature window investigated, with a rate of (1.19 ( 0.14)
-0.91
-
11
T
3
k(T) ) 1.11 × 10
cm /s
(1)
(
)
2
98
and
-
0.91
-
11
T
298
exp(-10.5K/T) cm /s (2)
3
*
To whom correspondence should be addressed. E-mail: msmith@
k(T) ) 1.06 × 10
(
)
u.arizona.edu.
1
0.1021/jp045540n CCC: $30.25 © 2005 American Chemical Society
Published on Web 04/13/2005

3894 J. Phys. Chem. A, Vol. 109, No. 17, 2005
Mullen and Smith
which were deemed to accurately model the data below 350 K.
These fits were also found to be in accord with the previous
recommendations of the IUPAC Subcommittee on Gas Kinetic
13
14
Data Evaluation for Atmopsheric Chemistry, and that of JPL,
of
-0.8
-11
T
3
k(T) ) 1.1 × 10
cm /s
(3)
(
)
298
and
(
0 ( 250)K
-11
3
k(T) ) 1.1 × 10 exp
cm /s
(4)
[
]
T
respectively.
The dependence of reactivity on isotopomer for a chemical
system is also of great importance. Deuterium enrichment found
throughout the interstellar medium is well-known, and efforts
to understand the origins of these effects have been con-
ducted.1
5,16
The enrichment arises due to differences in zero-
Figure 1. Schematic diagram of the pulsed supersonic Laval nozzle
flow reactor.
point energies between the deuterated and nondeuterated species
and is initiated via isotopic exchange chemistry, primarily in
+
+
+
ion-molecule reactions involving H3 , CH3 , and C2H2 with
understanding of this reaction with calculations using variational
transition state theory on a modified LEPS potential energy
surface, with the goal of understanding the nature of the kinetic
isotope effects and the fraction of vibrational energy transferred
to the departing H2O, HDO, and D2O molecules found from
infrared chemiluminescence measurements by Butkovskaya and
HD.1
7,18
Once the deuterated ions are formed, they participate
in a variety of subsequent chemistries, including dissociative
recombination, to pass on their deuterium content. In cold
clouds, the exothermic D + OH f H + OD (∆Hrxn ) 810 K)
is speculated to influence the local D/H ratio,19 and this
2
0
chemistry is included in the modeling of such environments.
27
Setser. In addition, a more recent direct ab initio dynamics
In addition, Lunine et al. point out that the D/H ratio in methane
might provide a complimentary chemical test to the origin of
Titan’s atmosphere,21 and therefore, knowledge of the subse-
quent chemistry for molecules of interstellar importance is
crucial for a complete physiochemical description of the
environment. Knowledge of the H/D atom abstraction reactions
of OH/OD with HBr/DBr, while not of astrophysical relevance
at the time, provides information on the dynamics of a neutral-
radical abstraction reaction occurring over a potential energy
surface without an apparent barrier. Efficient neutral-radical
reactions are now well-known,22 and the low-temperature
measurement of their reaction rates will further help modeling
efforts of low-temperature environments.
Two other studies have significantly contributed to the
temperature dependent knowledge on not only the OH + HBr
system but the isotopomers as well. The study of Bedjanian et
al. used a mass spectrometric discharge-flow reactor to make
measurements between 230 and 360 K, on the reactions R1
through R4.23 Further, Jaramillo and Smith used the pulsed
supersonic Laval nozzle flow reactor to study the kinetics of
reactions R1 through R4.24 These studies will be discussed in
detail later, but for now it is prudent to say that knowledge of
the kinetic isotope effect (KIE), whether they be primary or
secondary in nature, helps to provide constraints to important
regions of the reaction potential energy surface.
calculation by Liu et al. has found a hydrogen bonded complex
intermediate on the reactant side of the potential energy surface
at energies lower than that of reactants, and the rate coefficients
over a broad temperature range were calculated with improved
canonical variational transition state theory with a small-
28
curvature tunneling correction.
23
The kinetic isotope effects measured by Bedjanian et al.
2
4
and Jaramillo and Smith are extended in this study to lower
temperatures between 53 and 135 K using the pulsed supersonic
Laval nozzle flow reactor, in an effort to further understand
the nature of the reaction PES, the temperature dependent KIEs
observed in the two previous studies, and also to provide
additional data necessary for the theoretical chemists to ac-
curately describe the reaction mechanism, the entrance channel,
and transition state dependence on the reactivity.
Experimental Section
A detailed description of our pulsed uniform supersonic
expansion flow reactor is presented elsewhere, and thus, only a
10,24
brief overview will be given here.
A schematic diagram of
the instrument can be seen in Figure 1.
The kinetics of reactions R1 through R4 were studied by co-
expanding known quantities of reagent and buffer gases through
a supersonic pulsed Laval nozzle. An equilibrated flow ensues
for a number of nozzle diameters past the nozzle exit (15-20
cm), at a well defined hydrodynamic velocity and density,
allowing for enough time (approximately 300 µs) to perform
kinetic measurements. The experiments were conducted such
that the concentration of reagent [R], R ) HBr or DBr, was
much greater than that of the OH radical, ensuring that pseudo-
first-order conditions were established. OH or OD radicals were
created from water or deuterium oxide (Cambridge Isotopes
Laboratories, Inc., 99.9%) precursors, using a pulsed DC
discharge in the stagnation volume. The H2O/D2O was entrained
Theoretical efforts have also been conducted aimed at
describing the potential energy surface and the inverse temper-
ature dependence found from experiments. They are mentioned
here and discussed further in context of the current results. Clary
et al. performed quantum scattering calculations using the
rotating bond approximation (RBA) on a LEPS potential energy
surface and found good qualitative agreement between the
temperature dependence predicted from the calculations and that
experimentally observed, as well as qualitative agreement in
2
5
26
magnitude with the rates. Nizamov et al. extended the

OH + HBr Reaction
J. Phys. Chem. A, Vol. 109, No. 17, 2005 3895
in the gas phase using a bubbler running with either N2 (83
and 135 K) or Ar (53 K) depending on the buffer gas used for
the experiment. In this manner, a mixture containing the partial
pressure of H2O divided by the total bubbler backing pressure
(30 psig) could be delivered to the nozzle, in concentrations
high enough to provide sufficient signal for the kinetic experi-
ments. Using these numbers as a rough guide, the water
concentration used was approximately 0.17%, 0.05%, and 0.03%
of the total flow for the ArM32e16, N2M32e16, and N2M33e16
nozzle, respectively.
The time dependent OH/OD signal was monitored using laser
induced fluorescence (LIF). Both OH and OD radicals were
2
2
excited using the A r X ( Σ r Π3/2, V′ ) 1 r v′′ ) 0)
transition, using a pulsed dye laser (Continuum model ND-60)
pumped by a Nd:YAG operating on the second harmonic
(Continuum model NY61). In both cases, kinetic experiments
were conducted by monitoring the S21(1) line. For OH this
occurs near 280.6 nm, whereas for OD it is at 286.9 nm. These
wavelengths were created by doubling the output from the dye
laser operating with Rhodamine 590 and a Rhodamine 590/
6
10 mixture, respectively, in a KD*P crystal. The laser
frequency was calibrated using the optogalvanic lines of Fe and
Ne. The resulting (0,0) and (1,1) fluorescence was collected
with a photomultiplier tube (Hamamatsu R3896) perpendicular
to the flow, in conjunction with a 310 ( 10 nm band-pass filter
and red pass filter (Schott WG29). The LIF signal was amplified
and sent to either a boxcar averager (SRS 250) or oscilloscope
Figure 2. Pseudo-first order decays of the OH radical in the presence
of HBr, for the reaction of OH + HBr at 53 K taken in the post
ArM32e16 nozzle flow. % HBr in flow: 9, 0.00; O, 0.04; 2, 0.07; 0,
0
.14; b, 0.17; 4, 0.25.
(LeCroy 9400) and averaged for 200-500 shots. The gases used
for these studies are as follows: N2, US Airweld 99.99%; Ar,
US Airweld; UHP, 99.999%; HBr, Matheson C. P. Grade
9
9.8%; DBr, Cambridge Isotope Laboratories, Inc. 99%. The
HBr and DBr gases were each treated to three freeze-degas-
thaw cycles with liquid nitrogen to remove the H2 impurities.
The rest were used without further modification.
Kinetic experiments are conducted after the flow exits the
nozzle, by following the relative OH(OD) concentration as a
function of distance in the flow. The reaction time is extracted
from the distance between the probe laser and nozzle exit and
is determined through knowledge of the flow velocity. This in
turn is known from the flow Mach number obtained from impact
and LIF measurements. The OH(OD) signal follows a single
exponential decay, as evidenced by the linearity of the natural
log of the normalized signal vs reaction time plot, Figure 2,
indicating that pseudo-first order conditions have indeed be
satisfied. The second order rate coefficient is extracted from a
plot of the pseudo-first order decay constant versus the
concentration of reactant under which it was obtained, Figure
3. The three nozzles used for this study have been previously
characterized and as a result only their flow properties are shown
2
9
here, Table 1.
It is believed that under these experimental conditions the
influence of secondary reactions on the extracted second order
rate coefficient is minimized. Two arguments can be made to
support this statement. First, the decay of OH or OD radicals is
measured in the absence of reactant (HBr/DBr). Any reactivity
under these conditions with Ar, N2, OH(OD), or other radical
species created in the flow due to the discharge is accounted
for, and results in all or part of the nonzero intercept observed
in the plot of k′ vs [R] (Figure 3). Second, the large concentration
of reactant added, HBr or DBr, allows for isolation of the
process of interest, due to the concentration dependence of the
decay of OH on R, through d[OH]/dt ) -k[OH][R]. For the
secondary processes to contribute significantly to the measured
second order rate coefficients the concentration of the secondary
Figure 3. Graph of k′ (s 1) versus the concentration of HBr (1013
-
3
molecules/cm ) for the OH + HBr reaction taken in the post ArM32e16
nozzle flow. The slope of this plot is used to extract the second order
rate coefficient. Error bars on the experimental points are at the 2σ
confidence limit and were obtained from linear least-squares fitting of
the pseudo-first order decays of Figure 2.
species would have to be quite high, or the rate of the process
be particularly faster than the rate of the primary process, or
both; neither of which are likely. A number of the rates for
secondary reactions (to our kinetic scheme) have been measured
and are found to be either slow or rely on the formation of a
reactive species such as Br2 or H2O2. In particular measurements

3896 J. Phys. Chem. A, Vol. 109, No. 17, 2005
Mullen and Smith
et al.10 It can be seen for all cases, except for OD + HBr, good
agreement between the measurements of this work and of
Bedjanian et al. is realized. For the case of OD + HBr, Figure
4b, it appears that the steepness of the inverse temperature
dependence in the region from 53 to 135 K, causes the rate
calculated from the fit of the low temperature data only, to be
underestimated in comparison to the measurement of Bedjanian
et al. However, this underestimation can easily be overcome
with a fit to both data sets but was not done here, as the goal
was to illustrate the difference or similarity in the three data
sets. Table 3 lists the best fit parameters obtained from fitting
the data of this work to the power law form.
TABLE 1: Calibrated Nozzle Flow Characteristics for the
Nozzles Used in This Study
mach stagnation
no.
T
flow
T
flow
flow density
nozzle
temp (K) LIF (K) impact (K) (1016 cm
-3
)
ArM32e16 3.5
N2M32e16 3.2
N2M33e16 2.5
263
273
300
53 ( 4
83 ( 3
53 ( 3
89 ( 5
3.2 ( 0.2
1.7 ( 0.2
4.5 ( 0.5
135 ( 11 132 ( 6
TABLE 2: Summary of the Rate Coefficients for the
Reaction of OH + HBr and the H/D Isotopic Variants
Measured in This Study
temp
(K)
[R]
(1013 cm-3
k(10-11 cm molecule s-1
3
-1
reaction
)
)
The data of Jaramillo and Smith24 is seen to be markedly
steep in all cases, and as a result, a reevaluation of the data
was conducted. The errors reported in the original publication
for the data measurements were the standard error and the final
results (i.e., k(T)’s) represent the average of the measurements.
In this study, the standard deviation was calculated as the square
root of the sum of the squares of the individual standard errors
divided by the number of measurements, as would be anticipated
for a normal error probability function for a large number of
measurements. However, in cases where the number of mea-
surements is small, N < 20, it is desirable to use a statistical
treatment of random errors to place a confidence limit on the
mean, through use of the Student’s t distribution which takes
into account the joint probability that N observations fall within
a certain range and the number of degrees of freedom in the
OH + HBr
OH + HBr
OH + HBr
OD + HBr
OD + HBr
OD + HBr
OD + DBr
OD + DBr
OD + DBr
OD + DBr
OD + DBr
OD + DBr
53
83
135
53
83
135
53
83
135
53
83
135
8.5
6.2
9.0
9.5
6.2
6.5
7.2
5.8
11.9
7.5
3.46 ( 0.15
2.53 ( 0.21
1.86 ( 0.21
5.11 ( 0.29
2.61 ( 0.16
1.93 ( 0.25
2.25 ( 0.14
1.39 ( 0.12
1.19 ( 0.13
3.04 ( 0.16
2.08 ( 0.17
0.97 ( 0.15
5.5
12.1
of the isotope exchange channels
OH + DBr f OD + HBr
(5)
(6)
(7)
OD + HBr f OH + DBr
34
system. In this fashion, the raw data was re-plotted and a linear
least squares regression analysis was used to extract the
individual rates and errors in the rates at the 2σ (95%)
confidence level. The weighted average and error in the average
was then calculated in the same fashion as the numbers reported
in the present study so that a direct comparison of the data could
be made. Figure 5 shows the difference in the data before and
after being treated in this way, for reactions R1 through R4.
The revised data is used throughout the rest of this report. The
change in the rate and the error associated with it is reflective
of the quality of the data.
OH + D O f OD + HOD
2
OD + H O f OH + HOD
(8)
2
indicate that the upper limits for the rate coefficients are 3 ×
-
-
14
13
-13
3
23
-13
1
1
0
0
and 1 × 10
cm /s at 298 K and 3 × 10
and 5 ×
3
24
cm /s at 141 K for R5 and R6, respectively. An
independent verification of these rates was not conducted at
low temperatures in these studies. Similarly, the isotope
exchange reactions R7 and R8 are known to be slow at room
-
17
-16
temperature with rates <5 × 10
and (3.0 ( 1.0) × 10
As mentioned in the Introduction, great interest in the
temperature dependence of reaction R1 stems from its important
role in the atmospheric chemistry of the Br atom. A new
temperature-dependent fit of the global data set including this
work has been done and can be seen in Figure 6. All of the
data used for this graph are included in Table 4. A nonlinear
least-squares fitting routine was used to fit the data to a power
law and modified Arrhenius functional form, as shown in Figure
6. The fitting routine took into consideration the individual error
bars associated with each data point and minimized the sum of
the squares deviation. The shaded area represents the 95%
confidence limit interval of the modified Arrhenius fit. The best
fit parameters over the temperature range 23-360 K are found
3
30
cm /s. These reactions are further highly unlikely to be
occurring in the flow because the experiments were conducted
in pure H2O or D2O precursor. In addition, the reactions of OH
and OD radicals with Br231 and OH with H2O2 have been
studied in a temperature dependent fashion and shown to be
reasonably fast at low temperature but again are highly unlikely
to be influencing the kinetics of R1 through R4 due to the
anticipated low concentration of the Br2 and H2O2 species in
the flow.
32
Results
The rates of reactions R1 through R4 were measured at three
temperatures 53, 83, and 135 K under pseudo-first order
conditions. Table 2 shows the temperature-dependent results.
The errors reported in Table 2 are those at the 95% confidence
limit. The value and error in each rate represents a weighted
average and corresponding error in the mean with unequal
uncertainties from a number of measurements. Graphs of k
vs T for R1 through R4 can be seen in Figure 4, parts a-d,
respectively. Two fits to the functional form k(T) ) A(T/298)
are shown on each graph. They represent a fit to the low-
temperature data set only, for this work, solid line, and the work
of Jaramillo and Smith,24 dashed line, extrapolated to higher
temperatures so that the data could be compared to that of
Bedjanian et al.23 Figure 4a also depicts the data of Atkinson
-
11
(-0.90(0.11)
to be k(T) ) (1.06 ( 0.02) × 10 (T/298)
and (0.96
cm /s.
-
11
(-0.90(0.03)
((-2.88( 1.82 K)/T)
3
(
0.02) × 10 (T/298) exp
The data of Table 2 from this work was used in conjunction
with the revised data of Jaramillo and Smith and Bedjanian et
al. to examine the kinetic isotope effects as a function of
temperature over the region 53-360 K. The results for the
primary kinetic isotope effect (PKIE) for common reactant OH
and secondary kinetic isotope effect (SKIE) for common reactant
HBr can be seen in Figure 7. Similarly, the results for the PKIE
with common reactant OD and SKIE with common reactant
DBr can be seen in Figure 8. The plots are presented in this
fashion because they compare reactions that create similar
products: in the case of Figure 7, HOD vs HOH, whereas for
33
-n

OH + HBr Reaction
J. Phys. Chem. A, Vol. 109, No. 17, 2005 3897
Figure 4. Temperature dependence of the rate coefficients for the reactions (a) OH + HBr, (b) OD + HBr, (c) OH + DBr, (d) OD + DBr: 9,
1
0
24
23
-n
this work; ×, Atkinson et al.; [, Jaramillo and Smith; O, Bedjanian et al. The fits displayed are to the functional form k(T) ) A(T/298)
.
Solid line is the fit to the data of this work, extrapolated to higher temperature for comparison to the data of Bedjanian et al. The dashed line is the
fit to the Jaramillo and Smith data and extrapolated in the same manner.
TABLE 3: Best Fit Parameters to the k(T) ) A(T/298)-n
Power Law Functional Form for the OH + HBr and H/D
Isotopic Variant Reactions
(Figure 4a-d) to the power law form, and using the appropriate
ratio of the fits to predict the KIEs, in this manner reducing the
statistical fluctuations in the data. Including the data of Jaramillo
reaction
A(10- cm s-1)
12
3
-n
24
and Smith caused the fits to shift off the data sets, and this
OH + HBr
OD + HBr
OH + DBr
OD + DBr
10.84 ( 0.31
6.43 ( 2.60
5.89 ( 1.93
4.71 ( 1.56
0.67 ( 0.02
1.19 ( 0.26
0.76 ( 0.22
1.09 ( 0.21
data was not included for this reason. The fits to the KIE data
show only a weak temperature dependence and yield values of
k1/k2 ) (0.93 + 0.13, - 0.21), k1/k3 ) (1.75 + 0.09, - 0.16),
k2/k4 ) (1.69 + 0.06, - 0.11), and k3/k4 ) (0.90 + 0.11, -
0.19), where the (+) and (-) indicate the range with respect to
the average value. It can be seen that the fitting procedure
provides reasonable agreement with the data except in the case
of the 120 and 141 K PKIE (k2/k4) data of Jaramillo and Smith.
Figure 8, HOD vs DOD. Due to the scatter of the data, it was
desirable to include a temperature-dependent fit to the data, to
help guide the eye. The fits seen in Figures 7 and 8 were made
by fitting the data of this work and that of Bedjanian et al.

3898 J. Phys. Chem. A, Vol. 109, No. 17, 2005
Mullen and Smith
Figure 5. Comparison of the Jaramillo and Smith24 data before and after revision for the OH + HBr and H/D isotopic variants reactions. Open
symbols, original data; closed symbols, revised data.
Discussion
rotationally enhanced cross section at low temperature with a
1/2
(B/T) temperature dependence that qualitatively described the
Reactions displaying inverse temperature dependence for a
wide variety of systems are now widely known. These include
the addition reactions of OH radicals with unsaturated hydro-
experimental data. Unfortunately, calculations of the kinetic
isotope effects for the OH + HBr system were not conducted.
The current experimental findings are discussed in conjunction
with the other systems that have been studied to date to create
a framework within which the results can be understood. These
include the temperature-dependent studies of the reactions of
OH(D) + H(D)Cl, OH(D) + H(D)Br, and C2H + NH3(D3).
9
,35,36
37,38
carbons,
CN radical reactions,
various carbon atom
3
9-41
3
42
reactions,
O( P) atom with unsaturated species, and C2H
radical with a variety of species.4
3-47
Although the manifestation
of inverse temperature dependence is becoming commonplace,
measurements of temperature dependent KIE ratios remain
sparse. The inverse temperature dependence observed for these
reactions has been attributed to the absence of a barrier along
the reaction coordinate. At low temperature, fewer collisions
are occurring on rotationally excited surfaces, causing the cross
section for the process to increase. The rotating bond ap-
proximation applied by Clary et al.25 has enjoyed success when
applied to the heavy light heavy reactions of OH + HCl and
HBr. In this work, a correlation was found between the reactant
rotational states and the product bending states, leading to a
Battin-Leclerc et al. have studied the temperature-dependent
KIE ratios for the OH + HCl and all isotopic variants using a
pulsed laser photolysis-laser induced fluorescence flow reactor
4
8
between 200 and 400 K. They find a normal temperature-
dependent PKIE (k3/k4 and k1/k2, using their nomenclature) that
varies from approximately 2 to 6.5 over the temperature window
of their experiment and indicate that H atom tunneling becomes
significant at lower temperatures. They also conducted effective
barrier calculations which indicate that the barrier decreases from

OH + HBr Reaction
J. Phys. Chem. A, Vol. 109, No. 17, 2005 3899
TABLE 4: OH + HBr Rate Data Used to Obtain the
Temperature Dependent Global Fit in Figure 6
rate (10- cm /s)
11
3
error
investigator
temp (K)
Jaramillo and Smith24
120
3.15
2.53
0.936
1.01
1.46
1.2
0.53
0.3
1
1
2
40.8
85
24
0.274
0.15
0.17
0.14
0.13
0.13
0.12
0.12
0.14
0.08
0.05
0.07
0.08
0.05
0.1
Bedjanian et al.23
230
2
2
2
2
3
3
43
60
78
98
28
60
1.12
1.2
1.11
1.05
0.97
1.31
1.22
1.11
1.18
1.12
1.21
10.7
8.78
7.87
5.54
5.46
4.83
2.97
1.16
5.67
3.21
1.1
Ravishankara et al.8
249
2
2
3
3
4
73
98
26
69
16
23
Sims et al.9
0.4
3
4
5
5
7
0.5
4
2.1
2.3
5
0.44
0.27
0.15
0.13
0.22
0.46
0.04
0.11
0.18
0.1
1
70
Figure 6. OH + HBr global fit to the temperature-dependent rate data
295
48
97
242
222
194
10
Jaramillo et al.12
Atkinson et al.10
over the 23-360 K window. 0, This work; 9, Atkinson et al.; O,
Jaramillo and Smith; b, Bedjanian et al.; 4, Ravishankara et al.;8
2
2
4
23
9
12
, Sims et al.; ], Jaramillo et al. The solid line is the fit to the
power law functional form, and the dashed line is the fit to the modified
Arrhenius form. Grey region is the 95% confidence interval of the fit.
1.3
1
0.2
0.3
1
1
1
1
1
107
92
94
73
69
47
33
1.5
0.8
1.5
1.4
1.6
2
3
2.9
0.4
0.1
0.3
0.1
0.2
0.3
0.5
0.9
1
>
2.22 to 9.71 kcal/mol in the series OH + HCl > OH + DCl
OD + HCl > OD + DCl, with the reduction in barrier height
due to OD because of the zero-point energy difference and the
lower frequency modes in the transition state. Although the
primary KIE for OH + HCl gets quite high at low temperatures,
qualitative agreement is seen between the portion of the PKIE
not attributed to tunneling in the OH + HCl case and the PKIEs
of this work for OH + HBr, (k1/k3)Avg ) (k2/k4)Avg )1.64 and
the PKIE for OH + HBr of Bedjanian et al. k1/k4 ≈ k3/k5 ≈
7
6
This work
53
3.46
2.53
1.86
0.15
0.21
0.21
8
35
3
1
1
.7. However, it should be noted that the OH + HCl system
dictions that the reaction proceeds via the exothermic (∆H2°98K
) -121 kJ/mol) hydrogen abstraction mechanism without a
barrier, demonstrated by the strong negative temperature
dependence observed. In addition, and relevant to the OH +
HBr system, they observe a rather large PKIE of (2.0 ( 0.2)
independent of temperature over the range investigated. Al-
though they acknowledge that precise knowledge of the
observed KIE cannot be judged without accurate calculations,
the authors suggest the origin of the large KIE could be
contributions from tunneling. Alternatively, from a statistical
standpoint, the KIE could be due to an increase in the reactant
rotational density of states upon deuteration, without significant
effects on the activated complex, leading to a temperature
independent kinetic isotope effect. Further, they argue that
explanation of the kinetic isotope effect based solely on changes
demonstrates a positive activation energy at all temperatures,
whereas the OH + HBr reaction shows no indication of a
positive barrier. It is not clear how to directly compare the
kinetic isotope effects for reactions occurring over seemingly
quite different potential energy surfaces.
The SKIE’s for OH + HCl observed in Battin-Leclerc et al.48
are inverse in nature and vary from approximately 0.83 to 0.95,
with the k1/k3 (common HCl) ratio showing stronger temperature
dependence than that of k2/k4 (common DCl). Again, these ratios
are in accord with those observed in this study, (k1/k2)Avg )
0
.87 and (k3/k4)Avg ) 0.88 for OH + HBr. Similarly, Bedjanian
2
3
et al. receive SKIE ratios of k1/k3 ≈ k4/k5 ≈ 1 for OH + HBr.
The results of the three studies seem to indicate that the
secondary kinetic isotope effect is most sensitive to the transition
state for these two reactions, even though both occur over
different potential energy surfaces. The creation of the lower
frequency vibrational modes due to the spectator nature of the
OD bond and its correlation to water product states appears to
have a greater influence on the dynamics than it does from the
changes in number of states in the reactant manifold due to
zero-point effects.
in zero-point energies is inconsistent with the temperature
independence of the KIE. This is due to the exp(-∆E /kT)
factor that is obtained when the k /k ratio is derived from
q
0
H
D
classical transition state theory, but they also mention that
application of classical transition state theory may be too
simplistic for reaction systems occurring over potential energy
surfaces without a barrier. It is also interesting that the
temperature dependence observed for the NH3 + C2H system
More recently Nizamov and Leone have investigated the
reactions of C2H with NH3 and ND3 in a pulsed Laval nozzle
(-0.90(0.15)
T
is in accord with the temperature dependence
apparatus, at three temperatures of 104 ( 5, 165 ( 15, and
observed in this study for OH + HBr and all of the isotopic
variants, within the errors quoted. It seems that these two
96 ( 2 K.4 They find that in accord with theoretical pre-
4
2

3900 J. Phys. Chem. A, Vol. 109, No. 17, 2005
Mullen and Smith
A number of theoretical efforts have also been conducted
aimed at understanding the negative temperature dependence,
the vibrational energy distribution imparted to the exiting H2O
molecule, and the kinetic isotope effects observed for OH +
HBr and isotopic variants. The observed temperature dependence
-
0.90
of reaction R1 is best fit by a T
functional form, and this
dependence is consistent with that calculated using quantum
scattering calculations with the rotating bond approximation
2
5
26
using a LEPS surface. Nizamov et al. performed quasiclas-
sical trajectory calculations (QCT) to explore the dynamics of
reactions R1 and R2 using the Clary potential and a modified
form adjusted to match the fraction of H2O vibrational energy
dispersal experimentally measured by Butkovskaya and Setser.27
They also employed variational transition state theory to obtain
rate constants that could be compared to the QCT and
experimental values. They find the transition state to lie at a
classical energy of ∼ -1.75 kcal/mol with respect to reactants,
and with harmonic zero-point adjustment, the barrier shifts to
-0.12, +0.06, and -0.23 kcal/mol, for the Clary OH + HBr
PES, the modified OH + HBr PES, and the modified OD +
HBr PES, respectively. Due to the fact that the zero-point
adjusted barrier was lower for OD + HBr by 0.29 kcal/mol
than for OH + HBr, an inverse SKIE (k1/k2) was predicted and
attributed to the difference in DOH vs HOH bending frequencies
in the transition state. At 300 K, the VTST rates calculated on
the modified potential predict a SKIE of 0.76. Although a bit
low, the SKIE value predicted by the VTST calculation is in
qualitative agreement with the measurements of this work and
Figure 7. Primary and secondary kinetic isotope effects (k
versus temperature for the OH + HBr and H/D isotopic variants
reactions. k and k share the common reactant OH, whereas k and k
share the common reactant HBr. Closed symbols are for the primary
kinetic isotope effect (k /k
): 9, this work; b, Jaramillo and Smith;24
, Bedjanian et al. Open symbols are for the secondary kinetic isotope
H D
/k ) plotted
1
3
1
2
1
3
23
2
2
4
1 2
effect (k /k ): 0, this work; O, Jaramillo and Smith; 4, Bedjanian et
2
3
2
3
Bedjanian et al.
al.
An inverse PKIE (k1/k3) of 0.72 is also calculated in the
26
Nizamov et al. study which is similar in magnitude to the SKIE
calculated at 300 K using the modified potential. Again, the
PKIE arises due to a lowering of the zero-point energy adjusted
barrier for OH + DBr relative to OH + HBr. However, the
authors note that large kH/kD values are difficult to explain by
any transition state model, when the transition state is located
early in the entrance channel, because the HBr and DBr
frequencies are similar in the reactants and transition state. The
lack of agreement between the PKIE experimentally measured
23
at 300 K (kH/kD ≈ 1.7) and calculated using the semiempirical
surface is therefore not terribly surprising.
Direct ab initio dynamics calculations of the reaction rates
for the OH + HBr reaction have also been conducted.28 The
goal of using this approach was to obtain dynamical information
on an accurate potential energy surface obtained from accurate
ab initio electronic structure calculations. The study finds that
on the reactant side of the potential energy surface there is a
hydrogen bonded complex (HBC) lower in energy than reactants
by -1.71 kcal/mol, which looks similar in geometry to the
25
transition states calculated in the quantum scattering and QCT
2
6
calculations. The reaction is found to pass through a reactant-
like transition state with an energy slightly higher in energy
than that of the reactants (0.89 kcal/mol) in going from the HBC
to products. Further, the rates of reaction are calculated using
improved canonical variational transition state theory (ICVT)
and with a small curvature tunneling correction (ICVT/SCT).
Qualitative agreement is found between the rates calculated and
those found experimentally, but the ratio of the rate coefficients
calculated ([ICVT/SCT]/ICVT) is found to be dependent on
temperature, with the ICVT/SCT gaining importance as the
temperature is reduced, indicating the importance of tunneling
to the reaction at low temperatures. If this is indeed true, one
might understand the tunneling contribution to the atom transfer
as being responsible for the normal PKIE observed experimen-
Figure 8. Primary and secondary kinetic isotope effects (k
versus temperature for the OH + HBr and H/D isotopic variants reac-
tions. k and k share the common reactant OD, whereas k and k share
the common reactant DBr. Closed symbols are for the primary kinetic
isotope effect (k /k
): 9, this work; b, Jaramillo and Smith;24 2, Bed-
janian et al. Open symbols are for the secondary kinetic isotope effect
H D
/k ) plotted
2
4
3
4
2
4
23
): 0, this work; O, Jaramillo and Smith;2 4, Bedjanian et al.
4
23
3 4
(k /k
abstraction reactions, although differing in the number of degrees
of freedom, share similar characteristics due to the large
exothermicity involved and the lack of a barrier.

OH + HBr Reaction
J. Phys. Chem. A, Vol. 109, No. 17, 2005 3901
tally. The finding by Liu et al.28 that the reaction proceeds via
an “early” transition state which is reactant-like in nature also
indicates that the reaction is more sensitive to the reactant
energies than to changes in the transition state frequencies upon
deuteration.
Questions naturally arise regarding the difference in the data
measured using the pulsed supersonic Laval nozzle flow reactor
in Tucson. The scatter in the data of Jaramillo and Smith24 is
thought to reflect statistical or systematic errors in the data
obtained in those studies. Oftentimes rates were extracted from
k′ vs [R] plots containing four or five data points with
considerable deviation from linearity. Therefore, the error bars
most likely under represent the true error associated with the
measurements. Part of the scatter could have been introduced
by the method by which the HBr and DBr concentrations were
calculated. These concentrations were calculated from a mea-
surement of the absorption cross section at 220 nm (near the
threshold), so that the absorbance measured in the reactant
delivery line, in conjunction with the flow rate and line pressure,
could be converted into an absolute concentration in the flow.
It is difficult to determine whether these measurements suffered
from systematic errors due to baseline drift in the absorption
spectrometer or from adsorption of HBr and DBr molecules
onto window surfaces. Other sources of error such as improper
nozzle calibration leading to un-equilibrated flow and nonuni-
form flow are also candidates. In the present study, care was
taken to ensure that the flow was continually monitored to ensure
reliable flow conditions, and the HBr and DBr concentrations
were calculated solely from the gas flow rate, so that errors
associated with the absorption measurement could be minimized.
It seems reasonable to suggest that the KIE ratios are constant
over the temperature range explored in this study and that of
2
3
Bedjanian et al. Locating the origin of the effect, however, is
a bit more difficult. From a transition state theory perspective,
for a reaction occurring over a potential energy surface with a
barrier, the KIE ratio arises due to differences in zero-point
energies and the rotational, vibrational, and translational partition
functions according to eq 5
Trans
HOHBr OD
Trans
Vib
Vib
Rot
Rot
kH
Q
Q
Q
Q
Q
Q Q
HOHBr OD
HOHBr OD
)
(
Trans
DOHBr OH
Trans)( Vib
Vib)( Rot
Rot
)
kD
Q
Q
Q
Q
Q
DOHBr OH
DOHBr OH
Inter
Q
Q
HOHBr
([EHOHBr-E
]/k T)
DOHBr
b
exp
(5)
(
Inter
DOHBr
)
where QTrans, QVib, and QRot represent the translational, vibra-
tional, and rotational partition functions, respectively. QInter
represents the partition function associated with motion along
the reaction coordinate, the exponential term is the difference
in activation energy at the transition state, kb is Boltzmann’s
constant, with the reactant partition function indicated by the
subscript OH(D) and the transition state partition function by
the subscript H(D)OHBr. Equation 5 represents the situation
for the SKIE. The expression for the PKIE is similar, with HBr
and DBr substituted into the reactants and transition state.
Deuteration of either of the reactants leads to changes in the
reactant partition functions of QVib, QRot, and QTrans. These can
be estimated, but it is the transition state partition functions and
energetics that make assessment of the origin of the observed
KIEs difficult, due to the necessity of an accurate potential
energy surface. Even with an assumed transition state geometry,
state sums and densities have been difficult to assess due to
Conclusion
The rates of reaction for the OH + HBr and H/D isotopic
variants have been measured between 53 and 135 K using a
pulsed supersonic Laval nozzle flow reactor. For the OH + HBr
system, the new low-temperature results are found to be in
accord with the measurements of Atkinson et al.,10 but
2
4
systematically lower than the studies of Jaramillo and Smith,
1
2
11
Jaramillo et al., and Sims et al., however these data does
not alter our interpretation of the temperature dependence of
reaction R1. It most likely highlights the difficulty of working
with HBr at low temperatures.
2
6
The KIE’s were also investigated and found to be independent
of temperature between 53 and 135 K. These results seem to
anharmonic effects, as pointed out by Nizamov et al. Further,
the difference in zero-point energy of the transition state for
the deuterated vs nondeuterated case should introduce a tem-
perature dependence to the KIE, although it is not clear at this
time to what extent. One might argue that the rotational
dependence of the cross section offsets the temperature depen-
dence predicted by transition state theory, or that the exponential
term of eq 5 is not appropriate for reactions occurring without
an apparent barrier, and these points certainly warrant further
investigation.
2
3
be in accord with the study of Bedjanian et al. However, a
theoretical study capable of accurately treating the nature of
the electronic surface and the zero-point energy adjusted barriers
would surely lend insight into the dynamics leading to the kinetic
isotope effects measured for reactions R1 through R4.
Acknowledgment. The authors gratefully acknowledge
financial support of this work by the National Science Founda-
tion through Grant No. CHE-9984613.
As previously mentioned, Nizamov et al. attribute the PKIE
(k1/k3) and SKIE (k1/k2) to a lowering of the zero-point adjusted
References and Notes
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HOH bending frequency in the transition state. A rigorous
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temperature-dependent expression for the inverse PKIE of
Nizamov et al. is provided in that study, which indicates an
increased reaction efficiency of kD vs kH as the temperature is
lowered. Since neither the absolute value of the PKIE nor the
temperature dependence of the PKIE calculated appear to be
observed experimentally, it is unclear whether it is a limitation
in transition state theory to accurately predict KIEs, as suggested
by Nizamov et al., or whether it is another offsetting factor,
such as tunneling, as suggested by the calculations of Liu et
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