Temperature-dependent kinetic isotope effects in the gas-phase reaction: OH + HBr

Article abstract of DOI:10.1021/jp004328q

The temperature dependence of the hydrogen transfer rate coefficients for the reactions: OH + HBr (Reaction 1), OD + HBr (Reaction 2), OH + DBr (Reaction 3), and OD + DBr (Reaction 4) have been investigated at temperatures between 120 and 224K using a pulsed uniform supersonic flow monitoring hydroxyl reactive loss. The lack of observed isotopic scrambling indicates the reaction occurs by H/D atom transfer from HBr/ DBr at all temperatures. The rate coefficients demonstrate little temperature dependence above 200 K, but strong inverse temperature behavior below 200 K. The current work provides unequivocal experimental evidence of temperature dependent and inverse primary and secondary kinetic isotope effects (k_H/k_D < 1) at low temperatures. The observed kinetic isotope ratios, k_H/k_D, at 120 K are for primary substitution on HBr; k₁/k₃ = 1.00 (±0.17) and k₂/k₄ = 0.46 (±0.08), while for secondary substitution on OH; k₁/k₂ = 0.94 (±0.20) and k₃/k₄ = 0.43 (±0.05). At the lowest temperature employed (120 K), deuterated reactants react as fast or faster than their natural hydrogen isotopomer and there is no significant difference between the primary and secondary kinetic isotope effect. The results are discussed within the framework of recent theoretical models.

Full text of DOI:10.1021/jp004328q

5854
J. Phys. Chem. A 2001, 105, 5854-5859
Temperature-Dependent Kinetic Isotope Effects in the Gas-Phase Reaction: OH + HBr
Veronica I. Jaramillo and Mark A. Smith*
Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721
ReceiVed: NoVember 29, 2000; In Final Form: March 8, 2001
The temperature dependence of the hydrogen transfer rate coefficients for the reactions: OH + HBr (Reaction
1), OD + HBr (Reaction 2), OH + DBr (Reaction 3), and OD + DBr (Reaction 4) have been investigated
at temperatures between 120 and 224 K using a pulsed uniform supersonic flow monitoring hydroxyl reactive
loss. The lack of observed isotopic scrambling indicates the reaction occurs by H/D atom transfer from HBr/
DBr at all temperatures. The rate coefficients demonstrate little temperature dependence above 200 K, but
strong inverse temperature behavior below 200 K. The current work provides unequivocal experimental
evidence of temperature dependent and inverse primary and secondary kinetic isotope effects (kH/ kD < 1) at
low temperatures. The observed kinetic isotope ratios, kH/kD, at 120 K are for primary substitution on HBr;
k1/k3 ) 1.00 ((0.17) and k2/k4 ) 0.46 ((0.08), while for secondary substitution on OH; k1/k2 ) 0.94 ((0.20)
and k3/k4 ) 0.43 ((0.05). At the lowest temperature employed (120 K), deuterated reactants react as fast or
faster than their natural hydrogen isotopomer and there is no significant difference between the primary and
secondary kinetic isotope effect. The results are discussed within the framework of recent theoretical models.
Introduction
OH + HBr f H2O + Br
(1)
Isotope distributions in naturally occurring environments
provide direct insight into both physical and chemical dynamics.
In particular, minor isotopes can play key roles in radiative
heat transfer in the interstellar media.1 Pooling of heavy iso-
topes into molecular components can occur due to zero point
energy differences which can greatly exceed kT in low-
temperature media.2,3 In the case of stratospheric ozone, the
debate continues on the origins of the observed terrestrial non-
equilibrium isotope distributions.4 Studies of isotope-specific
rate coefficients and kinetic isotope effects can help elucidate
origins of particular deviations from natural abundance as well
as provide detailed insight into isotope-dependent reaction
mechanisms.
OD + HBr f HOD + Br
OH + DBr f HOD + Br
OD + DBr f D2O + Br
(2)
(3)
(4)
The kinetic isotope effect, KIE, is defined for the purpose of
this work as the ratio of the rate coefficient observed for a
particular reactant pair to the rate coefficient observed when
one atom in the reactant pair has been isotopically substituted
(for purposes of this paper, replacing H with the heavier D
isotope). In this regard, it is also convenient to categorize
primary and secondary KIEs. A primary KIE corresponds to
one where the atom substituted is involved in a bond being
formed or broken along the reaction coordinate. The secondary
KIE then involves isotopic substitution associated with bonds
not formed or broken during the reaction. The ratios, k1/k3 and
k2/k4 thus correspond to primary kinetic isotope effects, while
k1/k2 and k3/k4 correspond to secondary KIEs. In the study of
Bedjanian et al., both of these primary KIEs are found near
1.8, and both secondary KIEs are measured to be near unity.
Such observations of normal kinetic isotope ratios are consistent
with transition state theory predictions for reactions occurring
on potential surfaces with negligible or positive activation
barriers. These observations may not be that surprising in the
sense that they occur over a temperature window for which
Reaction 1 displays no significant temperature dependence.
The reaction
OH + HBr f H2O + Br
(1)
besides being significant in determining the active bromine
fraction in the middle to lower terrestrial stratosphere,5 has
become a well studied bimolecular radical-molecule reaction
demonstrating significant non-Arrhenius rate behavior.6-15 The
rate coefficient of Reaction 1 has attracted much attention due
to the fact that it displays very weak temperature dependence
at higher temperatures, but strong inverse temperature depen-
dence at low temperatures.13,14,16 Bedjanian et al. have recently
investigated the H/D isotope dependence of the reaction between
isotopomers of OH and HBr, thus all Reactions 1-4, at
temperatures above 230 K.15
In view of the strong inverse temperature dependence of
Reaction 1 seen below 200 K,13,14,16 we have investigated the
low-temperature rate coefficients of Reactions 1-4. These
results show that both the primary and secondary kinetic isotope
effects are sensitive functions of temperature below 200 K. More
importantly, interesting inverse kinetic isotope ratios (kH/kD <
* Author to whom correspondence should be addressed at University of
Arizona, Department of Chemistry, 1306E, University Drive, Tucson, AZ
85721. Tel: (520) 621-2115. Fax: (520) 621-8407. E-mail: msmith@
u.arizona.edu.
10.1021/jp004328q CCC: $20.00 © 2001 American Chemical Society
Published on Web 05/19/2001

Gas-Phase Reaction: OH + HBr
J. Phys. Chem. A, Vol. 105, No. 24, 2001 5855
densities ranging from 3 × 1016 to 2 × 1017 cm-3 and flow
temperatures from 224 to 120 K. Unfortunately, in these studies
we were unable to perform measurements at stagnation tem-
peratures below 300 K and thus with the nozzles available to
us, we were limited to a lowest temperature of 120 K for N2
buffered flows.
The background pressure in this chamber is matched to the
internal flow-pressure such that the supersonic flow, once
leaving the nozzle body, proceeds without further radial
expansion down the reactor vessel. In this way, the reaction
flow environment is surrounded by a subsonic gaseous layer (a
boundary shock) and does not experience solid walls. This latter
point corresponds to one significant difference between these
supersonic techniques and their conventional flow tube coun-
terparts. In the post-Laval nozzle flow, there can be no
complications due to heterogeneous wall effects.
In the preexpansion region a pulsed cold cathode discharge
is used to generate the OH radical or its isotopomer from the
radical precursors, H2O or D2O, seeded into the N2 buffer flow.
A mixing ratio of 1:100: >1000 of the radical precursor/
reactant/N2 was introduced into the reservoir, thus ensuring
pseudo- first-order conditions in the OH/OD radical. The radical
concentration was followed by LIF, exciting the Q1(1) and Q21-
(1) lines of the (1,0) band of the A 2Σ+ r X 2Π system for OH
near 281.9 nm and for OD near 287.6 nm, while detecting the
(1,1) and (0,0) off-resonance fluorescence through a 310 nm
notch filter (Corion P310) with a photomultiplier tube perpen-
dicular to the flow. The relative radical concentration, as
determined by fluorescence intensity, was measured as a
function of flow distance, and therefore reaction time. The
excitation is performed in a saturated mode which allows simple
confirmation of both OH internal temperature (via scanning
excitation wavelengths) and local relative density.
Figure 1. Diagram of the pulsed uniform supersonic flow reactor used
in this study.
1) for both primary and secondary substitutions of a bimolecular
gas reaction are observed. These results are discussed in the
context of recent theoretical models.
Experimental Section
The reported temperatures were measured in the post nozzle
flow using LIF, exciting the S21 branch of the (1,0) band of the
A 2Σ+ r X 2Π system for OH and detecting the (1,1) and (0,0)
off-resonance fluorescence. Rotational line intensities, corrected
for line strength factors,18 are found to be completely described
by a Boltzmann distribution and thus yield the local rotational
temperature. This rotational temperature allows the derivation
of the flow Mach number through the isentropic expansion
relationship,17 as well as provides a direct measurement of the
local thermal conditions. These LIF excitation scans were
conducted at several flow distances to determine the temperature
uniformity of the flow. Flow conditions employed in this work
guaranteed flow uniformity better than 10%. Also as a further
check of flow uniformity, the velocity of the flow was measured
via pitot impact pressure measurements.17 Temperatures derived
from these impact velocities agreed to within 9% of the
measured rotational temperatures. In this study all nozzles
employed a nitrogen buffer and stagnation or reservior temper-
atures were held at 300 K. With the Mach number range of
these nozzles, a temperature window of 120 to 224 K was
accessed.
The details of our approach to low-temperature OH radical
rate coefficient measurements have been described elsewhere,
so only a brief review will be provided here.14,16,17 The rate
coefficients of Reactions 1-4 were determined by laser-induced
fluorescence (LIF) monitoring of OH/(OD) concentration under
pseudo first-order conditions in a gas flow comprised of HBr/
(DBr) seeded in low concentration into the buffer gas, N2. The
first-order rate is obtained from the time-dependent decay of
the OH/(OD) LIF signal as a function of flow distance by means
common to many flow kinetic methods. Particular to these
studies, however, is the way by which the low temperatures
are obtained and the nature of the gas flow. The pulsed uniform
supersonic flow reactor, shown in Figure 1, employs supersonic
expansion of the reaction mixtures within a Laval nozzle to
produce a low-temperature uniform density environment, analo-
gous to conventional flow reactors, except with supersonic
hydrodynamic velocity and without communication with physi-
cal walls. The density conditions of the expansion ensure that
the axisymmetric gas flow exiting the nozzle remains in
complete local thermodynamic equilibrium at a temperature
determined by the controlled nozzle feed conditions of T0, P0,
and γ, (the latter being the ratio of constant pressure and
temperature heat capacities of the expansion mixture), as well
as the design contour of the particular nozzle. Using a single
buffer/nozzle combination, a particular post-nozzle flow density
and temperature may be produced for kinetic studies. In
particular for these studies, the reservoir pressure was varied
from 6 to 51 Torr, and Mach number from 1.2 to 2.7 (using
different nozzle bodies), while the reservoir temperature was
held constant at 300 K using a closed cycle liquid temperature
controller. These conditions allowed for uniform flows with
The absolute HBr and DBr partial pressures prior to delivery
to the reservoir were actively monitored through UV absorption
measurements at 220 nm, using a 10-cm path flow cell. The
absorption cross section for HBr was independently determined
using a Beckman DU-40 UV/VIS spectrometer. The absorbances
were taken for different pressures of the absorbing gas, HBr or
DBr, in a 10.0 cm static cell. These pressures were measured
with a capacitance manometer (MKS Baratron 220 CD). The
absorption cross section for HBr was found to be σHBr (220
nm) ) 2.49 ((0.10) × 10-19 cm2. This value is in good

5856 J. Phys. Chem. A, Vol. 105, No. 24, 2001
Jaramillo and Smith
TABLE 1: Rate Coefficients for the Reaction of OH + HBr
and the Isotopic Variants, with the Experimental Conditions
Used for Their Measurements
reaction temp. (K) density (×1017 cm-3
)
k (×1011 cm3s-1
)
ref.
OH + HBr
OH + HBr
OH + HBr
OH + HBr
OH + HBr
OH + HBr
OH + HBr
OH + HBr
OH + HBr
OH + HBr
OH + HBr
120
141
185
224
230
243
260
278
298
328
360
1.65
3.23 ((0.46)
2.56 ((0.32)
1.72 ((0.40)
1.31 ((0.35)
1.46 ((0.17)
1.20 ((0.14)
1.12 ((0.13)
1.20 ((0.13)
1.11 ((0.12)
1.05 ((0.12)
0.97 ((0.14)
a
a
a
a
b
b
b
b
b
b
b
0.343
1.41
1.04
0.420
0.397
0.371
0.347
0.324
0.294
0.268
OD + HBr
OD + HBr
OD + HBr
OD + HBr
OD + HBr
OD + HBr
OD + HBr
OD + HBr
OD + HBr
OD + HBr
OD + HBr
OD + HBr
120
141
185
224
230
243
260
278
297
298
328
360
1.65
0.343
1.41
3.45 ((0.59)
2.46 ((0.27)
1.93 ((0.27)
1.45 ((0.22)
1.58 ((0.21)
1.40 ((0.16)
1.21 ((0.11)
1.21 ((0.11)
1.11 ((0.12)
1.22 ((0.14)
1.09 ((0.12)
1.01 ((0.13)
a
a
a
a
b
b
b
b
b
b
b
b
1.65
0.420
0.397
0.371
0.347
0.325
0.324
0.294
0.268
OH + DBr
OH + DBr
OH + DBr
OH + DBr
OH + DBr
OH + DBr
OH + DBr
OH + DBr
OH + DBr
OH + DBr
120
141
185
224
230
260
278
296
328
360
1.65
0.343
1.41
3.22 ((0.30)
1.71 ((0.11)
0.91 ((0.15)
0.65 ((0.14)
0.74 ((0.11)
0.68 ((0.08)
0.64 ((0.08)
0.59 ((0.09)
0.57 ((0.07)
0.60 ((0.11)
a
a
a
a
b
b
b
b
b
b
1.65
0.420
0.371
0.347
0.326
0.294
0.268
OD + DBr
OD + DBr
OD + DBr
OD + DBr
OD + DBr
OD + DBr
OD + DBr
OD + DBr
OD + DBr
OD + DBr
OD + DBr
120
141
185
224
230
243
260
278
300
328
360
1.65
0.343
1.41
7.50 ((0.46)
3.12 ((0.21)
1.36 ((0.13)
0.84 ((0.17)
0.72 ((0.09)
0.74 ((0.11)
0.71 ((0.10)
0.77 ((0.10)
.072 ((0.11)
0.66 ((0.09)
0.63 ((0.09)
a
a
a
a
b
b
b
b
b
b
b
1.65
0.420
0.397
0.371
0.347
0.322
0.294
0.268
Figure 2. The temperature dependence of the rate coefficients for:
OH + HBr; OH + DBr; OD + HBr; OD + DBr are displayed. This
work and the results of Bedjanian et al.15 are included.
temperature-dependent studies of Reactions 1-4 above 230 K
using a conventional subsonic flow reactor accompanied by
modulated molecular beam mass spectrometric detection.15 The
combined results are presented in Figure 2. Reactions 1-4 have
no significant temperature dependence above 200 K, but clearly
show inverse temperature dependence at T < 200 K.
The rate coefficients in Table 1 and Figure 2 are all obtained
from bimolecular OH/OD loss rate measurements. Two possible
reactions can effectively lead to such loss. In the case of OH +
DBr, for instance, these are the atom transfer reaction:
a This work. b Bedjanian et al.15
agreement with the value measured by Hubert et al.19 of 2.37
((0.05) × 10-19 cm2, but falls outside of the value measured
by Nee et al.20 of 3.5 ((0.56) × 10-19 cm2. Further, the
absorption cross section for DBr was measured to be σDBr (220
nm) ) 1.24 ((0.05) × 10-19 cm2. To the best of our knowledge,
there have been no published measurements of this latter value.
As a cross check this setup and procedure was used to measure
the absorption cross section for methylbromide at 220 nm, 3.79
((0.15) × 10-19 cm2. This value is in excellent agreement with
previous measured cross sections for CH3Br.21,22 This same
spectrometer was used for active measurements of flow
concentrations. The purity of the gases used were as follows:
N2 > 99.99 (Matheson), HBr > 99.8% (Matheson, degassed of
H2), and DBr > 99% (Cambridge Isotopes, 99% isotopic purity,
degassed of D2).
OH + DBr f HOD + Br ∆H0° ) -126 kJ/mol (3)
and the isotope exchange reaction:
OH + DBr f OD + HBr
∆H0° ) -1.45 kJ/mol (E/R ) -174 K) (5)
For the reactant combination OH + DBr, the isotope exchange
is exothermic. For all others the isotopic exchange enthalpy is
either endothermic, for example in
Results
The results of this investigation are summarized in Table 1,
along with a list of the reaction conditions used. Also given
are the results of Bedjanian et al., who performed similar
OD + HBr f OH + DBr
∆H0° ) + 1.45 kJ/mol (E/R ) +174 K) (6)

Gas-Phase Reaction: OH + HBr
J. Phys. Chem. A, Vol. 105, No. 24, 2001 5857
TABLE 2: Summary of Kinetic Isotope Effects as a
Function of Temperature
temperature primary
secondary
primary
secondary
study
(K)
(OH) k1/k3 (HBr) k1/k2 (OD) k2/k4 (DBr) k3/k4
a
a
a
a
b
b
b
b
b
b
b
120.0
140.8
185.0
224.0
230.0
243.0
260.0
278.0
298.0
328.0
360.0
1.00((0.17) 0.94((0.20) 0.46((0.08) 0.43((0.05)
1.50((0.21) 1.04((0.17) 0.79((0.10) 0.55((0.05)
1.90((0.54) 0.89((0.24) 1.42((0.24) 0.67((0.13)
2.01((0.68) 0.91((0.28) 1.73((0.44) 0.78((0.23)
1.97((0.37) 0.92((0.16) 2.19((0.40) 1.03 ((0.20)
0.86((0.14) 1.89 ((0.36)
1.65((0.27) 0.93((0.16) 1.70((0.32) 0.96((0.18)
1.88((0.31) 0.99((0.16) 1.57((0.28) 0.83((0.15)
1.88((0.35) 0.95((0.15) 1.62((0.31) 0.82((0.18)
1.84((0.31) 0.96((0.15) 1.65((0.29) 0.86((0.16)
1.62((0.30) 0.96((0.19) 1.60((0.31) 0(.95((0.18)
a This work. b Bedjanian et al.15
or exchange is of no consequence, (i.e., OD + DBr). However,
for both Reactions 5 and 6 we have measured upper limits to
the exchange rate coefficients by monitoring OH/OD inter-
change in the presence of HBr/ DBr. This corresponds, for
Reaction 5, to monitoring for exchange product OD when OH
is mixed in the presence of DBr. These measurements were
carried out at 141 K and no exchange could be detected. For
Reaction 5, k5 (141 K) < 3 × 10-13 cm3 s-1, and for Reaction
6, k6 (141 K) < 5 × 10-13 cm3 s-1. This observation of
negligible atom exchange in OH + HBr systems is consistent
with the observations of Bedjanian et al. at 298 K.15 Both of
these studies indicate that exchange does not play an important
role in OH + HBr kinetics and that direct atom transfer is the
dominant mechanism for OH loss. Thus the rate coefficients
listed in Table 1 represent those for H/D transfer to the hydroxyl
radical to produce bromine atom and water.
To better elucidate the effects of isotopic substitution, the
ratios of kH/kD were determined for both primary and secondary
substitutions. These ratios or kinetic isotope effects are listed
in Table 2, and illustrated in Figure 3. The primary KIE for
reaction with OD ranges from 2.2 to 0.46, while the primary
KIE for reaction with OH varies from 2.0 to 1.0 with decreasing
temperature. The secondary KIE values for reaction with DBr
range from 1.0 to 0.4, while for reaction with HBr the ratios
remain constant near unity. There appears to be a small
systematic discrepancy between the highest temperature ratios
of this study with the lowest temperature ratios observed by
Bedjanian et al. Although the origin of this discrepancy is not
entirely clear, we feel the trends observed between both data
sets in Figures 2 and 3 suggest a problem in the lowest
temperature measurement of Bedjanian et al. In particular, the
largest discrepancy occurs regarding the primary kinetic isotope
ratio, k2/k4. As will be discussed in the next section, there is no
fundamental reason a primary kinetic isotope effect should show
such a large increase as temperature drops between 260 and
230, whereas we feel that the drop in this ratio below 230 is on
sound fundamental foundation. It is important to note however,
that all of the data and trends discussed fall within the error
limits of both studies and it seems imprudent to apply
significance to this minor disagreement.
Figure 3. The ratios of the measured rate coefficients, for primary
(k1/k3 and k2/k4) and secondary (k1/k2 and k3/k4) kinetic isotope effects,
plotted versus temperature. This work and the results of Bedjanian et
al.15 are included.
generating D2O product. It thus appears that while high-
temperature kinetic isotope ratios in these reactions tend to
correlate to reactant states (thus, the individuality of primary
and secondary effects), the correlation at low temperatures seems
to be with product channels. At 120 K, it appears that the
concept of primary and secondary KIE has vanished for this
reaction.
Discussion
Reactions with inverse temperature dependent rate coefficients
are well-known in collision systems with strong long-range
attractive forces. Such behavior in radical-molecule systems
has long been fit using Arrhenius rate laws and since the
activation energy, Ea, is typically defined as -R times the slope
of a plot of ln k vs 1/T, these reactions have been termed as
possessing negative activation energies. Using statistical argu-
ments, Mozurkewich and Benson have demonstrated how
reactions on long range attractive surfaces can manifest negative
activation energies if they possess a late tight transition state
which follows a loose one early in the entrance channel.23 Such
a system leads naturally to a long-lived collision complex and
the branching of this complex between products (through the
tight transition state) and reactants (through the loose entrance
channel barrier) naturally leads to inverse temperature depen-
dence in the reactive rate coefficient. This model is only
The observations apparent in the current work from Figure 3
are the first unequivocal experimental documentation of inverse
kinetic isotope ratios (the heavier isotopomer having the larger
rate coefficient). The 120 K data also show correlation between
the pairs k1/k3 and k1/k2, as well as k2/k4 and k3/k4. Reactions 2
and 3 form the same products, HOD and Br. Thus, the ratio
pairs, k1/k3 and k1/k2, would seem to compare reactions
producing H2O product to those producing HOD while the pairs,
k2/k4 and k3/k4, compare reactions producing HOD against one

5858 J. Phys. Chem. A, Vol. 105, No. 24, 2001
Jaramillo and Smith
appropriate to reaction systems in a temperature regime where
the reaction efficiency is much less than unity. In the temperature
range between 120 and 300 K, Reaction 1 is calculated to have
a dipole-dipole capture collision rate coefficient approximately
10 to 20 times greater than the observed reaction rate coefficient
and so such a model may be appropriate.24 While the complex
model places emphasis on entrance channel effects governing
the overall temperature dependence of the rate coefficient,
kinetic isotope ratios would be sensitive to the state density in
the tight transition state. The model predicts in such circum-
stances that deuteration of reactants can lead to inverse primary
kinetic isotope effects since the state density in the deuterated
transition state is increased and the zero point energy lowered,
which lowers the effective activation energy and increases the
rate of passage to products. This prediction is supported by
similar modeling of McEwen and Golden.25 To date, these
predictions have not been supported by experimental observation
of inverse KIEs, though several studies have reported normal
primary kinetic isotope ratios which display weak inverse
temperature dependence.
and 2Π3/2 ground states accurately predicts the observed behavior
of k1(T).29 Unfortunately, parametrization of these results as a
function of OH and HBr rotor constant suggest kinetic isotope
ratios, kH/kD, of 21/2 independent of OH or HBr substitution site.
More recent quasi-classical trajectory calculations on this same
qualitative (Clary) PES and another (Modified potential)
adjusted to fit better the observed H2O product state vibrational
energy distributions have been performed at 300 K for Reactions
1 and 2.30 These results slightly over-predict the experimentally
observed 300 K rate coefficients and, contrary to observation,
predict an inverse secondary kinetic isotope ratio k1/k2(300 K)
of 0.76.
Nizamov et al. have performed variational transition state
theory (VTST) on both the Clary and Modified potentials
identifying a transition state lying early in the entrance channel
to this reaction.30 The OH and H′Br bond distances are
approximately 0.974 and 1.42 Å, respectively, while the critical
O′H distance is between 1.95 and 2.15 Å. The potential energy
barrier for these transition states is between -7.20 and -7.45
kJ mol-1; however, the harmonic zero point energy (ZPE)
corrected value is very close to 0 (-0.5 kJ mol-1 for the Clary
potential and +0.25 kJ mol-1 for the Modified potential). As
expected for such an attractive surface, the harmonic ZPE
corrected barrier for Reaction 2, even on the modified surface
is lower (-0.96 kJ mol-1). From these results, it is not surprising
that even at 300 K, VTST on these surfaces predicts strong
inverse primary and secondary kinetic isotope ratios at 300 K
with k1/k3(300 K) between 0.85 and 0.76, while for k1/k2(300
K) they obtain values between 0.8 and 0.72 depending on the
potential used. The inverse secondary isotope effect is attributed
to the differences of the HOD and HOH′ bend frequencies, and
the inverse primary kinetic isotope effect is thought to be a result
of the smaller zero point adjusted barrier due to the isotopic
substitution. Again, as seen in Table 2 and Figure 3, these
experimental 300 K kinetic isotope ratios are found to be
essentially k1/k3(300 K) ) 1.8 for primary substitution and k1/
k2(300 K) ) 1 for secondary substitution within the errors.
Though the trends of the VTST secondary KIE results agree
with the current low-temperature observations, the absolute
values calculated for the secondary KIEs do not agree with
experimental results even below 300 K. Nizamov et al. suggest
that VTST has difficulty predicting accurate isotope effects when
the transition state is early in nature as was employed for this
system. However, it needs to also be realized that the potentials
employed for all of these models are semiempirical.
Battin-Leclerc et al. studied the temperature dependence (T
) 200 to 400 K) of kinetic isotope effects in the reaction of
OH + HCl and all H/D isotopic variants.26 They observed that
the primary kinetic isotope effect increases as temperature
decreases which is contrary to what is observed in the present
study of OH + HBr. However, this reaction is known to have
a positive activation barrier at these temperatures. Their
observation of an inverse secondary kinetic isotope effect is in
accord with what is observed in this study and has been argued
as a natural consequence of secondary effects of deuteration
on the zero point energy of the transition state. In fact, effective
barrier calculations suggested the largest positive barrier exists
for the OH + HCl reaction with barriers decreasing monotoni-
cally across the series OH + DCl, OD + HCl, and OD + DCl.
From this result, it is not immediately clear why an inverse
primary KIE was not observed in that study.
The reaction of H + HBr and its isotopic variants have also
been studied from 214 to 300 K.27 Unlike the present system
of OH + HBr, this reaction has a large positive temperature
dependence (Ea/R ) 400 K - 790 K) and apparently adheres
well to an Arrhenius rate form with a positive activation energy.
The measured isotope effects were normal, increasing with lower
temperature unlike the behavior observed for the present system.
Nicovich et al. have studied primary kinetic isotope effects of
alkyl radicals with HBr/DBr.28 These systems were found to
have negative activation energies, thus increasing rates as
temperature is decreased, similar to the present system. They
also found that as the activation energy becomes more negative,
the magnitude of the primary kinetic isotope effect is reduced.
It should be noted that these studies were done at temperatures
greater than 250 K. Unfortunately this work has not been
extended to temperatures beyond those for which the KIE is
anything but normal.
It appears that although inverse kinetic isotope effects have
been predicted for reactions on purely attractive surfaces, for
the OH + HBr reaction in particular, current level of knowledge
governing the OH + HBr potential or the ability to model the
dynamics in accurate trajectory calculations prohibits a global
description of the reaction mechanism. Scattering approaches
which incompletely model reactant rotation, and thereby dipole-
dipole coupling, appear to be reasonably successful in describing
the gross features of the temperature dependence of the rate
coefficient (but still not an accurate absolute value), as well as
product state energy disposal. Aspects of statistical rate theory
and variational transition state theory appear to successfully
predict manifestation of inverse kinetic isotope effects but
quantitatively fail to predict sensitive dependence on temper-
ature. The very fine balance between positive and negative ZPE
corrected activation energies between isotopomeric reactions
may play a role here. The effect of H2O, HOD, and D2O
vibrational frequencies in governing the sign of Ea may place
this reaction in a situation where the effective activation energy
The observed temperature dependence of Reaction 1 is well
fit by a T-n functional dependence where n is approximately
0.9, but does not fit well to a strict Arrhenius rate law with a
temperature-independent activation energy.13-16 This inverse
temperature dependence is consistent with the best available
potential surface (LEPS) which displays no barrier for this
exoergic reaction. Quantum scattering calculations on the ground
electronic LEPS surface (Clary potential) predicts a T-1/2
dependence in the rate coefficient which when convolved with
the electronic partition coefficient between the OH 2Π1/2 excited

Gas-Phase Reaction: OH + HBr
J. Phys. Chem. A, Vol. 105, No. 24, 2001 5859
(a temperature-dependent function in cases of negative Ea) is
only significantly negative at reactant energies below 200 K.
In this low-temperature limit, both k(T) and the KIE ratios would
be expected to display inverse behavior as is observed. In the
high-temperature limit, where the transition state has population
in modes above the ZPE level the system may manifest positive
or zero Ea values with normal KIE ratios. Unfortunately, the
observed k(T) behavior above 250 K for Reactions 1-4 does
not suggest the presence of a sufficiently positive activation
energy to support the large primary KIE values seen at the higher
temperatures.
In heavy-light-heavy reaction systems such as this where
both reactants are hydrides and the vibrational frequencies are
generally high, the low-temperature limit, as nearly reached at
120 K in this study, leads to reaction on extremely few
rovibronic surfaces. In the case of activation energies nearly
zero in value, and with a potential surface governed strongly
by dipole-dipole forces, molecular rotation in the reactants and
thus bending modes in the transition state are expected to play
a key role in the low energy reaction dynamics and energetics.
It would appear from all of the models that the qualitative picture
of the low-temperature behavior of this reaction is well
explained, owing to effects of deuteration on transition state
zero point energy for strongly attractive reaction potentials.
Quantitative agreement between models and the low-temperature
results, as well as explanation of the precise dynamics leading
to such a rapid transition to normal KIE values and flat k(T)
dependence at only modestly higher temperatures, is now clearly
needed. Certainly determination of a precise reaction PES would
assist this, as may refinement of the treatment of rotations in
the scattering models. On the experimental side, extension of
the current results below 120 K would be useful to determine
the 0 K limit of the KIE values, as well as measurements of the
low-temperature rates and KIE values for other comparable
systems such as OH + HI, CN + HI, and alkyl radical +
hydrogen halides. Any of these results would be expected to
add critical insight into the detailed nature of energy dependent
dynamics on attractive reaction potentials.
Acknowledgment is made to the National Science Founda-
tion and to the donors of the Petroleum Research Fund,
administered by the American Chemical Society, for the partial
support of this research.
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