On the mechanism of the BrO+HBr reaction

Article abstract of DOI:10.1016/S0009-2614(99)01093-3

The reaction of the bromine oxide radical, BrO, with HBr has been examined with coupled-cluster methods. The HO+HCl reaction is also examined and is used to calibrate the results for the BrO+HBr reaction. The heat of reaction and activation energy barrier

Full text of DOI:10.1016/S0009-2614(99)01093-3

3 December 1999
Ž
.
Chemical Physics Letters 314 1999 341–346
www.elsevier.nlrlocatercplett
On the mechanism of the BrOqHBr reaction
Jaron C. Hansen , Yumin Li , Zhuangjie Li , Joseph S. Francisco
a
a
b
a,)
a
Department of Chemistry and Department of Earth and Atmospheric Sciences, Purdue UniÕersity, West Lafayette, IN 47907-1393, USA
b
Department of Atmospheric Sciences, UniÕersity of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Received 29 June 1999; in final form 15 September 1999
Abstract
The reaction of the bromine oxide radical, BrO, with HBr has been examined with coupled-cluster methods. The
HOqHCl reaction is also examined and is used to calibrate the results for the BrOqHBr reaction. The heat of reaction and
activation energy barrier for BrOqHBr are calculated to be y9.3"4 and 3.6 kcal moly1, respectively. q 1999 Elsevier
Science B.V. All rights reserved.
1. Introduction
boundary layer troposphere by the following mecha-
nism,
Ozone depletion has been observed in the bound-
BrOqBrO
BrqO3
2BrqO2 ,
BrOqO2 .
1
Ž .
w
x
ary layer troposphere in the Arctic region 1–3 .
During the ozone depletion episodes, mixing ratios
of alkanes, alkenes, and alkynes have been found to
2
Ž .
These studies also suggest that the HBr and HOBr
mixing ratios are smaller than that of BrO. It has
been suggested that most of the HBr produced in the
gas phase is scavenged by aerosol particles, and the
heterogeneous reaction of HOBr with HBr results in
reactive bromine, which reenters into the ozone de-
struction cycle. The reaction of BrO radicals with
w x
w x
decrease 4 , while formaldehyde increases 5 . Job-
w x
son et al. 4 showed that bromine atoms, rather than
chlorine atoms, were responsible for most of the
w x
ozone destruction. Studies by Hausmann and Platt 6
showed the presence of BrO radicals in the lower
Arctic troposphere. These measurements showed that
BrO concentrations in the boundary layer were about
two orders of magnitude higher than that found in
the stratosphere. It has been suggested that the bulk
of the ozone loss is most likely caused by BrOx
catalyzed reactions. Modeling studies of Sander et al.
Ž
HBr to form HOBr allows active bromine Br atoms
and BrO radicals to form in the gas phase,
.
BrOqHBr
HOBrqhn
BrqO3
HOBrqBr .
OHqBr ,
3
Ž .
4
Ž .
5
Ž .
w x
7 show that the BrO self-reaction is a major con-
tributing pathway to the depletion of ozone in the
BrOqO2 .
There has been one previous study of this reaction
w x
by Turnipseed et al. 8 . These authors showed that
the rate for BrOqHBr reaction has an upper limit of
)
Corresponding author. Fax: q1-765-494-0239; e-mail:
6.3=10y15 cm3 moleculey1 sy1 at 298 K, suggest-
jfrancis@purdue.edu
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
Ž
.
PII: S0009-2614 99 01093-3

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)
342
J.C. Hansen et al.rChemical Physics Letters 314 1999 341–346
Ž
.
ing that the reaction is slow. No other experimental
studies have been reported for the BrOqHBr reac-
tion. Moreover, no computational studies have been
reported for this reaction. The importance of HBr as
a sink for bromine in the atmosphere depends criti-
cally on the processes that form and destroy HBr. In
order to gain some insight into the kinetics of the
BrOqHBr reaction, we examine the energetics of
this reaction using ab initio molecular orbital theory.
We also show the experimental evidence of HOBr
formation as a product of BrO reaction with HBr.
31G d, p level of theory. The spin contamination
before and after annihilation for radical species, and
the transition state involved in the BrOqHBr reac-
tion were examined. Before annihilation, s ranged
from 0.787–0.778, and after annihilation,
0.751. This suggested that the wavefunction was not
strongly contaminated by states of higher multiplic-
ity.
2
²
:
s
2
²
:
was
3. Results and discussion
3.1. Mass spectroscopic obserÕation of the BrOq
HBr reaction
2. Computational methodology
All calculations were performed using the GAUSS-
A discharge flow combined with mass spectrome-
w x
Ž
.
IAN 94 program 9 . Geometry optimizations were
ter DFrMS technique has been employed to briefly
Ž .
carried out for all structures using Schlegel’s method
study Reaction 3 . The detail of the DFrMS setup
˚
w
x
w
x
10 to better than 0.001 A for bond lengths and
has been described previously 18 . Fig. 1 shows the
mass spectrum for the BrOqHBr system, in which
the profile in solid line shows 1.4=1013 molecule
cmy3 of BrO produced by reacting Br2 with atomic
oxygen in the absence of HBr.
0.018 for angles, with a self-consistent field conver-
gence of at least 10y9 on the density matrix. The
residual rms force is -10y4 a.u. Initial searches for
the transition state were performed at the B3LYPr6-
31G d, p level of theory 11,12 . Once the transition
state was found, vibrational frequencies were calcu-
lated analytically to verify if the transition state was
a first-order saddle point. The geometries and second
derivatives from the B3LYPr6-31G d, p searches
were then used in optimizations with the second-order
Møller–Plesset perturbation theory MP2 13 and
with the coupled-cluster method, which included sin-
gle and double excitations CCSD 14–17 . With
the MP2 optimizations, Schlegel’s analytical gradi-
ents method was used. The eigenvalue following
method was used to locate the transition state struc-
ture, as well as the minimum energy structures with
the CCSD method. To refine the energies, single-
point calculations were performed with the coupled-
cluster method, which included single and double
excitations with perturbative corrections for triple
Ž
.
w
x
Br2 qO
BrOqBr .
6
Ž .
The atomic oxygen was produced by microwave
discharge of O2. The spectrum reveals two peaks at
mres95r97, corresponding to 79 BrO and 81 BrO
isotopes, respectively. The peaks at mres79r81
Ž
.
Ž .
are the atomic bromine due to both Reaction 5 and
Ž
. w x
fragmentation of Br2. The profile in the dotted line
was taken after addition of 1.4=1013 molecule cmy3
Ž
. w
x
w
Ž .x
excitations CCSD T , using a range of basis sets
which are enlarged by the inclusion of additional sets
of d-polarization and a set of f-polarization functions
on the bromine and oxygen. The geometry optimized
Ž
.
at the CCSDr6-31G d, p level of theory was used
in the single-point energy calculations. Frequencies
and zero-point energy for the species involved in
Ž .
1
Reaction
were evaluated at the B3LYPr6-
Fig. 1. Mass spectrum for the BrOqHBr chemical system.

(
)
J.C. Hansen et al.rChemical Physics Letters 314 1999 341–346
343
Table 2
of HBr into the reactor. It can be seen that two new
peaks appeared at mres96r98, assigned to be
HOBr, when the HBr was added to the reactor
containing BrO. The decrease of the BrO peaks and
the appearance of HOBr upon addition of HBr sug-
gest that the hydrogen abstraction of HBr by BrO is
one reaction pathway for the interaction between
BrO and HBr. The increase of the mres79r81 in
the dotted profile may be due to the additional
Harmonic vibrational frequencies for species involved in the
BrOqHBr reaction
Species
Frequencies
ZPE
y1
a
y1
Ž
cm
.
Ž
.
kcal mol
BrO
HBr
HOBr
705
2622
1.0
3.7
8.0
3776, 1190, 636
1003, 842, 668, 343, 68, 922i 4.2
‡
w
x
BrOqHBr
a
Ž
.
Calculated at the B3LYPr6-31G d,p level of theory.
Ž .
atomic bromine produced by Reaction 3 and by the
fragmentation of HBr.
oxygen atom and the hydrogen and bromine atoms
are predicted to be not co-linear, as is usually the
case for most hydrogen abstraction reactions by
3.2. Geometries and Õibrational frequencies for the
BrOqHBr reaction
w
x
halogen atoms 19,20 . For BrOqHBr reaction, the
optimized OHBr angle in transition state is predicted
to be 152.48, although optimization was started with
a linear configuration. The transition state was started
in this position due to results presented by Clary et
Table 1 lists the geometries for the reactants,
transition state, and products of the BrOqHBr reac-
Ž
.
tion. Table 2 lists the CCSDr6-31G d, p vibrational
frequencies and zero-point energies for the BrOq
HBr reaction. The transition state for the BrOqHBr
reaction is shown in Fig. 2. In the approach of the
BrO into the entrance channel, the H–Br bond length
begins to elongate. The transition state involves
mainly three atoms in the abstraction process. They
are the oxygen atom from the BrO, and the hydrogen
atom and the Br atom from HBr. In the transition
state, the H–Br bond elongates by 13% of its equi-
librium value. The O–H bond length in HOBr is
only 29% of that of the transition state. The attacking
w
x
al. 21 . Note that the resultant transition state struc-
ture is found to be non-planar with a BrOHBr dihe-
dral angle of 81.78. From the geometric changes in
the forming OH and breaking HBr bonds, the saddle
point for the BrOqHBr appears to be more reac-
tant-like. This is consistent with Hammond’s rule
w
x
22 for exothermic systems.
The vibrational frequencies, the reactants, and
Ž .
product in Reaction 3 are all real, and the transition
state for the BrOqHBr reactions shows one imagi-
nary frequency of 922i cmy1. The transition state
vibrational reactors show that the main molecular
motions are the H–Br and OH stretching motions, as
indicated in Fig. 2.
Table 1
Geometriesa for species involved in the BrOqHBr reaction
Species
Coordinate
CCSD
Expt.
Ž
.
BrO
r BrO
1.777
1.728
3.3. Energetics of the BrOqHBr reaction
Ž
.
HBr
r HBr
1.410
1.448
In order to obtain an estimate of the reliability of
the prediction for the energetics for the BrOqHBr
Ž
.
.
HOBr
r HO
0.968
1.869
Ž
r BrO
Ž
.
u HOBr
102.1
‡
w
x
Ž
.
.
.
BrOqHBr
r BrO
1.806
1.246
1.588
Ž
r OH
Ž
r HBr
Ž
.
.
u HOBr
109.6
152.4
81.7
Ž
u OHBr
Ž
.
t BrOHBr
a
Ž
.
The CCSD structures are obtained with the 6-31G d,p basis set.
˚
Bond distances are in units of A, and bond angles are in degrees.
Fig. 2. Transition state structures for the BrOqHBr reaction.

(
)
344
J.C. Hansen et al.rChemical Physics Letters 314 1999 341–346
Ž .
Ž
.
reaction, we investigated the HOqHCl reaction, for
At the CCSD T r6-311qqG 2df, 2p rrCCSDr
Ž
.
which there have been considerable experimental
6-31G d, p level of theory, the barrier is estimated
as 3.1 kcal moly1. This barrier is corrected for
zero-point energy, but not tunneling corrections.
When tunneling corrections are included in the bar-
w
x
and theoretical studies 21,23–30 . The most exten-
sive experimental studies of the HOqHCl reaction
w
x
have been those of Smith and Zellner 24 who
covered the temperature range between 220 and 480
w
x
rier using the Wigner correction 32 employing the
w
x
K, Ravishankara and co-workers 25 who measured
rate constants from 240 to 1055 K, and the recent
low-temperature measurements of Sharkey and Smith
imaginary frequency of 2003i from the UMP2r6-
Ž
.
31G d, p frequency calculation, the resultant barrier
for the HOqHCl reaction is 2.4 kcal moly1. This
suggests that the calculations overestimate the exper-
w
x
30 from 138 to 298 K. The Jet Propulsion Labora-
Ž
.
w x
tory JPL compilation 31 in evaluating all mea-
surements of the HOqHCl reaction recommends
that the best activation barrier is 0.695"0.2 kcal
imental barrier by 1.7 kcal moly1
.
o
Ž
.
The experimental heat of reaction D Hr, 0 is well
established as y16.0"0.01 kcal moly1. At the
moly1
.
CCSD T r6-311G 2df, 2p rrCCSDr6-31G d, p
Ž .
Ž
.
Ž
.
w
x
Clary and co-workers 21 obtained an activation
level of theory, the predicted heat of reactions is
y13.9 kcal moly1, as shown in Table 3, which is
overestimated by 2.1 kcal moly1 from the experi-
barrier height of 24.7 kcal moly1 at the UHFr6-311
Ž
.
qqG d, p level of theory. The authors acknowl-
edged that the calculated barrier height is much too
large at this level of theory. When electron correla-
tion is included at the MP2 level, the barrier is
predicted as 7.2 kcal moly1. The barrier height for
Ž .
mental heat of reaction. At the CCSD T r6-311q
Ž
.
Ž
.
qG 2df, 2p rrCCSDr6-31G d, p level of theory,
the calculations are within 0.4 kcal moly1 of the
experimental heat of reaction. This suggests that the
energetics for the BrOqHBr reaction can be reason-
ably predicted at the highest level of theory of the
present study, keeping in mind that the barriers are
the HO q HCl reaction calculated with the
y1
Ž
.
CCSDr6-31G d, p level of theory is 6.7 kcal mol
.
Ž .
Ž
.
With the CCSD T r6-31G d, p , the barrier is low-
ered by 1.8 kcal moly1. These computational results
suggest that the high-level calculations are necessary
to predict the activation energy barrier of hydrogen
abstraction processes, but the predicted Ea in previ-
ous studies is still too high. Extending the size of the
basis set improves the results, as shown in Table 3.
probably overestimated by 2 kcal moly1
.
The experimental heats of formation at 0 K are
30.2"1, y10.93"1, 28.2"0.0, and y6.8"1
kcal moly1 for BrO 33 , HOBr 34 , Br 33 , and
w
x
w
x
w x
w
x
HBr 33 , respectively. This leads to an experimental
heat of reaction of y6.1"1 kcal moly1. The calcu-
Table 3
Total and relative energies for the HOqHCl reaction
y1
.
Level of theory
Total energies hartree
Relative energiesa kcal mol
Ž
.
Ž
‡
D Hro, 0
barrier height
w x
HOqHCl
Cl
HO
HCl
H2O
Ž
.
CCSDr6-31G d, p
y459.56897
y459.57048
y75.54673
y75.54845
y460.22194
y460.22457
y76.22877
y76.23158
y535.75791
y535.76524
y14.3
y14.2
6.7
4.9
Ž .
CCSD T r
Ž
.
6-31G d, p
Ž .
CCSD T r
y459.60325
y459.62456
y459.65734
y459.65873
y75.58917
y75.60811
y75.62701
y75.63348
y460.26331
y460.28753
y460.32131
y460.32249
y76.27611
y76.29891
y76.31934
y76.32826
y535.84541
y535.89073
y535.94427
y535.95102
y13.0
4.4
Ž
.
6-311G d, p
Ž .
CCSD T r
y13.6
2.5
Ž
.
6-311G 2d, 2p
Ž .
CCSD T r
y13.9
2.5
Ž
.
6-311G 2df, 2p
Ž .
CCSD T r6-311qq
y15.6
3.1
Ž
.
G 2df, 2p
Expt.
y16.0"2
0.695"0.2
a
Ž
.
Relative energies are corrected for zero-point energy calculated at the MP2r6-31G d, p level of theory.

(
)
J.C. Hansen et al.rChemical Physics Letters 314 1999 341–346
345
Table 4
Total energiesa for the BrOqHBr reaction
‡
w x
BrOqHBr
Level of theory
Br
BrO
HBr
HOBr
Ž
.
CCSDr6-31G d, p
y2569.96967
y2569.97056
y2572.46866
y2572.47042
y2572.50377
y2572.50408
y2644.92974
y2644.93731
y2647.46533
y2647.49246
y2647.54997
y2647.55596
y2570.60728
y2570.60916
y2573.10788
y2573.11326
y2573.14621
y2573.14667
y2645.58623
y2645.59393
y2648.12629
y2648.15451
y2648.21239
y2648.21854
y5215.52223
y5215.53460
y5220.56125
y5220.59439
y5220.68604
y5220.70767
Ž .
Ž
.
CCSD T r6-31G d, p
Ž .
Ž .
Ž .
Ž .
Ž
Ž
Ž
.
CCSD T r6-311G d, p
.
.
CCSD T r6-311G 2d, 2p
CCSD T r6-311G 2df, 2p
Ž
.
CCSD T r6-311qqG 2df, 2p
a Total energies are in units of hartree.
lated total energies for the reactants and products and
contributions, a reasonable estimate of the barrier is
3.6 kcal moly1
Ž .
the relative energetics for Reaction 3 at various
.
levels of theory are presented in Tables 4 and 5,
3.4. Estimation of the reaction rate for the BrOq
Ž .
respectively. At the CCSD and CCSD T levels, the
HBr reaction
heat of reaction for the BrOqHBr reaction is pre-
dicted to be exothermic by 8–10 kcal moly1
,
To estimate the rate constant for the BrOqHBr
Ž .
as shown in Table 5. At the CCSD T r6-
Ž
.
reaction, transition state theory TST is used. The
basic postulate of transition state theory is that the
rate of transformation of the reactants to products is
given solely by the passage in the forward direction
of reactants through the transition state, then onto
products. Calculation of the partition functions for
the transition state and reactants coupled with the
activation energy then yields a thermal rate constant.
This is given by the following equation:
Ž
.
Ž
.
311G 2df, 2p rrCCSDr6-31G d, p level of theory,
the heat of reaction is predicted to be y9.3 kcal
moly1. There is a 3.2 kcal moly1 difference between
the calculation and experimental estimate for the
BrOqHBr reaction.
The calculated barrier height for the abstraction of
hydrogen from HBr by BrO ranges from 8.8 to 6.4
kcal moly1, depending on the level of theory and
Ž .
basis set, as seen in Table 5. At the CCSD T r6-311
kBT
Q‡
Ž
.
Ž
.
qqG 2df, 2p rrCCSDr6-31G d, p level of the-
ory, the activation barrier for the BrOqHBr reac-
tion is estimated as 6.8 kcal moly1. Adding tunnel-
ing corrections, and from our examination of the
HOqHCl reaction, we find that the barrier calcu-
lated at this high level is probably overestimated by
an additional 1.7 kcal moly1. If we include these
k T s
Ž .
exp yE rRT .
7
Ž .
Ž
.
0
ž /
ž /
h
QA QB
In order to evaluate the reasonableness of the A-fac-
tor calculated solely from ab initio data, a calibration
calculation was first carried out on the HOqHCl
reaction. From the geometries and vibrational fre-
Ž
.
quencies for the reactants HO and HCl and the
abstraction transition state, the partition functions are
Table 5
Ž .
calculated. Using the first two terms in Eq. 7 , the
Heat of reaction and barrier height for the BrOqHBr reaction
A-factor can be calculated. The recommended A-fac-
Level of theory
BrOqHBr
D Hro, 0
BrqHOBr
barrier heighta
w
x
tor from the JPL compilation 31 for the HOqHCl
reaction is 3.2=10y12 cm3 moleculey1 sy1. Using
the ab initio data and transition state theory, our
estimated A-factor is 2.6=10y12 cm3 moleculey1
sy1. There is a difference of 23.1% between the
experimental and the calculated value. The differ-
ence between the two values is attributed to the
uncertainty in the calculated rotational constants and
vibrational frequencies in the calculations. From our
examination of the A-factor from the HOqHCl
a
Ž
.
CCSDr6-31G d,p
y8.6
y8.1
8.8
6.9
7.0
7.1
6.4
6.8
Ž .
Ž
.
CCSD T r6-31G d,p
Ž .
Ž .
Ž .
Ž .
Ž
Ž
Ž
.
CCSD T r6-311G d,p
y10.4
y8.8
.
CCSD T r6-311G 2d,2p
.
CCSD T r6-311G 2df,2p
y9.3
Ž
.
CCSD T r6-311qqG 2df,2p
y9.3
Expt.
y6.1"1
a The heat of reaction and barrier are corrected only for zero-point
energy and are reported in units of kcal moly1
.

(
)
346
J.C. Hansen et al.rChemical Physics Letters 314 1999 341–346
w x
7
R. Sander, R. Vogt, G.W. Harris, P.J. Crutzen, Tellus 49B
reaction, we find that it may be necessary to scale
the A-factor calculated from the ab initio results.
This further suggests that in order to estimate the
A-factor for the BrOqHBr reaction, it is necessary
to scale the A-factor. In the BrOqHBr, we use the
scale factor derived from the HOqHCl reaction in
conjunction with the A-factor derived from transition
state theory using the ab initio parameters. The
estimated kinetic rate constant for the BrOqHBr
reaction is 2.1=10y14 cm3 moleculey1 sy1 at 298
K. This value represents an average of rates over the
uncertainty range of the activation energy barrier for
the BrOqHBr reaction. The results suggest that the
BrOqHBr reaction is slow, and is roughly of a
magnitude that is similar to the upper limit result of
Ž
.
1997 522.
w x
8
A.A. Turnipseed, J.W. Birks, J.G. Calvert, J. Phys. Chem. 95
Ž
.
1991 4356.
w x
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17 T.J. Lee, A.P. Rendell, J. Chem. Phys. 94 1991 6229.
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reaction of BrO with HBr was found to produce
HOBr. In general, increasing the basis set and im-
proving the level of theory lowers the calculated
activation barrier. This trend shows that it is neces-
sary to do these kinds of calculations with large basis
sets and at high levels of theory. The heat of forma-
x
Ž
.
18 Z. Li, J. Phys. Chem. 103 1997 1206.
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Ž
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19 Y. Zhao, J.S. Francisco, J. Chem. Phys. 93 1990 276.
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x
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