Reaction of OH + NO2: High pressure experiments and falloff analysis

Article abstract of DOI:10.1021/jp0562734

High pressure experiments on the OH + NO₂ reaction are presented for 3 different temperatures. At 300 K, experiments in He (p = 2-500 bar) as well as in Ar (p = 2-4 bar) were performed. The rate constants obtained in Ar agree well with values which have been reported earlier by our group (Forster, R.; Frost, M.; Fulle, D.; Hamann, H. F.; Hippler, H.; Schlepegrell, A.; Troe, J. J. Chem. Phys. 1995, 103, 2949. Fulle, D.; Hamann, H. F.; Hippler, H.; Troe, J. J. Chem. Phys. 1998, 108, 5391). In contrast, the rate coefficients determined in He were found to be 15-25% lower than the values given in our earlier publications. Additionally, results for He as bath gas at elevated temperatures (T = 400 K, p = 3-150 bar; T = 600 K, p = 3-150 bar) are reported. The results obtained at elevated pressures are found to be in good agreement with existing literature data. The observed falloff behavior is analyzed in terms of the Troe formalism taking into account two reaction channels: one yielding HNO ₃ and one yielding HOONO. It is found that the extracted parameters are in agreement with rate constants for vibrational relaxation and isotopic scrambling as well as with experimentally determined branching ratios. Based on our analysis we determine falloff parameters to calculate the rate constant for atmospheric conditions.

Full text of DOI:10.1021/jp0562734

J. Phys. Chem. A 2006, 110, 6781-6788
6781
Reaction of OH + NO2: High Pressure Experiments and Falloff Analysis†
Horst Hippler,* Nikolina Krasteva, Steffen Nasterlack, and Frank Striebel*
Lehrstuhl fu¨r Molekulare Physikalische Chemie, UniVersita¨t Karlsruhe, Kaiserstrasse 12,
D-76128 Karlsruhe, Germany
ReceiVed: October 31, 2005; In Final Form: March 9, 2006
High pressure experiments on the OH + NO2 reaction are presented for 3 different temperatures. At 300 K,
experiments in He (p ) 2-500 bar) as well as in Ar (p ) 2-4 bar) were performed. The rate constants
obtained in Ar agree well with values which have been reported earlier by our group (Forster, R.; Frost, M.;
Fulle, D.; Hamann, H. F.; Hippler, H.; Schlepegrell, A.; Troe, J. J. Chem. Phys. 1995, 103, 2949. Fulle, D.;
Hamann, H. F.; Hippler, H.; Troe, J. J. Chem. Phys. 1998, 108, 5391). In contrast, the rate coefficients
determined in He were found to be 15-25% lower than the values given in our earlier publications.
Additionally, results for He as bath gas at elevated temperatures (T ) 400 K, p ) 3-150 bar; T ) 600 K,
p ) 3-150 bar) are reported. The results obtained at elevated pressures are found to be in good agreement
with existing literature data. The observed falloff behavior is analyzed in terms of the Troe formalism taking
into account two reaction channels: one yielding HNO3 and one yielding HOONO. It is found that the extracted
parameters are in agreement with rate constants for vibrational relaxation and isotopic scrambling as well as
with experimentally determined branching ratios. Based on our analysis we determine falloff parameters to
calculate the rate constant for atmospheric conditions.
Introduction
as well as Matthieu and Green5 published theoretical studies
on the title reaction. The aim of these calculations was to model
Due to its importance in atmospheric chemistry the OH +
NO2 reaction has been the subject of many experimental and
theoretical studies. In a recent data evaluation for atmospheric
chemistry 22 studies are listed.1 Despite the efforts made in the
past there are still open questions (see also ref 1). In particular
the following two questions have been discussed recently:
(i) What is the “best” set of falloff parameters (k0, k∞, Fc) to
describe the pressure and temperature dependence of the rate
constant?
(ii) What is the impact of HOONO formation on laboratory
experiments, and what is the role of HOONO formation under
atmospheric conditions?
Before we present our new experimental results, we will give
a brief summary of the current knowledge on this reaction. Due
to the large number of papers published we have to limit
ourselves to those which are most relevant to this paper.
Until recently it has been assumed that OH and NO2 react to
form nitric acid as the only product:
experimentally observed rate constants using statistical rate
theory and taking into account both reaction channels. Golden
and Smith concluded that HOONO formation might be con-
siderable at low temperatures (∼20%). This conclusion triggered
new interest in this reaction, and different research groups
attempted to detect HOONO as a reaction product. In 2001,
Dransfield et al. tried to detect HOONO using FTIR spectros-
copy. From their experimental observations they obtained no
evidence for HOONO formation in the temperature range from
230 to 300 K and at pressures up to 375 Torr.6 At the same
time this group also published a paper on the isotopic scrambling
of 18OH in the reaction with NO2,7 and the authors claim that
they have been able to obtain the high pressure limiting rate
constant for HNO3 formation. (We believe that this is not the
case, and we will return to this point in the discussion.) The
fact that the apparent high pressure rate coefficient extracted
from these experiments is a factor of 5 lower than what has
been reported by our group8 led the authors of ref 7 to the
conclusion that HOONO formation occurs at high pressures.
The first experimental evidence for the formation of HOONO
formation was reported in 2002 by Nizkodorov and Wennberg9
and by our group.10 The authors of ref 9 used an action
spectroscopy technique to detect HOONO. We used a rather
different approach using chemical kinetics instead of spectros-
copy to prove the formation of different HNO3 isomers.10 By
choosing proper conditions (elevated temperature and high
pressures) we observed biexponential [OH] decays in the
reaction of OH with NO2. At the conditions of our experiments,
HNO3 is stable and, thus, the observation of a biexponential
decay is only in agreement with the formation of a second, less
stable reaction product. Based on the results of ab initio
calculations (see, e.g., ref 11 and references cited therein) the
only possibility is formation of HOONO. In 2003, Bean et al.12
OH + NO2 + M f HONO2 + M
(R1)
However, Robertshaw and Smith suggested already in 1982 that
a second reaction channel leading to the formation of perox-
ynitrous acid,
OH + NO2 + M f HOONO + M
(R2)
might interfere.2 Early attempts to prove the HOONO formation
in the reaction of OH + NO2 failed.3 These studies allowed
only for estimating an upper bound for the HOONO yield which
has been determined to be 10%. In 2000, Golden and Smith4
† Part of the special issue “David M. Golden Festschrift”.
* Corresponding authors. E-mail: horst.hippler@chemie.uni-karlsruhe.de;
frank.striebel@chemie.uni-karlsruhe.de.
10.1021/jp0562734 CCC: $33.50 © 2006 American Chemical Society
Published on Web 04/08/2006

6782 J. Phys. Chem. A, Vol. 110, No. 21, 2006
Hippler et al.
detected HOONO as a reaction product in the OH + NO2
reaction using IR-cavity ringdown spectroscopy. They deter-
mined the yield to be 7% at 300 K and a pressure of 20 Torr.
Finally, D’Ottone et al. reported very recently the observations
of biexponential [OH] decays in the OH + NO2 reaction at 413
K and 400 Torr of He.13 They also found that the observed
biexponential decays are in agreement with a 10% yield of
HOONO. In conclusion one might say that there is now ample
experimental and theoretical evidence that HOONO is formed
in the OH + NO2 reaction. However, there is only little
information available about the temperature and pressure
dependence of the branching ratios between the competing
reaction channels available.
(C5H8O2) was photolyzed at 248 nm, and nitric acid (HONO2)
was photolyzed at 248 or 193 nm. While nitric acid is a common
precursor to generate OH radicals, acetylacetone has beensto
the best of our knowledgesonly used by our group in a kinetic
study.10 The photodissociation dynamics of acetylactone have
been studied in ref 21.
The different photochemical systems provided a check that
the method of OH radical preparation did not alter the kinetics.
In all cases we used an excimer laser (Lambda Physik, Compex
201) for the photolysis with a typical laser fluence of 60
mJ/cm2 at 248 nm and of 45 mJ/cm2 at 193 nm. The OH radi-
cals were detected using laser-induced fluorescence. We ex-
cited the radicals at 281.89 nm using a frequency doubled
dye laser (Rhodamine 6 G, Lambda Physik, FL 3002), pumped
by a frequency doubled Nd:YAG laser (Continuum PL7010)
and by recording the nonresonant fluorescence at about
308 nm.
The reaction mixtures for the 248 nm photolysis contained
as radical precursors typically 0.1 mbar of acetylacetone
(C5H8O2, Merck, >99%) or 1 mbar of nitric acid. The partial
pressure of nitrogen dioxide (NO2, Messer Griesheim, >98.0%)
has been varied between 1 and 10 mbar, and the mixtures were
completed with helium (Messer Griesheim, >99.999%) or Ar
(Messer Griesheim, >99.999%). The mixtures for the 193 nm
photolysis contained as radical precursor only 0.1 mbar of nitric
acid. All gases were premixed in commercially available gas
cylinders (Messer Griesheim, 40 dm3, 300 bar) and were allowed
to homogenize for at least 12 h. The pressure was measured
using pressure gauges (Okhura Electric, 0-500 bar), and a flow
of about 3 standard liters per minute was adjusted.
In some experiments, the NO2 concentration in the gas
mixture was measured directly in the gas flow with a UV
absorption cell which was inserted into the high pressure gas
flow directly behind the reaction cell. The UV absorption at
436 nm allowed for a continuous monitoring of the NO2
concentration and therefore for a reduction of the experimental
uncertainty.
So far, most experiments have been performed at temperatures
below 400 K. At these temperatures, R1 and R2 compete. Since
the branching ratio between these channels is not known, it is
impossible to extract reliable falloff parameters for the two
reactions from the experiments. One might use theory to
calculate these parameters, and Troe14 and Golden et al.15 have
recently published a theoretical analysis on the pressure and
temperature dependence of the rate constants. It is, however,
difficult to estimate the uncertainties of the statistical methods
used in refs 14 and 15. Therefore, it seems to be desirable to
have additional experimental data at hand in order to reduce
the uncertainties of the falloff parameters for R1 and R2.
It is the aim of this study to present further experimental data
to reduce existing uncertainties in the falloff parameters.
Therefore we will present new high pressure data at room
temperature for He. The motivation for these experiments is
2-fold: First, we reported indications that the rate coefficients
published earlier by our group for He were roughly 30% too
high.10 Thus, we wanted to remeasure the rate coefficient for
this reaction in order to reduce the uncertainties. We also
checked our earlier results for Ar as bath gas as well as for He
at 400 K, and these results are presented as well. A second
motivation for the room temperature experiments comes from
the fact that the rate for room temperature and p ≈ 1 bar of N2
(conditions typical for the lower troposphere) is remarkably
uncertain. This is mainly due to the fact that D’Ottone et al.16
reported a value for p ) 0.8 bar which is roughly a factor of
1.7 higher than the one reported by Donahue et al.17 The shape
of falloff curves does hardly depend on the bath gas. Thus, even
though our experimental results were obtained for He and Ar,
it should be possible to reduce the existing uncertainties. Finally,
we will present a falloff analysis of the rate constant. In order
to check the extracted data against all information which is
available, this is done in such a way, that not only thermal rate
constants are taken into account but also rate constants reported
for vibrational relaxation13,18 and isotopic scrambling.7,13,19 Since
the falloff analysis is complicated by the pressure dependent
branching between R1 and R2, rate coefficients for T ) 600 K
will be presented as well. At this temperature, HOONO
formation can be excluded and the rate coefficients reported
for T ) 600 K should be used in the future to check falloff
parameters for R1.
Experimental Results and Kinetic Background
The analysis of the experimental results is based on the
following assumptions: (i) OH is only consumed by reaction
with NO2, (ii) HNO3 is thermally stable at the conditions of
our experiments, and (iii) pseudo-first-order conditions are given.
The recombination of OH is not taken into account due to the
fact that [NO2] g 100 × [OH]0. Moreover, the isomerization
between HOONO and HNO3 does not occur under the condi-
tions of our experiment. Consequently, we are left with the
following mechanism:
OH + NO2 + M f HONO2 + M
OH + NO2 + M T HOONO + M
(R1)
(R2)
The kinetics of this mechanism is described by the following
set of coupled differential equations:
d[OH]
dt
Experimental Procedures
) -(k1,1st + k2,1st)[OH] + k-2[HOONO] (1)
The experimental setup has been described in earlier pa-
pers,10,20 and we will therefore only describe the generation and
the detection of OH radicals as well as typical experimental
conditions.
d[HOONO]
) k2,1st[OH] - k-2[HOONO]
(2)
dt
The OH radicals were produced by pulsed laser flash
photolysis of two different precursor molecules. Acetylacetone
k1,1st and k2,1st are the pseudo-first-order rate constants for
reaction R1 and R2, respectively, and k-2 is the rate constant

Reaction of OH + NO2
J. Phys. Chem. A, Vol. 110, No. 21, 2006 6783
for the decomposition of HOONO. The solution of this equation
system leads to the equation
we could recently determine the equilibrium constant as a
function of temperature in the range from 430 to 475 K.10 In
ref 10 we analyzed this data by performing a third-law analysis
and extracted ∆Hr(0 K) to be 83 kJ/mol. The analysis in ref 10
has been performed by calculating partition functions within
the harmonic oscillator approximation and neglecting contribu-
tions of (hindered) internal rotations. However, the falloff
analysis of this work indicated that contributions of internal
rotations should be taken into account, and thus we reanalyzed
the data of ref 10 to arrive at an internally consistent picture.
The treatment of the internal rotation is based on the ab initio
calculation by McGrath and Rowland.22 (We note that there has
been a more recent publication by the same authors23 in which
the barrier for the internal rotation is calculated to be higher.
Adopting this higher value would have led to changes in the
extracted heat of reaction smaller than 0.5 kJ/mol.)
We calculated the partition function for the internal rotation
using the approximation proposed by Troe24 and treating the
potential energy surface (PES) for the rotation as a single well
system. We tested this simplified procedure against a more
sophisticated one proposed by Shokhirev and Krasnoperov.25
The differences of the two procedures are found to be 5% or
less in the temperature range of interest and thus less than the
uncertainties arising from uncertainties of the PES for the
internal rotation. For the sake of simplicity we therefore decided
to stay with the method proposed by Troe.24 Analyzing the
temperature dependence of the equilibrium constant using this
formalism yielded an O-O bond energy of ∆H°(0 K) ) (80.5
( 2) kJ/mol for the cis-cis isomer. This is in good agreement
with recent theoretical predictions of (78.7 ( 4.2) kJ/mol11 and
(80.8 ( 1.7) kJ/mol23 as well as with the value extracted by
Golden et al.,15 who analyzed our data and obtained a value of
82.1 kJ/mol. For the falloff analysis described below we stayed
with the value obtained in this work in order to treat the internal
rotor consistently with the same formalism in the third-law
analysis as well as in the falloff analysis. The uncertainty in
the threshold energy affects only the calculated strong collision
rate constant noticeable. It leads to an uncertainty of the
calculated density of statessand thus of the calculated low
pressure rate constantsof roughly 10%. This uncertainty is
smaller than the uncertainty introduced by the simplified
treatments of anharmonic effects or internal rotors.
(k-2 + s1)
s1 - s2
[OH] ) [OH]0
exp(s1t) -
(k-2 + s2)
s1 - s2
[OH]0
exp(s2t) (3)
with the two eigenvalues
1
s1,2
)
-(k-2 + (k1,1st + k2,1st)) (
(
2
(k-2 + (k1,1st + k2,1st))2 - 4k1,1stk-2 (4)
x
)
s1 is greater than s2, and both eigenvalues are negative.
As discussed in our previous paper,10 one has to expect
biexponential decays. However, if the dissociation of HOONO
occurs on a different time scale than the OH consumption, single
exponential OH decays are observed. At low temperatures k-2
is much smaller than k1,1st and k2,1st, thus one obtains
[OH] ) [OH]0 exp(-(k1,1st + k2,1st)t)
(5)
On the contrary, at high temperatures k-2 is much greater than
k1,1st and k2,1st. OH is then only consumed by reaction R1, and
the following relation holds:
[OH] ) [OH]0 exp(-k1,1stt)
(6)
In this paper we present new data obtained at T e 400 K
and results at T ) 600 K and we use eq 5 and eq 6, respectively,
to analyze and interpret our results. We shall mention at this
point that the validity of either eq 5 or eq 6 is not connected
with a distinct temperature range but it depends on both
temperature and NO2 concentration. So far, experiments on
kinetics of the title reaction have been mostly performed at low
temperatures and relatively high NO2 concentrations. Under
these conditions eq 5 is valid (k1,1st, k2,1st . k-2). The results of
those studies have then been used in atmospheric modeling
studies. In the lower troposphere, however, the NO2 concentra-
tions are so low that eq 6 is valid ((k1,1st, k2,1st , k-2)) and OH
+ NO2 react forming HNO3 only. If one wants to measure the
rate constant for this process, one should work under sufficiently
high temperatures or low NO2 concentrations so that either eq
3 or eq 6 describes the kinetics of the reaction.
Falloff Analysis. We analyze the pressure dependence of the
rate constants using the Troe formalism.26 Within this model,
the pressure dependent rate equation is given by the following
equation:
The experimental results are summarized in Tables 1-4 (see
Supporting Information). We did not observe any influence of
the OH precursor on the extracted rate coefficient. Within the
experimental uncertainties (which are estimated to be 30%),
most of our new experimental results agree with what has been
reported previously by us.8 However, at 300 K the data obtained
at pressures of a few bar (2-20 bar) are systematically lower
(∼25%) than the values given in ref 8. At higher pressures, the
observed differences are smaller (15-20%). For T ) 400 K
and M ) He as well as for T ) 300 K and M ) Ar, the
experimental results reported in this work agree with the results
from ref 8. For reasons of brevity, the data obtained in Ar as
well as the data obtained in He at 400 K will not be discussed
in detail in the remainder of the paper.
k0/k∞
log Fc
1 + (log(k0/k∞)/N)2
k
log
) log
+
(7)
( )
(
)
k∞
1 + k0/k∞
N ) 0.75 - 1.27 log Fc
k∞ and k0 are the high and the low pressure limiting rate
constants, respectively. Fc is the broadening factor. The strategy
of the present analysis is as follows: we calculate the high
pressure limiting rate constants for the two competing reactions
using a simplified version of the statistical adiabatic channel
model.27 If our results are consistent with experimental observa-
tions (our own high pressure data, rate constants for vibrational
relaxation, and isotopic scrambling), we proceed and calculate
low pressure rate constants in the strong collision assumption.
The analysis of the high and low pressure rate constants allows
for a calculation of the strong and weak collision contributions,
respectively, of the broadening factor Fc.
Discussion
To analyze the pressure and temperature dependence of the
rate constants, thermodynamic data are necessary. For HNO3
the information needed is well established, and for HOONO

6784 J. Phys. Chem. A, Vol. 110, No. 21, 2006
Hippler et al.
for isotopic scrambling would be (2/3)k1,∞. The factor 2/3 stems
from the fact that the H atom will be randomly localized at the
3 different O atoms. From their measured rate constant for
isotopic scrambling Donahue et al. determined a high pressure
rate of k1,∞ ) 1.5 × 10-11 cm3 s-1. Our experimental
observations as well as the result of our SACM calculations
indicate that the high pressure rate for R1 is higher. Therefore,
we decided to check the validity of the assumptions mentioned
above.
Donahue et al. did DFT calculations on a relatively low level
to check the validity of the assumptions used. They found that
the barrier for isomerization (R3) is about 18 kcal/mol lower
than the one for the decomposition of HNO3 (-R1). Using
RRKM theory they calculated the rate for the isomerization
reaction of chemically activated HNO3 formed in reaction R1
and found it to be on the order of 1010 s-1. The rate constant
for back-dissociation was not calculated, but it was estimated
from a simple Lindemann-Hinshelwood model:
Figure 1. Calculated high pressure rate constants: k1,∞, dashed line;
k2,∞, dashed dotted line; k1,∞ + k2,∞, solid line.
High Pressure Rate Constant. We calculated the high
pressure rate using a simplified version of SACM.28,29 Within
this model, the high pressure rate depends on the threshold
energy, the frequencies of the reactants as well as the products,
the frequency associated with the motion along the reaction
coordinate, and a single interpolation parameter R. For HNO3,
the information needed is found, e.g., in ref 30. For HOONO,
we used the frequencies calculated in ref 11 for cis,cis-HOONO
and the threshold energy determined in this work. Thus we are
left with a single parameter R. In ref 31 it was found that this
parameter is typically half the Morse parameter â (which can
be calculated easily) for the vibration which is associated with
the motion along the reaction coordinate. Thus we did our
calculations with R/â ) 0.5 and calculated the high pressure
rates for R1 and R2 at 300 K to be 2.8 × 10-11 cm3 s-1 and 1.9
× 10-11 cm3 s-1, respectively. A weak negative temperature
dependence is predicted for both these rate constants (see Figure
1).
âcZ
k0 ) k∞
(8)
kd
In this equation, k0 and k∞ are the low and the high pressure
rate constant, respectively. Z is the second-order collision rate
constant, and âc is the collision efficiency. kd is the rate constant
for the dissociation of the chemically activated adduct, and it
was calculated from eq 8 to be ∼ 8 × 108 s-1. Based on this
simple estimate the experiments of Donahue et al. should allow
for a determination of k1,∞. We present here a more sophisticated
approach to check if assumption (i) is valid. First we calculated
initial distributions (F(E)) of the chemically activated HNO3
formed in reaction R1 using the following relation:32
-E
kBT
The sum of the two high pressure rate constants, which is
the observable in high pressure experiments on the thermal
reaction as well as in experiments of the vibrational relaxation
of OH(V ) 1) in collisions with NO2, is thus predicted to be
4.7 × 10-11 cm3 s-1. Experiments on the vibrational relaxation
of OH(V)1) by NO2 have been performed by Smith and
Williams18 as well as D’Ottone et al.,16 and values of 4.8 ×
10-11 cm3 s-1 and 6.4 × 10-11 cm3 s-1, respectively, have been
reported. The rate constants determined in this work at pressures
above 200 bar are in the range from 5.0 × 10-11 cm3 s-1 to 5.7
× 10-11 cm3 s-1. Due to the observed weak pressure dependence
of the rate at these high pressures, it is estimated that these
values deviate at most 20% from the high pressure limit. Our
experimental high pressure results agree within the experimental
uncertainties well with the results from studies on the vibrational
relaxation as well as with our calculated high pressure rate
constants. Taking into account all experimental information
available on the sum of k1,∞ and k2,∞ we conclude that the
calculated high pressure data are of sufficient accuracy and that
no further optimization is needed.
W(E) exp
(
(
)
)
F(E) )
(9)
∞ W(E) exp
dE
-E
kBT
∫
0
In this equation W(E) is the number of open channels, which
we obtained from our SACM calculations, E is the internal
energy of the HNO3 adduct, and kB is the Boltzmann constant.
Assuming that collisional stabilization can be neglected, we
calculated mean rate constants for the reactions -R1 and R3
of the chemically activated HNO3 from the following equa-
tion:
k ) ∞ki(E) F(E) dE
(10)
∫
i
0
The specific rate constants for reaction -R1 have been
calculated using the SACM formalism as described above. The
rate constants for reaction R3 have been calculated from RRKM
calculations using the Whitten-Rabinovitch approximation for
both density and sum of states of the reactant and transition
state, respectively. We used a threshold energy of 33.5 kcal/
mol, since Donahue et al. calculated this threshold to be 18
kcal/mol below the one for dissociation (-R1).7 All other
parameters used in the calculations of the rate constants for R3
have been adopted from ref 7.
A typical distribution as well as the specific rate constants
for the two competing reaction channels is shown in Figure 2.
For J ) 0 we calculate mean rate constants of k-1 ) 1.2 ×
1010 s-1 and k3 ) 9.3 × 109 s-1 at 300 K. Note that these rate
constants are so fast that our initial assumption that collisional
deactivation is unimportant holds for the conditions (p e 220
At this point we shall also discuss the work by Donahue et
al.,7 in which the authors claim they were able to extract the
high pressure limiting rate constant for HNO3 formation from
experiments on isotope exchange in the reaction 18OH + NO2.
This approach is based on the following idea: (i) if the rate for
the isomerization of the chemically activated HNO3 formed in
the reaction R1,
H18ONO2* f HON18OO*
(R3)
is much faster than the redissociation and (ii) if the chemically
activated adduct is not stabilized by collisions, the rate constant

Reaction of OH + NO2
J. Phys. Chem. A, Vol. 110, No. 21, 2006 6785
Our calculations show that the assumption that the isomer-
ization reaction is much faster than redissociation is not valid.
The reason is that, due to the stronger energy dependence of
the specific rate constants for -R1 compared to those for R3,
the rate constants “cross” (vibrational channel switching, see
also Figure 2). In other words, compared to R3, -R1 is getting
faster with increasing excitation energy (increasing temperature).
Only at temperatures well below 200 K the isomerization might
be much faster than the back-dissociation. Thus, experiments
on the isotopic scrambling at low temperatures should provide
experimental access to the high pressure rate for R1. If the
energetics for the isomerization reaction are better characterized,
one might also be able to extract the high pressure limiting rate
constant for HNO3 formation from the temperature dependence
of the rate coefficient for isotopic scrambling.
We conclude that our calculated high pressure rates are in
agreement with the experimental data available (high pressure
rate constants from this work, vibrational relaxation rate
constants from refs 16 and 18, and rate constants for isotopic
scrambling from refs 7, 16, and 19). Therefore, they should be
sufficiently accurate and we can proceed with the calculations
of the low pressure rate as well as the broadening factor.
Low Pressure Rate Constant and Broadening Factor. We
analyze the low pressure rate constant using the formalism
proposed by Troe.24,26 To do this, we first calculate the strong
collision rate constant for R1. Then we compare the calculated
strong collision rate constant with experimental results and
extract collision efficiencies. Next, we calculate strong collision
rate constants for R2 and check if the observed pressure
dependence for this reaction is consistent with our analysis.
(Again the calculations are performed for cis,cis-HOONO.)
Within this model, the low pressure rate constant for a
unimolecular reaction, which is related with the recombination
rate constant via the equilibrium constant, is given by the
following equation:
Figure 2. Calculated specific rate constants for the decomposition of
HNO3 (k-1(E)) and the isomerization of HNO3 (k3(E)). The dashed
dotted line is the initial distribution of the chemically activated HNO3
formed in R1. See text for further explanations.
Figure 3. Calculated specific rate constants for the isotopic scrambling
in the 18OH + NO2 reaction (open circles) compared to literature data
(b, ref 19; 9, ref 7; [, ref 16). For comparison, k1,∞ (open squares)
and (2/3)k1,∞ (dashed line) are added as well. See text for further
explanations.
FVib,h(E0)kBT
E
kBT
ks0c ) ZLJ [M]
exp -
Fanh FE Frot Frot int
Torr) of the experiments described in ref 7. We then set up a
chemical model for the isotopic scrambling experiments which
includes three HNO3 isomers, of which two might decompose
to form 16OH and the third one decomposes to form 18OH.
Further on, we assumed that both k-1 and k3 are the same
for the different isomers. Within this model we calculated
apparent rate constants for the isotopic scrambling from the [18-
OH] decay, and we compare these calculated rate coefficients
in Figure 3 with the experimental results reported in the
literature. Additionally, we added our calculated high pressure
rate constant as well as (2/3)k1,∞. From Figure 3 it is seen that
our model is able to predict the rate for isotopic scrambling
with an accuracy of 35%. Additionally, a weak temperature
dependence is predicted which is in agreement with the findings
of ref 16. Thus, we conclude that our calculated high pressure
rate constant for R1 is in agreement with the results from the
isotopic scrambling experiments.7,16,19 It has to be stressed that
we used some simplifications in the model. E.g., the mean
lifetimes have been calculated for J ) 0. In order to check if
the J dependence of the specific rate coefficients plays an
important role, we performed the same calculations for T )
300 K and J ) 20, 35, and 50. It is found that the J dependence
has only a minor effect (<10%) on the calculated rate constant
for isotopic scrambling. The main uncertainty of our model
arises from the fact that the threshold for R3 is not well-
characterized. As long as this quantity has not been calculated
with better ab initio methods, more sophisticated models seem
not to be more meaningful.
(
)
Qvib
(11)
The calculation of the Lennard-Jones collision number (ZLJ),
the harmonic density of states (Fvib,h), the vibronic partition
function (Qvib), and the correction factor FE is straightforward.
There are, however, some uncertainties and problems associated
with the calculation of the corrections factors Fanh, Frot, and
F
rot int. For the calculation of the factor Fanh we used the
expression proposed in ref 24. Since then different ways to
calculate Fanh have been proposed (see, e.g., refs 33 and 34).
However, there is still no simple and yet “universal” formalism
to calculate anharmonic density of states as well as correction
factors to account for anharmonic effects. Thus we stay with
the most simple and most commonly used way to calculate Fanh
.
The calculation of Frot has been done as described in ref 28
(see also ref 14 for a discussion), and the calculations are based
on centrifugal barriers calculated in the SACM calculations. The
factor Frot int accounts for an increase of the density of states
due to an internal rotor. While the calculations are relatively
easy for one hindered internal rotor, there is no simple way to
treat 2 different internal rotors. Thus, we calculated the
contributions arising from the hindered “OH rotor” both in
HNO3 and in HOONO and neglected the “NO rotor” in the
latter case.
One expects that in the low pressure regime reaction 1 is
much faster than 2, and we thus first calculate the strong
collision rate for this reaction and compare it to experimental

6786 J. Phys. Chem. A, Vol. 110, No. 21, 2006
Hippler et al.
data. This comparison yields the collision efficiency âc, which
is given by the relation
k0exp
ks0c
âc )
(12)
and thus indirect information on the energy transfer process.
The mean energy transferred per collision ( ∆E ) is related to
the collision efficiency as follows:
âc
- ∆E )
FE kBT
(13)
1 -
â
c
x
From the analysis, we extracted - ∆E for He, Ar, and N2
at 300 K to be 20, 41, and 63 cm-1, respectively. (The
corresponding values for âc at 300 K are 0.067, 0.12, and 0.17.)
The temperature dependence of the extracted - ∆E values was
found to be weak (changes of - ∆E smaller than 10% have
been calculated in the T range from 220 to 400 K), and we thus
assume temperature independent energy transfer parameters.
Absolute values, trends of the changes in the energy transfer
efficiency, and the independence of - ∆E on the temperature
are in agreement with the current knowledge on the still rather
poorly characterized energy transfer processes.
Figure 4. Falloff curve for helium at 600 K: b, this work; 0, ref 37;
solid line, falloff curves calculated for R1 from eq 7; parameters for
R1 are given in eq 14.
For HOONO we assume that the energy transfer parameter
- ∆E for reaction R2 is the same as for reaction R1 and
calculated the low pressure rate constants and the broadening
factor as described above. Based on this assumption, a pressure
dependence for k2 is predicted which is not in agreement with
our experimental results. If we instead choose - ∆E ) 80 cm-1
for M ) He, we obtain a good agreement between the calculated
falloff curve and our experimental data. Note that Golden et al.
observed as well better agreement between the results of a
master equation calculation and experimental results when they
assumed the energy transfer process for R2 to be more effective
than the one for R1.15 Compared to the - ∆E value extracted
for R1, this value seems to be too high. One has to admit,
however, that this parameter is without doubt associated with a
high uncertainty which arises from the treatment of the density
of states. As long as there is no 2-dimensional potential energy
surface for the two hindered internal rotors in HOONO available,
one is not able to treat the density of states properly. On the
other hand it should be kept in mind that (hindered) internal
rotorssor low frequency modessare believed to play a domi-
nant role in collisional energy transfer. E.g., for a variety of
colliders it has been found that - ∆E for toluene is a factor of
2-4 larger than the corresponding value for benzene.35 Since
the two molecules are very similar, this finding has been
explained by the presence of the internal rotor in toluene.
The extracted ∆E values do have only little influence on
the shape of the calculated falloff curves. Therefore, we content
ourselves with the adjusted value and do not discuss it further.
Additionally, we assume that - ∆E for Ar and N2 is 160 and
240 cm-1, respectively. Having set this parameter and assuming
that it is temperature independent, we are able to calculate the
low pressure rate constant for R2 as a function of temperature.
The calculation of the broadening factor Fc is straightfor-
ward: For the strong collision contribution one has to analyze
the temperature dependence of the transition state (pseudo-)
partition function. The weak collision contribution is related to
the collision efficiency. For N2 as bath gas we calculate Fc to
be 0.62 and 0.73 for R1 and R2, respectively. Again, the
deduced temperature dependence is negligible. These values are
higher than the ones discussed in the past;8,14,15 however, they
Figure 5. Falloff curve for helium at 430 K: 4, k1; O, k2; 0, k1 + k2
(data are taken from ref 10); dashed and dashed dotted lines, falloff
curves calculated from eq 7 for R1 and R2, respectively; solid line,
sum of the two falloff curves. The falloff parameters for R1 and R2
are given in eq 14 and eq 15, respectively.
are reasonable and in agreement with current knowledge of this
parameter. E.g., in ref 1 broadening factors ranging from 0.35
to 0.85 are reported for radical-radical reactions. It should be
mentioned that for R2 Fc might well be smaller than predicted
since there is some uncertainty associated with this value due
to the fact that the extracted energy transfer efficiency might
be too high.
Falloff Parameters. In this section we will limit the
discussion on falloff parameters for He and N2. The reason for
this limitation is that most of the experimental data has been
obtained using He as bath gas. N2 is of course of practical
interest and should thus be discussed as well.
For He, the following parameters are recommended:
k0,1 ) 1.6 × 10-30 × (T/300 K)-2.9 [He] cm6 s-1
k∞,1 ) 2.8 × 10-11 cm3 s-1
[ref 8]
(14)
Fc,1 ) 0.53
k0,2 ) 4.6 × 10-32 × (T/300 K)-2.8 [He] cm6 s-1
(15)
k∞,2 ) 1.9 × 10-11 cm3 s-1
Fc,2 ) 0.66
In Figures 4-6 we compare the falloff curves with experi-
mental data for T ) 600, 430, and 300 K, respectively. In all

Reaction of OH + NO2
J. Phys. Chem. A, Vol. 110, No. 21, 2006 6787
Figure 7. Falloff curve for nitrogen at 300 K: O: Ref. 37; open
triangle facing right, ref 38; 4, ref 17; 0, ref 39; ×, ref 16; dashed and
dashed dotted lines, falloff curves calculated from eq 7 for R1 and R2,
respectively; solid line, sum of the two falloff curves. The falloff
parameters for R1 and R2 are given in eq 16 and eq 17, respectively.
In order to compare the literature data for N2 with our results obtained
in He, we scaled the gas density for the latter data by a factor of 0.64
(k0,He/k0,N2) and added the results obtained in this way to the graph (9).
Figure 6. Falloff curve for helium at 300 K: O, k1 + k2, this work;
dashed and dotted lines, falloff curves calculated from eq 7 for R1 and
R2, respectively; solid line, sum of the two falloff curves. The falloff
parameters for R1 and R2 are given in eq 14 and eq 15, respectively.
cases the experimental data agree reasonably well with the falloff
parameters. At 600 K only HNO3 formation occurs. For this
temperature the calculated falloff overestimates the high pressure
data (see Figure 4). Two reasons are possible: First, we might
overestimate the broadening factor. Second, we might overes-
timate the high pressure limiting rate coefficient. This latter
explanation would be in line with the finding that our simple
model for the isotopic scrambling experiments overestimates
the rate for this process. In Figure 5 we compare the data we
extracted for k1 and k2 in a previous work at 430 K.10 At this
temperature, the calculated falloff curves agree with the
experimental data within the uncertainties of the latter. Finally,
we compare in Figure 6 our new data for k1 + k2 at high
pressures and room temperature with the calculated falloff
curves. Again we find that the agreement is within the
experimental uncertainties. Similar agreement is found for T )
400 K and for Ar as bath gas.36 However, for lack of space we
discuss neither these data in detail nor present the falloff curves.
Instead, we will now turn to a discussion on the data available
for nitrogen as collider. For this bath gas, the following falloff
parameters have been obtained from our analysis:
Figure 8. Falloff curve for nitrogen at 220 K: O, ref 37; 0, ref. 39;
4, ref. 40; dashed and dashed dotted lines, falloff curves calculated
from eq 7 for R1 and R2, respectively; solid line, sum of the two falloff
curves. The falloff parameters for R1 and R2 are given in eq 16 and
eq 17, respectively.
k0,1 ) 2.5 × 10-30 × (T/300 K)-3.0 [N2] cm6 s-1 [ref 16]
k∞,1 ) 2.8 × 10-11 cm3 s-1
0.64. The correction factor is calculated by dividing the low
pressure rate constants for R1 and M ) He by the one for M )
N2, and it accounts for the differences in the collision frequencies
and collision efficiencies. This way of comparing data obtained
in different bath gases has been applied before.4,40 Both our
new experimental results and our falloff analysis support the
data from the Hynes group. A similar finding has been been
found in the analysis performed by Golden et al.15 This leads
us to the conclusion that the data from ref 16 are more reliable
than the data reported in ref 17. In order to further validate our
falloff parameters we compare the calculated falloff curve for
T ) 220 K with experimental data (see Figure 8). The agreement
obtained is rather satisfying. For T ) 240 K and T ) 273 K we
as well obtained satisfying agreement.36
(16)
Fc,1 ) 0.62
k0,2 ) 9.2 × 10-32 × (T/300 K)-2.6 [N2] cm6 s-1
(17)
k∞,2 ) 1.9 × 10-11 cm3 s-1
Fc,2 ) 0.73
As we have already mentioned in the Introduction, discrep-
ancies have been reported for nitrogen as bath gas and at room
temperature. Thus, we should compare the result of our falloff
analysis with experimental results in order to reduce the
uncertainties. Basically, there are the results from Tony Hynes’s
group16 and Ian Smith’s group37 which are at pressures above
100 Torr about 30% higher than data reported by Wine et al.,38
Brown et al.,39 and Donahue et al.17 At pressures of 600 Torr,
the difference between the data from ref 16 and ref 17 is even
bigger (factor of 1.7). In Figure 7, we compare the experimental
data available for N2 and room temperature with the calculated
falloff curves. For comparison, we added our high pressure
results for M ) He by scaling the gas densities by a factor of
A final test for the falloff parameters comes from the
comparison of predicted branching ratios with experimental data.
In Figure 9, branching ratios for HOONO formation in N2 at
two different temperatures are shown. Our calculations predict
that under atmospheric conditions less than 10% HOONO is
formed. This prediction is in agreement with the first two studies
on HOONO yields published.3,6 More recently, Bean et al.12
determined the HOONO yield to be ∼7% at a pressure of 20
Torr and 300 K. (Note that these authors define the yield as

6788 J. Phys. Chem. A, Vol. 110, No. 21, 2006
Hippler et al.
Dave Golden during his stay in Karlsruhe in 2000. We thank
Dave for his continued interest in our work and many discus-
sions we had over the past few years.
Supporting Information Available: Four tables of experi-
mental results. This material is available free of charge via the
Internet at http://pubs.acs.org.
References and Notes
(1) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Crowley, J. N.; Hampson,
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Figure 9. HOONO yield as a function of number density for two
different temperatures: solid line, 300 K; dashed line, 220 K.
k2/k1 whereas our definition is k2/(k1 + k2).) Unfortunately, they
did experiments in a mixture of N2, Ar, and He (roughly 1:2:
2), which makes the comparison with our analysis more difficult.
At pressures of 20 Torr we predict from our analysis a yield of
∼4%. This value is in quite fair agreement with the result from
Bean et al. taking into account their uncertainty, which stems
mainly from the fact that they have to rely on relative absorption
cross sections from ab initio calculations. If we would try to
match their yield, we would have to increase the low pressure
rate constant for R2. Basically, we would have to increase the
energy transfer parameter - ∆E . However, the extracted value
for this parameter is a factor of 4 higher than the one we
extracted for R1 and, thus, higher than expected.
(13) D’Ottone, L. D.; Bauer, D.; Campuzano-Jost, P.; Fardy, M.; Hynes,
A. J. Faraday Discuss. 2005, 130, 111.
To summarize this section on the falloff parameters: We have
presented an analysis whichsto the best of our knowledges
includes all experimental information available. In contrast to
similar studies on the falloff behavior,14,15 we have also
discussed the isotopic scrambling experiments as well as our
new high pressure data. The parameters extracted areswithin
experimental uncertaintysin agreement with the experimental
data available. It is fair to note that for atmospheric modeling
the falloff parameters from this work are probably not more
accurate than the results from Troe14 and Golden et al.15 The
rate coefficients (k1 + k2) calculated with the different data sets
for atmospheric conditions do agree within the uncertainty of
the experimental data available. The main differences are in
the branching ratios which are predicted to be ∼2.5%,14 ∼10%
(this work), or even ∼15%15 at 300 K and 1 bar of N2. The
experimental information about this quantity is still very limited,
and more experiments seem to be needed. Additionally, high
temperature (500-800 K) data on the rate constant would allow
for a more precise determination of the falloff parameters for
R1 and, thus, more experiments under these conditions seem
to be desirable as well.
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Conclusion
We have presented new high pressure data for the rate
constant of the title reaction which should be used in further
falloff analyses. Additionally, an analysis of the pressure
dependence of the rate constant is given. The analysis allowed
for an extraction of falloff parameters which are in agreement
with most of the experimental data available so far. This data
includes results not only from studies on the thermal rate
constant but also from studies on the vibrational relaxation as
well as isotopic scrambling and experiments aimed on a
determination of the product branching ratios in the title reaction.
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Acknowledgment. At the early stages of this work we
enjoyed the stimulating and interesting discussion we had with