Rate constants, 1100 ≤ T ≤ 2000 K, for H + NO2 → OH + NO using two shock tube techniques: Comparison of theory to experiment

Article abstract of DOI:10.1021/jp0141023

Rate constants for the reaction H + NO₂ → OH + NO have been measured over the temperature range 1100-2000 K in reflected shock wave experiments using two different methods of analysis. In both methods, the source of H-atoms is from ethyl radical decomposition in which the radicals are formed essentially instantaneously from the thermal decomposition of C₂H₅I. The first method uses atomic resonance absorption spectrometry (ARAS) to follow the temporal behavior of H-atoms. Experiments were performed under such low [C₂H₅I]₀ that the title reaction could be chemically isolated, and the decay of H-atoms was strictly first-order. The results from these experiments can be summarized as k = (1.4 ± 0.3) × 10^-10 cm³ molecule^-1 s^-1 for 1100 ≤ T ≤ 1650 K. The second method utilizes a multipass optical system for observing the product radical, OH. A resonance lamp was used as the absorption source. Because this is the first OH-radical kinetics investigation from this laboratory, extensive calibration was required. This procedure resulted in a modified Beer'S law description of the curve-of-growth, which could subsequently be used to convert absorption data to OH-radical profiles. Rate constants by this method required chemical simulation, and the final result can be summarized as k = (1.8 ± 0.2) × 10^-10 cm³ molecule^-1 s^-1 for 1250 ≤ T ≤ 2000 K. Because the results from the two methods statistically overlap, they can be combined giving k = (1.64 ± 0.30) × 10^-10 cm³ molecule^-1 s^-1 for 1100 ≤ T ≤ 2000 K. The present results are compared to earlier work at lower temperatures, and the combined database yields the temperature dependence over the large range, 195-2000 K. The combined results can be summarized as k = (1.47 ± 0.26) × 10^-10 cm³ molecule^-1 s^-1 for 195 ≤ T ≤ 2000 K. The reaction is subsequently considered theoretically using ab initio electronic structure calculations combined with modern dynamical theory to rationalize the thermal rate behavior.

Full text of DOI:10.1021/jp0141023

BATCH: jp91a02 USER: amr69 DIV: @xyv04/data1/CLS_pj/GRP_jx/J OB_i36/DIV_jp0141023 DATE: August 21, 2002
J. Phys. Chem. A 2002, 106, 8261-8270
8261
Rate Constants, 1100 e T e 2000 K, for H + NO2 f OH + NO Using Two Shock Tube
Techniques: Comparison of Theory to Experiment†
M.-C. Su,‡ S. S. Kumaran, K. P. Lim, J. V. Michael,* A. F. Wagner,* L. B. Harding,* and
D.-C. Fang
Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439
ReceiVed: NoVember 8, 2001; In Final Form: January 7, 2002
Rate constants for the reaction H + NO2 f OH + NO have been measured over the temperature range
1100-2000 K in reflected shock wave experiments using two different methods of analysis. In both methods,
the source of H-atoms is from ethyl radical decomposition in which the radicals are formed essentially
instantaneously from the thermal decomposition of C2H5I. The first method uses atomic resonance absorption
spectrometry (ARAS) to follow the temporal behavior of H-atoms. Experiments were performed under such
low [C2H5I]0 that the title reaction could be chemically isolated, and the decay of H-atoms was strictly first-
order. The results from these experiments can be summarized as k ) (1.4 ( 0.3) × 10-10 cm3 molecule-1 s-1
for 1100 e T e 1650 K. The second method utilizes a multipass optical system for observing the product
radical, OH. A resonance lamp was used as the absorption source. Because this is the first OH-radical kinetics
investigation from this laboratory, extensive calibration was required. This procedure resulted in a modified
Beer’s law description of the curve-of-growth, which could subsequently be used to convert absorption data
to OH-radical profiles. Rate constants by this method required chemical simulation, and the final result can
be summarized as k ) (1.8 ( 0.2) × 10-10 cm3 molecule-1 s-1 for 1250 e T e 2000 K. Because the results
from the two methods statistically overlap, they can be combined giving k ) (1.64 ( 0.30) × 10-10 cm3
molecule-1 s-1 for 1100 e T e 2000 K. The present results are compared to earlier work at lower temperatures,
and the combined database yields the temperature dependence over the large range, 195-2000 K. The combined
results can be summarized as k ) (1.47 ( 0.26) × 10-10 cm3 molecule-1 s-1 for 195 e T e 2000 K. The
reaction is subsequently considered theoretically using ab initio electronic structure calculations combined
with modern dynamical theory to rationalize the thermal rate behavior.
Introduction
The most recent thermal rate constant investigations all agree
within experimental error that k1 = 1.3 × 10-10 cm3 molecule-1
s-1 at room temperature.4-9 If the results prior to 1979 are
The reaction
H + NO2 f OH + NO
(1)
excluded, there is also a consensus that there is little or no
temperature dependence up to 760 K. The temperature invari-
ance led Michael et al.7 to suggest that the rate constant was
determined solely by the collision rate and that there was no
electronic energy barrier for the reaction. Ko and Fontijn9 agree
with this latter point as do the dynamical studies even though
there is some question as to the extent of energy randomization
in the vibrationally excited adduct.15,16,18 Ko and Fontijn9 also
discuss the possibility of collisional stabilization with the
detailed mechanism H + NO2 h HONO* f OH + NO
followed by HONO* + M f HONO + M. Of course, the
question of stabilization is irrelevant at usual pressures if the
reaction is direct; that is, the lifetime of the adduct is the same
magnitude as that for a vibration. Irrespective of the adduct
lifetime, the dissociation channel is exothermic relative to
reactants by 29.6 kcal mol-1 at 0 K; that is, the dissociation
channel is lower-lying than the reactants. Because there is no
electronic barrier for association, the rate of reaction will depend
on long-range forces and the effective transition state (or states)
will be loose and near to reactants. The reaction then represents
a classic atom-radical recombination with a low-lying dis-
sociation channel, and the rate constant will be equal to that
for the infinite pressure limit. Hence, the reaction then becomes
quite interesting from a theoretical point of view.
has been of interest in chemical kinetics and dynamics for over
35 years.1-9 The reaction has been used for a variety of
purposes, and this has fostered the continuing interest. In
discharge flow tube investigations, it has been used as a source
for both ground-state and vibrationally excited OH-radicals for
the study of the reactions of these species with molecules.10,11
It has been used as a calibration reaction for determining
absolute H-atom concentrations in discharge flow tube stud-
ies.12,13 It is an interesting reaction because the OH that is
produced has a nonthermal vibrational distribution; that is, it is
vibrationally hot.14-19 The lowest energy dynamical experiments
at a relative collision energy of 0.93 kcal mol-1 document
forward peaking in the product angular distribution suggesting
an adduct lifetime that is less than a rotational period.18 Hence,
questions concerning the randomization of energy have to be
considered in the theoretical interpretation of results on this
reaction. Last, the reaction is now known to be important in
the high-temperature combustion kinetics of nitramine propel-
lants.20
† Part of the special issue “Donald Setser Festschrift”.
* To whom correspondence should be addressed.
‡ Sabbatical Leave. Permanent address: Department of Chemistry, Butler
University, Indianapolis, IN 46208.
10.1021/jp0141023 CCC: $22.00 © 2002 American Chemical Society
Published on Web 03/06/2002

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8262 J. Phys. Chem. A, Vol. 106, No. 36, 2002
Su et al.
In this paper, the rate constants are measured in reflected
shock waves using two different observations, H-atom depletion
and OH-radical formation. Experiments have been performed
from 1100 to 2000 K. These data are combined with the lower
temperature sets giving a composite rate behavior over the large
temperature range, 195-2000 K. New ab initio potential energy
calculations are also presented, and dynamics calculations based
on the theoretical potential energy surface are also presented
and compared to experiment.
Detection by Multipass Optical Absorption. In this work,
a long absorption path multipass detector system,23 which is
based on the original design of White28 with modifications from
Bernstein and Herzberg,29 has been used. The optical config-
uration consists of an OH resonance lamp, three multipass
reflectors (one split in half), an interference filter, and a
photomultiplier tube. The OH absorption lamp was constructed
from a 6.4 mm o.d. Pyrex tube. High-purity Ar at atmospheric
pressure was bubbled through distilled water in a glass trap,
and the mixture was then introduced through a needle valve
into the low-pressure (∼4 Torr) lamp. The microwave discharge
was operated at 50 W, and the resultant OH resonance radiation
was focused at the center of the shock tube, between the two
windows, with a 2.54 cm diameter planoconvex lens mounted
on the end of the lamp. The multipass optical system is
constructed from three concave reflectors with identical radii
of curvature. The reflectors and mounts were supplied by
Infrared Analysis, Inc., and the radius of curvature and the
aperture of the reflectors were customed designed for the present
separation and aperture of the windows. The reflectors are MgF2-
coated for use in the far UV region. The three pieces involved
in the reflector system are mounted outside the shock tube next
to the windows with the center points of the windows and
mirrors all in a coaxial position. The optical cavity thus formed
is a conjugated focus system, which induces the light to travel
back and forth between the reflectors in multiple passes. The
relative positions of images on the reflectors are determined by
set screw adjustments, allowing for changes in the number of
passes for use in an experiment. We have used 12 passes giving
a path length of 104.9 cm in this work. The light leaves the
multipass cavity through an exit notch and is focused onto an
interference filter (308 nm, fwhm of 17 nm, from Oriel Corp.).
Signal detection is with an RCA 1P28 PMT. The signal-to-
noise ratio is typically ∼80 for 12 passes, and this has given
quite satisfactory sensitivity for probing the kinetics of hydroxyl
radicals.
Experimental Section
Most of the experimental methods and techniques are
described elsewhere;21,22 however, in the present study, some
substantial modifications to the apparatus have been made in
preparation for multipass optical absorption experiments in the
reflected shock wave regime.23
Apparatus. The present experiments were performed in a
redesigned apparatus. The shock tube is constructed from 304
stainless steel in three sections. The first 4 in. o.d. cylindrical
section is separated from the He driver chamber by a 4 mil
unscored 1100-H18 aluminum diaphragm. A 0.25 m transition
section then connects the first and third sections. The third
section is of rounded-corner (radius, 1.71 cm) square design
and is fabricated from flat stock (3 mm) with a mirror finish.
Two sets of flat MgF2 crystal windows (2.54 cm) are mounted
with high-vacuum epoxy cement normal to one another at a
distance of 6 cm from the endplate. The aperture diameter is
2.29 cm. One set is used for atomic resonance absorption
spectrometric (ARAS) detection of H-atoms, and the other set
is used for OH-radical absorption using a multipass optical
technique. The windows are flush to the polished inside wall
of the tube. The path length between windows is 8.745 cm. All
connections are made through Varian “Conflat” flanges with
copper gaskets. As before,21,22 the incident shock wave velocities
are measured with eight fast pressure transducers (PCB Pi-
ezotronics, Inc., model 113A21), and both the velocity and
absorption signals are recorded with a digital oscilloscope
(Nicolet, model 4094C). The shock tube was routinely pumped
between experiments to <10-8 Torr by an Edwards Vacuum
Products model CR100P packaged pumping system. Temper-
ature and density in the reflected shock wave regime were
calculated from measured incident shock wave velocity and
initial thermodynamic conditions. This procedure has been given
previously, and corrections for boundary layer perturbations have
been applied.24-26
H-Atom ARAS Detection. The ARAS technique and pho-
tometer configuration for the detection of H-atoms has already
been discussed in detail.13,21,22 Unreversed H-atom Lyman-R
(LyRH) was produced by a 2450 MHz microwave discharge in
a 1.7 Torr flow of prepurified He. This transition at 121.6 nm
was further spectrally isolated by placing a 3 cm gas filter
section that contains dry air at atmospheric pressure in front of
the solar blind photomultiplier. There was always some radiation
that is not LyRH, and it was necessary to determine the fraction
of this spectral impurity. Therefore, an H-atom filter section
was placed in front of the resonance lamp.27 This filter section
is a fast discharge-flow system operating with ∼0.2 Torr of
H2. With the microwave discharge operating, sufficient H-atom
concentration was produced in the optical path to nearly remove
all LyRH radiation. The measurement of the fraction of light
that was resonance radiation was routinely made before each
kinetics experiment and allowed for the calculation of (ABS)H
≡ -ln(I/I0). In all experiments, [H]0 was kept low so that Beer’s
law holds.13 Hence, (ABS)H is directly proportional to [H] over
the entire time span of a given experiment.
Gases. Kr (scientific grade, 99.999%), used as the diluent,
and O2 (scientific grade, 99.999%) and H2 (scientific grade,
99.9999%), used in the experimental mixtures, were obtained
from MG Industries and were used without further purification.
He, used as received as the driver gas, was purified grade
(99.995%) and was obtained from Airco Industrial Gases. C2H5I
(99%) from Aldrich Chemical Co., Inc. and technical grade NO2
from Matheson Gas Products were both further purified by bulb-
to-bulb distillation with the middle thirds being retained. All
gas mixtures were accurately measured with a Baratron capaci-
tance manometer and were stored in an all-glass vacuum line.
Results
Kinetics results were obtained by observing both H-atom
depletion and OH-radical buildup in two separate sets of
experiments. Concurrent observations could not be carried out
because the H-atom ARAS method is much more sensitive than
OH-radical detection even with multipass enhancement. In
preparation for the latter experiments, [OH] calibration experi-
ments were necessary. The calibration is an extension of a
method used earlier for H-atoms30 involving the thermal
decomposition of C2H5I to give C2H4 + H + I in two steps.
Subsequently, the H-atoms produced by this method can react
with added NO2 giving OH + NO, and this is the basis for two
of the OH-radical calibration schemes. At higher [OH], the usual
H2/O2 branching chain reaction is used, and the combination
of the three types of experiments gives a curve of growth for
OH.23

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Rate Constants for H + NO2 f OH + NO
J. Phys. Chem. A, Vol. 106, No. 36, 2002 8263
TABLE 1: High-Temperature Rate Data for H + NO2
Using H-atom Detection
b
b
b
c
P5
F5
T5
(K)
kfirst
(s-1
k1
(10-10 cm3 s-1
)
c
(Torr)
Msa
(1018 cm-3
)
)
XC H I ) 5.018 × 10-7, XNO2 ) 1.102 × 10-5
2
5
386
428
548
507
424
344
119
163
167
173
136
151
266
366
354
270
192
253
2.290
2.780
2.897
3.140
3.064
2.877
2.661
0.948
1.089
1.084
1.108
1.019
1.051
1.916
2.146
2.124
1.934
1.683
1.886
1340
1426
1684
1600
1424
1247
1210
1447
1491
1504
1292
1388
1339
1646
1608
1350
1103
1296
3991
4670
4368
4443
4070
3388
2394
1855
1645
1717
2296
1841
2388
3213
3140
2617
2316
2955
1.3
1.5
1.3
1.3
1.3
1.2
2.3
1.6
1.4
1.4
2.0
1.6
1.1
1.4
1.3
1.2
1.3
1.4
2.377
2.608
2.534
2.370
2.203
2.169
2.394
2.430
2.446
2.250
2.341
2.295
2.569
2.537
2.304
2.060
2.254
a The error in measuring the Mach number, Ms, is typically 0.5%-
1.0% at the one standard deviation level. b Quantities with the subscript
5 refer to the thermodynamic state of the gas in the reflected shock
region. c The rate constants are derived as described in the text.
Figure 1. (top) A typical experimental record showing increasing
H-atom ARAS signal due to reaction 1 after instantaneous [H] formation
from C2H5I dissociation and (bottom) the first-order decay of atoms
derived from the transmittance record (top) plotted as ln(ABS)H against
time. The negative slope, 3991 s-1, is the first-order decay constant
for [C2H5I]0 ) 1.395 × 1012 cm-3 and [NO2]0 ) 3.064 × 1013 cm-3
giving k1 ) 1.3 × 10-10 cm3 molecule-1 s-1. T5 ) 1340 K, P5 ) 386
determined by dividing the first-order decay constant by [NO2]0.
Eighteen experiments between 1100 and 1650 K were carried
out with a 22-fold excess of added NO2. The conditions for
these experiments and results for k1 are given in Table 1. Even
though the two lowest-pressure experiments give slightly higher
results, there is no reason to reject these two experiments. Hence,
there is then no obvious temperature dependence for the reaction
over the temperature range of the experiments. The results can
then be summarized by the expression
Torr, and F5 ) 2.780 × 1018 cm-3
.
H-Atom Kinetics Analysis. Unlike previous studies from this
laboratory in which H-atoms were produced by flash or laser
photolysis,21,22 here, the thermal decomposition of C2H5I
supplies [H]0 for the kinetics experiments. In earlier work, the
thermal decomposition of C2H5I was studied, and by measuring
yields of both [H] and [I] using ARAS techniques, it was shown
that two decomposition pathways occur,31
k1 ) (1.4 ( 0.3) × 10-10 cm3 molecule-1 s-1 for
1100 e T e 1650 K (4)
where the error is one standard deviation.
C2H5I(+M) f C2H5 + I(+M)
(2a)
(2b)
(3)
OH-Radical Calibration and Kinetics Analysis. In addition
to the C2H5I/NO2 method (reactions 1-3) for producing OH-
radicals, experiments were also performed utilizing the H2/O2
branching chain oxidation. This latter method has already been
used by a number of investigators for the same reason, namely,
that [OH]∞ is completely specified by the thermochemistry if
the density, mole fraction of reactants, and temperature are
known.32-42 The mechanism for the H2/O2 reaction was taken
mostly from an evaluation from this laboratory21 that included
the most recent direct determinations of the important rate
constants. The details of these experiments and the results have
been given previously.23
The C2H5I/NO2 method can be illustrated by considering the
kinetics experiment of Figure 2. In all kinetics experiments,
[NO2]0/[C2H5I]0 = 2, and therefore, simulations will be required.
The top panel of Figure 2 shows a typical transmittance plot, T
) (It/I0) against time. After conversion to (ABS)t ≡ -ln(It/I0)
against time plots, the derived values at long times are compared
to chemical simulations using the mechanism of Table 2.
Because all rate constants except that of reaction 1 are known,
a scale factor between the experimental values of (ABS) and
the simulated values of [OH] is determined for varying values
of k1. This scale factor is the product of the effective cross
section for absorption and the path length, that is, σeffl. In
addition, we performed fourteen experiments (not shown) with
[NO2]0/[C2H5I]0 = 10. Hence, the simulated [OH] becomes
and
C2H5I(+M) f C2H4 + HI(+M)
Following (2a), the ultrafast ethyl radical decomposition,
C2H5(+M) f C2H4 + H(+M)
gives H-atoms indicating that the overall process, eqs 2a and
3, is C2H5I ) C2H4 + H + I. We found that k2b ) 0.15k2a.31
Above 1100 K, all processes are fast allowing for unambiguous
kinetics experiments to be performed. As discussed earlier,23 it
can be shown with chemical simulations that the subsequent
reactions of H- or I-atoms with either parent or product
molecules are negligibly slow due to the very high sensitivity
of the H-atom ARAS technique. Because H-atoms can be rapidly
produced and observed at low concentrations by the C2H5I
method, reaction 1 can be unambiguously studied provided the
condition [H]0 , [NO2]0 can be maintained. The top panel of
Figure 1 shows a transmittance record from a typical experiment.
Because (ABS)H is proportional to [H],13 first-order decay
constants can be determined from linear plots of ln(ABS)H
against time. This is illustrated in Figure 1 in which the plot
determined from the top panel is shown in the bottom panel.
The bimolecular rate constant for reaction 1 can then be

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8264 J. Phys. Chem. A, Vol. 106, No. 36, 2002
Su et al.
Figure 3. OH-radical absorption curve of growth derived as described
in the text. The line is calculated from eq 5.
is slightly different from that given previously23 because earlier
and less reliable values for both the rate constant for reaction
2a and the branching ratio between reactions 2a and 2b were
used.
Figure 2. (top) OH-radical transmittance against time for an experiment
at T5 ) 1313 K, P5 ) 376 Torr, and F5 ) 2.764 × 1018 cm-3 with
[C2H5I]0 ) 2.559 × 1013 cm-3 and [NO2]0 ) 4.770 × 1013 cm-3 and
(bottom) OH-radical profile derived from the transmittance record (top)
using the curve-of-growth expression, eq 5. The solid line is a simulation
based on the mechanism of Table 2 with k1 ) 2.1 × 10-10 cm3
molecule-1 s-1. The dashed lines are predicted profiles with k1 varied
by (20%.
Implicit in the determination of the scale factors from the
C2H5I/NO2 method is the specification of the rate constant values
for reaction 1. When sufficiently low [NO2]0 is used, temporal
resolution of [OH]t is possible. With the use of eq 5 to transform
the (ABS) data to an OH-radical profile, the value for k1 can
be iteratively varied in a simulation until the best fit with
experiment is obtained. The bottom panel of Figure 2 shows
the method, giving k1 ) 2.1 × 10-10 cm3 molecule-1 s-1 for
the experiment. It is important to note that the substantial gain
in OH-radical sensitivity with the multipass technique allows
for reaction 1 to be studied under conditions in which secondary
reaction perturbations are almost absent. In Figure 2, the minor
long time decrease in [OH] is due to small effects from reaction
2 in Table 2; that is, OH + OH f H2O + O. The dashed lines
show similarly calculated profiles with a (20% variation in
the assumed k1 value. A total of 26 experiments were carried
out under the conditions given in Table 3, and (20% is a typical
error for the rate constants listed in the table. The combined
rate constant results again show that there is no discernible
temperature dependence. The data can be best represented as
the constant value
TABLE 2: Reaction Mechanism Used for Determining the
Rate Constant for H + NO2 Using C2H5I as a Source of
H-atomsa
1. H + NO2 f OH + NO, k1 ) to be fitted
2. OH + OH f O + H2O, k2 ) 7.19 × 10-21T2.7 exp(1251/T)b
3. C2H5I(+M) f C2H4 + H + I(+M), k3 )
6.34 × 109 exp(-15 894 K/T)c
c
4. C2H5I + M f C2H4 + HI + M, k4 ) 0.15k3
5. H + HI f H2 + I, k5 ) 7.87 × 10-11 exp(-330 K/T)d
6. NO2 + M f NO + O + M, k6 ) F(1.96 × 10-8) exp(-33 162 K/T)e
7. O + NO2 f NO + O2, k7 ) 6.5 × 10-12 exp(120 K/T)f
a All rate constants are in cm3 molecule-1 s-1 except reactions 3
and 4, which are in s-1 b Reference 21. c Reference 31. d Reference
.
43. e F refers to total density, ref 44. f Reference 45.
nearly independent of the rate constant for reaction 1 because
the process then gives nearly instantaneous OH-radical produc-
tion. The H2/O2 experiments were also analyzed by comparing
(ABS)t to simulations.23 We combined all three sets of data
giving a database of 54 experiments. The dependence of (ABS)
on total density, [OH], and temperature was determined.23 This
method of empirically determining the curve of growth under
conditions that are to be used in the kinetics experiments has
already been used by a number of researchers.37-39,41 Using the
three types of experiments, we found that (a) (ABS) was
independent of density between 0.76 × 1018 and 5.6 × 1018
molecules cm-3, (b) it is slightly dependent on temperature, and
(c) it is not linearly dependent on [OH]. Within a 2σ error of
(25% (i.e., 95% confidence), the results can be represented by
the modified Beer’s law expression,
k1 ) (1.8 ( 0.2) × 10-10 cm3 molecule-1 s-1 for
1250 e T e 2000 K (6)
where the error is at the one standard deviation level. Comparing
the H-atom depletion results, eq 4, to eq 6 shows that there
may be a systematic difference between the two sets. Neverthe-
less, the values do in fact overlap within one standard deviation
limits, and therefore, we have combined the two sets and report
as the best representation
k1 ) (1.64 ( 0.30) × 10-10 cm3 molecule-1 s-1 for
1100 e T e 2000 K (7)
(ABS) ) 4.599 × 10-12T-0.443[OH]0.8757
(5)
Discussion
where [OH] is in molecular units and 1250 e T e 2050 K.
Figure 3 shows an experimental plot of (ABS)T0.443 against [OH]
along with the line determined from eq 5. Note that this result
The present results can be compared to those from earlier
studies. The data have been thoroughly reviewed by Michael
et al.,7 Ko and Fontijn,9 and in the NIST kinetics database.46 In

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Rate Constants for H + NO2 f OH + NO
J. Phys. Chem. A, Vol. 106, No. 36, 2002 8265
TABLE 3: High-Temperature Rate Data for H + NO2 f
OH + NO Using OH-Radical Detection
P5b (Torr)
Msa
F5b (1018 cm-3
)
T5b (K) k1c (10-10 cm3 s-1
)
XC H I ) 9.258 × 10-6, XNO2 ) 1.726 × 10-5
5
297
356
474
397
337
272
131
174
201
226
170
143
386
479
566
536
376
434
2.2385
2.545
2.847
2.646
2.492
2.314
2.217
2.449
2.582
2.691
2.428
2.288
2.293
2.477
2.635
2.582
2.268
2.392
2.005
2.127
2.302
2.196
2.090
1.930
1.008
1.113
1.166
1.217
1.107
1.037
2.771
3.000
3.182
3.131
2.764
2.907
1432
1617
1990
1744
1556
1359
1258
1507
1666
1793
1483
1336
1343
1541
1716
1654
1313
1443
2.1
2.2
1.6
1.5
2.0
1.5
1.5
1.7
1.9
1.9
1.9
2.0
1.7
1.6
1.5
1.5
2.1
1.6
Figure 4. Arrhenius plot of experimental and theoretical data.
Experiments include (4) present results, (b) Michael et al., ref 7, and
(0) Ko et al., ref 9. The line (-) with error bars represents the combined
experimental fit (eq 9). Theoretical results include (- - -) VRC-
FTST calculations, (- - -) calculations of the Lennard-Jones model, and
(-‚‚) calculations of Nyugen et al., ref 54.
XC H I ) 8.484 × 10-6, XNO2 ) 1.966 × 10-5
5
466
373
328
301
240
366
392
430
2.2456
2.589
2.476
2.397
2.219
2.249
2.308
2.383
2.977
2.156
2.054
2.006
1.842
2.730
2.798
2.906
1513
1670
1544
1449
1260
1293
1354
1429
2.0
2.0
1.8
1.8
1.5
1.9
1.7
1.9
Theory. The rate behavior for reaction 1, eq 9, is ultra-simple,
and the question arises as to whether such behavior is consistent
with chemical kinetics theory. In earlier work,7 it was shown
that the rate constants were closely similar to the collision rate
using a Lennard-Jones model; that is, the collision rate between
H and NO2 is calculated from the standard expression47 for
collisions under a Lennard-Jones interaction potential:
a The error in measuring the Mach number, Ms, is typically 0.5%-
1.0% at the one standard deviation level. b Quantities with the subscript
5 refer to the thermodynamic state of the gas in the reflected shock
region. c The rate constants represent best fits to experimental profiles
using the reaction scheme listed in Table 2.
g‡
g1g2
8πkT
µ
1/2
ꢀ12
kLJ
)
σ122Ω(2,2)*
exp
(10)
(
)
(
)
( )
kT
two of the earlier studies,4,5 a relatively strong temperature
dependence was suggested; however, the more recent studies
disagree with this claim.7,9 These latter studies used both the
flash photolysis-resonance fluorescence, FP-RF (and its high-
temperature modification, HTP9), and discharge flow-resonance
fluorescence, DF-RF, techniques.7 Hence, the results were
obtained over large ranges of both temperature and density. It
seems clear that the earlier claims of a strong temperature
dependence are not correct; however, Ko and Fontijn9 do suggest
a moderate effect, reporting
1
where the ratio of electronic degeneracy factors, g, is /4. The
interaction potential parameters σ and ꢀ for both H and NO2
are derived from polarizabilities (by methods described in
Hirschfelder, Curtiss, and Bird47) as suggested by Cambi et al.48
and combined as in that reference to obtain σ12 and ꢀ12 for use
in the above equation. We obtain σH,NO ) 3.416 Å and ꢀH,NO
2
2
) 64.135 K, which give values for the collision rate ranging
from 2.7 × 10-10 to 4.3 × 10-10 cm3 molecule-1 s-1 for 195-
2000 K. These results are plotted in Figure 4 and are ap-
proximately 2-2.5 times larger than the measurements. Because
this model involves many assumptions, more detailed theoretical
calculations are called for. We have accordingly considered this
system by first determining the ab initio potential energy surface
(PES) for the interaction and then applying flexible transition
state theory (FTST)49 to calculate the temperature dependence
and rate behavior.
Selected portions of the HNO2 PES have already been studied
by others.50-54 Of these, the most relevant study is that of
Nguyen et al.54 They used B3LYP density functional theory
(DFT), quadratic configuration interaction singles and doubles
with triples correction (QCISD(T)), and coupled cluster singles
and doubles with triples correction (CCSD(T)) electronic
structure calculations to map out the four isomers (HNO2,
HONO, HNOO, and H(NO2)triangle) and the reaction pathways
that connect them to each other and to the possible low-lying
asymptotes (H + NO2, OH + NO, and NH + O2). Their results
show that there are barrierless reaction pathways that directly
connect the reactants H + NO2 to either isomer HONO or
HNO2. H + NO2 collisions that lead directly to HONO
complexes quickly undergo decomposition to OH + NO
k1 ) 2.15 × 10-10 exp(-182 K/T) cm3 molecule-1 s-1 (8)
for 296 e T e 760 K. The present result, eq 7, can be compared
to the values implied by eq 8. Our result overlaps the range of
values calculated by eq 8 within experimental error. We
conclude that if the earlier data with corresponding errors are
taken into account then temperature dependence is clearly
indeterminate. If a barrier exists for reaction 1, it is <100 cal
mol-1. Michael et al. report (1.41 ( 0.26) for 195-400 K,7
Wategaonkar and Setser report 1.49 at 296 K,8 Ko and Fontijn’s
average value is (1.41 ( 0.23) for 296-760 K,9 and the present
value is (1.64 ( 0.30) for 1100-2000 K, all in units of 10-10
cm3 molecule-1 s-1. If the studies are weighed according to
the standard deviations, then the best representation for the entire
temperature range, 195-2000 K, is
k1 ) (1.47 ( 0.26) × 10-10 cm3 molecule-1 s-1 (9)
This expression and the above-mentioned data are shown as an
Arrhenius plot in Figure 4.

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8266 J. Phys. Chem. A, Vol. 106, No. 36, 2002
Su et al.
TABLE 4: Computed versus Experimental Properties for
NO2
Before describing the results of the electronic structure
calculations, a brief description of coordinates appropriate for
the H + NO2 complex formation reaction is required. Beyond
the separation coordinate between the two reactants that
measures progress along the reaction path, the PES is a function
of five other coordinates. Of these five, it is the variation of the
potential energy with the two transitional coordinates and how
that variation changes as a function of the separation coordinate
that has the most impact on the rate constant. These two
transitional coordinates can be described in terms of the spherical
(θ) and azimuthal (φ) angles of a spherical coordinate system
of which the z axis is the C2V axis of NO2 (+z pointing away
from bent NO2) and of which the origin is the N atom. The
remaining three coordinates describe the bend, asymmetric
stretch, and symmetric stretch of NO2. The separation coordinate
can be measured in terms of the RNH distance.
ONO asym. stretch sym. stretch bend
RNO (Å) (degree)
(cm-1
)
(cm-1
)
(cm-1
)
theory
1.1826
135.2
134.1
1867
1618
1514
1320
798
750
experimenta 1.1934
a Reference 58.
products (with an exothermicity of ∼30 kcal mol-1 relative to
the reactant asymptote). However, any HNO2 complex formed
has no energetically accessible reaction paths directly to
products. Instead, it must first isomerize to HONO, which then
decays to products. Nguyen et al. calculate that the isomerization
barrier is about 20 kcal mol-1 below the reactant H + NO2
asymptote, implying a facile isomerization. Indeed, their reaction
rate calculations (to be discussed later) show that this is so.
This is also consistent with the suggestion that the HONO
complex lifetime is less than one rotational period and probably
the same order of magnitude as that for a vibration.18 Thus, in
the context of the present experiments, the theoretical results
of Nguyen et al. confirm that the rate-limiting step to the loss
of reactant H or the formation of product OH is the total rate
of complex formation from the reactants H + NO2. Only at
much higher pressures than are experimentally sampled do the
details of the decay routes of the HONO and HNO2 complexes
become important.
In terms of these coordinates, the electronic structure calcula-
tions can ideally provide the structure and energetics as a
function of RNH along the reaction paths, the three conserved
vibrational frequencies as a function of RNH along the reaction
paths, and the interaction potential V(θ,φ,RNH) with NO2 fixed
at its reaction path structure for RNH. For the H + NO2 reaction,
all reaction paths have H in the NO2 plane. In the kinetically
important regions of the reaction path, the structure of NO2
differs marginally from the equilibrium structure (RNO ) 2.25
a0, ONO ) 135°). Thus, as a minor approximation, the
equilibrium geometry of NO2 was presumed to describe the NO2
geometry in calculations defining V(θ,φ,RNH). Under these
circumstances, as a function of φ, V(θ,φ,RNH) has unique values
only over the range 0°-90°.
Because of the location of the reaction paths, most of the
electronic structure calculations sampled that portion of the PES
in which the H atom lies in the plane of the NO2. With the
NO2 frozen at its equilibrium geometry, RNH was varied over
an unevenly spaced grid of 24 points from 3.5 to 9.0 a0, and
the angle of H with respect to the C2V axis of NO2 was varied
over an unevenly spaced grid of 49 points from 0° to 180°.
The resulting 1176 ab initio energies were fit to a 2D spline to
produce V(θ,φ)0,RNH) as displayed in Figure 5a. The bands in
the figure represent 2 kcal mol-1 increments with the light and
dark bands at the largest value of RNH representing the increment
just below or just above 0 kcal mol-1, respectively. By definition
of θ, 0° corresponds to H approaching the “frontside” of N along
the C2V axis (the two O atoms point away from the H) while
180° corresponds to the H approaching the “backside” of N.
The figure shows that both approaches are attractive. An H
attack along the extension of the N-O axis would occur at θ
) 112.5°, but the figure shows that that approach is repulsive.
At angles intermediate between θ ) 112.5° and 180°, there is
an attractive approach. Furthermore, inside a 20 kcal mol-1
barrier at close-in values of RNH, there is also an attractive
approach at angles intermediate between θ ) 0° and 112.5°.
NO2 has p orbital radical character in the plane on both the N
and the O atoms. Just as the H can access both the frontside
and backside of the p orbital on the N, it can do the same for
the O with the only attractive access being the backside attack
of the O. Thus, in this (θ,RNH) portion of the PES, there are
four reaction paths to complex formation, two of which involve
barrierless H attack on the N and two of which involve H attack
on the O. There are three saddle points in the figure, one for
the H attack on the O, which has a barrier, one connecting the
two O attack reaction paths, and one connecting the two reaction
pathways involving H attack on the backside of O or N. From
a thermal kinetics point of view, the frontside attack of O over
Nyugen et al. did not choose to study in detail the reaction
pathways that lead H + NO2 to either complex. Consequently,
we have carried out new electronic structure calculations to
survey enough of the PES to describe the reaction paths and
the dependence of the energy on three conserved and two
transitional degrees of freedom that describe deviations from
the path. The meaning of “conserved” and “transitional” are in
the FTST sense: conserved degrees of freedom are vibrations
found in both the H + NO2 reactants and either complex while
transitional degrees exist as free rotations in the reactants but
vibrations in the complexes. Transitional degrees of freedom
can display large amplitude, anharmonic motion away from the
reaction path and therefore can require the characterization of
a substantial portion of the PES.
Although NO2 is a stable gas, it has a radical character, and
the H-atom radical and the radical nature of the H + NO2
reaction accounts for its barrierless reaction paths to either
complex. Long-range potential surfaces for radical-radical
interactions are poorly described by single reference methods.
For this reason a multireference, singles and doubles, config-
uration interaction (MRSDCI) approach was used in the present
work. The reference space for the MRSDCI calculations was a
two electron-two orbital, complete active space, self-consistent
field wave function (CASSCF) in which the two active orbitals
are the two single occupied radical orbitals of the reactants. This
is the minimum reference space needed to allow for a correct
(i.e., not spin-contaminated) description of the reactants. The
calculations employed the correlation-consistent, polarized
double-ú (cc-pvdz) basis set of Dunning,55 which is similar in
size to that used by Nyugen et al. All calculations were carried
out using the MOLPRO program package.56,57 In Table 4, the
computed properties of NO2 at the H + NO2 asymptote are
compared to experiment.58 As the table shows for structural
properties, the computed bond angle and RNO distance are 1.1°
and 0.01 Å too small, respectively. The computed frequencies
are 48, 194, and 249 cm-1 too high relative to anharmonic
experimental frequencies58 for the bend, symmetric stretch, and
asymmetric stretch, respectively.

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Rate Constants for H + NO2 f OH + NO
J. Phys. Chem. A, Vol. 106, No. 36, 2002 8267
a ∼20 kcal mol-1 barrier cannot compete with the other
barrierless reaction paths and can be ignored.
No electronic structure calculations were done to systemati-
cally explore the φ dependence of V(θ,φ,RNH). Rather the
following approximations were used. At φ ) 90°, H moves on
the plane that perpendicularly bisects the NO2. Because the
radical p orbital of each O atom lies in the NO2 plane and is
largely aligned parallel to the perpendicularly bisecting plane,
it is unlikely that any attractive trace of the reaction paths for
H attack on the O atoms will be found in V(θ,φ)90°,RNH).
However, because the radical p orbital on the N atom lies along
the C2V axis, both frontside and backside H attack on the N
will be present but modified. In the terminology of nonbonded
and bonded interactions, at φ ) 90°, only the nonbonded and
the N-H bonded interactions will be important while the bonded
O-H interactions that are obvious in Figure 5 for φ ) 0° will
be negligible. The modifications to the H attack on N will occur
only because the nonbonded interactions of H with O will be
different because the ROH distances will be different. This
analysis suggests the following approximation for V(θ,φ,RNH):
V(θ,φ,RNH) ) V(θ,φ)0°,RNH) cos2 φ +
Vapp(θ,ROH,RO′H,RNH)(1 - cos2 φ) (11)
where Vapp has an argument list appropriate for nonbonded and
N-H bonded interactions and where cos2 φ acts as a switch to
turn on Vapp for deviations out of the four atom plane.
Through the use of typical representations of bonded and
nonbonded interactions, Vapp can take the form
V
app(θ,ROH,RO′H,RNH) ) VNH(RNH) cos2 θ +
Vnonbond(ROH,RO′H,RNH)(1 - cos2 θ) (12)
In this form, θ ) 0° or 180° leaves only the VNH term, which
therefore corresponds to frontside or backside attack attack on
N by H. Hence,
Figure 5. V(θ,φ,RNH) in kcal mol-1 as a function of θ (deg) and RNH
(a0) for φ ) 0° (a), φ ) 45° (b), and φ ) 90° (c). Each band in the
figure represents 2 kcal mol-1. At the largest values of RNH, the zero
contour separates the dark and the light band. Where V(θ,φ,RNH) is
lower than -12 kcal mol-1, the potential is represented by a dark floor.
Where V(θ,φ,RNH) is higher than 20 kcal mol-1, the potential is
represented by a light plateau.
VNH(RNH) ) V(θ,φ)0°,RNH) for θ ) 0°, 180° (13)
If one assumes that bonding interactions between H and either
O for φ ) 0° is negligible for θ e 90°, then
Vnonbond(ROH,RO′H,RNH)|φ)0° ) [V(θ,φ)0°,RNH) -
VNH(RNH) cos2 θ]/(1 - cos2 θ) (14)
13 determines Vapp of eq 12 and hence V(θ,φ,RNH) via eq 11
for any kinetically relevant values of its arguments.
The φ ) 0° constraint is imposed on the LHS of eq 14 because
ROH and RO′H depend on φ for a given θ and RNH. What is
needed is a parametrized functional form for Vnonbond that is a
function of the distance arguments without any φ constraint but
the parameters of which are set to minimize divergence from
the equality of eq 14. The form finally adopted is
Figure 5c displays V(θ,φ)90°,RNH) from the same perspective
as Figure 5a. From eq 11, V(θ,φ)90°,RNH) is exclusively due
to Vapp. Only the attraction to either side of the N atom remains
in the figure; all trace of H attack on O has disappeared because
of repulsive interactions. Figure 5b displays V(θ,φ)45°,RNH),
which is intermediate in character between the interaction
potential for φ ) 0° (Figure 5a) and φ ) 90° (Figure 5b).
Because Figure 5 parts b and c do not represent any electronic
structure calculations except along the two reaction paths
involving N attack by H, the final V(θ,φ,RNH) used in the kinetics
calculations is qualitatively correct but probably not quantita-
tively correct in detail away from the four atom plane. As will
be discussed later, it is unlikely that an ab initio map of the
PES like that of Figure 5 only for other values of φ would have
an important impact on the computed rate constants.
-RRO′H
Vnonbond(ROH,RO′H,RNH) ) A(e-RR + e
) +
OH
-2RRO′H
B(e-2RR + e
) + C(RNH) (15)
OH
where a common A, B, and R are fit for all RNH but C is
optimized at each RNH value. C(RNH) has a largely exponential
character but is exactly represented as an exponential spline of
R
NH. As Figure 5a indicates, for RNH e ∼5 a0 and θ g ∼50°,
bonding components for the frontside attack of H on O become
prominent and were therefore excluded from the fits. The final
fitting error of the RHS of eq 15 to the RHS of eq 14 is only
0.3 kcal mol-1. Given the optimized values of A, B, C(RNH),
and R, Vnonbond is determined, which together with VNH of eq
While V(θ,φ,RNH) gives the effect of transitional mode
deviations from the path, there is no information about the
change in vibrational frequencies for conserved modes or about
the distortion of NO2 from its equilibrium geometry with

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8268 J. Phys. Chem. A, Vol. 106, No. 36, 2002
Su et al.
progress along the reaction path. (For V(θ,φ,RNH), NO2 was held
at its asymptotic geometry.) That information was calculated
for the reaction paths involving H attack of the frontside of N
and of the backside of O, the two most prominent reaction paths
for V(θ,φ)0°,RNH). In these calculations, all degrees of freedom
were allowed to relax to produce the full dimensional paths.
As will be discussed shortly, the kinetically important region
of the reaction paths corresponds to separations of H from the
center-of-mass of NO2 of g∼5 a0. For H attack on N, over this
region, the NO2 is essentially unchanged and all of the conserved
vibrational frequencies increase but by less than 25 cm-1 (in
the largest frequency, the asymmetric stretch). The change in
freedom discussed above will only affect the highest temper-
atures. Microcanonical effects were found to be minor. With
the center-of-mass definition of the reaction coordinate, micro-
canonical and canonical rate constants are the same within the
2-3% integration error.
The reliability of the VRC-FTST calculations in Figure 4
depends in part on the accuracy of the computed PES which,
as discussed above, contains approximations. To gauge the
sensitivity of the computed rate constants to the PES, several
FTST calculations were performed on distorted representations
of V(θ,φ,RNH). In these calculations, for simplicity, the pivot
point for the transitional modes of motion was fixed at the center
of mass of NO2. A (30% variation in the size of Vnonbond [see
eq 15] results in at most a (10% variation in the computed
rate constant over the 200-2000 K temperature range. The use
of a cos4 φ switching function in eq 11 resulted in less than a
5% variation in the computed rate constant. These calculations
indicate that relatively substantial changes in those portions of
the PES that are approximated do not lead to substantial changes
in the results displayed in Figure 4.
zero-point energy is always less than about 0.06 kcal mol-1
.
For H attack on O, the geometry of NO2 also remains
unchanged. The same general behavior of the frequencies
remains true for center-of-mass separations greater than ∼5.5
a0. Over this region, no frequency changes by more than (10
cm-1 and the change in the zero-point energy is always less
than 0.05 kcal mol-1. For separations between 5.0 and 5.5 a0,
one frequency, the symmetric stretch, increases by ∼125 cm-1
while the other two increase by 25-50 cm-1, resulting in a
zero-point energy increase of 0.3 kcal mol-1. At these close
distances, the separability of the transitional and conserved
degrees of freedom is beginning to breakdown. However, the
breakdown is relatively small and, as will be discussed, applies
to only the highest temperature portion of the rate constant.
Given the approximations already in V(θ,φ,RNH), the variation
in the conserved vibrational frequencies along each reaction path
and between reaction paths was ignored.
Another source of uncertainty in the VRC-FTST calculations
comes from symmetry number assignments. At a fixed distance
of H from the center of mass of NO2 (the optimal pivot point
for the VRC-FTST calculations), the reaction path energy for
N attack is always more attractive than the reaction path energy
for O attack in the reaction bottleneck region. Thus, the reaction
path for O attack can be considered simply a feature on the
hindered rotation potential for the reaction path for N attack.
Because that reaction path has a C2V geometry, the symmetry
number should be 2, and the calculations in Figure 4 are with
this assignment. However, the appropriate method for assigning
symmetry numbers for a theory that rigorously classically
incorporates large amplitude internal motion and external
rotational motion is unclear. In this case, the reaction path energy
for O attack is not that much less attractive (∼1%-30%) than
that for N attack and has a larger range of angles for which the
PES is substantially attractive. A typical harmonic-oscillator
approach to H + NO2 would have two reaction paths, one for
N attack (symmetry number of 2) and one for O attack
(symmetry number of 1). For these reasons, an alternative
VRC-FTST model was studied in which parts of the PES away
from the region about each atom in NO2 were masked by a
uniformly high repulsive potential. This PES decomposition is
somewhat arbitrary but leads to a decomposition of the rate into
a part that goes to HNO2 (assigned a symmetry number of 2)
and a part that goes to HONO (assigned a symmetry number
of 1). Furthermore, with the PES decomposed, the pivot point
for the attack on each atom can be separately optimized. This
alternative VRC-FTST calculation produces rate constants
approximately 50%-60% larger than the VRC-FTST rate
constants shown in Figure 4. This 50%-60% variation repre-
sents the range of symmetry number treatments possible for H
+ NO2 within the context of FTST and is the largest uncertainty
in the calculation. The model used in Figure 4 is selected
because it is the simpler one and more consistent with
experiment. In the future, more analysis of the implications of
reaction path symmetry is required for theories such as FTST
that directly incorporate large amplitude motion. As an aside,
the alternative VRC-FTST calculations produce rate constants
noticeably lower than, but somewhat similar to, the Lennard-
Jones rate constants in Figure 4. This suggests that the Lennard-
Jones model is too high not only because its potential is too
simple but also because its spherically symmetric PES about
Given the computed structure and frequencies of the NO2,
the approximation that the structure and conserved frequencies
change negligibly along the reaction paths, and the computed
interaction potential V(θ,φ,RNH) for the transitional degrees of
freedom, a FTST calculation can be performed. The freeware
code VariFlex was used59 in this calculation. FTST calculations
are generally variational in that the minimum rate constant as
a function of progress along the reaction path is the most
accurate estimate (because it minimizes recrossing effects). In
addition to the usual variational options, VariFlex has a variable
reaction coordinate (VRC) option, which permits additional
minimization of the rate constant by varying the description of
the reaction coordinate. This option requires, at each distance
along the reaction path, a search for the optimal pivot point for
NO2 about which the two transitional degrees of freedom are
executed. VariFlex also allows canonical or microcanonical
calculations. At the microcanonical level, optimization of the
reaction path and the position on the path takes places at each
point on a grid of total energy and total angular momentum
that spans the range that contributes significantly to the thermal
rate constant over the temperatures of interest. At the canonical
level, variational studies are carried out only for each temper-
ature.
In Figure 4, the results of a canonical VRC-FTST rate
constant calculation are displayed relative to the measurements
reported here, to the two previous measurements, and to other
calculations or fits. VRC effects are minor; a rate constant,
determined with a center-of-mass separation distance as the
definition of the reaction path, would be no more than 10%
higher than that in the figure. However, as expected the location
of the reaction bottleneck does decrease with temperature. When
expressed in terms of the center-of-mass separation distance,
the location varies from 7.0 a0 at 200 K to 5.5 a0 at 1100 K to
4.9 a0 at 2000 K. This confirms that the small breakdown in
the separation between conserved and transitional degrees of

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Rate Constants for H + NO2 f OH + NO
J. Phys. Chem. A, Vol. 106, No. 36, 2002 8269
each reactant is only consistent with a symmetry number of
unity.
reaction coordinate flexible transition state theory calculation
of the rate constant. The resulting rate constant increases
somewhat with temperature and is on the high side of the spread
of measured data from this work and two other laboratories.7,9
The computed rate is 1.5-2 times higher than the only other
computed rate constant available in work by Nguyen et al.54
The Nguyen et al. computed rate constant came from an
application of canonical variational transition state theory to a
fully harmonic description of the reaction paths calculated with
different electronic structure methods than those employed here.
The convergence of measurements from three different
laboratories and calculations with two different relatively high-
level methods indicates that the rate constant for the H + NO2
f OH + NO reaction has at best a weak temperature
dependence and a value quite close to 1.5 × 10-10 cm3
As already discussed, the solid flat line with the error bars in
Figure 4 is the best representation of the experimental results
over 195-2000 K. The calculated VRC-FTST results are not
flat but show an increase with temperature. While the computed
rate constants are always above the best experimental repre-
sentation, these calculations are never more than about 40%
higher and are not inconsistent with the original experimental
data. They are in noticeably better agreement with experiment
than the simple Lennard-Jones model of eq 10 discussed above.
The VRC-FTST rate constants are about a factor of 1.5-
2.0 higher than the calculated rate of Nguyen et al. that tends
to lie below most of the measurements. In calculating their rate
constant, Nyugen et al. used canonical variational transition state
theory applied separately to the two reaction paths for H attack
on the frontside of N and on the backside of O. With either
path, harmonic energy changes are assumed for deviations
perpendicular to the path in all five available degrees of freedom.
Each path was determined with a B3LYP density functional
theory calculation, followed by a QCISD(T) refinement of the
energy on the B3LYP path, followed by a fit of the energy
variation along the path to a Morse oscillator functional form.
The variational location of the reaction bottleneck was carried
out on this Morse form and the resulting final rate constant was
then fit to a single exponential form. The A factor of this fit is
listed by Nguyen et al. for each path, but the activation energy
is not. From the figures in the Nguyen et al. study, the rate
constant temperature dependence and hence the activation
energy is quite small and not resolvable on the scale of Figure
4. What is shown for Nguyen et al. in Figure 4 is the sum of
the A factors alone with the activation energies being set to
zero.
molecule-1 s-1
.
Acknowledgment. This work was supported by the U. S.
Department of Energy, Office of Basic Energy Sciences,
Division of Chemical Sciences, under Contract No.W-31-109-
Eng-38.
References and Notes
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(3) Phillips, L. F.; Schiff, H. I. J. Chem. Phys. 1962, 37, 1233.
(4) Wagner, H. Gg.; Welzbacher, U.; Zellner, R. Ber. Bunsen-Ges.
Phys. Chem. 1976, 80, 1023.
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Conclusions
Rate constants for the reaction H + NO2 f OH + NO have
been measured over the temperature range of 1100-2000 K in
reflected shock experiments. The source of H-atoms is from
ethyl radical decomposition in which the radical is formed
essentially instantaneously from the thermal decomposition of
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extensive calibration was performed to obtain the curve of
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constants by this method required chemical simulation. The
results of both methods statistically overlap, combining to give
k ) (1.64 ( 0.30) × 10-10 cm3 molecule-1 s-1 for 1100 e T
e 2000 K. When combined with two earlier measurements at
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