Determination of the rate constant for the NCO(X2II) + O(3P) reaction at 292 k

Article abstract of DOI:10.1021/jp0222595

There is an increasing effort to reduce the emission of NO_x compounds from combustion sources due to their detrimental effects on air quality. The rate constant for the reaction of the isocyanate radical, NCO(X²II), with oxygen atoms

Full text of DOI:10.1021/jp0222595

J. Phys. Chem. A 2003, 107, 4625-4635
4625
Determination of the Rate Constant for the NCO(X2Π) + O(3P) Reaction at 292 K
Yide Gao and R. Glen Macdonald*
Chemistry DiVision, Argonne National Laboratory, 9700 South Cass AVenue, Argonne, Illinois 60439-4831
ReceiVed: October 18, 2002; In Final Form: March 6, 2003
The rate constant for the reaction of the isocyanate radical, NCO(X2Π), with oxygen atoms, O(3P), has been
measured at a temperature of 292 ( 2 K to be (2.1 ( 0.76) × 10-10 cm3 molecule-1 s,-1 where the error
estimate contains both systematic and random errors. The measurements were carried out in an excess of
either Ar or CF4 at pressures between 1.5 and 7.5 Torr and found to be independent of both the nature of the
third body and pressure. Equal concentrations of NCO and O were generated by the CN + O2 reaction. The
temporal dependence of NCO was followed using time-resolved infrared absorption spectroscopy on rotational
transitions of the NCO (1011) r (0010) combination band.
The ∆Hf0(0) for NCO was taken to be 129.5 kJ mol-1, as
I. Introduction
recommended by Smith.5 A unique feature of all radical-atom
There is an increasing effort to reduce the emission of NOx
compounds from combustion sources due to their detrimental
effects on air quality. There are three established sources for
NOx formation in combustion: the Zeldovich or thermal NOx
mechanism, the Fenimore or prompt NOx mechanism, and fuel-
fixed nitrogen sources.1 The latter two mechanisms are more
kinetically complicated than the first, involving a large number
of elementary reaction steps.2 In both the prompt and fuel-fixed
nitrogen mechanisms, CN and NCO radicals play key roles.
Many strategies have been proposed and implemented for
NOx abatement.3 Neglecting catalytic conversion processes,
these strategies involve the addition of various chemicals to the
exhaust gas stream (selective noncatalytic reduction of NO,
SNCR, processes) or the manipulation of the combustion
process, including staged combustion and exhaust gas reburn
techniques. The three main SNCR technologies are the follow-
ing: the thermal De-NOx process using NH3 addition, the
RAPRENOx process using (HOCN)3 addition, and the NOxOUT
process using (NH2)2CO addition. Again, the NCO radical plays
an important role in the chemistry of these NOx reduction
technologies.2,3
reactions is the influence of multiple potential energy surfaces
(PESs) on the reaction dynamics. For reaction 1, in Cs symmetry,
the reactants correlate to three A′ and three A′′ electronic PESs
and doublet and quartet spin states, for a total of 12 PESs. If
spin-orbit interaction is taken into account, there are 36 PESs
correlating to the reactants.
There have been only a few measurements of the rate constant
for reaction 1, k1. The most recent measurements have been
made by Becker et al.6 These workers used UV laser photolysis
to generate NCO from ClNCO and LIF to follow the time
dependence of the NCO radical in a known concentration of O
atoms. They reported k1 measurements as a function of
temperature from 297 to 757 K and found that k1 exhibited a
slight dependence on pressure near 300 K, increasing by a factor
of about 2 for a pressure change from 2.5 to 9.9 Torr. The only
other reported measurement of k1 near 300 K has been from
the early work of Schacke et al.7 There have been several
measurements of k1 at high temperatures8-11 and in flames.12
There have been no explicit theoretical studies of reaction 1;
however, this reaction is closely related to the CN(2Σ+) + O2(3
Σ-g ) reaction, for which a detailed theoretical investigation of
the saddle points and stationary points has been carried out on
the reactive 2A′′ PES.13 Thus, many features of the lowest-lying
2A′′ PES for the NCO + O system are known.
In the present work, k1 was measured at 292 K in two carrier
gases, Ar and CF4, and as a function of pressure over a modest
range from 1.5 to 7.5 Torr. Reaction 1 was initiated by
photolyzing (CN)2 at 193 nm to create CN radicals, which
rapidly reacted with O2 to produce equal concentrations of NCO
and O.14 The temporal dependence of the NCO radical was
followed using time-resolved infrared absorption spectroscopy
using several rotational transitions of the NCO(1011) r (0010)
combination band near 3.16 µm. The absorption coefficients
for the monitored transitions have been previously determined,15
so the absolute concentration of NCO was monitored. A
chemical model was used to generate NCO concentration
profiles to compare with experiment and determine k1 by
minimizing the sum of squares of the residuals between the
experimental and calculated NCO concentration profiles. The
In particular, one of the most important reactions involving
the NCO radical and the conversion of N atoms into NOx
compounds is the reaction NCO + O because it directly converts
a N atom into NO, and is also a chain termination step in the
radical pool.4 This reaction is important in both the chemistry
of NOx formation and its removal. There are three possible
exothermic product channels:
NCO(X2Π) + O(3P) f N(2D) + CO2(X1Σ)
∆H0f (0) ) -68.6 kJ mol-1 (1a)
f N(4S) + CO2(X1Σ)
∆H0f (0) ) -298.6 kJ mol-1 (1b)
f NO(X2Π) + CO(X1Σ)
∆H0f (0) ) -400.3 kJ mol-1 (1c)
* To whom correspondence should be addressed. E-mail: rgmacdonald@
anl.gov. Fax: (630) 252-9292.
10.1021/jp0222595 CCC: $25.00 © 2003 American Chemical Society
Published on Web 05/15/2003

4626 J. Phys. Chem. A, Vol. 107, No. 23, 2003
Gao and Macdonald
TABLE 1: The Peak Absorption Coefficient, σpk(ν), for the
Transitions Probed in This Work Assuming a Doppler Line
Shape for 292 K
temporal dependence of the CN radical was also recorded to
show consistency with the concentration of NCO.
σpk(ν)
II. Experimental Section
molecule
NCO
transition
wavelength
(cm2 molecule-1
)
The experimental apparatus has been described previously,
so only a brief description is given here.16 The reaction vessel
consisted of a rectangular stainless steel chamber containing a
Teflon box with interior dimensions of 100 × 100 × 5 cm3.
The chamber could be evacuated to a pressure of 5.0 × 10-6
Torr with a diffusion pump and had a leak rate of about 5 ×
10-4 Torr/min. Known flows of the reagent gases were admitted
to the chamber from separate vacuum systems. Partial pressures
were determined from the chamber pressure and known flow
rates of the various gases. The total flow rate varied between
150 and 250 sccm. The gases used were Ar (AGA Gas,
99.995%), CF4 (AGA Gas, 99.9%), O2 (AGA Gas, 99.98%),
and (CN)2 (Spectra Gases, 98.0%). Generally, the gases were
used as supplied by the manufacture except that the (CN)2 was
stored in a 20-L bulb and occasionally pumped on at liquid-
nitrogen temperatures.
(1011) r (0010) 3.145 200 µm (3.7 ( 0.4) × 10-19 a
(1011) r (0010) 3.165 073 µm (3.5 ( 0.4) × 10-19
R1(12.5)
P1(12.5)
CN
(A2Π r X2Σ)
R1(14.5)
790.029 nm
789.995 nm
(1.01 ( 0.05) × 10-16 b
(2.19 ( 0.11) × 10-16
(A2Π r X2Σ)
R1(4.5)
a The uncertainty is one standard deviation, (1σ, in the experimental
determination. b The uncertainty is estimated from the theoretical
calculation, ref 19, within the experimental determination, ref 20.
Lambert Law relates the absorbance, A(ν), at time t to the
concentration of species X, [X], according to17
A(ν) ) ln(I0(ν)/I(ν)) ) lσpk(ν)[X]
(2)
The photolysis laser was a Lamda-Physik Compex 205
excimer laser operating at a wavelength of 193 nm with an
estimated fluence of 5-18 mJ cm-2 delivered to the photolysis
region. To ensure that a fresh sample of gas was photolyzed on
each laser pulse, the repetition rate was kept low, 1-3 Hz, with
no detectable change in the rate constant measurements as a
function of repetition rate.
The NCO(X2Π) radical was monitored using the R1e/f(12.5)
or P1e/f(12.5) transitions of the (1011) r (0010) combination
band centered near 3.16 µm. Time-resolved absorption profiles
of NCO were obtained using the output of a Burleigh model
20 single-mode color center laser. The CN radical was also
monitored using several rotational transitions of the CN “red
system” (A2Π r X2Σ) (2,0) band near 790 nm. Time-resolved
absorption profiles of CN were obtained using the output of an
Environmental Optical Sensor model 2010-EU tunable external-
cavity diode laser. Both probe laser beams were spatially
overlapped and multipassed through the photolysis region using
a White cell. The photolysis laser was overlapped with the two
probe laser beams by a UV-IR dichroic mirror positioned on
the optical axis of the White cell.
The time-resolved absorption profiles for NCO and CN were
recorded and signal-averaged using a LeCroy 9410 digital
oscilloscope operating in the dc mode. The initial intensity, I0,
of the CN probe laser was obtained directly from the dc recorded
signal. For the NCO probe laser, I0 was measured using a box
car triggered 100 µs before the excimer laser was fired. The
infrared laser intensity before the White cell was held constant
using an electrooptical feedback loop. For the small absorption
signals observed in the infrared, a background signal due to
thermal lensing and refractive index changes in the UV
contacting optics was observed. This interference was removed
from the signal by recording a background signal with the
infrared laser tuned ∼600 MHz from the line center and
subtracting this background from the signal profile after
transferring the data to a laboratory computer.
where I0(ν) and I(ν) are the incident and transmitted laser
intensities, respectively, l is the path length, and σpk(ν) is the
peak absorption cross section at ν. The experiments were carried
out at sufficiently low pressure, 1.5-7.5 Torr, that the effect
of pressure broadening should be small and the shape of an
absorption feature should be well described by a Doppler line
shape function. This enables σpk(ν) to be readily calculated if
the line strength of the transition is known. The line strength
for the NCO(1011) r NCO(0010) R1(12.5) transition has been
measured in this laboratory under conditions similar to those
of the present experiment.15 Unfortunately, the UV-IR dichroic
optic has an absorption feature near 3.0 µm and improved signal-
to-noise could be obtained if NCO was monitored further to
the red of the R1(12.5) transition. Thus, the P1(12.5) transition
was generally used to monitor the NCO concentration. The
R1(12.5) line strength was converted to that for a P1(12.5)
transition using the usual Ho¨nl-London factor for a linear
molecule and the dependence of the line strength on frequency.
This procedure introduced a small uncertainty into the value of
σpk(ν) due to the unknown ratios of the Herman-Wallis factors
for these two transitions. The NCO rotational assignment
required a detailed analysis of the NCO(1011) r NCO(0010)
transition, and a combination-difference analysis confirmed the
rotational assignment.18 Similarly, the line strengths for the
2
2
CN(A Π r X Σ) (2,0) transitions used in the present work
were taken from a theoretical calculation19 and experimental
measurement.20 The σpk(ν) for NCO and CN used here are
summarized in Table 1.
B. Mechanism and the Determination of the Rate Con-
stant for NCO + O. Initially, the NCO radical and O atom
were generated in equal concentrations by the reaction of
CN + O2. The CN radical was created by the 193 nm
photodissociation of (CN)2. Unfortunately, NO is produced in
reaction 4b, and furthermore, NO + CO is expected to be the
dominant product channel for the NCO + O reaction.10 The
reaction between NCO + NO is fast and competes with the
NCO + O reaction for removal of NCO. The only other reaction
involving the NCO radical is the possible reaction with (CN)2.
There is no available data on this reaction; however, the N-C
bond is weak in NCO and the C-C bond is strong in (CN)2, so
a direct reaction is not possible. If the reaction proceeds by
complex formation, the possible product channels could be
CO + CN + NCN/CNN or N2 + CO + CCN/CNC. However,
all three channels are highly endothermic using the recent
III. Results
A. Determination of Concentrations. In the present experi-
ments, the probe laser bandwidth at frequency ν was much
narrower than the line width of a Doppler-broadened spectral
feature, so the laser frequency could be tuned to the peak
absorbance of the probed transition and the temporal dependence
of the transmitted laser intensity, I(ν), recorded. The Beer-

Rate Constant for the NCO(X2Π) + O(3P) Reaction
J. Phys. Chem. A, Vol. 107, No. 23, 2003 4627
TABLE 2: The Complete Chemical Model Describing the NCO + O Reaction System
no.
reactants
products
k (cm3 molecule-1 s-1
)
refs
1a
1b
1c
2
NCO + O
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
N(2D) + CO2
N + CO2
0.0a
NCO + O
0.0a
NCO + O
NO + CO
b
this work
23
24
5, 14
5, 14
5, 14
25
CN + CN + Mc
CN + O
(CN)2 + Mc
CO + N
5.14 × 10-29 d
3.70 × 10-11
1.87 × 10-11
5.41 × 10-12
4.9 × 10-13
1.64 × 10-30 d
5.5 × 10-11
2.0 × 10-11
1.6 × 10-11
5.0 × 10-12
5.7 × 10-14 f
3.40 × 10-11
g
3
4a
4b
4c
5
CN + O2
NCO + O
CN + O2
NO + CO
CN + O2
N + CO2
CN + NO + Mc
NCO + N
CNNO + Mc
N2 + CO
6
26
7a
7b
8
NCO + NO
NCO + NO
NCO + NCO
NCO + N2O
NO + N
N2 + CO2
27, 28
27, 28
29
30
31
N2O + CO
N2 + 2COe
N2 + NO + COe
O + N2
9
10
11
12h
13h
first-order loss
NO(v) + O2
NO(v) + Ar or CF4
diffusion
NO(0) + O2
NO(0) + Ar or CF4
2.4 × 10-14
32
33
1.0 × 10-17
a Products not determined. Channels 1a and 1b were assumed to be zero. b Varied. c M ) Ar, CF4, O2. d Termolecular rate constant has units cm6
molecule-2 s-1 e The most likely products. f Currently under investigation. The k9 is a current estimate. g Calculated from kdNiOff h Included to study
. .
the influence of NO(v) on reaction 7.
experimental measurements21 of ∆HfNCN ) 453 kJ mol-1 and
∆HfCNN ) 580 kJ mol-1 and a theoretical estimate22 of
∆HCf CN ≈ ∆HfCNC ) 670 kJ mol.-1 Other rearrangements of
these seven atoms seem unlikely. There are no other reactions
involving the O atom except reaction 1 and loss by diffusion.
Under these circumstances, it was felt that the best method for
evaluating k1 was to simulate the NCO temporal concentration
profiles using a computer model of the chemistry occurring in
the NCO + O system. The complete reaction mechanism,14,23-33
consisting of 13 species and 10 reactions, is given in Table 2.
For clarity, the most important reactions are
near 2.7 µm, but because of the small absorption cross section
and low NO concentration created in these experiments, the
signal-to-noise was insufficient to detect NO. The branching
ratios for reaction 1 will have little effect on the determination
of k1 because the reactive products of reactions 1b and 1c, N
and NO, respectively, react with NCO with similar rate
constants, see Table 2. As will be discussed, the reaction path
leading to channel 1a is expected to be much more constrained
than that for channel 1c and, hence, not to compete with the
much more exothermic channel 1c.
As noted above, NO produced in reactions 1c and 4b reacts
with NCO; however, both of these reactions are sufficiently
exothermic that a substantial amount of the reaction exother-
micity could appear as vibrationally excited NO, NO(v). The
influence of NO(v) on the determination of k1 will be discussed
in section III.C.
(CN)2 193 nm8 2CN(V,J)
CN + O2 f NCO(V1,V2,V3) + O
(4a)
f NO + CO
f N + CO2
(4b)
(4c)
The rate equations describing the reaction mechanism in Table
2 were integrated using a fourth-order Runge-Kutta integration
routine with variable step size,36 and k1 varied until the
difference in the sum of the squares of the residuals, chi-squared,
between the computer-generated and experimental NCO con-
centration temporal profiles was minimized. In the computer
simulation of the NCO concentration temporal profile, the initial
CN concentration, [CN]0, was varied until the computer-
calculated NCO concentration at a specified time, t, was within
1% of the experimentally observed NCO concentration at t. The
specified time was chosen to occur at or slightly past the
maximum in the experimental NCO concentration profile. The
computer-generated [CN]0 was compared to an experimental
measurement of [CN]0 to provide a consistency check on the
NCO concentration. Because of the large discrepancy in their
respective time scales, the CN radical was monitored in separate
experiments from the NCO radical but under identical experi-
mental conditions. However, the nonequilibrium internal energy
distribution of the photolytically generated CN radicals and rapid
reaction with O2 made the experimental determination of [CN]0
uncertain. These experimental measurements on CN will be
discussed further in section III.E.
NCO + O f NO + CO
NCO + NO f N2 + CO2
f N2O + CO
(1c)
(7a)
(7b)
kdiff
8
NCO, O, NO
(11)
The most significant reactions in the model, reactions 4 and 7,
have been studied by several groups,5,27,29,34,35 and their rate
constants have been well established at 292 K. The first-order
loss of each species from the photolysis region by diffusion,
k
diff, could not be directly measured in the present experiments,
but in another series of similar experiments, the loss of NO by
diffusion was determined. For the other species, the first-order
loss by diffusion was related to that for NO assuming kdiff was
inversely proportional to the reduced mass for the species under
consideration with respect to the average mass of the gas
mixture.
As noted in the Introduction, the NCO + O reaction is closely
related to the CN + O2 reaction, and the products of reaction 1
are expected to be dominated by the more exothermic channel
1c, NO + CO. Attempts were made to monitor the NO product
using the NO vibrational overtone (2) r (0) P1(7.5) transition
In an absorption experiment, the measured quantity is the
degeneracy-weighted difference in populations between the
quantum states connected by the radiative transition, so care
must be exercised to ensure that the observed signal is
indeed a true measure of the lower-state population, that is, the

4628 J. Phys. Chem. A, Vol. 107, No. 23, 2003
Gao and Macdonald
and the Renner-Teller interaction.43 These conclusions are
borne out in Figure 1 in that the decay rate of CN is only a
factor of 4 larger than the formation rate of NCO(0010) and
that the NCO(0010) formation rate is in good agreement with
the measured41 vibrational rate constant for NCO(0100) and
NCO(0120) f NCO(0010) in collisions with Ar. At higher total
pressures of Ar and CF4 and higher partial pressures of O2, the
vibrational relaxation of NCO is even more rapid. In all of the
experiments, the rate of the NCO(0010) rise was only slightly
smaller than the rate of loss of CN indicating that NCO
vibrational equilibration was rapid and after a few tens of
microseconds the measurement of the temporal dependence of
NCO(0010) concentration was a measure of the temporal
dependence of NCO concentration.
The initial concentrations of NCO, [NCO]0, and O, [O]0, were
varied by changing the photolysis laser power, keeping all other
conditions the same. Typical NCO concentration temporal
profiles are shown in Figure 2 in which the effects of varying
the photolysis laser fluence from 6 to 15 mJ cm-2 are shown.
The decay of NCO has a typical second-order appearance in
which there is an initial rapid decay and a slow approach to the
baseline. Note that the time to half-concentration becomes
progressively shorter in going from panel a to panel d of Figure
2, as the initial radical and atom concentrations increase. The
[NCO]0 also increases linearly with the photolysis laser fluence
with an intercept close to zero. The same behavior was found
in both Ar and CF4 carrier gases and a variety of O2 partial
pressures, clearly indicating that NCO was being removed by
a second-order process.
The solid line in each panel of Figure 2 is the computer-
generated NCO concentration temporal profile determined by
varying k1 to minimize the sum of the squares of the residuals
between the experimental and computer-calculated NCO con-
centration profiles. Although the k1 determined for each profile
decreases with photolysis laser fluence, this is a coincidence
for the chosen data set, and there is no correlation between k1
and the photolysis laser fluence. Figure 2b is shown in more
detail in Figure 3 to illustrate further the determination of k1.
In Figure 3, the open circles (O) are the experimental data points
shown every 20 time intervals, and the solid line is the calculated
NCO profile obtained by varying k1 in the ø2 minimization
procedure. The two-dashed lines give the 95% confidence level
in the determination of k1. The insert in Figure 3 shows the ø2
curve as a function of k1. In the insert, the three large circles
correspond to values of k1 indicated in the legend. The rather
large uncertainty in the evaluation of k1 arises from the initial
low concentration of the reacting transient species, NCO and
O, and indicates that good signal-to-noise is needed to extract
reliable rate constant data.
Figure 1. The initial temporal dependence of the concentration of
CN(0) and NCO(0010) measured simultaneously on the same photolysis
laser pulse showing the rapid equilibration among the NCO vibrational
manifolds. The measured absorbance profiles for each species were
converted to population profiles using absorption coefficients assuming
a temperature of 292 K and Doppler line widths. For the CN
concentration profile, the data points are displayed every 10th point
after 4 µs. The rates describing the CN concentration profile are krise
)
1.2 × 106 and kdecay ) 6.5 × 104 s-1 and those describing the NCO
concentration profile are krise ) 1.6 × 104 and kdecay ) 5.9 × 103 s-1
.
The conditions of the experiment were PAr ) 1.45, PO ) 0.109, and
2
P(CN) ) 0.0775 Torr.
2
upper-state population should be negligible. In Figure 1, the
simultaneous removal of CN by reaction 4 and the produc-
tion of NCO by reaction 4a are shown. Both profiles were
recorded following the same photolysis laser pulse. The initial
NCO(V1,V2,V3) vibrational level distribution from reaction 4a has
been studied by several different groups under both molecular
beam37 and bulb conditions.38,39 The most notable observation
is that under bulb conditions there is considerable excitation in
the bending mode of NCO and only a small fraction of the
reaction exothermicity appears in the stretching degrees of
freedom. There have also been a number of investigations40-42
on the vibrational relaxation of NCO, indicating that relaxation
of the NCO(0,Vl2,0) vibrational manifold is very rapid, even in
collisions with inert gases. Furthermore, Sauder et al.39 have
measured the disappearance rates for many NCO vibrational
levels with excitation in pure bend, stretch-bend, and combina-
tion stretch-bend manifolds. All of the relaxation measurements
indicate that under the conditions of the present experiments,
at a total pressure of 1.5-7.5 Torr, vibrational relaxation of
NCO would occur on a time scale of a several tens of
microseconds compared to the NCO + O reaction time scale
of many milliseconds, so after a short induction time, the
monitored NCO(0010) vibrational level was in thermal equi-
librium with the complete NCO vibrational manifold. Rapid
vibrational relaxation of NCO(0,Vl2,0) levels by inert gases is
facilitated by the low bending fundamental, ν2 ) 532 cm,-1
In dealing with a chemical mechanism involving many
reactions, it is important to be able to identify the major reactions
involved in the chemistry of any species in the reaction
mechanism.1 In the present work, this was accomplished by a
reaction contribution factor, RCF, analysis.1,2 For a reaction, I
+ J f products, with a rate constant kIJ, the reaction contribution
factor for species I reacting with species J at time t, RCFIJ, is
defined as the rate of reaction of I with J at time t, that is,
d[I]
dt
RCFIJ )
) -kIJ[J][I]
(3)
where RCFIJ, [J], and [I] are evaluated at time t in the reaction
mechanism. The utility of the RCF is that the integral of RCFJI
from t ) 0 to time t gives the concentration of species I that

Rate Constant for the NCO(X2Π) + O(3P) Reaction
J. Phys. Chem. A, Vol. 107, No. 23, 2003 4629
Figure 2. Typical experimental NCO concentration profiles and model calculations of NCO concentration for the value of k1 that produced the
best agreement between experiment and computer-calculated profiles as a function of photolysis laser fluence. The panels illustrate that the
decay of NCO concentration is dominated by a second-order process; see text for a discussion. The conditions of the experiment were PAr ) 3.15,
PO ) 0.423, and P(CN) ) 0.190 Torr.
2
2
for each species X that reacted with or produced NCO was
calculatedfor eachdeterminationof k1. The integrated RCFNCO’s
O
were found to vary between 0.4 and 0.8 depending on the
conditions of the experiment, while that for the corresponding
NCO
integrated RCF ’s were found to vary from 0.1 to 0.2.
NO
Removal by diffusion accounted for the other major pathway
for loss of NCO. A plot of the RCFNXCO’s calculated in the
computer simulation of the experiment illustrated in Figure 3
is shown in Figure 4. Note that reaction 1 accounts for 72% of
the removal of NCO under the experimental conditions of
Figure 3.
C. Influence of Vibrationally Excited NO. Oxygen atoms
and NO are the only species that react with NCO to any
significant extent. The rate constant, k7, has been measured by
several groups with good agreement. However, both reactions
1c and 4b are highly exothermic and could produce vibrationally
excited NO, NO(v), which might react more rapidly with
NCO than ground-state NO. Lin et al.44 have examined the
NCO + NO reaction using a theoretical description of the lowest
singlet and triplet surfaces based on a BAC-MP4 calculation
of the all of the stationary points and carried out detailed Rice-
Ramsperger-Kassel-Marcus (RRKM) calculations for the rate
constants and branching ratios. These theoretical calculations
are in excellent agreement with all of the available experimental
measurements on the NCO + NO system. Both product channels
are produced through tight exit channel transition states with
the result that as the temperature increases the initial OCNNO
Figure 3. Figure 2b shown in more detail illustrating the range of k1
values that describe the experimental NCO concentration profile. Every
20th experimental point is represented by the O’s. The solid curve is
the model NCO concentration profile that provided the best agreement
with experiment for k1 ) 2.4 × 10-10 molecules cm-3 s.-1 The smaller
and larger values of k1 provide estimates of k1 at the 95% confidence
interval, giving roughly a (20% uncertainty in the determination of
k1. The insert shows ø2 as a function of k1.
was removed in reaction with species J up to time t. Thus the
influence of species J on the concentration of I, either through
kIJ or the concentration of J, can be determined directly from
the integrated RCFJI value. The RCFXNCO and integrated RCFXNCO

4630 J. Phys. Chem. A, Vol. 107, No. 23, 2003
Gao and Macdonald
TABLE 3: Summary of the Experimental Measurements for
k1 in Ar at 292 ( 2 K
PAr
(Torr)
PO
(Torr)
P(CN)
(Torr2)
PT
(Torr)
k1 × 1010
2
(cm3 molecules-1 s-1
)
1.32
1.30
1.42
3.21
3.19
3.13
4.76
7.15
0.0677
0.135
0.214
0.193
0.298
0.460
0.169
0.277
0.0812
0.0808
0.0734
0.193
0.192
0.190
0.170
0.183
1.47
1.51
1.70
3.61
3.69
3.78
5.10
7.61
1.44 ( 0.30a
1.52 ( 0.30
1.92 ( 0.47
1.96 ( 0.069
1.87 ( 0.12
2.14 ( 0.30
2.45 ( 0.28
2.30 ( 0.46
Average of 27 Measurements:
k1 ) (1.94 ( 0.30) × 10-10 (cm3 molecule-1 s-1
)
a (1σ from the average.
TABLE 4: Summary of the Measurements for the
Determination of k1 in CF4 at 292 ( 2 K
PCF
(Torr)
PO
(Torr)
P(CN)
(Torr2)
PT
(Torr)
k1 × 1010
4
2
(cm3 molecules-1 s-1
)
1.56
1.48
2.48
2.25
3.13
3.89
0.123
0.249
0.212
0.501
0.487
0.306
0.0657
0.0682
0.177
0.160
0.205
0.205
1.75
1.80
2.88
2.91
3.82
4.40
2.06 ( 0.50a
1.97 ( 0.33
2.30 ( 0.28
2.51 ( 0.21
2.66 ( 0.47
2.91 ( 0.15
Average of 24 Measurements:
Figure 4. The (a) RCFNCO for the production of NCO from the CN +
O2 reaction and the (b) RCFNCO’s for the removal of NCO by species
with a final integrated RCF vXalue greater than 1% of the NCO product.
The computer calculation of the RCFs is for the determination of k1
shown in Figure 3. Note that the RCFNOCO is a factor of 10 larger than
any other RCFNXCO. The final integrated RCFNXCO’s were 0.722, 0.0293,
0.160, and 0.0886 for reaction of NCO with O, NCO and NO and
removal by diffusion, respectively.
k1 ) (2.37 ( 0.34) × 10-10 (cm3 molecule-1 s-1
)
a (1σ from the average.
D. Dependence on Third Body and Pressure. The results
of previous work suggested that k1 might exhibit a small pressure
dependence.6 To investigate this possibility, experiments were
carried out over a modest pressure range and in the presence of
a monatomic gas, Ar, and a polyatomic molecule, CF4. CF4 was
chosen as a collision partner because polyatomic molecules are
efficient at removing internal energy from highly excited
molecules.45 It also might enhance the vibrational relaxation of
NO(v), which could interfere in the determination of k1, as just
discussed in the previous section. Furthermore, it is unlikely to
react with CN and does not absorb at 193 nm. As noted
previously, NO(0) could not be reliably detected in the present
experiments, but other experiments in this laboratory indicated
that CF4 was about as efficient as Ar at vibrational relaxation
of NO, so it did not prove to be an efficient quencher of NO(v).
However, CF4 was found to enhance the vibrational relaxation
of NCO, as indicated by at least a factor of 2 increase in the
rate of appearance of NCO(0010) when Ar was replaced by CF4.
The results for the determination of k1 with Ar and CF4 as
carrier gas are summarized in Tables 3 and 4, respectively, and
are presented in Figure 5. The measurements of k1 were carried
out over a pressure range of 1.3-7.2 Torr in Ar and 1.6-3.9
Torr in CF4 with the partial pressure of O2 varying between
0.07 and 0.5 Torr. The dependence of k1 on O2 was also
adduct dissociates back to reactants rather than forward to
products and the overall rate constant decreases. Furthermore,
these entropic effects cause channel 7b to become dominant at
higher temperatures. Under these circumstances, the influence
of NO(v) would be expected to be similar to an increase in
temperature and NO(v) would be expected to react with a
smaller rate constant than NO(0). According to the RRKM
theory of unimolecular reactions, the initial vibrational energy
in NO would be rapidly randomized within the OCNNO adduct,
thus favoring redissociation to reactants rather than passage
through the tight transition states to products.
Although NO(v) should not react more rapidly with NCO
than NO(0), several calculations were performed to explore the
consequences of NO(v) on the determination of k1. A worst-
case scenario was adopted in that all of the NO produced in
reactions 1c and 4b was assumed to be a single vibrationally
excited species that reacted with NCO with a rate constant, kv7,
and was relaxed by O2 and Ar with the experimental32,33
NO(1) vibrational relaxation rate constants. This value for k12
substantially under estimates the vibrational relaxation of NO(v)
in the system because the vibrational relaxation of NO(v) by
O2 has been found33 to increase by a factor of 20 for V ) 1-7.
Thus, the results of the simulations provide a lower bound for
kv7. For the experimental run shown in Figure 3, the value
found for kv7 ranged from 5.7 × 10-11 for k1 ) 2.4 × 10-10 to
5.6 × 10-10 for k1 ) 6.6 × 10-11, in units of cm3 molecules-1
s.-1 Similar results were found for other simulations. It was
concluded that for NO(v) to account for the observed NCO time
dependence, the rate of kv7 would need to be substantially
larger than a hard sphere collision rate between NO and NCO,
a highly unlikely situation.
investigated by varying the partial pressure of O2, PO , at a fixed
total pressure. These results are displayed in Figure 5a. As can
be seen from the figure, within the scatter of the measurements,
2
the results are independent of PO . This experiment is also a
2
good indication that NO(v) had no effect on the determination
of k1 because k12PO changed by almost an order of magnitude
2
in these experiments and O2 was the predominant collision
partner for relaxation of NO(v).
From Figure 5b,c, it appears that k1 increases as the pressure
of the carrier gas increases; however, within the scatter in the
measurements, indicated by the (1σ error bars, the measure-
ments are independent of pressure. With Ar present, the value

Rate Constant for the NCO(X2Π) + O(3P) Reaction
J. Phys. Chem. A, Vol. 107, No. 23, 2003 4631
Figure 5. k1 independence (a) from O2 and likely NO(v), see text.
The total pressure was constant at 1.68 Torr, and the PO2 varied. Each
data point is the average of 3-5 measurements of k1 obtained by varying
the ArF fluence, and the error bars are (1σ from the average. The
dashed line is the average of the data weighted by the number of
measurements. Panel b provides the summary of the data for the
determination of k1 with Ar as carrier gas. Each data point is the average
of 3-5 measurements of k1, as in panel a. The dashed line is the average
of the data weighted by the number of measurements, giving k1 ) (1.94
( 0.30) × 10-10 cm3 molecule-1 s.-1 The data indicate that k1 is
independent of Ar pressure. Panel c provides the summary of the data
for the determination of k1 with CF4 as the carrier gas. As in panel b,
the average of the data weighted by the number of measurements of k1
gives k1 ) (2.37 ( 0.34) × 10-10 cm3 molecule-1 s.-1 The data indicate
that k1 is independent of CF4 pressure.
Figure 6. The temporal dependence of CN concentration determined
(a) from monitoring the R1(14.5) transition and (b) from monitoring
the R1(4.5) transition. The conditions of the experiment were PAr
)
3.15, PO ) 0.423, and P(CN)2 ) 0.190 Torr. Panel c shows the ratio of
2
the absorbance profiles used to calculate the CN concentration profiles
in panels a and b. The first point corresponds to a rotational temperature
of ∼1000 K, and the plateau region corresponds to a rotational
temperature of 305 K. The temperature of the reaction vessel was
292 K.
shown in Figure 6c. From this ratio and the CN R1(J) line
strengths, an estimate of the rotational temperature describing
the population in the two levels can be made. Following an
initial transient, the ratio of these absorbances reaches a plateau
corresponding to a rotational temperature of 305 K.
of k1 was determined to be (1.94 ( 0.30) × 10-10 cm3
molecule-1 s-1, and with CF4, the value of k1 was found to be
(2.34 ( 0.34) × 10-10 cm3 molecule-1 s-1, both at a temperature
of 292 ( 2 K. Within the scatter of these two measurements,
the results are equal, and the average of these two measurements
gives k1 equal to (2.14 ( 0.31) × 10-10 cm3 molecule-1 s,-1
independent of both pressure and the nature of the third body.
The quoted uncertainty is (1σ from the average value.
E. Comparison of NCO Concentration and CN Concen-
tration. As discussed in section III.A, the temporal dependences
of both NCO concentration and concentration of CN radicals
were monitored under the same experimental conditions. As
noted previously, the determination of CN concentration was
intended to serve as a consistency check on the measured NCO
concentration. This is important because the value of k1 depends
on the absolute concentration of NCO. In addition, two rotational
transitions of CN were monitored to provide an estimate of the
temperature in the photolysis region. The temporal dependence
of CN concentration calculated from the absorbance profiles
for the CN(A2Π r X2Σ) (2-0) R1(14.5) and R1(4.5) transitions
for the same experimental run as in Figure 3 is shown in Figure
6a,b. A plot of the ratio of these two absorbance profiles is
Generally, the CN rotational temperature varied between 300
and 330 K. The reason for the difference between the measured
rotational temperature and the temperature of the reaction vessel
is not known. An estimate of the temperature rise from the
absorbed photolysis energy can be made. Using the 193 nm
absorption coefficient46 for (CN)2 (1.1 × 10-19 cm2 molecule-1
)
and a P(CN) of 0.2 Torr, the maximum used in the experiments,
2
we calculated the attenuation of the photolysis laser intensity
to be 10% over the 140 cm long photolysis zone, giving a
maximum temperature rise of 1 K from the initial photodisso-
ciation step and the energy released in reaction 1. A further
temperature rise of 5 K was estimated from the subsequent NCO
+ O chemistry, according to the calculated integrated RCF
factors for the various reactions. Although care was taken to
ensure that the CN probe laser frequency was tuned to the peak
in the Doppler profile, uncertainty in this step would tend to
favor a higher rotational temperature especially because the CN
absorbances were large, varying between 1 and 2.5 for the lower
J transition. The 193 nm photolysis of (CN)2 produces an initial
rotational state distribution47 that has considerable rotational
excitation, with the peak of the J distribution around J ) 25.5
and a rotational temperature of approximately 2200 K. It is

4632 J. Phys. Chem. A, Vol. 107, No. 23, 2003
Gao and Macdonald
possible that quenching of rotational levels with large J values
contributes to the population into the lower levels at a rate slower
than the expected rotational relaxation rate for low J states
among themselves, giving rise to an apparently higher rotational
temperature, that is, an excess of population in the monitored
rotational state having the larger J value.
As discussed in section III.B., in the model simulations, [CN]0
was varied until the model [NCO]t agreed within 1% with the
experimentally observed [NCO]t value; thus, the simulations
returned a value of [CN]0 that can be compared to the
experimental measurement. However, there is some uncertainty
as to the best way to evaluate [CN]0 from the experimental
profiles shown in Figure 6a,b. Using a nonlinear least-squares
analysis, the CN concentration temporal profiles were fit to the
sum of two decaying exponential terms, having negative and
positive preexponential factors. A zero-order interpretation of
these terms is that the negative preexponential term describes
the formation of CN(J) from rotational relaxation of excited
rotational levels,47 krise, and the positive preexponential decay
describes the reaction of CN(J) with O2, kdecay. In a simple two-
step model, given by [CN]0 f [CN(J)] + O2 f products, the
coefficient of the positive exponential term is simply [CN]0 if
krise . kdecay. This suggests that the coefficient of the positive
exponential term should be identified with [CN]0. However,
there is some uncertainty in the determination of this preexpo-
nential factor because of the rapidly changing absorbance in
the first few microseconds of the CN profile, as shown in Figure
6. In this transient time interval, indicated by the rapid change
in the absorbance ratio in Figure 6c, not only is the rate constant
for reaction k4 changing and approaching its room temperature
value, but simultaneously both translational and rotational
relaxation are occurring. The influence of these transient events
on the determination of the preexponential factor for the kdecay
term is not easy to determine. Alternately, the decay could be
fit to a single-exponential term starting at sometime after this
transient interval has passed. However, in this case the deter-
mination of the starting time for the extrapolation and, also,
the correct t ) 0 are ambiguous, again because of the transients
just noted. The determination of [CN]0 by both methods gave
similar results with the single exponential fit method giving
consistently larger values (5%-10%). The two exponential term
method was adopted here because of its more unbiased
Figure 7. The [CN]0model/[CN(V)0)]e0xp is shown as a function of
photolysis laser fluence (a) with Ar as the carrier gas and (b) with CF4
as the carrier gas. The average of all the experiments is shown by the
dashed line. The arrow indicates the most recent experimental measure-
ment.47 The results indicate that within the scatter of the measurements
the NCO concentration was determined accurately.
initial transient region likely had more influence on the
measurement of k4 in the CF4 experiments.
Only the ground vibrational state of CN could be monitored
in the present experiments; however, vibrationally excited
CN(V)1, 2) can also be produced in the 193 nm photolysis of
(CN)2. The most recent CN vibrational state distribution
determined47 by North and Hall is 0.87 ( 0.02, 0.13 ( 0.02,
and 0.003 ( 0.001 for V ) 0, 1, and 2, respectively. The
ratios of [CN]0model/[CN(V)0]0exp, where [CN]0model was calcu-
lated in the computer simulations described in section III.B,
and [CN(V)0)]e0xp was determined using the preexponential
factor of the kdecay exponential term, are shown in Figure 7,
part a for Ar and part b for CF4, and the average values of
[CN]0model/[CN(V)0)]0exp were found to be 1.31 ( 0.10 and
1.39 ( 0.12 in Ar and CF4 carrier gases, respectively. When
the CN vibrational distribution measured47 by North and Hall
is used, the predicted value should be 1.15 ( 0.04. The
agreement between the model predictions of the [CN]0 and the
experimental values is not perfect, but on the other hand, they
are in agreement within the experimental uncertainty by (1σ
for Ar and (2σ for CF4. The experimental determination of
[CN]0 presented in Figure 7 indicates that the [CN]0 needed to
reproduce the NCO concentration used in the computer simula-
tions of the NCO concentration profiles was within 15%-25%
of the measured value. This is taken as an independent
confirmation that the NCO concentration determination was
correct at least within the experimental uncertainty in the
measured NCO peak absorption coefficient, Table 1.
implementation. With increasingly larger values of kdecay
)
k4PO , the transient region becomes a larger fraction of the
2
complete CN decay interval, and as a result, the experimental
determination of [CN]0 becomes more uncertain.
Although the intent of monitoring CN was to compare the
measured [CN]0 to the value predicted in the model calculations
and, hence, to provide a check on the measured NCO concen-
tration, it also provided an estimate of k4, assuming kdecay
)
k4PO . Indeed, the integrated RCFCN analysis indicated that under
2
all conditions reaction 4 accounted for more than 99% of the
removal processes for CN. With Ar and CF4 as carrier gas, k4
was found to be (2.31 ( 0.12) × 10-11 [35] and (1.95 ( 0.15)
× 10-11 [20] cm3 molecule-1 s-1, respectively, at a temperature
of 292 ( 1 K, where the numbers in brackets indicate the
number of measurements. Reaction 4 has been measured in
several laboratories,5 and a value of (2.42 ( 0.19) × 10-11 cm3
molecule-1 s-1 has been recommended for 292 K. The value
for k4 determined in Ar as the carrier gas is in good agreement
with the recommended value; however, that measured in CF4
is not. The reason for this discrepancy is not quite clear, but on
IV. Discussion
A. Error Analysis. There are several sources of error
contributing to the uncertainty in the determination of k1. The
first is the determination of the absolute concentration of the
average, the PO was higher in the CF4 experiments, and the
2

Rate Constant for the NCO(X2Π) + O(3P) Reaction
J. Phys. Chem. A, Vol. 107, No. 23, 2003 4633
TABLE 5: Summary of the Average Fractional Uncertainty
in the Fitted k1 and the Average Fractional Removal of NCO
by O and NO
considerations apply to the loss of species by diffusion. The
average removal rate by diffusion contributed 10% to the total
removal of NCO. The uncertainty in the diffusion rate was
estimated to be (20%, so the diffusion process also contributed
a -2% uncertainty to the determination of k1.
avg
avg
carrier
avg
gas (∆k1/k1 SD ∫RCFNOCO/total SD ∫RCFNCO/total SD
NO
Ar
CF4
0.15
0.14
0.09
0.09
0.66
0.72
0.14
0.07
0.15
0.11
0.035
0.015
The total uncertainty in the determination of k1 can be
summarized as follows: spectroscopic,15%; random scatter in
the determination of k1, 15%; uncertainty in the rate constants
directly influencing the determination of k1, 4%; determination
of partial pressures, 2%. Combining the measurements of k1
for the two carrier gases gives k1 equal to (2.1 ( 0.76) × 10-10
cm3 molecule-1 s,-1 at 292 K, independent of carrier gas and
pressure, where the quoted uncertainty reflects both systematic
and random errors.
B. Comparison with Previous Work. The available data6-12
for k1 is shown in Figure 8 as a function of temperature. As is
evident from the figure, the determination of k1 in the present
work is substantially larger than previous measurements near
300 K, although the results do just overlap those of Becker et
al.6 if the absolute error bars are extended to the (2σ level of
uncertainty. Furthermore, the previous suggestion6 that k1
exhibited a slight pressure dependence was not borne out in
the current work. Within the scatter of the measurements, k1
was found to be independent of both the nature of the third
body collision partner and pressure, as shown in Figure 5 and
Tables 3 and 4.
NCO radical. The details of the experiment carried out to
measure the σpk(ν) for the NCO transitions used in this work
will be presented elsewhere;15 however, the experimental
uncertainties in these measurements have been summarized in
Table 1. Two other effects related to the spectroscopy of NCO
that could influence the determination of the NCO concentration
are the Herman-Wallis effect and pressure broadening. Both
effects are presumed to be small under the present experimental
conditions. In molecules similar to NCO, NO, CO2, and N2O,
the Herman-Wallis effect contributes less than 2% to the line
strength for similar transitions.48,49 With increasing pressure,
pressure broadening causes a reduction in σpk(ν) from the
Doppler value and would result in an underestimation of the
NCO concentration, eq 2 and, hence, an overestimation of k1.
Indeed, the trend in k1 as a function of pressure for both Ar
and CF4, parts b and c of Figure 5, respectively, appears to be
in agreement with this prediction; however, the scatter in the
measurements is sufficient to obscure such behavior. The
uncertainty in the determination of σpk(ν) of (1σ results in an
uncertainty in the determination of k1 of -1σ. Note that the
uncertainty in the determination of NCO concentration does not
introduce any further uncertainty into the O concentration
because of the initial stoichiometric relationship between the
[NCO]0 and [O]0 initiated in reaction 4a.
The other factors influencing the uncertainty in the determi-
nation of k1 are the goodness-of-fit for the computer-generated
NCO concentration profiles to the experimental ones, and the
uncertainty in the rate constants used in the model simulations.
Fortunately, the kinetic scheme given in Table 2 is relatively
simple, and there are only three major processes contributing
to the removal of NCO, reactions 1 and 7 and diffusion. As
already discussed in section III.C, the NCO radical could react
more rapidly with NO(v); however, it was argued there that
this possibility was unlikely. The computer program used to
determine k1 provided an estimate of the goodness-of-fit for k1
(see the insert in Figure 3) and an RCF analysis, as discussed
in section III.B. As noted there, the integrated RCFNJ CO’s
provided a direct means of measuring the removal of NCO by
reaction with species J or removal by diffusion. For each
experiment, the fractional uncertainty in the fitted k1 and the
fractional contribution for the removal of NCO by O, NO, and
diffusion were tabulated. The average values and the standard
deviation in these quantities are listed in Table 5. From this
table, it can be seen that on average the value of k1 that was
found to best describe the NCO concentration temporal profile
was determined to within (15% at the 68% confidence level.
Note that this average uncertainty is the same as the standard
deviation in the scatter of the measurements for k1, Tables 3
and 4, which it should be if there are no other large sources of
random error.
As is evident from Figure 8, the low-temperature measure-
ment of k1 found in this work and the high-temperature data
show that k1 exhibits a negative temperature dependence. A non-
linear least-squares fit to the value of k1 measured in this work
and the high-temperature measurements from Prof. Hanson’s
laboratory10,11 gives k1 equal to 1.96 × 10-10(300/T)0.50 cm3
molecule-1 s.-1 This fit is illustrated by the dotted curve in
Figure 8. Interestingly, the temperature dependence of the rate
constant for the related reaction, CN + O2, also exhibits a similar
T-0.5 dependence.5 Reactions 1 and 4 can occur on the same
global CNOO PES but of course sample different regions. The
CN + O2 reaction leading to the NCO + O products occurs
through the C and O atom interaction, while the NCO + O
atom reaction is likely dominated by the N and O atom
interaction. Mohammad et al.50 have suggested that the CN +
O2 reaction channel leading to NO + CO products arises from
an exit channel interaction in which the rotational motion of
the departing NCO and O fragments results in a secondary
encounter between the N and O atom leading to the NO + CO
products. The large value for k1 measured in the present work
indicates that the chemical forces between the O atom and N
atom of NCO are strong and supports the interesting conjecture
of Mohammad et al.
There are several other important observations on the NCO
+ O reaction system. Approximating the collision diameter of
NCO to that of CO2, we estimate a hard-sphere collision rate
between NCO and O to be 1.8 × 10-10 cm3 molecule-1 s-1 at
292 K. Thus, every encounter between NCO and O within their
hard-sphere collision radius leads to reaction. These collisions
can occur on multiple PESs, involving both the electronic and
spin manifolds. Assuming Cs symmetry and neglecting spin-
orbit interactions, on the reactant side, NCO(2Π) and O(3Pg)
correlate with 3(4,2A′ + 4,2A′′) PESs, while on the product side,
the following correlations exist: the N(2Du) + CO2(1Σ+) product
channel correlates to 3(2A′′) + 2(2A′); the N(4Su) + CO2(1Σ+)
As is shown in Table 5, the average contribution of reaction
7 to the total NCO removal was 15% with Ar and 11% with
CF4 as carrier gas. Reaction 7 has been investigated by numerous
workers,27,29,34,35 and the average value for k7 is (3.6 ( 0.5) ×
10-11 cm3 molecule-1 s-1, where the uncertainty is (1σ. Thus,
on average, the 15% uncertainty in the literature value for k7
contributes -2% uncertainty to the determination of k1. Similar
4
channel correlates to A′′; the NO(2Π) + CO(1Σ+) channel
2
2
-
correlates to A′′ + A′. (Note that the CN(2Σ+) + O2(3Σu
)
reaction correlates to 4,2A′′ PESs.) Of course, in general C1

4634 J. Phys. Chem. A, Vol. 107, No. 23, 2003
Gao and Macdonald
Figure 8. The temperature dependence for k1. The error bars indicate an estimate of the absolute errors in the experiment, except for the work of
Becker et al.6 in which they indicate the scatter in the measurements. The dotted line is a fit of the room-temperature measurement of this work,
Louge and Hanson,10 and Mertens et al.11 of the form k1 ) A(300/T)n, where A ) 1.96 × 10-10 and n ) 0.50. The various measurements are (b)
this work, (9) Becker et al.,6 (2) Schacke et al.,7 (1) Louge and Hanson,10 ([) Mulvihill and Phillips,12 (- - -) Higashihara et al.,9 (\) Lifshitz
and Frenklach,8 and (- ‚ -) Mertens et al.11
symmetry, the A′ and A′′ symmetry labels are lost, but at least,
conceptually, it is easier to view the collision confined to a plane.
There have been no theoretical calculations undertaken to
explore the initial interaction between NCO and O; however,
simple electronic orbital considerations can provide some
reactants or to the N(2D) + CO2 channel, which was calculated
to be 30 kJ mol-1 (69 kJ mol-1 thermodynadically) lower in
energy. The competition between these two processes will
depend critically on the exact nature of the reaction path taken
in each case. It is expected that the reaction path leading to the
formation of adduct 6 (the formation of the N(2D) + CO2
channel) would be significantly more constrained than the one
along the path leading to the more exothermic NO + CO
channel, and the latter should be strongly favored. The product
channels for reaction 1 have not been determined experimentally
or examined theoretically; however, channel 1c is expected to
dominate. Nevertheless, if channel 1a is significant, the reaction
of N(2D) with O2 would generate NO(v) + O and could lead to
an over estimation of k1 because of the increased O and NO
concentrations.
2
insight. The most attractive interaction should occur on a A′′
PES described by a bonding interaction between one of the
singly occupied p-orbitals on the O atom approaching the singly
occupied p-orbital on the N atom, lying in the plane of the four
atoms. If the singly occupied N atom p-orbital is perpendicular
to the four atom plane, the PES is of 2A′ symmetry and should
be more repulsive because of electron-electron repulsion
between the in-plane singly occupied O atom p-orbital and the
now in-plane bonding N-C p-orbitals. On the lowest-lying 2A′′
PES, the interaction should proceed with little or no barrier
because there is nothing to impede the direct formation of a
chemical bond between the N and O atoms. This PES is likely
the same 2A′′ PES on which the CN + O2 reaction occurs and
has been described recently by Qu et al.13 at the B3LYP level
of theory for geometries and the CCSD(T) level of theory for
energies. Their Figure 3 can be used to extend the reaction
The theoretical calculations of Qu et al.13 dealing with the
CN + O2 4A′′ PES indicate that the interaction between CN
and O2 is mostly repulsive. This is in agreement with other
work.51 There are no theoretical descriptions for the interaction
4
between NCO and O on the global CNOO A′′ PES, and it is
2
sequence on this most attractive A′′ PES. (In the following,
assumed that the interaction will likely be repulsive or at least
the designations of Qu et al.13 for transition states and stationary
points will be used and indicated by bold type.) The initial
attractive interaction between the O and N atom should lead
directly to the most deeply bound intermediate on the 2A′′ PES,
structure 3, having a zigzag OCNO arrangement of atoms. A
small barrier of 14 kJ mol-1 through transition state TS3/B leads
directly to the NO + CO product channel (B). Other reaction
paths leading from adducts formed by the O atom approaching
the O end of NCO, structures 1 and 6, can also be formed
without barriers but connect to the NO + CO product channel
over transition states that lie above the NCO + O energy
asymptote and do not contribute to reaction at low temperatures.
Another possible channel for the NCO + O reaction on the
2A′′ PES is the N(2D) + CO2 channel. Again referring to Figure
3 of Qu et al.,13 the O atom can approach the central C atom of
NCO without a barrier to form adduct 6, having a C2V N-COO
structure. This adduct can dissociate back to the NCO + O
2
not as attractive as the A′′ PES.
There are still 10 other PESs within both the doublet and
quartet spin manifolds. Statistically, the collisions between NCO
and O should occur equally within the A′′ and A′ electronic
manifolds with 2/3 of the collisions occurring within the quartet
spin manifold; however, k1 is approximately the hard-sphere
collision rate at 292 K. Clearly, intersystem crossing and internal
conversion must be facile in this system if the experimental
measurement reported on here is correct. There must be some
mechanism to promote these processes. There are two possibili-
ties. The formation of long-lived adducts could allow the
crossing seams between electronic and spin manifolds to be
sampled multiple times.52,53 Alternately, these transitions could
occur at long range where the separations between the various
PESs are small and the newly forming spin quantum has not
been fully developed. In any case, detailed theoretical investiga-

Rate Constant for the NCO(X2Π) + O(3P) Reaction
J. Phys. Chem. A, Vol. 107, No. 23, 2003 4635
(11) Mertens, J. D.; Dean, A. J.; Hanson, R. K.; Bowman, C. T. Symp.
(Int.) Combust., [Proc.] 1992, 24, 701.
(12) Mulvihill, J. N.; Phillips, L. F. Symp. (Int.) Combust., [Proc.] 1975,
15, 1113.
tions of the influence of multiple PESs will be needed to address
this issue for the NCO + O system and other radical-radical
systems.54,55
It has recently been shown56 that the large reaction exother-
micity available in many radical-radical reactions can lead to
new dynamical features influencing product branching ratios.
Product channels can be produced without a transformation
through a localized transition-state configuration, and this direct
dynamics mechanism can be responsible for a large number of
reactive trajectories. Detailed theoretical calculations will be
necessary to determine whether this direct dynamics mechanism
also occurs in the NCO + O system.
(13) Qu, Z.-W.; Zhu, H.; Li, Z.-S.; Zhang, X.-K. Chem. Phys. Lett. 2001,
353, 304.
(14) Rim, K. T.; Hershberger, J. F. J. Phys. Chem. A 1999, 103, 3721.
(15) Decker, B. K.; Macdonald, R. G., manuscript in preparation.
(16) He, G.; Tokue, I.; Harding, L.; Macdonald, R. G. J. Phys. Chem.
A 1998, 102, 7653.
(17) Kroto, H. W. Molecular Rotational Spectra; Dover: New York,
1992.
(18) Decker, B. K.; Macdonald, R. G., manuscript in preparation.
(19) Knowels, P. J.; Werner, H.-J.; Hay, P. J.; Cartwright, D. C. J. Chem.
Phys. 1988, 89, 7334.
(20) He, G.; Tokue, I.; Macdonald, R. G.; J. Chem. Phys. 1998, 109,
6312.
(21) Sablier, M. S.; Fujii, T. Chem. ReV. 2002, 102, 2855.
(22) Martin, J. M. L.; Taylor, P. R.; Francois, J. P.; Gijbels, R. Chem.
Phys. Lett. 1994, 226, 475.
(23) Tsang, W. J. Phys. Chem. Ref. Data 1992, 21, 753.
(24) Titarchuk, T. A.; Halpern, J. A. Chem. Phys. Lett. 1995, 232, 192.
(25) Yang, D. L.; Lin, M. C. In The Chemical Dynamics and Kinetics
of Small Radicals; Liu, K., Wagner, A., Eds.; World Scientific: Singapore,
1995; Part I.
(26) Brownsword, R. A.; Hancock, G.; Heard, D. E. J. Chem. Soc.,
Faraday Trans. 1997, 93, 2473.
(27) Becker, K. H.; Kurtenbach, R.; Schmidt, F.; Wiesen, P. Ber. Bunsen-
Ges. Phys. Chem. 1997, 101, 128.
(28) Cooper, W. F.; Park, J.; Hershberger, J. F. J. Phys. Chem. 1993,
97, 3283.
(29) Wategaonkar, S.; Setser, D. W. J. Phys. Chem. 1993, 97, 10028.
(30) Gao, Y.; Decker, B. K.; Macdonald, R. G. Work in progress.
(31) Lee, J. H.; Michael, J. V.; Payne, W. A.; Stief, L. J. J. Chem. Phys.
1978, 69, 3069.
(32) Green, B. D.; Caledonia, G. E.; Murphy, R. E.; Robert, F. X. J.
Chem. Phys. 1982, 76, 2441.
(33) Wysong, I. J. J. Chem. Phys. 1994, 101, 2800.
(34) Juang, D. Y.; Lee, J.-S.; Wang, N. S. Int. J. Chem. Kinet. 1995,
27, 1111.
(35) Atakan, B.; Wolfrum, J. Chem. Phys. Lett. 1991, 178, 157.
(36) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T.;
Numerical Recipes; Cambridge University Press: Cambridge, U.K., 1988;
Chapter 15.
(37) Macdonald, R. G.; Sonnenfroh, D. M.; Liu, D.-J.; Liu, K. Can. J.
Chem. 1994, 72, 660.
(38) Philips, L. F.; Smith, I. W. M.; Tukett, R. P.; Whitham, C. J. Chem.
Phys. Lett. 1991, 183, 254.
V. Conclusion
The rate constant for the NCO(X2Π) + O(3P) reaction has
been measured to be (2.1 ( 0.76) × 10-10 cm3 molecule-1 s-1
at a temperature of 292 ( 2 K, where the error bars account
for both random and systematic error. The rate constant was
found to be independent of both pressure over the pressure range
of 1.5-7.6 Torr and the nature of a third-body collision partner.
The measured k1 is slightly larger than an estimate of the hard-
sphere collision rate constant between NCO and O and indicates
that intersystem crossing and internal conversion must be facile
in this system. The expected dominant product channel 1c, NO
+ CO, correlates with the doublet manifold; however, adiabati-
2
cally, /3 of the collisions initially start out in the quartet-spin
manifold. The identification of the product channels for this
reaction would confirm the speculation of the importance of
nonadiabatic effects in simple radical-radical reactions. Further
theoretical work on the nature of the complete 3(4,2A′′ + 4,2A′)
system of PESs would also be very useful.
The result of this work was combined with high-temperature
shock tube measurements to determine the temperature depen-
dence of k1 to be (1.9(300/T)0.50) × 10-10 cm3 molecule-1 s-1
temperature dependence as the CN + O2 reaction, that is, T-0.5
.
The NCO + O rate constant appears to have the same general
.
(39) Sauder, D. G.; Dipti, P.-M.; Dagdigian, P. J. J. Chem. Phys. 1991,
95, 1696.
(40) Hancock, G.; McKendrick, K. G. Chem. Phys. Lett. 1986, 127, 125.
(41) Astbury, C. J.; Hancock, G.; McKendrick, K. G. J. Chem. Soc.,
Faraday Trans. 1993, 89, 405.
(42) Fernandez, J. A.; Husain, D.; Sanchez Rayo, M. N.; Castano, F. J.
Chem. Phys. 1997, 106, 7090.
(43) Macdonald, R. G.; Liu, K. J. Chem. Phys. 1993, 98, 3716.
(44) Lin, M. C.; He, Y.; Melius, C. F. J. Phys. Chem. 1993, 97, 9124.
(45) Holbrook, R. Unimolecular Reactions; Wiley-Interscience: London,
1972.
Acknowledgment. This work was supported by the U.S.
Department of Energy, Office of Basic Energy Sciences,
Division of Chemical Sciences, Geosciences, and Biosciences,
under Contract No. W-31-109-ENG-38.
References and Notes
(1) Warnatz, J.; Maas, U.; Dibble, R. W. Combustion: Physical and
Chemical Fundamentals, Modeling and Simulation, Experiments, Pollution
Formation; Springer: Berlin, 1995.
(46) Balla, R. J.; Pasternack, L. J. Phys. Chem. 1987, 91, 73.
(47) North, S. W.; Hall, G. E. J. Chem. Phys. 1997, 106, 60.
(48) Pine, A. S.; Maki, A. G.; Chou, N.-Y. J. Mol. Spectrosc. 1985,
114, 132.
(49) Devi, V. M.; Benner, D. C.; Rinsland, C. P.; Smith, M. A. H. J.
Quant. Spectrosc. Radiat. Transfer 1998, 60, 741.
(50) Mohammad, F.; Morris, V. R.; Fink, W. H.; Jackson, W. M. J.
Phys. Chem. 1993, 97, 11590.
(2) Miller, J. A.; Bowman, C. T. Prog. Energy Combust. Sci. 1989,
15, 287.
(3) Bowman, C. T. In Pollutants from Combustion; Vovelle, C., Ed.;
Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000.
(4) Glarborg, P.; Miller, J. A. Combust. Flame 1994, 99, 475.
(5) Smith, I. W. M. In The Chemical Dynamics and Kinetics of Small
Radicals; Liu, K., Wagner, A., Eds.; World Scientific: Singapore, 1995;
Part I.
(51) Vallance, C.; Maclagan, R. G. A. R.; Phillips, L. F. Chem. Phys.
Lett. 1996, 250, 59.
(6) Becker, K. H.; Kurtenbach, R.; Schmidt, F.; Wiesen, P. Combust.
Flame 2000, 120, 570.
(52) Tully, J. C. J. Chem. Phys. 1971, 62, 1893.
(53) Phillips, L. F. J. Phys. Chem. A 1998, 102, 31.
(54) Graff, M. M.; Wagner, A. F. J. Chem. Phys. 1990, 92, 2423.
(55) Takayanagi, T.; Kurosaki, Y.; Sato, K.; Misawa, K.; Kobayashi,
Y.; Tsunashima, S. J. Phys. Chem. A 1999, 103, 250.
(56) Macy, T. P.; Diaz, R. R.; Heard, D.; Leone, S. R.; Harding, L. B.;
Klippenstein, S. J. J. Phys. Chem. A 2001, 105, 8361.
(7) Schacke, H.; Schmatjko, K.; Wolfrum, J. Arch. Procesow Spalania
1974, 5, 363.
(8) Lifshitz, A.; Frenklach, M. Int. J. Chem. Kinet. 1980, 12, 159.
(9) Higashihara, T.; Kuoda, H.; Saito, K.; Murakami, I. Combust. Flame
1985, 61, 167.
(10) Louge, M.; Y.; Hanson, R. K. Symp. (Int.) Combust., [Proc.] 1985,
20, 665.