Kinetics and mechanism of the NCN + NO2 reaction studied by experiment and theory

Article abstract of DOI:10.1021/jp805311u

The rate constant for the NCN + NO₂ reaction has been measured by a laser photolysis/laser-induced fluorescence technique in the temperature range of 260-296 K at pressures between 100 and 500 Torr with He and N2 as buffer gases. The NCN radical was produced from the photolysis of NCN ₃ at 193 nm and monitored by laser-induced fluorescence with a dye laser at 329.01 nm. The rate constant was found to increase with pressure but decrease with temperature, indicating that the reaction occurs via a long-lived intermediate stabilized by collisions with buffer gas. The reaction mechanism and rate constant are also theoretically predicted for the temperature range of 200-2000 K and the He and N² pressure range of 10^-4 Torr to 1000 atm based on dual-channel Rice-Ramsperger-Kassel-Marcus (RRKM) theory with the potential energy surface evaluated at the G2M//B3LYP/6-311+G(d) level. In the low-temperature range (<700 K), the most favorable reaction is the barrierless association channel that leads to the intermediate complex (NCN-NO₂). At high temperature, the direct O-abstraction reaction with a barrier of 9.8 kcal/mol becomes the dominant channel. The rate constant calculated by RRKM theory agrees reasonably well with experimental data.

Full text of DOI:10.1021/jp805311u

J. Phys. Chem. A 2008, 112, 10185–10192
10185
Kinetics and Mechanism of the NCN + NO2 Reaction Studied by Experiment and Theory
Tsung-Ju Yang,† Niann S. Wang,*,† L. C. Lee,‡ Z. F. Xu,§ and M. C. Lin*,†,§
Department of Applied Chemistry and Center for Interdisciplinary Molecular Science, Chiao Tung UniVersity,
Taiwan 30010, Taiwan, Department of Electrical and Computer Engineering, San Diego State UniVersity,
San Diego, California 92182, and Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322
ReceiVed: June 16, 2008; ReVised Manuscript ReceiVed: August 19, 2008
The rate constant for the NCN + NO2 reaction has been measured by a laser photolysis/laser-induced
fluorescence technique in the temperature range of 260-296 K at pressures between 100 and 500 Torr with
He and N2 as buffer gases. The NCN radical was produced from the photolysis of NCN3 at 193 nm and
monitored by laser-induced fluorescence with a dye laser at 329.01 nm. The rate constant was found to increase
with pressure but decrease with temperature, indicating that the reaction occurs via a long-lived intermediate
stabilized by collisions with buffer gas. The reaction mechanism and rate constant are also theoretically predicted
for the temperature range of 200-2000 K and the He and N2 pressure range of 10-4 Torr to 1000 atm based
on dual-channel Rice-Ramsperger-Kassel-Marcus (RRKM) theory with the potential energy surface
evaluated at the G2M//B3LYP/6-311+G(d) level. In the low-temperature range (<700 K), the most favorable
reaction is the barrierless association channel that leads to the intermediate complex (NCN-NO2). At high
temperature, the direct O-abstraction reaction with a barrier of 9.8 kcal/mol becomes the dominant channel.
The rate constant calculated by RRKM theory agrees reasonably well with experimental data.
1. Introduction
This result, in turn, proves that NCN is indeed an important
intermediate in hydrocarbon/air combustion media.
The cyanonitrene (NCN) radical has been observed by optical
emission and presumed as an intermediate in active-nitrogen
hydrocarbon flames long ago by Jennings and Linnett.1 This
radical was detected in a microwave discharge of a CF4/N2/He
mixture by laser-induced fluorescence (LIF) by Smith et al.,2
who further suggested that this radical could play a significant
role in the combustion of nitramine propellants. The LIF
technique is a sensitive method to detect this radical in
combustion media, and it is applied to kinetic measurement.
The importance of how this radical plays in hydrocarbon
combustion is well recognized only after Moskaleva et al.3,4
revealed by a computational study that it can be produced by
the spin-conserved reaction
Because NCN is a dominant prompt NO formation intermedi-
ate, knowledge of its reaction mechanism and kinetics is needed
for understanding NO formation in the combustion process. For
instance, El bakali et al.8 and Lamoureux et al.9 have demon-
strated that the NO fractions observed in natural gas (a methane/
ethane/propane mixture) flames agree better with the prediction
if NCN is included in kinetic modeling. The kinetic data of
NCN were almost not known prior to the new prompt NO
formation mechanism put forth by Lin and co-workers3,4 in
2000, and the database continues to build up since then.
Extensive theoretical calculations for reactions with various
combustion species, such as C, H, CHx (x ) 1-3), CN, etc.,
have been reported by Moskaleva10 in her Ph.D. dissertation.
Baren and Hershberger11 measured the reaction rates of NCN
with NO, O2, C2H4, and NO2 in a He buffer gas by the
photolysis/LIF technique. The rate constant for the reaction with
NO was measured more extensively over the temperature range
of 298-573 K at varied He pressures, but for the other reactions,
only the upper limits were estimated at 298 K at a low He
pressure (<3 Torr). The reaction mechanisms of NCN with NO
and NS were investigated by Chen and Ho.12 Zhu and Lin have
CH + N2 f cyclic -C(H)NN- f HNCN f H + NCN
This reaction suggests that NCN is the primary product
leading to prompt NO formation in the hydrocarbon flame
zone.3,4 This suggestion was shortly confirmed by Smith,5 who
observed the presence of NCN in a methane/air flame. The
production of NCN from the above reaction has recently been
confirmed by Vasudevan et al.,6 who detected NCN by optical
absorption in heating mixtures of diketene/N2 and ethane/N2
behind reflected shock waves. Their experimental data conclude
that H + NCN is the dominant (and possibly the only) path for
the CH + N2 reaction. Recently, Harding et al.7 revisited the
kinetics of CH + N2 with multireference ab initio calculations.
They found that the rates of this reaction at varied temperatures
are higher than those calculated by Moskaleva and Lin.4 The
higher reaction rate, resulting from the predicted lower heat of
formation of NCN, agrees better with recent experimental data.6,7
13
recently investigated the oxidation rates of NCN by O2 and
O(3P)14 by ab initio calculations with molecular orbital and
transition state (TS) theory.
Recently, Huang et al.15 have extensively measured the rate
constants for the NCN + NO reaction in the presence of He
(40-600 Torr) and N2 (30-528 Torr) buffer gases in the
temperature range of 254-353 K using the photolysis/LIF
technique. The NCN radical was produced from the photodis-
sociation of NCN3 at 193 nm and monitored by LIF with a dye
laser at 329.01 nm. They also calculated the rate constants by
dual-channel Rice-Ramsperger-Kassel-Marcus (RRKM) theory
based on the potential energy surface (PES) derived by the G2M
* To whom correspondence should be addressed.
† Chiao Tung University.
‡ San Diego State University.
§ Emory University.
10.1021/jp805311u CCC: $40.75
2008 American Chemical Society
Published on Web 09/25/2008

10186 J. Phys. Chem. A, Vol. 112, No. 41, 2008
Yang et al.
method.15 The theoretical results compare reasonably well with
experimental data.
The NCN radical has also been known as an interstellar
species16 and a critical growth species in the synthesis of carbon
nitride (C3N4)17 as well; thus, its reaction kinetics, in general,
may also be relevant to such fields.
with fresh gas for each laser pulse, but it was in a semistatic
condition during the time frame of kinetic measurement. The
pressure of the system was measured with a Baratron gauge
(MKS 122A). The flow rates of reactants and buffer gas were
measured with a calibrated mass flowmeter (Tylan FM360). A
temperature-controlled fluid flowed through the jacket of the
reactor to maintain a constant reaction temperature ((2 K),
which was measured with a K-type thermocouple placed 5 mm
from the detection region.
The study on NCN reaction kinetics is now extended to the
reactant NO2, and the results are reported in this article. Because
NO2 is the final product of nitrogen oxidation, it is expected to
be present in most combustion media. The rate constant of the
NCN + NO2 reaction is certainly of interest in modeling
combustion processes. However, up to now only an upper limit
was given11 for the NCN + NO2 reaction at 298 K and low He
pressure (<3 Torr).
In our current study, the rate constants for NCN + NO2 were
measured under varied pressures of He and N2 (100-500 Torr)
in the temperature range of 260-296 K using the experimental
setup and the photolysis/LIF technique that we used for
measuring the NCN + NO rate constants.15 We also calculated
the reaction rate constants using the PES evaluated at the G2M//
B3LYP/6-311+G(d) level of theory for the reaction of both
NCN (3Σg-) and NO2 (2A1) in the ground state. The results of
our calculations are compared with measured experimental data.
The concentrations of the reactants were determined by
[A] ) 9.66 × 1018PFA ⁄ FTT (molecules ⁄ cm3)
where P is the reaction pressure (in Torr), T is the reaction
temperature (K), and FA and FT are the flow rates (in STP cm/
s, STP ) 273.15 K, 760 Torr) of reactant A and the total reaction
mixture, respectively.
The initial concentration of NCN radicals is estimated by
[NCN]0 ) σΦF[NCN3]
where σ is the absorption cross section (3.6 × 10-18 cm2)20 of
NCN3 at 193 nm, Φ is the quantum yield of NCN from
photolysis (assumed to be ∼1), and F is the photon flux
(photons/cm2) of the ArF laser.
He (99.999%) and N2 (99.999%) were used without further
purification. NO2 was prepared by slowly reacting NO with
excessive O2 and stored in 3 atm of O2 for 2 days before use.
NO2 was purified in freeze-pump-thaw cycles and diluted in
He to a 2% mixture by a standard gas handling technique before
it was used in experiments. Fourier transform infrared (FTIR)
spectrometry was used to examine the impurities, mainly NO,
in NO2.
2.2. Rate Coefficient Measurement. All kinetic measure-
ments were made under pseudo-first-order conditions, with
[NO2] more than 200 times greater than [NCN]. The initial
concentrations for NCN were kept small, [NCN]0 e 1 × 1012
molecules/cm3, to avoid possible radical-radical reactions and
to ensure pseudo-first-order conditions. The rate equation is
expressed as
2. Experimental Section
2.1. Experimental Setup. The experimental setup for the
measurement of reaction rate constants has been described
previously.15,18 In brief, the reaction cell is a double-walled pyrex
flask of volume of about 250 mL. Photolysis and LIF laser
beams entered and exited the cell through two pairs of mutually
perpendicular baffled side arms and intersected at the center of
the cell. The LIF signal was projected through appropriate lenses
and an interference filter into a photomultiplier tube (Hamamatsu
R1136) mounted at a side window perpendicular to both laser
beams. The LIF signal was amplified (Hamamatsu C1053, 5
MHz) and averaged with a gated integrator (Stanford Research
System, SR250). The data were stored and analyzed by a
computer.
The NCN radical was produced by photolysis of NCN3 with
an ArF excimer laser at 193 nm (Lambda Physik LEXTRA 50).
NCN3 was prepared19 by the reaction of NaN3 + BrCN
overnight and then degassed under vacuum before dilution in
He or N2. The absorption band for NCN3 in the range 160-200
nm is very broad;20 optical excitation at this band mainly
dissociates into NCN + N2.20-22 The concentration of NCN3
was determined via absorption of a 184.9 nm Hg line with a
9.8 cm cell in the upstream of the reaction cell. The absorption
cross section of 5.7 × 10-18 cm2 at this wavelength20 is used to
determine the NCN3 concentration.
The NCN radical was excited from the ground state,
X3Σg-(0,01,0), to the excited state, A3Πu(0,20,0), at 329.01 nm
by a dye laser (Continuum ND60) that was pumped by a
doubled-output Nd:YAG laser (Continuum Surelite). The LIF
signal was isolated by an interference filter centered at 330 nm
(fwhm ) 10 nm, 15% transmission). A delay/pulse generator
(Stanford Research System, DG535) was used to control the
firing of photolysis and LIF laser beams and to initiate the
boxcar integrator as well. Typically, 30-100 laser shots at a
repetition rate of 5-10 Hz were averaged to obtain a single
LIF data point.
-d ln [NCN] ⁄ dt ) k′ ) kd + k′′[NO2]
where k′ (in s-1) is the first-order decay coefficient, kd is the
radical loss rate coefficient mainly due to diffusion from the
detection region, and k′′ is the second-order reaction-rate
coefficient of interest.
The rate coefficients of the NCN + NO2 reaction were
measured in the temperature range of 260-296 K at 100-500
Torr of He or N2 pressure. The plots of the pseudo-first-order
rate coefficients for k′ vs [NO2] at 296 K and He pressures of
100, 200, 300, 400, and 500 Torr are shown in Figure 1. The
line slopes give the second-order bimolecular rate coefficients,
k′′, which depend on the third-body pressure. The k′′ values
measured at temperatures of 260, 283, and 296 K with He and
N2 pressures of 100-500 Torr are summarized in Table 1. The
k′′ values at 283 K at varied He and N2 pressures are further
illustrated in Figure 2. As shown in the figure, the k′′ values
for N2 are generally larger than those of He, indicating
expectedly that N2 is more efficient as a third body.
To examine the temperature effect, the k′′ values at three
temperatures at varied pressures of He are plotted in Figure 3.
The log(k′′) values depend very linearly on T-1 with varying
negative slopes at different pressures; thus, they can be fitted
by the Arrhenius equation, k′′ ) A exp(Ea/T).
The Arrhenius parameters derived from fitting the data at He
and N2 pressures of 100-500 Torr are summarized in Table 2,
A radical precursor (NCN3), reactant (NO2), and buffer gas
(He or N2) were mixed in a flexible tube (30 cm long) before
entering the reactor. The flow velocity (10-20 cm/s) of the gas
mixture was adjusted so that the reaction zone was replenished

Kinetics and Mechanism of the NCN + NO2 Reaction
J. Phys. Chem. A, Vol. 112, No. 41, 2008 10187
Figure 1. Plots of the pseudo-first-order decay rates of NCN, k′ vs
[NO2] at 296 K, in He pressures of (9) 100, (b) 200, (2) 300, (1)
400, and (() 500 Torr.
Figure 3. Arrhenius plots of k′′ for He pressures of (O) 100, (9) 200,
(b) 300, (0) 400, and (2) 500 Torr.
TABLE 2: Arrhenius Parameters of the NCN + NO2
Reaction at Various Pressures of He and N2 [k′′ ) A
exp(Ea/T)]a
He
N2
A [10-15
P (Torr) cm3/(molecule s)]
Ea
(K)
A [10-15
Ea
(K)
cm3/(molecule s)]
100
200
300
400
500
2.12 ( 0.80
2.10 ( 0.38
1.37 ( 0.07
0.83 ( 0.11
0.65 ( 0.20
1530 ( 103
1686 ( 51
1878 ( 13
2068 ( 37
2166 ( 85
2.01 ( 1.56
2.93 ( 1.04
2.47 ( 0.22
1.99 ( 1.08
1.34 ( 0.53
1570 ( 199
1628 ( 96
1738 ( 24
1889 ( 145
2061 ( 106
a Error limits are 1σ.
of 193-nm photolysis of NO2 or both, might introduce errors in
our measurements due to the rapid NCN + NO reaction.15
Efforts to minimize this effect were needed. As stated in the
Experimental Section, NO2 was stored under a high pressure
of O2 to ensure that all NO was converted to NO2 before use.
The impurities, especially NO, were examined by FTIR
spectrometry, and the results showed no detectable NO in our
NO2 samples.
Figure 2. Plots of the reaction rate constants of NCN + NO2, k′′ vs
pressure at 283 K for He (9) and N2 (O).
TABLE 1: Experimental Conditions and Bimolecular Rate
Coefficients, k′′, of the NCN + NO2 Reaction
Because the ArF laser is powerful, its photodissociation of
NO2 may produce substantial photofragments, NO and O, to
distort reaction rate measurements. The absorption cross sec-
tion23 of NO2 at 193 nm is about 7 × 10-19 cm2, which may
totally dissociate into NO and O (i.e., Φ ∼ 1). This cross section
is about a factor of 5 smaller than that of NCN3.20 However,
[NO2] is about 200 times [NCN3], and the [NO] and [O]
produced by photodissociation could initially be 40 times as
high as [NCN], which may significantly distort the reaction rate
measured. However, the laser energy (6.4 eV) is much higher
than the dissociation energy of NO2 (3.11 eV24), and NO and
O may carry initial kinetic energies of about 1.1 and 2.2 eV,
which make the initial velocities about 8 × 103 and 1.6 × 104
m/s, respectively. The photofragments will thus fly fast away
from the laser zone (less than 0.2 µs), and their concentrations
are quickly diluted to far less than the initial value. Because
the dilution time (approximately microseconds) is very short
compared to the time frame of kinetic measurement (on the order
of milliseconds), the distortion of measured rate constants by
photofragments is negligible. This assertion is corroborated by
a previous kinetic modeling,25 in which [O] produced from
photodissociation of NO2 at 193 nm is less than 1% of [NO2].
Under our experimental conditions, [NO]/[NO2] was estimated
to be less than 0.004. At 260 K and 400 Torr of N2, the reaction
rate constant15 for NCN + NO is 9.75 × 10-12 cm3/(mole-
P (Torr)
k′′ [10-12 cm3/(molecule s)]a
T (K)
He
N2
He
N2
296
100
200
300
400
500
100
200
300
400
500
100
200
300
400
500
100
200
300
400
500
100
200
300
400
500
100
200
300
400
500
0.38 ( 0.03
0.63 ( 0.02
0.78 ( 0.06
0.90 ( 0.09
0.95 ( 0.09
0.46 ( 0.04
0.80 ( 0.02
1.05 ( 0.04
1.22 ( 0.03
1.38 ( 0.04
0.77 ( 0.05
1.38 ( 0.07
1.88 ( 0.05
2.36 ( 0.07
2.63 ( 0.09
0.42 ( 0.06
0.73 ( 0.04
0.88 ( 0.11
1.21 ( 0.06
1.44 ( 0.12
0.49 ( 0.03
0.90 ( 0.04
1.14 ( 0.03
1.52 ( 0.06
1.89 ( 0.10
0.86 ( 0.07
1.55 ( 0.12
1.98 ( 0.15
2.89 ( 0.10
3.74 ( 0.14
283
260
a Error limits are 1σ.
where A is in units of cm3/(molecule s) and both Ea and T are
in K. The uncertainty shown in Table 2 represents 1 standard
deviation in a linear least-squares fit. Both Figure 3 and Table
2 show that the k′′ values have negative-temperature dependence,
indicating that the NCN + NO2 reaction in this low-temperature
range is a typical associative one.
2.3. Discussion on Rate Measurements. The presence of
NO molecules in the system, as either an impurity or a product

10188 J. Phys. Chem. A, Vol. 112, No. 41, 2008
Yang et al.
Figure 4. Geometric parameters of reactants, intermediates, and TSs optimized at the B3LYP/6-311+G(d) level of theory (in units of angstroms
and degrees).
cule s), which is 3.4 times faster than that of NCN + NO2. A
0.4% NO impurity in NO2 would introduce an error of 1.4% in
our measurements, which is within the quoted error limits. No
further correction would be necessary. Another possible NO
source in the system was an impurity in NO2. Our FTIR
measurements showed that they were less than those from
photodissociation of NO2 and hence would introduce a negligible
error in the measured rate constants.
G2M(CC5) method,32 which calculated the base energy at the
MP4/6-311G(d, p) level of theory and improved with the
expanded basis set and the coupled cluster method as well as
“higher level corrections (HLC)”. All electronic structure
calculations were performed with the GAUSSIAN 03 program.33
The rate constant for the barrierless association reaction that
produces the NCNNO2 complex was calculated by the VARI-
FLEX program34 based on the microcanonical RRKM theory.35-38
The component rates were evaluated at the E/J-resolved level,
and the pressure dependence was treated by one-dimensional
master equation calculations using the Boltzmann probability
of the complex for the J distribution. For the barrierless
association/decomposition process, the fitted Morse function was
used to approximate the minimum potential energy path. The
Lennard-Jones parameters (ε/k ) 304 K and σ ) 4.44 Å)
required for the collisional stabilization of the excited NCNNO2
complex were computed from the NCNNO2-He molecular
interaction potential predicted at the B3LYP/6-311+G(d,p) level
similar to the analogous NCN + NO reaction.15 The Lennard-
Jones parameters for He and N2 were taken from the literature.39
The averaged step sizes for energy transfer per collision,
The bond energy of NCN-N2 is quite low (0.3 eV).20
However, this molecule is so complex that it may mainly
dissociate into electronically and/or vibrationally exicited
species;20,21 thus, NCN may not move as fast as NO and O, so
it can stay in the laser zone for kinetic measurement. The excited
species should be quickly quenched to the ground state by a
buffer gas. This assertion is corroborated by the fact that [NCN]
in the ground state was observed to decay by pseudo-first-order
kinetics in all of our measurements.
The NCN + NO2 reaction has been investigated only once
by Baren and Hershberger.11 NCN was produced by photolysis
of CH2N2 + C2N2 with a ArF excimer laser at 193 nm and
detected by the LIF technique. They found that the reaction
rate constant at 298 K and 3 Torr of He was very small; the
upper limit of 1.5 × 10-14 cm3/(molecule s) was given.11 We
did not do the measurement at such a low pressure, but the
data in Figure 2 show that the k′′ value at low pressure is indeed
very low. Our data are compared with theoretical calculations
as described below.
∆E down, for He and N2 were taken to be 150 and 250 cm-1
,
respectively.
3.2. Reaction Potential Surface. The geometric parameters
of the reactants, intermediates, and TSs optimized at the B3LYP/
6-311+G(d) level of theory are shown in Figure 4. The relative
potential energy diagram obtained at the G2M level based on
the optimized structures is drawn in Figure 5. The intermediate
complex LM0 is readily formed barrierlessly from the reactants
NCN (3Σg-) and NO2 (2A1) as shown Figure 5, where the NCN
in the ground state, 3Σg-, is designated as 3NCN. The barrierless
association minimum energy path is presented by the Morse
function, V(R) ) 22.7{1 - exp[-5.015(R - 1.595)]}2, as shown
in Figure 6. LM0 is in a planar symmetry of 2A′′, and it is 19.4
kcal/mol below the reactants. It can isomerize into the complex
LM1 (2A′) of 3.1 kcal/mol energy below the reactants via a
rotational TS0 with a potential barrier of 18.5 kcal/mol. NCO
+ NNO can be produced from LM1 via TS3, LM2, and TS4,
which are four-membered ring structures. The energies of TS3,
3. Computational Section
3.1. Computational Methods. The geometric parameters of
the reactants, products, TSs, and molecular complexes of the
NCN + NO2 reaction system are optimized at the spin-
unrestricted B3LYP/6-311+G(d) level of theory.26-29 All of the
stationary points were identified for local minima and TSs by
vibrational analysis. Intrinsic reaction-coordinate analyses30,31
were performed to confirm the connections of TSs with
designated reactants, products, and intermediates. On the basis
of the optimized geometries, higher level single-point energy
calculations with the stationary points were performed by the

Kinetics and Mechanism of the NCN + NO2 Reaction
J. Phys. Chem. A, Vol. 112, No. 41, 2008 10189
Figure 5. PES of 3NCN + NO2 at the G2M//B3LYP/6-311+G(d) level
1
of theory (in units of kilocalories per mole). Those of NCN + NO2
are also included.
Figure 7. Calculated rate constants for the formation of LM0 and NCO
+ NNO via LM0 and NCNO + NO by direct abstraction: (A) He buffer
gas and (B) N2 buffer gas at varied pressures as indicated.
Figure 6. Morse function, V(R), for the minimum energy path of the
association process, 3NCN + NO2 f LM0, at the B3LYP/6-311+G(d)
level of theory.
3NCN + NO2 f LM0 f LM1 f LM2 f NCO + NNO
(1)
3NCN + NO2 f NCNO + NO
(2)
LM2, and TS4 relative to the reactants are 8.2, -4.5, and
4.4 kcal/mol, respectively, and the formation of NCO + NNO
is an exothermal process of 69.6 kcal/mol. Another reaction
product, CNO + NNO, can be formed with higher barriers
of five-membered ring structures from LM1 via TS5, LM3,
and TS6, which have the relative energies of 25.2, 15.1, and
36.8 kcal/mol, respectively. The formation of CNO + NNO
is an exothermal process of 7 kcal/mol. In addition to the
association/isomerization decomposition channels, Figure 5
also shows two direct O-abstraction processes that produce
the NCNO + NO products via TS1 and TS2, which are
isomers with barriers of 9.8 and 22.1 kcal/mol, respectively.
The energy level for the products, NCNO + NO, is lower
than that of the reactants by 22.9 kcal/mol. The reaction
channel for NCN (1∆g) in the first excited state (designated
In channel (1), the decomposition of LM0 into the products
NCO + NNO is controlled by TS3; thus, TS0 and LM1 can be
ignored in the rate constant calculations. The k(LM0) and
k(NCO+NNO) values calculated at the He and N2 buffer-gas
pressures of 100 Torr to 100 atm are plotted as a function of
the temperature in Figure 7. The k(LM0) values increase with
pressure but decrease with temperature. This positive-pressure
and negative-temperature dependence effect is typical for an
associative reaction. The k(NCO+NNO) values are independent
of pressure but increase more than 5 orders of magnitude when
the temperature increases from 300 to 2000 K. This is consistent
with the calculated PES that the NCO + NNO products
produced in channel (11) go through a potential barrier. As
shown in Figure 7, the k(NCO+NNO) value is much less than
those of k(LM0) at low temperature (<1000 K), but it increases
systematically at high temperature.
1
as NCN) is also shown in Figure 5.
3.3. Rate Constant Prediction. The rate constants are
calculated based on the above PES using the VARIFLEX
program34 in the temperature range from 200 to 2000 K and in
the pressure range from 10-4 Torr to 1000 atm. Overall, the
most favorable reaction channels are
The rate constant for NCNO + NO production by channel
(2) is also shown in Figure 7 by the long-dashed curve. This
direct O-abstraction reaction does not depend on buffer gas
pressure, but it increases more than 12 orders of magnitude when
the temperature increases from 200 to 2000 K. This positive-

10190 J. Phys. Chem. A, Vol. 112, No. 41, 2008
Yang et al.
temperature effect is caused by the fact that the NCNO + NO
products produced in channel (22) go through the potential
barriers of TS1 and/or TS2, as shown in Figure 5. As shown in
Figure 7, the k(NCNO+NO) values are higher than the
k(NCO+NNO) values by about 3 orders of magnitude over the
whole temperature range of 200-2000 K. Thus, the contribution
of k(NCO+NNO) to the total rate constant is negligible.
Although k(NCNO+NO) is less than k(LM0) in the low-
temperature range (<700 K), it becomes dominant at high
temperature. The rate constants for the formation of LM0
(NCN-NO2) at the high- and low-pressure limits with He and
N2 as third bodies can be given by the expressions
k∞(LM0) ) 4.33 × 10-11
T
0.297 exp(-47 ⁄ T)
cm3 ⁄ (molecule s) (200-2000 K)
k0(He) ) 7.58 × 1020T-18.22 exp(-4354 ⁄ T)
cm6 ⁄ (molecule2 s) (200-2000 K)
k0(N2) ) 2.09 × 1022T-18.63 exp(-4532 ⁄ T)
cm6 ⁄ (molecule2 s) (200-2000 K)
The rate constant for the direct abstraction channel (2) can
be represented by
k(NCNO+NO) ) 1.22 × 10-11 exp(-5463 ⁄ T)
cm3 ⁄ (molecule s) (200-2000 K)
The total rate constants (kt) calculated at indicated buffer
pressures, including the high-pressure limit, are shown in Figure
8. As shown in the figure for the P and T effects, the kt curve
for every pressure shows a minimum, resulting effectively from
a combination of redissociation and stabilization of the excited
NCN-NO2 intermediate and the direct abstraction reaction
giving NCNO + NO. The minimum shifts to higher temperature
when the pressure increases. The kt values at low temperature
increase with pressure because they are mainly contributed from
k(LM0). On the other hand, the kt values at high temperature
do not depend on the pressure because they are mainly due to
contribution from the abstraction rate constant k(NCNO+NO).
As shown in Figure 8, at the high-pressure limit, the rate constant
increases moderately with temperature in the whole range
because the partition function of the loose association TS
increases more rapidly with temperature than those of the
reactants.
Figure 8. Calculated total rate constants of the NCN + NO2 reaction
at varied pressures as indicated: (A) He buffer gas; (B) N2 buffer gas.
This product relation is further illustrated by the branching
ratios calculated for producing LM0 and NCNO + NO at He
buffer gas pressures of 10 Torr, 1 atm, and 10 atm, as shown in
Figure 9. The branching ratio is almost equal to 1 for k(LM0)
at low temperature and equal to 1 for k(NCNO+NO) at high
temperature. The crossing points at the branching ratio of 0.5
are about 560, 700, and 780 K, when the He pressures are at
10 Torr, 1 atm, and 10 atm, respectively. This shift of the
branching ratio to higher temperature can be explained again
by the competition between stabilization and NCNO abstraction
product formation.
Figure 9. Calculated branching ratios for the production of LM0 and
NCNO + NO at varied He pressures as indicated.
4. Discussion
NCNO + NO, their appearance can occur only at T > 700 K;
at such high temperature, the radical precursor NCN3 is too
unstable for kinetic studies. Both Figures 10 and 11 indicate
that the observed P and T effects on kt can be quite reasonably
accounted for by the ab initio molecular orbital statistical RRKM
theory calculations, similar to the NCN + NO case.15
The measured rate constants and calculated values are
compared in Figures 10 and 11 as functions of pressure and
temperature, respectively. Because our measurements were
performed in the low-temperature range of 260-296 K, the
major product is LM0 (NCNNO2) as alluded to above. Because
of the high barriers for the formation of decomposition products
NCO + N2O via NCNNO2 and the direct abstraction products,
It is of interest to compare the current rate constants with
those of other reactants available in the literature. At 2000 K

Kinetics and Mechanism of the NCN + NO2 Reaction
J. Phys. Chem. A, Vol. 112, No. 41, 2008 10191
Figure 10. Comparison of the calculated rate constants with experi-
mental data at 260, 283, and 296 K for (A) He buffer gas and (B) N2
buffer gas.
Figure 11. Comparison of calculated rate constants with experimental
data at 100, 300, and 500 Torr for (A) He buffer gas and (B) N2 buffer
gas.
5. Conclusion
and ∼ 1 atm pressure, the total rate constant, kt, for the NCN
+ NO2 reaction is predicted to be 1.9 × 10-12 cm3/(molecule
s). This is much larger than the kt value of 7.2 × 10-16 cm3/
(molecule s) predicted for the NCN + O2 reaction13 under the
same temperature and pressure conditions, but it is much smaller
than that of the NCN + O reaction, 1.3 × 10-10 cm3/(molecule
s).14 These results show that NO2 is much more reactive than
O2 but much less than O, as one would expect.
The kinetics and mechanism for the NCN + NO2 reaction
have been investigated experimentally and computationally. In
our measured temperature range of 260-296 K, the reaction
was found to be strongly and positively dependent on the
pressure and negatively dependent on the temperature. The
observed pressure and temperature effects can be reasonably
accounted for by the results of a dual-channel RRKM calcula-
tion, with the predicted mechanism initially taking place via a
moderately strongly bonded NCNNO2 intermediate in the 2A′′
state. The reaction rate constant for the NCNO + NO products
by direct abstraction is calculated to be about 3 orders of
magnitude higher than that for NCO + N2O formation via
NCNNO2 in the temperature range of 200-2000 K. Although
the constant for the production of NCNO + NO is smaller than
of the association reaction at low temperatures (<700 K), this
O-abstraction channel is predicted to be dominant at high
temperatures, for example, under nitramine propellant combus-
tion conditions.
At 296 K and 300 Torr of He pressure, the association rate
constant for NCN + NO2 is 7.8 × 10-13 cm3/(molecule s), as
shown in Table 1. Interestingly, this value is smaller than that
of the NCN + NO reaction, 6.7 × 10-12 cm3/(molecule s), under
the same temperature and pressure conditions.11 Similarly, at
296 K and 400 Torr of N2 pressure, the association rate constant
for NCN + NO2 is 1.2 × 10-12 cm3 /(molecule s), which is
smaller than that of 7.4 × 10-12 cm3/(molecule s) for the NCN
+ NO reaction under the same temperature and pressure
conditions.15 Because both reactions take place by the barrierless
association mechanism, the apparent higher reactivity of NCN
toward NO than NO2 actually reflects the higher stability of
the NCNNO intermediate (31 kcal/mol for trans-NCNNO and
22 kcal/mol for cis-NCNNO)15 than NCNNO2 (19 kcal/mol as
shown in Figure 5). The higher stability of NCNNO is expected
to have a smaller redissociation rate, which, in turn, gives rise
to a higher stabilization and overall rate constant.
Acknowledgment. L.C.L. and M.C.L. acknowledge the
National Science Council of Taiwan for support of their visiting
professorships at Taiwan National Chiao Tung University.
Z.F.X. is grateful for partial support from the U.S. Office of
Naval Research under Grant N00014-02-1-0133. T.-J.Y. and
N.S.W. thank the National Science Council of Taiwan (Contract
NSC 95-2113-M-009-028) for support.

10192 J. Phys. Chem. A, Vol. 112, No. 41, 2008
Yang et al.
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