Kinetics and mechanism of the CN + NCO → NCN + CO reaction studied by experiment and theory

Article abstract of DOI:10.1021/jp901903n

The rate coefficients for the CN + NCO → NCN + CO reaction have been measured by a laser-photolysis/ laser-induced fluorescence technique in the temperature range of 254-353 K and the He pressures of 123-566 Torr. The CN radical was produced from the photolysis of BrCN at 193 nm, and the NCO radical from the CN + O₂ reaction. The NCN radical was monitored by laser-induced fluorescence with a dye laser at 329.01 nm. The rate constants derived from kinetic modeling, with a negative temperature dependence but no pressure effect, can be expressed by k = (2.15 ± 0.70) × 10 ^-11 exp[(155 ± 92)/T]cm³ molecule^-1 s^-1, where the quoted errors are two standard deviations. The reaction mechanism and rate constant have also been theoretically predicted for the temperature range of 200-3000 K at He pressures ranging from 10^-4 Torr to 1000 atm based on dual channel Rice-Ramsperger-Kassel-Marcus (RRKM) calculations with the potential energy surface evaluated at the G2M and CCSD(T) levels. The rate constant calculated by variational RRKM theory agrees reasonably with experimental data.

Full text of DOI:10.1021/jp901903n

6314
J. Phys. Chem. A 2009, 113, 6314–6325
Kinetics and Mechanism of the CN + NCO f NCN + CO Reaction Studied by Experiment
and Theory
Shiang-Yang Tzeng,† Po-Hsueh Chen,† 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, Department of Electrical and Computer Engineering, San Diego State UniVersity, San Diego,
California 92182, and Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322
ReceiVed: March 2, 2009; ReVised Manuscript ReceiVed: April 3, 2009
The rate coefficients for the CN + NCO f NCN + CO reaction have been measured by a laser-photolysis/
laser-induced fluorescence technique in the temperature range of 254-353 K and the He pressures of 123-566
Torr. The CN radical was produced from the photolysis of BrCN at 193 nm, and the NCO radical from the
CN + O2 reaction. The NCN radical was monitored by laser-induced fluorescence with a dye laser at 329.01
nm. The rate constants derived from kinetic modeling, with a negative temperature dependence but no pressure
effect, can be expressed by k ) (2.15 ( 0.70) × 10-11 exp[(155 ( 92)/T] cm3 molecule-1 s-1, where the
quoted errors are two standard deviations. The reaction mechanism and rate constant have also been theoretically
predicted for the temperature range of 200-3000 K at He pressures ranging from 10-4 Torr to 1000 atm
based on dual channel Rice-Ramsperger-Kassel-Marcus (RRKM) calculations with the potential energy
surface evaluated at the G2M and CCSD(T) levels. The rate constant calculated by variational RRKM theory
agrees reasonably with experimental data.
1. Introduction
study on the CN + O2 reaction. However, to the authors’
knowledge, the reaction rate constant is neither experimentally
measured nor theoretically predicted yet. Recognizing its
importance in propellant combustion, Tsang16 recommended the
rate constant for the CN + NCO reaction to be 3 × 10-11 cm3
molecule-1 s-1 with an uncertainty of a factor of 3. In fact, this
reaction rate constant could be useful in modeling of hydrogen/
cyanide oxidation, because both the CN and NCO radicals were
observed in a flow reactor.17
The measurement on the production channel of a radical-
radical reaction is a challenging task,18 because both the
concentrations and time profiles of reactants need to be
accounted for, which pose difficulties. The study of radical-
radical reaction becomes feasible by taking the advantage of
laser technology. The CN radical can be produced by laser
excitation of BrCN at 193 nm in situ in a reaction zone, and its
concentration can be determined by laser intensity. NCO is
produced by the reaction of CN with O2, and its concentration
can be obtained by kinetic modeling. The NCN radical produced
from the CN + NCO reaction can be detected by the LIF signal;
and its concentration can be determined by calibration with the
LIF signal from the photolysis of NCN3 at 193 nm, for which
the NCN concentration is determined by the laser intensity. The
reaction rate constant can thus be derived from simulating the
time profile of the NCN radical.
The cyanonitrene (NCN) radical has been recognized as an
important intermediate in combustion media, since Lin and
co-workers1,2 revealed by a computational study in 2000 that
this radical can be produced by the CH + N2 reaction. NCN
has been detected in the microwave discharge of CF4/N2/He
mixture3 and the methane-air flame4 by the laser-induced
fluorescence (LIF) technique, and in the heating mixtures of
diketene/N2 and ethane/N2 behind reflected shock waves by
photoabsorption.5 Recent shock tube experiments confirm that
H + NCN is the dominant channel of the CH + N2 reaction;5
and results are in better agreement with recent calculations6 than
an earlier calculation2 that predicted lower rates constants. The
higher reaction rate results from the predicted lower heat of
formation of NCN. All these studies show that NCN is indeed
an important intermediate in hydrocarbon/air combustion media.
It has been demonstrated that the NO fractions observed in
natural gas flames agree better with prediction if NCN is
included in kinetic modeling.7,8
Because of its importance, the reaction mechanism and
kinetics of NCN have been recently actively investigated. For
instance, the reaction rate constants of NCN with the combustion
species, such as (C, H, CH, CH2, CH3, and CN),9 O2,10 O (3P),11
(NO, O2, C2H4 and NO2),12 NO,13 and NO2,14 have been
investigated by either experimental measurements and/or theo-
retical calculations. However, all these investigations are related
to the consumption of NCN, but not the production, which is a
subject of this report.
The rate constant for the reaction of CN and NCO in the
ground state has also been calculated with dual channel RRKM
theory based on the potential energy surface (PES) derived by
high levels quantum chemical calculations. The results of our
calculations are compared with measured experimental data.
The production of NCN from the CN + NCO reaction has
been suggested long ago by Bullock and Cooper15 during their
2. Experimental Section
* Corresponding authors. E-mail: nswang7899@gmail.com (N.S.);
chemmcl@emory.edu (M.C.).
2.1. Experimental Setup. The experimental setup for the
measurement of reaction rate constant has been described
previously.13,19 In brief, the reaction cell is a double-walled Pyrex
† Chiao Tung University.
‡ San Diego State University.
§ Emory University.
10.1021/jp901903n CCC: $40.75  2009 American Chemical Society
Published on Web 05/13/2009

CN + NCO f NCN + CO Reaction
J. Phys. Chem. A, Vol. 113, No. 22, 2009 6315
Figure 1. Excitation spectra of laser-induced-fluorescence intensities
from the media: (A) NCN3 in 100 Torr of He and (B) BrCN/O2/He
mixture of 122 Torr total pressure excited by ArF excimer laser at 193
nm.
Figure 2. Temporal profiles of [NCN] at T ) 298 K, P ) 321 Torr,
[CN]0 ) 3.73 × 1013 molecules cm-3, and [O2]0 ) 3.07 × 1014
molecules cm-3: (b) measured data; (s) the best fit by simulation with
k1 ) 3.66 × 10-11 cm3 molecule-1 s-1; (· · ·) simulation with the k1
values (in 10-11 cm3 molecule-1 s-1): (A) 4.77; (B) 4.04; (C) 3.30.
flask of volume about 250 mL. The photolysis and the LIF laser
beams entered and exited the cell through two pairs of mutually
perpendicular baffled side arms, and intersected at the cell center.
The LIF signal was projected into a photomultiplier tube
mounted at a side window perpendicular to both laser beams.
The LIF signal was amplified and averaged with a gated
integrator. The data were stored and analyzed by a computer.
The dye laser was pumped by a doubled-output Nd:YAG
laser. A delay/pulse generator was used to control the firing of
both the 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.
The radical precursors (NCN3, BrCN, and O2) and the He
buffer gas were mixed in a flexible tube 30 cm long before
entering the reactor. The flow velocity (∼10-20 cm/s) of gas
mixture was adjusted so that the reaction zone was replenished
with fresh gas for each photolysis laser pulse.
The pressure of the system was measured with a Baratron
gauge. The flow rates of reactants and buffer gas were measured
with a calibrated mass flow meter. 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 concentrations of the reactants are determined by
of LIF is the same as that of the NCN radical observed in flame
by Smith et al.3 This result implies that NCN exists in the laser
excited BrCN/O2/He system.
After all possible processes are considered, NCN is most
likely produced by the reaction as suggested by Bullock and
Cooper15
CN + NCO f NCN + CO
(1)
where CN is produced by photolysis of BrCN at 193 nm
BrCN + hν f Br + CN
(II)
BrCN starts to absorb photons at wavelength 260 nm as
observed by Russell et al.21 Since the absorption band is broad
and smooth, the excitation at 193 nm will mainly result in
dissociation so that the quantum yield for the CN production,
Φ, is presumed to be equal to 1. The initial concentration of
CN is determined by
[CN]0 ) σΦF[BrCN]
(III)
where σ ) 3.3 × 10-19 cm2 is the photoabsorption cross section
at 193 nm,21 F is the ArF excimer laser flux (photons/cm2), and
the BrCN concentration, [BrCN], was determined from eq I.
The CN radical will then react with O2 to produce NCO by
[A] ) 9.66 × 1018PFA/FTT (molecules cm-3)
(I)
CN + O2 f NCO + O
(2)
where P is the reaction pressure in Torr; T is the reaction
temperature in K; FA and FT are the flow rates in STP cm/s
(STP ) 273.15 K and 760 Torr) of reactant A and the total
reaction mixture, respectively. The concentration of a specific
reactant was further checked via absorption of the 184.9 nmHg
line with a 9.8 cm cell in the upstream of reaction cell.
He (99.999%) and O2 (99.99%) were used without further
purification. BrCN was purified in freeze-pump-thaw cycles,
and diluted in He to a 2% mixture by a standard gas handling
technique typically employed in experiments. NCN3 was
prepared by the reaction of NaN3 with BrCN overnight20 and
then degassed under vacuum and diluted in He. FTIR spec-
trometry was used to verify purity.
At 300 K, the rate constant22-24 of this reaction is 1.73 ×
10-11 cm3 molecule-1 s-1. The NCO radical will then react with
CN to produce NCN.
2.3. Temporal Profile of [NCN] in BrCN/O2/He. The LIF
signal observed from the BrCN/O2/He medium excited by the
ArF excimer laser at 193 nm has a short induction period at
the beginning, then increases with time, and saturates eventually
as shown in Figure 2, where the NCN concentration, [NCN], is
proportional to the LIF signal. This time profile is explainable
by the presumption that the NCN radical is produced by the
reaction 1, for which the production rate is
d[NCN]/dt ) k1[CN][NCO]
(IV)
2.2. LIF Signal from BrCN/O2/He Excited at 193 nm.
After the BrCN/O2/He mixture was excited by an ArF excimer
laser pulse at 193 nm, a LIF signal from the medium excited
by a dye laser was observed. The excitation spectrum for the
total LIF intensity is shown in Figure 1. This excitation spectrum
where k1 is the rate constant of reaction 1 which is the parameter
to be measured in this study.
The CN radicals produced by the excimer laser initially carry
high kinetic energy, but they will be relaxed by He buffer gas

6316 J. Phys. Chem. A, Vol. 113, No. 22, 2009
Tzeng et al.
(>125 Torr) to the equilibrium condition in a short duration (<1
µs). Since the relaxation time is much less than the measurement
time scale (100 µs), [CN] can be approximated by an initial
value of [CN]0 at t ) 0, and then decays exponentially with
time
under the same experimental condition (i.e., same temperature,
pressure, and instrument settings).
NCN3 + hν f NCN + N2
(IX)
NCN3 has an absorption band25 in the range 160-200 nm.
This absorption band is very broad, and excitation of NCN3 at
this band mainly dissociates into NCN + N2.26,27 The dissocia-
tion quantum yield is assumable to be equal to 1. The
concentration of NCN3 was determined using eq I and cross
checked via absorption of the 184.9 nmHg line using the
absorption cross section25 of 5.7 × 10-18 cm2 at this wavelength.
The excitation spectrum of the LIF signal from NCN
produced by photolysis of NCN3 is shown in Figure 1 to
compare with the one produced from the BrCN/O2/He system
that is also shown in the figure. Both spectra are very similar,
which proves the existence of NCN in the BrCN/O2/He system.
The similarity also indicates that the NCN radicals produced
by both systems have the same rotational and vibrational
populations in the ground state. The initial populations produced
by the two systems are expected to be quite different; for
instance, the initial NCN radicals produced from UV excitation
of NCN3/He are mainly in electronically and vibrationally
excited states,25-27 in contrast to those from BrCN/O2/He that
are expected to be mainly in the ground state. However, under
high He buffer pressure (>125 Torr), the excited NCN radicals
could be quickly relaxed to the equilibrium condition; therefore,
the populations of NCN in both systems are about the same.
The same populations of NCN in both systems indicate that
the LIF signal produced by the photolysis of NCN3 can be used
to calibrate the [NCN] in the BrCN/O2/He system. Since the
[CN] ) [CN]0 exp(-Rt)
(V)
where R is the decay rate constant that contains reactions with
all species in the media. In addition to reactions 1 and 2, the
CN radical can be consumed by other reactions such as
CN + O2 f CO + NO
(3)
CN + CN + He f NCCN + He
CN + O f N + CO
CN + NO + He f ONCN + He
CN + BrCN f NCCN + Br
(4)
(5)
(6)
(7)
Thus, R ) (k2 + k3)[O2] + γ, where k2 and k3 are the rate
constants of reactions 2 and 3, and γ is the decay rate due to
reactions 4-7.
The NCO radical is produced by reaction 2, its concentration
can be approximated by
[NCO] ) η[CN]0(1 - exp(-ꢀt))
(VI)
where ꢀ ) k2[O2] and η ) ꢀ/R.
The [NCO] can be decreased by reactions such as
NCO + NCO f N2 + 2CO
NCO + O2 f NO + CO2
(8)
(9)
-
LIF signal from the transition between the ground state, X 3Σg
(0, 01, 0), and the excited state, A 3Πu (0, 20, 0), at 329.01 nm,
is the strongest as shown in Figure 1, we select this wavelength
for the detection and calibration of NCN concentration.
The NCN concentration produced by photolysis of NCN3 at
193 nm is determined by
NCO + O f NO + CO
NCO + NO f N2O + 2CO
(10)
(11)
NCO + NO f N2 + 2CO
(12)
There are two reactions that are worth considering
CN + NCCN f products
NCN + NO f NCO + N2
(13)
(14)
[NCN] ) σΦF[NCN3]
(X)
where σ ) 3.4 × 10-18 cm2 is the absorption cross section of
NCN3 at 193 nm,25 Φ (∼1) is quantum yield for the NCN
production, and F is the photon flux (photons/cm2) of the ArF
laser.
For predicting the general feature of the temporal profile of
[NCN], the reactions that involve secondary products are
temporarily ignored so that R is approximately a constant. After
integration with time, the NCN concentration is
The LIF signal was observed to be proportional to [NCN];
thus, it can be used to determine the [NCN] in the BrCN/O2/
He system. Calibration procedures were carried out before, in
between, and after kinetic measurements to ensure the accuracy.
The error limits (2σ) for the calibrations range between 2.5 and
13.2% and for the averaged value it is ∼6.5%.
[NCN] ) a - b exp(-Rt) + c exp(-(R + ꢀ)t)
(VII)
2
a ) k1η2[CN]0 /(R + ꢀ)
(VIII)
where a is the final [NCN] at long time later, b ) (1 + η-1)a,
and c ) a/η.
2.5. Reaction Rate Constant Determined by Simulation.
The typical temporal profile of [NCN] in the BrCN/O2/He
system shown in Figure 2 was measured at a temperature 298
K, a total pressure 321Torr, and the initial concentrations of
[CN]0 and [O2]0 of 3.73 × 1013 and 3.07 × 1014 molecules/
cm3, respectively. [NCN] increases from 0 to about 1012
molecules/cm3 in a time duration of 230 µs.
This equation qualitatively explains the time profile shown in
Figure 2, where [NCN] starts with 0 and approaches a constant
value at long time later. This result implies that the presumed
mechanism for the NCN production is sound; and the reaction rate
constant of k1 can be derived from the temporal profile.
It is noted that eq VII is derived only from a simplified
scheme; the actual reaction mechanism needs to be studied by
a sophisticated kinetic simulation. However, this equation does
represent the physical picture well so that it can be used to guide
the interpretation of simulation results.
The time profile of [NCN] is used to derive k1 by fitting the
data with simulation software Facsimile. All the 14 reactions with
the rate constants1,19,22-24,28-36 listed in Table 1 are included in the
kinetic simulation. Room temperature data were employed for some
of the reactions while their temperature dependence was not
available. The bold line in Figure 2 is generated with a simulated
k1 of 3.66 × 10-11 cm3 molecule-1 s-1, which fits the data best.
The simulated curves with different k1 values of (A) 30% and (B)
10% higher as well as (C) 10% lower than the best fit value are
2.4. Calibration of the NCN Concentration. In order to
confirm the NCN detection in the BrCN/O2/He system and also
to calibrate its concentration, the radical was produced by
photolysis of NCN3/He with the ArF excimer laser at 193 nm

CN + NCO f NCN + CO Reaction
J. Phys. Chem. A, Vol. 113, No. 22, 2009 6317
TABLE 1: Reaction Mechanism Used To Simulate the Rate Constant of CN + NCO
k ) A × (T/298)n × e-(E /RT)
a
rate const (298 K) (cm3 molecule-1 s-1)/
reaction
A (cm3 molecule-1 s-1
)
Ea (kJ/mol)
n
(cm6 molecule-2 s-1
)
1. CN + NCO f NCN + CO
2. CN + O2 f NCO + O
k1, to be determined
1.02 × 10-11
-1.83
-1.83
-
-
1.73 × 10-11a
5.52 × 10-12a
4.69 × 10-32b
3.69 × 10-11c
2.66 × 10-30d
2.24 × 10-13e
5.0 × 10-12f
5.0 × 10-17g
7.0 × 10-11h
1.54 × 10-11i
1.96 × 10-11i
3.53 × 10-15j
3.0 × 10-12k
3. CN + O2 f CO + NO
1.02 × 10-11
-
4. CN + CN + He f NCCN +He
5. CN + O f N + CO
-
-
-
-
-
6. CN + NO + He f ONCN + He
7. CN + BrCN f NCCN + Br
8. NCO + NCO f N2 + 2CO
9. NCO + O2 f NO + CO2
10. NCO + O f NO + CO
11. NCO + NO f N2O + CO
12. NCO + NO f N2 + CO2
13. NCCN + CN f products
14. NCN + NO f NCO + N2
-
-
-
2.01 × 10-11
11.14
-
-
-
-
-
-
-
-
-
-
-
-
-
1.29 × 10-10
1.05 × 10-14
-
4.66
2.7
-
-1.97
2.7
-
a References 22-24. b Reference 28. c Reference 29. d Reference 30. e Reference 31. f Reference 32. g References 19 and 33. h References 16
and 34. i Reference 35. j Reference 36. k Reference 1.
TABLE 2: Summary of CN + NCO f NCN + CO
Reaction Data
TABLE 3: Data of NCO + CN f NCN + CO at T ) 254
K and P ) 152-564 Torr (He)
[CN]0 (1013) [O2]0 (1014)
k1 (10-11
)
[CN]0 (1013)
[O2]0 (1014)
k (10-11) (cm3
T
(K)
P(He) no. of (molecules (molecules (cm3 molecule-1
P (Torr) (molecules cm-3
)
(molecules cm-3
)
molecule-1 s-1
)
a
(Torr)
data
cm-3
)
cm-3
)
s-1
)
557
564
561
561
558
557
458
460
462
464
458
466
360
365
366
366
368
364
258
266
263
266
259
263
156
155
155
157
152
1.86
2.91
2.44
2.42
1.80
2.89
1.74
2.69
2.25
2.35
1.73
2.75
1.65
2.49
2.09
2.12
2.54
1.65
1.41
2.27
1.92
2.17
1.48
1.94
1.36
1.19
1.16
1.36
0.90
2.92
2.85
2.89
5.69
5.68
5.52
3.27
3.28
3.12
6.03
5.22
5.67
1.94
3.27
3.43
6.13
6.10
6.22
2.47
2.67
2.74
5.01
4.21
4.11
1.40
1.37
2.68
2.64
2.24
4.57
4.79
4.52
4.84
4.46
3.63
3.45
3.39
3.60
4.05
4.65
3.74
4.34
3.35
4.25
3.53
2.84
3.76
4.13
3.32
4.85
4.50
4.41
4.29
3.65
254 152-564
273 123-509
298 123-501
353 252-566
29
32
44
23
0.90-2.91 1.37-6.22 4.08 ( 1.08
1.29-5.45 1.58-8.10 3.70 ( 1.46
1.78-5.15 0.81-5.89 3.51 ( 1.22
1.27-4.48 2.07-5.83 3.40 ( 1.35
a Error limits are 2σ.
also shown in Figure 2. For the same 10% difference, the curve
(B) is more close to the best fit curve than the curve (C);
that is, the fitting is less sensitive to increasing k1 value.
Nevertheless, the curve (C) is quite distinct from the best
fit, indicating that the uncertainty caused by simulation is
less than 5% of the best value.
At a fixed temperature, several measurements were per-
formed at various total gas pressures and initial concentra-
tions, [CN]0 and [O2]0. The experimental conditions and
results measured at four temperatures of 254, 273, 298, and
353 K are summarized in Table 2. Detailed data measured
at a temperature 254 K in the He pressure range 152-564
Torr are listed in Table 3. The k1 values of best fit are also
listed in Table 3. The k1 value averaged over 29 measure-
ments is 4.08 ( 1.08 cm3 molecule-1 s-1, where the quoted
errors are two standard deviations. Similarly, the detailed
data measured at temperatures 273, 298, and 353 K are listed
in Tables 4-6, in which the k1 values averaged over 32, 44,
and 23 measurements are 3.70 ( 1.46, 3.51 ( 1.22, 3.40 (
1.35 cm3 molecule-1 s-1, respectively.
4.56
4.10
4.21
4.63
av: 4.08 ( 1.08a
a Error limits are 2σ.
As shown in Tables 3-6, the reaction rate constants measured
at each temperature are fairly constant; that is, no obvious
pressure effect on k1 is observed. This result infers that the
assumption is valid that both the CN and NCN radicals are
quickly relaxed to equilibrium condition. On the other hand,
the averaged k1 values decrease with temperature; that is, the
reaction rate constant has a negative temperature dependence.
The Arrhenius plot for the k1 values is shown in Figure 3; and
the values can be expressed by
2.6. Discussion on Experimental Measurements. 2.6.1. Un-
certainty Related to the Branching Ratio of CN + O2. All
parameters that may introduce errors in k1 shall be examined in
detail to determine the accuracy of reported values. The results
of sensitivity analysis on our simulation mechanism are shown
in Figure 4, which indicates that the branching ratio for CN +
O2 in the reactions 2 and 3, k2/k3, plays a crucial role in our
simulation. This importance is also foreseen in eq VIII, where
k1 is related to k2/k3.
k1 ) (2.15 ( 0.70) × 10-11 exp[(155 ( 92)/T]
The reported branching ratios of k2/k3 vary from 0.76/0.2224
to 0.94/0.06.37 The 0.76/0.22 value was employed in our
simulation. If the other value of 0.94/0.06 was used, the
cm3 molecule-1 s-1 (XI)
where the quoted errors are two standard deviations.

6318 J. Phys. Chem. A, Vol. 113, No. 22, 2009
Tzeng et al.
TABLE 4: Data of NCO + CN f NCN + CO at 273 K and
P ) 123-509 Torr (He)
TABLE 5: Data of NCO + CN f NCN + CO at T ) 298
K and P ) 123-501 Torr (He)
P
[CN]0 (1013)
[O2]0 (1014)
k (10-11) (cm3
P
[CN]0 (1013)
[O2]0 (1014)
k (10-11) (cm3
(Torr) (molecules cm-3
)
(molecules cm-3
)
molecule-1 s-1
)
(Torr) (molecules cm-3
)
(molecules cm-3
)
molecule-1 s-1
)
506
497
502
502
509
504
395
402
403
396
403
398
400
323
327
326
320
324
247
252
248
252
245
252
247
247
123
126
126
124
125
125
5.45
2.79
4.35
4.32
5.32
2.34
3.44
5.18
3.46
1.48
5.34
3.45
1.43
4.90
3.82
3.80
2.65
4.96
3.18
1.32
4.83
3.15
4.86
3.18
4.83
1.39
1.34
4.28
1.29
2.97
2.91
2.19
2.65
2.74
2.70
6.01
8.10
4.69
1.77
3.16
3.34
2.23
1.58
2.48
3.00
5.02
5.15
2.58
2.73
2.52
4.96
2.27
3.49
3.79
2.08
2.17
4.90
5.34
2.23
4.68
5.48
2.41
4.78
4.40
3.08
4.23
3.56
3.22
4.46
3.57
3.79
3.15
4.33
5.09
3.23
4.01
5.03
4.43
4.95
4.29
4.29
3.28
3.36
4.31
2.78
3.60
2.70
3.14
3.24
3.96
3.14
2.66
4.74
2.89
3.43
501
497
495
500
496
321
321
321
322
324
396
401
403
398
398
245
245
246
250
250
251
255
255
256
126
126
123
126
123
124
127
127
127
128
126
126
127
128
129
129
129
130
131
132
5.15
3.91
3.93
5.12
2.78
3.73
2.50
4.68
4.67
3.61
2.33
3.39
3.37
4.38
4.36
1.92
1.91
1.86
2.98
2.95
2.92
5.12
5.10
5.07
1.82
1.80
1.83
1.84
1.82
1.78
1.81
2.49
2.45
2.27
2.45
2.76
2.82
2.85
2.9
5.22
5.40
3.65
2.41
2.00
3.07
3.25
3.00
5.33
5.89
5.31
3.05
5.08
2.88
4.94
1.53
2.93
4.45
1.53
2.93
4.45
1.53
2.93
4.45
0.81
1.30
1.50
1.83
2.33
2.48
4.69
0.81
1.30
1.83
2.33
1.50
2.48
5.69
0.81
1.30
1.83
2.33
1.50
2.48
3.87
4.92
3.38
3.07
3.97
3.66
4.61
3.14
3.78
5.00
3.14
3.45
2.86
2.99
2.53
4.15
4.46
4.64
4.44
4.06
4.27
3.49
3.54
3.84
2.73
3.11
3.55
3.32
3.10
3.84
3.59
2.99
3.19
3.24
3.55
2.95
3.41
3.33
2.86
2.59
3.34
3.11
3.29
3.01
av: 3.51 ( 1.22a
2.58
av: 3.70 ( 1.46a
a Error limits are 2σ.
simulation would give a k1 value of 20% smaller. This shows
the possible error that might be introduced to the reported k1
value by the uncertainty of k2/k3.
2.6.2. Uncertainty Related to Variation of [O2]0. The higher
the [O2], the faster will be the [NCN] produced so that the
induction period is shortened. However, the final [NCN] will
be smaller, because CN will be converted more to non-NCO
products by reaction 3. This expectation is foreseen in eqs VII
and VIII, where R and ꢀ increase with [O2] so that both the
induction period and the final [NCN], a, decrease.
2.87
2.91
2.92
4.66
4.46
a Error limits are 2σ.
The effects of [O2] on the temporal profiles of [NCN] were
investigated in detail both by measurement and simulation as
shown in Figure 5. The experimental condition was set at a
temperature 298 K, a pressure 250 Torr, and [CN]0 ) 2.95 ×
1013 molecules cm-3. The data were measured at [O2]0 of (1.53,
2.93, and 4.45) × 1014 molecules cm-3; and, they were best fit
as NCO + NCO and NCO + NO would expect no difference
on the final [NCN] at varied [O2]0, if the [CN]0 is kept at a
fixed value. The effect of these possible reactions on the
simulation can be examined by measuring k1 at varied [CN]0.
2.6.3. Uncertainty Caused by Variation of [CN]0. As shown
in eq VIII, k1 is roughly related to [CN]0-2; thus, the accuracy
of k1 is affected by the uncertainty of [CN]0. Since [CN]0 was
determined according to eq III, its uncertainty included those
of [BrCN], laser flux, absorption cross section, and quantum
yield. We estimate the overall uncertainty on the determination
of [CN]0 is less than 10%. Our simulation showed that a 10%
decrease of [CN]0 will yield a 21% higher k1, and vice versa.
In other words, a 10% uncertainty in [CN]0 will introduce that
of 21% in k1.
by k1 of (4.44, 4.06, and 4.27) × 10-11 cm3 molecule-1 s-1
,
respectively. The simulated results at higher [O2]0 of (6.0 and
20.0) × 1014 molecules cm-3 are also included in Figure 5.
These results are consistent with our expectation that the
induction period is shortened and the final [NCN] decreases
when [O2]0 is increased. The best fit k1 values were determined
with [O2]0 varied in the range of (0.81-8.10) × 1014 molecules
cm-3, no correlation between k1 and [O2]0 is found.
The noncorrelation between k1 and [O2]0 indicates that the
reaction kinetics used in the simulation is adequate, and no other
reactions that may be important in the system are not considered.
However, the possible NCN production from the reactions such
In our measurements, [CN]0 was varied over a wide range to
examine possible errors. As examples, the temporal profiles of
[NCN] measured at a temperature 273 K, a He pressure 500
Torr, [O2]0 ) 2.74 × 1014 molecules cm-3, and [CN]0 varied at

CN + NCO f NCN + CO Reaction
J. Phys. Chem. A, Vol. 113, No. 22, 2009 6319
TABLE 6: Data of NCO + CN f NCN + CO at T ) 353
K and P ) 252-566 Torr (He)
P
[CN]0 (1013)
[O2]0 (1014)
k (10-11) (cm3
(Torr) (molecules cm-3
)
(molecules cm-3
)
molecule-1 s-1
)
560
565
566
564
493
498
504
505
493
396
401
403
398
398
319
323
323
322
251
245
252
256
252
2.09
2.40
2.43
2.34
2.30
3.42
4.48
4.43
2.32
2.33
3.39
3.37
4.38
4.36
2.38
2.43
3.45
3.45
2.93
3.79
3.75
1.39
1.27
3.06
3.02
5.83
4.69
5.13
2.91
3.58
4.77
2.87
5.31
3.05
5.08
2.88
4.94
2.88
5.31
2.70
5.21
4.65
2.44
4.39
2.07
3.31
3.74
3.63
3.65
4.21
3.39
3.06
3.21
4.04
5.02
3.53
3.88
3.21
3.36
2.84
2.36
2.54
2.55
Figure 4. Sensitivity analysis at 254 K. Reaction numbers match with
those in Table 1.
2.64
3.06
3.09
2.73
4.43
4.09
av: 3.40 ( 1.35a
a Error limits are 2σ.
Figure 5. Temporal profiles of [NCN] at T ) 298 K, P ) 250 Torr,
and [CN]0 ) 2.95 × 1013 molecules cm-3. [O2]0 (in 1014 molecules
cm-3) are (A) 1.53 (9); (B) 2.93 (0); and (C) 4.45 (b). The solid lines
(s) show the best fit by simulations with k1 (in 10-11 cm3 molecule-1
s-1) of (A) 4.44; (B) 4.06; and (C) 4.27. The dotted lines ( · · ·) show
the simulated results at [O2]0 (in 1014 molecules cm-3) of (D) 6.0 and
(E) 20.0.
Figure 3. The Arrhenius plot of k1.
NCN production from CN + CN reaction is excluded in the
simulation; this is in fact justified by our observation that no
NCN is detected in the photolysis of BrCN/He at 193 nm.
2.6.4. Uncertainty Caused by Calibration of [NCN]. The
rate constants of reaction 1 were determined by simulating the
temporal profiles of [NCN]. Our simulation shows that a 10%
increase of [NCN] will yield a 10% higher k1, and vice versa.
In other words, a 10% uncertainty in [NCN] will introduce that
of 10% in k1. Uncertainty on [NCN] included those of [NCN3],
laser flux, absorption cross sections, and quantum yield. We
estimate the overall uncertainty on the determination of [NCN]
is less than 15%.
(2.79 and 4.35) × 1013 molecules cm-3 are shown in Figure 6,
where the best fit k1 values at varied [CN]0 are (4.23 and 3.56)
× 10-11 cm3 molecule-1 s-1, respectively. The simulated profiles
of [NCN] at [CN]0 of (7.17 and 14.3) × 1013 molecules cm-3
are also shown in Figure 6. Both the experimental data and
simulated profiles show that the induction periods do not vary,
but the final [NCN] increases with [CN]0. These results are
expected from eq VII where R and ꢀ do not depend on [CN]0
so that the induction period does not vary; and, from eq VIII
the final [NCN], a, increases with [CN]0. Over the [CN]0 range
of (0.90-5.45) × 1013 molecules cm-3 studied in our measure-
ments, no correlation between the best fit k1 value and [CN]0 is
found.
1
2.6.5. Quenching of NCN. Theoretical calculations (dis-
cussed later) showed that reaction 1 produced mainly electroni-
cally excited NCN under our experimental conditions. However,
the rate constants were obtained by measuring the LIF signal
of the ground triplet state on the assumption that all NCN
radicals were effectively quenched to their ground state in a
time scale of a few microseconds or less. The lack of correlations
These results of the noncorrelation between k1 and [CN]0,
again, show that the reaction kinetics used in the simulation is
adequate, and the measured k1 values do not contain systemati-
cally errors due to some possible CN reactions being excluded
from the simulation scheme. It is noted that the possibility of

6320 J. Phys. Chem. A, Vol. 113, No. 22, 2009
Tzeng et al.
the G2M(CC2) method,44 which calculated the base energy at
the PMP4/6-311G(d,p) level of theory and improved with the
expanded basis set and the coupled cluster method as well as
“higher level corrections (HLC)”. Also, for the lowest energy
channels, the stationary points were optimized by the QCISD
CCSD methods45 with the 6-311+G(d) basis set and their
energies were corrected by the QCISD(T) and CCSD(T)
method,45 respectively, with the 6-311+G(3df) basis set. All
electronic structure calculations were performed with the
Gaussian 03 program.46
The rate constants were calculated by the Variflex program47
based on the microcanonical variational transition state (VTST)
and Rice-Ramsperger-Kassel-Marcus (RRKM) theory.48-50
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
with the bond distance R(NC-NCO)was used to approximate
the minimum potential energy path (MEP); the potential for
the transitional modes was described in terms of three internal
angles (θ1 (∠CNC), θ2 (∠NCN), θ3 (∠NCNC)) with a sum of
products (in pairs) of sinusoidal functions.51 The coefficients
in the transitional potential expression as functions of the bond
distance R are estimated by calculating the appropriate force
constant matrix related to θ1, θ2, and θ3 at the singlet NCNCO
complex. These force constant matrix elements (Fij) are assumed
to decay exponentially with the bond distance R: Fij(R) ) Fij(R0)
exp[-η(R - R0)], in which η is decay parameter and R0 is the
bond length of NC-NCO. For the collisional stabilization of
the excited NCNCO intermediate, the Lennard-Jones parameters
(ε/k ) 201 K and σ ) 4.04 Å) are taken to be those of the
similar complex, NCNNO, in the NCN + NO reaction.13 The
Lennard-Jones parameters for He is taken to be ε/k ) 10.0 K
and σ ) 2.55 Å from the literature52 with the averaged step
size of 100 cm-1 for energy transfer per collision.
Figure 6. Temporal profiles of [NCN] at temperature 272 K, He
pressure 500 Torr, [O2]0 ) 2.72 × 1014 molecules cm-3, and [CN]0 (in
1013 molecules cm-3) ) (A) 2.79 (0) and (B) 4.35 (O). The solid lines
(s) show the best fit from simulations with k1(in 10-11 cm3 molecule-1
s-1) values of (A) 4.23 and (B) 3.56. The dotted lines ( · · ·) show the
simulated results at higher [CN]0 (in 1013 molecules cm-3): (C) 7.17
and (D) 14.3.
between the fitted k1 and both pressure (He) and [O2]0 may
clearly support this point. Further study in a bath gas of high
quenching efficiency, such as Xe, would be of interest to verify
the validity of our assumption.
2.6.6. Summary on Measurements. The difficulty for de-
termining the rate constant of a radical-radical reaction cannot
be overemphasized, because the procedure involves accurate
measurement of radical concentration and adequate kinetic
simulation. We have cautiously examined all possible error
sources in the current study. The quoted errors of two standard
deviations listed in Table 2 vary from 27 to 40% of the given
k1 values. The uncertainty that includes all possible errors in
experiment and simulation is estimated to be not beyond 40%
of the given value.
The current studied reaction rate constant has not yet been
measured or calculated. The only value of 3 × 10-11 cm3
molecule-1 s-1 estimated by Tsang16 for the NC + NCO f
NCNCO reaction coincides with our experimental value (3.51
( 1.22) × 10-11 cm3 molecule-1 s-1 at 298 K. However, the
production of NCN by the dissociation of the stabilized NCNCO
molecule is unlikely because of the high dissociation energy
which requires a positive temperature dependence; this contra-
dicts the current result that the reaction has a small negative
temperature dependence. The current results indicate that the
NCN radical is likely produced by a barrierless association/
dissociative process, as will be discussed below on the basis of
the mechanism derived from ab initio MO calculations.
3.2. Reaction Potential Surface. The optimized geometric
parameters of the reactants, intermediates, and transition states
are shown in Figure 7, while the relative potential energy
diagram is drawn in Figure 8. The frequencies and moments of
inertia of the reactants, intermediates, and transition states are
listed in Table 7. One can see that the reaction heats of the
products at the ground electronic state are -55.9 kcal/mol for
NCN(3Σg-) + CO, -45.5 kcal/mol for CCO(3Σ-) + N2, and
-26.2 kcal/mol for CNN(3Σ-) + CO at the G2M level. From
o
the literature data in refs 53-55 (∆fH0 (NCO(2Π)) ) 38.0 (
2.5 kcal/mol,53 ∆fH0 (CN(2Σ+)) ) 104.4 ( 2.4 kcal/mol,53
o
∆fH0 (NCN(3Σg-)) ) 111.0 kcal/mol,54 ∆fH0 (CO) ) -27.2
o
o
o
kcal/mol,53 ∆fH0 (CCO(3Σ-)) ) 91.1 ( 0.5 kcal/mol,56 and
o
∆fH0 (CCO(3Σ-)) ) 138.3 ( 1.2 kcal/mol56), the reaction heats
are obtained to be -58.6 ( 4.9, -51.3 ( 5.5, and -31.3 ( 6.5
kcal/mol for NCN(3Σg ) + CO, CCO(3Σ-) + N2, and CNN(3Σ-)
-
3. Computational Section
+ CO, respectively. Our predicted results at the G2M level are
within the error range of these literature data.
3.1. Computational Methods. All geometric parameters of
the reactants, products, transition states, and molecular com-
plexes of the NCO + CN reaction are optimized on the singlet
and triplet potential energy surfaces at the spin-unrestricted
B3LYP/6-311+G(d) level of theory.38-41 All the stationary
points were identified for local minima and transition states by
vibrational analysis. Intrinsic reaction-coordinate analyses42,43
were performed to confirm the connections of transition states
with designated reactants, products, and intermediates. Based
on the optimized geometries, higher level single-point energy
calculations with the stationary points were performed by
3.2.1. Singlet State Reaction Channels. Two channels are
considered on the singlet state potential energy surface. One is
a barrierless association reaction of NCO (2Π) + CN (2Σ+)
to form cyanogen isocyanate, NCNCO (1A′) (denoted as
1NCNCO), and then to go to the dissociation products of
1
CO+NCN (1∆g) (denoted as NCN). At the G2M/B3LYP/6-
31+G(d) level the 1NCNCO intermediate is 114.6 and 83.9 kcal/
1
mol lower than the reactants and the NCN + CO products,
respectively. There is no tight transtion state found by the
B3LYP/6-311+G(d) method on the dissociation process. So,

CN + NCO f NCN + CO Reaction
J. Phys. Chem. A, Vol. 113, No. 22, 2009 6321
Figure 7. Geometric parameters (angstroms and degrees) of reactants, intermediates, and transition states at the B3LYP/6-311+G(d) level of
theory. The numbers in parentheses, brackets, and braces are at the QCISD/6-311+G(d), CCSD/6-311+G(d), and CAS(10,10)/6-311+G(d) levels
of theory, respectively.
1
both minimum energy paths at the G2M/B3LYP/6-31+G(d)
level can be described by the Morse functions: V1(R) ) De(1 -
higher than that of the NCNCO intermediate, while it is 3.2,
1
0.4, and 0.6 kcal/mol, respectively, higher than that of NCN
+ CO. It implies that the reverse reaction NCNCO f NCN
+ CO would be a low barrier process.
1
1
1
exp[-3.745(R - 1.610)])2 kcal/mol for NCNCO f NCO +
CN and V2(R) ) De(1 - exp[-4.850(R - 1.314)])2 kcal/mol
1
1
for NCNCO f NCN+CO. For a more reliable estimate, the
The second channel of the CN + NCO reaction is another
association process to form cyanogen isofulminate, CNNCO
1
minimum energy path of NCNCO f NCO + CN was also
1
calculated at the CASPT2(10,10)/6-311+G(d)//CAS(10,10)/6-
311+G(d) level;57,58 the result can be expressed as V1′(R) )
De(1 - exp[-4.035(R - 1.530)])2 kcal/mol. However, at the
CAS(10,10), QCISD, and CCSD levels of theory with the
6-311+G(d) basis set, the transition state for 1NCNCO f 1NCN
+ CO, TS10, was found. It is a product-like transition state. Its
C-N breaking bond is 1.880, 2.204, and 2.209 Å at the
CAS(10,10), QCISD, and CCSD levels, respectively, while the
corresponding imaginary frequency is i596, i228, and i232 cm-1,
respectively. The energies of TS10 predicted by CASPT2(10,10)/
6-311+G(d)//CAS(10,10)/6-311+G(d),QCISD(T)/6-311+G(3df)//
QCISD/6-311+G(d), and CCSD(T)/6-311+G(3df)//CCSD/6-
311+G(d) methods are 80.1, 84.7, and 85.1 kcal/mol, respectively,
(1A′) (denoted as CNNCO), via the transiton state, TS1, with
a potential barrier of 5.6 kcal/mol at the G2M level. At TS1,
the N-N forming bond length is 2.300 Å and the imaginary
frequency is i215 cm-1 at the B3LYP/6-311+G(d) level. It is a
reactant-like transition state. The energy of the 1CNNCO
imtermediate is -65.1 kcal/mol relative to that of the reactants,
which is 49.5 kcal/mol higher than 1NCNCO. The isomerization
transition state, TS2, connects 1CNNCO and 1NCNCO with the
forward barrier of 30.5 kcal/mol and the reverse barrier of 80.0
1
kcal/mol. Also, the CNNCO intermediate can decompose to
give CO + CNN (1∆) (denoted as 1CNN) and N2 + CCO (1∆)
(denoted as 1CCO) via TS3 and TS4, respectively. The energies
of TS3 and TS4 relative to reactants are almost same; the former

6322 J. Phys. Chem. A, Vol. 113, No. 22, 2009
Tzeng et al.
Figure 8. Potential energy surfaces of the NCO + CN reaction at the G2M//B3LYP/6-311+G(d) level of theory. The numbers in parentheses,
brackets, and braces are at the QCISD(T)/6-311+G(3df)//QCISD/6-311+G(d), CCSD(T)/6-311+G(3df)//CCSD/6-311+G(d), and CASPT2(10,10)/
6-311+G(d)//CAS(10,10)/6-311+G(d) levels of theory, reaspectively.
TABLE 7: Frequencies and Moments of Inertia of Reactants, Intermediates, and Transition States at the B3LYP/6-311+G(d)
level of Theorya
species
Ia, Ib, Ic (au)
150.3, 150.3
(155.2, 155.2)
[154.6, 154.6]
(156.2, 156.2)
31.3, 31.3
(31.8, 31.8)
frequencies (cm-1
440, 440, 1272, 1563
(544, 573, 1278, 1968)
[501, 572, 1293, 1962]
(523, 563, 1260, 1970)
2146
)
NCO (2Π)
CN (2Σ+)
(2149)
[31.8, 31.8]
[2130]
(31.1, 31.1)
(2190)
1NCNCO (1A′)
16.4, 695.5, 712.0
(30.3, 658.6, 689.0)
[30.3, 657.0, 687.3]
(30.3, 658.6, 689.0)
24.2, 680.9, 689.1
(34.6, 653.5, 663.9)
[32.5, 658.1, 666.6]
25.5, 668.4, 690.7
(29.1, 666.6, 695.7)
[29.1, 664.6, 693.8]
24.8, 634.6, 659.4
27.9, 629.3, 657.3
117.8, 740.4, 850.9
(75.6, 1219.6, 1295.2)
[75.2, 1209.7, 1284.9]
123.8, 687.4, 811.3
(97.7, 585.0, 660.3)
[96.3, 583.4, 655.6]
53.6, 921.2, 974.8
59.7, 502.5, 523.6
38.3, 725.3, 763.6
94.4, 326.4, 398.4
15.8, 711.1, 715.8
(23.3, 698.4, 707.3)
[23.1, 696.4, 705.6]
38.0, 722.2, 760.3
(41.0, 704.4, 745.5)
[41.0, 701.5, 742.5]
94.8, 352.4, 447.2
36.1, 648.9, 665.6
36.2, 657.0, 693.2
(59.4, 854.9, 914.3)
[60.1, 852.2, 912.4]
(54.4, 757.3, 811.8)
118, 472, 491, 571, 605, 863, 1543, 2356, 2421
(166, 453, 485, 589, 657, 894, 1480, 2336, 2378)
[166, 474, 487, 605, 662, 898, 1495, 2359, 2397]
(131,465, 480, 593, 663, 936, 1567, 2350, 2511)
76, 174, 487, 550, 591, 897, 1479, 1615, 2344
(144, 334, 521, 596, 653, 959, 1466, 1764, 2309)
[144, 333, 522, 605, 656, 970, 1488, 1766, 2340]
30, 189, 439, 532, 570, 802, 1232, 1819, 1949
(153, 197, 455, 519, 555, 835, 1163, 1870, 1934)
[151, 199, 459, 521, 557, 836, 1164, 1889, 1953]
148, 297, 344, 547, 646, 875, 1452, 2198, 2342
114, 182, 327, 449, 494, 751, 1122, 1868, 1985
8, 35, 96, 162, 493, 581, 1271, 1982, 2144
(i42, 47, 81, 158, 555, 572, 1286, 1995, 2142)
[40, 78, 157, 178, 559, 585, 1295, 1960, 2126]
i53, 44, 105, 185, 491, 580, 1267, 1985, 2138
(i541, 118, 198, 438, 575, 603, 1202, 2069, 2497)
[i473, 119, 198, 410, 573, 604, 1220, 1981, 2131]
i215, 9, 41, 152, 552, 561, 1281, 2023, 2088
i264, 147, 166, 576, 604, 649, 1334, 1788, 2280
i628, 67, 156, 285, 414, 456, 1165, 1776, 2120
i638, 311, 457, 708, 730, 935, 1010, 1375, 1970
i1197, 129, 279, 446, 530, 915, 1147, 1776, 2059
(i1671, 162, 413, 472, 549, 907, 1046, 1778, 2028)
[i1801, 158, 407, 465, 549, 916, 1050, 1803, 2068]
i452, 61, 163, 420, 447, 576, 1190, 1798, 2048
(i547, 140, 178, 448, 457, 570, 1098, 1851, 2015)
[i538, 141, 179, 452, 460, 572, 1099, 1846, 2054]
i360, 234, 404, 641, 711, 812, 919, 1338, 2022
i1321, 97, 285, 382, 387, 533, 965, 1674, 1942
i436, 95, 174, 349, 420, 566, 1124, 1868, 1993
(i228, 189, 213, 291, 502, 546, 1200, 1815, 2199)
[i232, 189, 214, 290, 490, 539, 1205, 1835, 2242]
(i596, 113, 128, 275, 506, 563, 1095, 1980, 2455)
3NCNCO-a (3A)
3NCNCO-b (3A)
1CNNCO (1A′)
3CNNCO (3A′′)
LM (3A)
TS0 (3A)
TS1 (1A′)
TS2 (1A)
TS3 (1A′)
TS4 (1A)
TS5 (3A)
TS6 (3A)
TS7 (3A′′)
TS8 (3A)
TS9 (3A′′)
TS10 (1A′)
a The numbers in parentheses, brackets, and braces are at the QCISD/6-311+G(d), CCSD/6-311+G(d), and CAS(10,10)/6-311+G(d) levels
of theory, respectively.

CN + NCO f NCN + CO Reaction
J. Phys. Chem. A, Vol. 113, No. 22, 2009 6323
is -3.3 kcal/mol and the latter is -3.0 kcal/mol. They are higher
than TS2 by 31 kcal/mol. This means that the isomerization
1
subchannel from the CNNCO intermediate is more favorable
than its direct decomposition channels.
Also, the association process to singlet NCOCN was
examined at both B3LYP/6-311+G(d) and CCSD/6-311+G(d)
levels of theory. A transition state was found to be -0.1
and 4.5 kcal/mol relative to the reactants of NCO + NC with
the former and the latter methods, respectively. Corrected
by CCSD(T)/6-311+G(3df) based on the geometric param-
eters optimized at the CCSD/6-311+G(d) level, the transition
state is 1.9 kcal/mol over the reactants. The continuing
reaction following the formation of singlet NCOCN is back
to the reactants NC + NCO or possibly decomposing to NCN
+ CO. However, the production of the latter is very difficult
to take place because it involves breaking one of the triple
CN bonds. Thus, comparing with the barrierless association
process to singlet NCNCO, this reaction channel is expected
to be negligible, although the singlet NCOCN is predicted
to lie below the reactants by 68.6 kcal/mol at the CCSD(T)/
6-311+G(3df)//CCSD/6-311+G(d) level.
Figure 9. Predicted rate constants as a function of temperature and
comparison with experimental data: (---) based on the parameters by
G2M//B3LYP/6-311+G(d); (s) based on the parameters by CCSD(T)/
6-311+G(3df)//CCSD/6-311+G(d).
3.3. Rate Constant Prediction and Comparison with
Experiment. Based on the lowest energy reaction channels
3.2.2. Triplet State Reaction Channels. The reaction of
NCO (2Π) + CN (2Σ+) on the triplet state potential energy
1
1
NCO(2Π) + CN(2Σ+) f NCNCO f NCN + CO
surface includes three product channels. The first one
-
generates triplet electronic state cyanoinidogen NCN (3Σg
)
(15)
(denoted as 3NCN) and CO through a multiwell reaction
channel, as seen in Figure 8. In this channel, the complex
LM is first formed barrierlessly and its relative energy is only
-1.0 kcal/mol at the G2M level. This barrierless process can
be effectively expressed by the Morse function V3(R) ) De(1
- exp[-2.083(R - 2.400)])2 kcal/mol. Following LM, one
of the triplet cyanogen isocyanate isomers (denoted as
3NCNCO-a) is formed via the transition state, TS0, with the
relative energy of -0.7 kcal/mol at the G2M levels. Because
the C-N forming bond at TS0 is predicted to have a longer
distance of 2.306 Å at the B3LYP/6-311+G(d) level, TS0
has a small imaginary frequency of i53 cm-1. It is necessary
to confirm its existence by optimization with a higher level
of theory. By both QCISD and CCSD methods with the
6-311+G(d) basis set, the C-N forming bond lengths are
predicted to be 1.838 and 1.834 Å, respectively, and the
3
NCO(2Π) + CN(2Σ+) f LM f NCNCO-a f
3
3NCNCO-b f NCN + CO (16)
the rate constants are predicted using variational TST and
RRKM rate theory in the temperature range from 200 to 3000
K at He pressures ranging from 10-4 Torr to 104 atm. These
two product channels have been discussed above at three levels
of theory: G2M//B3LYP/6-311+G(d), QCISD(T)/6-311+G(3df)//
QCISD/6-311+G(d),
CCSD(T)/6-311+G(3df)//CCSD/6-
311+G(d), as well as CASPT2(10,10)/6-311+G(d)//CAS(10,10)/
6-311+G(d). The tight transition state, TS10, was found by the
latter three methods, but not by the first. The rate constants will
be calculated separately by employing the energetic and
geometric parameters obtained at the G2M//B3LYP/6-311+G(d),
CCSD(T)/6-311+G(3df)//CCSD/6-311+G(d),andCASPT2(10,10)/
6-311+G(d)//CAS(10,10)/6-311+G(d) levels.
imaginary frequencies increase to i541 and i474 cm-1
,
respectively, while the energies of TS0 are 2.3 and -0.6 kcal/
mol at the QCISD(T) and CCSD(T) levels, respectively. Next,
3NCNCO-a isomerizes to 3NCNCO-b with the conformation
changed via the transition state TS5, which is lower than
reactants by 8.0, 6.0, and 7.5 kcal/mol at the G2M,
QCISD(T), and CCSD(T) levels, respectively. The final step
from 3NCNCO-b to 3NCN) + CO needs to overcome a small
barrier of only 3.5 kcal/mol at the G2M level, 2.7 kcal/mol
at the QCISD(T) level, and 2.9 kcal/mol at the CCSD(T)
level.
Figure 9 shows the results of calculations using the Variflex
code based on the association Morse potential and transitional
potential for NCO + CN f 1NCNCO with different exit
transition states: the variational transition state predicted by the
G2M//B3LYP/6-311+G(d) and TS10 by CCSD(T)/6-311+
G(3df)//CCSD/6-311+G(d)andCASPT2(10,10)/6-311+G(d)//CAS-
(10,10)/6-311+G(d). Also, in this figure the predicted rate
constants are compared with the experimental data. The thicker
curves, including solid, dashed, and dotted lines, represent the
rate constants of the singlet reaction channel predicted with the
parameters at the CASPT2(10,10)/6-311+G(d)//CAS(10,10)/6-
311+G(d), CCSD(T)/6-311+G(3df)//CCSD/6-311+G(d), and
G2M//B3LYP/6-311+G(d) levels, respectively. The thinner
The second triplet channel undergoes by a four-membered
ring transition state, TS7, to generate N2 and CCO (3Σ-)
3
(denoted as CCO). At the G2M level, TS7 is 3.7 kcal/mol
3
higher than reactants and, at the B3LYP/6-311+G(d) level, its
imaginary frequency is i360 cm-1. The third channel has the
highest transition state, TS8, which is 34.9 kcal/mol above the
reactants at the G2M level. By TS8, the reaction proceeds to
the triplet cyanogen isofulminate, CNNCO (3A′′) (denoted as
3CNNCO), which is -2.1 kcal/mol relative to the reactants. It
is obvious that 3CNNCO is unstable and can decompose to CO
and CNN (3Σ-) (denoted as 3CNN) via TS9 with a small barrier
of 0.8 kcal/mol at the G2M level.
curve is the rate constant forming the triplet NCN + CO
products from the triplet reaction channel predicted by CCSD(T)/
6-311+G(3df)//CCSD/6-311+G(d). Because ktriplet is much less
than ksinglet by a factor of 20-80, the contribution of the triplet
channel to the NCO + CN reaction is negligible.
From Figure 9, it can be seen that ksinglet(CASPT2) and
ksinglet(CCSD(T)) are almost identical and slightly less than
ksinglet(G2M). These three predicted rate constants exhibit a small
positive temperature dependence because of the barrierless

6324 J. Phys. Chem. A, Vol. 113, No. 22, 2009
Tzeng et al.
Figure 11. Predicted rate constants as a function of pressure for
reaction 1.
Figure 10. Comparison of predicted rate constants (ksinglet, CASPT2)
at different decay parameters of force constants for transitional modes:
η1 ) (1.87, 3.49, 3.32), η2 ) (1.43, 3.49, 2.32), η3 ) (1.87, 1.85, 1.79).
4. Concluding Remarks
Kinetics and mechanism for the CN + NCO f NCN + CO
reaction have been investigated experimentally and computa-
tionally. In our measured temperature range of 254-353 K, the
reaction was found to be negatively dependent on temperature,
but not on pressure in the range of 123-566 Torr. The observed
pressure effect can be reasonably accounted for by the dual-
channel RRKM calculations. However, the temperature effect
observed by experiment is not consistent with calculations that
show slightly positive temperature dependence. We have exerted
a substantial effort trying to resolve this discrepancy. The
possible experimental errors have been examined in great detail,
and the calculations have been extended to very expensive
levels. Nevertheless, a noticeable discrepancy at higher tem-
peratures remains. Since the study of a radical-radical reaction
is a challenging task in both experiment and computation, further
investigation to resolve this discrepancy is of interest.
association and the exothermic product formation with the small
exit TS10 (by both CASPT2 and CCSD(T) methods) or VTS
(by the G2M method). Although the experimental data display
a weak negative temperature dependence that is different from
calculated results, the ksinglet(CASPT2) values are in good
agreement with experimental k(expt) in the experimental tem-
perature range of 254-353 K in the error fields of the
experimental data. For the major singlet product channel, the
rate constant predicted by the CASPT2 and CCSD(T) methods
that have an intrinsic exit barrier clearly agrees better with
experimental data. The presence of TS10 restricts the exit flux
and thus leads to a smaller value of rate constant.
For kinetic modeling applications, the predicted values are
fitted to the expressions in units of cm3 molecule-1 s-1
:
) 2.14 × 10-11
) 7.41 × 10-10
T
T
0.155 exp(-65/T)
0.30 exp(-479/T)
(200-1000 K)
(1000-3000 K)
k
Acknowledgment. Two of us, L.C.L. and M.C.L., want to
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
US Office of Naval Research under the grant No. N00014- 02-
1-0133. S.Y.T., P.H.C., and N.S.W. thank the National Science
Council of Taiwan (Contract No. NSC 95-2113-M-009-028) for
support.
It is worth mentioning that, in the above rate constant
calculation, the decay parameters (η) of the transition potential
are 1.43, 3.49, and 2.32 Å-1, which are obtained by the three-
dimensional force constant matrix of θ1, θ2, and θ3 at R0 and R
) 3.0 Å. Because the rate constant is sensitive to the decay
parameters, we compared ksinglet(CASPT2) obtained at three
group decay parameters, η1 ) (1.87, 3.49, 3.32), η2 ) (1.43,
3.49, 2.32), and η3 ) (1.87, 1.85, 1.79) in the variational
transition state range of R ) 2.5-3.5 Å. The result, as drawn
in Figure 10, shows that the rate constants calculated using η1
and η3 are respectively greater and less than the experimental
data. However, the predicted rate constants by η2 are in good
agreement with the experimental values. Accordingly, η2 can
give a closer presentation of rate constant for the singlet reaction
channel.
Figure 11 shows the pressure effect at three temperatures for
the rate constant of NCN production via the singlet reaction
channel. At 300 K, the rate constant is predicted to be
independent of pressure below 1500 Torr. However, the rate
constant steeply goes down with increasing pressure due to
the collisional deactivation of the excited NCNCO, resulting in
the decrease in the NCN + CO products. As indicated in this
figure, the turning points are about 5, 50, and 500 atm at the
temperatures of 300, 500, and 1000 K, respectively. At every
temperature, the predicted reaction rate constants are indepen-
dent of pressure below 1 atm. This is consistent with our
experimental observations.
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