An experimental and theoretical study of the reaction of ethynyl radicals with nitrogen dioxide (HC≡C+NO2)

Article abstract of DOI:10.1063/1.1573192

An experimental and theoretical study of the reaction of ethynyl radicals with nitrogen dioxide was performed. The reaction has a large rate constant that decreases with increasing temperature. The experimental temperature range covered allows reliable extrapolations of the rate coefficient to temperatures up to 1500 K.

Full text of DOI:10.1063/1.1573192

An experimental and theoretical study of the reaction of ethynyl radicals with nitrogen
dioxide ( HC ≡ C + NO 2 )
Shaun A. Carl, Hue Minh Thi Nguyen, Minh Tho Nguyen, and Jozef Peeters
Citation: The Journal of Chemical Physics 118, 10996 (2003); doi: 10.1063/1.1573192
View online: http://dx.doi.org/10.1063/1.1573192
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 118, NUMBER 24
22 JUNE 2003
An experimental and theoretical study of the reaction of ethynyl radicals
with nitrogen dioxide „HCCC¿NO2…
Shaun A. Carl,a) Hue Minh Thi Nguyen,b) Minh Tho Nguyen, and Jozef Peeters
Department of Chemistry, University of Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium
͑Received 10 February 2003; accepted 18 March 2003͒
A pulsed laser photolysis/chemiluminescence ͑PLP/CL͒ technique was used to determine absolute
rate constants of the reaction C2HϩNO2→products over the temperature range 288–800 K at a
pressure of 5 Torr (N2). The reaction has a large rate constant that decreases with increasing
temperature. It may be expressed in simple Arrhenius form as k1(T)ϭ(7.6Ϯ1.0)
ϫ10Ϫ11 exp (130Ϯ50) K/T , although there is an indication of a downward curvature for T
͓
͔
Ͼ700 K. A three-parameter Arrhenius fit to the data, which takes this into account gives k1(T)
ϭ(9.7Ϯ1.5)ϫ10Ϫ9TϪ0.68 exp (158Ϯ65) K/T . Our experiments also show that the 293 K rate
͓
͔
constant is invariant to pressure between 2 and 11 Torr (N2). We have also characterized the
C2HϩNO2 reaction theoretically. A large portion of the potential energy surface ͑PES͒ of the
C ,H,N,O system has been investigated in its electronic ͑singlet͒ ground-state using DFT with
͓
͔
2
2
the B3LYP/6-311ϩϩG(3df,2p) method and MO computations at the CCSD(T)/6-311ϩ
ϩG(d,p) level of theory. Seventeen isomers and thirty-two transition structures were found to
connect reactants to products following eighteen different channels. Hydroxyl cyano ketone 11 and
formylisocyanate 16 were found to be the most stable intermediates, although the reaction flux
through them, as a fraction of the total, is likely to be small over the temperature range studied. A
part of the PES corresponds with that of the HCCOϩNO reaction ͓I. V. Tokmakov, L. V. Moskaleva,
D. V. Paschenko, and M. C. Lin, J. Phys. Chem. A 167, 1066 ͑2003͔͒, and the dominant product
channels for C2HϩNO2 proceed via the same nitrosoketene intermediate that is formed initially in
the HCCOϩNO reaction. However, unlike in the latter reaction, the fate of the much more highly
excited nitrosoketene formed by C2HϩNO2 is likely to be governed dynamically. We present
arguments as to the likely product channels for C2HϩNO2 based on both statistical and dynamical
considerations. A statistical description overwhelmingly favors the product set HCCOϩNO.
Dynamical considerations on the other hand favor both the HCNϩCO2 and HCCOϩNO product
sets. Formation of HCNOϩCO appears unlikely. Energetically allowed paths, leading to five
other product sets, namely, HNCOϩCO, HOCNϩCO, HOCCϩNO, HONCϩCO, and HNC
ϩCO2 , have also been identified, and are discussed. © 2003 American Institute of Physics.
͓DOI: 10.1063/1.1573192͔
I. INTRODUCTION
Besides C2H formation in flames by H-atom abstraction
reactions of C2H2 with H, OH, or O, other routes have been
proposed in which C2H is formed by O or OH reactions with
a C3Hx (xϭ0 to 3͒ species; more specifically C2H was
shown to be formed by C3H2ϩO in C2H2 /H/O atomic
flames.20 Further reaction of C2H with C2H2 leads to the
C4Hn (2рnр5) series14,21,22 and by reaction of C2H2 with
C4H3 or C4H5 the aromatics C6H5 or C6H6 , respectively, are
formed.
The ethynyl radical (C2H) has been detected in interstel-
lar space1–4 and in planetary atmospheres.5,6 Thus its low-
temperature kinetics have received a great deal of attention
in recent years.7–12 It is also known to play a major role in
the high-temperature chemistry of combustion,13,14 where it
is linked to the ubiquitous acetylene oxidation reaction that
leads, via the highly reactive CH2(˜
a 1A1) and CH(X 2⌸)
radicals, to C3Hx (xϭ0–4).15 From this C3Hx backbone, the
different species within which are connected by reactions of
H2 and H, a number of routes have also been proposed for
formation of the first aromatic ring structures.16–19 These are
the building blocks of polycyclic aromatic hydrocarbons
͑PAH͒, which are the likely precursors of soot particles in
aliphatic hydrocarbon fuel combustion.
In order to refine our knowledge of the complex chem-
istry of small hydrocarbon radicals in combustion environ-
ments we have recently studied the kinetics of the reactions
of C2H with O2 , C2H2 , H2 , NO, CH4 , and C2H6 over an
extended temperature range.23–31 We have also unambigu-
ously identified the reactions of C2H with O atoms as the
dominant source of CH(A 2⌬) chemiluminescence in
C2H2 /O/H atomic flames,32 and in a separate study we have
shown that the CH(A 2⌬) yield of the very fast C2HϩO
→CHϩCO reaction33 is of the order of 8%.34
a͒
Author to whom correspondence should be addressed. Electronic mail:
Shaun.Carl@chem.kuleuven.ac.be
b͒
On leave from Faculty of Chemistry, University of Education, Hanoi,
Vietnam.
As with PAH and soot formation, reactions of the oxides
0021-9606/2003/118(24)/10996/13/$20.00
10996
© 2003 American Institute of Physics
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
The reaction of ethynyl with nitrogen dioxide
10997
of nitrogen NOx in combustion environments have continued
to attract the attention of experimental as well as theor-
etical scientists due to their detrimental implications for
our atmospheric environment. This has led to the de-
velopment of techniques to reduce NOx emissions such as
thermal DeNOx ,35 NOx-OUT,36 RAPRENOx ,37 and
NO-reburning,38–40 the underlying chemistry of which is still
not adequately characterized.41 We have contributed to im-
proving our understanding of this complex NOx chemistry by
investigating reactions such as C2HϩNO,28,24 NOϩC2H2 ,42
NOϩC2H3 ,43 and HCCOϩNO.44,45 Rate constants for the
reaction C2HϩNO2 represent significant missing data in
NOx chemistry at combustion temperatures. We have thus
focused our attention on this reaction in the present work.
In stationary source hydrocarbon combustion, a large
fraction of NOx is in the form of NO so that reactions of
small hydrocarbon radicals with this species usually domi-
nate their NO2 counterparts, particularly at high tempera-
tures. The degree of participation of NO2 in NOx flame
chemistry depends largely on the temperature-sensitive
NO ⇔ NO quasi-steady-state, which is controlled mainly
FIG. 1. Experimental pulsed photolysis/chemiluminescence apparatus used
to determine absolute rate constants of the reaction C2HϩNO2→products.
determine experimentally the absolute rate constants for the
reaction of C2H with NO2 for which no experimental data
exists. Secondly, to explore the PES in great detail and to
ascertain the likely products.
͓
͔
͓
͔
2
II. EXPERIMENT
by the reactions NOϩHO2→NO2ϩOH, NO2ϩH→NO
ϩOH, NOϩHϩM→HNOϩM, and HNOϩH→NOϩH2 .
They usually dictate that concentrations of NO2 are signifi-
cant at temperatures below about 1500 K. Thus in low-
temperature and fuel-rich regions—those found in typical
NO-reburning conditions, for example—radical reactions in-
volving NO2 are expected to be significant.
A. Apparatus and method
The pulsed-laser photolysis/chemiluminescence experi-
mental apparatus ͑Fig. 1͒ used here to determine the absolute
rate constants of C2HϩNO2 is described in detail
elsewhere.53 Here we give a general outline with details spe-
cific to the present experiments.
Further, the C2H radical is one of only a few radicals
that is amenable to detection in combustion systems by
C2H radicals were generated in a small volume along the
central axis and away from the walls of a stainless steel
reaction chamber by pulsed laser photolysis of C2H2 at 193
chemiluminescence
emissions
via C HϩO (and O )
͓
2 2
→CH(A 2⌬)ϩprod. .46,47 Thus in order to make full use of
͔
nm ͑ArF excimer laser; Ϸ15 mJ cmϪ2 pulseϪ1; 15 ns pulseϪ1
;
these easily-detectable chemiluminescence signatures and to
quantitatively relate them to the immediate chemical envi-
ronment it is necessary to characterize fully the reactivity of
the precursor species, viz., C2H, of the characteristic blue,
CH(A)→(X), emissions.
2 Hz repetition rate͒. The reaction cell was equipped with
three quartz windows; two for passage of the photolysis
beam through its center and one for UV-Vis detection at right
angles to the photolysis beam’s optical axis. The cell is con-
nected to a vacuum/gas-flow system and a rotary vacuum
pump allowing a continuous through-flow of gas mixtures of
known homogeneous composition and constant total pres-
sure ͑typically 5.0 Torr N2 , Ϸ666 Pa͒. All gases were ob-
tained commercially and, with the exception of C2H2 , used
without further purification. The purities were as follows:
N2 , 99.9997%, acting as a buffer; C2H2 , 99.6% ͑UCAR͒;
NO2 , 2.5% in ultrahigh purity He ͑Air Products͒. A further
verification of the NO2 fraction was performed in the labo-
ratory using long-path visible absorption. A fraction,
NO /͓Total͔, of (2.47Ϯ0.06)ϫ10Ϫ2 was determined, in
Of particular relevance to the present investigation are
the experimental and theoretical product distribution studies
of the reaction HCCOϩNO since part of the PES is common
to that of the C2HϩNO2 reaction. Experimental investiga-
tions of the product branching for the HCCOϩNO reaction
of Boullart et al.,48 Rim and Hershberger,49 and Eickhoff and
Temps50 show that the important reaction products are
(HCNO)isomerϩCO and (HCN)isomerϩCO2 , the former be-
ing dominant. In our earlier theoretical work51 on the
HCCOϩNO PES we have found that, besides the products
HCNOϩCO and HCNϩCO2 , a three-membered cyclic
structure and formyl isocyanate ͑structures 14 and 16 of this
work͒ are also stable isomers, but their connections with the
reactants were not clear. In a subsequent publication,52 we
have presented an improved treatment of the PES using
higher levels of theory and also performed RRKM-master
equation analyses incorporating the effect of internal rota-
tions on the state densities. Again only the two previously
reported product channels51 were found to be important, and
(HCNO)isomerϩCO, was shown to be the dominant product,
in agreement with direct experimental product data.48–50
The purpose of the present work is twofold. Firstly to
͓
͔
2
agreement with that stated by the manufacturer. Any acetone
contained in the C2H2 sample was removed by trapping at
195 K. The gas mixtures in the reaction chamber were able
to be heated to about 900 K by means of Ni/Cr resistive wire
coils surrounding a ceramic tube ͑99.7% Al2O3 , with an
internal, gray, oxidized SiC coating͒ through which the gas
mixtures flow. Temporal and spatial variations in the gas
temperature during the experiments ranged from Ϯ1 K at
288 K to Ϯ15 K at 800 K, our highest-temperature experi-
ment.
Concentrations of the co-reactant, NO , were accu-
͓
͔
2
rately determined using total reactor pressure—measured by
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10998
J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
Carl et al.
nm laser fluence (Ϸ1.5ϫ1016 photons cmϪ2 pulseϪ1) to
suppress possible production of other species by two-photon
absorption of C2H2 .57
Once generated, C2H radicals undergo rapid reaction
with the co-reactant NO2 and its precursor, C2H2 ,
a 10 Torr Barocel pressure sensor ͑Datametrics͒—and partial
flow rates—measured by calibrated mass flow controllers
͑MKS Instruments Inc.͒. Typical total flow rates through the
reaction chamber were 200 sccm ͑cm3 minϪ1 at STP͒; suffi-
ciently high to remove reaction products between successive
laser shots. Optical emissions from the center of the reaction
chamber ͑see below͒ were imaged onto a optically-filtered
photomultiplier tube ͑PMT͒. The resulting voltage was digi-
tized by a fast 8-bit analog-to-digital converter ͑ADC 200,
Pico Technology Ltd.͒ and stored on computer for analysis.
Typically between ten and twenty intensity-versus-time pro-
files were averaged for each measurement at each NO2 con-
centration. The concentration of C2H2 was on average ͑over
the T-range of 288 to 800 K͒ 2.0ϫ1014 cmϪ3 which, accord-
ing to our flow calibrations, was reproducible to within Ϯ3%
and remained stable to within Ϯ2% during the determination
of each rate constant. The average initial concentration of
C2H in our system was calculated to be about 4
ϫ1011 cmϪ3. This is based on an absorption cross section
for C2H2 of 1.4ϫ10Ϫ19 cmϪ2 at 193 nm ͑Ref. 54͒ and a
quantum yield for C2H production of near unity.55,56 The
C2HϩNO2→products,
C2HϩC2H2→products.
͑R1͒
͑R2͒
Earlier studies on C2H reactions in this laboratory23,24
have utilized a chemiluminescence method to follow the
concentration of C2H. It relies on the presence of a high
excess concentration of O2 , thus initiating the following pro-
cesses:
C HϩO →CH A 2⌬͒ϩproducts
͑R3a͒
͑R3b͒
͑R4͒
͑
2
2
→other products
CH A 2⌬͒→CH X 2⌸͒ϩh␯ Ϸ431 nm͒.
͑
͑
͑
Since the rate of process ͑R4͒ is ͑much͒ greater than the total
rate of loss of C H , the concentration of CH(A), and
͓
͔
2
concentration of the reactant, NO , was varied between 5
͓
͔
hence the observed CH(A→X) emission intensity, Iobs(t), at
2
ϫ1013 cmϪ3 and 1.5ϫ1015 cmϪ3 giving rise to I(CH ) in-
tensity profiles ͑see below͒ with decay rates ranging from
0.5ϫ105 sϪ1 to 4ϫ105 sϪ1. Thus the ratio C H / NO
*
Ϸ431 nm, is proportional to the product C H O . Thus,
͓
͔͓
͔
2
2
provided O remains constant during the measured decay
͓
͔
2
͓
͔ ͓
͔
2
of C H , I (t) is directly proportional to C H .
͓
͔
͓
͔
2
2
obs
2 t
was sufficiently small in these experiments ͑on average Ϸ5
ϫ10Ϫ4) to ensure negligible influence of any secondary or
side ͑radical–radical͒ reactions which would either consume
or regenerate C2H. The rate of C2H removal by its reactions
with NO2 and C2H2 is between two and three orders of mag-
nitude higher than the expected rate of C2H self-reactions or
of C2H with any product radicals.
For the experiments reported here however a variant of
the above chemiluminescence method was used that requires
no O addition and which has a greater sensitivity to C H
͓
͔
2
2
thus allowing a lower C H to be used. It relies on the
͓
͔
2
2
same emission as the former method, CH(A)→CH(X), but
here CH(A) is formed in high yields by the reaction of C2H
with O atoms that arise from the simultaneous 193 nm pho-
tolysis of NO2 .
According to a recent study by Sun et al.,60 photolysis at
193 nm of NO2 has two dissociation channels,
B. Monitoring C2H
3
NO ϩh␯ 193 nm͒→O P͒ϩNO
͑R5a͒
͑R5b͒
͑
͑
2
It has been shown that there exists only one fragment
channel for single-photon dissociation of C2H2 at 193 nm:
C2HϩH.55,56 A fraction of C H may however be formed in
1
→O D͒ϩNO
͑
͓
͔
2
with a branching fraction of 0.55Ϯ0.03 to ͑R5b͒. In the same
study a room temperature rate constant for O(1D)ϩNO2 was
determined as (1.5Ϯ0.3)ϫ10Ϫ10 cmϪ3 sϪ1 and the absorp-
tion cross section of NO2 at 193 nm was estimated to be
(2.9Ϯ1.2)ϫ10Ϫ19 cmϪ2. Under our experimental condi-
tions, a fraction of Ϸ4ϫ10Ϫ3 of NO should thus be pho-
its electronically excited A 2⌸ state.57,58 Under our experi-
mental conditions it is expected that the decay rate of the any
C H(A 2⌸) initially formed will be at least 6.7ϫ105 sϪ1
͓
͔
2
due to collisional quenching alone by 5 Torr of N2 : based on
kq(A 2⌸→X 2⌺)ϭ4ϫ10Ϫ12 cm3 sϪ1 for He.58 This decay
rate is more than a factor of 2 greater than the highest decay
rate measured in these experiments. It has also been sug-
gested that some C2H2 may remain electronically excited
following 193 nm absorption by residing in a metastable
triplet state—most likely as ‘‘unreactive’’ vinylidene
͓
͔
2
tolyzed. The fate and possible influence of O(1D) in our
system is discussed in the next section. Suffice it to say here
that O(1D) atoms were effectively quenched to (O 3P) by
collisions with N2 on time scales much shorter than the
C H (1/e) lifetime.
͓
͔
2
H2CC(˜
a 3B2).59 However, in contrast to earlier studies em-
The O(3P)-atoms generated by ͑R5a͒ and indirectly via
ploying end-product analysis of static samples, which in-
ferred a high quantum yield for production of the metastable
triplet species,54 state-resolved dynamic studies, in particular
predissociation reaction-time studies,55 found no indication
for formation of metastable acetylene or vinylidene. This is
in agreement with a very recent collision-free H-atom
quantum-yield investigation that determined an average yield
of 0.94 ͑Ϯ0.12͒ C2H produced per 193 nm photon
absorbed.56 In the present work we used a relatively low 193
͑R5b͒ will react with C2H yielding a high fraction of elec-
tronically excited CH,33
C HϩO→CH A͒ϩproducts
͑R6a͒
͑R6b͒
͑
2
→other products.
In the presence of O(3P) atoms and once a quasisteady
state is established ͓effectively within 2 ␮s given the 0.54 ␮s
radiative lifetime of CH(A 2⌬) ͑Ref. 61͔͒, Iobs(t) is propor-
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
The reaction of ethynyl with nitrogen dioxide
10999
tional to C H O(3P) t . However, the relatively low con-
where the term kqi represents the total pseudo-first-order rate
constant for physical quenching of CH(A).
After several (1/e) lifetimes of CH(A), or Ϸ2 ␮s, i.e.,
on a time scale much shorter than the removal of C2H,
͓
͔ ͓
͔
2
t
centration of O(3P) atoms generated in these experiments
are susceptible to a small decrease during measurement of
Iobs(t). It is therefore important to know the time depen-
dence of O(3P) in order to determine the relative C H
CH(A)
reaches
a
quasi-steady-state such that
͓
͔
͓
͔
͓
͔
2 t
t
d CH(A) /dtϭ0. Under these conditions,
͓
͔
from Iobs(t). More strictly, as shown below, it is only the
change in O(3P) due to reaction with NO2 that need be
͓
͔
t
k6a
known in order to derive the rate constant for NO2ϩC2H
from exponential decays of Iobs(t).
CH A͒
t͒ϭ
C H O .
͓ ͔ ͓ ͔
2
͑5͒
͓
͑
͔ ͑
ss
t
t
k4ϩkqi
Determination of O(3P) is straightforward in the
Since both NO and C H are in large excess of both
͓ ͔ ͓ ͔
2 2 2
͓
͔
t
present experiments since well-established reactions with
known concentrations of NO2 and with C2H2 are mainly
responsible for its time dependence,
O(3P) and C H —and therefore constant—and since re-
͔ ͓ ͔
2
͓
moval of O(3P) by C2H is negligible, the time dependence
of O(3P) should follow a simple exponential function de-
͓
͔
scribed by
3
O P͒ϩNO →NOϩNO,
͑R7͒
͑
2
3
3
O P͒ ϭ O P͒ exp Ϫ kЈϩkЈ͒t͒,
͑6͒
͓ ͑
͔
͓ ͑
͔
͑
͑
t
0
7
8
3
O P͒ϩC H →products.
͑R8͒
͑
2
2
where kЈϭk7 NO and kЈϭk8 C H .
͓
͔
͓
͔
2
2
2
7
8
O(3P) atoms will react with NO2 with removal rates for the
present experiments between 500 sϪ1 and 15 000 sϪ1 at 298
K and about half these values at 800 K. The rate of O(3P)
removal due to reaction with 4ϫ1014 cmϪ3ϫ(293/T) of
C2H2 is about 50 sϪ1 at 293 K and about 800 sϪ1 at 800 K,62
Substituting Eqs. ͑2͒ and ͑6͒ into Eq. ͑5͒ and using the
relation of Eq. ͑3͒ gives
k6a
3
Iobs t͒ϭ⌰
C H O P͒
͑
͓
͔ ͓ ͑
͔
2
0
0
k4ϩkqi
and with Ϸ5ϫ1011 cmϪ3 of C2H is about 50 sϪ1 20
NO is in large excess of O
.
As
, is described by a
͓ ͔ ͓ ͔
0
ϫexp Ϫ kЈϩkЈϩkЈϩkЈ͒t͒.
͑7͒
͑
͑
1
2
7
8
O
t
͓
͔
2
single-exponential decay function. This function has a much
weaker dependence on time than C H ͑see below͒.
Therefore the CH(A) chemiluminescence intensity follows a
simple exponential decay described by
͓
͔
t
2
Though the reaction C2HϩO is essential for monitoring the
relative C2H concentration ͓channel ͑R6a͔͒, the removal of
C2H due to reaction with O atoms is negligible in these
investigations. The rate constant for C2HϩO→products is
about 9ϫ10Ϫ11 cm3 sϪ1 ͑Ref. 20͒ and that of NO2ϩC2H
→products—as determined in these experiments—is 1.2
ϫ10Ϫ10 cm3 sϪ1. Thus C2HϩO contributes less than 0.3%
to the observed removal of C2H and is therefore neglected in
the following analysis.
Iobs t͒ϭA exp Ϫktotalt͒,
͑8͒
͑
͑
k
totalϭk2ЈϩkЈ8ϩk1Јϩk7Ј
ϭ k ϩk ͒ C H ϩ k ϩk ͒ NO .
͑9͒
͑
͓
͔
͑
͓
͔
2
2
8
2
2
1
7
The parameters ktotal ͑units sϪ1͒ and A are determined by a
weighted least-squares fit to Iobs(t). Each Iobs(t) profile is
determined from raw emission data by subtraction of an
emission profile taken in the absence of C2H2 from that
taken in the presence of C2H2 . This procedure effectively
distinguishes laser scattered light and window fluorescence
from the desired CH(A)→CH(X) emission.
The changing concentration of C2H with time is given
by
d C H
͓
͔
2
t ϭk1 NO C H ϩk C H C H .
͔͓ ͔͓
͑1͒
Since kЈ and kЈ are constants for a fixed C H the
͓
͔
Ϫ
͓
͔
͓
͔
2 t
2
2
2
8
2
2
t
2
2
2
dt
term (k ϩk ) C H appears only as the ordinate intercept
͓
͔
2
8
2
2
of plots of ktotal versus NO . The term kЈ is however a
͓
͔
Loss of C2H through molecular diffusion or convective flow
2
7
͑at rates of ϳ1000 sϪ1͒ is negligible in these experiments
function of NO , but since k is well established over the
͓
͔
2
7
temperature range of our experiments63–68 and since NO
with minimum C H decay rates of 5ϫ104 sϪ1
.
͓
͔
͓
͔
t
2
2
is known from flow calibrations, it may be readily calculated.
Actually, k7Ј contributes only about 8% to the gradient of
Solving Eq. ͑1͒ gives a simple exponential form for
C H ,
͓
͔
t
2
plots of ktotal versus NO at all temperatures ͓when em-
͓
͔
2
C H ϭ C H exp Ϫ kЈϩkЈ͒t͒,
͑2͒
͓
͔
͓
͔
͑
͑
2
t
2
0
1
2
ploying the k7(T) expression of Estupinan et al., k7(T)
ϭ4.21ϫ10Ϫ12 exp(273/T) ͑Ref. 68͔͒. Thus a straight line
where kЈϭk1 NO and kЈϭk2 C H .
͓
͔
͓
͔
2
2
2
1
2
may be fitted to plots of (ktotal-kЈ) versus NO and the
͓
͔
2
7
The chemiluminescence intensity Iobs(t) is directly pro-
portional to the concentration of electronically excited CH
radicals,
gradients will be equal to k1 : the rate constant to be deter-
mined.
Iobs t͒ϭ⌰k CH A͒ t͒,
͔ ͑
ss
͑3͒
͑
͓
͑
4
III. EXPERIMENTAL RESULTS
here ⌰ is a constant representing the overall photon collec-
tion efficiency of the detection system.
Our initial task was to establish whether or not the initial
presence of O(1D), produced by photolysis of NO2 , could
interfere with our determination of k1 . Figure 2 shows two
emission profiles each of 50 ␮s duration and collected at 298
The time rate of change of CH(A) is described by
d CH A͒
͓
͑
͔
t ϭk6a C H O Ϫ k ϩk ͒ CH A͒
͔ ͓ ͔ ͔
t
, ͑4͒
͓
͑
͓
͑
2
t
t
4
qi
dt
K under identical conditions of C H ϭ5.8ϫ1014 cmϪ3
,
͓ ͔
2 2
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11000
J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
Carl et al.
FIG. 2. Emission profiles from the center of the reaction chamber following
photolysis of C2H2 and NO2 in the presence excess He ͑plot a, diamonds͒
and N2 ͑plot b, circles͒ both at a total pressure of 2 Torr. Apart from the
different buffer gases the profiles were recorded under identical conditions
FIG. 3. Typical emission profiles, Iobs(t), from the center of the reaction
chamber following pulsed 193 nm photolysis of C2H2 and NO2 in the pres-
ence of N2 at a total pressure of 5 Torr and at a temperature of 293 K. Profile
͑a, diamonds͒: NO ϭ8.7ϫ1013 cmϪ3. Profile ͑b, circles͒: NO ϭ1.1
͓
͔
͓
͔
2
2
2
2
2
ϫ1015 cmϪ3
.
of temperature, pressure, C H (tϭ0), NO (tϭ0) and 193 nm pho-
͓
͔
͓
͔
tolysis energy. The initial intensity and gradient difference between the two
plots is attributed to the additional reactions, C2HϩO(1D)→CH(A)ϩCO
and O(1D)ϩC2H2→products, respectively in plot ͑a͒.
Thus it is clear from these measurements that, for t
у5 ␮s, 2 Torr N2 is sufficient to ensure no additional emis-
sion due to the initial presence of O(1D). Further, the very
large excess of the sum ͓C2H2͔ϩ͓NO2͔ over photolysis
products ensures that there are no additional secondary or
side reactions that may remove or regenerate C2H or O(3P)
sufficiently to cause a perturbation to the observed decay
profiles.
NO ϭ1.4ϫ1014 cmϪ3, and at 2 Torr total pressure but in
͓
͔
2
the presence of difference bath gases, He ͑plot a͒ and N2
͑plot b͒. Since the rate constant for quenching of O(1D) by
He is less than 3ϫ10Ϫ13 cm3 sϪ1 and that for N2 is 1.8
ϫ10Ϫ11 cm3 sϪ1 69 O(1D) will have a (1/e) lifetime in these
,
experiments with a lower limit of 51 and 0.8 ␮s, respec-
tively, due to these processes. Thus any influence of O(1D)
on the observed emission intensity should be revealed in the
difference between profiles ͑a͒ and ͑b͒.
Figure 3 shows two examples of CH(A) emission pro-
files, Iobs(t), which, as explained above, very closely repre-
sent ͓C2H͔t . Emission profile ͑a͒ is taken under conditions
of relatively low ͓NO2͔. The time dependence is therefore
mainly due to reaction ͑2͒. Emission ͑b͒ is recorded in the
presence of higher ͓NO2͔. A weighted least-squares fit ͑solid
line͒ of each profile to Eq. ͑8͒, yields ktotal . For tу5 ␮s,
both Iobs(t) profiles exhibit the expected simple exponential
function over about two orders of magnitude. The somewhat
greater emission intensity at short times of profile ͑b͒ simply
reflects the increased photolytic production of ͓O(3P)͔ due
to higher ͓NO2͔.
The most obvious difference is that the initial emission
intensity ͓i.e., the extrapolated long-time intensity to tϭ0
neglecting that of the first 5 ␮s, which is due to spontaneous
emission from CH(A) produced initially by two-photon ab-
sorption of C2H2 at 193 nm͔ is a factor of 5 greater for the
He experiment than for the N2 experiment. This intensity
difference is attributable to the presence of an additional
chemiluminescence reaction, viz., O(1D)ϩC2H→CH(A)
ϩCO. Further, the rate constant for this reaction channel
should be about four times greater than that for the reaction
Derived ktotal data for each ͓NO2͔ minus ͑the calculated͒
kЈ is plotted as a function of NO in Fig. 4 for all tempera-
͓
͔
2
7
O(3P)ϩC H→CH(A)ϩCO 4.5ϫ10Ϫ12 cm3 sϪ1 ͑Ref. 34͔͒
tures covered. A linear fit to the data gives k1 as the slope
and (k ϩk ) C H as the intercept. As shown in Table I,
͓
2
if one assumes the O(3P)/(O 1D) branching fraction in the
͓
͔
2
2
8
2
193 nm photolysis of NO2 derived by Sun et al.60 This im-
plies a large rate constant for O(1D)ϩC2H→CH(A)ϩCO
of about 2ϫ10Ϫ11 cm3 sϪ1—although this derivation ne-
glects the possibility that some O(1D) or O(3P) reactions
occurs with vibrationally excited C2H. The second obvious
difference between the two plots is the rate of decay of
Iobs(t). In He, this rate of decay is a factor of 2 greater. Since
we have found, in a separate experiment, that the actual in-
crease in decay rate of Iobs(t) with additional NO2 was simi-
lar for the He and N2 experiments, we attribute the difference
in slopes here mainly to fast O(1D) removal by reaction with
C2H2 . We also derive a rate constant for this reaction of
about 1.3ϫ10Ϫ10 cm3 sϪ1, similar to that of C2HϩC2H2 .23
Again, the possible influence of vibrationally excited C2H in
the He measurements is not considered here.
the magnitude of the intercept for each temperature is in
good agreement with the calculated product (k2ϩk8)
ϫ C H , where k has a T-independent value of 1.3
͓
͔
2
2
2
23
ϫ10Ϫ10cm3 sϪ1
,
k8(T)ϭ1.2ϫ10Ϫ17T2.09 exp͑Ϫ786 K/T͒
cm3 sϪ1 ͑Ref. 62͒ and C H varies with T according to 4
͓
͔
2
2
ϫ1014 cmϪ3ϫ293 K/T. Even at the highest temperature, the
term k8 C H contributes less than 5% ͑at 800 K͒ to the
͓
͔
2
2
intercept.
The derived k1 values of all measurement sets, also
listed in Table I, show that the title reaction, ͑1͒, has a large
rate coefficient of 1.17ϫ10Ϫ10 cm3 sϪ1 at 293 K that de-
creases slightly with increasing temperature as depicted also
in the Arrhenius plot of Fig. 5. Also included both in Table I
and in the Arrhenius plot of Fig. 5 are the results of 293 K
measurements taken at 2 and 11 Torr total pressure (N2).
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
The reaction of ethynyl with nitrogen dioxide
11001
FIG. 5. ͑a͒ Arrhenius plot of the data of absolute rate constants for the
reaction C2HϩNO2→products over the temperature range 288–800 K
FIG. 4. Pseudo-first-order removal rate of C H as a function of NO at
͓
͔
2
2
͑open circles͒ with least-squares fits; ͑i͒ simple Arrhenius fit k (T)ϭ(7.6
͕
1
several temperatures. The removal rate of C2H is the rate of decay of the
observed emission intensity minus k7 NO that represents the removal rate
Ϯ1.0)ϫ10Ϫ11 exp (130Ϯ50) K/T , ͑ii͒ a three-parameter Arrhenius fit
͓
͔
͖
͓
͔
2
k (T)ϭ(9.7Ϯ1.5)ϫ10Ϫ9TϪ0.68 exp (158Ϯ65) K/T . ͑b͒ Dotted curve: a
͓
͔
͖
͕
of O(3P) .
1
͓
͔
best fit to rate constant data for the isoelectronic reaction CNϩNO2
→products, taken from Refs. 72, 73, and 74.
These results show no dependence of the overall rate con-
stant with pressure. This finding will be expanded upon in
the next sections.
All calculations were performed using the GAUSSIAN 98
suite of programs.70 Geometry optimizations were conducted
using density functional theory ͑DFT͒ with the popular hy-
brid functional, B3LYP, in conjunction with the 6-311
ϩϩG(d,p) basis set. Electronic energies of the B3LYP-
optimized geometries were refined using a larger basis set,
6-311ϩϩG(3df,2p), and coupled-cluster theory with all
single and double excitations plus perturbative corrections
for triple substitutions, CCSD(T)/6-311ϩϩG(d,p). Har-
monic vibrational wavenumbers were calculated at both Har-
tree Fock ͑HF͒ and B3LYP levels to characterize the station-
ary points as equilibrium or transition structures. The zero-
point energies ͑ZPE͒ were derived from B3LYP frequencies
and scaled down by the standard factor of 0.97. In the
CCSD͑T͒ calculations, the core orbitals were kept frozen.
Intrinsic reaction coordinate ͑IRC͒ calculations were also
performed to confirm the intermediates connected to the
transition structures.
The straight line in Fig. 5 represents the best simple
Arrhenius
fit
to
the
͔
data:
k1(T)ϭ(7.6Ϯ1.0)
ϫ10Ϫ11 exp (130Ϯ50) K/T . The highest-temperature mea-
͓
surements however indicate a downward curvature in the
Arrhenius plot. To allow for this, we also fitted a three-
parameter Arrhenius expression to the data. This gives
k1(T)ϭ(9.7Ϯ1.5)ϫ10Ϫ9TϪ0.68 exp (158Ϯ65) K/T . For
͓
͔
both expressions, the stated uncertainties encompass both
statistical ͑2␴͒ and likely systematic errors.
IV. QUANTUM CHEMICAL CALCULATIONS
Having established the rate constants of the C2HϩNO2
reaction, we now attempt to identify the possible and prob-
able product channels making use of quantum chemical cal-
culations.
TABLE I. Measured rate constants for C2HϩNO2→products. These data
also include 293 K measurements taken at 2 and 11 Torr total pressure. The
experimentally determined ordinate intercepts may be compared with those
expected based on k2 C H ϩk C H .
͔
2
͓
͔
͓
2
2
8
2
Temperature/ k1 /(10Ϫ10
Ordinate
k2 C H
ϩ
͔
Pressure/
Torr
͓
2
2
K
cmϪ3 sϪ1
)
intercept/sϪ1 a,b k8 C H /sϪ1 a,c
͓
͔
2
2
288
293
293
293
380
500
650
800
1.20Ϯ0.08 (50Ϯ3)ϫ103
1.14Ϯ0.09 (50Ϯ3)ϫ103
1.20Ϯ0.10
53ϫ103
52ϫ103
5
5
2
11
5
5
1.18Ϯ0.11
1.15Ϯ0.07 (39Ϯ3)ϫ103
1.01Ϯ0.10 (26Ϯ2)ϫ103
1.00Ϯ0.11 (25Ϯ2)ϫ103
0.76Ϯ0.08 (25Ϯ2)ϫ103
41ϫ103
30ϫ103
24ϫ103
20ϫ103
5
5
aOnly values for 5 Torr experiments are given.
Scheme 1. A summary of the reaction paths available to the C2HϩNO2
reaction with the exception of some minor paths leading from structure 11.
The solid arrows show the likely dominant paths. These paths lead to the
product sets HCCOϩNO and HCNϩCO2 , and to redissociation to reac-
tants.
bErrors are 2␴.
cCalculations based on C H ϭ4ϫ1014 cmϪ3ϫ293 K/T,
a
k2 of
͓
͔
2
2
1.3ϫ10Ϫ10 cm3 sϪ1 ͑Ref. 23͒ and
ϫexp(Ϫ786 K/T) cm3 sϪ1 ͑Ref. 62͒.
a
k8 of 1.2ϫ10Ϫ17 T2.09
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11002
J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
Carl et al.
FIG. 6. The potential energy surface ͑PES͒, calculated at the CCSD͑T͒/6-311ϩϩG͑d,p͒//B3LYP/6-311ϩϩG͑d,p͒ϩZPE level, for C2HϩNO2. ͑a͒ The
intermediates and products directly accessible from structure 4, which is always formed in this reaction. B3LYP/6-311ϩϩG͑d,p͒-optimized geometrical
structures of the relevant intermediates are displayed at the bottom, the transition state structures are displayed at the top ͓TS 6/9, TS 9/P2, TS 7/10, and TS
7/P7 are displayed in Fig. 6͑c͔͒. Bond lengths are given in angstroms and bond angles in degrees. ͑b͒ The intermediates and products directly accessible from
structure 5. ͑c͒ The intermediates and products directly accessible from structure 11.
The important reaction paths ͑together with some minor
ones͒ investigated in this study are shown in Scheme 1.The
important paths ͑see Sec. VI͒ are shown with solid lines. For
the sake of brevity some minor paths leading from structure
11 have been omitted from Scheme 1 but may be ascertained
from Figs. 6͑b͒ and 6͑c͒. We have identified seventeen iso-
mers, which are both open-chain and cyclic structures. The
connections between them and to products are described by
32 transition structures ͑TS͒. These are all displayed in Figs.
6͑a͒, 6͑b͒, and 6͑c͒ together with their associated potential
energies and connections, showing all eighteen reaction path-
ways identified. In Figs. 6͑a͒–6͑c͒ and Scheme 1 the various
6͑c͒ bond lengths have units of angstroms and bond angles
are represented in degrees, iÕj stands for a transition structure
connecting the equilibrium structures i and j, a number in
front of TS iÕj is added if a distinction need be made between
transition states connecting the same iÕj products. The rela-
tive energies of the stationary points on the C ,H,N,O
͓
͔
2
2
PES, which are obtained using three distinct methods, are
listed in Table II. In general, the B3LYP values are compa-
rable to those derived from the CCSD͑T͒ method. In the
following discussion, unless otherwise stated, the energies
refer to those obtained from CCSD(T)/6-311ϩϩG(d,p)
ϩZPE.
isomers of the C ,H,N,O system are labeled from 2 to 18,
͓
͔
2
2
the
product
sets
are
labeled
as
follows:
P3ϭ(NO
V. QUANTUM CHEMICAL CALCULATION RESULTS
P1ϭ(HCNϩCO2),
P2ϭ(HNCϩCO2),
ϩHCCO), P4ϭ(COϩHNCO), P5ϭ(COϩHOCN), P6
ϭ(COϩHCNO), and P7ϭ(COϩHONC). In Figs. 6͑a͒–
Although the C2HϩNO2 reactive system is complex, an
important simplifying feature is that all channels connecting
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
The reaction of ethynyl with nitrogen dioxide
11003
FIG. 6. ͑Continued.͒
and 11 with barriers of 20 and 95 kcal molϪ1 for forward and
reverse directions, respectively. The low-lying isomer 11
subsequently provides the last step for this path by undergo-
ing a concerted 1,3-H migration and breaking of the C–C
bond yielding P1, HCNϩCO2 .
The final path to P1 occurs via TS 11Õ12, which de-
scribes an exchange of the C and N atoms by an in-plane
rotation yielding 12. From 12, C–N bond rupture together
with an O-to-N H migration gives P1,
C2HϩNO2 to products pass through intermediate 4, cis ni-
trosoketene, which lies 122 kcal molϪ1 below the reactants.
The paths leading to 4 are shown with thick dashed lines in
Fig. 6͑a͒. Thus, excepting for the chance of redissociation of
2 to C2HϩNO2 ͑discussed later͒, the distribution of the vari-
ous product channels depends upon the fate of the highly
excited cis nitrosoketene intermediate 4. This has already
been the subject of detailed RRKM-master equation analyses
by Vereecken et al.44 and Tokmakov et al.76 in the context of
the HCCOϩNO reaction system, which is common to the
present system at energies of 82 kcal molϪ1 below C2H
ϩNO2 . However, in the HCCOϩNO reaction, the cis ni-
trosoketene intermediate is formed with that much less inter-
nal energy.
CPs→ 4Õ6→6→6ÕP1 →P1
Path 1 P1͒
͑
͓
͔
CPs→ 4Õ5→5→5Õ8→8→8Õ11→11→11ÕP1 →P1
͓
͔
Path 2 P1͒
͑
Before further discussion of the likely product distribu-
tion we briefly give a description of the various product path-
ways. To simplify and shorten the description below we refer
to the processes following the paths C2HϩNO2 , 1→2
→2Õ3→3→3Õ4→4 or C2HϩNO2 , 1→3→3Õ4→4 as com-
mon pathways ͑or CPs͒ since every product channel of
C2HϩNO2 begins with either of these paths.
CPs→ 4Õ5→5→5Õ8→8→8Õ11→11→11Õ12→12
͓
→12ÕP1 →P1 Path 3 P1͒.
͔
͑
The sections of the paths ͑above͒ enclosed with square
brackets indicate the differences between paths leading to the
same products. This notation will be used throughout.
A. Formation of HCN¿CO2 , P1
B. Formation of HNC¿CO2 , P2
Three pathways terminate at HCNϩCO2 , the most
stable products. The first path contains the lowest barrier
heights of the entire energy surface ͓Fig. 6͑a͔͒. Proceeding
from the cis nitrosoketene intermediate ͑4͒, two rearrange-
ments have been identified. Isomer 4 has an appropriate
nuclear configuration for a 1,4 electrocyclization via TS 4Õ6,
which has a barrier of 6 kcal molϪ1. Thus, 4 leads to the
four-membered ring 6 ͑Ϫ131 kcal molϪ1͒. Intermediate 6 can
subsequently undergo a concerted cycloreversion, over a bar-
rier of 18 kcal molϪ1 ͑TS 6ÕP1͒, yielding P1.
The second path involves a transformation from 4 to 5.
Intermediate 5 is a rotamer of 4, which is accessible by an
out-of-plane N–O rotation over a small but significant ͑see
later͒ barrier.44 Structure 8 can be formed by a 1,4 hydrogen
migration from 5. TS 8Õ11 ͑Ϫ90 kcal molϪ1͒, is the transition
structure for a 1,3 hydroxyl migration connecting minima 8
The production of P2 may occur by two pathways. One
pathway ends by breaking the C–C bond of structure 11
accompanying a 1,4-hydrogen migration via TS 11ÕP2
͑Ϫ137 kcal molϪ1͒. The other path involves formation of a
four-membered ring, 9, from structure 6 via TS 6Õ9 ͑Ϫ58
kcal molϪ1͒. Ring 9 subsequently undergoes a concerted 2
͓
ϩ2 cycloreversion yielding P2 via the TS 9ÕP2 ͑Ϫ87
͔
kcal molϪ1͒ with an energy barrier of only 5 kcal molϪ1
,
CPs→ 4Õ5→5→5Õ8→8→8Õ11→11→11ÕP2 →P2
͓
͔
(Path 1 P2)
CPs→ 4Õ6→6→6Õ9→9→9ÕP2 →P2
͓
͔
Path 2 P2͒.
͑
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11004
J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
Carl et al.
TABLE II. Relative energies ͑kcal/mol͒ of the C HNO stationary points
calculated using different methods.
͓
͔
2
2
C. Formation of HCCO¿NO, P3
Scheme 1 reveals that NOϩHCCO formation could oc-
cur by passage through ͑at least͒ either two, three or four
isomers, depending upon the entrance channel traversed, in
which the system initially passes through either the ni-
troacetylene 2 or the ethynylnitrite 3 isomer. We have made
extensive attempts to locate a one-step transition structure
directly connecting isomer 3 and HCCOϩNO products, but
there appears to be no such connection that lies low enough
to be of any relevance. This can be readily rationalized by
recognizing that breaking of the N–O͑–C͒ bond of 3 actually
leads to an HCCO structure with the unpaired electron on the
B3LYP
B3LYP
6-311ϩϩG
(3df,2p)a
CCSD͑T͒
6-311ϩϩG
(d,p)a
6-311ϩϩG
System
(d,p)a
0
Ϫ72
Ϫ84
Ϫ126
Ϫ127
Ϫ129
Ϫ126
Ϫ115
Ϫ90
0
Ϫ73
Ϫ84
Ϫ126
Ϫ127
Ϫ130
Ϫ127
Ϫ115
Ϫ91
0
Ϫ69
Ϫ80
Ϫ122
Ϫ123
Ϫ131
Ϫ120
Ϫ110
Ϫ92
1 (C2HϩNO2)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
˙
O-atom. Such an HCCO state corresponds to linear,
Ϫ83
Ϫ84
Ϫ80
2
˜
˙
electronically-excited HCCO(B ⌸) (H–CwC–O) and not
Ϫ183
Ϫ168
Ϫ150
Ϫ159
Ϫ155
Ϫ197
Ϫ126
Ϫ168
Ϫ204
Ϫ190
Ϫ84
Ϫ197
Ϫ168
Ϫ128
Ϫ109
Ϫ27
Ϫ184
Ϫ169
Ϫ151
Ϫ159
Ϫ155
Ϫ197
Ϫ126
Ϫ168
Ϫ204
Ϫ190
Ϫ84
Ϫ197
Ϫ168
Ϫ129
Ϫ110
Ϫ27
Ϫ185
Ϫ170
Ϫ149
Ϫ155
Ϫ151
Ϫ193
Ϫ129
Ϫ169
Ϫ207
Ϫ192
Ϫ82
Ϫ199
Ϫ176
Ϫ130
Ϫ118
Ϫ28
to its ground electronic state. The B state of HCCO lies about
95 kcal molϪ1 higher71 than the HCCO(X A ) ground state
2
˜
Љ
and is thus not accessible by C2HϩNO2 . The only product
path available to 3 then is a 1,3-NO migration over a low-
lying TS 3Õ4 leading to cis nitrosoketene. From either 4 or 5
a simple dissociation of the C–N bond leads to HCCO
ϩNO,
P1 (CO2ϩHCN)
P2 (CO2ϩHNC)
P3 (NOϩHCCO)
P4 (COϩHNCO)
P5 (COϩHOCN)
P6 (COϩHCNO)
P7 (COϩHONC)
P8 (NOϩHOCC)
TS 2Õ3
TS 3Õ4
TS 4Õ5
TS 4ÕP6-trans
TS 4ÕP6-cis
TS 4Õ6
CPs→P3
Path 1 P3͒
͑
CPs→ 4Õ5→5 →P3
Path 2 P3͒.
͑
͓
͔
D. Formation of HNCO¿CO, P4
These products lie 69 kcal molϪ1 below HCNOϩCO.
Their formation involves traversal of at least seven transition
states. There are three pathways, namely,
Ϫ12
Ϫ78
Ϫ13
Ϫ78
Ϫ9
Ϫ74
Ϫ110
Ϫ103
Ϫ110
Ϫ118
Ϫ69
Ϫ85
Ϫ114
Ϫ56
Ϫ110
Ϫ103
Ϫ110
Ϫ119
Ϫ70
Ϫ85
Ϫ114
Ϫ57
Ϫ109
Ϫ103
Ϫ109
Ϫ114
Ϫ59
Ϫ79
Ϫ113
Ϫ58
CPs→4Õ5→5→5Õ8→8→8Õ11→11→11Õ13→13
→ 13Õ14→14→14ÕP4 →P4
Path 1 P4͒
͑
͓
͔
TS 4Õ7
TS5Õ8
CPs→4Õ5→5→5Õ8→8→8Õ11→11→11Õ13→13
→ 13Õ15→15→15Õ16→16→1-16ÕP4
TS 6ÕP1
TS6Õ9
TS 7ÕP6
TS 7ÕP7
TS7Õ10
͓
͔
Ϫ68
Ϫ81
Ϫ51
Ϫ69
Ϫ82
Ϫ52
Ϫ54
Ϫ82
Ϫ43
→P4
Path 2 P4͒
͑
TS 8ÕP7
TS 8Õ11
TS 9ÕP2
TS 11ÕP1
TS 11ÕP2
TS 11Õ12
TS 11Õ13
TS 12ÕP1
TS 12Õ15
TS 13Õ14
TS 13Õ15
TS 14ÕP4
TS 15ÕP5
TS 15Õ16
TS 1-16ÕP4
TS 2-16ÕP4
TS 11Õ17
TS 17Õ18
TS 18ÕP5
Ϫ87
Ϫ90
Ϫ88
Ϫ87
Ϫ89
Ϫ88
Ϫ89
Ϫ90
Ϫ87
CPs→4Õ5→5→5Õ8→8→8Õ11→11→11Õ13→13
→ 13Õ15→15→15Õ16→16→2-16ÕP4
͓
͔
Ϫ134
Ϫ136
Ϫ137
Ϫ115
Ϫ134
Ϫ115
Ϫ96
Ϫ141
Ϫ153
Ϫ114
Ϫ122
Ϫ144
Ϫ125
Ϫ94
Ϫ134
Ϫ136
Ϫ137
Ϫ115
Ϫ134
Ϫ116
Ϫ98
Ϫ142
Ϫ153
Ϫ115
Ϫ122
Ϫ144
Ϫ125
Ϫ95
Ϫ136
Ϫ137
Ϫ141
Ϫ112
Ϫ135
Ϫ116
Ϫ93
Ϫ140
Ϫ150
Ϫ114
Ϫ117
Ϫ138
Ϫ123
Ϫ95
→P4
Path 3 P4͒.
͑
These three paths diverge only after isomer 13. All processes
up to minimum 11 have already been discussed, thus we
proceed from there. Isomer 11 has to overcome the TS 11Õ13
͑Ϫ112 kcal molϪ1͒ which describes a 1,2-OH migration lead-
ing to isomer 13 ͑Ϫ149 kcal molϪ1͒. From here two options
that lead to P4 are available: a 1,4-H migration via the high-
lying TS 13Õ14 ͑Ϫ93 kcal molϪ1͒ to 14 or C–C bond rupture
to open the three-membered ring via TS 13Õ15 ͑Ϫ140
kcal molϪ1͒ to give the linear 15. The first path proceeds
directly from 14 via TS 14ÕP4 ͑Ϫ150 kcal molϪ1͒ to P4
which involves a breaking of both the C–C and C–N bonds
to eliminate CO.
Ϫ91
Ϫ129
Ϫ92
Ϫ129
Ϫ93
Ϫ126
Isomer 15 may proceed by a 1,2 H migration to 16.
There exists from here two paths directly connecting to P4.
The two transition structured involved TS 1-16ÕP4 ͑Ϫ138
aUsing B3LYP/6-311ϩϩG(d,p) optimized geometries. All values are cor-
rected for ZPEs obtained from B3LYP/6-311ϩϩG(d,p) harmonic fre-
quencies and scaled down by 0.97.
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
The reaction of ethynyl with nitrogen dioxide
11005
kcal molϪ1͒ and TS 2-16ÕP4 ͑Ϫ123 kcal molϪ1͒ describe the
progress of a simultaneous 1,2-H migration and a C–N bond
cleavage. They differ in their orientation of CO and in the
position of the H-atom.
CPs→4Õ7→7→7Õ10→10→P8
VI. DISCUSSION
Path 1 P8͒.
͑
As, from a theoretical point of view, a three-parameter
Arrhenius expression is generally expected to provide better
fits, this form of expression appears to be better suited to
extrapolate our data to higher temperatures. Still, for T
у1500 K, extrapolations should be done with caution, as the
precise form of the T-dependence is not known. At T
ϭ1500 K, an error of some 25% can be expected. Anyhow,
for temperatures above 1500 K, NO2 becomes less important
in hydrocarbon combustion systems due to reactions such as
NO2ϩH→NOϩOH.
E. Formation of HOCN¿CO, P5
These products lie at Ϫ176 kcal molϪ1. There are two
pathways to these products, which deviate only after isomer
11. There final step is a C–N bond cleavage of isomer 15 via
TS 15ÕP5 ͑Ϫ114 kcal molϪ1͒ and a C–O bond cleavage of
18 accompanied by a C-to-O migration of the H atom ͑TS
18ÕP5͒,
CPs→4Õ5→5→5Õ8→8→8Õ11→11→ 11Õ12→12
͓
As far as the authors are aware, ours are the first rate
constant determinations for the C2HϩNO2 reaction. Rate
constant values for the isoelectronic reaction CNϩNO2 have
however been published72–74 and the best modified Arrhenius
fit through the available data is displayed in Fig. 5 along with
the present results for C2HϩNO2 . Both reactions have rate
coefficients with a negative temperature dependence—not at
all unusual for radical–radical reactions. This is the result of
͑i͒ a loose variational entrance transition state, combined
with ͑ii͒ a lower-lying but tight transition state from the ini-
tial intermediate to fragmentation or isomerisation products.
This leads to ͑i͒ a decreased rate coefficient of the initial
reactant association step with increasing temperature, due to
the entrance channel variational TS becoming tighter, and ͑ii͒
to an increased preference with increasing temperature for
redissociation to reactants over product formation. Which of
the two effects dominates depends on the particular case.
Similar negative temperature dependencies have also been
observed for other reactions closely related to C2HϩNO2 ,
namely NCOϩNO ͑Ref. 75͒ and HCCOϩNO.45,76
Whilst it is difficult to predict the importance of the
C2HϩNO2 reaction in reburning environments without de-
tailed kinetic modeling and without accurate knowledge of
the branching fractions for C2HϩNO2 ͑see below͒, a crude
comparison with the important reburning reaction, HCCO
ϩNO, may still be formulated.
Accepting that below about 1500 K the NO2 /NO ratio is
governed only by NOϩHO2→NO2ϩOH and NO2ϩH
→NOϩOH,77 one can write a simplified expression for the
ratio of HCN formation by the reactions C2HϩNO2 and
HCCOϩNO,
→12Õ15→15→15ÕP5 →P5
CPs→4Õ5→5→5Õ8→8→8Õ11→11→ 11Õ17→17
Path 1 P5͒
͑
͔
͓
→17Õ18→18→18ÕP5 →P5
Path 2 P5͒.
͑
͔
F. Formation of HCNO¿CO, P6
There are three relatively simple and distinct pathways.
The first two originate from minimum 4 by C–C bond rup-
ture described by two transition states TS 4ÕP6-cis ͑Ϫ109
kcal molϪ1͒ and TS 4ÕP6-trans ͑Ϫ103 kcal molϪ1͒, which
are distinguished by the different orientations of CO ͓Fig.
6͑a͔͒. The third pathway involves more steps and a passage
over the relatively high TS 4Õ7 forming 7 before passing
over the even higher TS 7ÕP6 to products, which involves a
concerted 1,2-H migration and rupture of the C–C bond,
CPs→ 4ÕP6-cis →P6
Path 1 P6͒
Path 2 P6͒
Path 3 P6͒.
͓
͔
͑
͑
͑
CPs→ 4ÕP6-trans →P6
͓
͔
CPs→ 4Õ7→7→7ÕP6 →P6
͓
͔
G. Formation of HONC¿CO, P7
These products may be formed from 8 by breaking the
C–C bond, via the TS 8ÕP7 ͑Ϫ89 kcal molϪ1͒. Another path-
way starts from 4, in which the 1,2 hydrogen migration re-
quires much energy to overcome TS 4Õ7 ͑Ϫ59 kcal molϪ1͒ to
yield the isomer 7. Structure 7 may undergo a 1,4-H migra-
tion at the same time as breaking the C–C bond to form the
P7 via TS 7ÕP7,
CPs→ 4Õ5→5→5Õ8→8→8ÕP7
͓
͔
R HCN͒
͑
C HϩNO
2
2
→P7
Path 1 P7͒
͑
R HCN͒
͑
HCCOϩNO
NOϩHO
CPs→ 4Õ7→7→7ÕP7 →P7
Path 2 P7͒.
͑
͓
͔
k T͒
HO
k T͒
B1 T͒ C H
͑ ͓ ͔
C HϩNO 2
2
͑
͓
͔
͑
2
2
2
ϭ
,
k T͒
H
͓ ͔
k T͒HCCOϩNOB2 T͒ HCCO
͑ ͑ ͓ ͔
͑
NO ϩH
H. Formation of HOCC¿NO, P8
2
͑10͒
These are the least stable products, lying only Ϫ28
kcal molϪ1 below the reactants. Through a 1,2-H migration
isomer 7 transforms to isomer 10 via TS 7Õ10 ͑Ϫ43
kcal molϪ1͒. The product channel P8 is formed from isomer
10 by simple bond cleavage without a transition state. This is
the highest lying product pathway that is accessible to the
C2HϩNO2 reaction,
where k(T)XϩY represent the overall rate constant for the
given XϩY reaction,45,78,79 while B1(T) and B2(T) are the
branching fractions to the HCN product channels for the
C2HϩNO2 and HCCOϩNO reactions, respectively.44,76
In the above ratio, the strong T-dependence of the rate
constant for the channel leading to HCN of the HCCO
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11006
J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
Carl et al.
ϩNO ͑Refs. 44, 76͒ reaction is compensated by the
T-dependencies of the other k(T)’s, such that the factor
per vibrational mode is close to the reaction barriers that 4
faces. Thus 4 lives only for one or two vibrational periods
(ϳ10Ϫ13 s); too short by at least an order of magnitude for
statistical redistribution of its internal energy over all its vi-
brational modes. Therefore only a dynamical description can
reliably predict the product distribution. Such a treatment is
far beyond the scope of this work, so the following discus-
sion is necessarily limited to qualitative considerations.
In the recent detailed RRKM master equation analysis
by Tokmakov et al.76 of intermediate 4 as formed in the
HCCOϩNO reaction, where its internal energy is much
lower ͑only у 41 kcal molϪ1͒ it was calculated that 4 under-
goes only minor redissociation to HCCOϩNO but mainly
traverses the lower-lying structures TS 4Õ5, TS 4Õ6, TS 4ÕP6-
cis or TS 4ÕP6-trans, with the latter two ͑loose͒ TS’s domi-
nant. However when 4 is formed in the present system, with
an internal energy of у122 kcal molϪ1, the number of states
available at the ͑variational͒ bottleneck for HCCOϩNO for-
mation will completely dominate those associated with the
aforementioned TS’s. Therefore if the C2HϩNO2 system
would still behave statistically, HCCOϩNO should be the
dominant products. Any crossing of TS 4Õ5 will still result in
HCCOϩNO as TS 5Õ8 lies approximately equally high as
the variational TS 5ÕP3, but is much more rigid.
The dynamics will be driven by the initially highly ex-
cited modes resulting from the large potential energy release
from 1 to 4. The initial excitation of each bond will depend
on which of the CPs is traversed. On examination of the
various bond-length and bond-angle changes in traversing
each of the CPs it is clear that relatively little of the 122
kcal molϪ1 internal energy of 4 will reside in the C–C stretch
as its bond length suffers relatively little change. Rather, it is
expected that, after both CPs, the C–N- and C–O-stretching,
and the C–C–N- and C–N–O-bending modes will be con-
siderably excited. This situation will favor either a crossing
of TS 4Õ6 forming the ring structure 6 to finally yield HCN
ϩCO2 , or, alternatively, a direct C–N scission of 4 to give
HCCOϩNO. Formation of P6 (HCNOϩCO) from 4 is un-
likely under these conditions as this requires significant ini-
tial energy in the C–C stretching mode.
The product branching fraction of this system will be
influenced by increasing temperature, but only due the effect
on redissociation from minimum 2. Structures that reach TS
2Õ3 or pass directly to 3 from C2HϩNO2 should show a
branching to products that is only marginally dependent on
temperature.
By elimination then, it is unlikely, from either a dynami-
cal or statistical view point that the reaction C2HϩNO2 will
yield either HNCϩCO2 ͑P2͒, HNCOϩCO ͑P4͒, HONC
ϩCO ͑P7͒ or HOCCϩNO ͑P8͒. Formation of HCNOϩCO
͑P6͒ also seems unlikely but, at present, cannot be entirely
ruled out.
Finally, even though significant redissociation to reac-
tants is expected to occur at higher temperatures from mini-
mum 2 ͑following one of the two initial association chan-
nels͒, the C2HϩNO2 reaction should exhibit no pressure
dependence. This is because the lifetime of 2 is too short for
any collisional energy transfer to occur at pр1 bar and effect
the steady-state energy distribution; hence the ratio of rates
k T͒
k T͒
͑
C HϩNO
2
͑
NOϩHO
2
2
͑11͒
k T͒
k T͒HCCOϩNOB2 T͒
͑ ͑
͑
NO ϩH
2
has only a very weak T-dependence, ranging from 0.42 at
900 K to 0.49 at 1500 K. Thus over the typical reburning
temperature range ͑1200–1500 K͒ Eq. ͑10͒ may be well ap-
proximated by
R HCN͒
͑
C HϩNO
C H HO B T͒
͔͓
͓
͔
͑
2
2
2
2
1
ϭ0.46
.
͑12͒
R HCN͒
HCCO H
͓ ͔͓ ͔
͑
HCCOϩNO
We also note here that at the lower end of the tempera-
ture range used for reburning, large HO2 concentrations are
generated by oxidation of the hydrocarbon fuel.80
As explained in the experimental section, the observed
downward curvature of the Arrhenius plot for C2HϩNO2
should be due to a combination of a loose ͑variational͒ en-
trance channel TS and redissociation of a short-lived, inter-
nally excited isomer to reactants. Redissociation cannot rea-
sonably occur beyond intermediate 2 ͓see Fig. 6͑a͔͒. This is
because intermediate 3 will almost certainly traverse the low-
lying and fairly loose TS 3Õ4 rather than reform reactants.
Once 4 is formed, the fraction of redissociation is expected
to be negligibly small as there is comparatively little ener-
getic hindrance for passage to the most likely product chan-
nels.
Redissociation from minimum 2 is however very likely.
The deep well of 2 will ensure complete randomization of
the internal energy over all modes. Whereas it is expected
that a traversal of TS 2Õ3 ͑lying only 9 kcal molϪ1 below
reactants͒ will be favored at very low-temperatures, redisso-
ciation will gradually prevail with increasing temperature as
the number of accessible internal states in the very loose
variational entrance TS 1Õ2 eventually overwhelms those of
the tight TS 2Õ3. Redissociation itself is not a sufficient ex-
planation for the rapidly diminishing rate constant at T
Ͼ700 K observed for this reaction, nor for that at T
տ900 K predicted theoretically for the similar HCCOϩNO
reaction.76 This is because both systems posses two entrance
channels, one of which appears not to be subject to redisso-
ciation. Thus at very high temperatures, when dissociation
from one entrance channel is complete, the likely cause for
the rapid decrease in rate constant for both HCCOϩNO and
C2HϩNO2 at high temperatures is the gradual tightening of
the variational transition state of the entrance channel that
remains operative.
As mentioned earlier, partitioning between the various
product channels hinges on the fate of the cis nitroketene
rotamer 4. Given the large amount of internal energy of 4 ͑at
least 122 kcal molϪ1͒ one expects rapid interchange between
4 and its trans counterpart 5, as the energy barrier to the
pertinent ͑out-of-plane͒ rotation is only 13 kcal molϪ1. How-
ever, several other possibilities exist for the transformation of
4. A quantitative prediction of the possible fate of 4, how-
ever, is no easy task, because the conventional statistical-rate
approaches ͑RRKM and master equation analysis͒ cannot be
applied here. The average internal energy of ϳ10 kcal molϪ1
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
The reaction of ethynyl with nitrogen dioxide
11007
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expect that this reaction shows no pressure-dependence until
pressures much greater than 1 bar.
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The absolute rate coefficient for the reaction C2H
ϩNO2 has been measured for the first time. The experimen-
tal temperature range covered allows reliable extrapolations
of the rate coefficient to temperatures up to 1500 K. As is
typical of many radical–radical reactions, the rate constant
for the C2HϩNO2 reaction decreases with increasing tem-
perature and also exhibits a downward curvature. This tem-
perature dependence is attributed to ͑i͒ an increased redisso-
ciation to reactants of one of the two initially formed adducts
with increasing temperature and ͑ii͒ a tightening of the en-
trance channel transition states with increasing temperature.
Because of its high rate constant, the title reaction is
expected to participate in NOx flame-chemistry at tempera-
tures below 1500 K. The likely product channels, HCN
ϩCO2 and HCCOϩNO, which are based on our qualitative
dynamical considerations, also make C2HϩNO2 a poten-
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͑below 1500 K͒, although its impact will be less than the
HCCOϩNO reaction. A detailed experimental study of the
temperature dependence of the product distribution of C2H
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Ϯ1.8)ϫ10Ϫ12 cm3 sϪ1
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ACKNOWLEDGMENTS
The authors are indebted to the Fund for Scientific Re-
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