Ab initio chemical kinetics for the ClOO + NO reaction: Effects of temperature and
pressure on product branching formation
P. Raghunath and M. C. Lin
Citation: The Journal of Chemical Physics 137, 014315 (2012); doi: 10.1063/1.4731883 View online: http://dx.doi.org/10.1063/1.4731883
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/137/1?ver=pdfcov Published by the AIP Publishing
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Ab initio
chemical kinetics for the ClOO
+ NO reaction: Effects
of temperature and pressure on product branching formation
P. Raghunath and M. C. Lina)
Center for Interdisciplinary Molecular Science, Department of Applied Chemistry, National Chiao Tung University, Hsinchu 300, Taiwan
(Received 5 March 2012; accepted 21 May 2012; published online 6 July 2012)
The kinetics and mechanism for the reaction of ClOO with NO have been investigated by
ab initio molecular orbital theory calculations based on the CCSD(T)/6-311
+G(3df)//PW91PW91/6-311+G(3df) method, employed to evaluate the energetics for the construction of potential energy surfaces and prediction of reaction rate constants. The results show that the reaction can produce two key low energy products ClNO+3O2via the direct triplet abstraction path and ClO+ NO2via
the association and decomposition mechanism through long-lived singlet pc-ClOONO and ClONO2
intermediates. The yield of ClNO+ O2 (1) from any of the singlet intermediates was found to
be negligible because of their high barriers and tight transition states. As both key reactions ini-tially occur barrierlessly, their rate constants were evaluated with a canonical variational approach in our transition state theory and Rice–Ramspergen–Kassel–Marcus/master equation calculations. The rate constants for ClNO+3O
2 and ClO+ NO2 production from ClOO+ NO can be given
by 2.66× 10−16T1.91 exp(341/T) (200–700 K) and 1.48× 10−24T3.99 exp(1711/T) (200–600 K),
respectively, independent of pressure below atmospheric pressure. The predicted total rate constant and the yields of ClNO and NO2 in the temperature range of 200–700 K at 10–760 Torr pressure
are in close agreement with available experimental results. © 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4731883]
I. INTRODUCTION
Chlorine and chlorine oxide radicals play an impor-tant role in the destruction of atmospheric ozone in the polar stratosphere, through various photolytic or chemical processes.1–3 The self-reaction of ClO radicals can produce
ClOO, OClO, Cl, O2, and Cl2, in addition to the
recombi-nation products including the three isomers of Cl2O2. The
reaction has been investigated extensively experimentally3
and computationally.4 Although the ClOO radical is
short-lived as a result of its low Cl-O2 bond energy of around
4.8 kcal/mol,5–7it has been considered to be a temporary sink
for the Cl atoms at low temperature in the stratosphere. The kinetics for the formation of ClOO from Cl + O2 reaction
and decomposition of ClOO radicals have been investigated extensively both experimentally and theoretically.5–14 Along with ClOx radicals, NOx (x = 1,2) are also very important
in ozone destruction processes;15 their interaction is of great
relevance to the stratospheric chemistry.
For the interaction of the ClOO radical with NO, a sub-ject of interest in the present work, Enami et al.16 first
mea-sured the rate constant using the ultra-sensitive cavity ring-down spectrometry (CRDS) technique17,18 by monitoring
both ClOO and NO2 in the temperature range of 205–243 K
at pressures 50-150 Torr; they proposed the following reaction mechanism:
ClOO+ NO → ClNO + O2, (1)
a)Author to whom correspondence should be addressed. Electronic mail:
chemmcl@emory.edu.
→ ClONO2, (2)
→ ClO + NO2. (3)
The dominant products of the reaction were reported to be ClNO+ O2; the value for k(ClOO+NO)was measured to be
(4.5± 0.9) × 10−11cm3molecules−1s−1at 213 K. Branching
ratios of NO2 and ClNO were concluded to be 0.18± 0.02
and≈0.80, respectively at 213 K.16
The mechanism and kinetics of the related ClO + NO2 reaction system, including its forward and reverse
processes as well as the decomposition of its stable inter-mediate ClONO2, have been studied in detail in 2005 at
the CCSD(T)/6-311+G(3df)//B3LYP/6-311+G(3df) level of theory in conjunction with variational Rice–Ramspergen– Kassel–Marcus (RRKM) calculations.19 In this work, we
fo-cused on the effects of temperature and pressure on chlorine nitrate formation and decomposition. The heats of forma-tion of many of unstable intermediates such as ClOONO isomers have been predicted in this study. At the time, the importance of the ClOO + NO reaction in the strato-sphere was not recognized as the kinetics and mechanism for the reaction were not available. In 2006, the excellent work of Enami et al.16 on the kinetics of the ClOO + NO
reaction employing the CRDS technique to measure the de-cay rate of ClOO and the production rate of NO2 revealed
very significantly that the ClOO+ NO reaction occurred at a near gas-kinetic rate, but not forming the expected NO2
prod-uct by the obvious radical-radical head-to-head association/
014315-2 P. Raghunath and M. Lin J. Chem. Phys. 137, 014315 (2012)
decomposition mechanism. The authors suggested that as much as 80% of the “dark products” undetectable by their CRDS probing laser should be ClNO and O2most likely
pro-duced by the head-to-tail abstraction reaction.
In light of the interesting result of the ClOO+ NO reac-tion by Enami et al.16on the production of the ClNO and NO
2
metathetical products, from the Cl-atom and the terminal O-atom abstractions by NO, respectively, as aforementioned, we have carried out a comprehensive ab initio quantum calcula-tions to study the reaction system and clarify the mechanism involved. The computed potential energy surface and associ-ated transition state parameters have been utilized to predict the rate constant as a function of temperature and pressure with variational transition state theory (TST) and/or multi-channel (RRKM) theory for comparison with experimental values. The result is discussed in Secs.II–IVin detail.
II. COMPUTATIONAL METHODS
We have carried out the geometry optimization and en-ergy prediction for all the molecules related to the ClOO + NO reaction using the GAUSSIAN 03 program.20 The ge-ometries of the reactants, intermediates, transition states, and products of the reaction were computed at the PW91PW91/ 6-311+G(3df) level with Perdew–Wang functionals21,22
which have been shown to perform better than the commonly used B3LYP method for open-shell ClOxmolecules with less
spin contaminations.23 Theoretically, the optimized
geome-tries, frequencies and heat of formation of ClOO radicals are calculated at various methods and compared with experimen-tal data.23,24 The differences in the bond length and bond
an-gle of the radical between the predicted values with B3LYP/ 6-311+G(3df) and the experimental values reach as much as 0.422 Å and 6.5◦, respectively. These deviations could be at-tributed to the large electron correlation effect in the ClOO radical. When PW91PW91/6-311+G(3df) method was used to optimize the geometry of ClOO in this work, the above dif-ferences were reduced to 0.16 Å and 6.6◦with the Cl-O bond length closer to the experimental one. PW91PW91 provides more reasonable molecular geometries for ClOO comparing with experimental results.23,24
All geometries were analyzed by harmonic vibrational frequencies obtained at the same level to characterize station-ary points and were used for the rate constant calculations. The transition state geometries were then used as an input for IRC calculations to verify the connectivity of the reactants and products.25 For a more accurate evaluation of the energetic
parameters, single-point energy calculations of the station-ary points were carried out by the CCSD(T)/6-311+G(3df) method.26
For the entrance channel such as direct Cl-abstraction producing ClNO +3O2 and the formation of pc-ClOONO,
the canonical variational transition-state theory (CVTST) (Refs. 27and28) approach was utilized to locate transition states for the key steps which occur without well-defined transition states. The rate constant and product branching ra-tios were computed with a microcanonical variational RRKM
by the VARIFLEX program.29 The component rates were
evaluated at the E/J-resolved level and the pressure
depen-dence was treated by one-dimensional master equation cal-culations using the Boltzmann probability of the complex for the J distribution.30,31 For the barrierless association/ decomposition process, either the individual points or the fitted Morse function, V (R)= De{1 − exp[− β(R − Re)]}2,
were used to represent the minimum potential energy path (MEP) which will be discussed later. Here, Deis the bonding
energy excluding zero-point vibrational energy for an associ-ation reaction, R is the reaction coordinate (i.e., the distance between the two bonding atoms), and Re is the equilibrium
value of R at the stable intermediate structure. For the tight transition states, the numbers of states were evaluated accord-ing to the rigid-rotor harmonic-oscillator approximation.
III. RESULTS AND DISCUSSION
A. Potential energy surfaces and reaction mechanism
The optimized geometries of the reactants, intermedi-ates, transition stintermedi-ates, and products as well as the avail-able experimental values for them are shown in Fig. 1. The bond lengths and bond angles of these species optimized at the PW91PW91/6-311+G(3df) level are close to the ex-perimental values.24,32–33 The vibrational frequencies and
FIG. 1. The optimized geometries of the reactant, intermediates, transition states, and products computed at the PW91PW91/6-311+G(3df) level. The values in parenthesis are the experimental values (Refs.24,32–33). (Length in Å and angle in degree).
TABLE I. Calculated rotational constant and vibrational frequencies of the species involved in the ClOO+ NO reaction computed at PW91PW91/6-311+G(3df) level of theory. Species B (GHZ) Frequencies (cm−1) 2ClOO 71.1, 5.3, 4.9 297, 516, 1418 2NO 0.0, 50.7, 50.7 1897 1ClNO 88.5, 5.6, 5.2 327, 598, 1842 3O 2 0.0, 42.7, 42.7 1562 Pc-ClOONO 8.3, 2.6, 2.2 99, 207, 220, 299, 422, 550, 692, 1075, 1905 Pt-ClOONO 14.5, 1.8, 1.7 87, 169, 215, 298, 416, 533, 712, 960, 1850 ClONO2 11.8, 2.7, 2.2 137, 225, 381, 519, 673, 744, 798, 1306, 1785 3LM1 9.3, 1.0, 0.9 17, 23, 33, 33, 40, 328, 596, 1562, 1842 2ClO 0.0, 18.4, 18.4 863 2NO 2 236.9, 12.9,12.2 742, 1337, 1658 2NO 3 13.6, 13.6, 6.8 487, 487, 774, 1086, 1229, 1229 TS1 10.8, 1.8, 1.6 i403, 48, 98, 123, 194, 657, 827, 1289, 1808 TS2 7.3, 2.5, 2.0 i159, 88, 199, 275, 327, 504, 568, 1091, 1914 TS3 37.3, 1.6, 1.5 i589, 58, 147, 267, 313, 738, 788, 866, 1536 TS4 4.4, 3.6, 2.1 i97, 153, 168, 275, 362, 404, 446, 1358, 1892 TS5 4.5, 3.3, 2.0 i126, 101, 222, 263, 336, 383, 531, 1373, 1928 TS6 20.4, 1.5, 1.4 i720, 63, 115, 197, 248, 387, 584, 804, 1671
rotational constant of all species are summarized in Table I. The potential energy diagram obtained at the CCSD(T)/ 6-311+G(3df)//PW91PW91/6-311+G(3df) level with zero point energy corrections is presented in Fig. 2 and the rel-ative energies are calculated with respect to the reactants
ClOO+ NO.
The PES shown in Fig. 2 indicates that both
Cl-abstraction and O-N association and dissociation reactions producing radical products occur without well-defined tran-sition states. The dominating low energy reaction paths are discussed below.
Cl-atom abstraction: The Cl-abstraction reaction takes
place without an intrinsic transition state through a triplet PES via van der Waals complex of the O2+ ClNO products,
OO· · ClNO (LM1), with Cs symmetry (see Figs.1 and2).
FIG. 2. Schematic energy diagram for the ClOO + NO reaction com-puted at the CCSD(T)/6-311+G(3df)//PW91PW91/6-311+G(3df) level with ZPE corrections. Relative energies are given in kcal/mol at 0 K. Data in the round bracket are predicted at CCSD(T)/6-311 +G(3df)//B3LYP/6-311+G(3df) level from Ref. 19 and in square bracket at CASPT2/6-311+G(3df) //PW91PW91/6-311+G(3df) level of theory. Data in the curly bracket are predicted at G2M(RCC2)//PW91PW91/6-311+G(3df) method.
The complex is more stable than the ClOO+ NO reactants by 34.7 kcal/mol at the CCSD(T)//PW91PW91 level. Forma-tion of the complex LM1 occurs smoothly along the MEP by the concurrent shortening of the O2Cl· · NO bond and
the lengthening of the OO· · ClNO bond. LM1 has the O-Cl separation 3.592 Å and its geometrical parameters are almost equal to those in the ClNO +3O
2 products with a
small binding energy (0.4 kcal/mol). The ClNO and3O 2
prod-ucts with an overall exothermicity of 34.3 kcal/mol, which is close to the experimental heat of reaction, 32.5± 1 kcal/mol based on the experimental heats of formation (fH◦) at 0 K
for ClOO (23.8± 0.7 kcal/mol), NO (21.5 kcal/mol), ClNO (12.8 ± 0.1 kcal/mol), 3O
2 (0 kcal/mol) and ClONO2 (7.9
± 0.2 kcal/mol), ClO (24.2 ± 0.02 kcal/mol), NO2 (8.6
± 0.2), NO3(18.5± 5 kcal/mol), and Cl (28.6 kcal/mol).32,34
Association/dissociation reactions: In the initial steps
of second mechanism, the terminal O atom of ClOO bonds with the reactive N atom in NO by a barrierless process forming pc-ClOONO which is an exothermic complexa-tion process. The exothermicity is around 10.6 kcal/mol at the CCSD(T)//PW91PW91 level. Its related trans-type pt-ClOONO isomer is less stable by 0.3 kcal/mol. As shown in Fig. 1, the O-N bond lengths in pc-ClOONO and pt-ClOONO are 1.825 Å and 1.673 Å, respectively. As the reaction proceeds, pc-ClOONO intermediate can isomer-ize to the most stable intermediate ClONO2 with a total
exothermicity of 38.3 kcal/mol via TS1 with a small barrier of 2.6 kcal/mol. Barrier energy for same reaction was re-ported to be 6.7 kcal/mol by Zhu et al. at the CCSD(T)/6-311+G(3df)//B3LYP/6-311+G(3df) level.19The
exothermic-ity for formation of ClONO2 (38.3 kcal/mol) from ClOO
+ NO reaction is in good agreement with the experimen-tal heat of reaction, −37.4 ± 0.7 kcal/mol.32,34 In this po-tential energy surface, the cleavage of the O-N and O-Cl bond in the ClONO2isomer giving the products ClO+ NO2
and Cl + NO3 is predicted to be endothermic by 25.0 and
39.1 kcal/mol, respectively. For the reaction ClOO+ NO, the calculated heats of reaction for ClO+ NO2 and Cl+ NO3,
−13.3 and −0.8 kcal/mol, are in reasonable agreement
with the experimental values, −12.6 ± 0.7 and 1.83
± 5.0 kcal/mol.12 The isomerization between pc-ClOONO
and pt-ClOONO occurs mainly through the rotation of the NO group, with a barrier of 9.5 kcal/mol. The correspond-ing transition state TS2 is presented in Fig. 2. After the isomerization of pt-ClOONO, it can further dissociate at
the O-O bond to produce ClO + NO2 with a barrier of
17.5 kcal/mol (or 7.2 kcal/mol above the reactants). The
for-mation of ClNO +1O2 from pc-ClOONO and pt-ClOONO
occurs via TS4 and TS5, in which the Cl atom migrates to the neighboring N atom with the high barriers of 16.1 and 19.7 kcal/mol, respectively, above the reactants (see Fig. 2). The direct abstraction formation of ClO + NO2
from ClOO+ NO requires a very high energy above the re-actants via the triplet transition state TS6 (39.9 kcal/mol).
It should be mentioned that the formation of ClNO + O2 (1) on the singlet surface from pc-ClOONO via
the four-member-ring TS4 is not competitive with the loose variational triplet TS path giving the triplet products, ClNO + O2 (3), presented above because of the former’s
014315-4 P. Raghunath and M. Lin J. Chem. Phys. 137, 014315 (2012)
tight structure with a high barrier (16.1 kcal/mol at the CCSD(T)/6-311+G(3df)//PW91PW91/6-311+G(3df) level and 13.3 kcal/mol by the G2M method37) above the reac-tants as shown in Fig. 2. The predicted heat of reaction, −4.3 kcal/mol, is as much as 30.0 kcal/mol above the triplet products. The computed singlet-triplet splitting for the O2 is
thus 7.5 kcal/mol higher than the experimental value. The deficiency of the single reference methods in predicting the singlet-splitting gap of O2 is well-known.35,36 Based
on the geometries predicted at the
PW91PW91/6-311+G(3df) level, however, the full valence CASPT2 method reduces the size of the splitting to 23.7 kcal/mol,
which is much closer to the experimental value. We also calculated the singlet-triplet splitting energy difference to be 25.7 kcal/mol with the G2M(RCC2) method.
B. Rate constant calculation
The rate constants of the following low energy product channels are calculated by variational TST and RRKM rate theory using the energetics presented in Fig. 2 and the vibrational frequencies and rotational constants displayed in TableI.
C1OO + NO−−−→ C1NO +VTS1 3O2 (k1)
C1OO + NO−−−→ pc-C1OONOVTS2 ∗−−−→ C1ONOTSI ∗2−−−→ClONO2(+M) (k2) VTS3
−−−→ C1O + NO2 (k3),
where * denotes the chemically activated species.
Variational approach: As stated above, for both the
di-rect Cl-abstraction and the formation of pc-ClOONO, their initial steps occurring without well-defined transition states, we predicted their rate constants by using the CVTST approach26,27 to locate their transition states based on the
maximum Gibbs free energy criterion at each temperature. To evaluate the variational potential energy curves, the reac-tion pathways have been mapped out along the MEP with the tight convergence criterion and the projected frequency cal-culations were performed at the PW91PW91/6-311+G(3df). For instance, the MEP curve of the Cl-abstraction reaction forming LM1, OO· · ClNO, was obtained by varying the Cl-N bond distance from its equilibrium value (1.997 Å) at an interval of 0.1 Å, up to the separation at which the ClOO and NO fragments are completely separated at 4.5 Å. In order to obtain more reliable energies along the reaction path, we calculated the single-point energies, corrected by the second-order multireference perturbation theory (CASPT2)31 based
on the CASSCF optimized geometries with eight active elec-tons and eight active orbitals with the 6-311+G(3df) basis set. These calculations are performed with theMOLPROcode.38In
the same manner, we also located the loose transition states for the variational formation of the O-N bond in pc-ClOONO from ClOO+ NO and the breaking of ClO · · NO2 bond in
ClONO2. The resulting energies can be approximated with
the Morse potential energy functions in units of kcal/mol: VTS1(RCl-N)= 34.7{1 − exp[−2.12(R − 1.99)]}2, (4)
VTS2(RO-N)= 10.6{1 − exp[−2.32(R − 1.83)]}2, (5)
VTS3(RN-O)= 27.8{1 − exp[−2.57(R − 1.58)]}2. (6)
Using the Morse potential energies, computed moments of inertia and the vibrational frequencies of LM1 and pc-ClOONO parameters (see Tables S1 and S2 of the supplemen-tary material39), we searched for maximum G(T,s) or the
transition state which is approximately located at each tem-perature. The approximate locations of the dividing surfaces by the CVTST method estimated Cl-N bond as 4.298 Å and 4.198 Å at 200–400 K and 500–700 K, respectively, for the formation of ClNO+ O2via LM1. And similarly, for the
for-mation of pc-ClOONO, the estimated O-N bond separation was 2.85 Å at 200–700 K. The Morse potential of VTS3 was determined to be β= 2.57 Å for the dissociation of ClONO2.
These values will be used in the following rate constant cal-culation to confirm the reliability of treating these barrierless processes.
The rate constant for the forward reaction of the low en-ergy channels, ClOO+ NO, have been computed in the tem-perature range of 200–700 K and the pressure range of 10– 760 Torr with the Variflex code, whereas the higher energy channels are neglected. The VTST calculations were carried out with the unified statistical formulation of Miller40
includ-ing multiple reflection corrections41 above the shallow wells
of the prereaction and postreaction complexes. The Lennard-Jones parameters employed for the ClOO+ NO reaction are as follows: for LM1, ε/k= 230 K, and σ = 4.2 Å which are approximated to be the same as HOOClO system;42ClONO2
isomers are taken to be ε/k = 364.7 K and σ = 4.47 Å
(Ref.43) and for buffer gas N2, ε/k= 82 K and σ = 3.74 Å.44
For the electronic partition functions ClO (2
3/2 and21/2)
and NO (2) the energy gap of 318 cm−1 and 121.1 cm−1,
respectively, between their two spin-orbit states have been taken into consideration.32 The energy-transfer rate
coeffi-cients were computed on the basis of the exponential down model with theEdownvalue of 400 cm−1. To achieve
con-vergence in the integration over the energy range, an energy grain size of 100 cm−1 was used. This grain size provides
TABLE II. Three-parameter Arrhenius expressionsaof predicted individual product rate constants (cm3molecule−1s−1). P (Torr) T/K ClNO+3O2(k1) 10–760 200–700 2.66× 10−16T1.91exp(341/T) P (Torr) T/K ClONO2(k2) 10 200–700 1.20× 10−9T−4.37exp(570/T) 50 200–700 5.49× 10−9T−4.36exp(574/T) 150 200–700 1.78× 10−8T−4.37exp(571/T) 300 200–700 3.36× 10−8T−4.36exp(574/T) 400 200–700 4.65× 10−8T−4.37exp(572/T) 760 200–700 9.16× 10−8T−4.37exp(570/T) high-P 200–600 1.32× 10−24T4.0exp(1715/T) P (Torr) T/K ClO+ NO2(k3) 10–760 200–600 1.48× 10−24T3.99exp(1711/T) P (Torr) T/K ktot= k1+ k2+ k3 10–760 200–400 1.05× 10−19T3.06exp(746/T) 400–700 2.61× 10−15T1.60exp(−201/T) ak(T)= ATnexp (− E
a/RT) predicted for various temperature range in unit of cm3molecule−1s−1.
numerically converged results for all temperature studies with
the energy range spanning from 13 396 cm−1 below to
79 000 cm−1above the threshold. The total angular momen-tum J covered the range from 1 to 250 in steps of 10 for the
E- and J-resolved calculations.
ClOO + NO → ClNO + 3O
2: The rate
con-stant for the ClOO + NO → ClNO + 3O2 reaction
by abstraction via LM1 was calculated in the tempera-ture range of 200 to 700 K for comparison with the available experimental data measured by Enami et al.16
using the cavity ring-down spectroscopy method in 50–
150 Torr pressure of O2/N2 diluent at 205–243 K.
As alluded to above, the transition states of the barrierless en-trance treated by the CVTST approach were located at the Cl-N separation of 4.297 Å at 200–400 K and 4.197 Å at 500–700 K. In our calculations, the lowest vibrational modes 33.9 cm−1and 33.99 cm−1in both temperature regimes corre-sponding to the NO torsional motions, were treated as a one-dimensional free rotor. The predicted rate constants for the Cl-abstraction reaction for ClOO+ NO → ClNO +3O2(k1)
is a pressure-independent process as shown in Table IIand Fig.3are given by the following three parameter expression covering the temperature range of 200–700 K at the 10–760 Torr pressure:
k1= 2.66 × 10−16T1.91 exp(341/T)cm3 mol−1s−1 The experimentally measured rate constants for this re-action are 3.69 × 10−11 and 3.82× 10−11cm3 molecule−1
sec−1 at 213 K and 223 K, respectively;16 they are in good
agreement with our predicted values 3.78× 10−11and 3.83 × 10−11 cm3 molecule−1 sec−1, respectively, at the two
temperatures.
ClOO + NO → ClONO2 and ClOO + NO → ClO
+ NO2: The rate constants of these reactions have been
treated with multiple reflections above the entrance well using the molecular parameters and the energies presented in TableI and Fig.1. For the barrierless entrance pc-ClOONO associa-tion reacassocia-tion, the CVTST approach with a free rotor for ClO gives rise to a transition state at the O-N separation of 2.85 Å at 200–700 K. For the rate constant calculation, the
inter-nal rotation of the NO group in pc-ClOONO is hindered by a 9.5 kcal/mol barrier. The barrier energy is calculated for isomerization between pc-ClOONO and pt-ClOONO occur-ring mainly through the rotation of the NO group. This vi-brational mode (219 cm−1) is thus treated as a hindered rotor. Also, the internal rotation of the ClO group with the vibra-tional frequency of 137 cm−1at the ClONO2is hindered by a
7.3 kcal/mol barrier and thus also treated as a hindered rotor. Furthermore, the low frequencies at 99 cm−1for pc-ClOONO, 48 cm−1at TS1, 71 cm−1for the entrance transition state es-timated with the CVTS geometry were treated as free inter-nal rotors. For the exit channel of ClONO2 → ClO + NO2
reaction, we used the Morse potential with β= 2.57. The re-sults of our calculations are plotted in Figures 4 and 5 for the temperature range of 200–700 K and the pressure range of 10–760 Torr for comparison with all existing experimen-tal data. The calculations show that below 760 Torr, forma-tion of ClO + NO2 from ClOO + NO is a pressure
inde-pendent process. The calculated rate constant expressions for all the reaction product channels obtained by three-parameter
FIG. 3. Plot of predicted rate constant for ClOO+ NO → ClNO +3O 2(k1)
channel with respect to temperature. Experimental data (O) at 213 and 223 K and 50–150 Torr pressure is taken from Ref.16.
014315-6 P. Raghunath and M. Lin J. Chem. Phys. 137, 014315 (2012)
FIG. 4. Predicted rate constant for ClOO+ NO → ClONO2 (k2) channel
with respect to temperature and pressure.
fitting at 10–760 pressure range and 200–700 K temperature range are given in Table II. Recent results for ClOO+ NO → ClO + NO2reaction measured by the CRDS technique in
50–150 Torr pressure at 213–243 K16 are in good agreement
with our predicted results. At 213 K, the experimental rate 8.1 × 10−12 cm3 molecule−1 sec−1 compares closely with our
predicted rate 8.8 × 10−12 cm3 molecule−1 sec−1. The
ClONO2molecule was not detected experimentally; its yields
under experimental conditions are predicted to be negligible. Figure6summarizes the total and individual product rate con-stants of the ClOO+ NO reaction at the 10–760 Torr N2
pres-sure to compare with experimental data.
Product branching ratios: The branching ratios for all
product channels are shown in Fig.7as the functions of tem-perature and compared with experimental values measured for 50 Torr N2pressure. The results show that at temperature
213 and 223 K, the branching ratio of ClO+ NO2 yields are
0.19 and 0.16 which are in excellent agreement with experi-mental result 0.18± 0.02 and 0.15 ± 0.02, respectively. It is evident from Figure 7, channel 2 producing ClONO2 (k2) is
noncompetitive and its branching ratio is zero throughout the
FIG. 5. Predicted rate constant for ClOO+ NO → ClO + NO2(k3) channel
with respect to temperature at pressures (10–760 Torr). Experimental data (O) at 213 and 223 K and 50–150 Torr pressure is taken from Ref.16.
FIG. 6. Plot of predicted rate constant for individual product rate constant with respect to temperature and pressure at 150 Torr. Experimental data at 213–243 K and 50–150 Torr pressure is taken from Ref.16.
entire temperature range. In Figure7, the predicted branch-ing ratio for ClNO formation is 77%–98% in the temperature range 200–700 K; this implies that the contribution from the direct Cl-abstraction process is predominant.
IV. CONCLUSIONS
The mechanism, rate constants, and product branching ratios for the ClOO + NO reaction have been investigated at the CCSD(T)/6-311+G(3df)//PW91PW91/6-311+G(3df) level of theory in conjunction with CVTST and RRKM cal-culations. The results show that the most favorable low en-ergy products for the title reaction are ClNO+3O2, produced
readily by NO abstracting the Cl atom from ClOO via the triplet ground state surface. This pressure-independent pro-cess occurs without an intrinsic barrier with the predicted rate constant k1= 2.66 × 10−16T1.91exp(341/T) cm3molecule−1
sec−1 for 200–700 K. Another low energy product pair ClO + NO2occurs by a stepwise mechanism via the association of
FIG. 7. Branching ratios of the products ClNO+3O
2(k1), ClONO2(k2) and
ClO+ NO2(k3) as functions of temperature relative to the total rate constant
the terminal O atom of ClOO with the reactive N atom in NO forming pc-ClOONO barrierlessly and subsequently followed by ClO migration to form the internally excited ClONO2
in-termediate with a 2.6 kcal/mol barrier. The excited ClONO2
thus formed rapidly dissociates into the ClO + NO2
prod-ucts with no pressure effects below atmospheric pressure be-cause of the relatively low ClO−NO2 dissociation energy
(25 kcal/mol) and the 13.3 kcal/mol overall exothermicity. The pressure independent rate constant for this reaction can be represented by k3 = 1.48 × 10−24T3.99exp(1711/T) cm3
molecule−1sec−1(200–600 K) for N2buffer gas. The
branch-ing ratios of the major product channels ClNO + 3O 2 (k1)
and ClO+ NO2(k3) account for 0.77–0.98 and 0.23–0.02 in
the temperature range 200–700 K, respectively, agreeing very satisfactorily with experimental values. The channel produc-ing ClONO2 is negligible below atmospheric pressure over
the entire range of temperature studied.
ACKNOWLEDGMENTS
The authors deeply appreciate the support of this work by the MOE ATU program. M.C.L. also wants to acknowledge the support from the Taiwan Semiconductor Manufacturing Company for the TSMC Distinguished Professorship and for the National Science Council of Taiwan for the Distinguished Visiting Professorship at National Chiao Tung University in Hsinchu, Taiwan. We are grateful to the National Center for High-performance computing for computer time and facili-ties. R. P. would also like to thank Dr. Z. F. Xu for useful discussions.
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