On the mechanism and branching ratio of the cyanogen + oxygen

of CF4 before any CO could be detected in the u"· 0 state.15 This implies that most of the CO ..... at the UMP2 level of theory.29 Table II lists the...
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11590

J. Phys. Chem. 1993,97, 11590-1 1598

On the Mechanism and Branching Ratio of the CN Transient IR Emission Spectroscopy

+0 2

-

CO

+ NO Reaction Channel Using

Fida Mohammad, Vernon R. Morris, William H. Fink, and William M. Jackson’ Department of Chemistry, University of California, Davis, California 95616 Received: June 7, 1993”

+

The contribution of the title reaction to the total reaction of CN 02 has been determined, using time-resolved IR emission spectroscopy of the product CO(u”). This product channel is found to contribute up to 29% with 2% experimental variance to the total reaction. A contribution of this magnitude to the total reaction of CN 02 by this product channel proceeding via a four-center transition state is energetically improbable. A b initio calculations have been performed on two- and four-center transition states which are presumably formed in the reaction between CN radicals and molecular oxygen. The results of these calculations confirm the existence of a very high barrier to the formation of a four-center transition state. Consequently, a new mechanism for the formation of CO in reaction 1 is proposed. This new mechanism consists of two sequential steps rather than two parallel steps to explain the formation of the products NCO, 0, and CO in the reaction CN 0 2 .

+

+

Introduction The radical-radical reaction between C N and 0 2 is believed to proceed through three product channels:’

CN

+ 0,

--

-

NCO(u”)

+ O(3P) -29

+ NO(u’9 N(4S) + CO,(u’9

CO(u”)

kJ/mol

(la)

-461 kJ/mol ( l b ) -359 kJ/mol

(IC)

The reaction of C N with 0 2 is an important reaction both in the combustion of nitrogen-bearing fuel and as a copious source of N C O radicals; thus, it has been intensively studied by many gr0ups.3-~ The results of these studies showed that the overall rate constant of this reaction is 2.5 X 10-l’ cm3/s. Channel l a is a simple abstraction reaction that is believed to make up most of reaction 1. For this reason the C N + 0 2 reaction has been used as a source of the NCO radicals in various st~dies.~-Is The relative importance of the other two product channels 1b and I C is still being debated. To our knowledge, no experimental evidence exists for channel IC;so it will not be discussed any further in this paper, and its branching ratio will be assumed to be close to zero. The 1b product channel is highly exothermic, but it is not obvious that it can proceed through a simple mechanism. In the following paragraphs the results of previous studies on the l a and 1b product channels will be summarized. Both experimental and theoretical results will be presented which provide new information about the branching ratio and mechanism for this reaction. The dynamics of channel l a have been the more thoroughly studied of these two channels thanks to the ease with which C N and N C O can be characterized by laser-induced fluores~ence.~-l3 The results of these studies show that product channel 1a proceeds via simple abstraction reaction on a highly attractive surface with almost no barrier.9J0 The N C O product that is formed in reaction l a has been found to be highly vibrationally excited and to contain 65-8095 of the 29 kJ/mol energy available from the reaction exothermicity.9JO Most of this vibrational excitation (50-60%) appears as excitation in the u2 bending mode of NCO, where vibrational levels up to 0’’ = 8 have been o b ~ e r v e d .An ~ induction period for the appearance of the NCO product has been observed which is believed to be due to the effects of translational and rotational excitation in the reactants.10 Three previous studies to determine the branching ratio of the l b channel appear to be in conflict with each other.lp2J5 Basco *Abstract published in Aduance ACS Abstracts. October 1, 1993.

employed flash kinetic spectroscopy to determine the concentrations of the CN, NCO, and N O radicals produced during the flash photolysis of BrCN (1600 J) in the presence of molecular oxygen.’ H e estimated that the contribution of channel l b was only 15% of the total reaction. Wolfrum’s group undertook an extensive study of the reactions of C N radicals with atomic and molecular oxygen.2 They specifically studied reactions la, lb, and 2.

CN + 0

--

+ N(4S) -326 kJ/mol CO(v”) + N(*D) -95 kJ/mol

CO(v”)

(2a)

(2a) In their experiments C N radicals were produced by flash photolysis of C2N2 with a C N yield of 0.4% using a broad-band vacuum UV flash lamp centered a t 165 nm.2 These radicals were allowed to react with molecular and atomic oxygen. Atomic oxygen was produced either via a microwave discharge in O2/He mixtures or alternatively through the chemical reaction of N O with nitrogen atoms. The CO molecules formed by the reaction of C N radicals with either atomic or molecular oxygen were monitored by IR transient absorption spectroscopy using a CO laser.2 They found that the vibrational excitation of the product CO from channel 1b populated levels up to u”= 4, although the reaction exoergicity is sufficient to produce them with v”up to 18. Using the ratio of the overall rate constants of reactions 1 and 2 in conjunction with the yields of the product C O obtained from reactions 1b and 2, Schmatjko and Wolfrum determined that channel l b contributes less than 6% to reaction 1.2 Earlier we reported the observation of highly vibrationally excited CO produced in the photolysis of C2N2 in the presence of 0 2 using transient IR emission spectroscopy.16 The intensity of I R emission that we obtained from the CO product in the reaction C N + 0 2 was much stronger than one would expect if reaction 1b were contributing only 6% to the total reaction. Very recently Cooper et al. using transient IR diode laser absorption spectroscopy also detected CO as a product when they photolyzed mixtures of ICN and 0 2 at 266 nm.15 They had to cool the C O to the vibrational ground state by adding a few torr of CF4 before any C O could be detected in the v”= 0 state.15This implies that most of the CO is produced in excited vibrational states. Their results indicate that channel l b contributes 1333% to the overall reaction of C N with 0 2 . 1 5 If channel l b is assumed to proceed via a four-centered transition state, its contribution to the overall reaction should be very small because the activation energy for such a transition

0022-365419312097- 1 1590%04.00/0 0 1993 American Chemical Society

CN

+02

---+

CO

+ N O Reaction Channel

The Journal of Physical Chemistry, Vol. 97, No. 45, 1993 11591

state is usually very high. As a consequence, it is believed that this channel will not effectively compete with channel la, which occurs as a simple abstraction reaction without a barrier. For this reason channel l b has been assumed to be ~ n i m p o r t a n t . ~ We have observed IR emission from vibrationally excited C O produced in the photolysis of acetone using the same experimental system. Since the acetone system is a well-characterized source of vibrationally excited CO, it can be used to quantify the amount of CO produced in the reaction of C N with 0 2 on a relative basis.17J8 For this reason thenascent COvibrational distributions obtained for the two systems were compared in order to determine the contribution of product channel 1b to reaction 1. The results of these studies along with preliminary a b initio calculations at the U H F and UMP2 levels of theory have been used to propose a new mechanism for the production of C O from the reaction of C N with 02. To our knowledge the calculations reported herein represent the first quantum mechanical treatment of the NCO2 potential energy surface.

Experimental Method Details of the apparatus used for the time-resolved infrared experiments have been previously published and will only be briefly described.19 A modified Perkin-Elmer Model 180 IR monochromator was used to detect and resolve transient I R emission from the vibrationally excited CO produced in the l b channel. An unfocused Lambda Physik 103 ArF excimer laser with a rectangular-shaped beam (3.2 X 1.2 cm2) and an output energy from 40 to 70 mJ per pulse (for an illuminance of 14 mJ/cm2) is used to pass light through a quartz window into the reaction cell. The laser is run at 28 H z by enslaving it to the chopper of the spectrometer. For this purpose a 14-Hz signal from the chopper’s motor is used after doubling its frequency. The IR emission is collected by an optical arrangement in the Welsh configuration.20 After leaving the reaction cell, this emission is collected by the spherical mirrors of the spectrometer and focused onto its entrance slit where it can be resolved. This wavelengthresolved emission is then detected by a 2-mm liquid nitrogen cooled InSb detector (Sant Barbara Research Associates). The transient photocurrent (5-30 nA) produced when the IR photons strike the detector is transformed into a voltage signal by using a high-impedance Perry preamplifier ( los il input impedance). The output from this preamplifier (typically 0.5-3 mV) is further amplified by a second amplifier which has a variable gain that is adjustable between 100 and 1600. Thevoltage signal is digitized by a Laser Interfaces lZbit, 1-ps transient digitizer and stored in an IBM/XT-compatible computer which is interfaced to the experiment. The detector and the measuring electronics have a response time of 1 ps. The IR voltage signal obtained from each laser pulse is accompanied by a substantial amount of noise which usually yields a signal to noise ratio that is less than unity. The sources of this noise are mainly thermal infrared background, radio-frequency noise from the laser discharge, and Johnson noise from all the passive and reactive electrical components of the measuring electronics. The DC components and the coherent radiofrequency noise associated with the laser are removed when the chopper wheel blocks the direct emission from the reaction cell on alternate laser shots and the voltage signals with and without the infrared fluorescence are subtracted in the computer. This increases the signal to noise ratio from less than unity to between 2 and 3. The remaining random noise is removed by signal averaging. Typically, an average of 500-1000 laser shots are required to further improve the signal to noise ratio to a value of 50. Spectra as a function of delay time can then be obtained by sorting all of the collected data to obtain a matrix of intensity as a function of wavelength and delay time. C N radicals were initially produced by photolyzing C2N2 (Matheson) with an ArF laser, but due to the unavailability of

-

this gas, BrCN (Fluka) was used in the rest of the experiments.21 Precursors of the C N radicals were premixed with 0 2 gas to ensure complete mixing. C N radicals produced in the 193-nm photolysis of BrCN and C2N2 carry substantial amounts of translational, rotational, and vibrational energy.22-24 The translational and rotational degrees of freedom of the C N radicals were thermalized by adding 3-5 Torr of Ar to the photolysis samples.10923-24 Vibrational excitation in the C N radical is not completely relaxed by Ar, and the 15-25% of the C N radicals that are produced in the u” = 1 states in these systems survive for much of the duration of the r e a c t i ~ n . ’ O * ~Since ~ - ~ ~the C N radical behaves as a pseudo-halogen, the influence of its vibrational excitation on its reaction dynamics has been shown to be negligible. A typical reaction mixture consisted of 30-100 mTorr of the C N precursor, 100-300 mTorr of oxygen, and 3-5 Torr of Ar. The study of radical-radical reactions such as reaction 1 generally has two inherent problems. The first is the in situ generation of the two reacting radicals. For reaction 1 molecular oxygen is a kinetically stable molecule, thereby simplifying our problem to the in situ generation of only the C N radical. The second problem is the potential for fast secondary radical reactions. This is simplified in our system, since the reaction is carried out under pseudo-first-order conditions, i.e. with an excess of oxygen. By keeping the concentration of oxygen sufficiently high, we can dictate a rate of consumption of the C N radicals with oxygen such that side and secondary reactions which are occurring in these systems are suppressed. The low laser illuminances also suppress secondary side reactions. To determine the contribution of the product channel l b to reaction 1, the I R emission signals from the CO(u”) produced in reaction l b were compared to similar IR emission signals obtained from CO(v’9 which are produced during the photolysis of acetone at 193 nm. Photolysis of acetone at 193 nm is a clean source of vibrationally excited CO, since the nascent vibrational population distribution of the CO(u”) photolysis product has been well characterized and remains intact for many microseconds.17J8 We have thus developed a relationship between the total unresolved emission signals observed for CO(u’9 in both systems which will allow the facile determination of the total branching ratio for the l b channel, @tot. The details of the derivation are given in the appendiix.

Where S is the signal strength due to the total unresolved I R emission, 1, = C ( A d ~ , ~ & ~is) the integrated emission intensity factor, u is the absorption cross section a t 193 nm, CP is the total quantum yield of the photodissociation, 5 is the laser illuminance used in the photolysis, and p is the number density of photolysis gas. In order to solve the above equation for Btot,a set of experiments, to bedescribed below, werecarried out todetermine thequantities appearing in the expression for @tot. Some of these quantities were calculated from the data reported in the literature. For instance, the integrated CO(u”) emission intensities, I,, were calculated from the experimental data of Schmatjko and Wolfrum for the CN-O2 system and from Fletcher et al. and Trentelman et al. for CO produced in the photolysis of a ~ e t o n e . ~ J ~ J ~ The total unresolved emission intensity, S , appearing in the expression above for was measured in our experiments by bypassing the grating of the spectrometer and using an IR filter to integrate the emission signals from all the vibrational levels of the CO. The total emission resulting from CO(u”) produced in the CN-02 system or from acetone photolysis was collected and focused directly onto the detector after passing it through an IR band-pass filter (21 14 f 185 cm-1). The detector was placed behind the chopper a t the focal point of an off-axis paraboloid collecting mirror for these experiments. One such signal as a function of time delay is shown for the CN-02 system (plot a)

Mohammad et al.

11592 The Journal of Physical Chemistry, Vol. 97, No. 45, 1993 1E4

0000

.-c 3 e

8ooo

v)

.w

7000 6000

0

\>\ . e4ooo v)

t w3OOo

4

-t 2000 1000 0

-15

0

15

30

45

Delay time

/ ps

tK1

75

Figure 1. Total unresolved IR emission intensity for CO(v’9 vs time delay: ( 0 )22 mTorr of acetone and 2 Torr of argon; (0)34 mTorr of BrCN, 300 mTorr of 02,and 3.5 Torr of argon.

and for the acetone system (plot b) in Figure 1. Time decay curves were taken to determine the Ser and SA^ as a function of pressure of the photolysis gas. The intensities, and SA^, of the total IR emission signal at 20 fis at various pressures of BrCN and acetone were used to determine &I, (see Figure 1). It is important to note that we did not observe an induction period in the time decay profiles of the CO emission signal at any partial pressure of 0 2 . If the CO were primarily arising from secondary processes, an induction period corresponding to the accumulation of critical concentrations of the secondary reactants should be present. This provides justification for direct production of CO from the C N 0 2 reaction. The ratio of the absorption coefficients for BrCN and acetone which appears in the equation for g,, was measured experimentally. To determine this ratio more precisely, both the absorption coefficients were measured under the same conditions. This relative measurement of the two cross sections should minimize any systematic errors which usually accompany these measurements, and for these reasons our experimental relative value for the absorption cross sections was used in the expression for determining &,I. The measured value of the ratio of absorption cross sections is 13.6. This ratio may also be calculated on the basis of current literature values 3.8 X 10-’8 cm2/molecule for acetone and 2.1 X l t I 9 cm2/molecule for BrCN.17*25The latter values give a ratio of 18:1.

+

Experimental Results we need, among other things, the To solve the equation for values of the integrated emission intensities, I,, which are calculated from a knowledge of population distribution and Einstein A-coefficients. We have used BrCN and C2N2 as the C N precursors to obtain wavelength-resolved spectra of the product C O at a resolution of 60 cm-1.2’ This is shown for the case of BrCN in Figure 2 as open circles. Thesedata are confined to a wavelength region of less than 2160 cm-1, which is the limit of the sensitivity of the grating that we are using in these experiments. The solid curve shown in Figure 2 is based on the experimental data of Schmatjko and Wolfrum and is obtained when theoretical vibrational bands of CO for the states u”= 1 - 4 are mixed in the ratio of A,,~,~~-lfu“,Br given in Table 1.2 We are in the process of improving the resolution in our experiment and

eventually deconvoluting the experimental spectra to determine the population distribution of C O produced in the reaction C N 02.For these reasons we have used values of integrated emission intensities for the product CO appearing in the above equation which were calculated from the experimental results given in ref 2 for the C N 02 reaction and from the experimental results given in refs 17 and 18 for the photolysis of acetone (Table I). Using the experimental data given in refs 2 and 18 has the additional advantage that the population of C O in u” = 0 is known, which cannot be obtained from the IR emission experiments. It is interesting to note that slight changes in the population distribution of the product CO do not cause significant changes in the value for Btot. As a sample calculation for the determination of pm, we use our typical experimental value for SB,/S*~ of 11.3, a value for the ratio of the absorption cross section of 13.6, and values of 0.96 and 1 for the quantum efficiencies for the photolysis of acetone and BrCN at 193 nm, respectively.26 The values for the integrated emission intensities are given in Table I as 0.35 for the acetone system and 0.91 for the C N + 0 2 system. When these values are substituted in the equation for Btot, a value of 29% is obtained for the contribution of reaction 1b to the total reaction CN 0 2 . A contribution of 20-30% by channel 1b to reaction 1 is very significant, and it is difficult to reconcile a contribution of this magnitude with a four-centered transition state presumably formed en route to the products. We have therefore carried out ab initio calculations to determine the contours of the potential energy surface near the two- and four-centered transition states which are formed in reaction 1 and to gauge the energeticsrelevant to the barrier for passage through the critical configurations. The results of these calculations are reported below.

+

+

+

Theoretical Results The Gaussian 86,Revision C, package of programsz’ implementedona VAX3lOOwasusedfor allcalculations. Unrestricted Hartree-Fock (UHF) and second-order Maller-Plesset manybody perturbation theory (UMP2) calculations were performed to obtain equilibrium structures and relative energies for the twoand four-centered NCOO minima and critical points.28 The 3-21G and 6-31G* split-valence basis sets were employed at the

CN

+0 2

+

CO

+ N O Reaction Channel

1850

1900

The Journal of Physical Chemistry, Vol. 97, No. 45, 1993 11593

2000

1950

2060

2100

2200

2154

2250

2500

Frequency / cm-’ Figure 2. Spectral profile of the IR emission intensity obtained at 60 cm-1 from CO(v”) produced in the CN + 0 2 reaction at a time delay of 40 ps: ( 0 )experimental data for 37 mTorr of BrCN, 350 mTorr of 02, and 4 Torr of argon; (solid line) theoretical fit based on the population analysis of Schmatjko and Wolfrum (ref 2, Figure 5).

TABLE I: Total Integrated Emission Intensities, Z(A,,,,,-lf,t), Calculated for the Product CO from the CN 0 2 Reaction and Photolysis of Acetone vibrational CN + 0 2 reaction“ photolysis (40-a~data) of acetoneb quantum number Ad!& A ~ ~ ~ L ~ / fdl A L , Adi~i-LfJP o fdi Adt,di-ddF

+

0 1 2 3 4

33.4 64.5 92.9 118

1.0 1.94 2.79 3.54

0.45 0.29 0.17 0.08 0.02

0.29 0.33 0.22 0.07

0.73 0.20 0.06 0.01

0.20 0.12 0.03

200

-50

TABLE 11: Relative Energies’ of Reactants, Adducts, and Products

-

hf/6-31gs

mp2/3-21g

UHF level of theory, but only the 3-21G basis set was employed at the UMP2 level of theory.29 Table I1 lists the relative energies of the separated reactants, products, collision complexes, and transition states. The relative energies predicted for the NCOO structures and the energies of the separated reactants are in qualitative agreement with predictions of a shallow minimum for the two-centered structures and high barriers for the four-centered structures relative to reactants and products. Not surprisingly, the most stable species a t all levels of treatment was found to be

P€sE3-

0-0.

0 -CN+02

--50

hf/3-21g

L1

150

0 Reference 2, Figure 5. C2N2 was used as the CN precursor for the CN + 02 experiments. b Based on an average vibrational temperature for CO obtained from refs 16 and 17. Reference 34. C(Adt+.-tfd*) = 0.91. * z(Adt+Lf~‘) = 0.35.

0.0 0.0 0.0 CN + 0 2 -325.6 -238.1 -95.8 NCO + 0 -369.1 -430.9 -402.4 CO + NO 116.3 2.3 62.9 (2A”) two-centered TSb -3 1 .O -140.2 (2A”) two-centered NCOOC 35 1 .O 200.v (ZA”) two-centered TS -87.6 -316.7 (’A”) three-centered NCO@ -345.6 -262.8 -187.6 (2A1)three-centered N C W -224.7 39.8 185.8 (ZA’) four-centeredNCOO 68.6 45.3 (ZA’) four-centeredTS 177.8 * Energies in kJ/mol. Transition state with linear geometry. Minimum with nonlinear geometry. d Minimum with nonplanar geometry. * Minimum with asymmetric geometry. /Symmetric (Ca) geometry.

h====C*

-

E C -

-100

0-0.

NCO + 0

0

-150

-C-/

-

-200

A

--350

-

-400

CO + NO

Figure 3. Schematic diagram of the general nuclear configurations for

the two-, three-, and four-centered NCOO minima and critical points and their relative energiesin kl/mol. The transition state structuresare indicated by asterisks. a Y-shaped structure with near-Cb nuclear symmetry (Figure 3). These species would intuitively correspond to reaction IC leading to N CO2. The significance of this channel on the ground potential energy surface will be investigated using more sophisticated techniques because of the high spin contamination

+

Mohammad et al.

11594 The Journal of Physical Chemistry, Vol. 97, No. 45, 1993

TABLE 111: Two-Centered Transition State Geometrical Parameters' and Harmonic Frequencies HF/3-21Gb

NC

co

0 2

a(CO0)

1.1446

1.2679

1.3899

180.0

603.451 (42.1)

525.01 (33.5)

2

3 427.1 (20.7)

4 429.1 (20.54)

5 825.8 (21.1)

6 1572.5 (562.2)

7 2545.5 (318.2)

deg COOO bendCyz)

deg COOO bend(xz)

deg OOCN wagW

deg OOCN wag(xz)

joint CO 00 sym str

joint CO 00 asym str

asym OCN str

1

HF/6-31GS'

NC

co

1.1405

1.2438

1 712.51 (53.3)

2 597.81 (50.0)

4COO)

02 1.3077

4

3 430.1 (0.0)

454.2 (0.0)

5 857.9 (4.59)

180.0 6 1644.4d (495.6)

7 2573.1 (4.4)

deg OOCN deg COO deg OOCN joint CO sym COO sym NCO and deg COO out-of-plane 00 sym stretch 00 stretch bend(xy) out-of-plane bend(xy) torsion wag(xY) stretch torsion wag(xy) 4 Bond lengths in A; angles in deg. Frequencies in cm-I; IR intensities in km/mol. b Linear transition state; 2.3 kJ/mol above separated reactants. C UHF/6-31GS linear transition state at 31.2 kJ/mol below separated reactants. d Modes 5 and 6 also have CN stretch character with less than 50% of the lowest net displacement between CO and 00.

TABLE I V Four-Centered Transition State Geometrical Parameters,' Frequencw IR Intensities,* and Normal Coordinate Descriptions CN NO co 00 a(CN0) a(NO0) 1.2581

1.5078

1.4124

1.4624

85.8

89.3

Harmonic Vibrational Analysis 1

479.91 (18.7)

2 642.9 (4.0)

3

4

1102.2 (9.9)

1524.0 (41.4)

5c

1619.2 (59.2)

6 2462.2 (56.5)

NOCO C N 0 0 OOC nonplanar out-of-plane OON bending sym str asym str bending ring breathing wagging a UMP2/3-21G results. Bond lengths in A and bond angles in deg. * Frequencies in cm-' and IR intensities in km/mol. Only mode 5 is strictly planar. in the UMPZ wave functions arising from higher spin state interactions with the ground double state. The geometrical configurations and relative energies for the two-, three-, and four-centered NCOO structures are shown schematically in Figure 3. The optimized geometrical parameters and harmonicfrequenciesof the two- and four-centered transition states are given in Tables 111and IV. The equilibrium geometry for the two-centered minima is predicted to be significantly bent with a COO angle of 112O. The 02 bond in the two-centered structures is much longer (13-16%) than the equilibrium bond length for molecular 0 2 a t the U H F level of theory. These data are suggestive of a late barrier in the exit channel for reaction 1a and support models invoking large exit impact parameters for reacton 1 and also experimental observations of preferential excitation in the product NCO bending mode. The nonlinear configuration can be rationalized in terms of the overlap between the frontier orbitals of the unpaired electrons on the C N radical and the 0 2 molecule. In the linear configuration the net overlap of the T*(o) and q c ) orbitals is zero. The bonding interaction increases as the angle between the N C and 0 2 bond vectors decreases from 180O. At the UHF level of theory the four-centered minima range from 41 to 185 kJ/mol above the separated reactants. On inclusion of correlation using UMP2/3-2 lG, the energy separation between the four-centered transition states and the separated reactants increases the height of the transition state to a167 kJ/mol. It is seen that the four-centered complexes possess a loosely bound structure relative to both reactant and product

optimized geometries a t the same level of theory. Only the C N bond is shorter than 1.4 A. The elongated bonds of the fourcentered transition state relative to reactants are consistent with a sizable activation energy barrier and are also indicative of a late barrier in the reaction. It is interesting that the bond lengths and angles do not resemble either the reactants or products. This may be indicative of a reaction path involving several transition states between reactants and products. The planar box-like fourcentered transition state occurs on a 2A'surface with the unpaired electron localized on the carbon atom in the plane of the four atoms. However, there are also triangular four-centered transition states located a t the U H F level of theory which are consistently of lower energy than the box-like forms. The energetics predicted a t the UMP2/3-2 1G level of treatment are by no means quantitative. In fact, there is good reason to believe that a single reference treatment of correlation is inadequate for a quantitative description of this system. CASSCF and MCSCF studies are required for a more complete picture of the reaction path and the potential surface. More sophisticated theoretical studies are currently underway. However, the qualitative prediction from the UMPZ results that the barrier to the four-centered tight complex is far larger than the barrier associated with the two-centered interaction is in agreement with intuition and experiment. A potential energy contour as a function of the peroxy (0-0) bond length and the COO bond angle was also calculated a t the UMP2/3-21G level of theory. The N - C and C-0 bonds were fixed at the UMP2/3-21G optimized values in the two-centered configuration. The general features of the surface indicate a sharply rising potential for increasing the COO angle toward linearity (180') relative to the optimized value of 112O. The potential energy also rose sharply as the 0-0 bond length increased for obtuse COO bond angles. The potential decreases smoothly, however, for an increasing 0-0 bond length and decreasing (acute) COO bond angles. The picture derived from these admittedly 'rough" calculations is that the terminal oxygen atom is 'tossed" from the oxygen end of the two-centered complex to the other end, being deflected off steep potential barriers at large distances until it is recaptured by the unpaired electrons of the nitrogen at the other end. Alternatively, the NCOO collision complex may pass through multiple short-lived transition states beginning with the two-centered structure which involves the most facile approach of the C N and 02 fragments. The subsequent saddle points may be three- or four-centered and

CN

+ 02

-

CO

+ N O Reaction Channel

involve the migration of the oxygen atom from one end of the N C O fragment to the other, essentially following the localization of the unpaired electron. This is essentially a description of a persistent collision complex whose bonding changes dramatically over the lifetime of the extended collision.

Mscussion

Our experimental finding for a PtOtof 29% f 2 and that of Cooper et al. of 13-33% are in close agreement. The 2%variance associated with our branching ratio represents the scatter in this quantity when calculated from our own experimental data. A recalculation of Btotusing the experimental data of Schmatjko and Wolfrum is given below. Schmatjko and Wolfrum used the same initial concentrations of the C N radical while studying the C N + 0 and C N + 0 2 reactions.2 The C N + 0 reaction has a very large rate constant, 1.3 X 10-10 cm3/s, and its mechanism suggests that every C N radical is converted to CO.238 Under these conditions it can be assumed that the absolute concentration of the total product CO when the reaction is over can be set equal to the initial concentration of the C N radical, i.e. [ColCN+O = [CN1O (3) On the other hand the C N 0 2 reaction has a rate constant of 2.5 X cm3/s, and the C N is converted to either the product N C O or C0.’v4 Hence, the absolute concentration of the product CO when the reaction is over can be set equal to a fraction of the initial C N radical concentration:

+

Since the initial C N radical concentrations were the same in both reactions, dividing eq 4 by eq 3 gives

The [CO]CN+02is calculated from Figure 5 of ref 2 as 7.3 X 10” molecules/cm3, and the [co]CN+O is calculated from Table I of ref 2 as 3.5 X 1012 molecules/cm3. Substitution of these values into eq 5 gives Btot = 0.21. This is in good agreement with the mean value of 23%recently reported by Cooper et al. and also in good agreement with our own average value of 29% f 2.15 The results of the three studies mentioned above suggest that reaction l b contributes 20-3076 to the total reaction 1. A contribution of this magnitude is very significant. Our theoretically estimated energy barrier of over 100 kJ/mol for the occurrence of reaction 1b via a presumed four-center critical configuration seems to be at odds with a contribution of this magnitude. To reconcile these facts, new thinking is required about the changes in theconfiguration of atoms when the reactive encounter between the C N radical and molecular oxygen is in progress and when the products are formed via the main reaction (product channel l a ) but are not yet separated from each other. In the following paragraphs we reject the Occurrence of product channel I b via direct passage through a four-centered critical configuration and suggest a new mechanism to explain the formation of the products NCO, 0, CO, and N O in reaction 1 by focusing on product channel l a alone. The essential difference between theold mechanism and thenew one that we are proposing is that the former mechanism leads to the formation of the products NCO and C O in two parallel steps (reactions l a and 1b) whereas the new mechanism leads to the same products through two sequential steps (see schematic representation in Figure 4). The radical-radical reaction CN + 0 2 Occurs on an attractive surface without an entrance channel barrier.30 The exoergicity of the l a channel leading to N C O + 0 products is 29 kJ/mol. On average, 70% of this available energy was found as internal excitation in the product NC0.9 This means that an average of only about 9 kJ/mol is available to the relative translation of the

The Journal of Physical Chemistry, Vol. 97, No. 45, 1993

11595

step 1

P

x- - -

r

step 2

-O

Figure 4. Schematic representation of the proposed mechanism for the formation of the products NCO,0, and CO in the reaction CN + 02.

NCO radical and 0 atom products. The implication is that a significant fraction of the reactive collisions can be imagined as leading to N C O and 0 product pairs with relative translational energies of less than 9 kJ/mol. Our semiempirical calculations based on the London equation and including only the dispersion and dipoleinduced-dipole forces between the separating product N C O radical and 0 atom suggest that a potential well of significant depth exists between the N C O and 0 products.31 Thevery small amount of energy available to the product pairs as relative translation and the nature of the attractive forces between them will have the consequence that a significant number of product pairs will be trapped together in the vicinity where they were produced. If this trapping persists long enough, rotation of the N C O will bring the N atom closer to the unbound 0 atom and a secondary encounter can occur between the N end of the N C O fragment and the 0 atom.32 This is shown schematically in Figure 4. Our a b initio calculations show that the transition vector for the formation of NCO and 0 is a bending motion. This ensures that the repulsive force, if any, when the products N C O and 0 separate will be specifically channeled into the N C O rotation. Not only will this further reduce the relative velocity with which the product pair separate but it will also speed up the rotation of the N C O as viewed by the 0 atom. Slow relative velocity of separation between the 0 atom and N C O radical, enhanced rotation of the NCO radical induced by the kick from the departing 0 atom, and the attractive potential operating between the separating products N C O and the 0 atom will conspire to facilitate the secondary reactive encounter between the nitrogen end of the NCO radical and the trapped oxygen atom. This secondary reactive encounter will follow the first reactive encounter on a time scale of a quarter period of rotation of the N C O radical and will lead to the product C O and NO. The average relative translational energy available to the fragments, N C O and 0, is 9 kJ/mol, which corresponds to a relative velocity of 15 A/ps. The expression for the time of a rotational period, tR, is given by t R = h/2irJB.” For J = 16 and a B value of 0.39 cm-1, t R for N C O is 0.84 ps. The time for one quarter of a rotation is 0.21 ps. During this time the centers of mass of the two fragments will be separated by (15 A/ps)(0.21 ps) = 2.7 A. This should be regarded as the upper limit to the separation for the following reasons: (1) Since the internal excitation found for N C O may be higher than the reported estimates, the 9 kJ/mol available for relative translation represents an upper limit.9JO Furthermore, the 9 kJ/mol available energy

11596 The Journal of Physical Chemistry, Vol. 97, No. 45, 1993

is an average quantity; thus, a significant number of the NCO and 0 pairs will have less than 9 kJ/mol of energy available for the relative translation. (2) The NCO produced in states with J > 16 will have even shorter rotational periods, which will effectively decrease the separation between the centers of masses of NCO and 0.(3) The separation between the nitrogen end of the NCO and the departing oxygen atom will be even smaller after the NCO has rotated about its center of mass (see Figure 4). (4) Finally, the strongly attractive anisotropic forces in the exit channel will act to retard the relative translation between the NCO and 0 fragments, and the distance between the center of mass of the NCO and the departing oxygen atom will be less than 2.7 A. The above-proposed mechanism carries two implications. The rotationally hot NCO produced in the first reactive encounter will be preferentially consumed in the secondary reactive encounter, and as a result, the surviving NCO will have a colder rotational distribution. Experimental evidence suggests that rotational distribution of the NCO product is cold, peaking at J = 6 and 8.” The rotational constant of NCO is 0.39 cm-l, and a relatively small amount of energy is required to excite NCO rotationally. At 300 K the rotational quantum number J has a maximum at 15 for this radical. Given the bent transition state for the formation of NCO, the kick that NCO receives from the departing 0 atom at its 0 end, and the small B value of NCO, one would expect significant rotational excitation in the NCO. Therefore, the cold rotational distribution found in the beam experiments for NCO is surprising.ll Subject to the validity of our proposed mechanism, we suggest that the rotationally hot NCO will be preferentially consumed by the secondary reactive encounter and converted into the products CO and NO. This will leave behind NCO in lower J levels. This explanation can tentatively account for the observed cold rotational distribution for NCO. The observed induction period for the appearance of the NCO product in bulk LIF studies of the CN 02 reaction is believed to be due to the significant reduction of the cross section for reaction l a with increasing translational and rotational excitation of the CN fragmentlo This induction period was not observed in the beam experiments.” Our model can tentatively explain this observation by assuming that the rotationally hot CN radicals preferentially produce rotationally hot NCO, i.e. rotational adiabaticity. The rotationally hot NCO are then preferentially sampled by the secondary reactive encounter to produce CO and NO. The second implication that our proposed mechanism carries is that the NO produced in the secondary reactive encounter should be highly vibrationally excited. The reaction exoergicity of the second encounter is about 15 times larger than the one for the first encounter, Le. 422 kJ/mol compared to 29 kJ/mol. Much of the 29 kJ/mol energy which is available in the first reactive encounter is preferentially channeled into the v2 bending mode of the NCO, and it seems that the newly formed C-0 bond in the NCO is not excited significantly. This is also supported by the results of our ab initio calculations which show that the N-C and C-0 optimized bond lengths in the transition state for the formation of NCO are very close to their equilibrium values. The purely attractive natureof the 0 + NCO potential surface implies that the reaction exoergicity will be preferentially channeled into exciting the newly formed NO bond formed in the secondary encounter. An investigation of the vibrational excitation in the NO produced in the CN + 0 2 reaction would be worth undertaking to verify the validity of the proposed mechanism. We cannot detect IR emission from NO in our experiments because the response of our InSb detector falls off very sharply in this region. Normal mode analysis of the a b initio harmonic frequencies confirms earlier suggestions that the N-C and C-0 stretching modes are strongly coupled.1o Thus, part of the energy initially

+

Mohammad et al. deposited in the N - 0 bond may flow into the C-0 bond before the two product molecules CO and NO separate. The modest vibrational excitation found experimentally in the product CO agrees with the foregoing analysis. Conclusion

The experimental findings for the contribution of the CO product channel to the total reaction CN + 0 2 of 29% in our study, of 21% when recalculated from the experimental data of Schmatjko and Wolfrum, and of the average value of 23% reported by Cooper et al. clearly indicate that this product channel is much more significant than has been assumed so far. A contribution of this magnitude cannot be explained on the basis of a four-centered atomic configuration in the transition state. Our theoretical calculations confirm the existence of a very high energy barrier to the formation of a four-center transition state. The new mechanism proposed in this paper to explain the formation of the products NCO, 0, and CO in two sequential steps attempts to reconcile the apparent contradiction between the experimentally observed high yields of the CO and the high energetic requirements for the formation of a four-centered transition state.

Appendix In the CN-02 system the initial concentration of CN radicals produced in the photolysis of BrCN is converted into vibrationally excited CO via reaction 1b on a time scale of 20 ps. The nascent vibrational distribution of CO and its absolute concentration obtainable from this reaction are subject to secondary processes such as relaxation and CO(u”) production in secondary reactions. To accurately determine the branching ratio of reaction 1, we must take into account the following physical and chemical processes affecting the concentration of CO(u”). The physical processes are mainly diffusion, quenching by the bath gas, and radiative relaxation. Diffusion processes are negligible due to the pressures employed and the optical configuration of the Welsh cell. It can be shown that quenching reactions and radiative relaxation are much slower than the production of CO(u”) by reaction lb. The rate constant for the total loss of CN is 2.5 X 10-11cm3/s, andsince0.32 Torr of 0 2is used for these experiments, the pseudo-first-order rate constant for the production of CO in a particular u”leve1 will be ,343 X lo6s-l). The in the latter expressions is defined as kdt/kl. Thus, it is the fraction of CN radicals that react to form CO(u’9. The Einstein A-factor for spontaneous emission will vary from 33 to 118 s-l for u ” = 1-4, which is many orders of magnitude less than &43 X 106 s-1).26 A similar argument may be given for neglecting quenching of CO(u”) compared to the production of CO(u’9 by reaction 1. No data for the quenching rate constants of CO(u”) with argon, oxygen, cyanogen, and the halogen cyanides as a function of vibrational state u”is available, so the values of k given for CO(u”= 1) are assumed to represent an average rate constant over CO(u” = 1-4). The quenching rate constants for CO(u” = 1) by Ar and 0 2 are 2 X 10-16 and 1 X 10-13cm3/s, respectively.2 On the basis of analogy with the reported quenching rate constants of CO(u” = 1) with C2N2 the average kq,XCNcan be estimated at c m 3 / ~ .Under ~ our experimental conditions of 5 Torr of Ar, 0.3 Torr of 0 2 , and 0.05 Torr of BrCN, this leads to an average first-order quenching rate constant of 657 s-1, which is again much slower than &,43 X lo6 s-l), so it can be neglected. In addition to reaction 1, several exoergic secondary reactions may be responsible for the production of CO(u’9 in our system. These reactions and their rate constants are presented in Table V. We have used the Acuchem kinetics program to model the contributions of these secondary reactions to the production of CO in our system. This is shown in Figure 5 as the open triangles (A).33 This figure also shows a simulation of the CO production in the CN + 0 2 reaction under pseudo-first-order conditions and

CN

+0 2

-

CO

+ N O Reaction Channel

The Journal of Physical Chemistry, Vol. 97, No. 45. 1993 11597

1wo

1200

m I

E 0 0

Q)

900

U J 0 r

\

800

n

0 0

Y

300

0 0

20

Bo

40

Time

80

loo

/ ps

Figure 5. Production of CO as a function of time: (A)Acuchem simulationof the CO production incorporatingthe secondary reactions listed in Table V; (0)experimental data points selected from plot a of Figure 1. A polynomial has been fit through these data as a guide for the eye. The 0 refer to a simulation of the CO production from the CN + 02 reaction based on the assumption of pseudo-first-orderconditions and a CO branching ratio = 9.6 X 1015 of 29% according to q Ib of the appendix. The concentrations for the simulations are [CN] = 4.3 X 1OI2 molecules/cm~and [02] molecules/cm3.

TABLE V List of Secondary Reactions Responsible for Producing CO in the CN 0 2 System. &/10-11 cm3 reaction ref molecule-’ s-I CN + 0 -c CO + N (2) 13 8 CN + NCO -.NCN + CO (3) 3.3 38 0 + NCO+ CO + NO (4) 3.3 36 NO + NCO NzO + CO (5) 1.5 15 N + NCO +N2 + CO (6) 3.3 38 See Figure 5 and discussion in the text for the significanceof theses reactions.

+

observation is minimal and can be neglected. Thus, for short times of -20 ps, equation Ib reduces to equation IC.

= @dt[CNIO,Br (14 The initial concentration [CN]O,B~ of the C N radical used in eq IC is given by the following expression [c0(u’3120@r

+

a 29% branching ratio for the CO channel as the filled circles (0).For comparative purposes selected experimental data points from plot a of Figure 1 are shown as the open circles (0). This figure clearly shows that the experimental curve is closely mimicked by the simulation based on pseudo-first-order conditions. The contributions from the secondary reactions are seen to be inconsequential on the same time scale. One can further observe that the experimental curvedoes not exhibit any induction period, which should be expected if secondary reactions were primarily responsible for the production of CO in our system. Under the conditions discussed in the preceding paragraphs, the rate law expression for the production of CO(u”) can be written as d[CO(u”)]/dr = k , [ C N ] [O,] This can be integrated to give”

where US, is the absorption cross section of BrCN at 193 nm, ,$er is the laser illuminance used for the photolysis of BrCN, p~~ is the density of BrCN, and +er is the quantum yield for the production of C N from BrCN a t 193 nm. Substitution of this expression for [CN]O,B~ from eq 11 into eq IC and defining @dt = gives eq Id. @to&”,Br, where @tot = The IR emission intensity due to CO in any vibrational state

at time t is given by 4P.dLl

= (A,,dL,) [CO(uf?l,0,

-

(IIIa)

where A d t , d ~ lis the Einstein coefficient for a u” u” - 1 spontaneous emission. On substitution of eq I1 into eq IIIa and summing over all vibrational states, we have

(Ia)

At 20 ps, for a kl = 2.5 X 10-11 cm3/s and when the 0 2 pressure is 0.3 Torr, the term in parentheses has a value of 1. The above analysis of reaction 1 as a source of CO(v”)and of the subsequent effects of secondary processes on the nascent distribution of the CO product shows that the net effect of these processes on our

(IIIb) The initial concentration of the CO produced in the photolysis of acetone is given by [colO,Ac ‘A&A@A~*AC (IV) where U A ~is the absorption cross section of acetone at 193 nm, EA^ is the laser illuminance used in the photolysis, p~~ is the number density of acetone molecules, and is the total quantum yield for producing CO in all the states, including u” = 0. In order to know the concentration of CO in a particular vibrational state u“at time t , the effect of quenching by Ar and

11598 The Journal of Physical Chemistry, Vol. 97, No. 45, 1993

acetone should be taken into consideration and be related to the nascent concentration of C O in that state. This quenching is described by the following equation

+

-

+

CO(U”) M CO(U”- 1) M (6) where M represents either an Ar atom or an acetone molecule or both. The time decay of CO(v”) is given by

(Va) The rate constant for quenching of CO( 1-0) by acetone is 1 10-13 cm3/s.17 For pressures of 5 Torr of Ar and 0.1 Torr of acetone, the exponential term in eq Va is =l at 20 ps. Thus, the quenching effects due to argon and acetone can be neglected in our system. The foregoing analysisconfirms that thevibrationally excited CO produced in the photolysis of acetone will retain its nascent character on the time scale of our experimental observation, which is 20-30 ps, and that eq Va can be approximated to X

[CO(U’?12Ofis,Ac = [CO(U’?IO,Ac = f d ’ , A ~ [ ~ ~ 1 0 ,(Vb) Ac Here [CO]O,Ac is the total C O produced in all the vibrational states and fdJ,Ac is the fraction of vibrationally excited [Co(u”)] in a given vibrational state relative to the total amount of CO produced, including v” = 0. Substituting the expression for [CO]o,Ac from eq IV into eq Vb gives the following expression. [Co(u’?120p,Ac =~~’,AC~AC~A@AC@AC (VC) Equation Vc is parallel in form to Id except that, since only CO production is involved, no 0 factor to account for an alternative channel in product formation is required. If eq Vc is substituted into eq IIIa and summed over all v”, this will give eq Vd, which is the intensity of the total unresolved emission. SAC C ( ~ d ~ . d ~ - ~ f v “ , A c ) u A c t A c ~ A c ~ A c(Vd) If eq IIIb is divided by eq Vd, the following equation is obtained.

sBr/sAc

= (C(Adf,u’~-~d’.Br@tot)uBr@BrtBrPBr)/

( ~ A ~ ~ : ~ ~ ~ - s ~ ~ ~ , A C ~ A C (~vA~C a~ )A ~ The factors ,&4u~~,u~~-Lfu~,~r) and X(Ad’,d’-Lfu”,Ac) represent the integrated emission intensity for the C N + 0 2 and acetone systems, respectively, and will be abbreviated as by l i , and ~ ~ l i , ~ ~On . substitution of eq VI1 into eq VIa, we have.

’BI/’Ac

= (@totzi,BruBr@BrEBrPBr) / (‘i,Ac‘Ac@ActA@Ac) (VIb)

On arrangement of eq VIb, we have an expression for Ptot in terms of experimentally measured quantities, SA^ and SB~.

Acknowledgment. The authors gratefully acknowledge the support of NSF Grant 9008095 and of the NASA Planetary

Mohammad et al. Astronomy Program under Grant NAGW 1144. V.R.M. also thanks the University of California Presidential Postdoctoral Fellowship Program.

References and Notes (1) Basco, N. Proc. R . SOC.1965, A283, 302. (2) Schmatjko, K. J.; Wolfrum, J. Ber. Bunsen-Ges. Phys. Chem. 1978, 82, 419. (3) Atakan, B.; Wolfrum, J. Chem. Phys. Lett. 1991, 178, 157. (4) Sims, I. R.; Smith, I. W. J. Chem. Soc., Faraday Trans. 1988,84, 527. (5) Durant, J. L.; Tully, F. P. Chem. Phys. Lett. 1989, 154, 568. (6) Jensen, R. C.; Walton, D. B.; Coombe, R. D. Chem. Phys. Lett. 1990, 169, 441. (7) Balla, R. J.; Casleton, K. H. J . Phys. Chem. 1991, 95, 2344. (8) Davidson, D. F.; Dean, A. J.; DiRosa, M. D.; Hanson, R. K. Int. J. Chem. Kinet. 1991, 23, 1035. (9) Phillips, L. F.; Smith, I. W.; Tuckett, R. F.; Whitham, C. J. Chem. Phys. Lett. 1991, 183, 254. (10) Sauder, D. G.; Patel-Misra, D.; Dagdigian, P. J. J. Chem. Phys. 1991, 95, 1696. (11) Sonnenfroh, D. M.; McDonald, R. G.; Liu, K. J . Chem. Phys. 1990, 93, 1478. (12) Hancock,G.;McKendrick, K.G. Chem. Phys. Lett. 1986,127,125. (13) Wu,M.;Northrup,F.J.;Sears,T.J.J.Chem.Phys.1992,97,4583. (14) Cooper, W. F.; Hershberger, J. F. J . Phys. Chem. 1992, 96, 771. (1 5 ) Cooper, W. F.;Park, J.; Hershberger, J. F. J . Phys. Chem. 1993,97, 3283. (16) Mohammad, F.; Morris, V. R.; Fink, W. H.; Jackson, W. M. Abstacrs of Papers, 203rd National Meeting of the American Chemical Society, San Francisco, CA, April, 1992; American Chemical Society: Washington, DC. 1992. (17) Woodbridge, E. L.; Fletcher, T. R.; Leone, S. R. J. Phys. Chem. 1988. 92. .- -, . -, 5387. --- .. (18) Trentelman, K. A.; Kable, S . H.; Moss, D. B.; Houston, P. L. J . Chem. Phys. 1989, 91, 7498. (19) Copeland, L. R.; Mohammad, F.; Zahedi, M.;Volman, D. H.; Jackson, W. M. J. Chem. Phys. 1992,98, 5817. (20) (a) Welsh, H. L.; Cumming, C.; Stanbury, E. J. J . Opt. SOC.Am. -1951,41, 712. (b) Welsh, H. L.; Stanbury, E. J.; Romanko, J.; Feldman, J. J. Opt. SOC.Am. 1955, 45, 338. (21) Initially ClNl (Matheson) was used in our experiments, but since the production of this compound in the US has been discontinued because of its hazardous nature, subsequent experiments were performed using BrCN. (22) Eres, D.; Gurnick, M.; McDonald, J. D. J . Chem. Phys. 1984.81, 5552. (23) Halpern, J. B.; Jackson, W. M. J . Phys. Chem. 1982,86, 3528. (24) Lu, R.; Halpern, J. B.; Jackson, W. M. J. Phys. Chem. 1984, 88, 3419. (25) Felps, W. S.;Rupnik, K.; McGlynn, S.P. J . Phys. Chem. 1991,95, 639. (26) Lightfoot, P. D.; Kirwan, S. P.; Pilling, M. J. J . Phys. Chem. 1988, 92, 4938. A C ) (27) Frisch, M. Gaussian 86 User’s Guide and Programmers Reference, Revision C Version; Carnegie-Mellon University: Pittsburgh, PA, 1982. (28) Moller, C.; Plesset, M. S . Phys. Reu. 1934, 83, 6154. (29) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973,28,213 and references therein. (30) Smith, I. W. M. J . Chem. SOC.,Faraday Trans. 2 1991,87, 2271. (31) London, F. Trans. Faraday Soc. 1937,33, 8. (32) Smith,I. W. M. KineticsandDynamicsofEIementaryGasReactions; Butterworths: London, 1980; Chapter 3. (33) Levine, R. D.; Bernstein, R. B. Reaction Dynamics and Chemical Reactiuity; Oxford University Press: New York, 1987; Chapter 5 . (34) Hancock, G.;Ridley, B. A.; Smith, I. W. M. J . Chem. Soc., Faraday Trans. 2, 1972, 68, 21 17. (35) Braun, W.; Herron, J. T.; Kahaner, D. K. Int. J . Chem. Kinet. 1988, 20, 51. (36) Lifshitz, A.; Frenklach, M. Int. J . Chem. Kinet. 1991, 23, 289. (37) Capellos, C.; Bielski, B. H. J. Kinetic Systems; Robert Krieger Publishing Co.: Huntington, NY, 1980; Chapter 11. (38) Baulch, D. L.; C o b , C. J.; Cox, R. A.; Esser, C.; Frank, P.; Just, T. H.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker, R. W.; Warnatz, J.J. Phys. Chem. Ref. Data 1992, 21, 41 1.