1

Ab Initio Study of the CH3 + O2 Reaction: Kinetics,Mechanism and Product Branching Probabilities

Rongshun Zhu, C.–C. Hsu and M. C. Lin*Department of Chemistry, Emory University, Atlanta, Georgia 30322

AbstractThe reaction of CH3 radical with molecular O2 has been investigated by ab initio

molecular orbital theory and variational transition state theory calculations. The detailedpotential energy surfaces (PES), including the crossing seams between the PES, located bymeans of the intrinsic reaction coordinate (IRC) approach are presented. The rate constants forthe association and product formation channels have been calculated and compared with theexperimental data. The branching probabilities for channels (b) and (c) producing CH2O + OHand CH3O + O, respectively, are compared. Under atmospheric- pressure conditions, channel (b)is predicted to be dominant below 2000 K with the rate constant kb = 1.14µ10-22T2.86 exp (-5115.4/T) cm3molecule-1 s-1. Over 2000 K, channel (c) becomes competitive; its rate constantcould be represented by kc= 1.01µ10-16T1.54exp(-13275.7/T) cm3molecule -1 s-1 in the temperaturerange of 1000~3000 K. In addition, the most exothermic products, CHO + H2O, were found tobe kinetically inaccessible because of the large barrier, 47.4 kcal/mol above the reactants.

-------------------------------------------------* Corresponding author: chemmcl@emory.edu1. Introduction

The oxidation of CH3, the most stable alkyl radical, by molecular oxygen is one of themost important reactions in the combustion of hydrocarbons and hence has been the subject ofnumerous experimental and theoretical studies.1-44 The reaction has been shown to occur mainlythrough three channels: CH3 + O2 Ø CH3O2 (a) Ø CH2O + OH (b) Ø CH3O + O (c) There are, however, two references,26,27 which reported the possibility of the followingmost exothermic product channel: CH3 + O2 Ø HCO + H2O (d)

The association process (channel a) is pressure-dependent and dominant at temperaturesbelow 1000 K.28-44 At higher temperatures, channels (b) and (c), which are chain-branchingreactions, become important and possibly competitive. The degree of competition between thetwo reactions has been a subject of much controversy over the years. One of the major goals ofthe present study is to quantitatively characterize channel (b) theoretically. Experimentally, it hasbeen difficult to determine the product branching ratios quantitatively for these two competitivechannels on account of the fact that the reactions are slow and only high-temperaturemeasurements above ~1300 K in shock waves could produce some meaningful data. Underhigh-temperature conditions, however, fast secondary radical reactions generated by thefragmentation of CH3, CH3O and CH2O and their reactions with H, O and OH rapidly

2

overwhelm the primary process of interest, CH3 + O2, rendering an accurate determination of thetotal rate constant and product branching probabilities very difficult. This difficulty has beenpartially overcome by the development of sensitive and reliable diagnostics such as atomicresonance absorption spectroscopy (ARAS)11,15,17,20,21 resonance absorption spectroscopy(LRAS)15, 17, 21 which makes kinetic measurements under highly diluted conditions (to minimizesecondary reactions) possible. Recent measurements by the combination of these techniquesaided by kinetic modeling of measured data have led to a near convergence for the rate constantof channel (c).17,20,21 These and earlier results will be cited and compared with our predictedvalues later.

Theoretically, the key feature of the potential energy surfaces (PES) of the CH3 + O2reaction has been investigated by Walch23 using the complete active space SCF/internallycontracted configuration interaction (CASSCF/ICCI) method with the polarized double-zetabasis set of Dunning and Hay.45 He qualitatively discussed the coupling between the initiallyformed 2A” CH3OO species and the exit portion of the 2A’ surface leading to CH2O + OH. Nominimum corresponding to CH2OOH was found on the surface producing CH2O + OH in hiscalculation. Green24 briefly studied this system using density functional theory (DFT) based onDZVP and TZVP basis sets.46,47 Independently, Sicilia et al.25 investigated the reaction at theUMP4//UMP2/DZP and QCISD(T)//UMP2/DZP levels of theory. Symmetry constraint andsurface coupling were not considered in these two studies, although the existence of theCH2OOH intermediate was reported. None of these theoretical studies attempted to predict thetotal reaction rate and product-branching ratios for the three channels (a-c) mentioned above; nordid they rule out theoretically the possibility or impossibility of the most exothermic productchannel (d).

In the present work, we attempt to map out the complete PES for the system and carry outdetailed rate constant calculations for all accessible channels cited above on the basis of thecomputed PES using a variational statistical method. The results of this comprehensive study arepresented herein.

2. Computational Methods2.1 Ab initio calculations

The geometries of the reactants, intermediates, transition states, and products of the CH3+ O2 reaction were optimized at the B3LYP/6-311G(d,p) (i.e., Becke’s three-parameter nonlocalexchange functional48-50 with nonlocal correlation functional of Lee et al.51 The energies of allspecies were calculated by the G2M52 method, which uses a series of calculations withB3LYP/6-311G(d,p) optimized geometries to approximate the CCSD(T)/6-311+G(3df,2p) levelof theory, including a “higher level correction (HLC)” based on the number of paired andunpaired electron. The total G2M energy with zero-point energy (ZPE) correction is calculatedas follows52:E[G2M(RCC, MP2)] = E[RCCSD(T)/6-311G(d, p)] + ∆E(+3df, 2p) + ∆E(HLC) +

ZPE[B3LYP/6-311G(d, p)].∆E(+3df, 2p) = E[MP2/6-311 + G(3df, 2p)] - E[MP2/6-311G(d, p)].∆E(HLC) = -0.00525 nβ - 0.00019 nα;where nα and nβ are the numbers of valence electrons, nα ≥ nβ. All calculations were carried outwith Gaussian 9853 and MOLPRO 9654 programs.

3

2.2 RRKM calculationsThe rate constant and product branching ratios were computed with a microcanonical

variational RRKM (Variflex55) code which solves the master equation55-58 involving multi-stepvibrational energy transfers for the excited intermediate (CH3O2

÷). The ab initio PES calculatedat the G2M level, to be discussed in the next section, was used in the calculation.

Similar to our previous calculation59 with the Variflex code, the component rates wereevaluated at the E, J-resolved level. The pressure dependence was treated by 1-D master equationcalculations using the Boltzmann probability of the complex for the J distribution. The masterequation was solved by an inversion based approach.55,56 In order to achieve convergence in theintegration over the energy range, an energy grain size of 100 cm-1 was used, this grain sizeprovides numerically converged results for all temperatures studies with the energy spanningrange from 15,000 cm-1 below to 64,900 cm-1 above the threshold. The total angular momentumJ covered the range from 1 to 241 in steps of 10 for the E, J-resolved calculation. For thebarrierless transition states, the Varshni potential60, 61

V(R) = De{1 - a exp[- b(R2 - R02)]}2 - De

was used to represent the potential energy along the individual reaction coordinate. In the aboveequation, De is the bond energy excluding zero-point vibrational energies and a = R0/R, where Ris the reaction coordinate (i. e. the distance between the two bonding atoms, in the present caseC—O, or O—O) and R0 is the equilibrium value of R. For the tight transition states, thenumbers of states were evaluated according to the rigid-rotor harmonic-oscillator assumption.3. Results and Discussion3.1. Potential Energy Surfaces and Reaction Mechanism

The optimized geometries of the reactants, intermediates, transition states and products areshown in Fig. 1; the potential energy diagram obtained at the G2M level is presented in Fig. 2;the total and relative energies are compiled in Table 1 and the vibrational frequencies andmoments of inertia of all species are summarized in Table 2. As shown in Fig. 2, the CH3 + O2reaction can occur by two association processes involving O2 in the two lowest electronic states.The reaction of CH3 with the ground electronic state O2 (3∑ − )g occurs barrierlessly to form theCH3O2 (LM1) intermediate with 2A” symmetry. The association process is predicted to beexothermic by 30.4 kcal/mol, which agrees excellently with the value determined by Slagle andGutman, 30.9 ± 0.9 kcalmol.62 In the 2A” CH3O2 state, there are two electrons doubly occupyingthe in-plane 2p-like orbital of the terminal oxygen atom; therefore, the migration of a hydrogenatom to the terminal oxygen atom is energetically unfavorable.23 However, the reaction canproceed by breaking the O-O bond producing the CH3O + O products with an overallendothermicity of 27.7 kcal/mol, to be compared with the experimental value, 28.7 kcal/mol.63 Afurther discussion on the endothermicity will be made later because of its critical effect on thepredicted rate constant for this important product channel.

In the second association process, the reaction takes place by the interaction of theelectronically excited O2 (1Dg) with CH3 to form the electronically excited CH3O2 intermediate,LM2, with 2A’ symmetry. The intermediate is more stable than the CH3 + O2 (3∑ − )g reactantsby 9.2 kcal/mol. The association reaction was also found to occur barrierlessly without a well-defined transition state. In the 2A’ state, there is only one electron occupying the in-plane 2p-likeorbital of the terminal oxygen atom; thus, the migration of a hydrogen atom to the oxygen atomis favorable with this symmetry. The reaction can proceed further by elimination of OH as willbe discussed below. It should be noted that the predicted relative energy between the excited andthe ground state CH3 + O2 reactants is 26.3 kcal/mol, which is much larger than the experimental

4

value of the singlet-triplet energy difference, 22.5 kcal/mol.64 The G2-like methods52 predict theheats of atomization of molecular oxygen in these two states rather poorly. By CASSCF, Walchcalculated the energy difference to be 24.6 kcal/mol.23

Decomposition of the CH3O2 intermediates: The excited LM1 formed by CH3 +O2(3∑ − )g can undergo decomposition via two transition states, TS2 and TS3. TS2 lies 68.8kcal/mol above the intermediate with Cs symmetry, directly producing CH2O + OH by aconcerted H-migration/OH-elimination mechanism. Interestingly, the result of an IRC analysisalong both Cs and C1 symmetry paths shows that TS2 originates from LM1 having a cis-HCOO/planar structure with Cs symmetry. TS3, however, has C1 symmetry; it is formed by H-migration from one of the two equivalent C-H bonds in the staggered position with the O-Obond to give the CH2OOH isomer, LM3, with a barrier of 59.8 kcal/mol. LM3 lies 18.5 kcal/molbelow the reactants; it fragments readily to produce CH2O + OH with a small barrier (7.2kcal/mol) at TS4. LM3 can, inprinciple, also undergo H2O elimination producing the mostexothermic products, HCO + H2O, via TS5 with a large barrier of 65.9 kcal/mol. The largebarrier effectively rules out the possibility of this reaction step, despite its high exothermicity,83.9 kcal/mol. As alluded to above, LM1 can also decompose directly by breaking the O-O bondto give CH3O + O. This endothermic process occurs barrierlessly without a well-defined TS.The large barriers at TS2 and TS3 also effectively prevent the decomposition of the 2A” CH3O2intermediate, producing CH2O + OH directly over the 2A” PES.

The 2A’ CH3O2 intermediate, LM2, formed by the association of CH3 with O2 (1Dg),however, can undergo a concerted H-migration/OH-elimination reaction readily (see Fig. 2)producing CH2O + OH via TS1. This channel is computed to be exothermic by 53.5 kcal/mol,compared to 53.2 kcal/mol from experiment.63 The barrier height at TS1 is 15.0 kcal/mol abovethe ground state reactants, which is very close to the 15.4 kcal/mol activation energy reportedby Yu et al.,22 13.7 kcal/mol calculated by Walch23 with CASCCF and 14.0 kcal/mol estimatedby Green with DFT.24 All these values are, however, significantly higher than 7.4 kcal/molsuggested by Zellner and Ewig.8 The existence of this low energy path and the possibility ofcurve-crossing, as pointed out by Walch,23 may be the direct source of OH in the CH3 + O2reaction. In the following section, we search for the location where the 2A’ and 2A” surfacesmay cross each other.

Location of Seam of Crossing: To determine the location of the seam of crossing, weperformed intrinsic reaction coordinate (IRC)65 calculations along the three minimum energypaths, starting from TS1, TS2 and TS3, moving back toward the CH3O2 intermediates. Asimilar method was employed by Yoshizawa et al.66 to study the crossing seams in the PES of theFeO+-CH4 system. The solid, dotted and dashed lines in Fig. 3 indicate the computed potentialenergy profiles along these minimum energy paths. As shown in the figure, one crossing pointMSX1 was found to locate at s = - 2.0 with the relative energy of -3.9 kcal/mol at the G2M level;where s is the path length with an accuracy of 0.1 amu1/2 ∏bohr. Another crossing point MSX2was found to locate at s = - 0.46 from TS3 with a relative energy of 10.6 kcal/mol at the G2Mlevel. The structures at these crossing points are shown in Fig. 1. The energies calculated withthe crossing-point structures with either 2A’ or 2A” symmetry agree with each other to within0.19 kcal/mol. The fact that these crossing points lie much lower than TS1 suggests that thechemically activated CH3O2 2A” intermediate (LM1) can decompose effectively over the 2A’surface via TS1 to produce CH2O + OH, as first pointed out by Walch.23

3.2 Rate Constant Calculations

5

As the population of the electronically excited state of O2 is too small to contribute evenunder combustion conditions, the key mechanism for the CH3 + O2

reaction involves primarily the ground electronic state O2 (3∑ − )g , producing the vibrationallyexcited CH3O2 (2A”) radical, which can be stabilized by collisions, fragment to give CH3O + Oand undergo surface-crossing to the 2A’ surface to produce the CH2O + OH products via TS1.The probability for the 2A” Ø 2A’ surface-crossing cannot be readily determined quantum-mechanically, it was assumed to be unity in our calculation. This is probably not a poorassumption because the crossing does not involve a spin multiplicity change and the extensiveinternal and CH3 torsional excitation should help break the symmetry constraint.23 Thesymmetry breaking effect of torsional motion can be qualitatively envisaged by comparing theterminal O natural atomic orbital occupancies as a function the torsional angle of the CH3 group.In the 2A’ state, the px, py and pz orbital occupancies are predicted to be 1.0, 1.0, and 2.0,respectively, in both c- and t-LM2 configurations and the corresponding values in the 2A” stateare 1.1, 1.8 and 1.3 in both c- and t-LM1 configurations. The rotation of the CH3 group in the2A” state from the c-LM1 configuration by 20o and 40o gave rise to the predicted occupancies,1.3, 1.6, 1.3 and 1.3, 1.6 and 1.4, respectively. These values are close to the predicted ones at thecrossing point MSX1, 1.5, 1.5 and 1.3. The large internal excitation resulting from theassociation reaction is, therefore, expected to promote the 2A” → 2A’ symmetry change duringthe course of the OH elimination reaction. On account of the high barrier for OH production, 45kcal/mol (see Fig. 2), the effect of temperature on the crossing probability is expected to benegligible. A multi-channel variational RRKM calculation has been carried out for this reaction with theVariflex code55 including the three major competitive product channels: CH3 + O2 Ø CH3O2 (+M) (a) Ø CH2O + OH (b) Ø CH3O + O (c)excluding the most exothermic, but kinetically noncompetitive channel forming CHO + H2O.The energies used in the calculation are plotted in Fig. 2 and the vibrational frequencies andmoments of inertia are listed in Table 2. In the RRKM calculation, we ignore the contributionfrom TS2 and TS3 since their barrier heights are 24.2 and 14.4 kcal/mol higher than that of TS1,respectively, as mentioned in previous section. For the prediction of the quenching rates, reliableLennard-Jones (L-J) parameters are needed. The L-J parameters for CH3O2 (e = 303 K and s =5.4 Å) were derived from deconvoluting the L-J potential of the He-CH3O2 system obtained byour ab initio calculation at the MP2/6-311+G(3df, 2p) level (see Fig. 4). The ε and σ parametersfor the He-CH3O2 collision pair were determined to be 55 K and 4.0 Å by fitting the L-Jfunction,67 V= 4ε [(σ/r)12-(σ/r)6]. The L-J parameters of Ar and N2 were taken from theliterature.68

A. The Association Reaction CH3 + O2 Æ CH3O2The association reaction (a) producing the methylperoxy radical dominates the CH3 + O2

process up to ~1500 K, before the fragmentation reactions (b) and (c) become competitive,according to the early RRKM calculation of Hsu et al.14 The reaction occurs without a well-defined transition state due to the absence of reaction barrier. To reliably predict the associationrates, the flexible variational transition state approach originally developed by Marcus and co-workers69 has been employed by means of the Variflex code as alluded to above. Theassociation potential energy for the approach of CH3 and O2 forming CH3O2 (2A”) was

6

calculated by varying the forming C-O bond distance from 3.5 Å to its equilibrium value, 1.449Å, with an interval of 0.1 Å. Other geometric parameters were fully optimized withoutconstraints for each C-O separation at the B3LYP/6-311G(d,p) level of theory. For eachstructure, we calculated the 3N-7 vibrational frequencies, projected out of the gradient direction.The B3LYP calculated total energy at each point along the reaction path was used to evaluate theVarshni potential energy function60,61 given previously and then scaled to match the dissociationenergy predicted at the G2M level of theory. The values of De and b in the Varshni potentialwere determined to be 33.7 kcal/mol and 1.009 Å-2, respectively. This potential was used in allsubsequent RRKM calculations.

The theoretically predicted pressure-dependent rate constants at 298 K in He arecompared with available experimental data in Fig. 5; those predicted for the association in Arand N2 buffer gases are compared with experimental data in Fig. 6. In the inset of Fig. 6 (a), wealso compare the predicted pressure effects on ka at different temperatures with Ar as the buffergas. Figure 7 compares the theoretical rate constants calculated for the high- and low-pressurelimits (in Ar) with those obtained, typically, by extrapolation of experimental data measured inthe fall-off region.

Inspection of the results presented Fig. 5 indicates that the predicted absolute rateconstants for He buffer gas with <∆E>down (average downward energy transferred per collision)of 70 cm-1 agree quite well with the experimental data.35,38,39,40,43 Similarly for both Ar and N2buffer gases, the experimental data28,29,35,36,44 can be very well accounted for with <∆E>down of130 and 140 cm-1, respectively. The <∆E>down values obtained in our calculations are similar tothose evaluated by others. Keiffer et al.36 fit their experimental results (Ar gas) with the entrancebarrier constrained at 0 and 0.45 kcal/mol to get the optimal <∆E>down values of 40 cm-1 and 80cm-1, respectively. They can also fit their experimental data with the <∆E>down of 285 cm-1. Yu etal.22 fit their experimental data (in Ar) at the same temperature range (298-580 K) with the<∆E>down in the range of 220~300 cm-1, assuming the entrance barrier of 0.9 kcal/mol.

From Fig. 7(a) one can see that the high-pressure limit rate constant, ka∞ , predicted in

the present work has positive temperature dependence. At room temperature, the presentpredicted rate constant is in good agreement with the values of Cobos et al.,28 Yu et al.,22 andLaufer and Bass; 40 it is, however, higher than the extrapolated results of Pilling et al.29,36 Athigher temperatures, our value lies within those of Yu et al.,22 Forst et al.37 and Keiffer et al.36

Our low-pressure limit in Ar buffer gas, ka0, as shown in Fig.7 (b), is close agreement with the

literature data.22,28,29, 36,37

B. The CH3 + O2 Æ CH2O + OH reactionFigure 8 compares the predicted rate constant for the production of CH2O + OH, kb, with

published data. The theoretical result computed for 1000 – 3000 K at atmospheric pressure couldbe fitted to give the following expression: kb = 1.14µ10-22T2.86 exp (-5115.4/T) cm3molecule-1 s-1

As shown in the figure, there is a large scatter in the literature data which could be classifiedapproximately into high1-8,31,32,33 and low value groups.9-22 The high-value group contains thoseresults obtained with channel (b) assumed to be the dominant one; the kinetics of the overallCH3 + O2 reaction were mostly determined without the benefit of ARAS or LRAS for O or OHconcentration measurements. On the other hand, the low-value group consists of those studieswhich employed either ARAS for O detection or LRAS for OH measurement. The predicted rateconstant agrees better with the more recent measurements with ARAS and/or LRAS diagnostics.

7

C. The CH3 + O2 Æ CH3O + O reactionThe decomposition of CH3O2 to CH3O + O, similar to its formation by the entrance

channel, does not have a well-defined transition state. The variational treatment was employed toobtain the dissociation potential energy function by varying the breaking O-O bond from 2.2 to3.2 Å at an interval of 0.1 Å. The computed potential energies could be fitted to the Varshnifunction with the parameter of b =0.637 Å-2. The value of De was obtained by using the heatformation of CH3O predicted by a series of isodesmic calculations because of the underprediction of the endothermicity for the CH3 + O2 Ø CH3O + O overall reaction as previouslymentioned. As shown in Table 4, the average heat formation of CH3O, calculated with 5 differentisodesmic reactions is 5.4 ≤ 0.5 kcal/mol, agrees very well with most recent experimental values,5.47 ≤ 0.770, 5.6 ≤ 0.271 and 5.9 ≤ 0.9 kcal/mol,72 except that of Neumark and co-workers, 6.8 ≤0.4 kcal/mol determined by the photo-fragmentation dynamics of CH3OH.73 For our multi-channel RRKM calculations of the rate constant, the dissociation energy of 59.2 kcal/mol basedon the isodemic result was used.

The predicted rate constant is compared with existing experimental data in Fig.9. Theleast-squares fitted theoretical expression, kc =1.01µ10-16T1.54exp(-13275.7/T) cm3 molecule-1s-1

covering the temperature range 1000-3000 K under atmospheric conditions, agrees closely withthe results of Bhaskaran et al.,11 Klatt et al.15 Yu et al.,22 and Braun-Unkhoff and coworkers,17

but somewhat higher than the most recent works of Michael et al.20 and Hwang and coworkers.21

D. Product branching ratiosRRKM calculations can provide the individual rate constants for any practical conditions

of interest to combustion. In Table 5, we present the values for the high pressure limit (k ∞ ) andthe total rate constants (ktot) as well as the product branching ratios calculated for theatmospheric pressure. These data are also graphically presented in Fig. 10. As can be morereadily seen from the figure that under atmospheric pressure conditions, the formation of CH3O2by collisional stabilization dominates the reaction up to about 1250 K, at which the CH2O + OHproduct formation becomes competitive. The production of CH3O + O, contrary to recentassumption,20,21 appears to be a minor process below 2000 K.

4. Concluding RemarksThe detailed potential energy surfaces computed at the G2M level and the rate constants

predicted with the Variflex code of Klippenstein et al. for three product channels of the CH3 +O2 reaction have been presented. The predicted rate constants for the formation of three majorproducts, CH3O2, CH2O + OH and CH3O + O, agree well with published experimental data.Under atmospheric pressure conditions, the formation of the collisionally stabilized CH3O2 wasfound to dominate up to ~ 1200 K, above which the formation of the CH2 + OH products becomecompetitive. The CH2O + OH products were formed by the crossing of the excited CH3O2 fromthe 2A” to the 2A’surface, followed by fragmentation with a barrier of 15 kcal/mol above thereactants. Significantly, the most exothemic product channel producing HCO + H2O was foundkinetically unimportant due to its very high barrier.

The predicted relative energies for the CH3OO intermediate and the products, CH2O+OH and CH3O + O, agree with experimental values within ≤ 1 kcal/mol, typical for the G2Mmethod for the present size systems.52 We have tested the effect of the possible error in energyon the predicted rate constants for the two product channels by raising the energy at TS1 and the

8

enthalpy change associated with the variational TS producing CH3O + O each by 1 kcal/mol. Thepredicted rate constant for CH2O + OH formation decreases by 7.6% at 1500 – 3000 K,independent of temperature, whereas, the corresponding changes in the rate constant for CH3O +O production are 25% at 1500 K and 6.5% at 3000 K. The result of this brief test suggests thatour theoretical rate constants for the formation of these products are reliable within ≤ 25%, ashas been supported by the reasonable agreement with recent experimental data.

Mechanistically, the reaction of CH3 with O2 differs significantly from its analogousprocesses involving larger alkyl radicals, which contain one or more β -CH bonds. For example,C2H5 + O2; it can undergo facile isomerization and disproportionation reactions producing C2H4+ HO2. A similar process in CH3 + O2 producing CH2 + HO2 is highly endothermic. A detailedmechanism for the C2H5 + O2 reaction has been presented recently by Rienstra-Kiracofe et al.76

It should also be mentioned that the present system differs noticeably from the analogousSiH3 + O2 reaction in several respects.77,78 First of all, the formation of H2SiOOH following theexothermic association/isomerization reaction is non-thermally activated. The chemicallyactivated H2SiOOH can undergo several isomerization/ fragmentation reactions producingH2SiO + OH, HSiOH + OH, Si(OH)2 + H, and SiO + H2 + H exothermically. Secondly, theproduction of H3SiO + O is endothermic by about 11 kcal/mol;77 it cannot compete effectivelywith all the aforementioned exothermic product channels.

AcknowledgmentsThis work is sponsored partially by the Basic Energy Science, Department of Energy

under grant No. DE-FG02-97-ER14784 (to RZ) and partially by the Caltech MultidisciplinaryUniversity Research Initiative under ONR grant No. N00014-95-1-1388 (to CCH and MCL).

References[1] A. M. Dean, G. B. Kistiakowsky, J. Chem. Phys. 54, 1718 (1971).[2] T. P. Izod, G. B. Kistiakowsky, S. Matsuda, J. Chem. Phys. 55, 4425 (1971).[3] C. Jachimowski, J. Combust. Flame 23, 233 (1974).[4] T. Tsuboi, Jpn. J. Appl. Phys. 15, 159 (1976).[5] D. B. Olson, W. C. Gardiner, Jr. Combust. Flame, 32, 151 (1978).[6] K. Tabayashi, S. H. Bauer, Combust. Flame, 34, 63 (1979).[7] K. Saito, R. Ito, T. Kakumoto, A. Imamura, J. Phys. Chem. 90, 1422 (1986).[8] R. Zellner, F. Ewig, J. Phys. Chem. 92, 2971 (1988).[9] C. T. Bowman, Fifteenth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1975; p 869.[10] A. C. Baldwin, D. M. Golden, Chem. Phys. Lett. 55, 350 (1978).[11] K. A. Bhaskaran, P. Frank, Shock Tubes and Shock Waves, Proceedings of the Twelfth International Symposium on Shock Waves; A. Lifshitz, R. Rom, Eds.; Magnes Press: Jerusalem, 1980; p 503.[12] M .A. Teitelboim, V. I. Vedeneev, N. Y. Goldenberg, A. A. Karnaukh, Eleventh International Symposium on Gas Kinetics; Assissi, Italy, 1990.[13] C. H. Wu, C. –Y. Lin, H. –T. Wang, M. C. Lin, In Current Topics in Shock Waves; Kim,Y. W., Ed.; Seventeenth International Symposium on Shock Waves and Shock Tubes, AIPConference Proceedings 208; American Institute of Physics: New York, 1990; p 450. [14] D. S. Y. Hsu, W. M. Shaub, T. Creamer, D. Gutman, M. C. Lin, Ber. Bunsen- Ges. Phys. Chem. 87, 909 (1983).

9

[15] M. Klatt, M. Röhrig, H. Gg. Wagner, Ber. Bunsen-Ges. Phys. Chem. 95, 1163 (1991).[16] M. A. Grela, V. T. Amorebieta, A. J. Colussi, J. Phys. Chem. 96, 7013 (1992).[17] M. Braun-Unkhoff, C. Naumann, P. Frank, In Shock Waves; Brun, Raymond, Cumitrescu, Lucien, Eds.; Nineteenth International Symposium on Shock Waves; Springer: Berlin, Germany, 2, 203 (1995).[18] T. A. Brabbs, R . S. Brokaw, Fifteenth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1975; p 147.[19] A. M. Dean, P. R. Westmoreland, Int. J. Chem. Kinet. 19, 207 (1987).[20] J. V. Michael, S. S. Kumaran, and M. C. Su., J. Phys. Chem. A 103, 5942 (1999).[21] S. M. Hwang, Si-Ok Ryu, and K. J. De. Witt, M. J. Rabinowitz, J. Phys. Chem. A, 103,5949 (1999).[22] C. L. Yu, C. Wang, and M. Frenklach, J. Phys. Chem. 99, 14377 (1995).[23] S. P. Walch, Chem. Phys. Lett. 215, 81 (1993). [24] W. H. Green, Int. J. Quantum Chem. 52, 837 (1994). [25] E. Sicilia, F. P. DiMaio, N. Russo,. Chem. Phys. Lett. 225, 208 (1994).[26] D. Seery, J. Symp. Int. Combust. Proc. 12, 588 (1969).[27] F. B. Marcotte, W. A. Jr. Noyes, Discuss. Faraday Soc. 10, 236 (1951).[28] C. J. Cobos, H. Hippler, K. Luther, A. R. Ravishankara, J. Troe, J. Phys. Chem. 89, 4332 (1985).[29] M. J. Pilling, M. J. C. Smith, J. Phys. Chem. 89, 4713 (1985).[30] M. A. Teitelboim, L. B. Romanovich, B. I. Vedeneev, . Kinet. Katal. 19, 399 (1978).[31] D. F. Cooke, A. Williams, A. Symp. Int. Combust. Proc. 13, 757 (1971).[32] D. L. Baulch, C. J. Cobos, R. A. Cox, C. Esser, P. Frank, Th. Just, J. A. Kerr, M. J.Pilling, J. Troe, R. W. Walker, J. Warnatz, J. Phys. Chem. Ref. Data, 21, 411 (1992).[33] A. A. Borisov, E. V. Dragalova, V. M. Zamanskii, V. V. Lisyanskii, G. I. Skachkov, Kinet.Catal. 22, 305 (1981).[34] J. Warnatz, Combustion Chemistry (ed. W. C. Gardiner, Jr.) Springer-Verlag, NY1984,197.[35] E. A. Selzer, K. D. Bayes, J. Phys. Chem. 87, 392 (1983).[36] M. Keiffer, M. J. Pilling, M. J. C. Smith, Phys. Chem. 91, 6028 (1987).[37] W. Forst, F. Caralp, J. Chem. Soc. Faraday Trans., 87, 2307 (1991).[38] J. Washida, Chem. Phys. 73, 1665 (1980).[39] I. C. Plumb, K. R. Ryan, Int. J. Chem. Kinetics, 14, 861 (1982).[40] A. H. Laufer, A. M. Bass, Int. J. Chem. Kinetics, 7, 639 (1975).[41] C. J. Hochanadel, J. A. Ghormley, J. W. Boyle, P. J. Ogren, J. Phys. Chem. 81, 3 (1977)[42] D. A. Parkes, Int. J. Chem. Kinet. 9, 451 (1977).[44] N. Basco, D. G. L. James, F. C. James, Int. J. Chem. Kinetics. 4, 129 (1972).[43] E. W. Kaiser J. Phys. Chem. 97, 11681 (1993).[45] T. H. Dunning, Jr and P. J. Hay, in: Methods of electronic structure theory, ed. H. F.Schaefer III (Plenum Press, New York, 1977).[46] N. Godbout, J. Andzelm, E. Wimmer,. and D. R. Salahub, Can. J. Chem. 70, 560 (1992). [47] J. Andzelm, E. Radzio, and D. R. Salahub, J. Comput. Chem. 6, 520 (1985).[48] A. D. Becke, J. Chem. Phys.98, 5648 (1993).

10

[49] A. D. Becke, J. Chem. Phys. 96, 2155 (1992).[50] A. D. Becke, J. Chem. Phys. 97, 9173 (1992).[51] C. Lee, W. Yang, R. G. Parr, Phys. Rev. 37B, 785 (1988).[52] A. M. Mebel, K. Morokuma, M. C. Lin, J. Chem. Phys. 103, 7414 (1995).[53] M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M . W. Gill, B. G. Johnson, M. A. Robb, J. R.Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V.G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M.Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R.Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez and J. A. Pople, GAUSSIAN 98, REVISION A.1; Gaussian, Inc., PittsburghPA, 1998.[54] MOLPRO is a package of ab initio programs written by H.-J. Werner and P. J. Knowles,with contributions from J. Almlöf, R. D. Amos, A. Berning, D. L. Cooper, M. J. O. Deegan, A. J.Dobbyn, F. Eckert, S. T. Elbert, C. Hampel, R. Lindh, A. W. Lloyd, W. Meyer, A. Nicklass, K.Peterson, R. Pitzer, A. J. Stone, P. R. Taylor, M. E. Mura, P. Pulay, M. Schütz, H. Stoll and T.Thorsteinsson.[55] S. J. Klippenstein, A. F. Wagner, R. C. Dunbar, D. M. Wardlaw, and S. H. Robertson,VARIFLEX: VERSION 1.00, 1999.[56] R. G. Gilbert, S. C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell Scientific, Carlton, Australia, 1990.[57] K. A. Holbrook, M. J. Pilling, and S. H. Robertson, Unimolecular Reactions, Wiley, 1996.[58] J. Troe, J. Chem. Phys. 66, 6745 (1977).[59] R. S. Zhu, M. C. Lin, J. Phys. Chem. A, 104 10807 (2000).[60] V. P. Varshni, Rev. Mod. Phys. 29, 664 (1957).[61] S. J. Klippenstein, L. R. Kundhar, A. H. Zewail, R. A. Marcus, J. Chem. Phys. 89, 4761 (1988).[62] I. R. Slagle and D. Gutman, J. Am. Chem. Soc., 107, 5432 (1985).[63] Jr. M. W. Chase, C. A. Davies, Jr. J. R. Downey, D. J. Frurip, A. A. McDonald, and A. N.Syverud, J. Phys. Chem. Ref. Data, 14, Suppl. 1 (1985).[64] B. Rosen, ed., Spectroscopic data relative to diatomic molecules (Pergamon Press, Oxford,1970)[65] C. Gonzalez, H. B. Schlegel, J. Phys. Chem.90, 2154 (1989).[66] K. Yoshizawa, Y. Shiota, T. Yamabe, J. Chem. Phys. 111, 538 (1999).[67] J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular theory of gases and liquids. 2nd ed. John Wiley and Sons Inc., New York, NY., 1964.[68] H. Hippler, J. Troe, and H. J. Wendelken, J. Chem. Phys. 78, 6709 (1983).[69] D. M. Wardlaw and R. A. Marcus, Chem. Phys. Lett. 110, 230 (1984); J. Chem. Phys. 83, 3462 (1985); S. J. Klippenstein, J. Chem. Phys. 96, 367 (1992); S. J. Klippenstein and R. A. Marcus, J. Chem. Phys. 87, 3410 (1987).[70] O. A. Mazyar, T. Baer, J. Phys. Chem. A, 103, 1221 (1999).

[71] J. L. Holmes, F. P. Lossing, Int. J. Mass Spectrom. Ion Processes, 58, 113 (1984).

[72] Handbook of Chemistry and Physics, D. R. Lide, editor-in-chief, 78th edition, p. 9- 71, CRC, Press, 1997-1998, Boca Raton, Florida.

11

[73] D. L. Osborn, D. J. Leahy, E. M. Ross, D. M. Neumark, Chem. Phys. Lett., 235, 484 (1995).[74] M. W. Chase, Jr. NIST-JANAF Thermochemical Tables, Fourth Edition, Woodbury, NewYork, 1998.[75] C. W. Jr. Bauschlicher, H. Partidge, Chem. Phys. Lett. 208, 241 (1993).[76] J. C. Rienstra-Kiracofe, W. D. Allen and H. F. Schaefer, III. J. Phys. Chem. A. 104, 9823(2000).[77] C. L. Darling and H. B. Schlegel, J. Phys. Chem. 98, 8910 (1994).[78] Y. Murakami, M. Koshi, H. Matsui, K. Kamiya and H. Umeyama, J. Phys. Chem. 100,17501 (1996).

12

Table 1. Total and Relative Energies of Reactants, Intermediates, Transition States and Products for the Reaction of CH3 with O2 Calculated at Different Levels of Theory with B3LYP/6-311G(d, p) Optimized Geometries.

Energiesb

Species ZPEa B3LYP/

6-311G (d, p)

MP2/

6-311G(d, p)

MP2/

6-311+G(3df, 2p)

CCSD(T)/

6-311G (d, p)

G2M

CH3 + O2(3 −Σg ) 20.9 -190.218548 -189.7307117 -189.8393013 -189.769878 -189.8783

CH3 + O2(1g∆ ) 20.9 39.0 31.9 30.1 30.6 26.3

CH2O+OH 21.9 -45.4 -48.4 -52.9 -50.0 -53.5

CH3O+O 22.7 29.5 32.7 35.8 23.5 27.7

HCO+H2O 21.5 -72.5 -79.5 -87.7 -76.4 -83.9

t-LM1c, Cs, 2A'' 26.9 -33.4 -24.0 -29.7 -30.6 -30.4

c-LM1c, Cs, 2A'' 26.6 -32.6 -23.1 -28.9 -29.4 -29.6

t-LM2 c, Cs, 2A' 26.6 -11.6 -3.7 -8.9 -9.7 -9.2

c-LM2 c, Cs, 2A' 26.2 -8.2 -0.1 -5.6 -6.2 -6.4

LM3, C1 25.2 -16.7 -13.2 -20.9 -15.0 -18.5

TS1, Cs, 2A' 22.4 17.7 35.9 28.8 20.7 15.0

TS2, Cs, A'' 24.3 36.3 56.4 49.3 43.0 39.2

TS3, C1 23.0 30.5 35.9 27.6 35.5 29.4

TS4, C1 24.2 -13.2 17.3 11.3 -8.6 -11.3

TS5, C1 21.6 49.5 60.9 53.4 54.2 47.4

MSX1 23.4 11.6 30.2 24.4 13.8 10.6

MSX2 25.6 -5.5 4.4 -1.5 -2.7 -3.9

aValues are in units of kcal/molbThe total energies are in units of a.u and the relative energies are in units of kcal/mol.c c-LM1 , t-LM1 and c-LM2, t-LM2 are defined as those in Fig. 1

13

Table 2. Vibrational Frequencies and Moments of Inertia for Reactants, Intermediates, Transition States and Products of the CH3 + O2 Reaction at B3LYP/6-311G(d, p) Level of Theory.a

Species Ii (au) Frequencies

CH3 6.3, 6.3, 12.6 504, 1403, 1403, 3105, 3284, 3284

O2(3 −Σg ) 41.5, 41.5 1638

O2(1∆g) 41.5, 41.5 1628

CH2O 6.3, 46.2, 52.6 1202, 1270, 1539, 1827, 2868, 2917

OH 3.2, 3.2 3704

c-LM1 33.5,162.4,184.3 -137i,527, 907, 1113, 1131,1234, 1432, 1472, 1481, 3044, 3129, 3162

t-LM1 34.2, 160.0, 182.7 135, 294, 914, 1129, 1156, 1218, 1446, 1469, 1484, 3049, 3140, 3156

c-LM2 37.1, 163.2, 188.6 -280 i, 367, 908, 1008,1146,1177,1457,1475,1493, 3035, 3115,3134

t-LM2 37.4, 159.6, 185.4 256, 371, 916, 1028, 1169, 1176, 1453, 1459, 1510, 3018, 3086, 3147

LM3 33.9, 161.9, 187.8 156, 237, 480, 653, 841, 1134, 1192, 1363,1432, 3115, 3259, 3744

TS1 51.5, 126.3, 165.1 1882i, 202, 751, 762, 1013, 1078, 1109, 1165, 1474, 1950, 3048, 3164

TS2 34.6, 158.0, 181.3 -555 i, 518, 749, 907, 924, 958, 1223, 1369, 1391, 2945, 2983, 2996

TS3 41.1, 131.3, 164.9 -2566, 572, 635, 848, 999,1099, 1160, 1290, 1549, 1884, 2959, 3104

TS4 33.9, 175.2, 206.5 -1373 i, 188, 409, 502, 826, 1123, 1148, 1260, 1449, 3053, 3198, 3783

TS5b 39.9, 141.3, 172.7 -3176 i, 431, 707, 797, 963, 1118, 1148, 1399, 1899, 2575, 3102, 3697

MSX1 47.6, 129.9, 165.9 364 i, 706, 903, 1094, 1145, 1187, 1463,1507,1512, 3016, 3160, 3231

MSX2 38.1,146.2, 172.8 403, 730, 869, 1101,1135,1157, 1328,1416,1484, 2159, 3046, 3097

a.The geometries of various species are given in Fig. 1.b. This transition state was located at the MP2/6-311(d, p) level since we failed to locate it byB3LYP/6-311G(d, p).

14

Table 3. Calculated High Pressure and Low Pressure Limiting Rate Constants forAssociation Reaction of CH3+O2→CH3O2 in Ar at some Selected Temperatures.

T ( K) k∞

(cm3molecule-1s-1)k0

(cm6molecule-2s-1)298 1.80×10-12 2.52×10-30

334 2.17×10-12 1.49×10-30

382 2.71×10-12 7.87×10-31

420 3.16×10-12 4.96×10-31

474 3.85×10-12 2.68×10-31

530 4.61×10-12 1.49×10-31

583 5.37×10-12 8.9×10-31

Table 4. The Heat Formation of CH3O Calculated by the Isodemic Method at the G2M level. Values are in units of kcal/mola.

Reaction DrH0 (0K) DfH0 (CH3O, 0K)CH3 + NO2 Ø CH3O + NO -17.36 5.37≤0.3CH3 + OH Ø CH3O + H 12.30 5.50≤0.5CH3 + O2H Ø CH3O + OH -24.86 5.36≤1.1CH4 + OH Ø CH3O + H2 12.29 5.48≤0.4CH3 + H2OØ CH3O + H2 26.64 5.10≤0.2

Average 5.36≤0.5

Exp 5.47≤0.7 70

5.6≤0.2 71

5.9≤0.9 72

6.8±0.4 73

a The species heats of formation at 0 K, were taken from Ref. 74, except that of HO2 from Ref. 75. The errors given in the calculated values convolute all reported experimental ones.

15

Table 5. Theoretically Predicted Branching Ratios and ktot. at 1 atm. and High Pressure in Ar in units of cm3 molecule-1 s-1

T(K) ka/ ktot kb/ ktot kc/ ktot ktot kinf

500 1.00 0.00 0.00 2.99×10-13 4.37×10-12

800 1.00 0.00 0.00 4.00×10-14 9.16×10-12

1000 0.97 0.03 0.00 9.86×10-15 1.28×10-11

1110 0.86 0.13 0.01 4.41×10-15 1.50×10-11

1200 0.59 0.38 0.03 2.69×10-15 1.68×10-11

1300 0.21 0.70 0.09 2.57×10-15 1.88×10-11

1400 0.05 0.80 0.15 3.67×10-15 2.09×10-11

1500 0.01 0.79 0.20 5.79×10-15 2.31×10-11

1800 0.00 0.67 0.33 2.05×10-14 2.97×10-11

2000 0.00 0.59 0.41 4.14×10-14 3.43×10-11

2500 0.00 0.47 0.53 1.67×10-13 4.62×10-11

3000 0.00 0.39 0.61 4.69×10-13 5.83×10-11

16

Figures captions

Fig.1 The optimized geometries of the reactants, intermediates, transition states and

products (except O2, H2O, and CH2O) computed at the B3LYP/6-311G(d, p)

level.

Fig. 2 Schematic energy diagram of the CH3-O2 system computed at the G2M level.

Fig. 3 Potential energies along those IRC paths from TS1, TS2, TS3 to intermediates for

s<0 (s is the length of IRC).

Fig. 4 The L-J potential of the He-CH3O2 system computed at the MP/6-311+G(3df,

2p) level, solid circles are the calculated data, solid curve is the fitting result.

Fig. 5 Comparison of the predicted rate constants (curves) with experimental literature

data (symbols) in bath gas He for CH3 + O2 Ø CH3O2.

Fig. 6 Comparison of the predicted rate constants (curves) with experimental literature

data (symbols) in bath gases Ar and N2 for CH3 + O2Ø CH3O2.

Fig. 7 Comparison of the experimental and calculated rate constants for high-pressure

(a) and low-pressure (b) limits in Ar bath gas.

Fig.8 Comparison of the predicted and experimental rate constants for

CH3 + O2 ØCH2O + OH. References are given as labeled.

Fig.9 Comparison of the predicted and experimental rate constants for

CH3 + O2 Ø CH3O + O. References are given as labeled.

Fig.10 Predicted rate constants, plotted in the Arrhenius form, for the three product

channels as well as the total rate constant at 1 atm. and the high-pressure limit.

17

H

H

H

O

O

H

H

H

H

H

O

O

H

O

O

H

H

H H

H

O

O

H

OH

O

H

H

HO

OH

H

H

O

H

O

H

H

O

O

H

H

H

H

H

O

O

O

O

H

H

H

H O

O

H

H

H

O

H

H

OO HH

H

O

O

H

H

120.0

1.080

CH3, D3h, 2A" c-LM1, Cs,2A"

(O-O-C-H1=0.0)

1.3171.453112.4

108.31.088

1.091 1.449

1.317113.3

109.9

t-LM1, Cs, 2A"

(O-O-C-H1=180.0)

c-LM2, Cs,2A'

(O-O-C-H1=0.0)

1.389108.01.448

110.41.089

1.092t-LM2, Cs,

2A' (O-O-C-H1=180.0)

1.386107.8

1.435

104.21.089

1.0941.358

109.11.456

100.4

0.969

1.083

1.094

LM3

1.268

1.5091.336101.883.3

88.7

115.41.379

1.9681.012

1.4131.397

108.3

95.1126.1

TS1, Cs, 2A' TS2, Cs,

2A"

1.384

1.394

1.341

1.389 99.8

77.9

TS3, C1

1

1

1

11

1

1.300

1.62695.3

107.3117.4

1.087

1.090

0.968

1.504 1.098

108.91.325

1.523

1.177 105.0 77.480.8 96.8

TS5, C1TS4, C1

1.327102.9

1.221

81.6

1.473

MSX1

1.3791.216

97.6

1.397

MSX2

1.365

105.31.109

1.127124.0

1.174

CH3O, Cs, 2A'HCO, Cs,

2A'

Fig. 1 Zhu, J. Chem. Phys.

1

18

-60.0

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

10.0

20.0

30.0

40.0 CH3+1O2

26.3

CH3+3O2

t-LM1, 2A"-30.4

c-LM2, 2A'-6.4

CH3O+O27.7

TS1 2A'15.0

CH2O+OH-53.5

LM3,2A-18.5

TS3,2A29.4

HCO+H2O-83.9

TS2, 2A" 39.2

-70.0

-80.0

-90.0

50.0

TS5,2A47.4

TS4,2A-11.3

MSX1

MSX2

c-LM1, 2A"-29.6

Kcal/mol

Fig. 2 Zhu, J. Chem. Phys.

19

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

-190.28

-190.26

-190.24

-190.22

-190.20

-190.18

-190.16

MSX2

TS3(2A)

t-LM1(2A")(see Fig.1)

MSX1

TS1(2A')

TS2 2A"

c-LM1(2A") (see Fig.1)

LM2(2A')

Tota

l Ene

rgy

(Har

tree)

-s(amu1/2 bohr)

Fig. 3 Zhu, J. Chem. Phys.

20

Fig. 4 Zhu, J. Chem. Phys.

3 4 5 6 7 8

-80

-40

0

40

80

120

Calculated data solid line is the fitting result

V(R

)/K

Interaction Coordinate Ao

21

10-1 100 101 102 103 104 105 106

0.1

1

10

He 298 K

CThis work

ESelzer et al.35

HWashida38

JLaufer et al.40

NKaiser43

PPlumb et al. 39

k a /10

-13 c

m3 m

olec

ule-1

s-1

He Pressure (Torr)

Fig.5 Zhu, J. Chem. Phys.

22Fig.6 Zhu, J. Chem. Phys.

0 100 200 300 400 5000

2

4

6

8

530 K

420 K

334 K"Data from Ref. 36"

k/10

-13 c

m3 m

olec

ule-1

s-1

Pressure (Torr)

10-1 100 101 102 103 104 105 1060.01

0.1

1

10(a)

exp. Pilling and Smith 29

exp. Cobos et al.28

exp. Selzer et al.35

k a/10-1

3 (cm

3 mol

ecul

e-1s-1

)

Ar Pressure (Torr)

10-1 100 101 102 103 104 105 106

0.1

1

10

(b)

k/10

-13 c

m3 m

olec

ule-1

s-1

This work

Cobos et al.28

Basco et al. 44

Selzer et al.35

Kaiser43

N2 Pressure (Torr)

23

1.5 2.0 2.5 3.0 3.5

10-32

10-31

10-30

(b)

Yu et al.22

Cobos et al.28

Pilling et al.29

Keiffer et al.36

Forst et al.37

k a0 cm6 m

olec

ule-2

s-1

1000/T K

1.5 2.0 2.5 3.0 3.5

1

2

3

4

5

6

7

8

(a) Current work

Yu et al.22

Cobos et al.28

Baulch et al.32

Keiffer et al.36

Pilling and Smith et al.29

Kaiser et al.43

R Laufer et al.40

S Hochanadel, et al.41

TParkes et al.42

k a∞∞ ∞∞/1

0-13 c

m3 m

olec

ule-1

s-1)

1000/T

Fig. 7 Zhu, J. Chem. Phys.

24

Fig.8 Zhu, J. Chem. Phys.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.110-16

10-15

10-14

10-13

10-12

10-11

10-10

32

This work

9 78

31

1722

11

3325

6

1

k (c

m3 m

olec

ule-1

s-1)

1000/T (K)

25

Fig.9 Zhu, J. Chem. Phys.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

10-17

10-16

10-15

10-14

10-13

10-12

11

21

20

22

15

17 8

34

7

18

14

This work

13

k (c

m3 m

olec

ule-1

s-1)

1000/T (K)

26

Fig.10 Zhu, J. Chem. Phys.

0.4 0.8 1.2 1.6 2.010-20

10-18

10-16

10-14

10-12

10-10

ktot

CH3OO (ka)

1 atm

k∞

CH3O+O (kc)

CH2O+OH (kb)

k c

m3 m

olec

ule-1

s-1

1000/T (K)