A Theoretical and Computational Analysis of the Methyl-Vinyl + O2

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A Theoretical and Computational Analysis of the MethylVinyl + O Reaction and Its Effects on Propene Combustion 2

Xi Chen, and C. Franklin Goldsmith J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b07594 • Publication Date (Web): 07 Nov 2017 Downloaded from http://pubs.acs.org on November 7, 2017

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The Journal of Physical Chemistry

A Theoretical and Computational Analysis of the Methyl-vinyl + O2 Reaction and its Effects on Propene Combustion Xi Chen† and C. Franklin Goldsmith∗,‡ †Chemistry Department, Brown University, Providence, RI ‡Chemical Engineering Group, School of Engineering, Brown University, Providence, RI E-mail: [email protected]

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Abstract A detailed analysis of the reaction of CH3 CCH2 and CH3 CHCH with molecular oxygen is presented. The C3 H5 O2 potential energy surface (PES) has been characterized using a combination of electronic structure methods. The majority of the stationary points on the PES were determined at the CCSD(T)-F12a/cc-pVTZ-F12//B2PLYPD3/ccpVTZ level of theory, with the remaining transition states computing using multireference methods. Microcanonical rate theory and the master equation are used to determine the temperature- and pressure- dependent rate coefficients for each reaction channel. The main product channels are CH2 O + CH3 CO for CH3 CCH2 and CH3CHO + CHO for CH3 CHCH. The rate constants for these two reactions at 1 atm are k = 9.03 × 1022 × T −3.21 × exp−2162/T cm−3 molecule−1 s−1 and k = 1.50 × 1019 × T −2.10 × exp−1260/T cm−3 molecule−1 s−1 respectively. In contrast to C2 H3 + O2 , the methyl-vinyl + O2 reactions remain chain propagating, even at high temperatures. The new rate coefficients were implemented in a detailed mechanism taken from the literature. These changes have a modest effect on the ignition delay time and laminar flame speeds for propene combustion.

1

Introduction

Propene is a important intermediate in many combustion and pyrolysis processes. 1–5 It is also a key component of Liquefied Petroleum Gas (LPG). 6 The combustion properties of propene have been investigated using a variety of methods, including Some of the more recent experimental investigations into propene oxidation include: jet stirred reactors (JSR), 7–9 flow reactors, 9–11 shock tube 5,12–14 and rapid compression machines (RCM) 5 studies. Radical such as R = OH, CH3 and O can abstract an H atom from the three different carbon atoms in propene to form CH2 CHCH2 (allyl), CH3 CCH2 (1-methyl-vinyl, C3 H5 −t), and CH3 CHCH(2-methyl-vinyl, C3 H5 −s). The bond dissociation energy for the allylic hydrogen is significantly weaker (86.2 kcal/mol vs 106.1 kcal/mol and 109.7 kcal/mol for CH3 CCH2 2


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and CH3 CHCH, 15–17 respectively), and consequently the majority of H-abstraction reactions for propene produce allyl as the main product, with the two vinylic isomers produced in much smaller amounts. 9 Owing to its resonance stabilization, the allyl radical is difficult to oxidize, and the CH2 CHCH2 + O2 reaction is not significant in most kinetic analyses. 18 However, a recent modeling investigation into propene oxidation by Burke et al. 5,9 revealed that the reactions of CH3 CCH2 and CH3 CHCH with O2 were important, despite the comparatively low yield of these radicals from R + C3 H6 reactions. For example, a brute-force sensitivity analysis of ignition delay times in propene combustion found normalized sensitivity coefficients of 0.2 for the reaction CH3 CCH2 + O2 → CH3 C(−O)CH2 + O and -0.25 for CH3 CCH2 + O2 → CH3 CO + CH2 O. The product branching fractions in Ref. 9 for these two reactions were taken by analogy from CH2 CH + O2 : 18,19

CH3 CCH2 + O2 −−→ CH3 C(−O)CH2 + O

(R1a)

−−→ CH2 O + CH3 CO

(R1b)

−−→ C3 H4 −a + HO2

(R1c)

CH3 CHCH + O2 −−→ CH3 CHCHO + O

(R2a)

−−→ CH3 CHO + HCO

(R2b)

−−→ C2 H3 CHO + OH

(R2c)

More recently, Goldsmith et al. completed a high-level investigation into the kinetics of vinyl oxidation. 20 The authors found that the branching fractions were significantly different from those used in Ref. 18, with 8 C2 H3 O2 unimolecular intermediates and 8 bimolecular

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product channels. Of the 8 unimolecular itermediates, only the initial adduct, CH2 CHOO, is collisionally stabilized, with the majority of the flux going to either CH2 O + HCO (chain propagating) at lower temperatures and CH2 CHO + O (chain branching) at higher temperatures. Given the aforementioned sensitivity of the propene ignition delay to the CH3 CCH2 + O2 and CH3 CHCH + O2 reactions, as well as the uncertainty regarding the product distribution and branching fractions, the aim of the present work is to provide a rigorous determination of the temperature- and pressure-dependent rate coefficients for methyl-vinyl + molecular oxygen. Accordingly, we present the first detailed analysis of the two relevant sections of the C3 H5 O2 potential energy surface. Temperature- and pressure-dependent rate coefficients for all elementary reactions on the PES are predicted by the combination of electronic structure theory and microcanonical rate theory (RRKM/ME) methods. The new rate constants are implemented into the original mechanism of Burke et al. 5,9 to quantify their effects on propene oxidation.

2 2.1

Computational Methods Electronic Structure Methods

The oxidation of the two isomers of methyl-vinyl radical, CH3 CCH2 and CH3 CHCH, were studied separately. The compound methods used in Ref. 20, ANL0, 21 was computationally prohibitive for this system. Instead, combined methods were used in which geometry optimization and normal mode analysis were performed using density functional theory (DFT), and single-point calculations were performed using coupled cluster theory with explicit correlations, UCCSD(T)-F12. 22–24 To select the appropriate DFT functional, two sets of benchmark calculations were performed. In the first analysis, the torsional rotation about the CH2 C-OO bond in CH3 C(OO)CH2 was analyzed. This torsional rotation has two distinct minima (syn and anti with respect to the C=CH2 moiety, with the latter being the global 4


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minimum) and two equivalent eclipsed maxima. Five different functionals were considered: B3LYP, 25–27 B2PLYPD3, 28,29 M062X, 30 B3PW91, 31 and B1B95. 32 For each functional, several triple-zeta basis sets were considered: 6-311++G(d,p), cc-pVTZ, MG3S, and Roos Augmented Triple Zeta ANO. 33,34 These results were compared with coupled-cluster calculations on the four stationary points. The ANL0 method was used to obtain these four reference energies. The results of this analysis are provided in the Supplemental Material. This analysis found that the B2PLYPD3 functional with the cc-pVTZ basis set gave the best performance. In the second set of calculations, the C2 H3 + O2 PES of Ref. 20 was re-optimized using B3LYPD3/cc-pVTZ. These calculations were followed by UCCSD(T)/cc-pVTZ and UCCSD(T)-F12/cc-pVTZ-F12 single point calculations. The resulting UCCSD(T), UCCSD(T)F12a, and UCCSD(T)-F12b energies were compared against the original values of Ref. 20, and the F12a energies were the closest to the benchmark. Accordingly, all stationary points on the C3 H5 O2 PES in the present work were computed using UCCSD(T)-F12a/cc-pVTZ-F12//B2PLYPD3/cc-pVTZ. For the first-order saddle points, intrinsic reaction coordinate (IRC) calculations and visual inspection of the imaginary mode were performed to confirm that the correct transition state was obtained. Several transition states in the C3 H5 O2 system required multi-reference theory. These transition states and the methods used to compute them are addressed individually in the Results section. All DFT calculations were performed in Gaussian09; 35 all wavefunction calculations were performed in MOLPRO. 36

2.2

Variable Reaction Coordinate TST calculation

The addition of oxygen to methyl-vinyl radical is a barrierless reaction, and harmonic transition state theory cannot be used to calculate the microcanonical rate constant. Instead, Variable Reaction Coordinate Transition State Theory (VRC-TST) was used. 37–39 In VRCTST, when evaluating the partition function of the transition state, the internal degrees 5



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of freedom are separated into conserved and transitional modes. The internal vibrational modes of two fragments are conserved modes, and the transitional modes are the coupled anharmonic degrees of freedom that govern the relative motion of the two radical fragments. The multi-dimensional partition function for the transition modes is computed from classical Phase Space Theory via Monte Carlo sampling, in which the potential energy at each sampling point is computed using CASPT2(9e7o)/cc-pVTZ.

The VRC-TST calculation of the oxygen addition reactions were implemented using the code VaReCoF, which is part of the PAPR package from Argonne National Laboratory. 40 The minimum reaction paths were optimized under two different settings, one for relaxed geometry, the other for frozen internal geometries. The difference between these two optimization paths was used as a 1-D correction for geometry relaxation to the energy potential. Similar corrections for basis set extrapolation and active space expansion were included.

2.3

RRKM/ME

The temperature- and pressure- dependent rate coefficients were calculated by the RRKM/ME code, MESS. 40–42 For all tight transition states, conventional harmonic transition-state theory was used. Torsional modes were treated separately using 1D or 2D hindered internal rotors, where appropriate. The rotational potentials were calculated by a relax scan at the B2PLYPD3/cc-pVTZ level in 10◦ increments. Tunneling was included by using an asymmetric Eckart approximation. Collision parameters used in the master equation were taken from vinyl oxidation work; 20 a single-exponential down model was used for the collisional energy transfer, 43,44 with ∆Edown = 200(T /300)0.85 ; the collision frequency was estimated using a Lennard-Jones (LJ) model, with LJ parameters of σ = 2.55 Å, ǫ = 6.95 cm−1 for He, 45 and σ = 5.18 Å, ǫ = 285.2 cm−1 for the C3 H5 O2 intermediates. 43

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CH3 CCH2 + O2 −−→ CH3 C(OO)CH2

(R1d)

−−→ CH3 C(−O)CH2 + O

(R1a)

−−→ CH2 O + CH3 CO

(R1b)

−−→ C3 H4 −a + HO2

(R1c)

−−→ CH3 C(−O)CH + OH

(R1e)

−−→ CH3 CCH + HO2

(R1f)

−−→ CH2 C(−O)CH2 + OH

(R1g)

−−→ CH3 O + CH2 CO

(R1h)

−−→ CH3 C(−O)CHO + H

(R1i)

−−→ CH2 OH + CH2 CO

(R1j)

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CH3 CHCH + O2 −−→ CH3 CHCHOO

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(R2d)

−−→ CH3 CHCHO + O

(R2a)

−−→ CH3 CHO + HCO

(R2b)

−−→ CH2 CHCHO + OH

(R2c)

−−→ CH3 CCHO + OH

(R2e)

−−→ CH3 CCH + HO2

(R2f)

−−→ CH2 CHCHO + OH

(R2g)

−−→ CH2 CHOCHO + H

(R2h)

−−→ CH3 C(−O)CHO + H

(R2i)

−−→ CH2 OH + CH2 CO

(R2j)

−−→ OCHCHO + CH3

(R2k)

−−→ CH2 O + CH3 CO

(R2l)

−−→ CO2 + C2 H5

(R2m)

The PES for CH3 C(OO)CH2 and CH3 CHCHOO are qualitatively similar to that of CH3 CHOO in Ref. 20, in that they can be divided into two regimes: a highly exothermic regime that is accessed via cleavage of the O-O bond in a cyclic intermediate (illustrated with the black lines in Figure 1 and 2), and a less exothermic regime. In C2 H3 + O2 , the dominant product from the highly exothermic pathway is CH2 O+HCO, and the dominant product from the less exothermic region is CH2 CHO + O. The corresponding products for CH3 CCH2 (CH3 CHCH) are CH2 O + CH3 CO (CH3 CHO + HCO) and CH3 C(−O)CH2 + O (CH3 CHCHO + O), respectively. As described in Ref. 20, the branching fractions to these competing pathways are sensitive to two key transition states. The kinetic bottleneck for the CH2 O + CH3 CO (CH3 CHO + HCO) pathways is the isomerization between two three-member ring interme10


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diates, whereas the bottleneck for the formation of resonantly stabilized CH3 C(−O)CH2 + O (CH3 CHCHO + O) products is the O-O bond fission reaction (shown in blue). These transition states, as well as other key transition states, are described in greater detail below. 3.1.2

TS1: CH3 CCH2 + O2 and TS24: CH3 CHCH + O2

The first transition state is the addition of O2 to CH3 CCH2 and CH3 CHCH. For these calculations, CASPT2 was used, with an active space of 9 electrons and 7 orbitals (9e7o); this active space consists of the π and π ∗ orbitals of O2 , the π and π∗ orbitals of C−C, and the in carbon-centered radical orbital. For each fixed C-O distance r, the remaining degrees of freedom were optimized using CASPT2(9e7o)/cc-pVTZ, which included a level shift of 0.2 and an IPEA shift of 0.25. 48 For each optimized geometry, subsequent calculations were performed to include the effects of larger space active space, basis set extrapolation, and different multi-reference methods. The active space was expanded to include the σ and σ∗ orbital of O-O bond (11e9o) and then the σ, σ∗ orbital beneath the C-C π system (13e11o). For each of these calculations, the single point energy was calculated using cc-pVTZ and cc-pVQZ basis sets, and the basis set limit was extrapolated using the formula: 49

∆Ecc−pV ∞Z = ∆Ecc−pV QZ − ∆(Ecc−pV T Z − Ecc−pV QZ ) ·

44 54 − 44

(1)

Additional single-point energies were computed using MRCI+Q(9e7o)/cc-pV∞Z and MRCI+Q(11e9o)/cc-pVTZ; the MRCI+Q(13e11o)/cc-pV∞Z were computationally prohibitive. Finally, the doublet-quartet correction used in Ref. 20,50 was employed to further reduce the uncertainty of this potential. For each CASPT2(9e7o)/cc-pVTZ optimized geometry, singlepoint calculations were performed on the quartet spin state using CASPT2, MRCI+Q, and UCCSD(T)-F12. The final doublet energy was obtained from the 4 F12 energies by subtracting the multireference quartet-doublet splitting:

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Table 1: Multireference results for reaction CH3 C(OO)CH2 −−−→ CH3 C(O)CH2 + O method CASPT2(7e6o) (3_state averaging) CCSD(T)-F12a CCSD(T)4 -F12a + CASPT2(7e6o)4−2

barrier height relative to excited state - ground state CH3 C(O)CH2 + O (kcal/mol) (kcal/mol) 1.54 1.81 2.25 0.618

Table 2: Multireference results for reactionCH3 CHCHOO −−−→ CH3 CHCHO+O method CASPT2(7e6o) (3_state averaging) CCSD(T)-F12a CCSD(T)4 -F12a + CASPT2(7e6o)4−2

3.1.4

barrier height relative to excited state - ground state CH3 CHCHO + O (kcal/mol) (kcal/mol) 1.29 1.56 2.04 0.33

TS9: CH3 C(OOH)CH −−−→ CH3 C(−O)CH + OH and TS31: CH3 CCHOOH −−−→ CH3 CCHO + OH

These two bond fission reactions require multireference methods, owing to the two-fold spatial degeneracy of the products. As shown in the vinyl + O2 reaction system, the similar reaction, CHCHOOH −−→ CHCHO + OH, has a well-defined saddle point, and considering computational cost, variational TST rather than variable reaction coordinate TST was used to evaluate this reaction channel. The minimum energy path (using CH3 C(OOH)CH as an example) was determined using CASPT2 method with an active space of 7e6o, which includes 2 orbitals of the C-O π, π∗ orbitals and the two radical electrons on C atom of CH3 C(−O)CH, and the lone pair and radical orbital in OH. The energy potential was explored by fixing the distance between the O-O atom of each products from 1.7 angstrom to 2.4 angstrom with CASPT2(7e6o)/ccpVTZ averaged over two states. A first-order saddle point was confirmed at r = 2.03 Å for CH3 C(OOH)CH with the barrier height of -0.98 kcal/mol relative to CH3 C(−O)CH + OH, 15



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and r = 2.08 Å for CH3 CCHOOH with the barrier height of -0.13 kcal/mol relative to CH3 CCHO + OH. 3.1.5

TS13: c-CH3 (COO)CH2 −−−→ c-(CH2 OC)CH3 O and TS34: c-(CHOO)CHCH3 −−−→ c-CH3 (CHOCH)O

The isomerization from c-CH3 (COO)CH2 to c-(CH2 O)CH3 O involves a tight transition state. As documented in analogous C2 H3 + O2 system, 20,51 the presence of a low-lying excited state induces strong multi-reference effects. The two saddle points were optimized using CASPT2(9e8o)/cc-pVTZ, which includes the 2 C-O σ, σ∗ orbitals, the O-O σ, σ∗, the radical orbital of the C and the lone pair electrons on the transferring O atom. In order to maintain a consistent active space for the reactant, transition state, and product, the relative single-point energies were computed using an active space of 13e11o, which included the CC σ, σ∗, contributing to the ring of product, and the lone pair of the other oxygen. The barrier height for the analogous reaction in the CH3 CHCH + O2 system, c-(CHOO)CHCH3 to c-CH3 (CHOCH)O, was calculated based on the same schema. All the barrier heights were calculated relative to the reactant. Doublet/quartet splitting with different coupled cluster method were implemented as well. The results are listed in the Table 3 below. The RRKM/ME calculations used the CASPT2(13e11o)/cc-pV∞Z results (second row). We estimate the 2σ of uncertainty of these values as ± 1.5 kcal/mol.

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Table 3: Barrier height for three-member-ring isomorization reaction method CASPT2(9e8o)/cc-pV∞Z CASPT2(13e11o)/cc-pV∞Z MRCI+Q(9e8o)/cc-pVTZ CCSD(T)/cc-pVTZ CCSD(T)-F12a/cc-pVTZ-F12 CCSD(T)4 - CASPT2(9e8o)4−2 CCSD(T)4 - CASPT2(13e11o)4−2 CCSD(T)4 - MRCI+Q(9e8o)4−2 CCSD(T)-F12a4 - CASPT2(9e8o)4−2 CCSD(T)-F12a4 - CASPT2(13e11o)4−2 CCSD(T)-F12a4 - MRCI+Q(9e8o)4−2

3.2 3.2.1

c-CH3 (COO)CH2 barrier height(kcal/mol) 17.09 16.86 18.68 18.26 17.89 17.30 19.22 17.11 18.11 20.03 17.92

c-(CHOO)CHCH3 barrier height(kcal/mol) 15.69 15.11 17.56 15.93 14.95 17.17 16.82 17.25 18.15 17.80 18.23

RRKM/ME Total rate constant

The total capture rate of the two reaction systems are shown in the Figure 6. For each methyl-vinyl + O2 reaction, the potential energy computed with the VaReCoF procedure was computed using CASPT2(9e,7o)/cc-pVTZ, and several different 1D corrections were applied. The dashed red line includes the correction from CASPT2(9e,7o)/cc-PVTZ geometry relaxation, the CAPST2(13e,11o) active space expansion, and the cc-pVTZ and cc-pVQZ basis set extrapolation. The dashed blue line is for the MRCI + Q results, except that the active space expansion is limited to MRCI+Q(11e,9o). The solid lines are the corespondent results for each method by implementing the doublet/quartet splitting method referred as Eq (2). With the implementation of this method, the percent deviation between the two multireference method reduced to ∼30%. In the vinyl + O2 system, based on the same calculation strategy, the capture rate shows an excellent agreement with the available experiment data (agreeing to within 25%); similar accuracy is expected for the present work, though there are no data against which this claim can be validated.

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with the other channels for CH3 CHCH + O2 . This effect can be explained by subtle changes barrier heights. One key difference between the C2 H3 + O2 system and the present work concerns the possibility of chain branching at higher temperatures. For the vinyl system, the CH2 CHO+O pathway becomes the dominant product channel above 1400 K, and the system is chain branching. For the methyl-vinyl system, in contrast, this behavior is not observed. Instead, the CH3 CO + CH2 O (HCO + CH3 CHO) product channel remains the dominant bimolecular pathway for all temperatures of kinetic relevance. This surprising change in behavior can be explained by consideration of the two key transition states that govern the competition between CH3 CO + CH2 O (HCO + CH3 CHO) and CH3 C(−O)CH2 + O (CH3 CHCHO + O). When an H-atom on the radical carbon in C2 H3 is replaced with a methyl group, the kinetic bottleneck for the CH3 CO + CH2 O pathway, TS13, decreases by -2.6 kcal/mol, whereas the kinetic bottleneck for the CH3 C(−O)CH2 + O pathway, TS2, actually increases by 1.1 kcal/mol. Consequently, the two pathways that were competitive for vinyl + O2 are no longer competitive for methyl-vinyl + O2 . Similar results are observed for the other methyl-vinyl. The comparative barrier heights for these competing bottlenecks are summarized in Table 4. Table 4: The barrier height of two key TS comparison reaction C2 H3 + O2 CH3 CCH2 + O2 CH3 CHCH + O2

relative barrier heigher for 3-member ring isomerization (kcal/mol) 27.3 24.7 23.8

21


relative barrier heigher for O-O fission (kcal/mol) 35.3 36.4 34.6



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new rate coefficients effectively reduce the reactivity of the mixture (slower flame speeds, longer ignition delays), with a reduction in ignition delay on the order of 10 to 20 percent – consistent with the sensitivity analysis of Burke et al. 9 3.3.3

Sensitivity Analysis

The original analyses in Ref. 5,9 performed a brute-force sensitivity analysis for the ignition delay, and the authors found that this reaction was among the more important reactions at 950 K and 10 atm. At first, this sensitivity is difficult to see in Figures 13 and 14, and the present work suggests that the ignition delay and the flame speed is less sensitive than expected. Ultimately, this discrepancy results from the initial estimates that were used in Ref. 9 for the reactions. In the original manuscript, the rate constants for the chain propagating (R1b) and chain branching (R1a) reactions were quite close in magnitude (e.g. within 50% at 900 K.). Consequently, a small decrease in one rate constant for one channel will automatically favor the other channel. However, the present work suggests that the chain propagating and chain branching pathways are not at all competitive. As illustrated in Figures 9 and 10, the chain propagating pathway is an order of magnitude larger at the conditions of interest.

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is to the chain propagating pathway (blue), but because the computed rate constant is somewhat smaller than the original estimate, the sensitivity is modestly reduced.

3.4

Conclusions

We present the first detailed electronic potential energy surface and kinetic study for the methyl-vinyl + O2 reactions. The CH3 CCH2 + O2 and CH3 CHCH + O2 potential energy surfaces show many similarities to CH2 CH + O2 , albeit with more product channels. The critical difference between vinyl oxidation and methyl-vinyl oxidation is that the latter reaction does not become chain branching at higher temperature. The methyl substitution subtly alters a few key barriers that render the chain branching pathway, methyl-vinoxy + O, a minor channel. The new temperature- and pressure-dependent rate coefficients were implemented in a detailed mechanism taken from the literature.

Acknowledgement The authors gratefully acknowledge support from Brown University, and would like to thank Prof. Curran for helpful discussions on this subject.

Supporting Information Available Cartesian coordinates are provided for all the stationary points on the potential energy surface. The temperature and pressure dependent rate coefficients are provided in a CHEMKIN compatible PLOG format. • Filename: ch3c_oo_ch2_geom.txt, ch3chchoo_geom.txt • Filename: chem.cti • Filename: energy_tables.pdf 28


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This material is available free of charge via the Internet at http://pubs.acs.org/.

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A Theoretical and Computational Analysis of the Methyl-Vinyl + O2

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