Thermochemistry, Reaction Paths, and Kinetics on the tert-Isooctane

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Thermochemistry, Reaction Paths and Kinetics on the tert-Isooctane Radical Reaction with O 2

Suarwee yui Snitsiriwat, and Joseph William Bozzelli J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp502702f • Publication Date (Web): 03 Jun 2014 Downloaded from http://pubs.acs.org on June 8, 2014

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The Journal of Physical Chemistry

Thermochemistry, Reaction Paths and Kinetics on the tert-Isooctane Radical Reaction with O2 Suarwee Snitsiriwat, and Joseph W. Bozzelli*. Department of Chemistry and Environmental Science, New Jersey Institute of Technology University Heights, Newark, NJ 07102 USA [email protected] Abstract Thermochemical properties of tert-isooctane hydroperoxide and its radicals are determined by computational chemistry. Enthalpies are determined using isodesmic reactions with B3LYP density function and CBS QB3 methods. Application of group additivity with comparison to calculated values is illustrated. Entropy and heat capacities are determined using geometric parameters and frequencies from the B3LYP/6-31G(d,p) calculations for the lowest energy conformer. Internal rotor potentials are determined for the tert-isooctane hydroperoxide and its radicals in order to identify isomer energies. Recommended values derived from the most stable conformers of tert-isooctane hydroperoxide of are 77.85 ± 0.44 kcal mol-1. Isooctane is a highly branched molecule and its structure has a significant effect on its thermochemistry and reaction barriers. Intramolecular interactions are shown to have a significant effect on the enthalpy of isooctane parent and its radicals on peroxy/peroxide systems, the R• + O2 well depths and unimolecular reaction barriers. Bond dissociation energies; well depths, for tert-isooctane hydroperoxide R• + O2 is 33.5 kcal mol-1 compared to values of ~ 38 to 40 kcal mol-1 for the smaller tertiarybutyl-O2 R• + O2. Transition states and kinetic parameters for intramolecular hydrogen atom transfer and molecular elimination channels are characterized to evaluate reaction paths and kinetics. Kinetic parameters are determined versus pressure and temperature for the chemical activated formation and unimolecular dissociation of the peroxide adducts. Multi-frequency quantum RRK (QRRK) analysis is used for k(E) with Master Equation analysis for fall off. The major reaction paths at 1000 K, are formation of isooctane plus HO2 followed by cyclic ether plus OH. Stabilization tert-isooctane hydroperoxy radical becomes important at lower temperatures. Keywords Oxidation, Isooctane hydroperoxide, Alkyl peroxy radical, Group additivity, Enthalpy of formation. Introduction

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Isooctane (2,2,4-trimethylpentane, neopentylpropane) is a component of Primary Reference Fuel1-3 and elementary mechanisms for its oxidation have been studied extensively4-11, although a detailed analysis of its thermochemistry and oxidation kinetics by high-level quantum chemical methods has been limited by its complex structure and large size. Reduced reactivity of isooctane at low-temperature and its resistance to ignition, as opposed to linear alkanes, are generally attributed to its high degree of branching. Current kinetic models are mainly based on empirical rules, bond enthalpies and generic rate parameters, yet branched semi-rigid structural features of isooctane introduce specific reaction channels that are either irrelevant or non-feasible in smaller model systems. This research, to the best of our knowledge, is the first fundamentally based study of relevant pathways on the potential energy surfaces of tert-isooctane radicals + O2 using DFT and higher composite level calculations. Isooctane is a highly branched molecule and its structure may have a significant affect on its thermochemistry and reaction barriers. A previous study12 on isooctane parent molecule and its radicals from loss of hydrogen atoms shows that carbon-hydrogen bond energies in isooctane were weaker than the conventional primary, secondary and tertiary C—H bonds by ~1-2 kcal mol-1. In this study, standard enthalpy (∆fHo298) and dissociation bond enthalpies are reported for the species resulting from reactions in the tert-isooctane radicals + O2 system. Transition state structures and intermediates that result from the isomerization and reactions of the radical are calculated using Density Functional and higher level composite ab initio based calculations. Kinetics parameters are reported for association reactions of tertisooctane radicals with molecular oxygen to form R-O2* chemically activated adducts from variational transition state theory. Computational Methods The relative stabilities of tert-isooctane hydroperoxide, bond dissociation energies and the heats of formation of its radicals and molecules have been calculated using B3LYP hybrid density functional theory in conjunction with the 6-31G(d,p) basis set13,14, as well the complete basis set-QB3 composite method Higher level ab initio and DFT-based composite methods G3MP2B315, 16 and CBS-QB317 are utilized in work reaction calculations which are more reliable in predicting accurate energies as shown in our previous studies12, 18-20 G3MP2B3 is a modified version of the G3MP221 method where the geometries and zero-point vibration energies are from B3LYP/6-31G(d) calculations. CBS-QB3 uses the B3LYP/6311G(2d,d,p) level to calculate geometries and frequencies followed by several single point energy calculations at the MP2, MP4SDQ, and CCSD(T) levels. The final energies are determined with a CBS


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extrapolation. CBS-QB3 is considered a complete basis set method that is practical for the molecules and radicals in this study with an addition of G3MP2B3 method for transition states. All calculations were performed using the Gaussian 03 program suite22. Standard enthalpy values are determined with both the B3LYP density functional theory and CBS-QB3 method where the B3 method has lower computational costs and plausible application to larger molecules when using isodesmic work reactions. The B3LYP is thought to be one of the most reliable DFT methods available23 and has been shown by Curtiss et. al.24 to have the smallest average absolute deviation, 3.11 kcal mol-1, of the seven DFT methods studied using the G2 test set of molecules. Curtiss et al., and Ochterski co-workers reported mean absolute deviations of 1.1 kcal mol-1for CBS-Q methods by comparing the energies of 125 computationally reactions to their corresponding experimental values.25-28 To more accurately evaluate the heats of formation (∆fHo298) of the molecule systems, a variety of homodesmic and isodesmic work reactions were used, where the bonding environments are similar in products and reagents. An isodesmic reaction is a hypothetical reaction where the number and type of bonds is conserved on each side of the work reaction; a homodesmic reaction conserves number and type of bonds, but also conserves hybridization29 ∆rxnHo298 is calculated and known ∆fHo298 values of the reference molecules are used with the calculated ∆rxnHo298 to determine the standard enthalpy. The similar structure components on both sides of the work reaction provides a cancellation of systematic errors in ∆fHo298 values by using the calculated ∆rxnHo298 and a thus provides increased accuracy.30 This cancellation can be observed in the good relative accuracy of the B3 method calculation relative to the higher level CBS-QB3 data provided below. Results and Discussion The optimized geometries at the CBS-QB3 composite level of theory, viz., B3LYP/6-311(2d,d,p) calculations, for the target molecules and corresponding abbreviated nomenclatures are presented in Figure 1. Optimized geometry coordinates, vibration frequencies, and moments of inertia for all structures are available in the supplementary data. 7 CH3 1 H3C

2

C CH3 8

H2 C 3

1 2 OOH 4 CH C 5 3 CH3 6

Scheme 1. Definition of skeletal atom in tert-isooctane hydroperoxide and its radicals.



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The lowest configuration of tert-isooctane hydroperoxide; 2,4,4-trimethylpentan-2-yl hydroperoxide (C3CCCQC2) has two methyls on the tertiary carbon (C4) near eclipsed to two methyl on the quarternary (C2) and hydro peroxide group eclipsed to the third methyl. The position of the hydroperoxide group for the lowest energy conformer is when the oxygen (O1) of the hydroperoxide is gauche between secondary carbon (C3) and one methyl on the tertiary carbon (C5 or C6).

C3CCCQC2 (CH3)3C-CH2-C(OOH)(CH3)2

C3CCCQ•C2 (CH3)3C-CH2-C(OO•)(CH3)2

C3CCCQC2• (CH3)3C-CH2-C(OOH)(CH3)(C•H2)

C3•CCCQC2 (CH3)2(C•H2)C-CH2-C(OOH)(CH3)2

C3CC•CQC2 (CH3)3C-C•H-C(OOH)(CH3)2

Figure 1. Geometry of lowest energy conformer of tert-isooctane hydroperoxide and its radicals. Internal Rotation Potentials Energy profiles for internal rotations about the C-C, C-OO and CO-OH bonds in tert-isooctane hydroperoxide and its radicals were calculated to determine lowest energy configuration and energies of the rotational conformers. The total energies as a function of the corresponding dihedral angles were computed at the B3LYP/6-31G(d) level of theory by scanning the torsion angles between 0O and 360O in steps of 15O, while all remaining coordinates were fully optimized. All potentials were re-scanned when a lower energy conformer, relative to the initial low energy conformer was found. The total energy of the corresponding most stable molecular conformer was arbitrarily set to zero and used as a reference point to plot the potential barriers. The resulting potential energy barriers for internal rotations in the tertisooctane hydroperoxide is shown in Figure 2. Torsional potentials in the tert-isooctane hydroperoxy radicals are available in the supplementary data. The calculated rotational barriers of methyl groups in tert-isooctane hydroperoxide show three-fold symmetry with barriers of 3.0 kcal mol-1; these are similar to the methyl rotor potentials in n-


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hydrocarbons. Rotational barriers of butyl group (C3C—CCQC2) exhibit three-fold symmetry with barriers of 4.1 kcal mol-1. The C3CC—CQC2 rotor has asymmetry three-fold potential barriers at 5.8 kcal mol-1. The maximum of the RO—OH rotor potential; 7.0 kcal mol-1 barrier, is when the hydrogen atom on the hydroperoxide eclipse with tertiary carbon (C4)

12 Relative energy (Kcal/mol)

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10 1 c3ccc(--ooh)c2

8

2 c3cc--c(ooh)c2

6

3 c3c--cc(ooh)c2

4

4 c3ccc(o--oh)c2

2 0 0

60

120 180 240 Dihedral angle

300

360

Figure 2. Potential energy profiles for internal rotations in tert-isooctane hydroperoxide Enthalpies of Formation and Bond Dissociation Energies The methods of isodesmic or homodesmic work reactions rely on the similarity of bonding environment in the reactants and products, which leads to the cancellation of systematic errors in calculation of reaction enthalpy(∆rxnHo298) in the ab initio and density functional theory calculations. The zero point energies are scaled by 0.9806 for B3LYP/6-31G(d,p) calculations as recommended by Scott et al.31 The standard enthalpies of formation at 298.15 K for reference species used in these reactions are summarized in Table 1. The enthalpies of formation of the target molecules obtained from the use of the reaction schemes are shown in Table 2. Bond enthalpies are derived from ∆rHº298 of parent molecules and its radicals corresponding to the loss of hydrogen atoms. The standard enthalpy of formation at 298.15 K of hydrogen atom as 52.10 ± 0.003 kcal mol-1 were used 32. The resulted bond dissociation enthalpies computed from isodesmic enthalpies of formation are in Table 2. The bond energies are compared against primary, secondary and tertiary bonds in normal alkanes33. C—H bond dissociation enthalpy (BDE) for secondary carbon (C3) at 98.1 kcal mol-1 is similar to that in secondary carbon on a normal alkane (98.6 kcal mol-1); and the primary C—H bonds energies for primary methyl radicals on the tert-butyl group ( C1, C7 and C8) are at 100.2 kcal mol-1 are ~ 1 kcal mol-1 lower



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than that in primary C—H bonds on normal alkanes (101.1 kcal mol-1). The C—H BDE of the primary methyl carbons on the isopropyl group adjacent to the peroxide (C5 and C6 positions) is 101.4 kcal mol-1, similar to primary C—H bonds energies on normal alkanes. Bond energy for ROO—H in tert-isooctane hydroperoxide is 84.2 kcal mol-1 as computed at the CBSQB3 level, ~1 kcal mol-1 lower than ROO—H bond on tert-butyl hydroperoxide (85 ± 2 kcal mol-1)33. The peroxy radical center being located in the middle of molecule has access to all other H-atoms to undergo intramolecular H atom transfer (5 – 7 member rings) to form hydroperoxide-alkyl radicals. These values are important for the determination of the kinetic properties, since small changes in the activation energies will cause larger changes in the rate constants especially at the lower temperatures. Table 1. Standard enthalpies of formation at 298 K for reference species. ∆fHo298 for reference molecule Species

kcal mol-1

Species

kcal mol-1

C2H6

-20.04 ± 0.07 70

(CH3)2(C•H2)CH

17.00 ± 0.50 71

C2H5

28.40 ± 0.50 71

(CH3)3COOH

-57.24 ± 0.22 53

C3H8

-24.82 ± 0.14 72

(CH3)3COO•

-24.67 ± 0.19 53

CH3CH2C•H2

23.90 ± 0.50 71

CH3CH2OO•

-6.00 62

CH3C•HCH3

21.50 ± 0.40 73

CH3CH2OOH

-39.50 ± 0.70 56

CH3CH2CH2CH3

-30.03 ± 0.16 70

(CH3)2CHOOH

-47.86 ± 0.22 53

CH3CH2C•HCH3

16.00 ± 0.50 71

(CH3)2CHOO•

-14.80 ± 0.22 53

(CH3)3CCH2CH3

-44.35 ± 0.23 72

(CH3)3CCH2CH2CH3

-49.29 ± 0.32 72

(CH3)3CH

-32.07 ± 0.15 70

(CH3)3CCH2CH(CH3)2

-53.57 ± 0.32 72


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Table 2. Evaluated enthalpies of formation and bond energies at 298 K for tert-isooctane hydroperoxide and its radicals.

Work Reactions

C3CCCQC2 C3CCCQC2 C3CCCQC2

+ + +

C3CCCQ•C2 + C3CCCQ•C2 + C3CCCQ•C2 +

C3•CCCQC2 + C3•CCCQC2 + C3•CCCQC2 +

C3CC•CQC2 + C3CC•CQC2 + C3CC•CQC2 +

C3CCCQC2• + C3CCCQC2• + C3CCCQC2• +

C3CCCQC2 C2H6 --> (CH3)3COOH + (CH3)3CCH2CH3 C3H8 --> (CH3)3COOH + (CH3)3CCH2CH2CH3 (CH3)3CH --> (CH3)3COOH + (CH3)3CCH2CH(CH3)2 Average C3CCCQ•C2 CH3CH2OOH --> C3CCCQC2 + CH3CH2OO• (CH3)2CHOOH --> C3CCCQC2 + (CH3)2CHOO• C3CCCQC2 (CH3)3COOH --> + (CH3)3COO• Average (CH3)3CCH2C(OO---H)(CH3)2 Bond dissociation energy C3•CCCQC2 C2H6 --> C3CCCQC2 + C2H5 C3H8 --> C3CCCQC2 + CH3CH2C•H2 (CH3)3CH --> C3CCCQC2 + (CH3)2(C•H2)CH Average (CH3)2(H---CH2)CCH2C(OOH)(CH3)2 Bond dissociation energy C3CC•CQC2 C2H6 --> C3CCCQC2 + C2H5 C3H8 --> C3CCCQC2 + CH3C•HCH3 CH3CH2CH2CH3 --> C3CCCQC2 + CH3CH2C•HCH3 Average (CH3)3C(HC---H)C(OOH)(CH3)2 Bond dissociation energy C3CCCQC2• C2H6 --> C3CCCQC2 + C2H5 C3CCCQC2 C3H8 --> + CH3CH2C•H2 (CH3)3CH --> C3CCCQC2 + (CH3)2(C•H2)CH Average (CH3)3CCH2C(OOH)(H---CH2)(CH3) Bond dissociation energy


∆fHo298 kcal mol-1 B3LYP/ CBS-QB3 6-31g(d,p) -76.54 -76.91 -77.04 -76.83 ± 0.26

-78.11 -78.09 -77.35 -77.85 ± 0.44

-45.45 -45.77 -45.64 -45.80 -45.37 -45.76 -45.49 ± 0.14 -45.78 ± 0.02 84.2 -30.75 -29.49 -31.15 -29.91 -30.95 -29.82 -30.95 ± 0.20 -29.74 ± 0.22 100.2 -34.45 -32.14 -32.66 -31.48 -33.17 -32.00 -33.43 ± 0.92 -31.87 ± 0.35 98.1 -29.21 -28.30 -29.61 -28.71 -29.41 -28.62 -29.41 ± 0.20 -28.54 ± 0.22 101.4


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Group Additivity Method for Estimation of Thermochemical Properties. Group additivity34, 35 is a straightforward and reasonably accurate calculation method used to estimate thermodynamic properties of hydrocarbons and oxygenated hydrocarbons36; it is particularly useful for application to larger molecules, for use in codes or databases, and for the estimation of thermochemical properties in reaction mechanism generation. Heat of formation at 298 K of tert-isooctane hydroperoxide and its radicals estimated by group additivity after adding interaction groups result in good agreement to DFT and ab initio calculated values. Group additivity contributions for tert-isooctane hydroperoxide include three gauche interaction and two 1,5 interaction34 All tert-isooctane hydroperoxide radicals have three for gauche interaction and one of 1,5 interaction in their low energy form. Heat of formation at 298 K of tert-isooctane hydroperoxide and its radicals are summarized in Table 3. Table 3. Summary of formation enthalpies (∆fHo298)

Species C3CCCQC2 C3CCCQ•C2 C3•CCCQC2 C3CC•CQC2 C3CCCQC2•

B3LYP/6-31g(d,p)

CBS-QB3

-76.83 -45.49 -30.95 -33.43 -29.41

-77.85 -45.78 -29.74 -31.87 -28.54

∆fHo298 kcal mol-1 By Therm (Group additivity) No interaction After adding interaction -83.83 -78.43 3 Gauche and 2 of 1,5 Interaction -49.63 -45.73 3 Gauche and 1 of 1,5 Interaction -34.83 -30.93 3 Gauche and 1 of 1,5 Interaction -37.48 -33.58 3 Gauche and 1 of 1,5 Interaction -32.83 -28.93 3 Gauche and 1 of 1,5 Interaction

Entropy and Heat Capacity Data Entropy and heat capacity contributions as a function of temperature are determined from the calculated structures, moments of inertia, vibration frequencies, symmetry, electron degeneracy, number of optical isomers and the known mass of each molecule. The calculations use standard formulas from statistical mechanics for the contributions of translation, external rotation and vibrations using the “SMCPS” program37 This program utilizes the rigid-rotor-harmonic oscillator approximation from the frequencies along with moments of inertia from the optimized CBS-QB3 structures, viz. B3LYP/6-311G(2d,d,p) level. Contributions from internal rotors using Rotator38, are substituted for contributions from the corresponding internal rotor torsion frequencies. The rotator is a program for the calculation of thermodynamic functions from hindered rotations with arbitrary potentials based on the method developed by Krasnoperov, Lay and Shokhirev38. This technique employs expansion of the hindrance potential in the Fourier series, calculation of the Hamiltonian matrix in the basis of the wave functions of free internal rotation, and subsequent calculation of energy levels by direct diagonalization of the


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Hamiltonian matrix. Entropy and heat capacity calculation were performed using CBS -QB3 determined geometries and harmonic frequencies are summarized in Table 4. Table 4. Ideal gas-phase thermodynamic property vs. temperature

Species

So(298) cal mol-1 K-1

Isooctane Peroxide and its radicals C3CCCQC2 112.44 C3CCCQ•C2 109.43 C3•CCCQC2 107.61 C3CC•CQC2 117.63 C3CCCQC2• 117.39

Cp (cal mol-1 K-1) 300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

54.00 52.29 52.93 54.53 54.26

67.67 65.60 66.45 67.34 67.06

79.37 76.99 77.76 78.21 77.96

89.01 86.35 86.93 87.13 86.89

103.74 100.66 100.78 100.83 100.58

114.59 111.18 110.91 110.96 110.70

131.61 127.63 126.85 126.96 126.73

Transition State Structures Transition states are characterized as having only one negative eigenvalue of Hessian (force constant) matrices. The absence of imaginary frequencies verifies that structures are true minima at the respective levels of theory. Intrinsic reaction coordinate (IRC) calculations were performed at the B3LYP/631G(d,p) level to ensure connectivity of stationary points. The final point geometries at both sides of TS were re-optimized to proper minima. The energy of each transition state structure is calculated from the corresponding reactant plus the energy difference between the TS structure and the reactant (adduct). If the TS is closer in structure to the product, then the energy of the transition state species is calculated from the corresponding product plus the energy difference between TS and product. The Enthalpy of the transition state structures in tert-isooctane radical + O2 reaction system calculated using B3LYP/6-31g (d,p), CBS-QB3 and G3MP2B3 are shown in Table 5. The G3MP2B3 calculation shows good agreement with the CBS-QB3 calculation. The average energy from CBS-QB3 and G3MP2B3 is used in this work. Intramolecular isomerization in peroxy radicals is often the most important step in oxidation of hydrocarbons at lower temperatures. Geometry of lowest energy conformer transition state structures for intramolecular H transfer from ROO• (peroxy radical) to •ROOH (alkyl radical) are determined in this study. These isomerization processes involving peroxy radical abstraction of a hydrogen atom from the secondary carbon C3-position. TS1 is a 5-member ring transition state structure with H abstraction from C3. TS2 is also 5-member ring transition state with an abstraction of H either from the two isopropyl carbons C5 or C6. H abstraction from either C1, C7 or C8 is TS3 with a 7-member ring transition state structure. The lowest energy conformers of transition states for H-Transfer are shown in Figure 3.



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1.42 1.13 1.41 1.23

1.42

1.40 1.20

1.35 1.37

TS1

TS2

TS3

Figure 3. Geometry of lowest energy conformer of the transition state for H-transfer (isomerization) Table 5. Evaluated energy of the transition states at 298 K in tert-isooctane radical + O2 reaction system. Data used in this study are in bold. Energies (kcal mol-1) Reaction

B3LYP/ 6-31g(d,p)

CBSQB3

G3MP2B3

Average CBS-QB3 and G3MP2B3

TS1

C3CCCQ•C2 --> C3CC•CQC2

-16.91

-16.52

-14.70

-15.61

TS2

C3CCCQ•C2 --> C3CCCQC2•

-12.19

-10.90

-9.08

-9.99

TS3

C3CCCQ•C2 --> C3•CCCQC2

-26.74

-25.06

-23.96

-24.51

TS4

C3CCCQ•C2 --> C3CC=CC2 + HO2

-22.94

-19.31

-18.56

-18.93

TS5

C3CCCQ•C2 --> C3CCC(C)=C + HO2

-24.58

-19.96

-19.21

-19.59

Species

Isomerization

Molecular elimination


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Dissociation

TS6

C3CC•CQC2 --> C2C=CC(OOH)C2 + CH3

-3.09

-4.68

-3.17

-3.92

TS7

C3CC•CQC2 --> C3CC=CC2 + HO2

-16.82

-16.07

-13.84

-14.96

TS8

C3CC•CQC2 --> C3COXRC2

-24.71

-22.82

-19.91

-21.37

TS9

C3CCCQC2• --> C3CCj + CC(OOH)=C

1.84

0.22

1.92

1.07

TS10

C3CCCQC2• --> C3CCC(C)=C + HO2

-16.09

-15.25

-13.51

-14.38

TS11

C3CCCQC2• --> C3CCYC2OC

-19.99

-18.52

-15.76

-17.14

TS12

C3•CCCQC2 --> C2C=C + C3jCOOH

-2.36

-4.36

-2.61

-3.48

TS13

C3•CCCQC2 --> C2YC4OC2

-19.65

-17.4

-14.25

-15.82

TS14

C3•CCCQC2 --> C2C(COH)CC(Oj)C2

-11.17

-10.89

-9.27

-10.08



Variational Transition State Theory Analysis Potential energy surfaces for RC—O2 bond dissociation in tert-isooctane hydroperoxide shown in Figure 4. The R• + O2 R-O2 association reaction proceeds without any barrier, and determination of the kinetics of this reaction utilized via variational transition state theory (VTST). The simple dissociation reaction of the oxygen atom, R-OO RO + O is also found to dissociate without a barrier, and this transition state is also treated variationally. Potential energy scans were performed along the barrierless dissociations R–O2 R• + O2 and RO–O RO• + O bond cleavage reactions at 0.1A˚ intervals, and variational transition state kinetics calculated from thermochemical data at the unrestricted B3LYP/6-31G(d,p) level. For each point on the UB3LYP reaction potential energy scans, the complex and reactant energies were multiplied by a scaling factor, that accounted for the ratio of the CBS-QB3 reaction enthalpy to the B3LYP reaction energy in order to obtain more correct dissociation limit energy. Frequency and thermodynamic calculations were performed at the discrete points along the potential energy surface. Thermochemical properties and rate constants as a function of temperature were evaluated at each point along the potential energy surface. The minimum rate constant was located as a function of temperature and position for each reaction, providing the variational rate constant. Rate constants were fit to the three parameter form of the Arrhenius equation to yield the rate parameters A’, n and Ea

-10

energy (kcal/mol)

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-20

-30

-40

-50 1

1.5

2

2.5

3

3.5

4

4.5

5

0

Distance A

Figure 4. Potential energy surface for dissociation of the tert-isooctane hydroperoxide ((CH3)3CCH2C(-OO•)(CH3)2) the R—O2 → R• + O2


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For the tert-isooctane radical + O2 association, the transition state occurs at R—O2 bond length of 3.0 A˚ at 300 K, and decreases to 2.5 A˚ at 2000 K. Fitting the minimum rate constant as a function of temperature to the three parameter Arrhenius equation for the association reaction is A’ = 6.88 x 1022, n = -3.3, Ea = 1.9 kcal mol-1 and A’ = 6.85 x 1022, n = -2.5, Ea = 34.7 kcal mol-1 for dissociation reaction. (CH3)3CCH2C•(CH3)2 + O2 (CH3)3CCH2C(OO•)(CH3)2 k association = 6.88 x 1022 T -3.3 exp(1005/T) cm3 mol-1 s-1 k dissociation = 6.85 x 1022 T -2.5 exp(-17456/T) s-1 There are several studies on rate constants for the association reaction of R + O2. Lenhardt et al.39 investigated reaction of tert-butyl radical with O2 using tubular flow reactor and reported rate constant as 1.41 x 1013 cm3 mol-1 s-1 at room-temperature. This same reaction was also studied using muon spin relaxation at a pressure of 1.5 bar by Dilger et al. 40. They reported rate constant at room-temperature as 1.07 x 1013 cm3 mol-1 s-1. Rate constants for the association reaction of tert-R• + O2 at 298 K is investigated using computational study by Villano et al.41 and Miyoshi 42 reported as 1.41 x 1013 cm3 mol1

s-1 and 1.26 x 1013 cm3 mol-1 s-1, respectively. Rate constant of tert-isooctane radical + O2 at 298 K in

this study is 1.54 x 1013 cm3 mol-1 s-1 which is slightly higher than that of tert-R• + O2 Similar analysis was performed for the C3CCC(OO•)C2 C3CCC(O•)C2 + O (R—O2 → RO• + O) dissociation reaction. The location of the variational transition state is at an RO—O bond length of 2.8 A˚ at 300K, tightening to the 2.3 A˚ at 2000K. Fitting the variational rate constants to a three-parameter rate law, we obtain k (s-1) = 1.01 x 1013 T 0.30 exp(-30011/T) (A’ = 1.01 x 1013 n = 0.30 Ea = 59.6 kcal mol-1) for dissociation reaction. Kinetics The potential energy surface and thermochemical properties are calculated with forward and reverse rate constants (high-pressure limit) for each elementary reaction step determined. Multifrequency quantum Rice Ramsperger- Kassel (QRRK) analysis is used for k(E)43-46 with master equation analysis47-49 is used for falloff. The QRRK analysis is described by Chang et al.50 It is shown to yield reasonable results and provides a framework by which the effects of temperature and pressure can be evaluated in complex reaction systems. The QRRK code utilizes a reduced set of three vibration frequencies for densities of states which accurately reproduce the molecules’(adduct) heat capacity51-52 and include one external rotation in calculation in the density states. Comparisons of ratios of these ρ(E)/Q (partition function Q)



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Page 14 of 37

with direct count ρ(E)/Q are shown to be in good agreement52. Nonlinear Arrhenius effects resulting from changes in the thermochemical properties of the respective transition state relative to the adduct with temperature are incorporated using a two parameter Arrhenius pre-exponential factor (A, n) in ATn. The master equation analysis uses an exponential-down model for the energy transfer function with (∆E°down) 900 cal mol-1 for N2 as the third body. Rate constants, k(E), were evaluated using energy 1.0 kcal mol-1 increments up to 70 kcal mol-1 above the highest barrier. Lennard-Jones parameters, σ (Å), and ε/κ (K) are obtained from tabulations and from an estimation method based on molar volumes and compressibility; σ = 6.3 Å and ε/kb = 584 K. Table 6 presents high-pressure-limit elementary rate parameters used as input data to the QRRK calculations and the results versus pressure and temperature are presented in Appendix data. Table 6. High-pressure-limit elementary rate parameter for reactions in the tert-isooctane radical + O2

Reaction C3CCCJC2 + O2 C3CCCQJC2 C3CCCQJC2 C3CCCQJC2 C3CCCQJC2 C3CCCQJC2 C3CCCQJC2 C3CCCQJC2 C3CCJCQC2 C3CCJCQC2 C3CCJCQC2 C3CCJCQC2 C3CCCQC2J C3CCCQC2J C3CCCQC2J C3CCCQC2J C3JCCCQC2 C3JCCCQC2 C3JCCCQC2 C3JCCCQC2

=> => => => => => => => => => => => => => => => => => => =>

C3CCCQJC2 C3CCCJC2 + O2 C3CCJCQC2 C3CCCQC2J C3JCCCQC2 C3CCDCC2 + HO2 C3CCC2DC + HO2 C3CCCOJC2 + O C3CCCQJC2 C3CCDCC2 + HO2 C2CDCCQC2 + CH3 C3COXRC2 + OH C3CCCQJC2 C3CCC2DC + HO2 C3CCJ + CCQDC C3CCYC2OC + OH C3CCCQJC2 C2CDC + C3JCQ C2YC4OC2 + OH C2C(COH)CC(OJ)C2

k = A(T/K)n exp(-Ea/RT) A

n

Ea (kcal mol-1)

6.88 × 1022 6.85 × 1022 7.79 × 1010 6.45 × 1010 2.76 × 109 3.99 × 1011 1.34 × 1012 1.01 × 1013 2.95 × 109 7.14 × 1012 4.63 × 1010 3.16 × 1011 1.19 × 109 4.02 × 106 5.07 × 105 2.82 × 105 9.06 × 109 3.98 × 1014 7.39 × 1011 2.58 × 1015

-3.30 -2.48 0.65 0.66 0.83 0.75 0.48 0.30 0.47 -0.13 0.59 0.16 0.61 1.55 2.10 1.87 0.76 -0.40 0.18 -0.98

2.00 34.66 30.40 35.93 21.20 27.02 26.47 59.57 16.34 17.44 28.05 10.92 18.47 13.19 28.39 10.26 5.05 27.67 14.39 21.17


Page 15 of 37

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Comparison of the High-Pressure Rate Constants Obtained in this Study with Literature Values A comparison was carried out between the rate constants obtained in this study and generic rate constants for model (smaller) systems in the literature 40, 53, 71, 72 The calculated rate constants in this study tend to be slightly higher than values in the literature; we interpret this as due, in part, to lower BDE’s resulting in lower barriers. The lower BDEs are probably from release of strain that is a result from the branching in this isooctane hydroperoxide—peroxy radical system. Comparison of the high-pressure rate constants obtained in this study with literature values are shown Table 7. (and below) Table 7. Comparison of the High-Pressure Rate Constants Obtained in this Study with Literature Values p = primary radical site, s = secondary radical site and t = tertiary radical site A (s-1 or cm3/mole-s)

n

Ea (kcal mol−1)

Reference

Association reaction of R• + O2 C3CCC•C2 + O2 --> C3CCCQ•C2 R• (t) + O2 --> RO2 R• (t) + O2 --> RO2 C3C• + O2 --> C3COO•

6.88 × 1022 9.75× 1011 4.20 × 1015 2.59 × 1015

-3.3 0.3 -1.0 -1.0

1.9 -0.4 0.0 0.0

This work Miyoshi.42 Villano et al.41 Dilger 40

Concerted Elimination Reaction C3CCCOO•C2 --> C3CCC(C)=C + HO2• RO2• →olefin (tp) + HO2• CCC(C2)OO• --> CCC(C)=C + HO2•

1.34 × 1012 1.26 × 1013 4.08 × 109

0.5 0.0 0.9

26.5 31.1 29.5

This work Miyoshi.42 Villano et al.41

C3CCCOO•C2 --> C3CC=CC2 + HO2• RO2• →olefin (ts) + HO2• CCC(C2)OO• --> C2C=CC + HO2•

3.99 × 1011 1.77 × 1013 5.62 × 1010

0.8 0.0 0.6

27.0 30.4 29.6

This work Miyoshi.42 Villano et al.41

RO2 Isomerization Reaction C3CCC(OO•)C2 --> C3CC•C(OOH)C2 1,4ts H-Shift 1,4s rate rule 1,4s H-Shift

7.79 × 1010 1.44 × 1012 4.78 × 107 4.10 × 1011

0.6 0.0 1.4 0.7

30.4 28.8 28.6 30.1

This work Miyoshi.42 Villano et al.41 Sumathi et al.58

C3CCC(OO•)C2 --> C3CCC(OOH)C2• 1,4tp H-Shift 1,4p rate rule 1,4p H-Shift

6.45 × 1010 1.80 × 1012 2.17 × 106 2.00 × 1012

0.7 0.0 1.7 1.2

35.9 33.4 32.0 33.5


C3CCC(OO•)C2 --> C3•CCC(OOH)C2 1,6tp H-Shift 1,6p rate rule 1,6p H-Shift

2.76 × 109 5.04 × 1010 3.42 × 105 1.30 × 1010

0.8 0.0 1.5 1.5

21.2 22.7 20.2 20.0


Reactions



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Cyclic Formation C3•CCC(OOH)C2 --> C2YC4OC2 + OH C3CCCQC2• --> C3CCYC2OC + OH Cyclic ether formation (pt)

7.39 × 1011 2.82 × 105 1.70 × 1013

0.2 1.9 0.0

14.4 10.3 12.8

This work This work Miyoshi.42

C3CC•CQC2 --> C3COXRC2 + OH Cyclic ether formation (st)

3.16 × 1011 4.16 × 1012

0.2 0.0

10.9 11.7

This work Miyoshi.42

Tertiary Isooctane Radical + O2 Reaction System Figure 5. shows the potential energy diagram for the C3CCC•C2 + O2; the enthalpy values for reactants, intermediates and products are from the calculations at the CBS-QB3 level. Energies of TS structures are from the average between CBS-QB3 and G3B3MP2 calculation. C 3CC C(Oj)C2+O TS9

14.3

1 .1

TS12

-3 .5

TS6 -3 .9

C3C Cj + CC (OOH)=C

TS2

C2C=C + C3jCOOH

-6.9 -10 .0

TS14

-1 0.1

-14.7

C3C CCjC2+O2

-11.0 TS11

C2C =C C(OOH)C2+C H3

-12.3

-1 5.6 -1 5.0

TS1

TS8 -21 .4

-1 4.4

-1 7 .1

TS7

TS10 TS13

TS5

-1 8 .9

-1 5 .8

-1 9 .6

TS4 C 3CCC (C )=C +HO2 C 3CC=CC 2+HO2 -26.7

-2 4 .5

-24.7 TS3

-28.5 C3C CC(OOH)C 2j

-31.9

C3jCC C(OOH)C2 -29.7

C3C CjC (OOH)C2 (C3CCYC2O C) O C 3C-C-C -C 2 + OH -45.8

-45.8

C 3C CC (OOj)C 2

(C2Y C4OC2) O

-50.1

C3C-C -C -C2 O

+ OH

C 3C -C -C-C2 + OH -77

(C3COX RC2)

C OH Oj

C 2C-C-C -C 2

Figure 5. Potential energy diagram for C3CCC•C2 + O2 → Products reaction system Bond dissociation energies; well depths, for tert-RO2 R• + O2 have been reported using computational study by Villano et al.41 as 38.7 kcal mol-1, by Simmie et al.53 as 37.8 kcal mol-1, by Zhu et al.54 as 37.5 kcal mol-1 and by Miyoshi42 as 40.0 kcal mol-1. Reported experimental data for well depth of tert-butyl


-67.5

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RO2 R + O2 by Knyzev et al.55 is 36.5 kcal mol-1, by Blanksby et al.56 is 37.5 kcal mol-1, and Shuman et al.57 is 35.8 kcal mol-1. The well depth of C3CCC•C2 + O2 reported by this study is 33.5 kcal mol-1 which is low compared to the literature data. The decrease in well depth is a result of the 93.1 kcal mol-1 tertiary C—H bond energy on isooctane relative to the model compounds of the above studies, where the bond energies are ~ 96.5 kcal mol-1.33 Addition of oxygen to the tertiary isooctane radical forms a chemically activated tertiary isooctane peroxy radical with a well depth of 33.5 kcal mol-1. This study shows 7 possible reactions for this activated adduct at or below the entrance channel, these include: •

Reverse reaction back to tert-isooctane radical + O2 (non reaction)

•

RO—O bond cleavage (Unimolecular dissociation), which is a chain branching channel.

•

The intramolecular hydrogen transfer from the two different primary and the secondary carbon sites to the peroxy radical forming primary and secondary hydroperoxide isooctyl radicals (TS1, TS2 and TS3).

•

HO2 molecular elimination (TS4 and TS5) from tertiary isooctane peroxy radical to form isooctene (+ HO2)

•

Beta scission and elimination reactions from hydroperoxide isooctyl radicals, TS7 and TS10 to form isooctene (+ HO2); TS6, TS9 and TS12 to form an alkyl radical

•

Three cyclic ether ring formations plus OH radical (TS8, TS11 and TS13)

•

OH-transfer from the hydroperoxide to the alkyl radicals reaction (TS14)

Oxygen Atom Dissociation from the tert-Isooctane Hydroperoxide Dissociation of the tert-isooctane peroxy radical adduct to C3CCC(O•)C2 + O is endothermic by 60.1 kcal mol-1 relative to the stabilized C3CCC(OO•)C2 radical; this is 26.6 kcal mol-1 above the entrance chanel. At low temperature, this reaction channel is not significant compare to the other channels; but it has a loose transition state structure and is important under higher temperature thermal and combustion conditions. Intramolecular Hydrogen Transfer Reactions (isomerization) There are generic notations for descriptions on isomerization reactions of alkyl peroxy radicals. In this notation, the first number refers to the peroxy radical site, while the second number refers to the location of the radical site in the product relative to that in the reactant. The “p”, “s” and “t” refer to reacting



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primary, secondary and tertiary sites. For example, CH3CH2OO• C•H2CH2OOH is called 1,4p and CH3CH2CH2OO• CH3C•HCH2OOH is called 1,4s; the 4 signifies the number of central atoms the hydrogen atom transfers over. There are 1,4 and 1,6 H atom transfers to the peroxy radical in this tertiary peroxy isooctane system; TS1 is 1,4S; TS2 is 1,4P and TS3 is 1,6P. Intramolecular H-transfer in smaller peroxy hydrocarbon radicals has been studied and general trends are established 54,58-61 Chan et al.62 studied the H-migration reactions involving a primary and radical adjacent secondary abstraction site in the ethylperoxy through pentylperoxy radicals. Pfaendtner et al.63 looked at 1,5 and 1,6 reactions involving a primary, terminal adjacent secondary, and tertiary abstraction site in methylated and unmethylated alkyl-2-peroxy radicals. Sharma et al.58 reported on a series of 1,3 through 1,7 H-migrations involving primary, terminal adjacent secondary, and tertiary abstraction sites in alkylperoxy and hydroperoxyalkyl radicals. Alexander et al.59 investigated all possible hydrogen migration pathways for the 1-ethyl, 1-propyl, 1-butyl, 1-pentyl, and 1-hexylperoxy radicals. The 1,4-hydrogen migration barrier heights have been calculated for ethylperoxyl by Sheng et al.64 as 36.3 kcal mol-1, by Carstensen et al.65 as 35.9 kcal mol-1, by Miller et al.66 as 36.0 kcal mol-1, and by Sharma et al.58 as 35.9 kcal mol-1. Huynh et al.61 reports 35.8 kcal mol-1 for CH3CH(OO•)CH3 C•H2CH(OOH)CH3. These data agree within 1.0 kcal mol-1 with the value of 35.8 kcal mol-1 calculated here for TS2; C3CCC(OO•)C2 C3CCC(OOH)C2• . We attribute the higher barrier to increased strain for this highly substituted alkane. We note that the primary bond energies on the methyl sites are similar to methyl bond energies on smaller hydrocarbon. This tertiary isooctane peroxy system has two different hydrogen transfer reactions that involve 5membered ring TS (1,4 shift) structures. One is an abstraction of the hydrogen atom from secondary carbon (C3); it has an activation barrier of 30.2 kcal mol-1 and a pre-exponential factor of 2.01 x 1011per hydrogen atom at 298 K. This data is in agreement with 1,4-hydrogen shift in n-propyl peroxy from Huynh et al.56 at 31.2 kcal mol-1 The slightly lower barrier calculated for this secondary isooctane system results from the lower bond energy for the secondary hydrocarbon in this system, 98.1kcal mol-1 versus a normal secondary C—H bond of 98.6 kcal mol-1 . A second 5 member ring path is transfer of a hydrogen atom from either of the primary carbons on the isopropyl group C5 or C6, where the barrier is 35.8 kcal mol-1 (and the pre-exponential factor is 1.07 x 109/H at 298K)


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In previous studies for a 1,4p H-shift, Sharma et al. reported k = 1.19 x 10-13 s-1 for (CH3)3COO• (CH3)2(C•H2)COOH at 298 K while Miyoshi (1,4tp) and Villano et al. (1,4p) reported 5.71 x 10-13 s-1 and 1.33 x 10-13 s-1, respectively. These 1,4p reaction class above can compare to C3CCC(OO•)C2 C3CCC(OOH)C2• reaction in this study for which reports a rate constant at room temperature as 1.15 x 10-14 s-1 Rate constant for C3CCC(OO•)C2 C3CCC(OOH)C2• ; 1,4s H-shift, is calculated in this study as 1.47 x 10-10 s-1. Miyoshi, Sharma et al. and Villano et al. reported rate constant as 1.03 x 10-9 s-1 for 1,4ts, 1.40 x 10-11 s-1 for CH3CH2C(CH3)2OO• CH3C•HC(CH3)2OOH and 1.11 x 10-10 s-1 for 1,4s, respectively. Table 8 presents a comparison of the different classes of rate constants. For the 1,6 H atom transfers Villano et al.41 evaluated rate constants and formed a rate rule for 1,6p hydrogen shift from four 1,6p hydrogen shift reactions as 2.32 x 10-6 s-1 at 298 K and Sharma et al.58 reported 4.38 x 10-6 s-1 from CH3CH2CH2CH2OO• C•H2CH2CH2CH2OOH. Miyoshi42 investigated rate constant for 1,6 tertiary alkylperoxy radical abstracting a primary hydrogen(tp) as 1.15 x 10-6 s-1 at 298 K. The present study reports k = 8.52 x 10-5 s-1 for the C3CCC(OO•)C2 C3•CCC(OOH)C2; 1,6p H-shift. The abstraction of the hydrogen atom from one of the three primary, methyl carbons of the tert-butyl group (C1, C7 and C8) by peroxy radical (TS3) involves a 7-membered ring TS and has a degeneracy of 9. This has the lowest energy barrier of the H-transfer reactions involving any tert-isooctane peroxy radical. The Ea is 21.3 kcal mol-1, which is 10-15 kcal mol-1 lower than the two five member ring H-transfer paths (see below) but the pre-exponential factor is also lower, 2.75 x 108 per hydrogen atom at 298 K. The low pre-exponential is due to the extra internal rotor(s) lost in the TS structure relative to smaller ring TS structures. Comparison of high-pressure-limit rate constants for intramolecular hydrogen transfer reactions to peroxy radicals are shown in Figure 6a for 1,6P H-Shift, Figure 6b for 1,4P H-Shift and Figure 6c for 1,4S HShift. The calculated high-pressure limit rate constants for the 1,4P and 1,4S hydrogen shift in tertisooctane hydroperoxide are in good agreement with rate rules from literature

53, 71, 72

The observed rate

constant for the 1,6P hydrogen shift in tert-isooctane hydroperoxide is higher than rate rules from the literature;53, 71, 72 this may result from relief of strain on a methyl of the tert-butyl resulting in less steric interaction with the isopropyl and peroxy groups. A slight increase in the 1,4s rate constant over that of the literature may result from relief of strain as the secondary carbon move toward sp2 geometry.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6a. Comparison of high-pressure-limit rate constants for isomerization of peroxy radicals; 1,6P Hydrogen shift reactions

Figure 6b. Comparison of high-pressure-limit rate constants for isomerization of peroxy radicals; 1,4P Hydrogen shift reactions

Figure 6c. Comparison of high-pressure-limit rate constants for isomerization of peroxy radicals; 1,4S Hydrogen shift reactions


Page 20 of 37

Page 21 of 37

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Table 8. Comparison of high-pressure-limit rate constants at room-temperature for isomerization of peroxy radicals (Hydrogen shift) reactions in the tert-isooctane radical + O2 (s-1) C3CCQjC2 --> C2CCjCQC2

C3CCQjC2 --> C3CCCQC2j

C3CCQjC2 --> C3jCCCQC2

Sumathi et al.58

1.40 × 10-11

1,4s H-shift

1.19 × 10-13

1,4p H-shift

4.38 × 10-6

1,6p H-shift

Miyoshi.42

1.03 × 10-9

1,4ts H-shift

5.71 × 10-13

1,4tp H-shift

1.15 × 10-6

1,6tp H-shift

Villano et al.41

1.11 × 10-10

1,4s rate rule

1.33 × 10-13

1,4p rate rule

2.32 × 10-6

1,6p rate rule

This work

1.47 × 10-10

1.15 × 10-14

8.52 × 10-5

Concerted Elimination and Beta Scission Reaction The HO2 direct molecular elimination reaction to form isooctene (C3CC=CC2, C3CCC(C)=C) + HO2 from the peroxy radical can occur from both the chemically activated adduct and the stablilized peroxy radical. The barrier for this molecular elimination path is ~7 kcal mol-1 below the entrance channel for direct molecular elimination (TS4, TS5). The activation barrier to form the isooctenes + HO2 is ~ 26.5 kcal mol-1 respective to isooctane peroxy radical. Comparison of high-pressure-limit rate constants for concerted elimination reaction of peroxy radicals yielding olefin + HO2• are shown in Figure 7a and Figure 7b. The observed rate constants are higher than rate constants from smaller molecule found in literature 53, 71, 72 and we note that this tertiary – OO bond energy (well depth) is weaker at 33.5 kcal mol-1 compared to the values for smaller reference tert-butyl radical of 38 kcal mol-1.

Figure 7a. Comparison of high-pressure-limit rate constants for concerted elimination reaction of peroxy radicals forming double bone on primary carbon + HO2•



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Page 22 of 37

Figure 7b. Comparison of high-pressure-limit rate constants for concerted elimination reaction of peroxy radicals forming double bone on secondary carbon + HO2• There are two additional paths which yields the same two isooctene + HO2 product sets; these are βscission (elimination) reactions from each of the two hydroperoxide alkyl radicals, where the radical sites are on the secondary and primary carbons adjacent to the tertiary peroxy carbon. Barriers and rate constants for the required first isomerization step are describe above. The activation energies for (TS7, TS10) elimination reaction from the hydroperoxide alkyl radicals are ~4 kcal mol-1 below the entrance channel. This β-scission - elimination of HO2 requires a previous step, that is a 1,4H-transfer reaction to the peroxy oxygen atom forming the two radicals: C3CC•C(OOH)C2 and C3CCC(OOH)C2•. C3CC•C(OOH)C2 C3CC=CC2 + HO2 with 16.9 kcal mol-1 barrier respective to isooctane hydroperoxide alkyl radical; 2.7 kcal mol-1 below entrance channel and C3CCC(OOH)C2• C3CCC(C)=C + HO2 with a barrier of 14.1 kcal mol-1 from isooctane hydroperoxide alkyl radical that is 2.1 kcal mol-1 below entrance channel. Cyclic Ether Ring Formation In an early n-hexane combustion study, Jones and Fenske68 reported the formation of significant quantities of cyclic ethers in addition to olefins between 580 and 930 K. Our results below show that one of the most important reaction channels in this tertiary isooctane radical plus O2 system is the formation of a cyclic ether + OH. These reactions occur from the hydroperoxide alkyl radical isomers formed via the intramolecular H transfer reactions. Here the alkyl radical center attacks the oxygen on the carbon of the


Page 23 of 37

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peroxide group; this results in a ring-closure (cyclic ether) and elimination of an OH-radical. The mechanism of this reaction step has been described by Chan et al. 67. It is important to note that an H atom transfer from the alkyl carbon atom to the peroxy oxygen atom must occur prior to this cyclic ether + OH path. The activation barrier to cyclic ether formation from secondary carbon (C3); 3 member ring, is 10.5 kcal mol-1 respective to hydroperoxide alkyl radical. This is 9.1 kcal mol-1 below entrance channel. The cyclic ether formation from one of the two primary carbons of iso-propyl group (C5, C8) resulting in a 3 member ring, to form C2YC4OC2 is 11.4 kcal mol-1 from the hydroperoxide alkyl radical, 4.8 kcal mol-1 below entrance channel. The cyclic formation activation barrier from primary carbon at tert-butyl group (C1, C6, C7); 5 member ring, is 3.5 kcal mol-1 below entrance channel and 13.9 kcal mol-1 respective to hydroperoxide alkyl radical. Among cyclic ethers formed, the 2,2,4,4-tetramethyl-tetrahydrofurane (C2YC4OC2) is the most abundant product under higher temperature, combustion, conditions as shown in isooctane experiments 6-11 OH-Transfer Reactions An OH-transfer reaction can also occurs after H transfer to the peroxy oxygen forms a hydroperoxide alkyl radical. Here the alkyl carbon radical site attacks the oxygen of the OH of the hydroperoxide group and the peroxide RO—OH bond cleaves as the stronger C—OH bond forms. Wijaya et al.69 have previously described these reactions for a series of different carbon number hydrocarbon. An alkoxy radical remains on the initial peroxide carbon (C2C(C•)CC(OOH)C2 C2C(COH)CC(O•)C2). Under combustion or thermal conditions, the alkoxy radical will rapidly form a carbonyl bond via a beta scission reaction. In the OH transfer to the primary carbon site here, the tertiary alkoxy radical decomposes to acetone and hydroxyl-neopentyl radical. Acetone is an experimentally observed product 8, 9. The cyclic ether formation has a lower barrier than the OH-transfer reactions and overall all these two channels are the two lowest energy pathways in oxidation of isooctane. However both channels require a higher barrier H atom transfer to occur first. Chemical Activation Results Figure 8 presents a comparison of the chemical activation results obtained when using different highpressure rate constants for the association reaction of the tertiary isooctane radical with O2 (this study) versus several literature values for smaller systems 40, 71, 72 (summarized in Table 7). At the lower



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temperatures, the results obtained when using the value from this study show good agreement with the generic rules in literature. The calculated rates are slightly higher at higher temperatures, which is a result of the slightly larger high pressure rate constants note above. The results show the importance of using correct high-pressure rate constants for this somewhat more strained isooctane system. Rate constants to the different isomers and product sets versus temperature and pressure obtained by applying the QRRK– master equation analysis for the determination of chemical activation reaction of the tertiary isooctane and O2 are illustrated in Figures 9 -12 of the text.

C3CCCCQJC2

C3CCCCJC2 + O2

C3CCCC2DC + H

C3COXRC2 + OH

Figure 8. Comparison of chemical activation results obtained using different literature generic rate constants for the addition reaction (CH3)3CCH2C•(CH3)2 + O2 → (CH3)3CCH2C(OO•)(CH3)2 to stabilization and to several reaction to products at 1 atm. Values obtained using the variational transition state analysis in this study, and the generic rules by Miyoshi, Villano et al. and Dilger et al. for tert-butyl radical + O2. Plots of calculated rate constants versus 1000/T (K) from chemical activation for C3CCC•C2 + O2 products at 1 atm and 60 atm are shown in Figure 9a and Figure 9b, respectively. Stabilization to adduct C3CCC(OO•)C2 channel is the most important reaction path in low to moderate temperature hydrocarbon oxidation. As temperature is increased, the rate through other channels begins to increase, while the stabilization rate decreases. At the higher temperatures, there is sufficient reaction of the energized adducts over the barriers associated with the five-membered and seven-membered ring TS from both H-


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transfer reaction and HO2 elimination, before stabilization. Important forward reactions go to molecular elimination to form isooctene + HO2 and to form cyclic ethers + OH. Dissociation to C3CCC(O•)C2 + O has an endothermicity of 26.6 kcal mol-1 above the reactant channel. And the rate constant at low temperature is not significant compared to the stabilization, HO2 elimination, OH transfer and cyclic ether + OH channels. At high pressure; 60 atm, the major reaction channels follow the same trend as the one at 1atm. Plots of calculated rate constants versus log P from chemical activation for C3CCC•C2 + O2 products at 298 K and 1000 K are shown in Figure 10a and Figure 10b, respectively. At room temperature tertiary isooctane peroxy radical adduct is the most important reaction path and is independent of the pressure. Other important product channels are molecular elimination reactions to form isooctene + HO2 and cyclic ether + OH. At low pressures, some of the energized C3CCC(OO•)C2 adduct can isomerize to energize hydroperoxide alkyl radical prior to stabilization, but the subsequent rate of stabilization of energized alkyl radical in the low-pressure environment is slower than the rate through concerted elimination to form isooctane + HO2 and cyclic ether + OH, so the overall rate for stabilization remains low. At high temperatures; above 1000 K, all reactions are independent of pressure. Important forward reactions go molecular elimination to form isooctane + HO2 and the cyclic ether + OH channels.

C3CCCQjC2 Reactant; C3CCCjC2 + O2

Figure 9a. Chemical activation plot of rate constants versus 1000/T (K) at 1atm for C3CCC•C2 + O2 → Products



Reactant; C3CCCjC2 + O2

C3CCCQjC2

Figure 9b. Chemical activation plot of rate constants versus 1000/T (K) at 60 atm for C3CCC•C2 + O2 → Products From the chemical activation plot of rate constants versus pressure at low temperatures, stabilization of the peroxy adduct and the two reactions to isooctane plus HO2 (molecular elimination) are important paths. At higher temperatures, the two isooctane + HO2 products sets remain most important paths. At higher pressure; 60 atm, the stabilization and isooctane products are still most important. At lower pressure, 0.01 atm, the major reaction channels follow the same trend as the one at 1Atm and 60 atm. Plots of calculated rate constants versus 1000/T (K) from chemical activation for C3CCC•C2 + O2 products at 0.01 atm is shown in supplementary data. 15

C3CCCQjC2

13

3

log k (cm /mol-s)

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C3CC=CC2 + HO2 C3CCC(C)=C + HO2


11

C3CCJCQC2 C3COXRC2 + OH

9

C3JCCCQC2 7

C2YC4OC2 + OH C2C(COH)CC(Oj)C2

5 3 -4

-3

-2

-1

0

1

2

3

log P (Atm)

Figure 10a. Chemical activation plot of rate constants versus log pressure (atm) at 298 K for C3CCC•C2 + O2 → Products


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Figure 10b. Chemical activation plot of rate constants versus log pressure (atm) at 1000 K for C3CCC•C2 + O2 → Products Plots of log rate constant versus log pressure at 298 K show stabilization to the peroxy adduct as the dominant product with molecular elimination to form isooctane isomer plus HO2 becoming important at low pressure. At 1000 K, plots of log rate constant versus log pressure show major products are isooctane isomer plus HO2 and formation of cyclic ether + OH next most important but more than one order of magnitude lower. Unimolecular Dissociation of tert-isooctane peroxide Plots of rate constants versus 1000/T for dissociation of the stabilized peroxy adduct C3CCC(OO•)C2 at 1 atm pressure are illustrated in Figures 11. Plots of rate constants versus log pressure at 500 K and 1000 K are illustrated in Figures 12a and Figure 12b, respectively. Forward reactions are molecular elimination to isooctene + HO2 and isomerization to C3•CCC(OOH)C2 and these are important at lower temperature with least activation energy; 21.8 kcal mol-1, when compare to other dissociation reaction paths. At high temperature all dissociation reactions show some pressure dependence. The important reaction paths are formation of isooctene + HO2 and isomerization to C3•CCC(OOH)C2.



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Figure 11. Plots of rate constants versus 1000/T (K) at 1atm for C3CCCQ•C2 dissociation

Figure 12a. Plot of rate constants versus log pressure (atm) at 500 K for dissociation of C3CCCQ•C2


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Figure 12b. Plot of rate constants versus log pressure (atm) at 1000 K for dissociation of C3CCCQ•C2 Plots of unimolecular dissociation rate constants for the stabilized tertiary isooctane peroxy adduct versus 1000/T (K) at 1 atm are shown in Figure 11. Results show forward reactions are the formation of isooctene + HO2 channels from both molecular elimination and beta scission paths. Figures 12a and 12b show plots of the stabilized peroxy radical dissociation at 500 K and 1000 K, respectively. At 500 K, molecular elimination to form isooctane + HO2 channels are the most important reaction paths with a smaller fraction to the hydroperoxy alkyl radical (C3•CCCQC2). At higher pressure, dissociation back to isooctane radical plus O2 becomes an important channel. At 1000 K, formation of the isooctane + HO2 channels are still the dominant reaction paths with hydroperoxy alkyl radical (C3•CCCQC2) isomers are also important at high pressure. Summary Thermochemical properties including standard enthalpies of formation for tert-isooctane hydroperoxide 77.85 kcal mol-1, peroxy radical and hydroperoxide alkyl radicals are determined. Bond energy values for the radicals are 100.2, 98.1, 101.4 and 84.2 kcal mol-1 for C3•CCCQC2, C3CC•CQC2, C3CCCQC2• and C3CCCQ•C2, respectively. The carbon-hydrogen bond energies were observed to be weaker than the conventional primary and secondary carbon-hydrogen bond by ~1 kcal mol-1. Well depths for tertisooctane hydroperoxide R• + O2 reaction are 33.5 kcal mol-1, this value is lower than in tert-butyl radical RO2 R• + O2 reaction; 37.8 kcal mol-1. These values are important for the determination of the kinetic properties, since small changes in the activation energies will cause larger changes in the rate



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constants especially at the lower temperatures. Group additivity, tert-isooctane hydroperoxide has three gauche interactions and two of 1,5 interaction. The radicals have three gauche interactions with one 1,5 interaction. The major reaction path at 1atm pressure is the stabilization of tert-isooctane peroxy radical adduct (C3CCCQ•C2) below 650 K. The major new products are isooctene + HO2 from four channels; two channels from molecular elimination and two channels from isomerization and subsequent beta scission. One other important reaction channel is formation of cyclic ethers + OH. The OH-transfer reactions from the hydroperoxy radical to the alkyl-radical centers with formation of an alkoxy radical are observed identified to be lower. The observed importance of this OH-transfer reaction is, however, new with this reaction system, and propagation (acceleration) pathways from the formed alkoxy radicals may be important. Supporting Information Supporting information contains optimized geometry coordinates, vibration frequencies, moments of inertia, potential energy profiles for internal rotations and resulting rate constants in QRRK calculations. This information is available free of charge via the Internet at http://pubs.acs.org. Nomenclature C = Carbon with hydrocarbons assumed to satisfy respective valence TS = Transition state J, j, • = Radical site D = Double bond Equal sign = Double bond Y = Cyclic C3COXRC2 = 2,3-epoxy-2,4,4-trimethylpentane C3CCYC2OC = 1,2-epoxy-2,4,4-trimethylpentane


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C2YC4OC2 = 2,2,4,4-tetramethyltetrahydrofuran References 1.

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TOC Bond Dissociation Enthalpies (kcal mol-1) 84.2 100.2

101.4 98.1


Thermochemistry, Reaction Paths, and Kinetics on the tert-Isooctane

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