(CH3C(=O)CH CH3)

Thermochemistry and Kinetics for 2-Butanone-3yl Radical (CH3C(=O)CH•CH3 ) Reactions with O2 By Nadia Sebbar1 , ∗, Joseph William Bozzelli2 , and Henning Bockhorn1 1 2

KIT – Karlsruhe Institut of Technology, Engler-Bunte-Institut, Verbrennungstechnik, Engler-Bunte Ring 1, 76131 Karlsruhe, Germany Department of Chemical Engineering, Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, NJ 07102, USA

Dedicated to Prof. Horst Hippler on the occasion of his 65th birthday (Received July 5, 2011; accepted in revised form September 16, 2011)

Thermochemistry / Reaction Kinetics / Quantum Chemistry / Butanone Radical Oxidation Thermochemistry and chemical activation kinetics for the reaction of the secondary radical of 2-butanone, 2-butanone-3yl, with 3 O 2 are reported. Thermochemical and kinetic parameters are determined for reactants, transition states structures and intermediates. Standard enthalpies and kinetic parameters are evaluated using ab initio (G3MP2B3 and G3), density functional (B3LYP/6311g(d, p)) calculations and group additivity (GA). The C−H bond energies are determined for the three carbons of the 2-butanone, showing that the C−H bond energy (BE) on the secondary carbon is low at 90.5 kcal mol−1 . The CH3 C(=O)CH• CH3 radical + O2 association results in chemicallyactivated peroxy radical with 26 kcal mol−1 excess of energy. The chemically activated adduct can dissociate to butanone-oxy radical + O, react back to butanone-3yl + O2 , form cyclic ethers or lactones, eliminate HO2 to form an olefinic ketone, or undergo rearrangement via intramolecular abstraction of hydrogen to form hydroperoxide and/or OH radicals. The hydroperoxide-alkyl radical intermediates can undergo further reactions forming cyclic ethers (lactones) and OH radicals. Quantum RRK analysis is used to calculate k(E) and master equation analysis is used for evaluation of pressure fall-off in these chemical activated reaction systems.

1. Introduction Ketones are a major class of organic compounds. They are important in the chemistry of the atmosphere and in combustion systems. Their photo-dissociation in the lower atmosphere results in formation of free radicals and may influence the atmospheric oxidation capacity. Ketones are also used as fuel tracers for monitoring fuel properties such as concentration, temperature, density, pressure, velocity, and distribution using laser-induced fluorescence [1,2] and as fuel additives in reducing soot emissions [3,4]. * Corresponding author. E-mail: [email protected]

This article is protected by German copyright law. You may copy and distribute this article for your personal use only. Other use is only allowed with written permission by the copyright holder.

Z. Phys. Chem. 225 (2011) 993–1018 / DOI 10.1524/zpch.2011.0144 © by Oldenbourg Wissenschaftsverlag, München

N. Sebbar et al.

However, little is known about the chemical fate of current fuel tracers, such as acetone and 3-pentanone, in hot oxidizing atmospheres [5]. Carbonyls are also known to be important intermediates in pyrolysis and combustion processes on saturated and unsaturated hydrocarbons. Important atmospheric and combustion loss processes for ketones involve hydrogen abstractions by OH radicals, a process that is partially controlled by carbon-hydrogen bond energies, and by photolysis resulting from absorption by the carbonyl group [6– 9]. The photolysis is reported to account for significant overall global presence of OH and HO2 radicals particularly in the upper troposphere [10,11]. There are no studies to our knowledge, on the thermochemistry of these carbonyl alkyl radicals or on the effect the carbonyl group has on the association reactions of radicals with O2 in atmospheric or in combustion systems. In this study carbon-hydrogen bond energies are determined for the different carbons of the 2-butanone and the C−H bonds on the carbons adjacent to the carbonyl group are found to be weaker than previously estimated. The thermochemistry of reaction intermediates and the oxidation reaction paths of the 2-butanone-3-yl radical CH3 C(=O)CH• CH3 + O2 are also determined and reported in this study. Structures and enthalpies of formation for important intermediate radicals, products and transition state barriers resulting from the reaction paths of this system are reported. Standard 0 , are calculated using ab initio, density functional calculations and enthalpies, Δf H298 group additivity (GA) with comparison to literature data. Kinetics and important intermediates for reaction paths are determined using bimolecular chemical activation analysis as a function of temperature and pressure. High pressure limit kinetic parameters are obtained from canonical Transition State Theory calculations. Multifrequency Quantum Rice–Ramsperger–Kassel (QRRK) analysis is used to calculate k(E) data and master equation analysis is applied to evaluate fall-off in the chemically activated and dissociation reactions.

2. Computational methods Molecular properties of reactants, adducts, transition state structures and products in the CH3 C(=O)CH• CH3 + O2 reaction system are calculated by means of several methods and with the Gaussian 03 program suite [12–14]. Enthalpies for reactants, adducts, and products are estimated using DFT [15,16], Gaussian-3 (G3) [17] composite method and the modified G3 reported as G3MP2B3 which uses B3LYP geometries. The hybrid DFT method B3LYP, which combines the three parameter Becke exchange functional, B3, with the Lee-Yang-Parr non-local correlation functional, LYP, and with a double polarized set, 6-311G(d, p), is used to optimize geometries [18–20]. B3LYP/6-311G(d, p) is chosen because it is commonly used and is reported to yield accurate geometry and reasonable energies [21,22]. Curtiss et al. [23] reported that G3(MP2) with B3LYP/6-31G(d) geometries yield overall enthalpy values for alkyl hydrocarbons showing a low overall deviation from experimental values. From the G3/99 test set, they report deviations of 0.71 kcal mol−1 for 38 hydrocarbons and 0.83 kcal mol−1 for 91 substituted hydrocarbons. Durant [21] has compared Density Functional Theory calculations on BHandH and B3LYP with MP2 and Hartree–Fock


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methods for geometry and vibration frequencies. He reports that these Density Functional methods provide excellent geometry and vibration frequencies, relative to MP2 at reduced computation expense. Petersson [24] et al. compared energies of Density Functional Theory methods: B3LYP/6-311+G(3d f, 2 p)//B3LYP/6-31G with G2 study, and his CBS calculation methods and report that they have been successful for a wide range of molecules. Wong and Radom [25,26] indicated the B3LYP/631G(d, p) geometry corresponds closely to QCISD(T)/6-31G(d, p). Zero-point vibration energies (ZPVE), vibration frequencies and thermal correction contributions to enthalpy from harmonic frequencies are scaled in accordance to the factors recommended by Scott and Radom [27]. Two composite methods are utilized as well, Gaussian-3 (G3) [17], which results from the well regarded Gaussian-2 (G2) [28] method and the modified G3 theory that used B3LYP geometries and referred as G3MP2B3 [15,16]. The G3 theory performs a sequence of ab initio molecular orbital calculations selected to remove errors and further calibrated to yield an accurate total energy for a species. Optimized structure and frequencies (scaled at 0.8929) are obtained at the Hartree–Fock HF/6-31G(d) level. The final equilibrium geometry is obtained by refining the HF geometry at the MP2(full)/6-31G(d) level. A series of single-point energies calculations are performed at higher levels of theory. The first higher level calculation is Møeller–Plesset perturbation theory [28] with the 6-31G(d) basis set, i.e., MP4/631G(d). This energy is modified by adding four corrections from additional calculations (correction for diffuse functions, correction for higher polarization functions on nonhydrogen atoms and p-functions on hydrogens, correction for correlation effects and correction for large basis set effects and for the non-additivity) and, when appropriate, by adding the spin-orbit correction, ΔE(SO). The final total energy at 0 K is obtained by adding a “higher level correction” (HLC) and the zero point energy obtained from the frequencies. The G3MP2B3 geometries and the zero-point energies, scaled by 0.96 are obtained at the B3LYP/6-31G(d) level. A single-point quadratic configuration interaction is carried out at the QCISD(T)/6-31G(d). Second-order Møeller–Plesset perturbation theory, MP2(FC), is performed with the basis sets 6-31G(d) and 6-311+G(2d f, 2 p) on Li-Ne, and 6-311+(3d2 f, 2 p) on the second row atoms (Na-Ar), called G3MP2 large. The overall accuracy of DFT methods is lower than that achieved with the highlevel ab initio and composite calculation methods, however the accuracy of density functional theory can, be improved by use of isodesmic reactions where DFT calculation errors can be reduced. This is a hypothetical reaction that has the same number and type of bonds on both sides and is used to calculate the enthalpy of the reaction 0 ). Here the errors on a given type of bond on each side of the reaction will (ΔHrxn,298 0 will be improved over atomization. The cancel, and the resulting accuracy of ΔHrxn,298 enthalpy of formation of a species is determined as follows: 0 = ΔHrxn,298

(total energies at 298 K of products) − (total energies at 298 K of reactants) 0 0 = (experimental of ΔHf,298 products) ΔHrxn,298


Thermochemistry and Kinetics for 2-Butanone-3yl Radical Reactions with O2

N. Sebbar et al.

−

0 (experimental of ΔHf,298 reactants)

The isodesmic reactions used experimental or computed standard enthalpies of formation values for the reference species. In developing the isodesmic work reactions, efforts were made to preserve the bonding environment in the target species, including aromaticity and ring structure, so as to effectively cancel errors in the DFT calculations. We try to include the same number and type of radicals, internal rotors, and molecular fragments on each side of the reaction; but this is not always possible because accurate enthalpies of formation for the reference species are not always available. Transition states were identified by their single imaginary frequency, whose mode of vibration connects the reactants and products. For transition states, enthalpies of formation were obtained from the computational enthalpy of activation and from the calculated enthalpies of formation of the reactants or products. Nomenclature in this work is as follows: Y(A) indicates a cyclic structure, D represent a double bond (CDO is C=O), A• or AJ represent a radical site on the structure, TS is a transition state structure.

3. Results and discussion 3.1 Enthalpy of formation, f H0298 calculations Standard enthalpies of formation for reactants, transition states and products of the CH3 C(=O)CH• CH3 + O2 reaction system are calculate and reported in Tables 2 and 3. The enthalpy values for standard reference species used in the work reactions are listed in Table 1 along with literature references. Literature enthalpy values for reference species are determined either experimentally or computationally. Enthalpy values of species which could not be found in the literature were also calculated using DFT, G3MP2B3 and G3 methods. The group additivity (GA) method of Benson [29] with the hydrogen bond increment method of Ritter and Bozzelli [30] has also been applied. Enthalpy values of some reference species were also further calculated to provide additional support to our isodesmic reaction analysis. Table 2 reports the enthalpies calculation of fifteen species as well as their structures and the work reactions used. When comparing the enthalpy values of the radicals and stable species, in Table 2, we note an excellent agreement (< 1 kcal mol−1 and one species < 2 kcal mol−1 ) between G3MP2B3 and G3 results via the different work reactions. The DFT calculations also show good agreement with the two ab initio methods as well. The difference between DFT and G3MP2B3 is < 1 kcal mol−1 for 6 species, < 2 kcal mol−1 for 4 species and < 3 for 2 species. The difference between DFT and G3 is: < 1 kcal mol−1 for 4 species, < 2 kcal mol−1 for 7 species and a difference of 2.4 kcal mol−1 is noted for only one species. Values were also compared to GA values. While these species illustrated are all radicals, our method for GA requires estimation of the parent stable molecule with H atom on the radical site before the radical value can be estimated. Table 2 shows that the deviation between GA and B3LYP and/or G3MP2B3 and G3 calculated values is less than 2 kcal mol−1 .


996

Table 1. Enthalpies of formation for stable and radical species used in work reactions. Species

CH4 CH3 CH3 CH2 =CH2 CH3 CH=CH2 CH3 CH2 CH=CH2 CO2 CO CH2 O2 (dioxirane) CH2 =C=O Y(C2 H4 O2 ) C2 H4 O (Y(C2 H4 O)) CH3 CH=O O=CHCH=O CH3 OH CH3 CH2 OH CH3 OOH CH3 CH2 OOH CH3 C(=O)CH=CH2 CH3 C(=O)C(=O)CH3 Y(CH2 COO)=O CH2 =CHOOH CH3 C(=O)CH2 CH3 CH3 CH=O CH3 C(=O)OH CH3 C(=O)CH3 CH2 =CHC(=O)OH CH3 CH2 C(=O)OH CH2 =C=CHCH3

0 Δf H298 (kcal mol−1 )

−17.89 ± 0.07 −20.24 ± 0.12 12.55 ± 0.1 4.879 −0.15 ± 0.19 −94.05 ± 0.03 −26.41 ± 0.04 −18.65 ± 0.95 −20.85 10.26 −12.58 −40.80 ± 0.35 −50.66 ± 0.19 −48.08 ± 0.05 −56.23 ± 0.12 −31.8 ± 0.94 −39.28 ± 0.01 −27.4 ± 2.6 −78.10 −35.92 ± 0.42 −9.63 ± 0.08 −57.02 ± 0.20 −40.80 ± 0.35 −103.5 ± 0.6 −51.9 ± 0.12 −80.51 ± 0.55 −108.9 ± 0.48 39.53 ± 0.28

Source Species

1 1 2 3 4 5 4 6 7 8 2 9 10 11 11 12 13 14 15 16 13 17 18 17 19 4

CH3 OCH3 Y(C3 H4 O)=O CH2 CH2 OCH3 CH3 C(=O)OOH H O HO• HOO• CH•3 CH3 CH•2 CH• =C=O CH2 =CHCH=CH• C6 H•5 CH3 O• CH•2 OH CH3 CH2 O• CH•2 CH2 OH CH3 OO• CH3 CH2 OO• CH•2 CH2 OOH CH3 C• =O Y(C6 H•7 ) CH•2 CH=O O=CHCH=CH• CH2 =CHC(=O)O• CH3 C(=O)O• CH3 CH• OH CH2 =CHCH•2

0 Δf H298 (kcal mol−1 )

−43.99 ± 0.12 −67.61 ± 0.2 −51.73 ± 0.16 −84.22 ± 1.23 52.103 ± 0.001 59.55 ± 0.024 8.93 ± 0.03 2.94 ± 0.06 34.82 28.4 ± 0.5 40.4 86.73 81.4 ± 0.16 4.1 ± 1.0 −2 ± 1 −2.03 ± 0.39 −5.7 ± 0.85 2.15 ± 1.22 −6.5 ± 2.36 11.2 ± 2.1 −2.9 ± 0.7 49.94 ± 0.74 3.52 ± 0.38 41.76 ± 0.7 −22.47 −46.53 ± 1.04 −13.34 ± 0.84 40.9 ± 0.7

Source

20 21 20 16 4 22 23 23 2 24 8 8 13 2 24 13 25 24 26 27 2 8 28 6 6 16 29 24

Sources: 1. E. J. Prosen and F. D. Rossini, J. Res. NBS (1945) 263–267. 2. M. W. Chase Jr., NIST-JANAF Themochemical Tables, Fourth Edition, J. Phys. Chem. Ref. Data, Monograph 9 (1998) 1–1951. 3. S. Furuyama, D. M. Golden, and S. W. Benson, J. Chem. Thermodyn. 1 (1969) 363–375. 4. E. J. Prosen, F. W. Maron, and F. D. Rossini, J. Res. NBS 46 (1951) 106–112. 5. J. D. Cox, D. D. Wagman, and V. A. Medvedev, Hemisphere Publishing Corp., New York 1984, p. 1. 6. N. Sebbar, H. Bockhorn, and J. W. Bozzelli, J. Phys. Chem. A 109 (2005) 2233–2253. 7. V. M. Orlov, A. A. Krivoruchko, A. D. Misharev, and V. V. Takhistov, Bull. Acad. Sci. USSR, Div. Chem. Sci. (1986) 2404–2405. 8. N. Sebbar, H. Bockhorn, and J. W. Bozzelli, Int. J. Chem Kinet 40 (2008) 583–604. 9. K. B. Wiberg, L. S. Crocker, and K. M. Morgan, J. Am. Chem. Soc., 1991, 113, 3447–3450. 10. R. A. Fletcher and G. Pilcher, Trans. Faraday Soc. 66 (1970) 794–799. 11. J. H. S. Green, Chem. Ind. (London) (1960) 1215. 12. T. H. Lay and J. W. Bozzelli, J. Phys. Chem. A 101 (1997) 9505–9510. 13. N. Sebbar, H. Bockhorn, and J. W. Bozzelli, Phys. Chem. Chem. Phys. 4 (2002) 3691. 14. J. P. Guthrie, Can. J. Chem. 56 (1978) 962–973. 15. G. R. Nicholson, M. Szwarc, and J. W. Taylor, J. Chem. Soc. (1954) 2767–2769. 16. N. Sebbar, H. Bockhorn, and J. W. Bozzelli, J. Phys. Chem. A., doi:10.1021/jp2078067 (2011). 17. J. Chao and B. J. Zwolinski, J. Phys. Chem. Ref. Data 5 (1976) 319–328.


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Table 1. Continued. 18. Average of 8 values, Individual data points-NIST. 19. N. D. Lebedeva, Heats of combustion of monocarboxylic acids, Russ. J. Phys. Chem. 38 (1964) 1435–1437 [Engl. Transl.]. 20. G. Pilcher, A. S. Pell, and D. J. Coleman, Trans. Faraday Soc. 60 (1964) 499–505. 21. A. A. Yevstroprov, B. V. Lebedev, T. G. Kulagina, Ye. B. Lyudvig, and B. G. Belenkaya, Polym. Sci. USSR 21 (1979) 2249–2256. 22. R. J. Kee, F. M. Rupley, and J. A. Miller, SAND87 8215B, Sandia National Laboratories, 1994. 23. B. Ruscic, R. E. Pinzon, M. L. Morton, N. K. Srinivasan, M.-C. Su, J. W. Sutherland, and J. V. Michael, J. Phys. Chem. A 110 (2006) 6592–6601. 24. W. Tsang, J. A. Martinho Simoes, A. Greenberg, and J. F. Liebman (Eds.), Blackie Academic and Professional, London 1996, pp. 22–58. 25. H. Sun and J. W. Bozzelli, J. Phys. Chem. A 105 (2001) 9543. 26. V. D. Knyazev and I. R. Slagle, J. Phys. Chem. A 102 (1998) 1770–1778. 27. C. Sheng, A. M. Dean, J. W. Bozzelli, and A. Y. Chang, J. Phys. Chem. A 106 (2002) 7276–7293. 28. J. Lee and J. W. Bozzelli, J. Phys. Chem. A 107 (2003) 3778. 29. S. J. Blanksby and B. G. Ellison, Acc. Chem. Res. 36 (2003) 255–263.

Table 3 illustrates the structures and lists the transition state structure enthalpies 0 (Δf HTS(298) ) for fifteen transition states; it also identifies and help describing the reaction 0 enthalpy values are calculated from both the reactant and the prodpaths. The Δf HTS(298) 0 from this difference reaction is similar to an isodesmic uct. The calculation of Δf HTS(298) reaction and includes cancellation of errors for similar bonds in the reactant and TS 0 of reactant or product, structure. This difference is then added to the absolute Δf H298 0 which are from isodesmic reaction analysis to obtain Δf HTS(298) . The computational methods used for the enthalpy calculations are G3MP2B3, G3 and B3LYP. The DFT method does not show the same accuracy in determination of the transition state structures, as it did for the radicals and stable species. While G3MP2B3 and G3 show good agreement, nine transition state structure DFT values deviate by 3 to 8 kcal mol−1 from the G3MP2B3 and G3 calculations. Only for TS11, TS41 and TS51 does the DFT show good agreement with ab initio results. G3 values are used in the kinetic calculations.

3.2 Entropy S0 (298) and heat capacities, Cp(T) (300 ≤ T/K ≤ 1500) calculations ) The entropy Sf0298 and heat capacity C p(T f 298 for intermediates, transition state structures and final products are calculated using the rigid-rotor-harmonic-oscillator approximation [31,32] and based on the calculated parameters: frequencies, moments of inertia, symmetry, spin degeneracy and optical isomers. These entropies and heat capacities are listed in Table 4. Vibration frequencies and moments of inertia from the optimized B3LYP/6-311G(d, p) structures were used to calculate the contributions to entropy and heat capacity from vibration, translation, and external rotation (TVR) on the basis of formulas from statistical mechanics and by use of the SMCPS [33] program. The DFT data is chosen for the stable species and the radicals because the it is the same method but larger basis set, 6-311G(d, p), than the B3LYP/6-31G(d) used in G3MP2B3 and is considered better than the HF/6-31G(d) used in G3. For the transition state structures


998

16.81

−2.5

Li Zhu PhD, NJIT, Newark, USA

−43.30 −43.77 −44.17 −45.36 −44.85 −45.13 −46.18 −44.11 −45.04 −44.95 ± 1.48 −44.24 ± 0.55 −44.78 ± 0.53 −45.28

CH3 C(=O)CH(OO• )CH3 + CH4 → CH3 CH2 OO• + CH3 C(=O)CH3 CH3 C(=O)CH(OO• )CH3 + CH3 CH3 → CH3 CH2 OO• + CH3 C(=O)CH2 CH3 CH3 C(=O)CH(OO• )CH3 + CH3 CH3 → CH3 CH•2 + CH3 C(=O)CH(OOH)CH3 Average

999


∗

–

15.05 16.36 14.06 15.16 ± 1.15

0.70

GA

−19.16 −18.64 −17.97 −19.32 −19.01 −18.38 −19.24 ± 0.11 −18.83 ± 0.26 −18.17 ± 0.29 −17.48

–

0.83

0 Δf H298 (kcal mol−1 ) G3MP2B3 G3

−76.73 −76.81 −77.05 −78.79 −77.88 −78.02 −77.76 ± 1.46 −77.35 ± 0.76 −77.54 ± 0.69 −79.48

Average

Average

0.87

B3LYP/ 6-311G(d, p)

CH3 C(=O)CH(OOH)CH3 + CH4 → CH3 CH2 OOH + CH3 C(=O)CH3 CH3 C(=O)CH(OOH)CH3 + CH3 CH3 → CH3 CH2 OOH + CH3 C(=O)CH2 CH3 Average

CH3 C(=O)CH• CH3 + CH3 CH3 → CH3 CH•2 + CH3 C(=O)CH2 CH3 CH3 C(=O)CH• CH3 + CH4 → CH3 CH•2 + CH3 C(=O)CH3

CH•2 OOH = BE − H + CH3 OOH = 99∗ − 52.1 − 31.8 = 15.1

CH•2 OOH + CH4 → CH•3 + CH3 OOH CH•2 OOH + CH3 OH → CH•2 OH + CH3 OOH CH•2 OOH + CH3 CH3 → CH3 CH•2 + CH3 OOH

CH•2 C(=O)CH3 + CH3 CH3 → CH3 CH•2 + CH3 C(=O)CH3

Reactions

0 Table 2. Calculated Δf H298 for species using isodesmic reactions.


Average


−18.02 −13.08 −12.89 −7.95 −12.18 −12.07 −12.98 ± 7.12 −12.63 ± 0.64 −12.48 ± 0.58

B3LYP/ 6-311G(d, p)

Average

–

−29.61 −29.38 ± 0.28

−30.98

−11.32

GA

−28.48

−79.16 −79.17 −79.18 −81.30 −78.95 −78.50 −80.23 ± 1.51 −79.06 ± 0.16 −78.84 ± 0.48 −78.36/ −78.10

–

−29.01 −29.40 −29.69 −29.19

CH3 C(=O)CH(OOH)CH•2 + CH4 → CH3 C(=O)CH3 + CH•2 CH2 OOH −26.26 −26.01 −26.49 −27.72 −26.72 −26.99 CH3 C(=O)CH(OOH)CH•2 + CH3 CH3 → CH3 C(=O)CH(OOH)CH3 + CH3 CH•2 −27.21 −26.64 −27.16 CH3 C(=O)CH(OOH)CH•2 + CH4 → CH3 C(=O)CH• CH3 + CH3 OOH Average −27.06 ± 0.74 −26.46 ± 0.39 −26.88 ± 0.35

CH3 C(=O)C(=O)CH3 + CH3 CH3 → 2CH3 C(=O)CH3 CH3 C(=O)C(=O)CH3 + H2 → O=CHCH=O + CH3 CH3

CH3 C(=O)C• (OOH)CH3 + H2 → CH3 CH=O + CH3 CH• OOH CH3 C(=O)C• (OOH)CH3 + CH3 CH3 → CH3 C(=O)CH(OOH)CH3 + CH3 CH•2 CH3 C(=O)C• (OOH)CH3 + CH4 → CH3 C(=O)CH3 + CH•2 CH2 OOH CH3 C(=O)C• (OOH)CH3 + CH3 CH2 OH → CH3 CH• OH + CH3 C(=O)CH(OOH)CH3 CH3 C(=O)C• (OOH)CH3 + H2 → CH3 C(=O)CH3 + CH•2 OOH Average

CH3 Y(CHOCH2 C(=O)) + CH3 OCH3 → Y(C3 H4 O)=O + CH3 C(=O)CH3 + H2 −44.96 −52.98 −53.70 −60.54 −54.86 −54.00 CH3 Y(CHOCH2 C(=O)) + CH3 CH3 + H2 → CH3 C(=O)CH3 + CH3 CH2 OCH3 Average −52.75 ± 11.02 −53.92 ± 1.33 −53.85 ± 0.21

CH3 Y(C(O• )OOCH)CH3 + H2 → Y(CH2 CH2 OO) + CH3 CH2 O• CH3 Y(C(O• )OOCH)CH3 → Y(CH2 OOC)=O + CH3 CH•2

Reactions

N. Sebbar et al.


Table 2. Continued.

1000

Average

CH2 =C(OH)CH• CH3 + CH4 → CH3 CH2 OH + CH2 =CHCH•2 CH2 =C(OH)CH• CH3 + CH3 CH3 → CH•2 CH2 OH + CH3 CH2 CH=CH2 Average

CH3 C(=O)OOCH• CH3 → CH3 CH=O + CH3 C(=O)O• CH3 C(=O)OOCH• CH3 + H2 → CH3 CH•2 + CH3 C(=O)OOH

−11.72 −11.25 −11.48 ± 0.33

–

−8.99 −9.60 −9.29 ± 0.43

–

−9.28 −11.17 −10.23 ± 1.34

−42.68 −43.33 −43.00 ± 0.46

−40.72 −43.02 −42.47 −46.74 −42.34 −42.39 −46.58 −41.98 −41.98 −44.68 ± 3.43 −42.45 ± 0.53 −42.28 ± 0.26

−33.41 −34.27

CH3 C(=O)CH(O• )CH3 → CH3 CH=O + CH3 C• =O CH3 C(=O)CH(O• )CH3 + CH4 → CH3 CH2 O• + CH3 C(=O)CH3 CH3 C(=O)CH(O• )CH3 + CH3 CH3 → CH3 CH2 O• + CH3 C(=O)CH2 CH3 Average

−35.10 −35.88

−34.69 −34.99 −34.13 −35.21 ± 0.46 −35.32 ± 0.49 −33.94 ± 0.46

−35.53 −35.42

CH•2 C(=O)CH(OOH)CH3 + H2 → CH•2 CH=O + CH3 CH2 OOH CH•2 C(=O)CH(OOH)CH3 + H2 + CH3 OH → CH•2 CH=O + CH3 OOH + CH3 CH2 OH CH•2 C(=O)CH(OOH)CH3 + CH3 CH3 → CH3 C(=O)CH(OOH)CH3 + CH3 CH•2 Average

−55.99 −54.36 −53.89 −53.03 −52.33 −52.68 −54.51 ± 2.09 −53.35 ± 1.44 −53.28 ± 0.86

CH3 C(=O)Y(CHOCH2 ) + H2 → Y(CH2 CH2 O) + CH3 CH=OH CH3 C(=O)Y(CHOCH2 ) + CH4 → CH3 C(=O)CH3 + Y(CH2 CH2 O) Average


−27.36 −26.17 −26.49 −29.56 −28.15 −28.43 −30.05 −28.55 −28.78 −28.99 ± 1.43 −27.63 ± 1.27 −27.90 ± 1.23

B3LYP/ 6-311G(d, p)

CH3 C(=O)CH=CH2 + CH4 → CH3 C(=O)CH3 + CH2 =CH2 CH3 C(=O)CH=CH2 + CH3 CH3 → CH3 C(=O)CH2 CH3 + CH2 =CH2 CH3 C(=O)CH=CH2 + CH3 CH3 → CH3 C(=O)CH3 + CH3 CH=CH2 Average

Reactions

−9.26

−43.20

−43.62

−35.53

−51.95

−30.90/ −27.4

GA

1001


Table 2. Continued.


N. Sebbar et al.

0 Table 3. Calculated Δf H298 of transition state structuresa .

Transition state structure

Reactions Radical → TS → Products

0 −1 Δf HTS (298) (kcal mol ) B3LYP/ G3MP2B3 G3 6-311G(d, p)

CH3 C(=O)CH• CH3 → TS0 TS0 → CH2 =C(OH)CH• CH3 Average

34.28 33.70 33.99 ± 0.41

37.52 38.11 37.82 ± 0.42

38.24 38.47 38.35 ± 0.16

CH2 =C(OH)CH• CH3 → TS01 TS1 → CH2 =C=CHCH3 + OH Average

39.73 44.68 42.21 ± 3.50

45.25 47.00 46.13 ± 1.24

45.05 45.86 45.45 ± 0.57

CH3 C(=O)CH(OO• )CH3 → TS1 TS1 → CH3 Y(C(O• )OOCH)CH3 Average

−14.29 −5.50 −9.03 −11.09 −9.70 −10.43 −12.69 ± 2.26 −7.60 ± 2.97 −9.68 ± 0.99

CH3 Y(C(O• )OOCH)CH3 → TS11 TS11 → CH3 C(=O)OOCH• CH3 Average

−12.62 −10.15 −10.75 −11.23 −14.27 −15.43 −13.67 ± 0.98 −12.21 ± 2.91 −13.09 ± 3.31

CH3 C(=O)CH(OO• )CH3 → TS2 TS2 → CH3 C(=O)C• (OOH)CH3 Average

−11.51 −6.01 −6.49 −12.59 −6.06 −6.10 −12.05 ± 0.76 −6.03 ± 0.04 −6.29 ± 0.28

CH3 C(=O)C• (OOH)CH3 → TS21 TS21 → CH3 C(=O)C(=O)CH3 + OH Average

−45.70

−41.04

−45.03

–

–

–

CH3 C(=O)CH(OO• )CH3 → TS3 TS3 → CH3 C(=O)CH(OOH)CH•2 Average

−12.22 −7.75 −8.72 −12.80 −7.35 −8.86 −12.51 ± 0.41 −7.55 ± 0.28 −8.79 ± 0.10

CH3 C(=O)CH(OOH)CH•2 → TS3-1 TS3-1 → CH3 C(=O)CH=CH2 + • OOH Average

−18.75 −12.60 −13.67 −13.27 −11.87 −13.51 −16.01 ± 3.87 −12.23 ± 0.52 −13.59 ± 0.11

CH3 C(=O)CH(OOH)CH•2 → TS3-2 TS3-2 → CH3 C(=O)Y(CHOCH2 ) + OH Average

−20.34 −14.89 −21.57 −13.43 −20.96 ± 0.87 −14.16 ± 1.03

CH3 C(=O)CH(OO• )CH3 → TS4 TS4 → CH•2 C(=O)CH(OOH)CH3 Average

−22.47 −17.63 −17.59 −24.22 −17.84 −17.66 −23.34 ± 1.24 −17.74 ± 0.15 −17.63 ± 0.05

– – –

CH•2 C(=O)CH(OOH)CH3 → TS41 −14.63 −7.09 −7.03 – −13.11 −13.82 TS41 → CH3 CH• OOH + CH2 =C=O −9.39 −13.24 −14.30 TS41 → CH3 CH=O + CH2 =C=O + OH Average −12.01 ± 3.71 −11.15 ± 3.51 −11.72 ± 4.07 CH•2 C(=O)CH(OOH)CH3 → TS42 TS42 → CH3 Y(CHOCH2 C(=O)) Average

−14.28 −7.06 −11.48 −3.58 −12.88 ± 1.98 −5.32 ± 2.46


1002

Table 3. Continued. Transition state structure

Reactions Radical → TS → Products

CH3 C(=O)CH(OO• )CH3 → TS5 CH3 C(=O)CH(O• )CH3 → TS5-1 TS5-1 → CH3 CH=O + CH3 C• (=O) Average

0 −1 Δf HTS (298) (kcal mol ) B3LYP/ G3MP2B3 G3 6-311G(d, p)

–

–

9.22

−42.65 −40.09 −40.93 −38.69 −40.66 −41.12 −40.67 ± 2.80 −40.37 ± 0.40 −41.03 ± 0.13

CH3 C(=O)CH(OO• )CH3 → TS6 −27.12 −16.80 −17.68 −22.21 −15.67 −17.67 TS6 → CH3 C(=O)CH=CH2 + • OOH Average −24.66 ± 3.47 −16.23 ± 0.80 −17.68 ± 0.01

) the G3 data are selected. The contributions to Sf0298 and C p(T f 298 from low barrier (below −1 6.5 kcal mol ) torsion frequencies were removed from the calculations and contributions from internal rotations (IR) were substituted. This 6.5 kcal mol−1 parameter results from our study comparing calculated entropy and heat capacity with experimental data, which will be reported in a separate publication. The torsion frequencies are identified by viewing bond motions using the GaussView program.

3.3 Bond dissociation energies The values of C−H bond energies in the 2-butanone allows the estimation of initial abstraction reaction kinetics in this system. The C−H bond dissociation energies for the CH3 C(=O)CH2 CH3 are determined by DFT and ab-initio (G3MP2B3, G3) calculations. Table 5 shows an excellent agreement among the DFT and the ab initio bond energy values. Comparison of the C−H bonds in the 2-butanone, shows that bond energies are influenced by the carbonyl group. As shown in a previous study [34,35] and in Table 5, the sp2 structure with π bonding of the carbon oxygen double bond, allows for resonance when a radical is on an adjacent carbon and results in a lower bond energies. Only carbon 4 on the 2 butanone shows a conventional C−H bond for a primary carbon. Table 5 shows that the C−H bond in the secondary carbon (C-3) adjacent to the carbonyl group CH3 C(=O)CH(−H)CH3 has the lowest bond energy value with 90 kcal mol−1 . The BE increases by some 6 kcal mol−1 for the primary carbon (C-1) in (H−)CH2 C(=O)CH2 CH3 and by 10 kcal mol−1 in the primary carbon (C-4) which is not directly attached to the carbonyl group CH3 C(=O)CH2 CH2 (−H). In this study we report the oxidation reactions on carbon 3 (CH3 C=OCH• CH3 ) for which C−H bond energy is 90 kcal mol−1 .

3.4 Potential energy diagram of CH3 C(=O)CH• CH3 + O2 It is interesting to first evaluate the stability of the 2-butanone-3yl radical before starting the analysis of the reaction paths for the CH3 C(=O)CH• CH3 + O2 reaction system. This 2-butanone-3yl radical can react to allene + • OH; the reverse of this reaction has been


1003


TVRc

CH3 C(=O)C• OOHCH3

28.56

23.83 2.09 2.09 3.28 31.29

22.05 2.09 2.09 26.23

17.97 2.09 2.83 22.89

18.35 2.09 2.09 3.28 25.81

300 K

34.26

29.33 2.06 2.06 2.69 36.14

27.38 2.06 2.06 31.5

23.11 2.06 3.07 28.24

24.20 2.06 2.06 2.69 31.01

400 K

39.54

34.27 1.93 1.93 2.20 40.33

32.13 1.93 1.93 35.99

27.66 1.93 3.08 32.67

29.63 1.93 1.93 2.20 35.69

500 K

44.15

38.48 1.78 1.78 1.87 43.91

36.18 1.78 1.78 39.74

31.49 1.78 2.97 36.24

34.32 1.78 1.78 1.87 39.75

600 K

51.45

45.07 1.55 1.55 1.50 49.67

42.51 1.55 1.55 45.61

37.44 1.55 2.62 41.61

41.79 1.55 1.55 1.50 46.39

800 K

Cp (T) cal mole−1 K−1

56.85

49.92 1.39 1.39 1.32 54.02

47.13 1.39 1.39 49.91

41.79 1.39 2.28 45.46

47.33 1.39 1.39 1.32 51.43

1000 K

65.27

57.36 1.19 1.19 1.13 60.87

54.14 1.19 1.19 56.52

48.46 1.19 1.72 51.37

55.87 1.19 1.19 1.13 59.38

1500 K

N. Sebbar et al.


a 0 Thermodynamic properties are referred to a standard state of an ideal gas at 1 atm; b ΔHf0298 in kcal mol−1 ; S298 in cal mol−1 K−1 ; c density functional theory at B3LYP/6-311G(d, p).

85.61

TVRc IR IR IR Total

CH3 C(=O)CH• CH3 C−CH3 C−CH3 CH3 CH2 −C=O

70.91 4.52 4.52 79.95

−29.31

−80.23

TVRc IR IR Total

CH3 C(=O)C(=O)CH3 C−CH3 C−CH3

66.68 4.52 3.79 74.99

−19.24

−28.99

TVRc IR IR Total

CH3 C(=O)CH=CH2 C−CH3 CH3 C(=O)−C=C

68.59 4.52 4.52 6.10 83.73

S

0 b 298

80.78 4.52 4.52 6.10 95.92

−57.02

TVRc IR IR IR Total

Δf H 0 b 298

CH3 C(=O)CH2 CH3 C−CH3 C−CH3 CH3 CH2 −C=O

Species

Table 4. Calculated thermochemical properties of radicals and stable species and transition state structuresa .

1004

−77.76

TVRc IR IR IR IR Total TVRc IR IR IR IR Total TVRc IR IR IR IR Total TVRc

CH3 C(=O)CHOOHCH3 CC(=O)−C C−OOH C−CH3 C−CH3

CH3 C(=O)CHOOHCH•2 CC(=O)−C C−OOH C−CH2 C−CH3

CH3 C(=O)CHOO• CH3 CC(=O)−C C−OO• C−CH3 C−CH3

CH3 C(=O)OOCH• CH3

89.61

−44.95 −43.00

77.53 6.10 3.99 4.52 4.52 96.66

73.63 6.10 3.99 4.52 4.52 92.76

70.97 4.52 4.52 80.01

S

0 b 298

74.66 6.10 5.61 4.52 4.52 95.41

−27.06

−44.68

TVRc IR IR Total

Δf H 0 b 298

CH3 C(=O)CHO• CH3 C−CH3 C−CH3

Species

28.93

22.63 3.28 2.10 2.09 2.09 32.19

25.59 3.28 3.12 2.09 2.09 36.17

24.86 3.28 3.12 2.09 2.09 35.44

21.32 2.09 2.09 25.5

300 K

35.01

29.17 2.69 2.19 2.06 2.06 38.17

32.00 2.69 2.72 2.06 2.06 41.53

31.71 2.69 2.72 2.06 2.06 41.24

26.90 2.06 2.06 31.02

400 K

40.62

34.96 2.20 2.21 1.93 1.93 43.23

37.42 2.20 2.41 1.93 1.93 45.89

37.79 2.20 2.41 1.93 1.93 46.26

32.11 1.93 1.93 35.97

500 K

45.47

39.82 1.87 2.18 1.78 1.78 47.43

41.86 1.87 2.18 1.78 1.78 49.47

42.90 1.87 2.18 1.78 1.78 50.51

36.66 1.78 1.78 40.22

600 K

53.11

47.27 1.50 2.01 1.55 1.55 53.88

48.58 1.50 1.86 1.55 1.55 55.04

50.77 1.50 1.86 1.55 1.55 57.23

43.91 1.55 1.55 47.01

800 K


58.72

52.63 1.32 1.81 1.39 1.39 58.54

53.44 1.32 1.66 1.39 1.39 59.2

56.50 1.32 1.66 1.39 1.39 62.26

49.30 1.39 1.39 52.08

1000 K

67.36

60.70 1.13 1.47 1.19 1.19 65.68

60.92 1.13 1.38 1.19 1.19 65.81

65.27 1.13 1.38 1.19 1.19 70.16

57.69 1.19 1.19 60.07

1500 K

1005


Table 4. Continued.


84.72

66.06 4.52 70.58 81.38

84.77

−35.21

−52.75 −9.68

−6.46

TVRc

TVRc IR Total TVRc

TVRc

CH3 Y(CHOCH2 C(=O)) C−CH3

TS1

TS2

CH•2 C(=O)CHOOHCH3

69.78 6.10 4.52 80.40

S

0 b 298

−12.98

TVRc IR IR Total

CH3 Y(C(O• )OOCH)CH3 C−CH3 C−CH3

−54.51

Δf H 0 b 298

75.00 4.52 4.52 84.04

TVRc IR IR Total

CH3 C(=O)Y(CHOCH2 ) CC(=O)−C C−CH3

Species

28.84

26.93

15.92 2.09 18.01

31.10

22.97 2.09 2.09 27.15

20.10 3.28 2.09 25.47

300 K

35.02

33.14

21.68 2.06 23.74

38.17

29.53 2.06 2.06 33.65

26.11 2.69 2.06 30.86

400 K

40.58

38.85

26.91 1.93 28.84

44.05

35.59 1.93 1.93 39.45

31.40 2.20 1.93 35.53

500 K

45.36

43.77

31.31 1.78 33.09

48.81

40.79 1.78 1.78 44.35

35.77 1.87 1.78 39.42

600 K

52.81

51.45

38.06 1.55 39.61

55.92

48.82 1.55 1.55 51.92

42.40 1.50 1.55 45.45

800 K


58.21

57.03

42.88 1.39 44.27

60.99

54.61 1.39 1.39 57.39

47.11 1.32 1.39 49.82

1000 K

66.35

65.58

50.08 1.19 51.27

68.71

63.38 1.19 1.19 65.76

54.15 1.13 1.19 56.47

1500 K

N. Sebbar et al.


Table 4. Continued.

1006

1007

Table 4. Continued. Cp (T) cal mole−1 K−1

Species 0 b Δf H298

0 b S298 300 K 400 K 500 K 600 K 800 K 1000 K 1500 K

TS3

TVRc

−8.79 82.26 27.03 33.78 39.79 44.85 52.57 58.07

66.28

TS4

TVRc −17.63 80.43 26.96 33.77 39.80 44.88 52.62 58.12

66.33

TS5

TVRc

9.22 84.86 28.44 34.14 39.44 44.08 51.48 56.98

65.51

TS6

TVRc −17.68 87.20 29.96 36.61 42.40 47.23 54.54 59.71

67.35

TS1∗ 1 TVRc −12.88 81.94 27.17 33.45 39.18 44.07 51.68 57.20

65.66

TS2∗ 1 TVRc −45.37 89.19 30.21 35.77 40.88 45.31 52.31 57.48

65.59

TS3∗ 1 TVRc −13.59 88.46 30.30 36.24 41.44 45.83 52.64 57.66

65.60

TS3∗ 2 TVRc −14.16 89.31 30.95 37.25 42.70 47.21 54.08 59.04

66.69

TS4∗ 1 TVRc −10.67 85.72 29.75 35.82 41.11 45.55 52.44 57.51

65.52

−5.32 88.37 31.65 38.10 43.49 47.88 54.53 59.35

66.82

TS5∗ 1 TVRc −41.03 84.41 25.81 30.85 35.60 39.81 46.63 51.79

59.92

TS4∗ 2 TVRc



N. Sebbar et al.

Table 5. Bond energy calculation in kcal mol−1 .

CH3 C(=O)CH(−H)CH3 (H−)CH2 C(=O)CH2 CH3 CH3 C(=O)CH2 CH2 (−H)

B3LYP

G3MP2B3

G3

89.88 96.32 100.58

90.29 95.55 100.65

90.95 95.67 100.54

Fig. 1. Potential energy curve for CH3 C(=O)CH• CH3 to ketene + methyl and allene + OH.

studied by Alligood et al. [36]. This radical can also undergo a beta scission to methylketene + CH3 . Figure 1 shows the energetics of these reactions. A hydrogen abstraction from the first carbon (C-1) to the oxygen takes place to form the CH2 =C(OH)CH• CH3 radical through a high barrier of 56 kcal mol−1 (TS0). The alcohol radical formed reacts further and undergoes a dissociation reaction to CH2 =C=CHCH3 + • OH (TS01) but needs to surmount a 55 kcal mol−1 barrier. A dissociation reaction is also possible to form ketene plus a CH3 radical (TS02) over a lower barrier of 44 kcal mol−1 . This lower energy path dominates the dissociation. These scissions have significant barriers which leaves this alkyl radical subject to reaction with O2 . Figure 2 illustrates five major reaction paths in the CH3 C(=O)CH• CH3 + O2 reaction system. The association results in a chemically activated peroxy radical [CH3 C(=O)CHOO• CH3 ]# which reactions available to this energized adduct include: 1. 2. 3. 4. 5. 6. 7. 8.

Formation of a stable peroxy radical Reverse reaction back to 2-butanone-3yl radical + O2 (no reaction) Peroxy radical addition at the carbonyl carbon forming a cyclic peroxide ring (TS1) Intramolecular abstraction of H from the carbon (C-3) by the peroxy site (TS2) Intramolecular abstraction of H from the carbon (C-4) by the peroxy site (TS3) Intramolecular abstraction of H from the carbon (C-1) by the peroxy site (TS4) RO−O bond cleavage, (only important at very high temperature) (TS5) Elimination of HO2 radical (TS6)

A detailed description of these reaction paths is given in the following sections. The transition state structures of the continuing reactions from each of these primary paths


1008

Table 6. Input parametersa and high-pressure limit rate constants (k∞ ) for QRRK calculations. Reaction

CH3 C(=O)CH• CH3 + O2 → CH3 C(=O)CHOO• CH3 CH3 C(=O)CHOO• CH3 → CH3 C(=O)CH• CH3 + O2 CH3 C(=O)CHOO• CH3 → CH3 Y(C(O• )OOCH)CH3 CH3 C(=O)CHOO• CH3 → CH3 C(=O)C(=O)CH3 + OH CH3 C(=O)CHOO• CH3 → CH3 C(=O)CHOOHCH•2 CH3 C(=O)CHOO• CH3 → CH2 C(=O)CH(OOH)CH3 CH3 C(=O)CHOO• CH3 → CH3 C(=O)CHO• CH3 + O CH3 C(=O)CHOO• CH3 → CH3 C(=O)CH=CH2 + HO2

A

1.00 × 10+12 1.02 × 10+15 2.37 × 10+14 8.69 × 10+12 7.34 × 10+12 2.52 × 10+12 9.02 × 10+14 1.65 × 10+11

k∞ n

Ea (kcal mol−1 )

0.0 0.0 −0.83731 −0.07671 −0.27081 −0.25097 0.0 0.69995

0.0 25.1 36.33 39.2 36.81 27.95 58.5 27.49

The units of A factors and rate constants k are s−1 for unimolecular reactions and cm3 mol−1 s−1 for bimolecular reactions. All parameters A, n, and E a are fit over the temperature range of 500–2400 K.

a

Fig. 2. Major channels for the CH3 C(=O)CH• CH3 + O2 reaction system.

are numbered according to the respective initial path TS1-1, TS1-2 ... for TS1, TS2-1 for TS2 etc., as illustrated in Tables 3 and 4 and Fig. 3. 3.4.1 Formation of the stabilized peroxy radical The association reaction of the 2-butanone radicals with O2 results in formation of activated peroxy radicals. 2-butanone has three radical sites for the addition of O2 . The reaction forms the activated peroxy [CH2 OO• C(=O)CH2 CH3 ]# , [CH3 C(=O)CHOO• CH3 ]# and [CH3 C(=O)CH2 CH2 OO• ]# intermediates with no barrier and a relatively loose transition state structures. In recent studies we have determined the potential energy surface (PES) for the dissociation of C6 H5 C(=O)OO• to C6 H5 C• (=O) + O2 [34,35] and


1009


N. Sebbar et al.

Fig. 3. The CH3 C(=O)CH• CH3 + O2 system.

of the C6 H5 COO• to C6 H5 C• + O2 [37,38] by calculating the structure and energy of C6 H5 C(=O)OO• and C6 H5 COO• vs. the C−OO distance. Our DFT calculations did not show a saddle point for these benzoyl and the phenyl systems. Only one peroxy radical system is considered in this study. We selected CH3 C(=O)CHOO• CH3 since the C−H bond in the secondary carbon adjacent to the carbonyl group (−C=O) in CH3 C(=O)CH(−H)CH3 has the lowest bond energy value at 90 kcal mol−1 as shown in Table 5. Preliminary BE values on the two primary radical sites are included in conference proceedings [39,40]. The peroxy intermediate form association of 3 O2 with the 2-butanone-3yl radical, CH3 C(=O)CHOO• CH3 shows a fairly shallow well depth of 26.6 kcal mol−1 from the G3 calculation level at 298 K. This shallow well is a result of loss of resonance between the carbon radical and the carbonyl group. This stabilized CH3 C(=O)CHOO• CH3 peroxy radical is an important product at lower temperatures. At moderate to higher temperature combustion conditions it will undergo a reverse reaction due to the shallow, 26 kcal mol−1 , well depth and loose transition state structure. Figure 3 shows the reactions available to this adduct. 3.4.2 Addition of the peroxy-oxygen radical to the carbonyl group carbon C-2 (TS1) Intramolecular addition of the peroxy oxygen radical site on the carbonyl group is generally not considered in the peroxy chemistry, because it is endothermic relative to the R• + O2 entrance channel. It breaks the strong (∼ 80 kcal mol−1 ) carbonyl double bond with the formation of a highly reactive dioxetane-ring radical (see Fig. 3). This addition to the carbonyl has a barrier of 35 kcal mol−1 , relative to the peroxy rad-


1010

1011

ical, and a tight transition state; it is 9 kcal mol−1 above the entrance channel. This dioxetane radical, when formed, dissociates rapidly through a very low or no barrier (TS11 < 1 kcal mol−1 ) to CH3 CH=O + CH3 C(=O)O• with a release of 96 kcal mol−1 . 3.4.3 Intramolecular hydrogen abstraction (ipso) from secondary carbon C-3 (TS2) The peroxy oxygen radical attacks (abstracts) the H atom located on the secondary carbon (C-3), adjacent to the carbonyl group, via a strained four-member-ring transition state structure. The reaction forms a transient intermediate, CH3 C(=O)C• (OOH)CH3 . In this radical, the RO−OH bond cleaves immediately via electron re-arrangement as the O−OH bond is very weak (∼ 45 kcal mol−1 ) and this allows formation of the strong π bond (carbonyl) at 80 kcal mol−1 . The overall reaction forms the stable 2,3-butadione CH3 C(=O)C(=O)CH3 plus OH radical. The overall reaction is exothermic and releases some 25 kcal mol−1 relative to the stable peroxy. The initial H atom abstraction has a barrier of 36 kcal mol−1 , which is 9 kcal mol−1 higher than the entrance channel. The high barrier for the H transfer step and shallow chemical activation well limit the importance of this reaction path at low temperature, but it increases its importance at higher temperatures. 3.4.4 Intramolecular hydrogen abstraction from the primary carbon C-4 (TS3) A second hydroperoxide radical is formed via an intramolecular hydrogen atom abstraction from the C-4 primary carbon. This CH3 C(=O)CH(OOH)CH•2 is formed through a cyclic five-member ring structure. This H atom transfer has a 31 kcal mol−1 barrier relative to the peroxy radical, which is 4 kcal mol−1 above the entrance channel. The high barrier is a result of ring-strain and a strong primary C−H bond. The newly formed hydroperoxide radical will further dissociate to form a set of two energetic stable compounds with relatively low barriers. The first product set results from a beta scission reaction eliminating the hydroperoxide radical; it forms methyl vinyl ketone CH2 =CHC(=O)CH3 plus HO2 through a barrier of 13.3 kcal mol−1 (TS31). The second product set results from a ring closure and • OH elimination, through 12.3 kcal mol−1 (TS32) with G3MP2B3 calculations, to form an oxiraneketone (CH3 C(=O)Y(CHOCH2 ), see Fig. 3) after dissociation of • OH. The overall reaction is exothermic with 17 kcal mol−1 . The high barrier, 10 kcal mol−1 above the entrance channel limits the importance of this channel to some extent. 3.4.5 Intramolecular hydrogen abstraction from primary carbon C-1 (TS4) Abstraction of a H atom from the primary carbon (C-1) adjacent to the carbonyl group, is the most energy favoured forward channel in this system. This is due to the low C−H bond energy on this methyl adjacent to the carbonyl group. It has the lowest barrier and the radical formed, CH•2 C(=O)CHOOHCH3 is the lowest-energy peroxide intermediate, at −34 kcal mol−1 . The energy needed by the peroxy radical to form this hydroperoxide is 27 kcal mol−1 (TS4) which is just at the energy level of entrance channel. The CH•2 C(=O)CHOOHCH3 further reacts to a set of products through two different barriers having energies similar to that of the entrance channel. The first set of low energy products formed are ketene (CH2 =C=O), acetaldehyde (CH3 CH=O) and • OH (TS41) with an excess of energy of 35 kcal mol−1 relative to the entrance chan-



N. Sebbar et al.

nel. The second set of products is formed at −45 kcal mol−1 (TS42) to a cyclic lactone CH3 Y(CHOCH2 C)=O and • OH (see Fig. 3). 3.4.6 Simple dissociation of the RO–O bond of the peroxide radical (TS5) A simple dissociation of the CH3 C(=O)CH(OO• )CH3 radical to CH3 C(=O)CHO• CH3 + O incurs a relatively high barrier (TS5) requiring 54 kcal mol−1 above the peroxide radicals energy. This barrier, is however, 6 kcal mol−1 lower than the reaction energy for a corresponding RO−O dissociation reaction on an alkane-peroxy radical and suggests that the adjacent carbonyl system reduces significantly the peroxy RO−O bond energy. While this is 27 kcal mol−1 above the entrance channel, this is a chain branching reaction and may have importance at high temperatures. The relatively unstable CH3 C(=O)CHO• CH3 radical will not exist, it dissociates rapidly through a low (less than 2 kcal mol−1 ) barrier (TS51), forming more energetically favorable products, acetaldehyde plus acetyl radical (CH3 CH(=O) + CH3 C• =O). 3.4.7 Molecular elimination of OOH radical from C-3 and C-4 (TS6) A molecular elimination reaction can occur from the interaction of the peroxy oxygen radical with the hydrogen atom of the adjacent carbon (C-4). HOO• elimination takes place via a concerted path with the formation of a carbon–carbon double bond. The energy needed by the peroxy radical (TS6) is at the same level of the entrance channel and the reaction is favorable. This molecular elimination reaction results in the formation of a stable methyl-vinyl-ketone and HOO• at an energy −26 kcal mol−1 which is 6.7 kcal mol−1 , (at the G3 level) below the entrance channel. This reaction is a second path to this product set formation and is responsible for a major fraction of the HOO• formation.

3.5 Kinetic calculations Multi-channel, multi-frequency QRRK [41] calculations are performed for k(E) with master equation analysis (CHEMASTER code) for fall-off on the CH3 C(=O)CH• CH3 + O2 , reaction systems to estimate rate constant and to determine important reaction paths as a function of temperature and pressure. The chemical activated peroxy radical intermediate [CH3 C(=O)CHOO• CH3 ]# is formed and can undergo further reactions before it is stabilized. The calculations provide sets of rate constants for the formation of the stabilized adduct or reaction products as a function of pressure and temperature. The bimolecular chemical activated kinetics use the barriers after the entrance channel as illustrated in Figs. 4 and 5. The QRRK with Master equation analysis is also used for unimolecular dissociation of each adduct. Pressure dependence is shown to be important for several product sets which can have effects in different combustion and engine systems. For example, scram jet engines run at 0.3 atm, turbines run at pressure of 10–15 atm, internal combustion engines experience pressures to 100 atm and higher pressures are suggested for improved efficiency. Table 6 presents high-pressurelimit kinetic parameters used as input data and Table 7 lists the reaction parameters at P = 1 atm for the temperature range of 500–2400 K. Reaction parameters at pressure ranging from 0.01 to 500 atm are listed in the supplementary material.


1012

1013

Fig. 4. Calculated temperature-dependent rate constants for the chemically activated CH3 C(=O)CH• CH3 + O2 system at P = 1 atm (path b are lower rate channels).

Fig. 5. Calculated pressure-dependent rate constants for the chemically activated CH3 C(=O)CH• CH3 + O2 at T = 500 K and 1100 K (path b are lower rate channels).

The chemical activation reaction paths for CH3 C(=O)CH• CH3 + O2 system are illustrated in Fig. 4 and show that the important forward reaction paths are the stabilization reaction to the CH3 C(=O)CHOO• CH3 peroxy radical and the hydrogen



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abstraction reaction on the primary carbon C-1, adjacent to the carbonyl group, to form CH•2 C(=O)CHOOHCH3 . Overall there are 7 product sets and several important intermediate isomers in this reaction system. The apparent rate constant calculation results are listed in several figures for clarity. The calculated temperature-dependent rate constants for the chemically activated CH3 C(=O)CH• CH3 + O2 reaction system from 500 to 2500 K at 1 atm are illustrated in Fig. 4. Below 600 K (Fig. 4a), the dominant product channel for this system is stabilization to the peroxy adduct CH3 C(=O)CHOO• CH3 ; the reverse reaction CH3 C(=O)CH• CH3 + O2 is also important. The next important channel is the HOO• molecular elimination (TS6) followed by the intramolecular Habstractions. The two channels with low rate constant are the O atom dissociation and the intramolecular peroxy radical addition to the carbonyl group. Above 600 K reverse reaction back to the 2 butanone-3yl radical plus O2 is shown to be dominant, because of the loose transition state structure. This is a non reaction and the radical can continue to react. At temperatures above 1000 K, we note the falloff of the stabilized peroxy, the H-abstraction from the primary carbons (C-1 and C-4) and the carbonyl attack all increase. The unimolecular dissociation of the stabilized peroxy radical as well as the diketone plus OH radical channel shows some importance with increasing temperature. The channels represented in Fig. 4b are in competition and lower in importance than species represented in Fig. 4a, but they all increase in importance as the temperature increases. We note also that the methylvinyl ketone + HOO• product set is formed through two channels, the most important being through the direct HOO• molecular elimination (TS6) from the peroxy radical. Figure 5a illustrates the pressure dependence for the rate constants (log k vs. P) of the chemically activated reaction systems at 500 and 1100 K. At the low temperature, stabilization to CH3 C(=O)CH2 CH2 OO• peroxy radical is the dominant channel at pressures above 0.1 atm. The HOO• molecular elimination reaction from the stabilized peroxy (TS6) is an important channels in this system and increases with temperature. The next important reaction is the formation of the primary ketone radical hydroperoxide CH•2 C(=O)CH(OOH)CH3 via (TS4), which rate constant is slightly lower at 1000 K than at 500 K. This decrease in rate is due to the increases in this hydroperoxide methyl radical dissociation to products. This hydroperoxide reacts further through two channels to form CH3 CH=O + CH2 =C=O + • OH and CH3 Y(CHOCH2 C)=O + • OH. These products are illustrated in Fig. 5b, in which one can observe their increase at high temperatures. The H-abstraction from carbon (C-4) (TS3) to form CH3 C(=O)CH(OOH)CH•2 is markedly slower (due to the higher barrier) but exhibits similar trends in rate as the Habstraction from the first primary carbon. The rate constant is lower at high temperature because as the temperature increases, the formation of CH3 C(=O)CH=CH2 + HO2 and the parallel channel, ring closure to form CH3 C(=O)Y(CHOCH2 ) + • OH are favoured as shown in Fig. 5b. The addition (attack) of the peroxy site at the carbonyl carbon (TS1) has low importance. At 500 K and above 1 atm, it is in competition with the other high barrier channel, the O atom dissociation reaction (TS5), which shows a similar rate constant. This peroxy radical addition to the carbonyl results in products, CH3 C=O + CH3 C(=O)O• ,


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Table 7. Calculated rate constants with QRRK at P = 1 atm. Reaction Calculated reaction parameters at P = 1 atm, k = A(T/K)n exp(−E a /RT) CH3 C(=O)CH• CH3 + O2 ⇔ CH3 C(=O)CHOO• CH3 CH3 C(=O)CH• CH3 + O2 ⇔ CH3 C(=O)CH• CH3 + O2 CH3 C(=O)CH• CH3 + O2 ⇔ CH3 C(=O)C(=O)CH3 + OH CH3 C(=O)CH• CH3 + O2 ⇔ CH3 C(=O)CHO• CH3 + O CH3 C(=O)CH• CH3 + O2 ⇔ CH3 C(=O)CH=CH2 + HO2 CH3 C(=O)CH• CH3 + O2 ⇔ CH3 Y(C(O• )OOCH)CH3 CH3 C(=O)CH• CH3 + O2 ⇔ CH3 CH(=O) + CH3 C(=O)O• CH3 C(=O)CH• CH3 + O2 ⇔ CH3 C(=O)CHOOHCH•2 CH3 C(=O)CH• CH3 + O2 ⇔ CH3 C(=O)CH=CH2 + HO2 CH3 C(=O)CH• CH3 + O2 ⇔ CH3 C(=O)Y(CHCH2 O) + OH CH3 C(=O)CH• CH3 + O2 ⇔ CH•2 C(=O)CH(OOH)CH3 CH3 C(=O)CH• CH3 + O2 ⇔ CH3 CH(=O) + CH2 =C=O + OH CH3 C(=O)CH• CH3 + O2 ⇔ CH3 Y(CHOCH2 C(=O)) + OH CH3 C(=O)CHOO• CH3 ⇔ CH3 C(=O)CH• CH3 + O2 CH3 C(=O)CHOO• CH3 ⇔ CH3 C(=O)C(=O)CH3 + OH CH3 C(=O)CHOO• CH3 ⇔ CH3 C(=O)CHO• CH3 + O CH3 C(=O)CHOO• CH3 ⇔ CH3 C(=O)CH=CH2 + HO2 CH3 C(=O)CHOO• CH3 ⇔ CH3 Y(C(O• )OOCH)CH3 CH3 C(=O)CHOO• CH3 ⇔ CH3 C(=O)CHOOHCH•2 CH3 C(=O)CHOO• CH3 ⇔ CH•2 C(=O)CH(OOH)CH3 CH3 Y(C(O• )OOCH)CH3 ⇔ CH3 CH(=O) + CH3 C(=O)O• CH3 Y(C(O• )OOCH)CH3 ⇔ CH3 C(=O)CHOO• CH3 CH3 C(=O)CHOOHCH•2 ⇔ CH3 C(=O)CH=CH2 + HO2 CH3 C(=O)CHOOHCH•2 ⇔ CH3 C(=O)Y(CHCH2 O) + OH CH3 C(=O)CHOOHCH•2 ⇔ CH3 C(=O)CHOO• CH3 CH•2 C(=O)CH(OOH)CH3 ⇔ CH3 CH(=O) + CH2 =C=O + OH CH•2 C(=O)CH(OOH)CH3 ⇔ CH3 Y(CHOCH2 C(=O)) + OH CH•2 C(=O)CH(OOH)CH3 ⇔ CH3 C(=O)CHOO• CH3

A

n

Ea (cal mol−1 )

1.08 × 10+111 2.57 × 10+19 1.57 × 10+15 5.06 × 10+27 1.06 × 10+14 2.16 × 10+86 1.55 × 10+16 3.09 × 10+106 3.97 × 10+16 5.27 × 10+15 4.68 × 10+121 6.14 × 10+35 4.53 × 10+30 4.21 × 10+46 1.32 × 10+49 1.31 × 10+43 2.86 × 10+44 2.45 × 10+50 9.05 × 10+48 3.78 × 10+45 2.47 × 10+41 8.49 × 10+40 6.99 × 10+33 6.29 × 10+32 5.20 × 10+32 4.06 × 10+38 2.37 × 10+39 2.73 × 10+33

−31.44 −2.06 −1.64 −4.71 −0.93 −27.90 −2.30 −32.12 −2.41 −2.01 −35.05 −7.72 −6.00 −10.60 −13.57 −14.13 −10.58 −13.90 −13.41 −11.56 −8.91 −9.02 −7.11 −6.60 −7.73 −8.34 −8.55 −6.88

32 686.00 5663.00 16 620.00 40 563.00 6587.00 32 506.00 13 514.00 37 043.00 15 661.00 15 198.00 45 868.00 23 766.00 25 799.00 32 075.00 41 590.00 53 832.00 34 180.00 40 029.00 40 262.00 34 285.00 29 514.00 29 516.00 20 550.00 20 390.00 21 846.00 31 143.00 35 681.00 24 278.00

a The units of A factors and rate constants k are s−1 for unimolecular reactions and cm3 mol−1 s−1 for bimolecular reactions. All parameters A, n, and E a are fit over the temperature range of 500–2400 K.

which show dominance over the O atom dissociation channel, but all the lower barrier channels are faster, even at high temperatures. Figure 6 shows the rate constants for the dissociation of the peroxy radical CH3 C(=O)CH(OO• )CH3 and Fig. 7a and b show the dissociation of two hydroperoxide intermediates radicals, CH•2 C(=O)CH(OOH)CH3 and CH3 C(=O)CH(OOH)CH•2 , as function of temperature at 1 atm. The dissociation of CH3 C(=O)CH(OO• )CH3 is dominated by the reverse reaction and the HO2 molecular elimination followed in importance by the H-abstraction from the first carbon. The last three reactions are lower in magnitude but still important. For both CH•2 C(=O)CH(OOH)CH3 and CH3 C(=O)CH(OOH)CH•2 radicals, the dissociation reactions show three major paths to products. The major difference between Fig. 7a and b is the importance of the reverse reaction channel, back to peroxy, CH3 C(=O)CH(OO• )CH3 , which is high in Fig. 7a while not dominant in Fig. 7b.


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Fig. 6. Calculated pressure-dependent rate constants for the dissociation reaction of CH3 C(=O)CHOO• CH3 at P = 1 atm.

Fig. 7. Calculated pressure-dependent rate constants for the dissociation CH•2 C(=O)CHOOHCH3 and (b) CH3 C(=O)CHOOHCH•2 at P = 1 atm.

reaction

of

(a)

4. Conclusions 0 The 2-butanone-3yl radical, CH3 C(=O)CH• CH3 (Δf H298 = 10.52 kcal mol−1 ), reacts with O2 to form a CH3 C(=O)CHOO• CH3 radical with a 26 kcal mol−1 well 0 , of important intermediates, transition state structures and depth. Enthalpy, Δf H298 products resulting from this association were determined by using DFT (B3LYP/6311G(d, p) level), ab-initio (G3MP2B3 and G3) and group additivity. Reaction channels for the energized adduct [CH3 C(=O)CHOO• CH3 ]# include dissociation back to reactants, stabilization, intramolecular reactions by hydrogen transfer to the per-


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oxy radical from three different carbon sites, elimination of HO2 , ring closure reaction to CH3 Y(CHOCH2 C(=O)) and CH3 C(=O)Y(CHOCH2 ) and dissociation to stable products and radicals CH3 CHO, CH3 C(=O)CH=CH2 , CH3 C(=O)C(=O)CH3 , CH2 =C=O, CH3 C• =O, CH3 C(=O)O• and • OH. Stabilization to the CH3 C(=O)CHOO• CH3 peroxy radical is the important forward reaction channel at low temperature. This is followed by molecular elimination of HO2 plus vinyl ketone formation and by abstraction of a hydrogen atom on the peroxy carbon (C-3) to form a 2,3-diketobutane + OH radical. All forward reactions to new products are at or just above the energy of the reverse reaction.

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