Quantum Chemical Study of Autoignition of Methyl Butanoate - The

Article pubs.acs.org/JPCA

Quantum Chemical Study of Autoignition of Methyl Butanoate Yuge Jiao, Feng Zhang,† and Theodore S. Dibble* Department of Chemistry, State University of New York, College of Environmental Science and Forestry, Syracuse, New York 13210, United States S Supporting Information *

ABSTRACT: Methyl butanoate is a widely studied surrogate for fatty acid esters used in biodiesel fuel. Here we report a detailed analysis of the thermodynamics and kinetics of the autoignition chemistry of methyl butanoate. We employ composite CBS-QB3 calculations to construct the potential energy profiles of radicals derived from methyl butanoate. We compare our results with recently published G3MP2B3 results for reactions of peroxy (ROO•) and hydroperoxy alkyl (•QOOH) radicals and comment on differences in barrier heights and reaction enthalpies. Our emphasis, however, is on hydroperoxy alkylperoxy (•OOQOOH) radicals that are critical for autoignition of diesel fuel. We examined four classes of reactions: peroxy radical interconversion of •OOQOOH (•OOQOOH→ HOOQOO•), H-migration reactions (from carbon to oxygen), HO2 elimination, and cyclic ether formation with elimination of OH radical. We evaluate the significance of reaction pathways by comparing rate coefficients in the highpressure limit. Unexpectedly, we find a low activation barriers for 1,8 H-migration of RC(O)OCH2OO•. We also find peroxy radical interconversion of •OOQOOH radicals from methyl butanoate commonly possess the lowest barriers of any unimolecular reaction of these radicals, despite that they proceed via 8-, 10- and 11-member ring transition states. At temperatures relevant to autoignition, these peroxy radical interconversions are dominant or significant reaction pathways. This means that some • OOQOOH radicals that were expected to be produced in negligible yields are, instead, major products in the autoignition of methylbutanoate (MB). These reactions have not previously been considered for MB, and will require revision of models of autoignition of methyl butanoate and other esters. radicals (MB•).9 In this temperature range, MB• can react with O2 and form one of four corresponding peroxy radicals (MBOO•, Scheme 2). These peroxy radicals can react unimolecularly to produce an olefinic ester and HO2, or isomerize to hydroperoxy alkyl radicals (•QOOH). •QOOH can unimolecularly decompose via concerted OH-loss or β-scission; also they can isomerize back to the peroxy radical. OH-loss or β-scission reactions involving •QOOH either propagate the radical chain reaction or lead to radical chain branching.10−13 Therefore, the fate of •QOOH derived from MB is of great interest. Other unimolecular reactions involving •QOOH including H-migration, OH-migration, and HO2-migration, which typically have higher activation barriers and are not competitive with the three reactions previously mentioned.14,15 In addition, •QOOH can combine with O2 to yield hydroperoxy alkylperoxy radicals (•OOQOOH). •OOQOOH can isomerize to dihydroperoxy alkyl radical or another •OOQOOH isomer.

1. INTRODUCTION Biofuel derived from various organisms may provide humankind with renewable energy. The use of biofuels can reduce both the net production of carbon dioxide as well as our dependence on traditional fossil fuels. Biodiesel, one form of biofuel, is typically derived from vegetable oils and animal fats. It is mainly composed of methyl or ethyl esters of long-chain fatty acids.1 Common biodiesel molecules include methyl linoleate, methyl palmitate, and methyl oleate. Mixtures of 20% biodiesel and 80% petroleum diesel can be easily used in most current diesel engines without any modification of equipment.2 Methyl butanoate (MB) has been widely used in both experimental and modeling studies of combustion as a surrogate for larger biodiesel molecules.3−5 The small size of the MB molecule reduces the chemical complexity, relative to the use of a fatty acid ester, in both experimental and theoretical studies. Use of MB also reduces the computational cost of quantum chemical or kinetic modeling studies. Despite MB’s widespread use as a surrogate, it should be noted that it cannot reproduce the negative temperature effect in low-temperature combustion of actual biodiesel.4,6−8 The mechanism of low-temperature (∼500 to 900 K) combustion of MB is shown in Scheme 1. The ignition of MB is mainly initiated by hydrogen abstraction with free radicals (OH•, H•, CH3•, or O•) to form one of four carbon centered © XXXX American Chemical Society

Special Issue: 100 Years of Combustion Kinetics at Argonne: A Festschrift for Lawrence B. Harding, Joe V. Michael, and Albert F. Wagner Received: December 8, 2014 Revised: March 9, 2015

A

DOI: 10.1021/jp5122118 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Scheme 1. Main Reactions in the Methyl Butanoate Oxidative Decomposition Mechanisma

a

Green squares signify products of chain propagation steps and the red square indicates the product of a chain termination step. The arrows in red are in the focus of the current study.

The CBS-QB3 method first optimizes geometries and determines harmonic vibrational frequencies at the B3LYP/6-311G(d,p) level of theory. Next the CCSD(T)/6-31+G(d′) and MP4SDQ/ CBSB4 single point energies are obtained and MP2 energies are extrapolated to the basis set limit. Finally, an empirical correction term is added. In CBS-QB3 calculations, the B3LYP/ 6-311G(d,p) zero-point energy (ZPE) is scaled by a factor of 0.99. CB3-QB3 has been widely employed in the study of peroxy radical chemistry17,22−25 owing to its cost efficiency and good accuracy. We determined the lowest energy conformer of each MB• (R1, R2, R3, and R5) at the CBS-QB3 level of theory. This conformation was retained in optimizing each MBOO•, and the orientation of the OO groups were optimized at CBS-QB3. We also determine the lowest energy conformers of all transition states for H-migrations of MBOO• at the CBS-QB3 level of theory. These conformations were used as starting points when transition states were searched for H-migrations of OOQOOH•, H-migrations of methyl pentanoate peroxy radical (MPOO•), and H-migrations of methyl hexanoate peroxy radical (MHOO•). For other species, we typically did not attempt to determine the lowest energy conformer. Implications of this are discussed in the Results and Discussion. All transition states were confirmed to possess one imaginary frequency. The identities of some transition states were verified by intrinsic reaction coordinate (IRC) calculations, the rest were identified by visualization of their structures. Canonical transition state theory was used to calculate the rate constants in the high-pressure limit as the following equation:

Scheme 2. Methyl Butanoate (MB), the Four CarbonCentered Radicals Formed by Hydrogen Abstraction from MB, and the Four Corresponding Peroxy Radicals

They can also decompose to keto-hydroperoxide or keto-alkoxy radical plus OH•, which can further contribute to the chain propagation.16,17 In this manuscript, we present details of the mechanism for autoignition of MB. We use electronic structure calculations to compute relative energies of various isomers of MB•, MB-OO•, • QOOH, and •OOQOOH derived from MB. Furthermore, we evaluate the significance of reaction pathways involving these species by comparing the relative barrier heights and rate constants in the high-pressure limit. Although our discussion will touch on reactions of MB•, MBOO•, and the corresponding • QOOH that have been reported previously in the literature,10,18 our discussion will emphasize •OOQOOH chemistry and the unexpectedly low barriers to 1,8 H-migrations for RC(O)OCH2OO•.

k(T ) =

kBT Q‡ −E‡ / RT · ·e h Qr

where kB and h are Planck’s and Boltzmann’s constants, respectively, Q‡ and Qr are the total partition functions for the transition state and reactant, respectively, E‡ is the activation barrier, and R is the gas constant. Tunneling corrections are included for H-migration reactions using the asymmetric Eckart formula as described in ref 26. Note that we do not treat any internal rotations through hindered rotor approximation in the present work except for two competing reactions for •OOQ1OOH. For those two

2. COMPUTATIONAL METHODS All electronic structure calculations were performed using the Gaussian09 program.19 Geometries were optimized and energies computed using the CBS-QB3 composite method.20,21 B


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The Journal of Physical Chemistry A

Table 2. CBS-QB3 and G3MP2B3 Activation Barriers ΔH‡ (at 0 K, in kcal/mol) and Reaction Enthalpies ΔrHo (at 0 K, in kcal/mol) of Cyclic Ether Formation Reactions of •QOOH from MBOO• a

Table 1. CBS-QB3 and G3MP2B3 (from Ref 10 or, in Parentheses, Ref 18) Bond Energies for MB−OO• and Activation Barriers ΔH‡ (at 0 K, in kcal/mol) and Reaction Enthalpies ΔrHo (at 0 K, in kcal/mol) of Hydrogen Migration and HO2-Elimination Reactions of MBOO• CBS-QB3 reaction R1• + O2 → R1OO• R2• + O2 → R2OO• R3• + O2 → R3OO• R5• + O2 → R5OO• R1OO• 1,4 H-migration 1,5 H-migration 1,8 H-migration HO2-elimination R2OO• 1,4 H-migrationa 1,4 H-migrationb 1,7 H-migration HO2-eliminationa HO2-eliminationb • R3OO 1,4 H-migration 1,5 H-migration 1,6 H-migration HO2-elimination R5OO• 1,6 H-migration 1,7 H-migration 1,8 H-migration

ΔH‡

ΔrHo

G3MP2B3 ΔH‡

−35.3 −36.7 −25.8 −33.6

ΔrHo −34.3 −34.7 −25.0 −32.8

32.8 19.9 25.4 31.4

15.2 8.9 14.2 19.9

35.4 (35.1) 22.9 (22.0) 27.2 (26.0) 31.6

11.9 5.9 11.6 18.7

32.5 35.4 27.8 26.9 32.1

9.4 17.0 15.2 19.6 23.5

-- (37.0) 37.4 (39.4) 28.6 (30.3) 27.3 30.5

9.6 16.4 13.6 17.1 21.3

31.6 22.2 30.2 29.1

11.3 13.7 11.5 16.7

32.8 (33.9) 25.5 (25.6) 31.8 (31.5) 26.0

10.4 11.9 10.3 12.0

26.3 22.3 20.6

3.7 8.7 11.2

28.2 (25.8) 24.1 (22.5) 21.9 (19.6)

4.6 9.4 12.0

a

Oxygen abstracts the hydrogen on the primary carbon. bOxygen abstracts the hydrogen on the secondary carbon.

The favored QOOH from each MBOO is indicated by a *; note that for R2OO, HO2-elimination is favored. bFrom ref 10. cG3MP2B3 values in parentheses were recalculated in the present work at the TS geometry obtained at CBS-QB3. a

cases, we compute the hindrance potential of the reactants and the transition states by relaxed scans of each torsional with 10° resolution at M06-2X/6-31+G(d,p).27 The potential is fitted by a Fourier series to solve the Schrödinger equation for the 1-D hindered rotor using MESMER.28 Note that this treatment yields inaccurate results due to the coupling of the torsional potentials to each other, which is particularly severe in hydrogen-bonded systems.16,29 An accurate treatment of the contribution of multiple conformers and torsional anharmonicity to the rate constants30 is beyond the scope of the current study.

the barrier heights and reaction enthalpies of cyclic ether formations and β-scissions of •QOOH at those two levels of theory. In these tables and following text, we name all •QOOHs as QmOOH-1n(-s or -p), where m denotes the parent RmOO• of this •QOOH, n denotes that this •QOOH is produced via 1,n H-migration, and -s or -p denotes the secondary or primary carbon of the radical sites. The CBS-QB3 reaction enthalpies for O2 addition to MB• are consistently 0.8−2.0 kcal/mol more negative than G3MP2B3 values. For H-migrations, CBS-QB3 energy barriers are consistently lower than the G3MP2B3 values of Tao and Lin (by 1.8 ± 0.8 (1 s.d.) kcal/mol, neglecting the first 1,4 H-migration reaction listed for R2OO• in Table 1. By contrast, CBS-QB3 reaction enthalpies are more endothermic than G3MP2B3 values (by 1.0 ± 1.5 kcal/mol). Note that Tao and Lin found that the lowest energy conformers of all QOOHs from MBOO•, at B3LYP/6-31G(d), have intramolecular hydrogen bonds; however, this is not true at CBS-QB3. Therefore, some of the geometries we report for QOOH species differ from those of Tao and Lin. For the four HO2-elimination reactions, CBSQB3 tends to predict higher endothermicities than G3MP2B3 (by 2.6 ± 1.5 kcal/mol), but there is no clear trend in activation barriers. The G3MP2B3 activation barriers of Hayes and Burgess for H-migration are lower than those of Tao and Lin by 0.6 ± 1.3 kcal/mol).

3. RESULTS AND DISCUSSION 3.1. MB•, MBOO•, and •QOOH Chemistries. The reactions between methyl butanoate and H• or OH• has been investigated theoretically by Huynh and Violi,9 AkihKumgeh and Bergthorson,31 Lin et al.,13 Zhang et al.,32 and Mendes et al.33 Hydrogen abstraction leading to formation of carbon-centered radicals (MB•) is the dominant pathway of these reactions, as shown in Scheme 2. A detailed kinetic model of reactions of MBOO• and •QOOH has been described in Tao and Lin.10 Below in Table 1 we compare the MB−OO• bond energies and the barrier heights and reaction enthalpies of the unimolecular reactions of MBOO• at two levels of theory: G3MP2B3 (from Tao and Lin10) and CBS-QB3 (from the present work). 1,3 H-migrations of alkylperoxy radicals have high energy barriers (∼40 kcal/mol)34,35 and are, therefore, neglected in the present study. In Tables 2 and 3 we compare C


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Table 3. CBS-QB3 and G3MP2B3 Activation Barriers ΔH‡ (at 0 K, in kcal/mol) and Reaction Enthalpies ΔrHo (at 0 K, in kcal/mol) of β-Scission and HO2-Elimination Reactions of •QOOH from MBOO• a G3MP2B3b

CBS-QB3 ‡

reactant

product

ΔH

Q1OOH-14 Q2OOH-14-p Q2OOH-14-s Q3OOH-14 *Q1OOH-15 *Q3OOH-15 *Q5OOH-18 Q1OOH-18 *Q2OOH-17 Q3OOH-16 Q5OOH-16 Q5OOH-17

CH2CHCH2C(O)OCH3 + HO2 CH2CHCH2C(O)OCH3 + HO2 CH3CHCHC(O)OCH3 + HO2 CH3CHCHC(O)OCH3 + HO2 CH2CHC(O)OCH3 + HCHO + OH HC(O)C(O)OCH3 + CH2CH2 + OH CH2•C(O)OCH2OOH + CH2CH2 HOOCH2CH2CH2C(O)• + HCHO CH3CH(OOH)CH2C(O)• + HCHO CH3CH2CH(OOH)C(O)• + HCHO CH2CHC(O)OCH2OOH + CH3• C•(O)OCH2OOH + CH3CHCH2

13.8 17.3 17.2 11.9 22.4 23.6 24.2 32.2 32.4 30.2 36.3 31.7

‡

ΔrH

ΔH

4.7 6.5 10.2 2.7 −6.5 −9.1 19.7 21.8 22.2 22.2 28.0 29.2

16.3 14.6 17.7 16.7 (14.8c) 32.2 (26.5c) 25.5 24.0 34.1 30.3 31.1 36.0 31.2

o

ΔrHo 3.7 4.9 7.5 1.6 −5.8 −10.6 18.5 24.2 (23.0d) 21.3 26.4 28.9

a G3MP2B3 values in parentheses are recalculated by us at the conformation obtained at CBS-QB3. The favored QOOH from each MBOO• is indicated by a *; note that for R2OO, HO2-elimination is favored. bFrom ref 10 (Tao and Lin). Values in parentheses use the TS geometry found in the present work rather than that of Tao and Lin. cGeometries of transition states obtained in this work have intramolecular hydrogen-bonding and the geometries in Tao and Lin do not. dValue is not provided by Tao and Lin. The value listed here was calculated by us from the geometry provided in their paper.

the size of the ring in the ether. The barrier to formation of a three-member ring is lower than that for larger rings, but the limited data and its scatter obscure any trends among the barriers to formation of larger rings. Table 3 lists the computed activation barriers and reaction enthalpies for β-scission reactions of QOOH, organized by the nature of the products. Here, trends in barrier height with product type do appear. For cyclic ether formation reactions, CBS-QB3 gives energy barriers 2.8 ± 2.5 (1 s.d.) kcal/mol lower than G3MP2B3. For β-scission reactions, CBS-QB3 energy barriers are also smaller than G3MP2B3 values by 0.7 ± 2.0 kcal/mol (Table 3). The two methods give fairly similar reaction enthalpies: CB3QB3 values are slightly smaller than G3MP2B3 values by an average of 0.6 kcal/mol for cyclic ether formations and 0.7 kcal/mol for β-scissions. Particularly large discrepancies in activation barriers are found for cyclic ether formation of Q1OOH-14 and Q1OOH-18; in these cases, G3MP2B3 energy barriers are 6.3 and 7.0 kcal/mol higher, respectively, than CB3-QB3 values. Note that for Q1OOH-18, the discrepancy was originally larger due to finding different conformers here than in ref 10. As can be seen by examining Tables 2 and 3, the CBS-QB3 and G3MP2B3 calculations give different predictions of the low-barrier unimolecular reaction path for five of the QOOH. Most significantly, this includes one of the three QOOH most likely to be formed: Q5OOH-18. For Q5OOH-18, Tao and Lin found β-scission to be favored by 2.3 kcal/mol, whereas CBSQB3 favors cyclic ether formation by 0.3 kcal/mol. 3.2. •OOQOOH Chemistry. For •OOQOOH we focus on the isomers formed from the addition of O2 to the QOOH most likely to be formed from each ROO• described above. Potential energy profiles of the reactions of these •OOQOOH are shown in Figure 1. For clarity, Figure 1 omits the highbarrier 1,4 H-migration reactions. Table 4 lists activation barriers and reaction enthalpies for all reactions, along with modified Arrhenius fits to high-pressure limit rate constants computed over the range 333−1000 K. The potential energy profiles of •OOQOOH show many similarities with those of •QOOH. The most important reaction channels of •OOQOOH radicals are hydrogen migration from a carbon or

The discrepancies between CBS-QB3 values and G3MP2B3 values have little effect on predictions of the relative rates of the unimolecular reactions considered in Table 1, except in the case of R3OO•. At the CBS-QB3 level of theory, 1,5 H-migration is the predominant pathway for R3OO• over the temperature range 500−900 K (in the high-pressure limit). At G3MP2B3, however, the gap in activation barriers between 1,5 H-migration and HO2-elimination is narrowed from 6.9 to 0.5 kcal/mol, so results from G3MP2B3 (but not CBS-QB3) would indicate that HO2-elimination can compete with 1,5 H-migration over this temperature range. A complete list of rate constants is presented in the Supporting Information. Critically, the loss of the resonance stabilization of R3• upon O2 addition leads to relatively weak R3−OO• binding. At CBS-QB3, the barrier to 1,5 H-migration is 3.6 kcal/mol less than the R3−OO bond energy, but at G3MP2B3 the barrier to 1,5 H-migration it is actually 0.8 kcal/mol higher than the R3−OO• bond energy. So the CBS-QB3 results predict much more flux via 1,5 H-migration of R3OO• than do the G3MP2B3 results. Note that Tao and Lin used a 1-D hindered rotor treatment to account for torsions for ROO• reactions. We can determine the effect of the 1-D hindered rotor treatment on rate constants by comparing our rate constants computed by them and by us (after accounting for the difference in barrier heights). For example, the rate constants for the reactions of R1OO• and R5OO• are changed by no more than a factor of 3 in the temperature range relevant to autoignition chemistry (700− 1000 K). Because the number of torsional degrees of freedom change similarly in going from reactants to the transition states for HO2-elimination or the various H-migration, rate constant ratios experience smaller changes than the rate constants, themselves (less than a factor of 2) due to cancellation of errors. So although the rate constants reported here could benefit from refinement of the treatment of conformers and anharmonicity, the rate constant ratios implied by these rate constants are expected to be more robust. Rate constants ratios would not be robust if we were also considering bond-scission reactions. For QOOH, Table 2 lists the computed activation barriers and reaction enthalpies for cyclic ether formation, organized by D


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These reactions have not previously been considered for the combustion chemistry of MB, but Miyoshi previously found peroxy radical interconversions be important in alkane-derived • OOQOOH.17 His computed barrier heights at CBS-QB3 for the analogous 1,7 H-migrations (15−17 kcal/mol) are slightly higher than our values. For both •OOQ1OOH and •OOQ3OOH, 1,5 H-migration with barrier heights of 19.7 and 17.6 kcal/mol, respectively, are the next most feasible reaction (Figure 1). 1,5 H-migrations are commonly favored due to the low strain energies of the sixmember ring of their transition states. The products of these 1,5 H-migration are α-QOOH species, which will dissociate without an energy barrier to form OH + keto-hydroperoxides.

an oxygen site to the peroxy site. HO2-elimination is feasible, if not usually competitive, for all listed •OOQOOH except • OOQ2OOH. An important reaction available to •OOQOOH but not ROO• is peroxy radical interconversion of the type •OOQOOH → HOOQOO•. For •OOQ1OOH, the lowest energy barrier pathway is 1,7 H-migration to form •OOQ3OOH. These two •OOQOOH radicals can isomerize rapidly via an eight-member ring transition state in which H atom moves back and forth between the two peroxy groups. The barrier heights are only 12.0 and 12.9 kcal/mol for these two reactions, and both have far larger rate constants than competing reactions in the temperature range of 333−1000 K (Table 4 and Figure 2).

Figure 1. continued E


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Figure 1. CBS-QB3 potential energy profiles of four •OOQOOH radicals derived from MB.

still outcompetes the 1,5 H-migration for •OOQ1OOH at temperatures below 1000 K. Both •OOQ1OOH and •OOQ3OOH are expected to form from their parent •QOOH to a large extent. The rapid interconversion of these two radicals and their similar energies (ΔHr = −0.9 kcal/mol at 0 K for •OOQ1OOH → •OOQ3OOH) means that, regardless of the branching ratios for their formation from MB, they will be present in comparable concentrations. As can be seen from Figure 1 and Table 4, the transition state for the lowest barrier reaction of •OOQ3OOH (1,5 H-migration) lies 3.0 kcal/ mol below that of •OOQ1OOH (1,7 H-migration), so we can expect that the major removal pathway for both these radicals is through 1,5 H-migration of •OOQ3OOH.

Keto-hydroperoxides can further decompose to form a second OH radical plus keto-alkoxy radicals. The production of two OH radicals in this reaction sequence causes radical chain branching, which is critical to autoignition. Rate constants including the 1-D hindered rotor treatment of (uncoupled) torsions are shown in Figure 3 for the two most competitive reactions of •OOQ1OOH: 1,5 H-migration and 1,7 H-migration. By including the hindered rotor effect, the high-pressure limit rate constants are reduced enormously: by a factor of 690−730 for 1,5 H-migration of •OOQ1OOH, and a factor of 20−330 for 1,7 H-migration of •OOQ1OOH. This fact implies that our pre-exponential factors may be overestimated due to not including internal rotations. Nevertheless, the 1,7 H-migration F


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Table 4. CBS-QB3 Energy barriers (ΔH‡, at 0 K, in kcal/mol), reaction enthalpies (ΔrH, at 0 K, in kcal/mol), and Fitted Arrhenius Equation Parameters to the Equation k = ATne−(E/(RT)) for Reactions of Four •OOQOOH Derived from MB (A in s−1, E/R in K) •

OOQOOH

•

OOQ1OOH

•

OOQ1′OOH

•

OOQ2OOH

•

OOQ3OOH

•

OOQ5OOH

•

OOQ5′OOH

a

reaction

ΔH‡

ΔrH

A

n −11

E/R

1,4 H-migration 1,5 H-migration 1,6 H-migration 1,7 H-migrationa HO2-elimination 1,6 H-migration 1,7 H-migration 1,8 H-migration 1,10 H-migrationa 1,6 H-migration 1,7 H-migration 1,8 H-migration 1,9 H-migrationa

33.6 19.7 30.6 12.0 29.8 26.4 23.0 13.5 14.5 27.6 20.6 20.6 13.6

12.4 6.0 12.7 −0.9 15.0 3.9 9.0 6.7 −4.7 9.6 −28.2 16.7 −0.1

7.737 1.772 7.903 7.551 1.895 1.259 1.307 1.497 6.110 2.831 6.191 1.120 2.051

× × × × × × × × × × × × ×

10 1004 10−03 1004 1010 10−06 10−05 1002 10−02 10−09 10−16 1004 10−01

7.016 2.391 4.355 1.930 0.960 5.575 4.814 2.426 3.424 6.151 7.995 1.956 3.310

1.055 6.329 1.151 3.469 1.491 8.927 7.501 4.362 3.847 9.011 4.054 8.494 3.495

× × × × × × × × × × × × ×

1004 1003 1004 1003 1004 1003 1003 1003 1003 1003 1003 1003 1003

1,4 H-migration 1,5 H-migration 1,7 H-migrationa 1,8 H-migration HO2-elimination 1,4 H-migration 1,5 H-migration 1,8 H-migration 1,10 H-migrationa HO2-elimination 1,7 H-migration 1,9 H-migrationa

34.5 17.6 12.9 25.0 29.9 37.4 23.5 29.2 19.2 30.1 22.8 13.7

13.3 6.5 0.9 13.6 19.5 13.7 8.6 −32.1 4.7 18.5 −37.3 0.1

2.250 2.587 4.330 4.412 3.730 1.567 1.002 4.592 7.335 1.509 2.420 1.677

× × × × × × × × × × × ×

10−19 10−16 1004 1000 1009 10−28 10−04 10−17 10−02 1009 10−08 10−01

9.393 8.100 1.926 2.960 1.161 12.347 4.750 8.278 3.439 0.897 5.710 3.351

9.138 1.774 4.101 9.578 1.537 8.998 7.883 8.343 6.303 1.498 6.896 3.541

× × × × × × × × × × × ×

1003 1003 1003 1003 1004 1003 1003 1003 1003 1004 1003 1003

Peroxy radical interconversion reaction.

Other possible reactions of •OOQ1OOH include 1,6 Hmigration and HO2-elimination. The product of 1,6 H-migration can undergo further decomposition to a cyclic ether plus OH radical, a reaction that propagates the radical chain (see the Supporting Information for the barrier heights and reaction enthalpies). However, the 1,6 H-migration and the HO2-elimination are kinetically insignificant in the temperature range of interest, as their high barriers lead to noncompetitive rate constants. For •OOQ3OOH, other reactions include 1,8 H-migration and HO2-elimination, but their rate constants amount to less than 1% of the rate constant of the 1,5 H-migration of •OOQ3OOH reactions until the temperature approaches 1000 K. Turning now to •OOQ2OOH, we find that the lowest barrier pathway is, once again, peroxy-radical interconversion. For •OOQ2OOH this reaction is a 1,9 H-migration (Figure 1) which interconverts •OOQ2OOH to the •OOQOOH (hereafter labeled •OOQ5′OOH) that would form following 1,7 H-migration of R5OO• and subsequent addition of O2. The 1,7 H-migration of R5OO• accounts for 21%−31% of all isomerizations of R5OO• at 333−1000 K (Table S1, Supporting Information). •OOQ2OOH was not expected to form directly by O2 addition to any great extent, because HO2-elimination is the dominant reaction of R2OO• in this temperature range. The 1,9 H-migration of •OOQ2OOH and its reverse reaction possess much higher rate constants than competing reactions, and the reactant and the product are similar in energy (ΔrH = −0.1 kcal/mol at 0 K); therefore, we can expect that these two radicals will be present in comparable concentrations. In addition to isomerization to •OOQ5′OOH, •OOQ2OOH can undergo 1,7 H-migration and 1,8 H-migration, both of

which have barriers heights of 20.6 kcal/mol. The 1,7 H-migration benefits from a lower activation entropy than the 1,8 H-migration; thus, the 1,7 H-migration dominates over the 1,8 H-migration. Note that we did not successfully optimize the α-QOOH product of 1,7 H-migration. The instability of α-QOOH has been confirmed by experimental study36 and theoretical studies.12,34,37 Here we assume the product can directly fall apart to OH plus a keto-hydroperoxide. The 1,6 Hmigration of •OOQ2OOH will be insignificant because of its much higher barrier. For •OOQ5OOH, peroxy radical interconversion via a 1,10 H-migration channel has the lowest energy barrier (19.2 kcal/ mol). The product, identified here as •OOQ1′OOH, would have been formed subsequent to the 1,8 H-shift of R1OO• that accounts for less than 1% of all H-migrations of R1OO•. This peroxy radical isomerization has a higher barrier than the other •OOQOOH interconversions considered above (12.0− 13.6 kcal/mol). It is not clear why this is the case; strain energy may play a role, but it is also possible that our efforts to find the lowest energy transition state were not successful. Because of the high barrier to peroxy-radical interconversion, the concentration ratios of these two •OOQOOH will probably not approach equilibrium. Instead, 1,5 H-migration of •OOQ5OOH with a barrier height of 23.6 kcal/mol and 1,8 H-migration of • OOQ1′OOH (Figure 1) with a barrier of only 13.5 kcal/mol have higher rate constants than the interconversion reactions (Table S2, Supporting Information). 1,8 H-migration of •OOQ1′OOH leads to concerted OH loss and is effectively irreversible. 1,5 H-migration of •OOQ5OOH leads to a resonance-stabilized radical whose most G


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Figure 2. Rate constants in the high-pressure limit for reactions of six •OOQOOH derived from MB calculated by CBS-QB3. Rate constants that are smaller than 1 s−1 are not shown. The asterisk (“*”) denotes peroxy radical interconversion reactions.

favored unimolecular reaction is back-reaction to regenerate • OOQ5OOH. 3.3. 1,8 H-Migration of Methyl-Ester Peroxy Radicals. Previous kinetic modeling studies of oxidation of hydrocarbons paid little attention to H-migration from carbon atoms via a nine-member (or larger) ring transition state of peroxy radicals. Quantum chemical studies in alkane-derived peroxy radicals showed that these H-migrations always have relatively high energy barriers. For example, Davis and Francisco38 reported the energy barrier of 1,8 H-migration (via a nine-member ring

transition state) of 1-hexyl peroxy as 26.3 kcal/mol at CBS-Q and 26.1 kcal/mol at G2. These values are greater than energies barriers (at the same level of theory) of all 1,5, 1,6, and 1,7 H-migrations for 1-propyl peroxy, 1-butyl peroxy, 1-pentyl peroxy, and 1-hexyl peroxy. Miyoshi17 investigated a series of H-migrations of peroxy radicals from small alkyl radicals by CBS-QB3 and found that the energy barriers of 1,8 H-migration are close to or slightly higher than those of 1,5, 1,6, and 1,7 H-migrations. These trends for alkane-derived peroxy radicals are consistent with Benson’s rule39−41 that H


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Figure 3. Revised rate constants for the two fastest reactions of • OOQ1OOH including the 1-D hindered rotor treatment (HR) or using harmonic oscillator approximation (HO) on both reactants and transition states.

Figure 5. Isodesmic reactions used to estimate the strain energies of the cyclic transition states from Glaude et al.42

indicates that the activation barriers decrease from 1,6 H-migration to 1,8 H-migration and increase slightly from 1,8 H-migration to 1,10 H-migration. One possible explanation for this would be changes in strain energy with the size of the ring in the transition state. The strain energies of lactones are also plotted in Figure 4, but we cannot find any correlation between the strain energies of lactones and the activation enthalpies of H-migrations with same ring size. Strain energies of lactones with two additional oxygen atoms in the cycle have been analyzed previously by Glaude et al.42 and Sy Tran et al.43 They proposed that the trends in activation energies of H-migration reactions can be inferred by examining trends the strain energy of the lactones. The isodesmic reactions they used to reveal trends in strain energy are shown in Figure 5. Their results indicated that formation of an eight-member ring lactone had higher strain energy (by 5 kcal/mol) than formation of a seven-member ring lactone. Their proposal is inconsistent with our findings and those of Hayes and Burgess and Tao and Lin, that 1,7 H-migrations of R5OO• have lower energy barriers than do 1,6 H-migrations. This indicates that the isodesmic reactions proposed by Glaude et al. do not provide insight into the factors controlling the barrier heights for the H-migration reactions. We are unable to provide an explanation for the trends in activation barrier depicted in Figure 4.

Figure 4. CBS-QB3 energy barriers of H-migration of the radicals methyl butanoate peroxy (MBOO•), methyl pentanoate peroxy (MPOO•), and methyl hexanoate peroxy (MHOO•), compared with G3MP2B3 activation energies of H-migration of MBOO• by Hayes and Burgess,18 and strain energies (SE) of lactones from ref 44.

estimates the activation energy of H-migration for ROO• radicals by summation of the reaction barrier for a bimolecular H-abstraction between an alkane and a ROO• and the ring strain of an (n+1)-cycloalkane, where n is the sum of carbon and oxygen atoms in the ring portion of the H-migration transition state. Although the neglect of larger ring transition states may be justified for peroxy radicals derived from hydrocarbons, this is not the case for the C3H7C(O)OCH2OO• radical (R5OO• in this work). Hayes and Burgess18 first reported that 1,8 H-migration of R5OO• has lower energy barrier than those of 1,6 and 1,7 H-migration at G3MP2B3 level of theory. Tao and Lin10 verified that 1,8 H-migration is the dominant pathway of all isomerizations of R5OO• in the temperature range 500−1000 K. Neither of them gave an explanation of the unusually low energy barrier for this 1,8 H-migration. Figure 4 shows the energy barriers of H-migration for three methyl-ester peroxy radicals when the peroxy group is on the methoxyl moiety of the ester (RC(O)OCH2OO•) and the hydrogen is shifted from the alkyl chain of ester. Figure 4

4. CONCLUSIONS In this study, we report on mechanisms of oxidative decomposition of methyl butanoate at autoignition temperatures. We find that activation barriers for some reactions are significantly (≥3 kcal/mol) different for CBS-QB3 and G3MP2B3. In one case (R3OO•), this leads to significantly different predictions of the competition between radical chain propagation and chain termination. Also, G3MP2B3 energy barriers for cyclic ether formation from Q1OOH-14 and Q5OOH-18 are 6−7 kcal/mol higher than CB3-QB3 values. Q5OOH-18 will be formed to a significant extent from R5OO•, and the discrepancy we observe calls into question whether the dominant unimolecular reaction of Q5OOH-18 will be β-scission or cyclic ether formation We investigated the chemistries of •OOQOOH radical derived from MB that have never been explored before. We find that the H-shift between two peroxy groups of •OOQOOH I


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are dominant, or at least, significant, in the temperature range of interest (500−900 K). These reactions form •OOQOOH isomers that were not otherwise expected to form to a great degree. Kinetic models of •OOQOOH chemistries of MB, as well as other esters, should be enlarged to include peroxy radical interconversions. H-migrations of •OOQOOH that produce OH + ketohydroperoxides have moderate barrier heights (∼20 kcal/mol, at CBS-QB3) and will be the dominant fates of most •OOQOOH considered here. These reactions lead to chain propagation or branching and, thereby, contribute to autoignition. In addition, we confirm the previously studied low energy barrier of 1,8 Hmigration of one MBOO• isomer (R5OO•) and find the barrier to 1,8 H-migration is also low for the analogous peroxy radicals from methyl pentanoate and methyl hexanoate. These unexpectedly low barriers conflict with previous estimations, and this implies that it is necessary adjust some parameters currently used for kinetic modeling of methyl ster combustion.

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates, vibrational frequencies, and absolute energies for all species calculated at the CBS-QB3 level of theory; rate constants in the high pressure limit as a function of temperature; fitting parameters for a modified Arrhenius equation for major reactions; torsional potentials for (a) •OOQ1OOH, (b) transition state for 1,5 H-migration for •OOQ1OOH, and (c) transition state for 1,7 H-migration for •OOQ1OOH. Complete ref 19. This material is available free of charge via the Internet at http://pubs.acs.org

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AUTHOR INFORMATION

Corresponding Author

*T. S. Dibble. E-mail: [email protected]. Phone: 315-470-6596. Present Address †

National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230029, P. R. China. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based on work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award Number DE-SC0002511. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575; specifically, it used the Blacklight system at the Pittsburgh Supercomputing Center (PSC).

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