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Theoretical and Kinetic Study of the Hydrogen Atom Abstraction Reactions of Esters with HȮ 2 Radicals Jorge Mendes, Chong-Wen Zhou,* and Henry J. Curran Combustion Chemistry Centre, National University of Ireland, Galway, Ireland S Supporting Information *

ABSTRACT: This work details an ab initio and chemical kinetic study of the hydrogen atom abstraction reactions by the hydroperoxyl radical (HȮ 2) on the following esters: methyl ethanoate, methyl propanoate, methyl butanoate, methyl pentanoate, methyl isobutyrate, ethyl ethanoate, propyl ethanoate, and isopropyl ethanoate. Geometry optimizations and frequency calculations of all of the species involved, as well as the hindrance potential descriptions for reactants and transition states, have been performed with the Møller−Plesset (MP2) method using the 6-311G(d,p) basis set. A validation of all of the connections between transition states and local minima was performed by intrinsic reaction coordinate calculations. Electronic energies for all of the species are reported at the CCSD(T)/cc-pVTZ level of theory in kcal mol−1 with the zero-point energy corrections. The CCSD(T)/CBS (extrapolated from CCSD(T)/cc-pVXZ, in which X = D, T, Q) was used for the reactions of methyl ethanoate + HȮ 2 radicals as a benchmark in the electronic energy calculations. High-pressure limit rate constants, in the temperature range 500−2000 K, have been calculated for all of the reaction channels using conventional transition state theory with asymmetric Eckart tunneling corrections. The 1-D hindered rotor approximation has been used for the low frequency torsional modes in both reactants and transition states. The calculated individual and total rate constants are reported for all of the reaction channels in each reaction system. A branching ratio analysis for each reaction site has also been investigated for all of the esters studied in this work.

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INTRODUCTION Interest in renewable biofuels has increased considerably in recent years due to concerns regarding the future availability of fossil fuels and their harmful emissions.1 Oxygenated liquid hydrocarbon fuels are being generated from biomass and their use helps reduce greenhouse gas emissions.2 These fuels have a relatively lower impact on CO2 emissions that are implicated in global warming, and their use limits mankind’s dependence on fossil fuels. Esters, with different length alkyl chains, represent an important class of biofuels. They are the primary component of biodiesel and are obtained from vegetable and other oils.1 The presence of oxygen atoms within the biodiesel fuel molecule may also reduce soot production in diesel engines.1 Their low sulfur content makes them attractive, allowing for reductions in NOx emissions from lean-burn engine exhaust.2 Diesel and diesel-hybrid engines can readily use these biofuels due to their inherent high thermal efficiencies when compared to spark ignition engines.2 Bio-derived fuels, however, present several challenges such as the difficulty and cost of production © XXXX American Chemical Society

in large quantities and their impact on the animal and human food chains.3 Theoretical investigations such as chemical kinetic studies can be used, together with experimental studies, to predict the reactivity of these fuels. Conventional fuels do not contain oxygen atoms within the primary fuel molecules. However, biofuels contain oxygen atoms that change the rates and mechanism of the reactions, leading to different products.3 Some biofuels, like ethanol or butanol, can be incorporated into conventional gasoline and used in spark-ignition engines, whereas others can be used as supplements or replacements in diesel engines.3 In the combustion temperature regime, hydrogen atom abstraction reactions by small radicals (Ö , Ḣ , Ȯ H, HȮ 2, and Ċ H3) from fuel molecules are always important in the oxidation of fuels.4 When HȮ 2 Received: September 12, 2013 Revised: October 23, 2013

A

dx.doi.org/10.1021/jp409133x | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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Figure 1. Methyl pentanoate (a) trans and (b) gauche conformers.

for each transition state using intrinsic reaction coordinate9 (IRC) calculations. The determination of local minima, or first-order saddle points, was performed by vibrational frequency analyses. The coupled-cluster approach with single and double substitutions, including perturbative estimates of the connected triples or CCSD(T) method10 was used with cc-pVXZ (X = D, T, Q), extrapolated to the complete basis set limit (CBS) to obtain more reliable energies along the potential energy surface (PES) for the hydrogen atom abstraction reactions of methyl ethanoate + HȮ 2 radical. The extrapolation to the CBS limit was determined with the use of the three-parameter equation provided by Peterson et al.:11

radicals abstract a hydrogen atom from an ester, hydrogen peroxide (H2O2) and an ester radical are formed. Furthermore, two highly reactive Ȯ H radicals are formed when H2O2 decomposes: RH + HȮ 2 → Ṙ + H 2O2 ̇ + OH( ̇ +M) H 2O2 ( +M) → OH

The stepwise reaction mechanism including a reactant complex (RC) formed in the entrance channel and product complex (PC) formed in the exit channel has been found for every reaction process in the hydrogen atom abstraction reaction of an ester with an HȮ 2 radical; the same was also shown in our previous work on ketones with HȮ 24 and Ȯ H5 radicals. Zhou et al.5 determined that two conformers with similar chemical properties exist for the α and β channels of the reactions of ketones with an Ȯ H radical.5 In this work, we have performed a conformer search and a Boltzmann conformer distribution (1000 K) calculated at the MP2/6311G(d,p) level of theory6 and we have found that eleven conformers exist for methyl pentanoate. The three lowest energy gauche conformers contribute 12% each to the distribution and are within 0.1 kcal mol−1 relative energy of each other. The trans conformer (Figure 1a) contributes 9% of the distribution and is 0.57 kcal mol−1 from the lowest energy conformer. The energy of the trans conformer in Figure 1a lies 4 kcal mol−1 lower than the gauche conformer in Figure 1b and has energy barriers of 4.5 and 5.7 kcal mol−1 for the α′−β′ and β′−γ′ hindrance potentials, respectively. Therefore, as with our previous work with ketones,4,5 we only consider the trans reactant conformers in our calculations. We are interested in studying the influence of the ester functional group (R′COOR) on the reactivity of the different types of hydrogen atoms, primary (1°), secondary (2°), and tertiary (3°), on the fuel molecule undergoing abstraction by the HȮ 2 radical. To the best of our knowledge, high level ab initio calculations have not previously been performed on these reactions. In our previous study on the addition and abstraction reactions of HȮ 2 radicals with ethyl methyl ketone (EMK)4,7 we found that hydrogen atom abstraction is about 2 orders of magnitude faster than addition over the temperature range 600− 1600 K. Thus, in this work we only consider hydrogen atom abstraction reactions. Herein, we detail a systematic study of the reaction mechanisms, potential energy surfaces, and high-pressure limit rate constant calculations of these reactions.

E(X ) = ECBS + A exp[− (X − 1)] + B exp[− (X − 1)2 ]

where X = 2, 3, 4 for the D, T, Q extrapolation. T1 diagnostics, which provides a description of the wave function,12 were used in the CCSD(T) energy calculations for all of the species involved in the above reaction mechanisms. They are all almost equivalent to, or less than, the 0.02 critical value, which indicates that the single reference method provides an adequate description of the wave function. The results obtained by the CCSD(T)/CBS method were used as a benchmark to the energies obtained by the computationally less expensive method of CCSD(T)/cc-pVTZ. The electronic energies of all of the species are calculated using the CCSD(T)/cc-pVTZ method with zeropoint corrections. A scaling factor of 0.9496 was used for all of the harmonic frequencies, as recommended by Merrick et al.13 Gaussian-0914 was used for all quantum chemistry calculations. ChemCraft15 was used for the visualization and determination of geometrical parameters.

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POTENTIAL ENERGY SURFACE Figure 2 and Table 1 clarify the different types of hydrogen atoms present and depict the labels we use in the title reactions.

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Figure 2. Labels in use in this work.

COMPUTATIONAL METHODS The Møller−Plesset8 (MP2) method using the 6-311G(d,p) basis set was employed in the geometry optimizations, frequency calculations, and hindrance potential treatment of reactants and transition states. The connection between each transition state and the corresponding local minima was confirmed

Figure 3 shows optimized geometries of all of the esters in this study. In the Supporting Information, Table S1 shows the CCSD(T)/cc-pVXZ (X = D, T, Q) single point energy calculations extrapolated to the complete basis set limit, CCSD(T)/CBS, for the reactions of methyl ethanoate + HȮ 2 B



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Table 1. Types of Hydrogen Atoms in This Work δ′ a b c d e f g h

methyl ethanoate (ME) methyl propanoate (MP) methyl butanoate (MB) methyl pentanoate (MPe) methyl isobutyrate (MiB) ethyl ethanoate (EE) propyl ethanoate (PE) isopropyl ethanoate (iPE)

CH3COOCH3 CH3CH2COOCH3 CH3(CH2)2COOCH3 CH(CH2)3COOCH3 (CH3)2CHCOOCH3 CH3COOCH2CH3 CH3COO(CH2)2CH3 CH3COOCH(CH3)2

1°

γ′

1° 2°

β′ 1° 2° 2° 1°

α′

α

β

γ

1° 2° 2° 2° 3° 1° 1° 1°

1° 1° 1° 1° 1° 2° 2° 3°

1° 2° 1°

1°

Figure 3. Optimized geometries of the esters in this work at MP2/6-311G(d,p) level of theory, showing the different types of hydrogen atoms.

Figure 4. Optimized geometries of an (a) in-plane and an (b) out-of-plane transition states of methyl ethanoate in this work at MP2/6-311G(d,p) level of theory.

Some of the species formed have the same energy and similar geometries and frequencies. For simplicity, only one of these is shown in the potential energy diagrams.

radicals and Table S2 details all of the geometry coordinates and frequencies of all of the species in the hydrogen atom abstraction reactions of esters + HȮ 2 radicals. C



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Figure 5. Hindrance potential of methyl ethanoate showing an (a) inplane and (b) out-of-plane transition state local minima.

Figure 7. Potential energy surface of the reactions of methyl ethanoate + HȮ 2 radical at the CCSD(T)/cc-pVTZ level of theory, in kcal mol−1.

In our previous work on ketones4 and in this work on esters, two types of hydrogen atoms are present, namely in-plane and out-of-plane hydrogen atoms, leading to in-plane (Figure 4a) and out-of-plane (Figure 4b) transition states, respectively. An internal rotation of a hindered rotor of the out-of-plane transition state can lead to the in-plane transition state, where a hydrogen bond is formed between the hydrogen atom of the hydroperoxyl radical and the oxygen atom of the carbonyl group of the ester. Figure 5 shows a hindrance potential of methyl ethanoate showing the local minima corresponding to the (a) in-plane and (b) out-of-plane transition states. In the reactions of the esters with the HȮ 2 radical, these two different transition states have similar energies; therefore, we only consider the lowest energy transition states in this work and all the low frequency torsional modes are treated as hindered rotors. Most of the reactant complexes in this work will form a hydrogen bond between the oxygen atom of the carbonyl group of the ester and the hydrogen atom of the hydroperoxyl radical (Figure 6a). Some reactant complexes will form a hydrogen bond between the oxygen atom of the alkoxy moiety of the ester and the hydrogen atom of the hydroperoxyl radical (Figure 6b). The reactant complexes where a hydrogen bond

Figure 8. Potential energy surface of the reactions of methyl propanoate + HȮ 2 radical at the CCSD(T)/cc-pVTZ level of theory, in kcal mol−1.

is not formed undergo a weaker van der Waals interaction between the ester and the HȮ 2 radical. The energy of the

Figure 6. Reactant complexes showing the formation of a hydrogen bond between the hydrogen atom of the hydroperoxyl radical and (a) the oxygen atom of the carbonyl group of the ester and (b) the oxygen atom of the alkoxy moiety of the ester. D



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Figure 9. Potential energy surface of the reactions of methyl butanoate + HȮ 2 radical at the CCSD(T)/cc-pVTZ level of theory, in kcal mol−1.

Figure 12. Potential energy surface of the reactions of ethyl ethanoate + HȮ 2 radical at the CCSD(T)/cc-pVTZ level of theory, in kcal mol−1.

Figure 10. Potential energy surface of the reactions of methyl pentanoate + HȮ 2 radical at the CCSD(T)/cc-pVTZ level of theory, in kcal mol−1.

Figure 13. Potential energy surface of the reactions of propyl ethanoate + HȮ 2 radical at the CCSD(T)/cc-pVTZ level of theory, in kcal mol−1.

Figure 11. Potential energy surface of the reactions of methyl isobutyrate + HȮ 2 radical at the CCSD(T)/cc-pVTZ level of theory, in kcal mol−1.

Figure 14. Potential energy surface of the reactions of isopropyl ethanoate + HȮ 2 radical at the CCSD(T)/cc-pVTZ level of theory, in kcal mol−1.

products formed upon abstraction by the HȮ 2 radical is higher than the corresponding product complexes and their geometries are not considerably different (Table S2 in the Supporting Information). The potential energy surface for methyl ethanoate (ME) reacting with an HȮ 2 radical, obtained at CCSD(T)/cc-pVTZ

and CCSD(T)/CBS levels of theory (energies in kcal mol−1) is shown in Figure 7, from which we find that the relative energy obtained by these two methods are within 1 kcal mol−1 of one another. Due to the computational cost of the CCSD(T)/CBS E



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Table 2. Comparison of the Lowest Relative Electronic Energies of the Transition States to the Reactants for Ketones + HȮ 2 Radical4 with that of Esters + HȮ 2 Radical in This Work (in kcal mol−1) δ′ estersx

ketones

a

ME MP MB MPe MiB EE PE iPE DMK EMK nPMK iPMK iBMK

20.9

γ′

19.7 16.6a

β′ 18.6 15.5a 15.0a 18.5

α′

α

β

γ

20.3 17.1a 15.9a 15.7a 14.4b 20.0 20.0 19.8 20.2 19.7 19.6 19.1 19.6

18.7 18.5 18.5 18.4 18.2 15.5a 14.9a 14.1b

21.5 18.5a 22.2

20.7

16.6a 15.8a 14.2b 15.4a

18.6 15.5a 18.3 13.0

19.3 16.4

2° hydrogen atom. b3° hydrogen atom.

Figure 15. Rate constants comparison, in cm3 mol−1 s−1, for the reactions of esters + HȮ 2 radicals at the α′ position (1°, 2°, and 3° hydrogen atoms) and at the β′ position (1° hydrogen atom): (a) methyl ethanoate (green), ethyl ethanoate (red), propyl ethanoate (blue) and isopropyl ethanoate (magenta); (b) methyl propanoate (black), methyl butanoate (red), and methyl pentanoate (blue); (c) methyl isobutyrate (red); (d) methyl propanoate (blue) and methyl isobutyrate (red); ketones + HȮ 24 (dashed) and alkanes + HȮ 216 (dotted). F



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Table 4. Recommended Fit Parameters, A, n, and E, According to Hydrogen Atom Type and Position Relative to the Carbonyl Group of the Ester, on a per-Hydrogen Atom Basis, in cm3 mol−1 s−1 a

Table 3. Rate Constants on a per Hydrogen Atom Basis, in cm3 mol−1 s−1, for the Different Abstraction Positions of the Esters in This Work (a) Methyl Ethanoate: CH3COOCH3 + HȮ 2

k(α′) = 3.47 × 10−4T 4.61 exp(− 7896/T ) k(α) = 2.04 × 10−6T 5.23 exp(− 6992/T )

primary, α′ secondary, α′ tertiary, α′ primary, β′ secondary, β′ primary, γ′ secondary, γ′ primary, δ′ primary, α secondary, α tertiary, α primary, β secondary, β primary, γ

(2)

(b) Methyl Propanoate: CH3CH2COOCH3 + HȮ 2

k(β′) = 2.77 × 10−4T 4.61 exp(− 7473/T )

(3)

k(α′) = 7.41 × 10−4T 4.39 exp(− 6005/T )

(4)

k(α) = 1.63 × 10−5T 4.94 exp(− 6701/T )

(5)

(c) Methyl Butanoate: CH3(CH2)2COOCH3 + HȮ 2

k(γ′) = 9.80 × 10−1T 3.63 exp(− 8494/T )

(6)

−3

4.28

exp(− 6064/T )

(7)

−4

4.39

exp(− 5860/T )

(8)

−5

4.76

exp(− 6887/T )

(9)

k(β′) = 3.75 × 10 T k(α′) = 8.11 × 10 T

k(α) = 4.92 × 10 T

(d) Methyl Pentanoate: CH3(CH2)3COOCH3 + HȮ 2

a

+1 3.10

exp(− 8626/T )

(10)

−1 3.62

exp(− 6850/T )

(11)

k(β′) = 2.89 × 10−5T 4.85 exp(− 5521/T )

(12)

k(δ′) = 8.95 × 10 T

k(γ′) = 5.59 × 10 T

−3

4.22

k(α′) = 1.53 × 10 T

exp(− 5562/T )

(13)

k(α) = 3.05 × 10−6T 5.07 exp(− 6656/T )

(14)

exp(− 5062/T )

(16)

−6 5.15

exp(− 6464/T )

(17)

k(α′) = 5.68 × 10 T

k(α) = 3.02 × 10 T

A

(f) Ethyl Ethanoate: CH3COOCH2CH3 + HȮ 2

a

k(α′) = 1.39 × 10−3T 4.40 exp(− 7857/T )

(18)

k(α) = 3.26 × 10−5T 4.86 exp(− 5580/T )

(19)

k(β) = 1.23 × 10−2T 4.31 exp(− 9418/T )

(20)

−5

(21)

4.86

exp(− 5220/T )

(22)

+1 3.30

exp(− 8123/T )

(23)

−4

exp(− 8164/T )

(24)

k(α) = 1.90 × 10 T k(β) = 1.32 × 10 T k(γ ) = 1.39 × 10 T

4.87

(h) Isopropyl Ethanoate: CH3COOCH(CH3)2 + HȮ 2

k(α′) = 1.02 × 10−3T 4.39 exp(− 7827/T ) −2 3.94

k(α) = 5.16 × 10 T k(β) = 3.90T

3.52

exp(− 5790/T )

exp(− 9573/T )

10−3 10−4 10−2 10−4 10−4 10−1 10−1 10+1 10−6 10−5 10−2 10−1 10+1 10−4

n

E

4.41 4.41 3.86 4.50 4.52 3.63 3.62 3.10 5.09 4.90 3.94 3.98 3.30 4.87

−7920 −5738 −5062 −7508 −5830 −8494 −6850 −8626 −6666 −5380 −5790 −9424 −8123 −8164

9.28 1.24 3.36 1.67 4.55 7.35 8.77 1.74

× × × × × × × ×

10−5 10−5 10−4 10−3 10−8 10−9 10−8 10−8

n

E

4.99 5.20 4.82 4.64 5.82 6.17 5.91 6.04

−7359 −5980 −5909 −6038 −4110 −5076 −5388 −4886

k = A × Tn × exp(−E/T).

complexes are formed in the exit channels in the range −2.9 to +12.4 kcal mol−1. For the abstraction of an α′ hydrogen atom, the reactant complexes RC1a, RC2b, RC3c, RC4d, RC2e, RC1f, RC1g, and RC1h will go through TS1a for methyl ethanoate, TS2b for methyl propanoate, TS3c for methyl butanoate, TS4d for methyl pentanoate, TS2e for methyl isobutyrate, TS1f for ethyl ethanoate, TS1g for propyl ethanoate, and TS1h for isopropyl ethanoate. In the reaction mechanism of methyl ethanoate, TS1a will form the product complex PC1a in the exit channels with a relative energy of 6.2 kcal mol−1. For the above remaining esters the corresponding product complexes are formed with relative energies in the range −2.9 to +5.9 kcal mol−1. Subsequent abstraction of a hydrogen atom leads to the formation of H2O2 and a corresponding α′ radical: P1a (1° radical) for methyl ethanoate at 12.7 kcal mol−1, P2b (2° radical) for methyl propanoate at 7.7 kcal mol−1, P3c (2° radical) for methyl butanoate at 8.4 kcal mol−1, P4d (2° radical) for methyl pentanoate at 8.1 kcal mol−1, P2e (3° radical) for methyl isobutyrate at 4.6 kcal mol−1 and P1f, P1g, and P1h (1° radical) for ethyl ethanoate, propyl ethanoate, and isopropyl ethanoate, respectively, at 12.6 kcal mol−1. For the remaining sites (β′, γ′, δ′, α, β, and γ), hydrogen atom abstraction reactions by an HȮ 2 radical are similar to what we observed for the α′ position, where the energies calculated are similar to the same positions in a ketone (α, β, etc.). The relative energies are detailed in Table 2 and the

(g) Propyl Ethanoate: CH3COO(CH2)2CH3 + HȮ 2

k(α′) = 6.97 × 10−3T 4.25 exp(− 8057/T )

× × × × × × × × × × × × × ×

k = A × Tn × exp(−E/T)

ME MP MB MPe MiB EE PE iPE

(15)

−2 3.86

1.48 5.41 5.68 4.93 4.57 9.80 5.59 8.95 4.53 1.89 5.16 1.37 1.32 1.39

Table 5. Total Rate Constants Fit Parameters, A, n, and E, in cm3 mol−1 s−1 a

(e) Methyl Isobutyrate: (CH3)2CHCOOCH3 + HȮ 2

k(β′) = 1.55 × 10−3T 4.30 exp(− 7581/T )

A

hydrogen atom type

(1)

(25) (26)

(27)

method for the other larger reaction systems investigated in this work, we adopted the less expensive CCSD(T)/cc-pVTZ method to calculate the electronic energies for these reaction systems. Potential energy surfaces obtained at the CCSD(T)/cc-pVTZ level of theory are shown in Figure 8 for methyl propanoate (MP), in Figure 9 for methyl butanoate (MB), in Figure 10 for methyl pentanoate (MPe), in Figure 11 for methyl isobutyrate (MiB), in Figure 12 for ethyl ethanoate (EE), in Figure 13 for propyl ethanoate (PE) and in Figure 14 for isopropyl ethanoate (iPE). Reactant complexes are formed in the entrance channels and are in the range −9.8 to −1.9 kcal mol−1, and product G



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Figure 16. Rate constants comparison, in cm3 mol−1 s−1, for the reactions of esters + HȮ 2 radicals at the β′ position (2° hydrogen atom), at the γ′ position (1° and 2° hydrogen atoms) and at the δ′ position (1° hydrogen atom): (a) methyl butanoate (blue) and methyl pentanoate (red); (b) methyl butanoate (red); (c) methyl pentanoate (red); (d) methyl pentanoate (red); ketones + HȮ 24 (dashed) and alkanes + HȮ 216 (dotted).

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RATE CONSTANT CALCULATIONS The main objective of this work is to determine the highpressure limit rate constants for hydrogen atom abstraction reactions of the title reactions, based on the above potential energy surfaces and reaction mechanisms. Table S3 in the Supporting Information shows the individual rate constant comparisons for each ester, on a per site basis in cm3 mol−1 s−1. Conventional transition state theory with an asymmetric Eckart tunneling correction17 as implemented in Variflex v2.02m,18 is used in the temperature range 500−2000 K. The formation of the reactant complexes and the product complexes narrows the tunneling barrier which, at low temperatures, accelerates the tunneling effect and, consequently, the rate constants.4 The low-frequency torsional modes were treated as 1-D hindered rotors using the Pitzer−Gwinn-like19 approximation. The coupling that occurs between adjacent internal rotations and between internal and external rotations is sometimes too strong to be separated, which makes the torsional treatment difficult.

potential energy surfaces in Figures 8−14. A trend is observed where abstractions of 1°, 2°, and 3° hydrogen atoms at the α′ position have average relative energies of 20.0, 16.2, and 14.4 kcal mol−1, respectively. At the α position, abstractions of 1°, 2°, and 3° hydrogen atoms have average relative energies of 18.5, 15.2, and 14.1 kcal mol−1, respectively. At the β′ position, abstractions of 1° and 2° hydrogen atoms have average relative energies of 18.6 and 15.3 kcal mol−1, respectively. At the β position, abstractions of 1° and 2° hydrogen atoms have an average relative energy of 21.9 and 18.5 kcal mol−1, respectively. These energies are similar to the ones obtained at the corresponding sites in our previous work for the ketones4 (Table 2). At the γ′ position of MB and at the γ position of PE, the relative energies of the transition states are similar to the ones obtained at the γ position of nPMK and to those of an alkane.16 At the γ′ (2° hydrogen atom) and δ′ (1° hydrogen atom) positions of MPe the energies are also similar to those of an alkane.16 H



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Figure 17. Rate constants comparison, in cm3 mol−1 s−1, for the reactions of esters + HȮ 2 radicals at the α position (1°, 2°, and 3° hydrogen atoms) and at the β position (1° hydrogen atom): (a) methyl ethanoate (black), methyl propanoate (green), methyl butanoate (blue), methyl pentanoate (purple) and methyl isobutyrate (magenta); (b) ethyl ethanoate (blue) and propyl ethanoate (red); (c) isopropyl ethanoate (red); (d) ethyl ethanoate (red) and isopropyl ethanoate (blue); ketones + HȮ 24 (dashed) and alkanes + HȮ 216 (dotted).

group, with an average error of 4.6% and a maximum error of no more than 10.0% in the fit. The temperature dependence of the calculated rate constants is shown in Figures 15−18 for the α′ (1°, 2°, and 3°), β′ (1° and 2°), γ′ (1° and 2°), δ′ (1°), α (1°, 2°, and 3°), β (1° and 2°), and γ (1°) hydrogen atom abstraction reactions of esters + HȮ 2 radicals. A comparison is made with abstraction from ketones4 and alkanes16 by an HȮ 2 radical. Figures 15 and 16 show the calculated rate constants at the R′ side of the molecule (α′, β′, γ′, and δ′ positions). A trend is observed for all of the esters, where the calculated rate constants are similar to those of the ketones4 at the corresponding reaction site. Panels a−d of Figure 15 and panels a and c of Figure 16 show the rate constants for abstraction of a 1°, 2°, and 3° hydrogen atom at the α′ position, a 1° hydrogen atom at the β′ position, and a 2° hydrogen atom at the β′ and γ′ positions, respectively, and when compared to abstraction from

As all of the internal rotations in this study are separable, the 1-D torsional treatment is the best we can do, at present. Truhlar and co-workers20,21 have developed the multistructure method, which deals with this torsional coupling problem. It is shown by their application to the hydrogen atom abstraction reactions in the n-butanol + HȮ 2 system that their multistructure method results are quite similar to our 1-D hindered rotor treatment results in both the α and γ hydrogen atom abstraction rate constants.22 The hindrance potentials were determined around every possible dihedral angle for the reactants and transition states. The remaining modes were treated as harmonic oscillators. These rate constants have been fitted to a three parameter modified Arrhenius equation (Tables 3−5) and they are reported on a per hydrogen atom basis, in cm3 mol−1 s−1. Table 4 shows the Arrhenius fits for the calculated average high-pressure limit rate constants at the different positions relative to the R′COOR I



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Figure 18. Rate constants comparison, in cm3 mol−1 s−1, for the reactions of esters + HȮ 2 radicals at the β position (2° hydrogen atom) and at the γ position (1° hydrogen atom): (a) propyl ethanoate (red); (b) propyl ethanoate (red); ketones + HȮ 24 (dashed) and alkanes + HȮ 216 (dotted).

the alkanes,16 they are generally slower by about an order of magnitude from 500 to 2000 K. Figure 16b shows the rate constants for abstraction of a 1° hydrogen atom at the γ′ position, which is slower than that from an alkane16 by about a factor of 4 from 500 to 2000 K. At the δ′ position (Figure 16d), abstraction of a 1° hydrogen atom is slower than abstraction from alkanes16 by 40% at 500 K and by a factor of 3 at 2000 K. Figures 17 and 18 show the calculated rate constants at the R side of the molecule (α, β, and γ positions). Panels a−c of Figure 17 show the rate constants for abstraction of a 1°, 2°, and 3° hydrogen atom at the α position, respectively. When comparing to the case for the alkanes,16 abstraction of an α 1° hydrogen atom is slower by a factor of 2 and 7 at 500 and 2000 K, respectively. A 2° hydrogen atom is slower by a factor of 5 at 500 K and 8 at 2000 K whereas a 3° hydrogen atom is slower by a factor of 22 and 10 at 600 and 2000 K, respectively. Abstraction of a β 1° hydrogen atom (Figure 17d) is slower than abstraction from alkanes16 by a factor of 21 and 5 at 500 and 2000 K, respectively. Abstraction of a 2° hydrogen atom at the same position (Figure 18a) is slower by a factor of 40 at 500 K and a factor of 8 at 2000 K. For a γ 1° hydrogen atom (Figure 18b), abstraction is slower than abstraction from alkanes16 by a factor of 7 and 3 at 600 and 2000 K, respectively. The rate constants for hydrogen atom abstraction from the esters calculated in this work are similar for the same type of hydrogen atom (1°, 2°, or 3°) on either side of the ester functional group (R′COOR). Moreover, they are also similar to the calculated rate constants at the corresponding site in our previous work on ketones.4 Steric repulsion affects some of the geometries of the transition states (Table S2 in the Supporting Information), which have higher energies when compared to the corresponding position in the ketones.4 In our previous work23 we calculated the rate constants for the hydrogen atom abstraction by Ċ H3 radical from the different sites of n-butanol and the results from the three different kinetic programs are within a factor of 2.5. We have performed consistent similar kinetics treatment in this work, and on the basis of that comparison, we estimate that the overall uncertainty in our calculated rate constants is a factor of 2.5. This is due to uncertainties in the electronic energy

calculations, tunneling effects, treatment of some critical internal rotation modes, etc.

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BRANCHING RATIOS As shown in Figure 19, a branching ratio analysis for each reaction channel has been carried out in the temperature range 500−2000 K. Figure 19a shows the branching ratio for methyl ethanoate, and abstraction from the α position is dominant throughout. Figure 19b shows the branching ratios for methyl propanoate where the α′ position dominates from 500 K (73%) to 1200 K (37%) and the α position dominates above 1200 K. For methyl butanoate, Figure 19c, abstraction from the β′ position dominates from 500 K (55%) to 2000 K (34%). Figure 19d details the branching ratio for methyl pentanoate and shows that abstraction from the β′ position is dominant from 500 to 800 K. The branching ratio of this channel is 35% at 500 K decreasing to 22% at 2000 K. Abstraction from the δ′ position is dominant above 800 K, becoming more and more important as the temperature increases. The branching ratio of this channel increases from 6% at 500 K to 39% at 2000 K. For methyl isobutyrate, Figure 19e, abstraction from the α′ position is dominant in the temperature range 500−1600 K. The branching ratio of this channel decreases from 96% at 500 K to 36% at 1600 K and then to 26% at 2000 K. The other two channels of α and β′ become important as the temperature rises. The branching ratio of the β′ channel increases from 2% at 500 K to 36% at 2000 K. The branching ratio of the α channel increases from 3% at 500 K to 37% at 2000 K. Panels f−h of Figure 19 show the branching ratios for ethyl ethanoate, propyl ethanoate, and isopropyl ethanoate, respectively. For ethyl ethanoate, abstraction from the α position dominates at low temperatures in the range from 500 K (96%) to 1600 K (42%), reaching 34% at 2000 K. For propyl ethanoate, abstraction from the α position dominates from 500 K (83%) to 1200 K (27%). Above 1200 K abstraction from the γ position dominates, reaching 44% at 2000 K. For isopropyl ethanoate, abstraction from the α position dominates from 500 K (97%) to 1200 K (44%). Above 1200 K abstraction from the β position dominates, reaching 64% at 2000 K. J



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Figure 19. Predicted branching ratios for the different sites of each ester in this study, between 500 and 2000 K: (a) methyl ethanoate; (b) methyl propanoate; (c) methyl butanoate; (d) methyl pentanoate; (e) methyl isobutyrate; (f) ethyl ethanoate; (g) propyl ethanoate; (h) isopropyl ethanoate.

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SUMMARY

types of hydrogen atoms, are similar to the ones calculated in our previous work for the ketones,4 at the corresponding sites. Both the R′ and R sides of the ester behave similarly, which is possibly due to the electron delocalization of the R′COOR

In this work, a trend is observed where the rate constants for the hydrogen atom abstraction reactions of esters with HȮ 2 radicals at the α′, β′, γ′, δ′, α, β, and γ positions, with different K



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provided by the Irish Center for High-End Computing (ICHEC).

group. When comparing to the alkane behaviors calculated by Aguilera-Iparraguirre et al.,16 we observe that the rate constants for the esters in this work are slower throughout the entire temperature range from 500−2000 K. We also observe that the further the abstraction occurs from the R′COOR group of the ester, the lower its influence on the reactivity of the hydrogen atom.

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(1) Westbrook, C.; Pitz, W.; Westmoreland, P.; Dryer, F.; Chaos, M.; Osswald, P.; Kohse-Höinghaus, K.; Cool, T.; Wang, J.; Yang, B.; et al. A Detailed Chemical Kinetic Reaction Mechanism for Oxidation of Four Small Alkyl Esters in Laminar Premixed Flames. Proc. Combust. Inst. 2009, 32, 221−228. (2) Metcalfe, W. K.; Dooley, S.; Curran, H. J.; Simmie, J. M.; ElNahas, A. M.; Navarro, M. V. Experimental and Modeling Study of C5H10O2 Ethyl and Methyl Esters. J. Phys. Chem. A 2007, 111, 4001− 4014. (3) Westbrook, C. K.; Naik, C. V.; Herbinet, O.; Pitz, W. J.; Mehl, M.; Sarathy, S. M.; Curran, H. J. Detailed Chemical Kinetic Reaction Mechanisms for Soy and Rapeseed Biodiesel Fuels. Combust. Flame 2011, 158, 742−755. (4) Mendes, J.; Zhou, C.-W.; Curran, H. J. Theoretical and Kinetic Study of the Reactions of Ketones with HȮ 2 Radicals. Part I: Abstraction Reaction Channels. J. Phys. Chem. A 2013, 117, 4515− 4525. (5) Zhou, C.-W.; Simmie, J. M.; Curran, H. J. Ab initio and Kinetic Study of the Reaction of Ketones with Ȯ H for T=500−2000 K. Part I: Hydrogen-Abstraction from H3CC(O)CH3−x(CH3)x, x = 0 → 2. Phys. Chem. Chem. Phys. 2011, 13, 11175−11192. (6) Spartan’10 v1.1.0; Wavefunction Inc.: Irvine, CA, USA. (7) Zhou, C.-W.; Mendes, J.; Curran, H. J. Theoretical and Kinetic Study of the Reaction of Ethyl Methyl Ketone with HȮ 2 for T=600− 1600 K. Part II: Addition Reaction Channels. J. Phys. Chem. A 2013, 117, 4526−4533. (8) Møller, C.; Plesset, M. S. Note on an Approximation Treatment for Many-Electron Systems. Phys. Rev. 1934, 46, 618−622. (9) Gonzalez, C.; Schlegel, H. B. An Improved Algorithm for Reaction-Path Following. J. Chem. Phys. 1989, 90, 2154−2161. (10) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. Quadratic Configuration-Interaction - A General Technique for Determining Electron Correlation Energies. J. Chem. Phys. 1987, 87, 5968−5975. (11) Peterson, K. A.; Woon, D. E.; Dunning, T. H. Benchmark Calculations with Correlated Molecular Wave-Functions 0.4. The Classical Barrier Height of the H+H2 → H2+H Reaction. J. Chem. Phys. 1994, 100, 7410−7415. (12) Lee, T. J.; Rendell, A. P.; Taylor, P. R. Comparison of the Quadratic Configuration Interaction and Coupled-Cluster Approaches to Electron Correlation Including the Effect of Triple Excitations. J. Phys. Chem. 1990, 94, 5463−5468. (13) Merrick, J. P.; Moran, D.; Radom, L. An Evaluation of Harmonic Vibrational Frequency Scale Factors. J. Phys. Chem. A 2007, 111, 11683−11700. (14) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09 Revision A.1; Gaussian Inc.: Wallingford, CT, 2009. (15) Chemcraft v1.6, http://www.chemcraftprog.com/. (16) Aguilera-Iparraguirre, J.; Curran, H. J.; Klopper, W.; Simmie, J. M. Accurate Benchmark Calculation of the Reaction Barrier Height for Hydrogen Abstraction by the Hydroperoxyl Radical from Methane. Implications for C(n)H(2n+2) where n = 2 → 4. J. Phys. Chem. A 2008, 112, 7047−7054. (17) Eckart, C. The Penetration of a Potential Barrier by Electrons. Phys. Rev. 1930, 35, 1303−1309. (18) Klippenstein, S. J.; Wagner, A. F.; Dunbar, R. C.; Wardlaw, D. M.; Robertson, S. H. VariFlex, version 2.02m; Argonne National Laboratory: Argonne, IL, 1999. (19) Pitzer, K. S.; Gwinn, W. D. Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops. J. Chem. Phys. 1942, 10, 428−440. (20) Seal, P.; Papajak, E.; Truhlar, D. G. Kinetics of the Hydrogen Abstraction from Carbon-3 of 1-Butanol by Hydroperoxyl Radical: Multi-Structural Variational Transition-State Calculations of a

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CONCLUSIONS We have carried out a systematic detailed study of the potential energy diagrams, rate constant calculations, and branching ratio analysis of the hydrogen atom abstraction reactions by HȮ 2 radicals on a series of esters including methyl ethanoate, methyl propanoate, methyl butanoate, methyl pentanoate, methyl isobutyrate, ethyl ethanoate, propyl ethanoate, and isopropyl ethanoate. A stepwise mechanism that involved a reactant complex formed in the entrance channel and a product complex in the exit channel has been identified for all of the reaction channels in this work. A hydrogen bond is formed between the hydrogen atom of the hydroperoxyl radical and the oxygen atom of the carbonyl group of the ester for most of the reactant and product complexes. Abstraction of a hydrogen atom subsequently occurs, leading to the formation of product complexes leading to products. High-pressure limit rate constants have been calculated by using conventional transition state theory for all of the reaction channels, and a detailed comparison with our previous work on ketones + HȮ 2,4 and alkanes + HȮ 216 by Aguilera-Iparraguirre et al. has also been carried out. At the δ′ position of methyl pentanoate the carbonyl group of the ester has the least influence on the reactivity of the hydrogen atom when abstracted by an HȮ 2 radical, where the rate constants are similar to an alkane.16 On the basis of our results we observe that both R′ and R sides of the ester behave similarly to ketones,4 which is possibly due to the electron delocalization of the R′COOR group. Some of the geometries of the transition states (Table S2 in the Supporting Information) are affected by steric repulsion and have higher energies (Table 2) when compared to the energies of the corresponding position in ketones.4 A branching ratio analysis for every reaction channel in all the reaction systems of esters + HȮ 2 has been carried out in the temperature range 500−2000 K. At higher temperatures, the sites furthest from the carbonyl group of the ester become dominant over the closer sites, which are more influenced by the hydrogen bonding that occurs between the two reactants. This effect is also seen in the rate constants in Figures 15−18.

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ASSOCIATED CONTENT

S Supporting Information *

Tables of reaction energies, geometry coordinates, and frequencies. Figures of rate constants for each ester. This material is available free of charge via the Internet at http:// pubs.acs.org/.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*C. W. Zhou: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Science Foundation Ireland under grant number [08/IN1./I2055]. Computational resources were L



Article

Reaction with 262 Conformations of the Transition State. J. Phys. Chem. Lett. 2012, 3, 264−271. (21) Alecu, I. M.; Zheng, J.; Papajak, E.; Yu, T.; Truhlar, D. G. Biofuel Combustion. Energetics and Kinetics of Hydrogen Abstraction from Carbon-1 in n-Butanol by the Hydroperoxyl Radical Calculated by Coupled Cluster and Density Functional Theories and Multistructural Variational Transition-State Theory with Multidimensional Tunneling. J. Phys. Chem. A 2012, 116, 12206−12213. (22) Zhou, C.-W.; Simmie, J. M.; Curran, H. J. Rate constants for Hydrogen Abstraction by H2 from n-butanol. Int. J. Chem. Kinet. 2012, 44, 155−164. (23) Katsikadakos, D.; Zhou, C.-W.; Simmie, J.; Curran, H.; Hunt, P.; Hardalupas, Y.; Taylor, A. Rate Constants of Hydrogen Abstraction by Methyl Radical from n-Butanol and a Comparison of CanTherm, MultiWell and Variflex. Proc. Combust. Inst. 2013, 34, 483−491.

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