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Title
Author(s)
Theoretical and kinetic study of the hydrogen atom abstraction
reactions of esters with HO2 radicals
Mendes, Jorge; Zhou, Chong-Wen; Curran, Henry J.
Publication
Date
2013-10-31
Publication
Information
Mendes, Jorge, Zhou, Chong-Wen, & Curran, Henry J. (2013).
Theoretical and Kinetic Study of the Hydrogen Atom
Abstraction Reactions of Esters with H2 Radicals. The Journal
of Physical Chemistry A, 117(51), 14006-14018. doi:
10.1021/jp409133x
Publisher
American Chemical Society
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publisher's
version
http://dx.doi.org/10.1021/jp409133x
Item record
http://hdl.handle.net/10379/6110
DOI
http://dx.doi.org/10.1021/jp409133x
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Some rights reserved. For more information, please see the item record link above.
Hydrogen Atom Abstraction Reactions of Esters with
HȮ2 Radicals: A Theoretical Kinetic Study
Jorge Mendes, Chong-Wen Zhou,∗ and Henry J. Curran
Combustion Chemistry Centre, National University of Ireland, Galway, Ireland.
E-mail: [email protected]
∗ To
whom correspondence should be addressed
1
Abstract
Herein, a systematic rate coefficients calculation of the hydrogen atom abstraction reactions of
esters (methyl ethanoate, methyl propanoate, methyl butanoate, methyl pentanoate, methyl isobutyrate, ethyl ethanoate, propyl ethanoate and iso-propyl ethanoate) with the hydroperoxyl radical
(HȮ2) has been performed. The Møller–Plesset (MP2) method and the 6-311G(d,p) basis set have
been used in order to optimize and calculate the frequencies of all of the species involved in the title
reactions. MP2/6-311G(d,p) was used to determine the hindrance potentials for the reactants and
transition states. The connection between each transition state and the corresponding local minima
was validated by intrinsic reaction coordinate calculations. Electronic energies for all of the species
are reported, in kcal mol−1 , using the CCSD(T)/cc-pVTZ level of theory with the corresponding
zero-point energy corrections. The CCSD(T)/CBS (extrapolated from CCSD(T)/cc-pVXZ, where
X = D, T, Q) was calculated for the reactions of methyl ethanoate + HȮ2 radicals as a benchmark in
the electronic energy calculations. High-pressure limit rate coefficients were determined with the
use of the conventional transition state theory with corrections for the asymmetric Eckart tunneling
for all of the reaction channels in this study from 500–2000 K. In both reactants and transition
states, the 1-D hindered rotor approximation has been used in order to calculate the low frequency
torsional modes. The calculated individual, average and total rate coefficients are reported for all
of the reaction channels in every reaction system in this work. A branching ratio analysis for every
reaction site has also been investigated for all of the esters studied in this work.
Keywords
ab-initio, esters, hydroperoxyl radical, oxygenated fuels, hydrogen atom abstraction, rate coefficient
2
Introduction
Due to concerns regarding the future availability of fossil fuels and their harmful emissions, 1 there
has been an upsurge in interest in renewable biofuels over the past number of years. 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 which 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 can be obtained from several types of oil including soybean seed, rape seed and
palm seed oil, animal fats and used cooking oil. 1 The presence of oxygen atoms in a hydrocarbon molecule may reduce soot production when used 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 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, in order to predict the reactivity of these fuels. Oxygen atoms are not present within
the primary fuel molecule of conventional fuels. However, biofuels contain oxygen atoms which
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, while others can be used as supplements or replacements in diesel engines. 3
In the combustion temperature range of 500–2000 K, the oxidation reactions of radicals like
Ḣ, Ȯ, ȮH, HȮ2 and ĊH3 are always important when abstracting a hydrogen atom from the fuel
molecules. 4 When HȮ2 radicals abstract a hydrogen atom from an ester, hydrogen peroxide (H2O2 )
and an ester radical are formed. Furthermore, two highly reactive ȮH radicals are formed when
H2 O2 decomposes:
3
RH + HȮ2 → Ṙ + H2 O2
H2O2 (+M) → ȮH + ȮH (+M)
The stepwise reaction mechanism including a reactant (RC) and a product (PC) complex
formed in the entrance and exit channels, respectively, has been found for every reaction process in the title reactions; the same was also shown in our previous work on ketones with HȮ2 4
and ȮH 5 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 ȮH radical. 5 In this work, we
have performed a conformer search and a Boltzmann conformer distribution (1000 K) calculated
at the MP2/6-311G(d,p) level of theory 6 and found eleven conformers for methyl pentanoate. The
three lowest energy gauche conformers contribute 12% each to the distribution and are within 0.1
kcal mol−1 of each other. The trans conformer (Figure 1(a)) 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 1(a) lies 4 kcal mol−1 lower than the gauche conformer in Figure 1(b) and has energy barriers
of 4.5 and 5.7 kcal mol−1 for the α 0 –β 0 and β 0 –γ 0 hindrance potentials, respectively. Therefore,
as with our previous work with ketones, 4,5 we only consider the trans reactant conformers in our
calculations.
(a)
(b)
Figure 1: Methyl pentanoate (a) trans and (b) gauche conformers.
We have investigated how the rate coefficients for abstraction of different types of hydrogen
atoms, primary (1◦), secondary (2◦) and tertiary (3◦) in a fuel molecule, by a HȮ2 radical, are
influenced by the ester functional group (R0 C=OOR). To the best of our knowledge, high level
4
ab-initio calculations have not previously been done on these reactions. In our previous study on
the addition and abstraction reactions by HȮ2 radicals with ethyl methyl ketone (EMK) 4,7 in the
temperature range 600–1600 K, we found that hydrogen atom abstraction is faster by about two
orders of magnitude compared to addition. Thus, in this work we only consider hydrogen atom
abstraction reactions.
Computational methods
In this work we use the same computational methods as in our previous work with the hydrogen atom abstraction reactions of ketones + HȮ2 radicals. 4 The CCSD(T) 8/cc-pVTZ method and
extrapolation to the complete basis set limit (CCSD(T)/CBS), using the three-parameter equation
developed by Peterson et al., 9 were used in order to calculate the energies in the reactions of methyl
ethanoate + HȮ2 radicals. Both methods were compared against each other from which we find
that the relative energy obtained by these two methods are within 1 kcal mol−1 of one another. As
the computational cost of the CCSD(T)/CBS method is high 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 Surface
Figure 2 and Table 1 clarify the different types of hydrogen atoms present and depict the labels we
use in the title reactions. Figure 3 shows optimized geometries of all of the esters in this study.
The CCSD(T)/cc-pVXZ (X = D, T, Q) energy calculations and corresponding extrapolation to the
CBS limit for the reactions of methyl ethanoate with HȮ2 radicals are provided in Table S1 of the
Supporting Information. Table S2 details all of the geometry co-ordinates and frequencies of all of
the species present in these reaction systems.
Some of the species formed have the same energy, similar geometries and frequencies. For
simplicity, we only show one of these in the potential energy diagrams.
5
Figure 2: Labels in use in this work.
Table 1: Types of hydrogen atoms in this work.
δ0
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Methyl ethanoate (ME)
Methyl propanoate (MP)
Methyl butanoate (MB)
Methyl pentanoate (MPe)
Methyl iso-butyrate (MiB)
Ethyl ethanoate (EE)
Propyl ethanoate (PE)
iso-Propyl ethanoate (iPE)
CH3 C=OOCH3
CH3 CH2 C=OOCH3
CH3 (CH2 )2 C=OOCH3
CH3 (CH2 )3 C=OOCH3
(CH3 )2 CHC=OOCH3
CH3 C=OOCH2 CH3
CH3 C=OO(CH2 )2 CH3
CH3 C=OOCH(CH3 )2
γ0
1◦
1◦
2◦
β0
1◦
2◦
2◦
1◦
α0
1◦
2◦
2◦
2◦
3◦
1◦
1◦
1◦
α
1◦
1◦
1◦
1◦
1◦
2◦
2◦
3◦
β
γ
1◦
2◦
1◦
1◦
In our previous work on ketones 4 and in this work on esters, we observed the presence of
two types of hydrogen atoms, namely in- and out-of-plane hydrogen atoms, leading to in-plane
(Figure 4(a)) and out-of-plane (Figure 4(b)) 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 develops between the oxygen atom of the carbonyl group of the ester and the
hydrogen atom of the HȮ2 radical. Figure 5 shows a hindrance potential of methyl ethanoate
showing the local minima corresponding to the different transitions states: (a) in-plane and (b)
out-of-plane. In the reactions of the esters with the HȮ2 radical, these two different transition
states have similar energies; therefore, we only consider the lowest energy transition states in this
6
(a) Methyl ethanoate
(b) Methyl propanoate
(c) Methyl butanoate
(d) Methyl pentanoate
(e) Methyl iso-butyrate
(f) Ethyl ethanoate
(g) Propyl ethanoate
(h) iso-Propyl ethanoate
Figure 3: Optimized geometries of the esters in this work at MP2/6-311G(d,p) level of theory,
detailing all of the different types of hydrogen atoms present.
7
work and we treat as hindered rotors all of the low frequency torsional modes.
(a)
(b)
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.
Figure 5: Hindrance potential of methyl ethanoate showing an (a) in-plane and (b) out-of-plane
transition state local minima.
Most of the reactant complexes in this work will form a hydrogen bond between the oxygen
8
atom of the carbonyl group of the ester and the hydrogen atom of the HȮ2 radical (Figure 6(a)).
Some reactant complexes will form a hydrogen bond between the oxygen atom in the alkoxy moiety of the ester and the hydrogen atom present in the hydroperoxyl radical (Figure 6(b)). The
reactant complexes where a hydrogen bond is not formed undergo a weaker van der Waals interaction between the ester and the HȮ2 radical. The energy of the products that are formed upon
abstraction is higher than the energy of the corresponding product complexes. Their geometries
are not considerably different (Table S2 in the Supporting Information).
(a)
(b)
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.
The potential energy surface for methyl ethanoate (ME) reacting with an HȮ2 radical, obtained
at the CCSD(T)/cc-pVTZ level of theory and extrapolation to the CBS limit (energies in kcal
mol−1) is shown in Figure 7. 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 iso-butyrate (MiB), in Figure 12
for ethyl ethanoate (EE), in Figure 13 for propyl ethanoate (PE) and in Figure 14 for iso-propyl
ethanoate (iPE).
In the entrance channel, reactant complexes (RC) are formed with energies from −9.8 to −1.9
kcal mol−1 . Product complexes (PC) develop in the exit channel with energies from −2.9 to 12.4
9
TS1a
20.3
(20.7)
TS2a
18.7
(19.1)
P2a
13.0
(12.2)
PC2a
8.6
(8.6)
P1a
12.7
(11.8)
PC1a
6.2
(6.1)
(a) ME + HO2
0.0
RC2a
-8.8
(-8.4)
RC1a
-9.4
(-9.0)
Figure 7: Potential energy diagram, in kcal mol−1 , of the reactions of methyl ethanoate with HȮ2
radicals, calculated at the CCSD(T)/cc-pVTZ level of theory.
TS1b
18.6
TS3b
18.5
P1b
15.1
P3b
13.0
TS2b
17.1
PC1b
8.2
PC3b
7.8
P2b
7.7
(b) MP + HO2
PC2b
0.8
0.0
RC1b
-8.7
RC2b
-8.9
Figure 8: Potential energy diagram, in kcal mol−1 , of the reactions of methyl propanoate with HȮ2
radicals, calculated at the CCSD(T)/cc-pVTZ level of theory.
10
TS1c
19.7
P1c
15.0
P4c
13.0
TS2c
15.5
TS4c
18.5
PC1c
10.8
PC4c
7.7
TS3c
15.9
P2c
12.6
P3c
8.4
PC2c
5.8
(c) MB + HO2
PC3c
0.4
0.0
RC4c
-8.8
RC2c
-8.9
RC1c
-9.6
Figure 9: Potential energy diagram, in kcal mol−1, of the reactions of methyl butanoate with HȮ2
radicals, calculated at the CCSD(T)/cc-pVTZ level of theory.
TS1d
20.9
TS5d
18.4
TS2d
16.6
PC1d
11.8
PC5d
7.6
TS4d
15.7
P2d
12.3
P4d
8.1
PC3d
5.9
TS3d
15.0
(d) MPe + HO2
0.0
PC2d
7.5
P1d
15.0
P3d
13.0
PC4d
0.0
RC1d
-1.9
RC5d
-8.8
RC3d
-9.0
RC2d
-9.8
Figure 10: Potential energy diagram, in kcal mol−1, of the reactions of methyl pentanoate with
HȮ2 radicals, calculated at the CCSD(T)/cc-pVTZ level of theory.
11
TS1e
18.5
TS3e
18.2
P1e
15.7
TS2e
14.4
P3e
12.9
PC1e
8.7
PC3e
8.0
P2e
4.6
(e) MiB + HO2
0.0
PC2e
-2.9
RC1e
-9.0
RC2e
-9.3
Figure 11: Potential energy diagram, in kcal mol−1, of the reactions of methyl iso-butyrate with
HȮ2 radicals, calculated at the CCSD(T)/cc-pVTZ level of theory.
TS1f
20.0
TS3f
21.5
P3f
16.6
TS2f
15.5
P1f
12.6
PC3f
10.2
11.5
P2f
PC1f
5.9
PC2f
4.9
(f) EE + HO2
0.0
RC3f
-6.8
RC2f
-9.1
-9.6
RC1f
Figure 12: Potential energy diagram, in kcal mol−1 , of the reactions of ethyl ethanoate with HȮ2
radicals, calculated at the CCSD(T)/cc-pVTZ level of theory.
12
TS4g
20.7
TS1g
20.0
P4g
15.0
TS2g
14.9
PC4g
11.5
TS3g
18.5
PC3g
6.5
PC1g
5.9
11.7
P2g
P3g
13.1
P1g
12.6
PC2g
5.0
(g) PE + HO2
0.0
RC4g
-6.9
RC3g
-8.9
RC2g
-9.3
-9.6
RC1g
Figure 13: Potential energy diagram, in kcal mol−1, of the reactions of propyl ethanoate with HȮ2
radicals, calculated at the CCSD(T)/cc-pVTZ level of theory.
TS3h
22.2
TS1h
19.8
P3h
16.5
TS2h
14.1
PC3h
13.4
P2h
12.8
12.6
P1h
PC2h
6.1
PC1h
5.7
(h) iPE + HO2
0.0
RC2h
-9.6
-9.7
RC1h
Figure 14: Potential energy diagram, in kcal mol−1, of the reactions of iso-propyl ethanoate with
HȮ2 radicals, calculated at the CCSD(T)/cc-pVTZ level of theory.
13
kcal mol−1 .
For the abstraction reactions of a hydrogen atom at the α 0 site, 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 iso-butyrate, TS1f for ethyl ethanoate, TS1g for propyl ethanoate and TS1h for iso-propyl
ethanoate. In the reaction mechanism of methyl ethanoate, TS1a will form PC1a in the exit channel with an energy relative to the reactants of 6.2 kcal mol−1. For the above remaining esters the
corresponding product complexes are formed with relative energies from −2.9 to 5.9 kcal mol−1 .
Subsequent abstraction of a hydrogen atom forms H2 O2 and a corresponding α 0 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 iso-butyrate at 4.6 kcal mol−1 and P1f, P1g
and P1h (1◦ radical) for ethyl ethanoate, propyl ethanoate and iso-propyl ethanoate, respectively,
at 12.6 kcal mol−1 .
For the remaining sites (β 0 , γ 0 , δ 0 , α , β and γ ), the reactions with an HȮ2 radical are similar to
what we observed for the α 0 site, where the energies calculated are similar to the same sites in a
ketone (α , β , etc.). Energies relative to the reactants for each transition state are detailed in Table 2
and the potential energy surfaces in Figures 8–14. A trend is observed where abstraction of a 1◦ ,
2◦ and 3◦ hydrogen atom at the α 0 site has an average relative energy of 20.0, 16.2 and 14.4 kcal
mol−1, respectively. At the α site, abstraction of a 1◦ , 2◦ and 3◦ hydrogen atom has an average
relative energy of 18.5, 15.2 and 14.1 kcal mol−1 , respectively. At the β 0 site, abstraction of a 1◦
and 2◦ hydrogen atom has an average relative energy of 18.6 and 15.3 kcal mol−1, respectively.
At the β site, abstraction of a 1◦ and 2◦ hydrogen atom has 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 ketones 4 (Table 2). At the γ 0 site of MB and at the γ site of PE,
the transition states have similar relative energies to the ones obtained at the γ site of nPMK and
to an alkane. 10 At the γ 0 (2◦ hydrogen atom) and δ 0 (1◦ hydrogen atom) sites of MPe the energies
14
are also similar to an alkane. 10
Table 2: Lowest relative electronic energies comparison for the reactions of ketones + HȮ2 radical 4 with that of esters + HȮ2 radical in this work (in kcal mol−1).
Esters
ME
MP
MB
MPe
MiB
EE
PE
iPE
δ0
γ0
β0
20.9
19.7
16.6?
18.6
15.5?
15.0?
18.5
α0
20.3
17.1?
15.9?
15.7?
14.4
20.0
20.0
19.8
DMK
20.2
EMK
19.7
Ketones
nPMK
19.6
iPMK
19.1
iBMK
19.6
No symbol: 1◦ hydrogen atom; ? 2◦ hydrogen atom; 3◦ hydrogen atom.
α
18.7
18.5
18.5
18.4
18.2
15.5?
14.9?
14.1
β
γ
21.5
18.5?
22.2
20.7
16.6?
15.8?
14.2
15.4?
18.6
15.5?
18.3
13.0
19.3
16.4
Rate coefficient calculations
Similarly to our previous work with the ketones, 4 we use Variflex v2.02m 11 in order to calculate
the rate coefficients in this work, from 500–2000 K. The Pitzer-Gwinn-like 12 approximation was
used with the low-frequency torsional modes in order to treat them as 1-D hindered rotors. The
coupling that occurs between adjacent internal rotations and between internal and external rotations
is sometimes difficult to separate, which makes the torsional treatment difficult. As all the internal
rotations in this study are separable, the 1-D torsional treatment is the best that can be done, at
present. Truhlar and co-workers 13,14 multi-structure method deals with the problem of torsional
coupling. When applying to the reactions in the n-Butanol + HȮ2 system, it is shown that the
results of their multi-structure method are quite similar to our rate coefficient results using the
1-D hindered rotor treatment at the α and γ sites. 15 We have calculated the hindrance potentials
around every dihedral angle for the reactants and transition states. A modified three-parameter
Arrhenius equation was used in order to fit these rate coefficients (Tables 3–5) and they are shown
15
on a per hydrogen atom basis, in cm3 mol−1 s−1 . Table S3 in the Supporting Information shows
the individual rate coefficient comparisons for each ester, on a per site basis in cm3 mol−1 s−1 .
Table 4 shows the Arrhenius fits for the calculated average rate coefficients at each site relative to
the R0 C=OOR group, with a calculated average error of 4.6% and a maximum error of no more
than 10.0% in the fit.
The rate coefficients are detailed in Figures 15–18 for the reactions of esters + HȮ2 radicals:
α 0 (1◦, 2◦ and 3◦), β 0 (1◦ and 2◦), γ 0 (1◦ and 2◦), δ 0 (1◦ ), α (1◦, 2◦ and 3◦ ), β (1◦ and 2◦) and γ
(1◦). A comparison is made with abstraction from ketones 4 and alkanes 10 by an HȮ2 radical.
Figures 15 and 16 show the calculated rate coefficients at the R0 side of the molecule (α 0 , β 0 ,
γ 0 and δ 0 sites). A trend is observed for all of the esters, where the calculated rate coefficients are
similar to the ketones 4 at the corresponding reaction site. Figures 15(a), 15(b), 15(c), 15(d), 16(a)
and 16(c) show the rate coefficients for the reactions of a 1◦ , 2◦ and 3◦ hydrogen atom at the α 0 site,
a 1◦ at the β 0 site and a 2◦ at the β 0 and γ 0 sites, respectively, and when comparing to the alkanes 10
they are generally slower by about a factor of 10 from 500 to 2000 K. Figure 16(b) shows the
calculated rate coefficients for the reactions of a 1◦ hydrogen atom at the γ 0 site and is slower than
an alkane 10 by about a factor of 4 from 500 to 2000 K. At the δ 0 site (Figure 16(d)), alkanes 10 are
faster than a 1◦ hydrogen atom by 70% at 600 K, increasing to about a factor of 3 from 1600 to
2000 K.
Figures 17 and 18 show the calculated rate coefficients at the R side of the molecule (α , β
and γ sites). Figure 17(a), 17(b) and 17(c) show the rate coefficients for the reactions of a 1◦ ,
2◦ and 3◦ hydrogen atom located at the α site, respectively. When abstracting an α 1◦ hydrogen
atom, it is slower than alkanes 10 by a factor of 4 at 600 K and 7 from 1000 to 2000 K. In the
case of a 2◦ hydrogen atom, alkanes 10 are faster by a factor of 10 at 800 K, decreasing to 8 at
2000 K. A 3◦ hydrogen atom is slower than alkanes 10 by about two orders of magnitude from 500
to 800 K, decreasing to one order of magnitude at 2000 K. Abstraction of a β 1◦ hydrogen atom
(Figure 17(d)) is slower than alkanes 10 by two orders of magnitude at 500 K and a factor of 5 at
1600 K. A 2◦ hydrogen atom at the same site (Figure 18(a)) is slower by four orders of magnitude
16
at 500 K and a factor of 8 at 1800 K. A γ 1◦ hydrogen atom (Figure 18(b)) is slower than alkanes 10
by a factor of 7 at 600 K and 3 at 2000 K.
The rate coefficients for the reactions of 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 (R0 C=OOR).
In this work we show that the calculated rate coefficients of the esters are close to the calculated
rate coefficients 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 site in the ketones. 4
In our previous work 16 we have determined the rate coefficients for the hydrogen atom abstraction reactions by CH3 radicals from 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 based on that comparison we predict a factor of 2.5 in the overall uncertainty of our
calculated rate coefficients. This is attributed to uncertainties in the electronic energy calculations,
tunneling, treatment of internal rotation modes, etc.
Branching Ratios
As shown in Figure 19, a branching ratio analysis for each reaction channel has been carried out
from 500 to 2000 K. Figure 19(a) shows the branching ratio for methyl ethanoate and abstraction from the α site is dominant throughout. Figure 19(b) shows the branching ratios for methyl
propanoate where the α 0 site dominates from 500 (73%) to 1200 K (37%) and the α site dominates
above 1200 K. For methyl butanoate, Figure 19(c), abstraction from the β 0 site dominates from
500 (55%) to 2000 K (34%). Figure 19(d) details the branching ratio for methyl pentanoate and
shows that abstraction from the β 0 site is dominant from 500 to 800 K. The branching ratio here is
35% at 500 K decreasing to 22% at 2000 K. Abstraction from the δ 0 site is dominant above 800 K,
becoming more and more important with the increase in temperature. The branching ratio here
goes from 6% at 500 K to 39% at 2000 K. For methyl iso-butyrate, Figure 19(e), abstraction from
the α 0 site dominates from 500 to 1600 K. The branching ratio of this channel goes from 96% at
17
(a)
(b)
(c)
(d)
Figure 15: Rate coefficients comparison, in cm3 mol−1 s−1 , for the reactions of esters + HȮ2
radicals at the α 0 site (1◦, 2◦ and 3◦ hydrogen atoms) and at the β 0 site (1◦ hydrogen atom). (a)
methyl ethanoate (green), ethyl ethanoate (red), propyl ethanoate (blue) and iso-propyl ethanoate
(magenta); (b) methyl propanoate (black), methyl butanoate (red) and methyl pentanoate (blue);
(c) methyl iso-butyrate (red); (d) methyl propanoate (blue) and methyl iso-butyrate (red); ketones
+ HȮ2 4 (dashed) and alkanes + HȮ2 10 (dotted).
18
(a)
(b)
(c)
(d)
Figure 16: Rate coefficients comparison, in cm3 mol−1 s−1 , for the reactions of esters + HȮ2
radicals at the β 0 site (2◦ hydrogen atom), at the γ 0 site (1◦ and 2◦ hydrogen atoms) and at the δ 0 site
(1◦ hydrogen atom). (a) methyl butanoate (blue) and methyl pentanoate (red); (b) methyl butanoate
(red); (c) methyl pentanoate (red); (d) methyl pentanoate (red); ketones + HȮ2 4 (dashed) and
alkanes + HȮ2 10 (dotted).
19
(a)
(b)
(c)
(d)
Figure 17: Rate coefficients comparison, in cm3 mol−1 s−1 , for the reactions of esters + HȮ2
radicals at the α site (1◦, 2◦ and 3◦ hydrogen atoms) and at the β site (1◦ hydrogen atom). (a)
methyl ethanoate (black), methyl propanoate (green), methyl butanoate (blue), methyl pentanoate
(purple) and methyl iso-butyrate (magenta); (b) ethyl ethanoate (blue) and propyl ethanoate (red);
(c) isopropyl ethanoate (red); (d) ethyl ethanoate (red) and iso-propyl ethanoate (blue); ketones +
HȮ2 4 (dashed) and alkanes + HȮ2 10 (dotted).
20
Table 3: Rate coefficients, in cm3 mol−1 s−1 , for the different abstraction sites of the esters in this
work, on a per hydrogen atom basis.
(a) methyl ethanoate: CH3C=OOCH3 + HȮ2
k(α 0 ) = 3.47×10−4 T4.61 exp(−7896/T)
k(α ) = 2.04×10−6 T5.23 exp(−6992/T)
(1)
(2)
(b) methyl propanoate: CH3CH2 C=OOCH3 + HȮ2
k(β 0 ) = 2.77×10−4 T4.61 exp(−7473/T)
k(α 0 ) = 7.41×10−4 T4.39 exp(−6005/T)
k(α ) = 1.63×10−5 T4.94 exp(−6701/T)
(3)
(4)
(5)
(c) methyl butanoate: CH3CH2 CH2C=OOCH3 + HȮ2
k(γ 0 ) = 9.80×10−1 T3.63 exp(−8494/T)
k(β 0 ) = 3.75×10−3 T4.28 exp(−6064/T)
k(α 0 ) = 8.11×10−4 T4.39 exp(−5860/T)
k(α ) = 4.92×10−5 T4.76 exp(−6887/T)
(6)
(7)
(8)
(9)
(d) methyl pentanoate: CH3 CH2CH2 CH2C=OOCH3 + HȮ2
k(δ 0) = 8.95×10+1 T3.10 exp(−8626/T)
k(γ 0 ) = 5.59×10−1 T3.62 exp(−6850/T)
k(β 0 ) = 2.89×10−5 T4.85 exp(−5521/T)
k(α 0 ) = 1.53×10−3 T4.22 exp(−5562/T)
k(α ) = 3.05×10−6 T5.07 exp(−6656/T)
(10)
(11)
(12)
(13)
(14)
(e) methyl iso-butyrate: (CH3)2CHC=OOCH3 + HȮ2
k(β 0 ) = 1.55×10−3 T4.30 exp(−7581/T)
k(α 0 ) = 5.68×10−2 T3.86 exp(−5062/T)
k(α ) = 3.02×10−6 T5.15 exp(−6464/T)
(15)
(16)
(17)
(f) ethyl ethanoate: CH3 C=OOCH2CH3 + HȮ2
k(α 0 ) = 1.39×10−3 T4.40 exp(−7857/T)
k(α ) = 3.26×10−5 T4.86 exp(−5580/T)
k(β ) = 1.23×10−2 T4.31 exp(−9418/T)
(18)
(19)
(20)
(g) propyl ethanoate: CH3 C=OOCH2CH2 CH3 + HȮ2
k(α 0 ) = 6.97×10−3 T4.25 exp(−8057/T)
k(α ) = 1.90×10−5 T4.86 exp(−5220/T)
k(β ) = 1.32×10+1 T3.30 exp(−8123/T)
k(γ ) = 1.39×10−4 T4.87 exp(−8164/T)
(21)
(22)
(23)
(24)
(h) iso-propyl ethanoate: CH3C=OOCH(CH3)2 + HȮ2
k(α 0 ) = 1.02×10−3 T4.39 exp(−7827/T)
k(α ) = 5.16×10−2 T3.94 exp(−5790/T)
k(β ) = 3.90 T3.52 exp(−9573/T)
(25)
(26)
(27)
21
(a)
(b)
Figure 18: Rate coefficients comparison, in cm3 mol−1 s−1 , for the reactions of esters + HȮ2
radicals at the β site (2◦ hydrogen atom) and at the γ site (1◦ hydrogen atom). (a) propyl ethanoate
(red); (b) propyl ethanoate (red); ketones + HȮ2 4 (dashed) and alkanes + HȮ2 10 (dotted).
Table 4: Average Arrhenius fit parameters (A, n and E), on a per-hydrogen atom basis in cm3 mol−1
s−1 , according to hydrogen atom type (1◦, 2◦ or 3◦) and site (α 0 , β 0 , γ 0 , δ 0 , α , β or γ ) relative to
the carbonyl group of the ester.
Hydrogen atom type
Primary, α 0
Secondary, α 0
Tertiary, α 0
Primary, β 0
Secondary, β 0
Primary, γ 0
Secondary, γ 0
Primary, δ 0
Primary, α
Secondary, α
Tertiary, α
Primary, β
Secondary, β
Primary, γ
k = A × T n × exp(-E/T)
A
1.48 × 10−3
5.41 × 10−4
5.68 × 10−2
4.93 × 10−4
4.57 × 10−4
9.80 × 10−1
5.59 × 10−1
8.95 × 10+1
4.53 × 10−6
1.89 × 10−5
5.16 × 10−2
1.37 × 10−1
1.32 × 10+1
1.39 × 10−4
n
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
E
−7920
−5738
−5062
−7508
−5830
−8494
−6850
−8626
−6666
−5380
−5790
−9424
−8123
−8164
500 K to 36% at 1600 K and then to 26% at 2000 K. The remaining two channels of α and β 0
become important as the temperature rises. The branching ratio of the β 0 site goes from 2% at
500 K to 36% at 2000 K. The branching ratio of the α channel goes from 3% at 500 K to 37%
at 2000 K. Figures 19(f), 19(g) and 19(h) show the branching ratios for ethyl ethanoate, propyl
22
Table 5: Parameters of the fit (A, n and E) for the total rate coefficients in this work, in cm3 mol−1
s−1 .
ME
MP
MB
MPe
MiB
EE
PE
iPE
k = A × T n × exp(-E/T)
A
9.28 × 10−5
1.24 × 10−5
3.36 × 10−4
1.67 × 10−3
4.55 × 10−8
7.35 × 10−9
8.77 × 10−8
1.74 × 10−8
n
4.99
5.20
4.82
4.64
5.82
6.17
5.91
6.04
E
−7359
−5980
−5909
−6038
−4110
−5076
−5388
−4886
ethanoate and iso-propyl ethanoate, respectively. For ethyl ethanoate, abstraction from the α site
dominates at low temperatures in the range from 500 (96%) to 1600 K (42%), reaching 34% at
2000 K. For propyl ethanoate, abstraction from the α site dominates at from 500 (83%) to 1200 K
(27%). Above 1200 K, the γ site dominates, reaching 44% at 2000 K. For iso-propyl ethanoate, abstraction from the α site dominates at from 500 (97%) to 1200 K (44%). Above 1200 K abstraction
from the β site dominates, reaching 64% at 2000 K.
Summary
In this work, a trend is observed where the rate coefficients for the reactions of esters with HȮ2
radicals at the α 0 , β 0 , γ 0 , δ 0 , α , β and γ sites, with different types of hydrogen atoms, are similar
to the ones calculated in our previous work for the ketones, 4 at the corresponding sites. Both the
R0 and R sides of the ester behave similarly which is possibly due to the electron delocalization
of the R0 C=OOR group. When comparing to the alkanes calculated by Aguilera-Iparraguirre et
al. 10 we observe that the rate coefficients for the esters in this work are slower throughout from
500–2000 K. We also observe that the further the abstraction by an HȮ2 radical occurs from the
R0 C=OOR group of the ester, the lower its influence on the reactivity of the hydrogen atom.
23
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
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 iso-butyrate; (f) ethyl ethanoate; (g) propyl ethanoate; (h) iso-propyl ethanoate.
24
Conclusions
We have carried out a detailed systematic investigation of the energy diagrams, rate coefficient
calculations and branching ratio analysis on a series of esters when reacting with HȮ2 radicals,
including methyl ethanoate, methyl propanoate, methyl butanoate, methyl pentanoate, methyl isobutyrate, ethyl ethanoate, propyl ethanoate and iso-propyl ethanoate. Similar to our previous work
on ketones 4 a reactant and a product complex develops in the entrance and exit channels, respectively, for all of the reaction channels in this work. We have determined the high-pressure limit
rate coefficients for all of the reactions detailed in this study by conventional transition state theory
and a detailed comparison with our previous work on ketones + HȮ2 , 4 and alkanes + HȮ2 10 by
Aguilera-Iparraguirre et al. has also been carried out.
At the δ 0 site of methyl pentanoate the carbonyl group of the ester has the least influence on
the reactivity of the hydrogen atom when abstracted by an HȮ2 radical, where the rate coefficients
are similar to an alkane. 10
Based on our results we observe that both R0 and R sides of the ester behave similarly to the
ketones 4 which is possibly due to the electron delocalization of the R0 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 (Tables 2) when compared to the corresponding site in
the ketones. 4
A branching ratio analysis for every reaction channel in all the reaction systems of esters +
HȮ2 has been carried out in the temperature range from 500 to 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 coefficients in Figures 15–18.
25
Acknowledgement
This work was supported by Science Foundation Ireland under grant number [08/IN1./I2055].
Computational resources were provided by the Irish Center for High-End Computing (ICHEC).
Supporting Information Available
This material is available free of charge via the Internet at http://pubs.acs.org/.
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