DSpace at VNU: Mechanism and kinetics of low-temperature oxidation of a biodiesel surrogate-methyl acetate radicals with molecular oxygen By: Mai, Tam V. -T.; Le, Xuan T.; Huynh, Lam K.

Struct Chem
DOI 10.1007/s11224-014-0495-2

ORIGINAL RESEARCH

Mechanism and kinetics of low-temperature oxidation
of a biodiesel surrogate2methyl acetate radicals with molecular
oxygen
Tam V.-T. Mai • Xuan T. Le • Lam K. Huynh

Received: 24 May 2014 / Accepted: 11 August 2014
Ó Springer Science+Business Media New York 2014

Abstract Accurate description of reactions between
methyl acetate (MA) radicals and molecular oxygen is an
essential prerequisite for understanding as well as modeling low-temperature oxidation and/or ignition of MA, a
small biodiesel surrogate, because their multiple reaction
pathways either accelerate the oxidation process via chain
branching or inhibit it by forming relatively stable products. The accurate composite CBS-QB3 level of theory
was used to explore potential energy surfaces for MA
radicals ? O2 system. Using the electronic structure calculation results under the framework of canonical statistical mechanics and transition state theory, thermodynamic
properties of all species as well as high-pressure rate
constants of all reaction channels were derived with
explicit corrections for tunneling and hindered internal
rotations. Our calculated results are in good agreement with
a limited number of scattered data in the literature. Furthermore, pressure- and temperature-dependent rate constants were then computed using the Quantum Rice–
Ramsperger–Kassel and the modified strong collision theories. This procedure resulted in a thermodynamically
consistent detailed kinetic mechanism for low-temperature
oxidation of the title fuel. We also demonstrated that even
the detailed mechanism consists of several reactions of
Electronic supplementary material The online version of this

article (doi:10.1007/s11224-014-0495-2) contains supplementary
material, which is available to authorized users.
T. V.-T. Mai Á X. T. Le Á L. K. Huynh (&)
Institute for Computational Science and Technology at Ho Chi
Minh City, Ho Chi Minh City, Vietnam
e-mail:
L. K. Huynh
International University, Vietnam National University-HCMC,
Ho Chi Minh City, Vietnam

different reaction types, only the addition of the reactants
and the re-dissociation of the initially formed adducts are
important for low-temperature combustion at engine-liked
conditions.
Keywords Biodiesel surrogate Á Oxygenated
hydrocarbon Á Alkyl peroxy radical Á Detailed kinetic
model Á Low-temperature oxidation and ignition

Introduction
Biodiesel fuels (or biologically derived fuels in general)
have been emerging as one of most promising candidates to
meet the continually increasing demands on internal
combustion engine development for higher combustion
efficiency, reduced pollutant emissions, the depletion of
fossil fuels, and higher performance. Biodiesel is a
renewable and environmentally friendly fuel with low
emission of pollutants such as carbon monoxide, carbon
dioxide, sulfur compounds, and particulate matter [1],
while its effects on nitrogen oxides (NOx) remain uncertain. Such NOx emissions have been experimentally
observed either increasingly [2, 3] or decreasingly [4] with

the use of biodiesel as an alternative fuel or a blend component. Therefore, there is a need for further investigation
to shed more light on benefits, drawbacks of biodiesel fuels
as well as its influence on operational conditions of
engines.
Biodiesel fuels are often produced from mono-alkyl esters
of long-chain fatty acids derived from vegetable oils and
animal fats [1, 5, 6]. Typically, they have the structure of a
methyl ester group attached to a long hydrocarbon chain of
about 16–19 carbon atoms (C16–19Hx–C(=O)O–CH3). Due to
their large size and their chemical/physical complexity (e.g.,

123


Struct Chem

the introduction of the heterogeneous O atom compared to
hydrocarbon fuels), detailed kinetic study on these biodiesel
molecules is challenging both experimentally and
theoretically.
In terms of detailed kinetic modeling, surrogate molecules are widely used to study the chemistry/physics of real
fuels. Surrogates are simple molecules used to emulate the
physical and chemical properties of real conventional fuels
that are too complicated for detailed investigation. Therefore, it is necessary to determine optimal surrogate models
which are small enough to be investigated using accurate
calculations but also large enough to represent the chemistry/physics of real molecules. Such good surrogate
models will allow us to investigate the oxidation of real
methyl esters in internal combustion engine [7–12]. In this
context, because methyl acetate (MA) is the simplest
methyl ester molecule with a chain of only one carbon

atom connected to the methyl ester group, the chemistry as
well as the role of the methyl ester group can be explicitly
investigated. Importantly, because MA radical is an intermediate with relatively high concentrations in the pyrolysis
of larger surrogates (e.g., methyl propanoate [13]) as well
as real biodiesel molecules such as the rapeseed methyl
ester (RME) [14], understanding of mechanisms and
kinetics of MA will contribute to the development of
reliable kinetic models for larger methyl esters and biodiesels [15].
In this paper, we concentrate our efforts on characterizing detailed kinetics of MA radicals ? O2 reactions
which is believed, similar to the analogous alkyl systems,
to play a very important role in low-temperature oxidation
and auto-ignition processes [7]. Based on the well-constructed potential energy surfaces (PESs) explored at the
high level composite method CBS-QB3, the detailed
kinetic analysis is then carried out to investigate the
structural effects on the kinetic behavior of this system at
low-temperature conditions under the framework of the
Quantum Rice–Ramsperger–Kassel (QRRK) and the
modified strong collision (MSC) theories. The detailed
kinetic mechanism for the title reaction, MA radicals ? O2, was also compiled in the Chemkin format for a
wide range of temperatures and pressures. A simplified
mechanism, which consists of important reactions, is also
suggested for low-temperature combustion at engine-liked
conditions.

Computational details
Electronic structure calculations
The electronic structure calculations were carried out using
the Gaussian 09 program [16]. The composite CBS-QB3

123

method by Petersson and coworkers [17] was selected
because of its capability of predicting thermodynamic
properties to ‘‘chemical accuracy’’, which is normally
defined as within *1 kcal/mol of experimental data. It is
worth mentioning that the method has shown to be the
effective method for analogous alkyl?O2 systems [18, 19].
Moreover, the method was also intensively used to study
thermodynamics and kinetics of similar and/or larger
oxygenated systems. For example, CBS-QB3 numbers
were used to derive group additive values for different
oxygenated compounds [20]; bond dissociation energies
and enthalpies of formation of methyl/ethyl butanoate [21];
oxidation of methyl and ethyl butanoates [22]; and
abstraction reaction between MA and hydroxyl radical [23]
in which CBS-QB3 is the method of choice to refine the
energy for the use of other methods such as BH&HLYP
and MP2. A good agreement on calculated reaction barriers
and energies for several important reactions were also
observed with those by other methods, namely G3, G3B3,
and G4 (see supplementary Table S3 for details). The CBSQB3 method calculates geometries and frequencies at the
B3LYP/6-311G(2d,d,p) level of theory. The energy is
calculated at several levels of theory including CCSD(T)/631?G(d0 ) and then extrapolated to the complete basis set
limit. All reported results for stable molecules as well as
transition states (first-order saddle points on the PESs) were
obtained for the lowest-energy conformer of a given species. Normal-mode analysis was performed to verify the
nature of each of these stationary points. For complicated
reaction pathways, in order to confirm the correct transition
state, the minimum energy paths (MEP) from the transition
state to both the reactants to products were calculated using

the intrinsic reaction path (IRC) following method [24, 25].
Thermodynamic property calculations
The atomization method was employed to calculate the
heats of formation of all species, and standard statistical
mechanics methods were used to calculate thermodynamic
properties such as entropies and heat capacities. Because
only relative energies are required in this work, no attempts
were made to improve the heats of formation using, for
example, bond additivity corrections. All harmonic frequencies were scaled by a factor of 0.99 as recommended
by Petersson and coworkers [17] prior to their use. Using
the experimental vibrational frequencies of methyl acetate
[26], the calculated scale factor is 0.98 ± 0.01. Therefore,
the use of scale factor of 0.99 is expected to give reliable
results for both enthalpy and entropy. Some low-frequency
vibrational modes, which are better treated as internal
rotations around single bonds, were replaced in the thermodynamics calculations by an explicit evaluation of the
hindered rotations in the most accurate manner as


Struct Chem

described hereafter. The 1-D Schro¨dinger equation for a
hindered internal rotor (HIR) is given as
À

1 d2 Whir
Á
þ VðhÞWhir ¼ EWhir ;
2Ired dh2

ð1Þ

where E is the energy and Ired is the reduced moment of
inertia for the considered rotation and is calculated as I(2,3)
according to East and Radom [27] on the basis of the
original work by Kilpatrick and Pitzer [28]. The hindrance
potential, V(h), is directly computed as a function of torsional angle, h, with a step of 10°. Specifically for this
system, it was obtained at the B3LYP/6-31G(d) level via
relaxed surface scans with the step size of 10° for dihedral
angles that correspond to the rotations. In order to solve the
HIR equation, we cast it into a Mathieu-type equation by
representing the hindrance potential as a Fourier series,
P
V ðhÞ ¼ Ll¼ÀL cl eilh , in which L is some cut-off number
depending on the nature of the potential. The wave function was expanded as a harmonic series, jmi ¼ p1ffiffiffiffi
eimh ;
2p
and plugged into HIR equation. The matrix elements for
the Hamiltonian are then given by
Hmn

1
hmjH jni ¼
2p

Z2p

eÀimh

0

Â
¼

!
L
X
:
1 o2
ilh
À
þ
Cl e
einh dh
2
2Ired oh
l¼ÀL

ð2Þ

1
m2 dmn þ cmÀn
2Ired

The matrix can be diagonalized to obtain its eigenvalue
spectra which are the energy levels of the considered rotor.
These information are used to calculate the partition
function and the contributions to the thermodynamic
functions.
Rate constant calculations

High-pressure rate constant calculations were carried out
using canonical transition state theory (TST) with tunneling corrections based on asymmetric Eckart potentials [29].
Note that other empirical and/or ab initio-based methods
(e.g., Group Additivity [30, 31] and Reaction Class Transition State Theory [32]) to obtain reliable high-pressure
rate constants on the fly were extended to the kinetics of the
oxygenated species [33, 34]. The high-pressure rate constants for the barrierless recombination of MA radicals
with O2 were not calculated in this work but derived from
similar alkyl?O2 systems [18, 19].
Pressure- and temperature-dependent rate constants for
the multiwell-multichannel PES were calculated based on a
steady state analysis in which the energy-dependent unimolecular rate coefficients k(E) were computed using the

Quantum Rice–Ramsperger–Kassel (QRRK) theory. Collisional stabilization rate constants were calculated using
the modified strong collision assumption (MSC). More
details of the methodology can be found in the work of
Chang and coworkers [35]. In addition to the high-pressure
rate constants, Lennard-Jones collision diameters (rLJ) of
˚ and well depths (rLJ) of 669.8 K were estimated
5.94 A
from similar systems [36], thus used for all adducts and
isomers. The MSC model further requires a value for the
average energy transferred per collision hEalli to calculate
stabilization rate constants. We used hEall i ¼ 440 cal/mol
˚ LJ ¼ 71:4 K)
for the bath gas collider of N2 (rLJ ¼ 3:80 A,e
[36]. We also run calculations with the bath gas of He
˚ LJ ¼ 10:0 K) [36], and the simulation
(rLJ ¼ 2:55 A,e
results were generally found to be rather insensitive to the
nature of the collider, at least for the conditions considered

in this study. The results are provided in the accompanied
Supplementary material.

Results and discussion
Due to breaking of different bond types, MA molecule
produces several fragments (e.g., CH3C(=O)O, CH3C=O,
CH3O, CH3, CO, etc.) [21, 37] which are too many to
include this study; therefore, we limit ourselves on the
main fragments having the same carbon–oxygen backbone
of MA due to the breaking of C–H bond, namely CH3C(=O)OC•H2 and •CH2C(=O)OCH3. These two radicals
can isomerize to each other through the hydrogen migration reactions via five-membered ring transition states (cf.
Fig. 1). These radicals can react with molecular oxygen to
form chemically activated peroxy radicals which can
undergo the stabilization, isomerization, and dissociation
reactions to form back reactants and/or bimolecular products. Similar to the analogous alkyl systems [18, 19, 38],
these systems are expected to be more complicated (due to
the presence of heterogeneous O atom in the ester

(a)

(b)

Fig. 1 Two MA radicals, namely (a) 2-methoxy-2-oxoethyl and
(b) (acetyloxy)methyl, can isomerize through hydrogen migration
reactions via five-membered ring transition states given below and
above the reversible arrows

123

Struct Chem

Fig. 2 Simplified potential energy diagram for the reactions between
MA radicals with molecular oxygen at 0 K: (a) •CH2C
and
(b)
CH3C(=O)OC•H2 ? O2.
For
(= O)OCH3 ? O2

simplification, channels with barrier higher than 15.0 kcal/mol (e.g.,
beta-scission reaction from I2 and I4) are not included. Calculations
were carried out at the composite CBS-QB3 level of theory

functional group) and to play a central role in low-temperature combustion of the title fuel [39].

methyl acetate radicals and molecular oxygen were intensively explored at the CBS-QB3 level of theory, given in
Fig. 2. Even though both isomers react on the same surface, we artificially separate the surface in two parts, one
for 2-methoxy-2-oxoethyl (cf. Fig. 2a) and the other for
(acetyloxy)methyl (cf. Fig. 2b). This separation is feasible
because—as we will discuss later—the reaction pathways
connecting these parts are sufficiently slow that for all

Potential energy surface
Potential energy surfaces (PESs) play the central role in
computational chemistry, especially in detailed kinetic
modeling analysis. The PESs for the reactions between

123

Struct Chem
Fig. 3 Singly occupied
molecular orbitals (SOMO) for
the two initially formed adducts:
(a) •OOCH2C(= O)OCH3 (I1)
and (b) CH3C(=O)OCH2OO•
(I3)

practical purposes both parts are, from a kinetic point of
view, independent. To simplify the figure, dissociation
channels originating from the two initially formed adducts,
namely •OOCH2C(=O)OCH3 (I1) and CH3C(=O)OCH2OO• (I3), to form bimolecular products as well as highenergy pathways (e.g., having the barrier higher than
15 kcal/mol above the entrance channel) are omitted.
Formation/stabilization of initially formed adduct ROO•
The strength of the formed C-OO bond in the alkyl peroxy
radicals (or the ROO• well depth) determines the importance of the collisional stabilization channel and the temperature and pressure at which this reaction plays a role.
Re-dissociation of ROO• is believed to be the main cause
for negative-temperature coefficient (NTC) behavior [39];
thus, it is expected the behavior of biodiesel surrogates due
to the ester group –C(=O)O–, at least for this system, and is
different from the analogous alkyl systems. The combination of both MA radicals and molecular oxygen produces
the adducts via a barrierless reaction (cf. Fig. 2).
The C-OO bond energy at 298 K of •OOCH2C(=O)
OCH3 (I1) is about 8.4 kcal/mol smaller than that of
CH3C(=O)OCH2OO• (I3) (25.5 and 33.9 kcal/mol for I1
and I3, respectively). The latter value is closer to those of
alkyl systems (35.6, 37.4, and 38.7 kcal/mol for primary,
secondary, and tertiary carbon sites, respectively) [40, 41]
suggesting that the effect of –C(=O)O– group is less significant on this site. Note that the stabilization trend of the

adducts is opposite to that of the corresponding radicals
before adding O2. This can be explained in terms of
hyperconjugation effects as discussed for similar alkyl
systems by Villano et al. [40, 41] and Porter et al. [42].
This can be clearly seen by looking at the adducts’ singly
occupied molecular orbitals (SOMO), given in Fig. 3. The
SOMO of intermediate I3 occupies more space than that of
I1 makes I3 more stable. Specifically, the SOMO of I3
includes the two O atom of –C(=O)O– group while only
one O atom of –C(=O)O– group for I1. This leads to the

more sufficient hyperconjugation effect in I3, which lowered its energy of 7.5 kcal/mol compared to I1 at 0 K.
•
CH2C(=O)OCH3 ? O2 system. The initially formed
adduct, •OOCH2C(= O)OCH3 (I1), can isomerize to
HOOCH2C(= O)OC•H2 (I2) involving a seven-membered
ring TS with the energy barrier of 29.8 kcal/mol
(*4.7 kcal/mol above the entrance channel); thus, the
isomerization is not comparable to the re-dissociation of I1
at low temperature, making the consequent reactions of I2
less important. Intermediate I2 having the relative energy
of -15.7 kcal/mol can undergo the OH-group immigration
reaction with the rather high barrier of 28.5 kcal/mol
(12.8 kcal/mol above the reactant channel) to form
•
OCH2C(=O)OCH2OH. This channel is expected not to
play a role here (at least at the conditions that we are
interested in) even the product has the lowest relative
energy (-68.4 kcal/mol). This is confirmed in the rate
constant analysis session (cf. Rate Constant Calculations).

Alternatively, I2 can dissociate to form two bi-molecular
products: (1) aldehyde channel, CHO–C(=O)OCH3 ? OH,
and (2) cyclic ether channel, cy[CH2C(=O)OCH2O] ? OH. The latter goes through a five-membered ring
TS involving O–O bond breaking and C–O bond forming,
with the lower barrier energy compared to the other
channel (*2.9 vs. 9.9 kcal/mol), identified as one of the
important reaction pathways from an alkyl–ester radical to
formation of CO2 via the radical OCHO [7]. In summary,
the energetically important channels are the formation and
re-dissociation of the adduct I1 and due to the narrower of
the well-depth, the formation of the adduct plays a less
important role compared to the alkyl systems. A more
detailed picture can be seen in the rate constant analysis.
CH3C(=O)OC•H2 ? O2 system. Similarly, radical CH3
C(= O)OCH2OO• (I3) is formed via a barrierless reaction but
with a deeper well-depth of 33.9 kcal/mol at 298 K (compared to 25.5 kcal/mol of I1). This value is closer to those of
the alkyl systems (* 35.6 kcal/mol for primary carbon site)
suggesting that the effect of –C(= O)O– group is less significant on this site compared to the alkyl ones. In addition to

123


Struct Chem

dissociation back to the reactants, this adduct can isomerize to
form •CH2C(=O)OCH2OOH (I4) (through 1,6 hydrogen
migration) and CH3C(=O)OC•HOOH (through 1,3 hydrogen
migration) with the barrier height of 30.5 and 41.3 kcal/mol,
respectively. The latter radical is unstable; thus, it, once
formed, easily dissociates to form CH3C(=O)OCHO and OH.

The barrier difference between the two hydrogen migration
reactions is mainly due to the ring strain energy of different
ring sizes (7-membered vs. 4-membered ring). This leads to
the dominance of the formation of •CH2C(= O)OCH2OOH
(cf. rate constant calculations for detailed analysis) which can
dissociate to form several bi-molecular products among which
the formation of aldehyde (CH3C(=O)OCHO) and cyclic
(cy[CH2C(=O)OCH2O]) compounds has the barriers comparable to the entrance channel (0.3 and 0.5 kcal/mol at 0 K
above the entrance channel, respectively); thus, these two
channels are expected to be energetically important even at
low temperature. Note that the lower-energy conformers are
considered if there are more than two conformers including
the cyclic transition states (e.g., chair and boat for 6-membered ring conformers).
For the considered systems, the unimolecular degradation
due to beta-scission reaction will occur at intermediates I2
and I4, which are the products of the isomerization reaction.
Since the isomerization is not important in this system, the
consequent beta-scission does not play a role here. In addition, the barrier for these channels is high; specifically, the
barriers of the I2 ? HOOCC(=O) ? CH2O and
I4 ? CH2C=O ? OCH2OOH are 32.1 and 45.1 kcal/mol,
respectively (16.4 and 20.3 above the entrance channel,
respectively). For larger systems where isomerization can
dominate (i.e., molecules with longer carbon/oxygen backbone chains which allow faster isomerization due to the
larger ring size of the TS), the beta-scission reaction is
expected to play a more important role, especially in high
temperature regime.
Thermodynamic properties
Thermodynamic properties including heat of formation
(4fH), entropy (S), and heat capacity at constant pressure
(Cp) were calculated, following the procedure described in

the ‘‘Thermodynamic Property Calculations’’ session
above. The calculated numbers as well as literature values
for selected species are provided in Table 1 in an attempt
to evaluate the reliability of our numbers. The thermodynamic data for all species involved in the system can be
found in the accompanied Supplementary material. The
available experimental/calculated data (from NIST [43]
and Active Thermochemical Tables (ATcT) [44, 45])
confirm that our calculated values are within expected
uncertainty range for 4fH, S and Cp. The average differK
ences in 4fH298 K, S298 K, and C298
between our numbers
p

123

and ATcT approach are 0.8 kcal/mol, 1.9 cal/mol-K, and
0.5 cal/mol-K, respectively. The difference in 4fH is
normally less than 1 kcal/mol which is normally defined as
‘‘chemical accuracy’’. This excellent agreement gives us
more confidence on our calculations.
The good agreement with the literature data, together
with the previous success of this method for analogous
alkyl?O2 systems [18, 19, 40, 41], provides evidence that
the CBS-QB3 level of theory is adequate for calculating
accurate thermodynamic data for the title reactions. This
theory is a good compromise between accuracy and computing time, especially in the context of extending this type
of analysis to larger biodiesel methyl ester radical reactions
(perhaps up to the C8 level) in an attempt to derive the rate
rules for real biodiesel molecules. We anticipate that these
results can be generalized in the form of rate rules that

could then be applied confidently to ester alkyl?O2 reactions involving even larger ester alkyl radicals generated
from realistic biodiesel fuels.
Rate constant calculations
Calculation of the pressure-dependent rate coefficients using
QRRK theory requires specification of the high-pressure rate
coefficients for each reaction pathway. With the exception
of the addition of O2 to MA radicals whose rate constants
were adopted from the analogous propyl ? O2 system [19],
high-pressure rate coefficients for all important reaction
pathways were calculated using unadjusted CBS-QB3
results, following the procedure described earlier. Calculated high-pressure rate constants for all individual channels
for MA systems over the temperature range 300–1,500 K
are given in Table 2. The rate constants for the reverse
reactions, calculated from the corresponding equilibrium
constants and the forward rate constants, are also provided in
the table. The literature data for those reactions are limited.
For example, there are only two reactions (Rxn. 3 and Rxn. 9
in Table 2) whose rate constants were suggested by Hakka
and coworkers [22]. The ratios of our values to Hakka’s data
for these two reactions at 1,000 K are 1.8 and 0.25,
respectively. Since Hakka et al. reported no detail or justification for their suggested rate constants, we strongly
believed that our values, which are rigorously derived from
the accurate CBS-QB3 level under the solid statistical
mechanic framework (see Thermodynamic Property Section), are more reliable and thus should be confidently used
for analyzing the effect of pressure in the next section as well
as for other related applications.
Pressure dependence analysis
We have calculated high-pressure rate constants for the
reactions between two MA radicals with molecular oxygen.

Struct Chem
Table 1 Comparison of calculated thermodynamic properties of selected stable species involved in the system with experimental/calculated data
(ATcT = active thermochemical tables [44, 45]a, NIST Webbook NIST [43])
Species

Method

4fH298c

S298

C300
p

C400
p

C500
p

C600
p

C800
p

C1000
p

C1500
p

CH3COOCH3

This workb

-100.26

77.20

20.13

24.73

29.09

32.90

38.94

43.39

50.23

ATcT

-99.22

76.84

20.47

24.66

28.85

32.66

38.60

43.08

49.75

NIST

-98.00 [46]

–

20.64

25.17

29.49

33.28

39.31

43.75

50.51 [47]

This work

-11.75

57.67

12.28

14.09

15.55

16.76

18.66

20.11

22.44

ATcT

-11.61

60.09

12.40

14.20

15.68

16.90

18.79

20.25

22.48

NIST

-11.40 [48]

–

12.41

14.22

15.68

16.89

18.80

20.25

22.55 [49]

This work
ATcT

-27.34
-26.09

52.23
52.28

8.44
8.47

9.31
9.36

10.35
10.44

11.40
11.52

13.24
13.37

14.68

14.82

16.92
16.93

NIST

-27.70 [50]

52.33 [50]

8.47

9.38

10.45

11.52

13.37

14.81

17.01 [49]

This work

-140.62

74.19

20.43

25.20

29.17

32.21

36.26

38.79

42.39

ATcT

-139.33

76.14

20.90

25.74

29.81

32.99

36.92

39.53

43.12

CH2=C=O

HCHO

HOCH2COOH

CH3C(=O)OC•H2

•

CH2C(=O)OCH3

NIST

–

–

20.34

24.87

28.83

32.02

36.44

39.24

43.13 [51]

This work

-52.06

80.19

22.06

26.21

29.88

32.95

37.67

41.10

46.35

ATcTd

-52.97

75.75

20.46

24.94

28.95

32.35

37.32

40.89

46.05

NIST

–

–

–

–

–

–

–

–

–

This work

-53.17

77.91

21.10

25.46

29.36

32.64

37.69

41.31

46.69

ATcTd

-52.97

75.75

20.46

24.94

28.95

32.35

37.32

40.89

46.05

NIST

–

–

–

–

–

–

–

–

–

298

Units: kcal/mol for 4fH and cal/mol-K for S and Cp
a
Values collected from Burcat’s online database, (access date: Dec. 2013)
b

Data were calculated at CBS-QB3 level of theory

c

4fH298 was calculated by atomization method

d

The radical position cannot be identified

In this section, we investigate the effect of pressure on rate
constants, thus affecting the product distribution. The calculated high-pressure rate constants were used to compute
the pressure- and temperature-dependent rate constants.
This QRRK analysis included all the pathways shown in
Fig. 2 as well as several low-barrier dissociation channels
from all isomers. A complete list of the calculated rate

constants for all channels over the temperature range
300–1,500 K at 0.1, 1.0, and 10 atm was included in the
Supplementary Table S5.
Some representative results on the effect of pressure at
different temperatures (e.g., 300, 600, and 800 K) for both
chemically and thermally activated reactions for
•
CH2C(=O)OCH3 ? O2 and CH3C(=O)OC•H2 ? O2 systems are presented in Figs. 4 and 6. The effect of temperature at different pressures (e.g., 0.1, 1, and 10 atm) for
all channels for the two systems is also presented in Figs. 5
and 7.
For both radicals, the dominant reaction is formation of
the corresponding stabilized peroxy adducts. The importance of this channel is expected to be more profound for
the CH3C(=O)OC•H2 ? O2 system at the same condition
(cf. Fig. 6) due to the deeper well depth as discussed above.
The re-dissociation of the adduct to the reactants is less

profound for this system due to relatively low barrier of the
competing isomerization channel (2.9 kcal/mol lower than
the re-dissociation, cf. Fig. 2). The different pressure
dependencies observed for the two systems (cf. Figs. 4, 5,
6, 7) are consistent with the general pressure-dependent
features of the analogous alkyl?O2 reactions [18, 19],
which will be described in the following session.
The most important chemically activated channel
(reactants ? intermediates/products) is the stabilization
but its importance decreases with temperature (or the other
competing reactions become more and more important).
For example, for the •CH2C(=O)OCH3 ? O2 system, rate
constants to the adduct decrease from 300 to 800 K
(4 9 10?12 and 3 9 10?11 at 1 atm, respectively, cf.

Fig. 4a, c), while rate constants to other channels increase
(e.g., 4 9 10?4 and 7x10?7 for HOOCH2C(= O)OC•H2
(I2) formation). The ratios of the two most dominant
reactions (e.g., R ? I1 and R ? I2) at 1 atm are
1 9 10?8 and 4 9 10?3 at 300 and 800 K, respectively.
For the CH3C(= O)OC•H2 ? O2 system, the ratios of
R ? I3 to R ? I4 channels at 1 atm are 3 9 10?5 and
3 9 10?2 at 300 and 800 K, respectively (cf. Fig. 6a, c).
Therefore, for the chemically activated channels, the formation of the adducts is the dominant ones (e.g.,

123


Struct Chem
Table 2 High-pressure rate constants for reactions of MA radicals with O2 and comparison with available literature data
Aa

No.

Reaction

1

CC(=O)OC• ? O2 =[ CC(=O)OCOO•

0.00

-0.61

(see Huynh et al. [19])

1.38 9 1015

0.00

32.64

–

CC(=O)OCOO• =[ CC(=O)OC = O ? OH

5.48 9 102

3.18

36.61

–

•

0

3.33 9 10

3.32

71.35

–

6.03 9 103

2.48

26.71

1.25 9 105b (2.30 9 105)

CC(=O)OC = O ? OH =[ CC(=O)OCOO
•

4.39 9 10

-0.14

19.38

–

•

CC(=O)OCOOH =[ C=C(OH)OCOO•

2.35 9 106

2.13

38.82

–

C=C(OH)OCOO• =[ •CC(=O)OCOOH

7.34 9 1010

0.45

12.21

–

•

1.09 9 109

1.11

22.35

–

11

CC(=O)OCOOH =[ CC(=O)OCOO•

4
5

Literature data for ka at 1,000 K

CC(=O)OCOO =[ CC(=O)OC ? O2

•

CC(=O)OCOO• =[ •CC(=O)OCOOH

3

Ea (kcal/mol)

1.48 9 1012

•

2

n

CC(=O)OCOOH =[ CC(=O)OC=O ? OH
•

-2

CC(=O)OC = O ? OH =[ CC(=O)OCOOH

8.62 9 10

3.88

64.41

–

6

•

CC(=O)OCOOH =[ HOCC(=O)OCO•
HOCC(=O)OCO• =[ •CC(=O)OCOOH

1.16 9 1013
5.89 9 1010

-0.40
0.64

36.01
80.96

–
–

7

•

2.23 9 1014

CC(=O)OCOOH =[ cy[CC(= O)OCO] ? OH

-0.72

25.06

–

cy[CC(=O)OCO] ? OH =[ CC(= O)OCOOH

1.15 9 103

3.04

51.95

–

•

1.48 9 1012

0.00

-0.61

(see Huynh et al. [19])

1.92 9 1014

0.00

24.23

–

1.18 9 103

2.52

25.97

3.46 9 105b (8.62 9 104)

•

CC(=O)OC ? O2 =[ •OOCC(=O)OC

8

•

•

OOCC(=O)OC =[ CC(= O)OC ? O2

•

OOCC(=O)OC =[ HOOCC(=O)OC•

9

•

10
11

•

HOOCC(=O)OC =[ OOCC(=O)OC

13

2.58 9 10

-0.87

18.25

–

HOOCC(=O)OC• =[ O=CC(=O)OC ? OH

3.59 9 1010

0.36

23.25

–

O=CC(=O)OC ? OH =[ HOOCC(=O)OC•

6.12 9 10-5

4.60

52.20

–

HOOCC(=O)OC =[ OCC(= O)OCOH

3.68 9 1014

-0.97

28.20

–

•

5.29 9 1010

0.65

80.94

–

3.92 9 1016

-1.34

19.36

–

2.99

54.05

–

•

•

OCC(=O)OCOH =[ HOOCC(=O)OC•

12

HOOCC(=O)OC• =[ cy[CC(=O)OCO] ? OH
cy[CC(=O)OCO] ? OH =[ HOOCC(=O)OC

•

6.03 9 103

Rate constants are given as k(T) = A 9 Tn 9 exp(-Ea/RT), Valid for 300–1,500 K. Hydrogen is not explicitly given in the molecule formula for

simplicity
The maximum error for fitting to k(T) = A 9 Tn 9 exp(-Ea/RT) is generally less than 3.5 % but in a very few cases is about 5.0 %. The values
in parentheses obtained from this work at 1,000 K
a

Units of [s-1] for first-order reactions and [cm3 mol-1 s-1] for second-order reactions

b

From the work of Hakka et al. [22] at the same temperature

accounting for more than 99 % of the reactant consumption
in the temperature of 300–1,500 K and pressure of larger
than 1 atm).
•
CH2C(=O)OCH3 ? O2 system. As the temperature
increases, the stabilization channel appears to approach the
high-pressure limit at higher pressures (e.g., 0.1 atm and
1 atm at 300 and 600 K, respectively, cf. Fig. 4a, b), while
other rate constants for chemically activated bimolecular
product channels continue to decrease as pressure increases. For this reason, it is expected the complexities
involved in chemically activated reaction play a role at a
low pressure. For example, at 800 K and below 0.6 atm (cf.
Fig 4c), the rate constant of the cyclization channel is
higher than that of the isomerization even though the highpressure rate coefficient for the former is much lower due
to the multiple reaction pathways. The cyclization pathway
becomes more competitive as temperature increases and

123

pressure decreases because of the arrangement of the
transition state via five-membered ring with a high barrier
height of 18.6 kcal/mol. This process is believed to favor at
higher temperature and lower pressure. It is expected to be
a sensitive channel to the temperature and pressure.
For the thermally activated channels of the initially
formed adduct, the fastest channel is the dissociation back
to form the reactants as discussed above. This channel is
believed to be the main cause for NTC behavior for
hydrocarbon fuels [39]. Because this channel has the
lowest barrier (25.1 kcal/mol compared to the barrier of
29.8 kcal/mol for the second lowest reaction, isomerization), it plays a role up to 1,000 K (accounting for larger
than 99 % at P [ 1 atm). Again, the formation of cyclic
channel becomes more competitive as temperature
increased; however, it does not compete to the isomerization reaction to form I2 up to 800 K at low pressure of


Struct Chem

Fig. 4 Rate coefficients for •CH2C(=O)OCH3 ? O2 ? products (a–c) and •OOCH2C(=O)OCH3 ? products (d–f) as a function of pressure at
300, 600, and 800 K. Only the most important reaction pathways are shown

0.05 atm (cf. Fig. 4f). All of the major pathways are near
their high-pressure limiting rate constants at about 1 atm at
600 K. At higher temperatures, the pre-exponential term of
the rate constant becomes increasingly more important.
This is shown in the Fig. 5 which presents the temperature
dependence at 0.1, 1.0, and 10.0 atm for the most important
reaction pathways. As pressure increases, the stabilization
channel approaches the high-pressure limit at higher temperature (about 400 and 500 K at 1 and 10 atm, cf. Fig. 5b,

c). The stabilization channel is still the most important
one as we expected earlier; especially at high pressure

where the similar trend for n-C3H7 ?O2 system was
observed [19]. The rate constants of other channels generally decrease with increasing pressure. Note that the
cyclization channel through the five-membered TS has
been more affected by pressure as mentioned before. With
this reason, its rate constant decreases faster with increasing pressure compared to the remaining competitive
channels. These complexities illustrate the necessity of
properly accounting for pressure effects. The Fig. 5d–f
presents the pressure effects for the thermally activated
channels, I1 ? products. The most dominant channel is

123


Struct Chem

Fig. 5 Rate coefficients for •CH2C(= O)OCH3 ? O2 ? products (a–c) and •OOCH2C(=O)OCH3 ? products (d–f) as a function of
temperature at 0.1, 1.0, and 10.0 atm. Only the most important reaction pathways are shown

the re-dissociation to the reactants, which becomes much
more important with increasing pressure at lower temperature. Other pathways are less competitive again in this
system.
For the •CH2C(=O)OCH3 system, the important channels for this radical system are the formation of the initial
adduct and the re-dissociation back to the reactants of the
adduct. Other channels, having much higher barrier, do not
play a role for this system at least at low temperature and
the high pressure. Therefore, at engine-liked conditions
(e.g., pressure [30 atm), the significance of these two

reactions is expected to be more profound.
CH3C(=O)OC•H2 ? O2 system. Some representative
results on the effect of pressure at the temperature of 300,

123

600, and 800 K are presented in Fig. 6. For the chemicalactivated channels, the dominant reaction is the formation
of the corresponding stabilized adduct, CH3C(= O)OCH2OO• (I3). The different pressure dependencies observed in
this figure are consistent with the earlier discussion. The
stabilization channels appear to be approaching the highpressure limit near 1 atm at 600 K (cf. Fig. 6b), while the
rate constant for the bimolecular product channels continue
to decrease as pressure increases (cf. Fig. 6a–c).
With respect to thermally activated reactions of the stabilized adducts, the similar trend is observed for this system
(cf. Fig. 7). The isomerization to form I4 (via five-membered
TS), the concerted elimination to form the aldehyde channel,
and the cyclization channel can play a role at certain


Struct Chem

Fig. 6 Rate coefficients for CH3C(=O)OC•H2 ? O2 ? products (a–c) and CH3C(=O)OCH2OO• ? products (d–f) as a function of pressure at
300, 600, and 800 K. Only the most important reaction pathways are shown

conditions due to their lower barrier height. The pathway via
OH migration is much slower because of its higher barrier.
Again, all major channels are near their high-pressure limiting rate constants at *1 atm at 600 K. In conclusion, the
pressure behavior of the CH3C(=O)OC•H2 ? O2 system is
similar to that of •CH2C(=O)OCH3 ? O2, except for the
increasing importance of the concerted elimination channel.
The most dominant channel is the adduct stabilization which

is more competitive than other channels at low temperature
and high pressure. Therefore, it is necessary to investigate
the pressure effects for an accurate description of its kinetics.

The effect of the pre-exponential factor plays a more
and more important role with the temperature. This is
shown in Fig. 7 which presents the temperature dependence of the apparent rate constants for CH3C(=O)OC•H2 ? O2 ? products (cf. Fig. 7a–c) and
CH3C(=O)OCH2OO• ? products (cf. Fig. 7d–f), where
the most dominant channel is still re-dissociation to the
reactants. The increasing importance of the concerted
elimination reactions to form aldehyde ? OH at higher
temperature (cf. Fig. 7a–c) is due to its higher A-factor
relative to the cyclic ether ? OH channel and its lower

123


Struct Chem

Fig. 7 Rate coefficients for CH3C(=O)OC•H2 ? O2 ? products (a–c) and CH3C(=O)OCH2OO• ? products (d–f) as a function of temperature
at 0.1, 1.0, and 10.0 atm. Only the most important reaction pathways are shown

barrier height (0.3 and 0.5 kcal/mol above the entrance
channel, respectively). The higher A-factor value for the
concerted elimination can be explained by the fact that the
transition state of this pathway ties up one more hindered
rotor than the transition state for the 1,5-H shift isomerization reaction to form the cyclic ether compound.
Important channels
According to the pressure analysis above, it is noticed that at
common low-temperature combustion conditions in engine

(e.g., 300 K \ T \ 1,000 K and P [[ 1 atm), the most

123

important reactions are Rxns 1–4 (cf. Table 3) whose rate
constants sum up to 99 % or more of the overall rate constant for each of the two MA radicals ? O2 systems. The
other channels such as isomerization, cyclic ether formation,
and concerted HO2 elimination are less important at the
same conditions. The OH migration reactions discussed
earlier are even less important. Thus, in spite of the complexity of the full potential energy surface, only two
chemically activated reactions and two thermally activated
reactions are found to be important at practical low-temperature combustion conditions. Note that for larger systems
which allow faster isomerization reactions (due to larger TS


Struct Chem
Table 3 Simplified MA radicals ? O2 submechanism at low-temperature combustion conditions
Radicals ? O2 channels
•

CH2C(=O)OCH3 ? O2 ? •OOCH2C(=O)OCH3

(Rxn. 1)

CH3C(=O)OC•H2 ? O2 ? CH3C(=O)OCH2OO•

(Rxn. 2)

ROO dissociation channels
•

OOCH2C(=O)OCH3 ? C•H2C(=O)OCH3 ? O2

CH3C(=O)OCH2OO• ? CH3C(=O)OC•H2 ? O2

(Rxn. 3)
(Rxn. 4)

Valid in the temperature range of 300–1,000 K and P [ 1 atm

ring size), different subsequent reactions of the isomerization products such as beta-scission, cyclic ether formation,
and OH migration can compete with the dominant channels
observed in the MA ? O2 systems. The competition makes
the behaviors of larger systems more complicated, especially the pressure dependence of the rate coefficients.

Conclusions
We have constructed accurate potential energy surfaces for
methyl acetate radicals ? O2 reactions at the CBS-QB3 level
of theory. Thermodynamic properties of all species were
calculated with explicit corrections for hindered internal
rotations. Pressure- and temperature-dependent rate constants
for the various channels of this system were derived under the
QRRK/MSC framework with high-pressure rate constants
obtained from the transition state theory with explicit Eckart
tunneling treatment. A thermodynamically consistent detailed
kinetic mechanism, consisting of all elementary reactions
together with their thermodynamic and kinetic data (given in
the accompanied Supplementary Table S7), was constructed
for low-temperature oxidation and auto-ignition of the title
fuel. The simplified mechanism, consisting of 4 reactions (cf.

Table 3), was also composed specifically for the engine-liked
conditions. The mechanism, either full or simplified, can be
used as a solid building block to construct detailed kinetic
mechanisms for low-temperature combustion of real fuel
molecules. In addition, since MA is the smallest biodiesel
surrogate, the several unimportant reactions existing in the
system such as isomerization, cyclization, and concerted HO2
elimination can play an important role in larger systems; thus,
MA is not a good surrogate model for investigation of the lowtemperature oxidation of real methyl ester. For this purpose,
larger methyl ester molecules such as methyl propanoate and
methyl butanoate should be considered.

Supporting Information Available
(1) Conventional names, short notations, and 2-D structures
for all species; (2) Tabulated values for electronic structure

calculations (geometries, energies, frequencies) for the MA
radicals ? O2; (3) Calculated reaction barrier and reaction
energy at the CBS-QB3 level comparing with other
methods for several important channels; (4) Tabulated
calculated thermodynamic properties of species are formed
from reactions in system; (5) Tabulated values for the
pressure-dependent apparent rate constants for the various
reactions as a function of temperatures at 0.1, 1.0, and
10.0 atm; (6) Potential energy surfaces for the internal
rotations for some stable species; (7) Detailed kinetic
submechanism in Chemkin format for MA radicals ? O2 ? Products. This material is available free of
charge via the Internet at .
Acknowledgments We thank Dr. Carstensen (Ghent University) for
helpful discussion and Dr. Villano (Colorado School of Mines) for

providing calculation information on alkyl?O2 systems. This research
is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 104.032012.75. Computing resources and financial support were provided by
the Institute for Computational Science and Technology—Ho Chi
Minh City is gratefully acknowledged.

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