Detailed modeling of low-temperature propane oxidation: 1. The role of the propyl + O(2) reaction.

Abstract

Accurate description of reactions between propyl radicals and molecular oxygen is an essential prerequisite for modeling of low-temperature propane oxidation because their multiple reaction pathways either accelerate the oxidation process via chain branching or inhibit it by forming relatively stable products. The CBS-QB3 level of theory was used to construct potential energy surfaces for n-C(3)H(7) + O(2) and i-C(3)H(7) + O(2). High-pressure rate constants were calculated using transition state theory with corrections for tunneling and hindered rotations. These results were used to derive pressure- and temperature-dependent rate constants for the various channels of these reactions under the framework of the Quantum Rice-Ramsperger-Kassel (QRRK) and the modified strong collision (MSC) theories. This procedure resulted in a thermodynamically consistent C(3)H(7) + O(2) submechanism, which was either used directly or as part of a larger extended detailed kinetic mechanism to predict the loss of propyl and the product yields of propylene and HO(2) over a wide range of temperatures, pressures, and residence times. The overall good agreement between predicted and experimental data suggests that this reaction subset is reliable and should be able to properly account for the reactions of propyl radicals with O(2) in propane oxidation. It is also demonstrated that for most conditions of practical interest only a small subset of reactions (e.g., isomerization, concerted elimination of HO(2), and stabilization) controls the oxidation kinetics, which makes it possible to considerably simplify the mechanism. Moreover, we observed strong similarities in the rate coefficients within each reaction class, suggesting the potential for development of relatively simple rate constant estimation rules that could be applied to analogous reactions involving hydrocarbon radicals that are too large to allow accurate detailed electronic structure calculations.

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Detailed Modeling of Low-Temperature Propane Oxidation: 1. The Role of the Propyl + O2
Reaction
Lam K. Huynh, Hans-Heinrich Carstensen, and Anthony M. Dean*
Chemical Engineering Department, Colorado School of Mines, Golden, Colorado 80401
ReceiVed: February 25, 2010; ReVised Manuscript ReceiVed: May 4, 2010
Accurate description of reactions between propyl radicals and molecular oxygen is an essential prerequisite
for modeling of low-temperature propane oxidation because their multiple reaction pathways either accelerate
the oxidation process via chain branching or inhibit it by forming relatively stable products. The CBS-QB3
level of theory was used to construct potential energy surfaces for n-C3H7+ O2and i-C3H7+ O2. High-
pressure rate constants were calculated using transition state theory with corrections for tunneling and hindered
rotations. These results were used to derive pressure- and temperature-dependent rate constants for the various
channels of these reactions under the framework of the Quantum RicesRamspergersKassel (QRRK) and
the modified strong collision (MSC) theories. This procedure resulted in a thermodynamically consistent
C3H7+ O2submechanism, which was either used directly or as part of a larger extended detailed kinetic
mechanism to predict the loss of propyl and the product yields of propylene and HO2over a wide range of
temperatures, pressures, and residence times. The overall good agreement between predicted and experimental
data suggests that this reaction subset is reliable and should be able to properly account for the reactions of
propyl radicals with O2in propane oxidation. It is also demonstrated that for most conditions of practical
interest only a small subset of reactions (e.g., isomerization, concerted elimination of HO2, and stabilization)
controls the oxidation kinetics, which makes it possible to considerably simplify the mechanism. Moreover,
we observed strong similarities in the rate coefficients within each reaction class, suggesting the potential for
development of relatively simple rate constant estimation rules that could be applied to analogous reactions
involving hydrocarbon radicals that are too large to allow accurate detailed electronic structure calculations.
I. Introduction
Given its significant importance in combustion ignition
systems, low-temperature oxidation chemistry has been the
subject of intense studies for many years.1As a result, detailed
kinetic models are available to describe the ignition behavior
of a wide range of hydrocarbon fuels with good accuracy,2-4
and current efforts focus on extending those mechanisms to
surrogate mixtures for gasoline,5diesel,6and jet fuels.7One
common feature of the most widely used kinetic models is that
they are developed in a systematic way based on well-defined
reaction classes8and rate estimation methods. The modular
concept helps to make these mechanisms relatively easy to
maintain, transparent, and extendable.
A key reaction in the low-temperature oxidation of alkanes
is the addition of alkyl radicals to molecular oxygen. This
reaction produces either stabilized alkyl peroxy radicals and their
hydroperoxy alkyl isomers, or bimolecular products such as
hydroperoxy radicals together with olefins or cyclic alkanes, or
hydroxyl radicals with aldehydes, ketones, or cyclic ethers.
Shown in Scheme 1 are important channels for this reaction,
where “R” and “Q” denote CnH2n+1and CnH2ngroups, respec-
tively; “M” represents a collider; “•” symbolizes a radical site;
and “*” designates an energized/activated species.
Since the C-O bond is rather weak, alkyl peroxy radicals
(ROO•) can easily redissociate at elevated temperatures. The
reversibility of the R + O2reaction is considered the main cause
of the observed negative temperature coefficient region seen in
ignition experiments.1Note the multiple reaction pathways for
ROO•and its isomer Q•OOH. The rate constants for the various
pathways depend on both temperature and pressure, making the
kinetic analysis of this system quite complicated. These various
reaction channels might either accelerate the overall reaction
via chain branching or inhibit it by producing relatively inert
species such as HO2. Given the importance of this reaction class,
a kinetic description of it is found in every detailed kinetic
mechanism describing ignition chemistry, even though the level
of detail may vary.
Our understanding of the elementary steps of the R + O2
reaction changed profoundly when almost a decade ago Rien-
stra-Kirakofe et al.9discovered for the ethyl + O2reaction a
new reaction pathway: the concerted HO2elimination reaction.
Incorporation of this reaction channel into the ethyl + O2
submechanism10,11showed that it was able to predict experi-
mental results of several studies12-14that could not satisfactorily
be explained previously.15Similar conclusions can be drawn
* To whom correspondence should be addressed. E-mail: amdean@
mines.edu.
SCHEME 1
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6594
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 2010 American Chemical Society
Published on Web 05/28/2010

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for higher alkyl + O2 reactions.16Therefore, it has been
recognized that this reaction channel needs to be incorporated
into low-temperature oxidation mechanisms.3This in turn
requires a rate estimation rule be developed for this channel.
Additionally, since it competes with existing previously con-
sidered reaction pathways, rate constants for these reactions
might need to be modified as well. One way to obtain such rate
estimation rules is to investigate the R + O2reaction for small
alkyl radicals theoretically with high-level electronic structure
calculations. This is one of the motivations of the current study.
Since the ethyl + O2reaction has already been analyzed, we
focus here on the reaction of propyl radicals with molecular
oxygen.
The propyl + O2reaction is the smallest realistic prototype
of the alkyl + O2reaction class, because it contains most of
the essential reaction pathways that play a role in larger systems.
The short alkyl chains of methyl and ethyl radicals result in
high barriers for isomerization reactions of the alkyl peroxy
radicals; such isomerizations are much more important for
radicals with longer alkyl chains. Hence, methyl and ethyl
reactions with O2are special cases, which, although interesting in
their own right, are not suitable to create a general and complete
understanding of the alkyl + O2chemistry. Because of their role
as a model system, the reactions of propyl radicals with oxygen
have been subject of numerous experimental17-29and theoretical29-34
studies. For example, Taatjes and co-workers16,27,29reported PES
calculations for the major channels of this reaction and achieved
good agreement between their model and experimental data on
HO2and OH. However, this required adjustments of some well
depths and barriers within the expected accuracy limits of their
calculation method. Similarly, Naik30modified the PES at the
CBS-Q level35to improve predictions of the C3mechanism.
On the other hand, the earlier kinetic study on the ethyl + O2
reaction employing the CBS-QB3 level of theory10to compute
the PES was able to reproduce experimental results with high
accuracy without any barrier adjustments, although the authors
point out that this might be due to fortunate cancellation of
errors. Nevertheless, the good quality of this PES was recently
confirmed by Wilke et al.36by performing very sophisticated
calculations. In general, the CBS-QB3 method has in recent
years emerged as a reliable and popular tool for kinetic
studies,37,38and, therefore, the objective of the current work is
to apply this method to C3 + O2 reactions. Merle and co-
workers33reported recently CBS-QB3 calculations on this
system, but their focus was exclusively on the conformational
distribution and decomposition pathways of alkyl peroxy radicals
and not on a kinetic analysis. From comparisons to experimental
data, these authors concluded that CBS-QB3 results were the
most accurate among the several calculation methods tested. If
we can show that the kinetic analysis of the C3+ O2reaction
system based on CBS-QB3 energies and molecular properties
can successfully describe the major experimental observations,
we could use these results to provide the database required for
systematic generation of the rate rules. These rules could then
confidently be applied to reactions of longer alkyl radicals with
O2, for which experimental data are not (yet) available.
Another aspect of the alkyl + O2chemistry is its dependence
on both temperature and pressure as mentioned earlier (see
Scheme 1). Previous experimental and theoretical studies on
the ethyl + O2 system10,13,14,39clearly demonstrate pressure
effects. However, for a given temperature and pressure, uni-
molecular reactions of larger molecules (as a result of a higher
density of states) are closer to the high-pressure limit than
smaller species.40The same will be true for reactions of large
alkyl radicals with oxygen and the question arises at what size
of the alkyl radical do the rate constants for R + O2reactions
approach the high-pressure limit. Experimental studies of OH
and HO2production in the neopentyl + O241and cyclohexyl +
O242reactions show that even for alkyl radicals containing five
and six carbon atoms the high pressure limit is not fully reached
for all the reaction channels under the experimental conditions
employed. This conclusion holds even at pressures as high as
20.3 bar.43Although these observations do not necessarily mean
that the kinetically most important channels are not at or close
to their high pressure limits, they do indicate the need to perform
a pressure-dependent analysis to investigate the influence of
pressure on R + O2reactions, regardless of the size of the alkyl
radical.
In this paper we concentrate our efforts on characterizing the
kinetics of the propyl + O2 reactions at low-temperature
combustion conditions. We will demonstrate that although the
PES leads to a large set of possible reaction pathways, only a
few of those determine the propyl consumption and the product
distributions. Similar to the previous C2H5+ O2study,10we
find that the obtained C3H7+ O2subset based on CBS-QB3
calculations, combined with a transition state theory (TST) and
Quantum RicesRamspergersKassel (QRRK) treatment, is able
to reproduce experimental results quite well, at least for the
considered conditions. Initial implications for the development
of rate rules are also discussed. The study of addition of oxygen
to γ-hydroperoxy propyl radical, which is thought to be the key
to chain branching in autoignition chemistry of alkanes, will
be presented as part II of this series.
II. Calculation Methods
II.1. Electronic Structure Calculations. The electronic
structure calculations were carried out using the Gaussian 03
program.44The composite CBS-QB3 method by Peterson and
co-workers45was selected because of its capability of predicting
thermodynamic properties to “chemical accuracy”, which is
normally defined as within ∼1 kcal/mol of experimental data.
The method calculates geometries and frequencies at the
B3LYP/6-311G(2d,p) level of theory. The energy is calculated
at several levels of theory, including CCSD(T)/6-31+G(d′), and
is then extrapolated to the complete basis set limit. All reported
results for stable molecules as well as transition states 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) method.46,47For several important channels,
we also optimized the geometries (and calculated frequencies)
at the QCISD/6-31G(d) level of theory and used those structures
to calculate the CBS-QB3 energy. This was done to verify that
the B3LYP geometry optimization is adequate for this reaction
system. We will refer to these modified CBS-QB3 calculations
as “CBS-QB3//QCISD”.
II.2. Thermodynamic Property Calculations. The atomi-
zation 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. All harmonic frequencies were scaled by a
factor of 0.99 as recommended by Petersson and co-workers45
prior to their use. Some low-frequency vibrational modes, which
are better treated as internal rotations around single bonds, were
replaced in the thermodynamics calculations by an explicit
Modeling of Low-Temperature Propane Oxidation
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evaluation of the hindered rotations. The hindrance potentials
were obtained at the MP2/6-31G(d) level via relaxed surface
scans with the step size of 10 degrees for dihedral angles that
corresponds to the rotations. In a few cases, for which the
hindrance potential calculations failed at the MP2/6-31G(d)
level, those calculations were instead performed either at the
B3LYP/6-31G(d) or B3LYP/6-311G(2d,p) level. The reduced
moments of inertia required for the hindered rotor treatment
were calculated with the approach proposed by East and
Radom,48on the basis of the original work by Kilpatrick and
Pitzer.49With this information at hand, the Schro ¨dinger equa-
tions for the internal rotor could be formulated and solved
numerically, and the resulting energy levels are used to calculate
the partition function and the contributions to the thermodynamic
functions.
II.3. Rate Constant Calculations. High-pressure rate con-
stant calculations were carried out using canonical TST with
tunneling corrections based on asymmetric Eckart potentials.50
The high pressure rate constants for the barrierless recombination
of n- and i-C3H7with O2were not calculated in this work but
derived from existing literature values.
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 QRRK theory. The
vibrational frequencies needed to calculate the density of states
were extracted from an analysis of the heat capacity data
calculated from the CBS-QB3 data. 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 et al.51In addition to the high-
pressure rate constants, estimated Lennard-Jones collision
diameters (σLJ) of 5.20 Å and well depths (εLJ) of 533 K were
used for the adducts/isomers. The MSC model further requires
a value for the average energy transferred per collision 〈Eall〉 to
calculate stabilization rate constants. We used 〈Eall〉 ) 250 and
440 cal/mol for the colliders He and N2, respectively, which
are the bath gases used in the corresponding experiments. In
general, the simulation results were found to be rather insensitive
to the nature of the collider, at least for the conditions considered
in this study.
II.4. Numerical Integration Calculations. The pressure- and
temperature-dependent rate coefficients obtained from the kinetic
analysis were approximated with Chebyshev polynomials over
wide ranges of temperatures and pressures as proposed by
Venkatesh and co-workers.52For constant pressure conditions,
we preferably represented the rate constants in modified
Arrhenius form, because this reduced the simulation times. The
propyl + O2submechanism, consisting of all reactions together
with their newly derived kinetic and thermodynamic data, was
either used alone or incorporated into an existing detailed kinetic
mechanism. The CHEMKIN PRO package53was used to predict
the concentration-time profiles for comparison to the experi-
mental results.
III. Results and Discussion
III.1. Potential Energy Surface. Although the potential
energy surface for the propyl + O2reaction has been reported
previously,29,30,33we reconstruct the PES with consideration of
additional reaction channels using the CBS-QB3 level of theory.
Our intent is to determine if CBS-QB3 theory is able to generate
a PES that allows us, without adjustments, to generate rate
parameters suitable to satisfactorily predict a variety of experi-
mental data. If successful, we can use the same methodology
for the generation of rate estimation rules. The PES of the C3H7
+ O2at 0 K is shown in Figure 1. Even though both isomers
react on the same surface, we artificially separate it in two parts,
one for n-propyl and the other for i-propyl. This separation is
feasible because-as we will discuss later-the reaction pathways
connecting these parts are sufficiently slow that for all practical
purposes both parts are, from a kinetic point of view, indepen-
dent. To simplify Figure 1, dissociation channels originating
from isomers I6-I13 to form bimolecular products as well as
high energy pathways are omitted.
The major features of the PES are similar to those reported
in earlier studies, except that the present results are more
comprehensive, for example, hydroxyl radical migration reac-
tions are included and more product channels are considered.
Since the reaction of O2with either propyl isomer proceeds
without an energy barrier, the available energy of the initial
adduct is given by that of the reactants. Several reaction
pathways from the ROO•adduct proceed via barriers that are
below the entrance channel. Among those are the concerted HO2
elimination pathways from both C3H7O2 isomers as well as
isomerization to γ-hydroperoxy propyl isomers. Hydroxyl group
migration reactions also have rather low barriers, and their
importance cannot be ruled out a priori. Generally, it is crucial
to consider this reaction class because it provides a link between
the two subsets of the C3H7+ O2PES describing the reaction
channels of n-propyl or i-propyl (isomer I12). Migration of
methyl groups have not been considered due to the expected
high barriers, but would also provide an interconnection between
both PES parts.
In the following we discuss selected reactions proceeding on
the C3H7O2PES in more detail.
Formation/Stabilization of Initially Formed Adduct ROO•.
The strength of the formed C-O bond in 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. Redissociation of ROO•is
believed to be the main cause for NTC behavior.1Therefore, a
correct value for this bond strength is an essential prerequisite
for properly characterizing low-temperature oxidation.
The current results for the thermochemistry of the initially
formed peroxy adducts are in good agreement with earlier
calculations. Table 1 provides a comparison of the calculated
C-O bond energy at 0 K for different methods. The C-O bond
in n-C3H7O2is slightly weaker than in i-C3H7O2. The calculated
C-O bond energy in CH3CH2CH2OO•(I1) is 34.8 and 35.5
kcal/mol at 0 and 298 K, respectively. These values agree well
with the multistep calculations by DeSain et al.29(34.9 kcal/
mol at 0 K), and the adjusted value used by Naik30(34.9 kcal/
mol at 298 K). Simmie et al.54calculated bond energies between
34.7 and 36.6 kcal/mol at 0 K and their preferred result of 34.7
( 0.5 kcal/mol compares favorably with our calculations. For
i-C3H7O2, our calculated C-O bond energy is 36.2 and 37.3
kcal/mol at 0 and 298 K, respectively. These values are also in
good agreement with the value by DeSain et al. (36.8 kcal/mol
at 0 K), that by Simmie et al. (36.3 ( 0.7 (preferred) at 0 K),
and Naik’s value (38.2 kcal/mol at 298 K). Using the CBS-
QB3//QCISD method defined earlier, we obtained bond energies
for both adducts that are very similar to those calculated with
the regular CBS-QB3 method. This is very encouraging because
it suggests that the B3LYP geometries and frequencies used in
the CBS-QB3 method are of sufficient quality to obtain accurate
thermodynamic data for the reactants and adducts. It is worth
noting that Merle and co-workers33used the CBS-QB3 method
to explore the ambient distribution of all possible n-propyl
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Huynh et al.

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peroxy radical conformers. Using the reported distribution, we
derived a C-O bond energy of 35.8 kcal/mol, which is only
0.3 kcal/mol higher than our value. Such an explicit consider-
ation of all conformers requires considerably more effort and
computer time than our procedure while a small improvement
in the accuracy is obtained. For that reason, we chose to restrict
ourselves to the lowest energy conformer but to treat the
hindered rotations carefully. This approach provides a good
trade-off between accuracy and CPU time demand.
Our results are also consistent with thermodynamic data
reported by Knyazev and Slagle.21Using a mechanism that
accounts for further reactions of the ROO•adduct, they
reanalyzed earlier experimental data20over the temperature range
of 592-692 K for the reaction CH3C•HCH3 + O2 d
CH3CH(OO•)CH3 and suggested thermodynamic values of
-37.14 ( 2.23 and -37.3 cal/mol-K for ∆Hrxn
∆Srxn(298 K), respectively. These data are in excellent agreement
with our CBS-QB3 values (-37.3 kcal/mol and -37.0 cal/mol-
K). In addition, our calculated equilibrium constants for both
CH3C•HCH3+ O2d CH3CH(OO•)CH3and CH3CH2C•H2+
O2 d CH3CH2CH2OO•are within a factor of 2 to those
calculated by Taatjes and co-workers27,28in the same temperature
° (298 K) and
Figure 1. Potential energy diagram for the n-C3H7+ O2(Figure 1a) and i-C3H7+ O2(Figure 1b) systems at 0 K. Bimolecular product channels
of isomers (I6)-(I13) are not included. Notations: CH3CH2CH2OO•(I1), C•H2CH2CH2OOH (I2), CH3C•HCH2OOH (I3), CH3CH(OO•)CH3(I4),
C•H2CH(OOH)CH3(I5), HOCH2CH2CH2O•(I6), HOCH2CH2C•HOH (I7), HOCH2CH•CH2OH (I8), CH3CH(OH)CH2O•(I9), CH3CH(OH)C•HOH
(I10), CH3C•(OH)CH2OH (I11), CH3CH(O•)CH2OH (I12), and C•H2CH(OH)CH2OH (I13).
TABLE 1: Comparison of C-O Bond Energy in C3H7O2Radicals at 0 K. Values in Parentheses Are Calculated at 298 K
(Units: kcal/mol)
species CBS-QB3a
DeSain et al.29
Merle et al.33
Simmie et al.54
CBS-QB3//QCISDa,b
CH3CH2CH2OO•
34.8
(35.5)
36.2
(37.3)
34.9 34.8
(35.8)c
34.7 ( 0.5 and 36.6c
34.6
(35.5)
36.2
(37.3)
CH3CH(OO•)CH3
36.8 36.3 ( 0.7 and 38.7c
aThis work.bSee section Thermodynamic Property Calculations for details.cSee text for details.
Modeling of Low-Temperature Propane Oxidation
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range. Because dissociation from the C3H7O2adducts back to
the reactants plays an important role in the reactivity of the
system at moderate temperatures, the good agreement in C-O
bond strengths and their related reaction thermodynamic data
gives us added confidence in our simulation results.
Concerted HO2Elimination Reactions. This reaction class
might be considered a chain-termination pathway as the HO2
radical is relatively inert. On the C3H7O2PES, the adducts I1
and I4 form HO2+ C3H6with barriers of approximately 31
kcal/mol. These barriers are still below the reactant energy (-3.9
and -5.1 kcal/mol for n-C3H7O2and i-C3H7O2, respectively)
and therefore these channels should be important. The small
difference between the barriers can in part be explained by
the nature of the C-H bond that breaks during the reaction. In
the case of n-C3H7O2, a secondary C-H site participates in the
reaction, and in addition the C-O bond in n-C3H7O2is weaker
than in i-C3H7O2as discussed above (Table 1). The leaving
hydrogen in the concerted HO2elimination reaction of i-C3H7O2
stems from a primary C-H site. These differences are also
reflected in the transition state structures: the HO2elimination
reaction from i-C3H7O2proceeds through a later TS (longer
C-OO and shorter OO-H bonds) than that for n-C3H7O2. Table
2 provides the calculated barriers for the concerted HO2
elimination reactions at different levels of theory. The CBS-
QB3 results of this study are slightly higher than those from
DeSain et al., but the difference is less than 1.5 kcal/mol. When
compared with CBS-QB3//QCISD calculations, the agreement
is excellent at both 0 and 298 K (less than 0.4 kcal/mol
difference).
Isomerization Reactions Wia H Migration. These reactions
play an important role in the reactivity of the propyl + O2system
because their products, hydroperoxy alkyl radicals (Q•OOH),
are believed to be the key to chain branching.1In addition, the
ROO•f Q•OOH isomerization is important as a step in the
formation of cyclic ethers. The calculated CBS-QB3 barriers
for the isomerization of propyl peroxy radicals, given in Table
2, are close to the CBS-QB3//QCISD results and to those from
DeSain et al.29In contrast to the concerted elimination reaction,
the isomerization pathways lead to a significant difference in
the reactivity of n-C3H7O2compared to i-C3H7O2. This is due
to the 1,5-H shift reaction, which is only possible in n-propyl
peroxy and forms C•H2CH2CH2OOH. Since this reaction
proceeds through a 6-membered transition state with low ring
strain, its barrier height is only 22.7 kcal/mol. In comparison,
the 1,4-H shift reactions in n- and i-propyl peroxy, which yield
the products CH3C•HCH2OOH and C•H2CH(OOH)CH3, respec-
tively, have substantially higher barriers of 31.2 kcal/mol (for
n-propyl peroxy) and 35.8 kcal/mol (for i-propyl peroxy) at 298
K. Again, the difference between latter barriers can be explained
by the different nature of the C-OO and C-H bonds involved.
Cyclic Ether Pathways. Cyclic ethers (methyl oxirane and
oxetane) formation is only possible from Q•OOH radicals, hence
it requires an isomerization step. Therefore, the most likely
pathway will start from C•H2CH2CH2OOH. The transition state
energy is only slightly below that of the initial reactants (n-
C3H7+ O2). Whether this reaction channel is important cannot
be decided solely based on energetic grounds. Given the higher
barrier for isomerization, methyl oxirane formation from
CH3C•HCH2OOH seems unlikely in the n-C3+ O2reaction,
but one needs to keep in mind that the CH3C•HCH2OOH radical
can also be formed via propene + HO2, thus it will probably
be an important reaction at conditions that favor high propene
and HO2concentrations.55
OH Migration Reactions. In addition to hydrogen migration,
hydroxyl (OH) migration reactions from Q•OOH were also
included in the PES due to the weak O-O bond in the
hydroperoxy group. These reactions are shown to be energeti-
cally less important than their hydrogen counterparts. For
example, OH migration from I2 to I6, through a 5-membered
ring TS, is ∼5 kcal/mol above the reactant energy whereas the
competing H migration pathway from I2 to I1 through a
6-membered ring transition state has the barrier of 11 kcal/mol
below the reactant energy (cf. Figure 1). Similarly, the barrier
for OH migration from I3 to I9 via a 4-membered ring TS is
∼1 kcal/mol above the reaction energy, and the competing
reaction of I3 to form methyl oxirane + OH proceeds through
a barrier that is ∼10 kcal/mol lower. Hence, based on these
energetic considerations, contributions from hydroxyl migration
should be insignificant. A kinetic analysis confirmed this
conclusion. This observation allows us to decouple the two parts
of the propyl + O2surface, thereby simplifying the analysis of
the pressure-dependence. Our conclusion is in general agreement
with the work by Green et al.,56who have reported CBS-QB3
E0barriers for these two channels. Their values are even higher
than ours, specifically 27.5 and 23.6 kcal/mol compared to 23.9
and 22.12 kcal/mol for I2 f I6 and I3 f I9, leading them to
conclude that the OH migration channels are not competitive,
at least for the fuel ignition conditions they considered. (The
differences in barriers are likely due to the different TS
conformations.)
Summary. The good agreement with the literature data,
together with the previous success of this method for this
system33and the similar C2H5+ O2systems,10provides evidence
that the CBS-QB3 level of theory is adequate for calculating
accurate thermodynamic data for the propyl + O2reactions.
This theory is a good compromise in terms of accuracy versus
TABLE 2: Calculated Barrier Heights for Concerted HO2Elimination and Hydrogen Migration Reactions from C3H7O2at 0 Ka
CBS-QB3b
reactionsDeSain et al.29
CBS-QB3//QCISDb,c
Concerted HO2Elimination
30.9
(30.3)
31.2
(30.9)
Hydrogen Migration
23.8
(22.7)
32.1
(31.2)
36.4
(35.8)
CH3CH2CH2OO•f CH3CHdCH2+ HO2
29.731.0
(30.6)
30.8
(30.6)
CH3CH(OO•)CH3f CH3CHdCH2+ HO2
29.8
CH3CH2CH2OO•f C•H2CH2CH2OOH23.724.0
(23.0)
31.7
(31.0)
CH3CH2CH2OO•f CH3C•HCH2OOH32.3
CH3CH(OO•)CH3f C•H2CH(OOH)CH3
35.4
aValues in parentheses are calculated at 298 K. (units: kcal/mol).
details.
bThis work.
cSee section Thermodynamic Property Calculations for
6598
J. Phys. Chem. A, Vol. 114, No. 24, 2010
Huynh et al.