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Article

Theoretical Study of an Undisclosed Reaction Class: Direct H-Atom Abstraction from Allylic Radicals by Molecular Oxygen

by
Yang Li
1,*,
Jin Wu
2,
Qian Zhao
3,
Yingjia Zhang
3 and
Zuohua Huang
3
1
Science and Technology on Combustion, Internal Flow and Thermostructure Laboratory, School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China
2
Xi’an Aerospace Propulsion Test Technology Institute, Xi’an 710100, China
3
State Key Laboratory of Multiphase Flows in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
*
Author to whom correspondence should be addressed.
Energies 2021, 14(10), 2916; https://doi.org/10.3390/en14102916
Submission received: 20 April 2021 / Revised: 28 April 2021 / Accepted: 11 May 2021 / Published: 18 May 2021
(This article belongs to the Special Issue Kinetic Modelling of E-fuels Combustion)
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Abstract

The 1-methylallyl (C4H71-3) allylic radical is an important intermediate species in oxidation of linear C4 unsaturated hydrocarbons (1-butene, 2-butene, and 1,3-butadiene). This study reports the first high-level quantum chemical calculations for an undisclosed reaction class of this radical at intermediate to high temperatures: direct H-atom abstraction from terminal methyl group by molecular oxygen. Moreover, we systematically calculated rate constants for primary, secondary, and tertiary H-atom abstraction from the C4, C5, and C6 allylic radicals, respectively. Our results can be further used as rate rules for kinetic model development of unsaturated hydrocarbon oxidation. All calculations were implemented using two different ab initio solvers: Gaussian and ORCA, three sets of ab initio methods, and two different kinetic solvers: MultiWell and PAPR. Temperature dependent rate constants and thermochemistry were carried out based on transition state theory and statistical thermodynamics, respectively. H-atom abstraction from the primary site of C4 allylic radical is found to be faster than that from secondary and tertiary sites of C5 and C6 allylic radicals, contrary to common understanding. Barrier heights predicted by different ab initio solvers and methods are about 4–5 kcal/mol different, which results in a factor of 4–86 difference in rate constant predictions depending on the temperature. Using the Gaussian solver with Method 2 is found to be the most effective combination of predicting accurate rate constants when compared against experimental data. When comparing two kinetic solvers, both reaction rate coefficients and species thermochemistry show good agreement at a wide range of temperatures, except for the rate coefficients calculated for C5 and C6 reactions (about a factor of 5–17 and 3–4 differences were obtained, respectively). From an application point of view, we incorporated the calculation results into the AramcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation.

1. Introduction

The combustion of hydrocarbons or oxygenates typically proceeds with H-atom abstraction by small species or radicals (Ḣ, ȮH and O2 etc.) from the reactant to generate a fuel radical. At high temperatures, fuel radicals may undergo H-atom abstraction by O2 from the adjacent carbon atom to form a C = C double bond plus HȮ2. However, this direct abstraction reaction class: fuel radical +O2 Energies 14 02916 i001 unsaturated species +HȮ2 has not been found to be important; instead, fuel radicals typically undergo isomerization or β-scission reaction pathways breaking down to smaller species. This can be found in many typical and well-validated kinetic models for oxidation of alkanes [1,2,3], alkenes [4,5,6,7,8], aromatics [9,10,11], alcohols [12,13,14], aldehydes [15], ethers [16,17], and furans [18,19].
In recent mechanism development studies for 1-butene [20], 2-butene [21] and 1,3-butadiene [22] oxidation, 1-methylallyl (C4H71-3) allylic radical was found to be the most important intermediate species for both isomers. For 1- and 2-butene oxidation, it can be generated from allylic H-atom abstraction by hydroxyl radical (ȮH) across a wide temperature range (600–1500 K), or by molecular oxygen at high temperatures (1100–1500 K). For 1,3-butadiene oxidation, it can be produced from H-atom addition to the terminal carbon of the C = C double bond at high temperatures (1100–1500 K). At intermediate to high temperatures (900–1500 K), there are two reaction pathways for consuming this radical: (a) reactions on the Ċ4H7 potential energy surface (PES), and (b) direct H-atom abstraction by molecular oxygen, as shown in Figure 1.
For the first consumption reaction, a comprehensive theoretical study was performed to determine rate constants and thermodynamic properties of the C4H7 PES [23]. The scope of this study is to perform fundamental quantum chemical calculations for the second reaction route, as highlighted in red color in Figure 1. Moreover, we aim to systematically investigate rate coefficients for this reaction class, i.e., primary, secondary, and tertiary H-atom abstraction from C4, C5, and C6 allylic radicals, respectively, as shown in Figure 2. Finally, rate rules will be developed for this new reaction class, which can be further used to develop kinetic models for oxidation of unsaturated hydrocarbons.
We reviewed extensive publications regarding both experimental and theoretical studies of allylic radicals reacting with O2, and these are summarized in Table S1 of Supplementary Material 1. All these studies focused on either O2 addition reaction, or experimentally measured total rate constants. There is a lack of accurate rate coefficients for the direct H-atom abstraction reaction.

2. Computational Methods

In order to assess the accuracy of theoretical predictions, different computational methods and solvers have been employed for comparison:
  • Three sets of quantum chemical methods: Method 1, Method 2, and Method 3.
  • Two ab initio solvers: Gaussian 09 [24] and ORCA 4.0.0 [25].
  • Two kinetic solvers: MultiWell [26] and PAPR [27].
Table 1 summarizes the three sets of quantum chemical methods adopted. They have been used effectively for rate coefficient calculations in addition, isomerization, dissociation, and abstraction reactions of C2–C9 hydrocarbons and oxygenates [22,28,29].
Firstly, regarding the ab initio solvers, Gaussian 09 was used for performing all three methods, while ORCA 4.0.0 was used for the calculations using Method 1 and 2. The density functional theory (DFT) method M06-2X [30] with the 6-311++G(d,p) [31,32] basis set was used for geometry optimization, vibrational frequency, dihedral angle scan, and intrinsic reaction coordinate (IRC) simultaneously in all three methods. For the electronic single-point energies (SPEs) calculation, coupled cluster theory CCSD(T)/cc-pVXZ [33] and Møller–Plesset perturbation theory MP2/cc-pVXZ [34] (where X = D, T and Q) [35] were used in Method 1 and 2, followed by complete basis set (CBS) extrapolation. While in Method 3, G4 [36] level of theory was used to calculate the SPEs directly. The T1 diagnostic [37] of all species and transition states were ≤0.030 and ≤0.036, respectively, as summarized in Table S2 in Supplementary Material 1. This indicates the reliability of single-reference methods for describing the wave function. In addition, combined compound methods CBS-APNO/G3/G4 [36,38,39] were used to calculate zero Kelvin energies (ZKEs), which were further used to derive average atomization formation enthalpies for calculation of thermodynamic properties. This method has been proved to be reliable for the thermochemistry calculation of hydrocarbons [38]. Table 2 illustrates the scale factors used for the zero-point energies (ZPEs) and vibrational frequencies, and the equations used for conducting the complete basis set (CBS) extrapolation of SPEs.
In both kinetic solvers, quantum mechanical tunneling was taken into account using an unsymmetrical Eckart barrier model [40], and 1-D hindered internal rotation was treated for lower frequency modes. Rate constants and thermochemistry were carried out based on canonical transition state theory (TST) [41] and statistical thermodynamics, respectively.
The calculated rate coefficients were fitted to a modified Arrhenius expression as a function of temperature:
k = A ( T / T r e f ) n e x p ( − E / R T )
where A is the frequency factor, T is the temperature in Kelvin, Tref = 1 K, n is the temperature exponent at 1 K, and E is related to the activation energy (by Ea = E + nRT).
The thermochemical properties (enthalpy of formation, entropy, and heat capacity) were calculated as a function of temperature (298.15–2000 K), and are fitted to NASA polynomials [42] using the Fitdat utility in ANSYS CHEMKIN-PRO [43].
Notably, the above methods have also been employed and explained in our recent publication [44].

3. Results and Discussion

3.1. Potential Energy Surface for C4H71-3 + O2 Reaction

Figure 3 shows the potential energy surface (PES) for C4H71-3 + O2 reaction. These two reactants can undergo: a) direct H-atom abstraction to form 1,3-butadiene (C4H6) plus hydroperoxy (HȮ2) radical and b) a barrier-less addition pathway forming an alkenyl-peroxy (C4H71-3Ȯ2) radical, followed by HȮ2 concerted elimination resulting in the same products, C4H6 and HȮ2. The barrier height of the direct abstraction reaction in the first reaction pathway is 22.42 kcal/mol, and the well depth of the association reaction and the barrier height of the subsequent concerted elimination reaction in the second reaction pathway are 18.39 and 27.52 kcal/mol, respectively. Therefore, the direct abstraction pathway is kinetically favorable at intermediate to high temperatures.
It is worth nothing that the two transition states (TSs) for the abstraction (C4-TS) and concerted elimination (C4-TS-2) reaction are actually connected by an internal rotation of the CC−OO dihedral angle, as shown in Figure 4. C4-TS is located at a “shallow well” with about 12 kcal/mol higher energy relative to C4-TS-2, and it is found that some DFT methods, such as wB97XD [45], tend to fail in the geometry optimization of C4-TS, and this is probably due to its “shallow well depth”.
The PESs for C5H91-3 + O2 and C6H111-3 + O2 reactions have also been carried out, as shown in Figure S1 in Supplementary Material 1. Table 3 summarizes the forward and reverse barrier heights for all three abstraction reactions calculated by different methods and ab initio solvers (“-” sign means the SPE calculation was too expensive to perform). The forward barrier heights calculated by the Orca solver using Method 1 and 2 agree well with the values from the Gaussian solver using Method 3 (less than 1 kcal/mol difference). However, the results carried out by Gaussian using Method 1 and 2 are about 4-5 kcal/mol lower consistently.

3.2. Comparison of Rate Constants

All calculated rate constants were compared across the three different quantum chemical methods, two different ab initio solvers and two different kinetic solvers; all input and output results have been summarized in Supplementary Material 4. In this section, we pick two representatives to demonstrate the agreement or disagreement (all rate constants given are for abstraction on a per H-atom basis):
  • Comparing two ab initio solvers (Gaussian and Orca) when using the MultiWell kinetic solver with Method 2
  • Comparing two kinetic solvers (Multiwell and PAPR) using ab initio results from Gaussian with Method 2
Figure 5 compares the rate constants for two ab initio solvers: Orca and Gaussian. Solid and dash lines are results obtained from Gaussian and Orca solvers, respectively, and different colors correspond to three different abstraction reactions. In addition, the experimental data is plotted for the C4 reaction: C4H71-3 + O2 Energies 14 02916 i001 C4H6 + HO2 measured by Knyazev et al. [46], and C5 reaction: C5H91-3 + O2 Energies 14 02916 i001 C5H8 + HO2 measured by Baldwin et al. [47]. H-atom abstraction from the primary site (C4H71-3 + O2) was found to be faster than from secondary (C5H91-3 + O2) and tertiary (C6H111-3 + O2) sites, which seems counter-intuitive. Significant differences were found for the rate constants predicted using two ab initio solvers, being about a factor of 4–86 differences, depending on the temperature, and this is due to the difference in the barrier heights. When compared to experimental measurements, the results obtained from Gaussian solver with Method 2 show about a factor of 2 difference for both C4 and C5 reactions, which is in much better agreement with experimental data relative to the Orca solver.
Table 4 shows the rate constants comparison for two kinetic solvers: MultiWell and PAPR, over a temperature range of 600–1800 K. It is found that for the Ċ4H71-3 + O2 reaction, the two kinetic solvers show identical results, and the difference is within 10% across the entire temperature range. However, for the C5H91-3 + O2 and C6H111-3 + O2 reactions, a factor of 5–17 and 3–4 differences were obtained, respectively; the rates calculated using PAPR solver are consistently higher than those from the MultiWell solver.

3.3. Thermodynamic Properties

In order to demonstrate the reliability of the calculated thermodynamic properties, three widely accepted thermochemistry databases were selected for comparison:
  • This study: CBS-APNO/G3/G4//M06-2X/6-311++G(d,p).
  • Thermochemical Data of Organic Compounds (TDOC) by Pedley et al. [48]: experiments.
  • Active Thermochemical Tables (ATcT): refs. [49,50,51].
  • Goldsmith et al. [52]: RQCISD(T)/cc-pVT,QZ//B3LYP/6-311++G(d,p), with bond additivity correction.
Table 5 compares the thermochemistry for closed shell molecules: C4H6, C5H8, and C6H10. Excellent agreement is obtained for the 298 K enthalpies of formation (ΔfHӨ), 298 K entropies (SӨ), and heat capacities (Cp) at selected temperatures (the difference is within 0.5 kcal mol−1 and 0.5 cal K−1 mol−1).
Table 6 compares the thermodynamic properties calculated by two kinetic solvers (MultiWell and PAPR) for allylic radicals: Ċ4H71-3, Ċ5H91-3 and Ċ6H111-3. The ΔfHӨ, SӨ and Cp at selected temperatures calculated using MultiWell and PAPR are in excellent agreement, with less than 0.5 kcal mol−1 or 0.5 cal K−1 mol−1 difference of one another across the entire temperature range.

3.4. Application in Kinetic Model Development

One of the major applications of accurate rate constants and thermochemistry is for the development of detailed chemical kinetic models. In this section, we incorporated all rate coefficients and thermodynamic properties calculated using the combination of: (a) Gaussian solver, (b) Method 1, (c) MultiWell solver into AramcoMech 2.0 [21]. In addition, we included the other two recently published quantum calculations for two more important high-temperature oxidation reaction classes of C4 unsaturated hydrocarbons:
  • Reactions on the Ċ4H7 PES by Li et al. [23]
  • Allylic H-atom abstraction by O2 from 1- and 2-butene by Zhou et al. [28]
Here, 2-butene was selected as a representative in the AramcoMech 2.0 model, wherein the rate constant assigned to the Ċ4H71-3 + O2 Energies 14 02916 i001 C4H6 + HȮ2 reaction was based on analogy to the theoretical prediction of IĊ3H7 + O2 Energies 14 02916 i001 C3H6 + HȮ2 reaction from DeSain et al. [53]. A comparison against rates calculated here is given in Figure S2 in Supplementary Material 1. Figure 6 shows the validation results for the following key targets of high-temperature oxidation:
  • Ignition delay time [21]
  • Laminar flame speed [54]
  • Speciation in JSR [55]
In the figure, all symbols are experimental data obtained from literature, while the dash and solid lines are simulation results using the original AramcoMech 2.0 model and the model with new rate constants, respectively. The improvement of model prediction across-the-board further indicates the reliability of the above quantum calculation results. A further detailed analysis of its effects on kinetic mechanism is beyond the scope of this study and will be included in future works. Notably, the reactants’ profile shown in “(c) Speciation validation” shows quite large fluctuation, and the accuracy of these data is suspicious.

4. Conclusions

This work presented comprehensive quantum chemical calculations for a new reaction class: H-atom abstraction from C4-C6 allylic radicals by molecular oxygen. The calculated potential energy surface of Ċ4H71-3 + O2 reaction showed that direct H-atom abstraction has a lower barrier height compared to that of HȮ2 concerted elimination, which makes the former kinetically favorable at intermediate to high temperatures. Rate constants for the three reactions and thermochemistry of species involved in each reaction were systematically calculated using two different ab initio solvers (Orca and Gaussian), three sets of ab initio methods, and two different kinetic solvers (MultiWell and PAPR). The results were compared against each other, as well as against experimental results in literature. Notably, all fitted rate coefficients and thermodynamic properties were summarized in Supplementary Material 2, and species glossary was provided in Supplementary Material 3.
It was found that the Gaussian solver plus Method 1 and 2 generally predicts lower barriers than the Orca solver plus Method 1 and 2 and the Gaussian solver plus Method 3, by about 4-5 kcal/mol consistently; this results in about a factor of 4-86 difference in rate constant predictions in the temperature range of 600–1800 K. H-atom abstraction from the primary site (Ċ4H71-3 + O2) was found to be faster than from secondary (Ċ5H91-3 + O2) and tertiary (Ċ6H111-3 + O2) sites, and the Gaussian solver plus Method 2 (CCSD(T)/cc-pVXZ&MP2/cc-pVXZ//M06-2X/6-311++G(d,p), where X = D, T and Q) predicts rate constants with the highest accuracy; about a factor of 2 difference compared against the experimental data. For the thermochemistry calculations, the temperature dependent enthalpy of formation, entropy and heat capacity of closed shell molecules: C4H6, C5H8 and C6H10 were compared against some well-known literature values, and excellent agreement was obtained with less than 0.5 kcal mol–1 difference for standard enthalpy of formation and 0.5 cal K−1 mol−1 for entropy at 298 K and heat capacity from 300–2000 K, respectively. Good agreement was also obtained for both rate coefficients and thermodynamic properties calculations using two kinetic solvers, MultiWell and PAPR, except for the rate coefficients prediction of C5 and C6 reactions (about a factor of 5–17 and 3–4 differences were obtained, respectively). Finally, we incorporated all calculated results into the AramcoMech 2.0 model, and a systematic improvement was observed in ignition delay times, laminar flame speeds, and speciation for 2-butene oxidation.

Supplementary Materials

The following are available online at https://www.mdpi.com/article/10.3390/en14102916/s1, Figure S1: title, Table S1: title, Video S1: title. Supplementary Material 1: Additional information. Supplementary Material 2: All fitted rate coefficients and thermodynamic properties. Supplementary Material 3: Species Glossary. Supplementary Material 4: All input and output files for MultiWell and PAPR solvers. References [46,47,56,57,58,59,60,61,62,63,64,65,66,67,68,69] are cited in Supplementary Material 1.

Author Contributions

Funding acquisition, Y.L., J.W. and Y.Z.; Investigation, Y.L. and Q.Z.; Methodology, Y.L. and Q.Z.; Supervision, Z.H.; Writing–original draft, Y.L., J.W. and Q.Z.; Writing –review & editing, Y.L., Y.Z. and Z.H. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Startup Funds of Aoxiang Overseas Scholar (2020010157) at Northwestern Polytechnical Univer-sity, Stable Support 2019KGW YY4009Tm at Xi’an Aerospace Propulsion Test Technology Insti-tute, and the National Natural Science Foundation of China (No. 91741115 and 51888103) at Xi’an Jiaotong University.

Acknowledgments

The authors acknowledge the funding support from Startup Funds of Aoxiang Overseas Scholar (2020010157) at Northwestern Polytechnical University, Stable Support 2019KGW YY4009Tm at Xi’an Aerospace Propulsion Test Technology Institute, and the National Natural Science Foundation of China (No. 91741115 and 51888103) at Xi’an Jiaotong University.

Conflicts of Interest

The authors declare no conflict of interest.

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Energies 14 02916 g001
Figure 1. High temperature chemistry of 1-methylallyl (C4H71-3) allylic radical.
Figure 1. High temperature chemistry of 1-methylallyl (C4H71-3) allylic radical.
Energies 14 02916 g001
Energies 14 02916 g002
Figure 2. Reaction class for primary, secondary, and tertiary H-atom abstraction from C4, C5, and C6 allylic radicals, respectively.
Figure 2. Reaction class for primary, secondary, and tertiary H-atom abstraction from C4, C5, and C6 allylic radicals, respectively.
Energies 14 02916 g002
Energies 14 02916 g003
Figure 3. Potential energy surface (PES) for the Ċ4H71-3 + O2 reaction.
Figure 3. Potential energy surface (PES) for the Ċ4H71-3 + O2 reaction.
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Energies 14 02916 g004
Figure 4. Internal rotor potential of the CC−OO dihedral angle for the two TSs on C4H71-3Ȯ2 PES.
Figure 4. Internal rotor potential of the CC−OO dihedral angle for the two TSs on C4H71-3Ȯ2 PES.
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Figure 5. Rate constant comparison for two ab initio solvers: Orca and Gaussian.
Figure 5. Rate constant comparison for two ab initio solvers: Orca and Gaussian.
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Figure 6. Ignition delay time, laminar flame speed, and speciation validation results for 2-butene.
Figure 6. Ignition delay time, laminar flame speed, and speciation validation results for 2-butene.
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Table 1. Quantum chemical methods and ab initio solvers used in this study.
Table 1. Quantum chemical methods and ab initio solvers used in this study.
Method 1Method 2Method 3
Ab initio solverGaussian and OrcaGaussian
Geometry, frequency, scan and IRCM06-2X/6-311++G(d,p)
SPEsCCSD(T)/cc-pVTZCCSD(T)/cc-pVDZG4
CCSD(T)/cc-pVTZ
CCSD(T)/cc-pVQZMP2/cc-pVDZ
MP2/cc-pVTZ
MP2/cc-pVQZ
Zero Kelvin energiesCBS-APNO/G3/G4
Table 2. Parameters and equations used for energy calculation in this study.
Table 2. Parameters and equations used for energy calculation in this study.
Method 1Method 2Method 3
Scale factor for ZPEs0.9698
Scale factor for frequencies0.983
CBS extrapolation for SPEECCSD(T)/cc-pVQZ + (ECCSD(T)/cc-pVQZ − ECCSD(T)/cc-pVTZ) × 44/(54 − 44)ECCSD(T)/cc-pVTZ + (ECCSD(T)/cc-pVTZ − ECCSD(T)/cc-pVDZ) × 34/(44 − 34) + EMP2/cc-pVQZ + (EMP2/cc-pVQZ − EMP2/cc-pVTZ) × 44/(54 − 44) − EMP2/cc-pVTZ + (EMP2/cc-pVTZ − EMP2/cc-pVDZ) × 34/(44 − 34)EG4
Table 3. Comparison of barrier heights. (Unit: kcal/mol).
Table 3. Comparison of barrier heights. (Unit: kcal/mol).
Method 1Method 2Method 3
ReactionsOrcaGaussianOrcaGaussianGaussian
Forward barrier height
C4H71-3 + O2 Energies 14 02916 i001 C4H6 + HO222.4219.1523.2318.3023.35
C5H91-3 + O2 Energies 14 02916 i001 C5H8 + HO221.00-21.8016.6521.61
C6H111-3 + O2 Energies 14 02916 i001 C6H10 + HO221.12-21.9616.5821.02
Reverse barrier height
C4H71-3 + O2 Energies 14 02916 i001 C4H6 + HO225.2322.4826.2122.0025.90
C5H91-3 + O2 Energies 14 02916 i001 C5H8 + HO227.16-28.0923.6327.06
C6H111-3 + O2 Energies 14 02916 i001 C6H10 + HO228.39-29.3124.5826.94
Table 4. Rate constant comparison for two kinetic solvers: MultiWell and PAPR.
Table 4. Rate constant comparison for two kinetic solvers: MultiWell and PAPR.
C4H71-3 + O2 ReactionC5H91-3 + O2 ReactionC6H111-3 + O2 Reaction
T/KMultiWellPAPRMultiWellPAPRMultiWellPAPR
6001.43E + 061.28E + 061.17E + 055.49E + 051.81E + 055.10E + 05
8006.37E + 076.12E + 073.01E + 062.04E + 075.58E + 061.74E + 07
10008.61E + 088.62E + 082.71E + 072.41E + 085.77E + 071.91E + 08
11002.38E + 092.42E + 096.35E + 076.31E + 081.44E + 084.88E + 08
12005.75E + 095.92E + 091.33E + 081.45E + 093.17E + 081.10E + 09
13001.24E + 101.30E + 102.52E + 083.02E + 096.35E + 082.24E + 09
14002.46E + 102.59E + 104.44E + 085.78E + 091.17E + 094.21E + 09
15004.53E + 104.81E + 107.35E + 081.03E + 102.04E + 097.40E + 09
16007.82E + 108.39E + 101.16E + 091.73E + 103.34E + 091.23E + 10
17001.28E + 111.39E + 111.74E + 092.78E + 105.25E + 091.96E + 10
18002.01E + 112.20E + 112.53E + 094.28E + 107.91E + 092.98E + 10
Table 5. Thermochemistry comparison of closed shell molecules. (Units: kcal mol–1 for ΔfHӨ, cal K−1 mol−1 for SӨ and Cp.)
Table 5. Thermochemistry comparison of closed shell molecules. (Units: kcal mol–1 for ΔfHӨ, cal K−1 mol−1 for SӨ and Cp.)
ΔfHӨSӨCp
MoleculesSource298 K298 K300 K400 K500 K600 K800 K1000 K1500 K
C4H6This study26.766.618.924.328.732.137.140.746.3
ATcT26.5--------
TDOC26.3--------
Goldsmith et al.26.565.818.524.028.732.437.641.146.6
C5H8This study18.776.524.430.936.441.047.852.760.4
TDOC18.2--------
C6H10Current study11.084.929.837.644.349.758.164.374.2
Table 6. Thermochemistry comparison of allylic radicals. (Units: kcal mol−1 for ΔfHӨ, cal K−1 mol−1 for SӨ and Cp).
Table 6. Thermochemistry comparison of allylic radicals. (Units: kcal mol−1 for ΔfHӨ, cal K−1 mol−1 for SӨ and Cp).
ΔfHӨSӨCp
RadicalsSource298 K298 K300 K400 K500 K600 K800 K1000 K1500 K
C4H71-3MultiWell31.972.119.724.829.333.139.143.650.6
PAPR31.772.019.924.829.333.339.243.750.6
C5H91-3MultiWell26.883.125.231.837.642.550.155.864.8
PAPR27.283.325.532.638.243.150.556.164.9
C6H111-3MultiWell19.888.931.439.446.552.461.668.479.1
PAPR19.889.131.239.046.252.461.568.479.1
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Li, Y.; Wu, J.; Zhao, Q.; Zhang, Y.; Huang, Z. Theoretical Study of an Undisclosed Reaction Class: Direct H-Atom Abstraction from Allylic Radicals by Molecular Oxygen. Energies 2021, 14, 2916. https://doi.org/10.3390/en14102916

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Li Y, Wu J, Zhao Q, Zhang Y, Huang Z. Theoretical Study of an Undisclosed Reaction Class: Direct H-Atom Abstraction from Allylic Radicals by Molecular Oxygen. Energies. 2021; 14(10):2916. https://doi.org/10.3390/en14102916

Chicago/Turabian Style

Li, Yang, Jin Wu, Qian Zhao, Yingjia Zhang, and Zuohua Huang. 2021. "Theoretical Study of an Undisclosed Reaction Class: Direct H-Atom Abstraction from Allylic Radicals by Molecular Oxygen" Energies 14, no. 10: 2916. https://doi.org/10.3390/en14102916

APA Style

Li, Y., Wu, J., Zhao, Q., Zhang, Y., & Huang, Z. (2021). Theoretical Study of an Undisclosed Reaction Class: Direct H-Atom Abstraction from Allylic Radicals by Molecular Oxygen. Energies, 14(10), 2916. https://doi.org/10.3390/en14102916

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