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

: The 1-methylallyl (C 4 H 7 1-3) 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 C 4 , C 5 , and C 6 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. Abstract: The 1-methylallyl (C 4 H 7 1-3) 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 C 4 , C 5 , and C 6 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, respec-tively). From an application point of view, we incorporated the calculation results into the Ar-amcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation. H-Atom Abstraction from Allylic Radicals Molecular Oxygen Yang Li 1 Yingjia zhhuang@xjtu.edu.cn Correspondence: Abstract: The 1-methylallyl (C 4 H 7 1-3) allylic radical is an important intermediate species in oxida- tion of linear C4 unsaturated hydrocarbons (1-butene, 2-butene, and 1,3-butadiene). This study re- ports 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 C 4 , C 5 , and C 6 allylic radicals, respectively. Our results can be further used as rate rules for kinetic model development of unsaturated hydrocarbon oxidation. initio solvers and methods are about 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, respec-tively). From an application point of view, we incorporated the calculation results into the Ar-amcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation. by 2021 , 14 , x. https://doi.org/10.3390/xxxxx Pelucchi and (C 4 H 7 1-3) allylic radical is an important intermediate species in oxida- unsaturated hydrocarbons (1-butene, 2-butene, and 1,3-butadiene). This study re- quantum chemical calculations for an undisclosed reaction class of this intermediate to high temperatures: direct H-atom abstraction from terminal methyl group Moreover, we systematically calculated rate constants for primary, secondary, abstraction from the C 4 , C 5 and C 6 allylic radicals, respectively. Our results can 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, respec-tively). From an application point of view, we incorporated the calculation results into the Ar-amcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation. Li, 1-3) allylic radical is an important intermediate species in oxida- tion of linear C4 unsaturated hydrocarbons (1-butene, 2-butene, and 1,3-butadiene). This study re- ports 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 and Our results can 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, respec-tively). From an application point of view, we incorporated the calculation results into the Ar-amcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation. 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, respec-tively). From an application point of view, we incorporated the calculation results into the Ar-amcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation. Citation: 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 , x. by molecular oxygen. Moreover, we systematically calculated rate constants for primary, secondary, and tertiary H-atom abstraction from the C 4 , C 5 , and C 6 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, respec-tively). From an application point of view, we incorporated the calculation results into the Ar-amcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation. Abstract: The 1-methylallyl (C 4 H 7 1-3) 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 C 4 , C 5 , and C 6 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, respec-tively). From an application point of view, we incorporated the calculation results into the Ar-amcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation. Abstract: The 1-methylallyl (C 4 H 7 1-3) 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 C 4 , C 5 , and C 6 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, respec-tively). From an application point of view, we incorporated the calculation results into the Ar-amcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation. Abstract: The 1-methylallyl (C 4 H 7 1-3) 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 C 4 , C 5 , and C 6 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, respec-tively). From an application point of view, we incorporated the calculation results into the Ar-amcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation. Abstract: The 1-methylallyl (C 4 H 7 1-3) 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 C 4 , C 5 , and C 6 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, respec-tively). From an application point of view, we incorporated the calculation results into the Ar-amcoMech2.0 model, and found systematic improvements for predicting ignition delay time, laminar flame speed and speciation targets of 2-butene oxidation.


Introduction
The combustion of hydrocarbons or oxygenates typically proceeds with H-atom abstraction by small species or radicals (Ḣ,ȮH and O 2 etc.) from the reactant to generate a fuel radical. At high temperatures, fuel radicals may undergo H-atom abstraction by O 2 from the adjacent carbon atom to form a C = C double bond plus HȮ 2 . However, this direct abstraction reaction class: fuel radical +O 2 Energies 2021, 14

Introduction
The combustion of hydrocarbons or oxygenates typically proceeds with H-atom ab straction by small species or radicals (Ḣ, ȮH and O2 etc.) from the reactant to generate fuel radical. At high temperatures, fuel radicals may undergo H-atom abstraction by O from the adjacent carbon atom to form a C = C double bond plus HȮ2. However, this dire abstraction reaction class: fuel radical +O2 ↔ unsaturated species +HȮ2 has not bee found to be important; instead, fuel radicals typically undergo isomerization or β-scissio 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 theĊ 4 H 7 potential energy surface (PES), and (b) direct H-atom abstraction by molecular oxygen, as shown in Figure 1.
In recent mechanism development studies for 1-butene [20], 2-butene [21] and 1,3butadiene [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.

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. For the first consumption reaction, a comprehensive theoretical study was performed to determine rate constants and thermodynamic properties of the C 4 H 7 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 C 4 , C 5 , and C 6 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. 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 1,3butadiene [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.

Computational Methods
In order to assess the accuracy of theoretical predictions, different computational methods and solvers have been employed for comparison: • We reviewed extensive publications regarding both experimental and theoretical studies of allylic radicals reacting with O 2 , and these are summarized in Table S1 of Supplementary Material 1. All these studies focused on either O 2 addition reaction, or experimentally measured total rate constants. There is a lack of accurate rate coefficients for the direct H-atom abstraction reaction.

Computational Methods
In order to assess the accuracy of theoretical predictions, different computational methods and solvers have been employed for comparison: •  [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: where A is the frequency factor, T is the temperature in Kelvin, T ref = 1 K, n is the temperature exponent at 1 K, and E is related to the activation energy (by E a = 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].

Results and Discussion
3.1. Potential Energy Surface for C 4 H 7 1-3 + O 2 Reaction Figure 3 shows the potential energy surface (PES) for C 4 H 7 1-3 + O 2 reaction. These two reactants can undergo: a) direct H-atom abstraction to form 1,3-butadiene (C 4 H 6 ) plus hydroperoxy (HȮ 2 ) radical and b) a barrier-less addition pathway forming an alkenylperoxy (C 4 H 7 1-3Ȯ 2 ) radical, followed by HȮ 2 concerted elimination resulting in the same products, C 4 H 6 and HȮ 2 . 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.
The calculated rate coefficients were fitted to a modified Arrhenius expression as a function of temperature: 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]. 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 alkenylperoxy (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". 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".

Potential Energy Surface for C4H71-3 + O2 Reaction
The PESs for C 5 H 9 1-3 + O 2 and C 6 H 11 1-3 + O 2 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.  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.

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 ↔ C4H6 + HO2 measured by Knyazev et al. [46], and C5 reaction: C5H91-3 + O2 ↔ 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  www.mdpi.com/journal/energies implemented using two different ab initio solvers: Gaussian and ORCA, three ds, and two different kinetic solvers: MultiWell and PAPR. Temperature des and thermochemistry were carried out based on transition state theory and mics, respectively. H-atom abstraction from the primary site of C4 allylic radter than that from secondary and tertiary sites of C5 and C6 allylic radicals, understanding. Barrier heights predicted by different ab initio solvers and kcal/mol different, which results in a factor of 4-86 difference in rate constant g on the temperature. Using the Gaussian solver with Method 2 is found to be bination of predicting accurate rate constants when compared against experomparing two kinetic solvers, both reaction rate coefficients and species therod agreement at a wide range of temperatures, except for the rate coefficients C6 reactions (about a factor of 5-17 and 3-4 differences were obtained, respeclication point of view, we incorporated the calculation results into the Arand found systematic improvements for predicting ignition delay time, lamipeciation targets of 2-butene oxidation.
icals; H-atom abstraction; quantum chemistry; rate constants; thermochemisn of hydrocarbons or oxygenates typically proceeds with H-atom abpecies or radicals (Ḣ, ȮH and O2 etc.) from the reactant to generate a temperatures, fuel radicals may undergo H-atom abstraction by O2 rbon atom to form a C = C double bond plus HȮ2. However, this direct class: fuel radical +O2 ↔ unsaturated species +HȮ2 has not been nt; instead, fuel radicals typically undergo isomerization or β-scission www.mdpi.com/journal/energies rules for kinetic model development of unsaturated hydrocarbon oxidation. implemented using two different ab initio solvers: Gaussian and ORCA, three ds, and two different kinetic solvers: MultiWell and PAPR. Temperature des and thermochemistry were carried out based on transition state theory and mics, respectively. H-atom abstraction from the primary site of C4 allylic radter than that from secondary and tertiary sites of C5 and C6 allylic radicals, understanding. Barrier heights predicted by different ab initio solvers and kcal/mol different, which results in a factor of 4-86 difference in rate constant g on the temperature. Using the Gaussian solver with Method 2 is found to be bination of predicting accurate rate constants when compared against experomparing two kinetic solvers, both reaction rate coefficients and species therod agreement at a wide range of temperatures, except for the rate coefficients C6 reactions (about a factor of 5-17 and 3-4 differences were obtained, respeclication point of view, we incorporated the calculation results into the Arand found systematic improvements for predicting ignition delay time, lamipeciation targets of 2-butene oxidation.
icals; H-atom abstraction; quantum chemistry; rate constants; thermochemisn of hydrocarbons or oxygenates typically proceeds with H-atom abpecies or radicals (Ḣ, ȮH and O2 etc.) from the reactant to generate a temperatures, fuel radicals may undergo H-atom abstraction by O2 rbon atom to form a C = C double bond plus HȮ2. However, this direct class: fuel radical +O2 ↔ unsaturated species +HȮ2 has not been nt; instead, fuel radicals typically undergo isomerization or β-scission www.mdpi.com/journal/energies bstraction from the C4, C5, and C6 allylic radicals, respectively. Our results can rules for kinetic model development of unsaturated hydrocarbon oxidation. implemented using two different ab initio solvers: Gaussian and ORCA, three ds, and two different kinetic solvers: MultiWell and PAPR. Temperature des and thermochemistry were carried out based on transition state theory and mics, respectively. H-atom abstraction from the primary site of C4 allylic radter than that from secondary and tertiary sites of C5 and C6 allylic radicals, understanding. Barrier heights predicted by different ab initio solvers and kcal/mol different, which results in a factor of 4-86 difference in rate constant g on the temperature. Using the Gaussian solver with Method 2 is found to be bination of predicting accurate rate constants when compared against experomparing two kinetic solvers, both reaction rate coefficients and species therod agreement at a wide range of temperatures, except for the rate coefficients C6 reactions (about a factor of 5-17 and 3-4 differences were obtained, respeclication point of view, we incorporated the calculation results into the Arand found systematic improvements for predicting ignition delay time, lamipeciation targets of 2-butene oxidation.
icals; H-atom abstraction; quantum chemistry; rate constants; thermochemisn of hydrocarbons or oxygenates typically proceeds with H-atom abpecies or radicals (Ḣ, ȮH and O2 etc.) from the reactant to generate a temperatures, fuel radicals may undergo H-atom abstraction by O2 rbon atom to form a C = C double bond plus HȮ2. However, this direct class: fuel radical +O2 ↔ unsaturated species +HȮ2 has not been nt; instead, fuel radicals typically undergo isomerization or β-scission www.mdpi.com/journal/energies e to high temperatures: direct H-atom abstraction from terminal methyl group Moreover, we systematically calculated rate constants for primary, secondary, bstraction from the C4, C5, and C6 allylic radicals, respectively. Our results can rules for kinetic model development of unsaturated hydrocarbon oxidation. implemented using two different ab initio solvers: Gaussian and ORCA, three ds, and two different kinetic solvers: MultiWell and PAPR. Temperature des and thermochemistry were carried out based on transition state theory and mics, respectively. H-atom abstraction from the primary site of C4 allylic radter than that from secondary and tertiary sites of C5 and C6 allylic radicals, understanding. Barrier heights predicted by different ab initio solvers and kcal/mol different, which results in a factor of 4-86 difference in rate constant g on the temperature. Using the Gaussian solver with Method 2 is found to be bination of predicting accurate rate constants when compared against experomparing two kinetic solvers, both reaction rate coefficients and species therod agreement at a wide range of temperatures, except for the rate coefficients C6 reactions (about a factor of 5-17 and 3-4 differences were obtained, respeclication point of view, we incorporated the calculation results into the Arand found systematic improvements for predicting ignition delay time, lamipeciation targets of 2-butene oxidation. icals; H-atom abstraction; quantum chemistry; rate constants; thermochemisn of hydrocarbons or oxygenates typically proceeds with H-atom abpecies or radicals (Ḣ, ȮH and O2 etc.) from the reactant to generate a temperatures, fuel radicals may undergo H-atom abstraction by O2 rbon atom to form a C = C double bond plus HȮ2.
However, this direct class: fuel radical +O2 ↔ unsaturated species +HȮ2 has not been nt; instead, fuel radicals typically undergo isomerization or β-scission www.mdpi.com/journal/energies vel quantum chemical calculations for an undisclosed reaction class of this e to high temperatures: direct H-atom abstraction from terminal methyl group Moreover, we systematically calculated rate constants for primary, secondary, bstraction from the C4, C5, and C6 allylic radicals, respectively. Our results can rules for kinetic model development of unsaturated hydrocarbon oxidation. implemented using two different ab initio solvers: Gaussian and ORCA, three ds, and two different kinetic solvers: MultiWell and PAPR. Temperature des and thermochemistry were carried out based on transition state theory and mics, respectively. H-atom abstraction from the primary site of C4 allylic radter than that from secondary and tertiary sites of C5 and C6 allylic radicals, understanding. Barrier heights predicted by different ab initio solvers and kcal/mol different, which results in a factor of 4-86 difference in rate constant g on the temperature. Using the Gaussian solver with Method 2 is found to be bination of predicting accurate rate constants when compared against experomparing two kinetic solvers, both reaction rate coefficients and species therod agreement at a wide range of temperatures, except for the rate coefficients C6 reactions (about a factor of 5-17 and 3-4 differences were obtained, respeclication point of view, we incorporated the calculation results into the Arand found systematic improvements for predicting ignition delay time, lamipeciation targets of 2-butene oxidation. icals; H-atom abstraction; quantum chemistry; rate constants; thermochemisn of hydrocarbons or oxygenates typically proceeds with H-atom abpecies or radicals (Ḣ, ȮH and O2 etc.) from the reactant to generate a temperatures, fuel radicals may undergo H-atom abstraction by O2 rbon atom to form a C = C double bond plus HȮ2.
However, this direct class: fuel radical +O2 ↔ unsaturated species +HȮ2 has not been nt; instead, fuel radicals typically undergo isomerization or β-scission www.mdpi.com/journal/energies lallyl (C4H71-3) allylic radical is an important intermediate species in oxidaturated hydrocarbons (1-butene, 2-butene, and 1,3-butadiene). This study revel quantum chemical calculations for an undisclosed reaction class of this e to high temperatures: direct H-atom abstraction from terminal methyl group Moreover, we systematically calculated rate constants for primary, secondary, bstraction from the C4, C5, and C6 allylic radicals, respectively. Our results can rules for kinetic model development of unsaturated hydrocarbon oxidation. implemented using two different ab initio solvers: Gaussian and ORCA, three ds, and two different kinetic solvers: MultiWell and PAPR. Temperature des and thermochemistry were carried out based on transition state theory and mics, respectively. H-atom abstraction from the primary site of C4 allylic radter than that from secondary and tertiary sites of C5 and C6 allylic radicals, understanding. Barrier heights predicted by different ab initio solvers and kcal/mol different, which results in a factor of 4-86 difference in rate constant g on the temperature. Using the Gaussian solver with Method 2 is found to be bination of predicting accurate rate constants when compared against experomparing two kinetic solvers, both reaction rate coefficients and species therod agreement at a wide range of temperatures, except for the rate coefficients C6 reactions (about a factor of 5-17 and 3-4 differences were obtained, respeclication point of view, we incorporated the calculation results into the Arand found systematic improvements for predicting ignition delay time, lamipeciation targets of 2-butene oxidation. icals; H-atom abstraction; quantum chemistry; rate constants; thermochemisn of hydrocarbons or oxygenates typically proceeds with H-atom abpecies or radicals (Ḣ, ȮH and O2 etc.) from the reactant to generate a temperatures, fuel radicals may undergo H-atom abstraction by O2 rbon atom to form a C = C double bond plus HȮ2.
However, this direct class: fuel radical +O2 ↔ unsaturated species +HȮ2 has not been nt; instead, fuel radicals typically undergo isomerization or β-scission

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: C 4  Abstract: The 1-methylallyl (C4H71-3) allylic radical is an important intermediate specie tion of linear C4 unsaturated hydrocarbons (1-butene, 2-butene, and 1,3-butadiene). Thi ports the first high-level quantum chemical calculations for an undisclosed reaction c radical at intermediate to high temperatures: direct H-atom abstraction from terminal me by molecular oxygen. Moreover, we systematically calculated rate constants for primary, and tertiary H-atom abstraction from the C4, C5, and C6 allylic radicals, respectively. Our be further used as rate rules for kinetic model development of unsaturated hydrocarbon All calculations were implemented using two different ab initio solvers: Gaussian and OR sets of ab initio methods, and two different kinetic solvers: MultiWell and PAPR. Temp pendent rate constants and thermochemistry were carried out based on transition state statistical thermodynamics, respectively. H-atom abstraction from the primary site of C4 ical is found to be faster than that from secondary and tertiary sites of C5 and C6 allyl contrary to common understanding. Barrier heights predicted by different ab initio s methods are about 4-5 kcal/mol different, which results in a factor of 4-86 difference in ra predictions depending on the temperature. Using the Gaussian solver with Method 2 is f the most effective combination of predicting accurate rate constants when compared aga imental data. When comparing two kinetic solvers, both reaction rate coefficients and sp mochemistry show good agreement at a wide range of temperatures, except for the rate c calculated for C5 and C6 reactions (about a factor of 5-17 and 3-4 differences were obtain tively). From an application point of view, we incorporated the calculation results in

Introduction
The combustion of hydrocarbons or oxygenates typically proceeds with H straction by small species or radicals (Ḣ, ȮH and O2 etc.) from the reactant to g fuel radical. At high temperatures, fuel radicals may undergo H-atom abstract from the adjacent carbon atom to form a C = C double bond plus HȮ2.
However, abstraction reaction class: fuel radical +O2 ↔ unsaturated species +HȮ2 has found to be important; instead, fuel radicals typically undergo isomerization or     1-butene, 2-butene, and 1,3-butadiene). This stud ports the first high-level quantum chemical calculations for an undisclosed reaction class o radical at intermediate to high temperatures: direct H-atom abstraction from terminal methyl g by molecular oxygen. Moreover, we systematically calculated rate constants for primary, secon and tertiary H-atom abstraction from the C4, C5, and C6 allylic radicals, respectively. Our resul be further used as rate rules for kinetic model development of unsaturated hydrocarbon oxid All calculations were implemented using two different ab initio solvers: Gaussian and ORCA, sets of ab initio methods, and two different kinetic solvers: MultiWell and PAPR. Temperatu pendent rate constants and thermochemistry were carried out based on transition state theor statistical thermodynamics, respectively. H-atom abstraction from the primary site of C4 allyli ical is found to be faster than that from secondary and tertiary sites of C5 and C6 allylic rad contrary to common understanding. Barrier heights predicted by different ab initio solver methods are about 4-5 kcal/mol different, which results in a factor of 4-86 difference in rate con predictions depending on the temperature. Using the Gaussian solver with Method 2 is found the most effective combination of predicting accurate rate constants when compared against e imental data. When comparing two kinetic solvers, both reaction rate coefficients and species mochemistry show good agreement at a wide range of temperatures, except for the rate coeffi calculated for C5 and C6 reactions (about a factor of 5-17 and 3-4 differences were obtained, re

Introduction
The combustion of hydrocarbons or oxygenates typically proceeds with H-atom straction by small species or radicals (Ḣ, ȮH and O2 etc.) from the reactant to gener fuel radical. At high temperatures, fuel radicals may undergo H-atom abstraction b from the adjacent carbon atom to form a C = C double bond plus HȮ2.
However, this d abstraction reaction class: fuel radical +O2 ↔ unsaturated species +HȮ2 has not found to be important; instead, fuel radicals typically undergo isomerization or β-sci    [47]. H-atom abstraction from the primary site (C 4 H 7 1-3 + O 2 ) was found to be faster than from secondary (C 5 H 9 1-3 + O 2 ) and tertiary (C 6 H 11 1-3 + O 2 ) 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. 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.

Thermodynamic Properties
In order to demonstrate the reliability of the calculated thermodynamic properties, three widely accepted thermochemistry databases were selected for comparison:  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 theĊ 4 H 7 1-3 + O 2 reaction, the two kinetic solvers show identical results, and the difference is within 10% across the entire temperature range. However, for the C 5 H 9 1-3 + O 2 and C 6 H 11 1-3 + O 2 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.

Thermodynamic Properties
In order to demonstrate the reliability of the calculated thermodynamic properties, three widely accepted thermochemistry databases were selected for comparison:  Table 5 compares the thermochemistry for closed shell molecules: C 4 H 6 , C 5 H 8 , and C 6 H 10 . Excellent agreement is obtained for the 298 K enthalpies of formation (∆ f H Ө ), 298 K entropies (S Ө ), and heat capacities (C p ) 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:Ċ 4 H 7 1-3,Ċ 5 H 9 1-3 andĊ 6 H 11 1-3. The ∆ f H Ө , S Ө and C p 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.

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:

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 ↔ unsaturated species +HȮ2 has not been found to be important; instead, fuel radicals typically undergo isomerization or β-scission   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, respec-

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 ↔ unsaturated species +HȮ2 has not been found to be important; instead, fuel radicals typically undergo isomerization or β-scission  C 3 H 6 + HȮ 2 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 hightemperature 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.  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.

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.