The mechanism of hydrogen abstraction in the reaction of 3-methyl-1-butanol with an OH radical was investigated by quantum chemical calculations. The total reaction consists of five channels (R1–R5), with channel R3 having the lowest energy barrier (5.4 kcal·mol−1) and channel R4 having the highest energy barrier (13.2 kcal·mol−1). All channels are exothermic reactions with lower energy barriers. Thermodynamic parameters, including constant pressure molar heat capacity CPo, enthalpy of formation ΔfHo, and entropy So, for all reactants and products, were researched using the CBS-QB3 level across a temperature scale of 298–5000 K. The harmonic and anharmonic rate constants of all reaction channels were calculated at the CCSD(T)/6-311++G(d,p) level for a temperature range of 223–4000 K. Throughout the temperature range, except for R2, the harmonic rate constant of all reaction channels is consistently higher than the anharmonic one, and it can be seen from the results that the anharmonic effect is significant and cannot be ignored. Meanwhile, the polynomial coefficients a1–a7 for the thermodynamic parameters and the polynomial coefficients A, n, and E for the kinetic parameters were fitted using the principle of least squares.

Alcohol fuels can be produced from crops and other biomass through biochemical processes such as fermentation and are considered to be renewable resources. Several researchers have found that, compared to fossil diesel, alcohol fuels can significantly reduce emissions of NOx, HC, CO, and soot.1,2 At present, many countries encourage the production and use of biofuels through tax breaks, subsidies, and other policies to address the fossil fuel crisis and promote clean energy development.3,4 To better understand the combustion properties and environmental impact of alcohol fuels, it is important to investigate the pyrolysis and oxidation mechanisms of alcohols.

3-Methyl-1-butanol (abbreviated as 3M1B) is an isomer of n-pentanol with the molecular formula CH2(OH)CH2CH(CH3)2. In recent years, many researchers have attempted to use pentanol with diesel fuel or pentanol, biodiesel, and diesel fuel as blends in various engine applications. Raza et al.5 investigated the combustion characteristics and emission characteristics of n-pentanol, dimethyl ether, and diesel fuel blends in a diesel engine. Li et al.6 investigated the use of pure pentanol in compression ignition engines. Campos-Fernandez et al.7 studied the effect of pentanol blended with diesel fuel on the performance of direct injection diesel engines. Yilmaz and Atmanli8 investigated the fuel properties of diesel, biodiesel, and 1-pentanol blends and the effect of these blends on the performance and emissions of diesel engines. Atmanli9 investigated and compared the basic fuel properties of diesel, biodiesel, and ternary blends of higher alcohols such as propanol, n-butanol, and 1-pentanol in diesel engines. These studies have shown that pentanol has a higher energy density, a higher boiling point, better miscibility with fossil fuels, faster combustion, and better suitability for use in conventional engines than first-generation alcohol fuels (methanol, ethanol) without significant engine modification. As a result, it is considered one of the most promising second-generation alcohol fuels. Togbe et al.10 have investigated the dissociation of 1-pentanol and 3M1B with an experimental approach and reported the kinetic modeling of their reactions. Welz et al.11 have used an experimental method to investigate the oxidation mechanism of 3M1B across a temperature scale of 550–750 K. Zhang et al.12 have investigated the pyrolysis of 2-methyl-1-butanol (abbreviated as 2M1B) by an experimental method across a temperature scale of 750–1400 K. Mellouki et al.13 have studied the rate constants of 3M1B and 3-methyl-2-butanol (abbreviated as 3M2B), respectively, reacted with OH at low temperatures by the relative rate method. Baxley and Wells14 have investigated the rate constants of how 2-butanol and 2-pentanol, respectively, react with OH. Cavalli et al.15 have analyzed the gaseous reaction products of 1-pentanol with OH and speculated on the reaction mechanism. However, a detailed reaction mechanism could not be provided due to limitations in experimental conditions and detection technology. Quantum chemical calculations can provide detailed potential energy diagrams and structural parameters for reactants, products, intermediates, and transition states. This information can both validate experimental results and provide theoretical guidance for experiments. Zhao et al.16 have used computational methods to study the pyrolysis of n-pentanol, 2M1B, and 3M1B. Parandaman and Rajakumar17 have investigated the dissociation reaction of 2-pentanol using both single pulse excitation tube experiments and quantum chemical calculations and verified the reliability of the theoretical calculation methods. Aazaad and Lakshmipathi18 have studied the reaction mechanisms of 1-pentanol + OH, 2-pentanol + OH, and 3-pentanol + OH by quantum chemical calculation methods. Tang et al.19 reported the ignition delay times of 3M1B, 2M1B, and n-pentanol. They found that the hydrogen extraction reaction was the main fuel consumption pathway for the combustion of the above three pentanol isomers. It is shown that the hydrogen extraction reaction in the combustion process of alcohol fuels is a key reaction affecting the ignition process and combustion rate. To date, there are no reports on using quantum chemical calculations to study the reaction mechanism between 3M1B and OH.

In this paper, five reaction paths R1–R5 of the hydrogen abstraction reaction of 3-methyl 1-butanol with OH radical have been investigated using quantum chemical calculations. The reaction mechanism and reaction energy barriers of the competing reaction paths in the conversion process have been analyzed in detail. The potential energy profiles of the reaction have been constructed. The thermodynamic parameters of the reactants and products were calculated across a temperature scale of 298–5000 K. These parameters include the constant pressure molar heat capacity (CPo), enthalpy of formation (ΔfHo), and entropy (So). Based on these calculations, the polynomial coefficients a1a7 of the thermodynamic parameters were fitted using the least-squares method for the low-temperature (300–1000 K) and the high-temperature (1000–5000 K) regions. The reaction rate constants kR1kR5 of the reaction paths R1–R5 in the temperature scale of 223–4000 K were calculated by applying the transition state (TS) theory and the Yao–Lin (YL) method, and the influence of the anharmonic effect on the reaction rate constants was analyzed in detail. In addition, the polynomial coefficients A, n, and E of the kinetic parameters were fitted using the least-squares method. This paper aims to serve as a valuable reference for chemists working in the fields of alcohol fuel applications and oxygenated volatile organic compounds (VOCs).

  • Step 1: The geometries of all species involved in the 3M1B + OH hydrogen abstraction reaction system were optimized using the M062X/6-311++G(d,p) level. The intrinsic reaction coordinates of the transition state were calculated at the same level to verify the correlation between the transition state and the reactant and product.

  • Step 2: The values of zero point energy correction and frequency for all reactants and transition states of the 3M1B+OH reaction system were calculated using the M062X/6-311++G(d,p) level.

  • Step 3: The thermodynamic parameters of all reactants and products were calculated at the CBS-QB3 level across the temperature region of 298–5000 K. These values include the constant volume molar heat capacity CVo, entropy So, and enthalpy of formation ΔfHo.

  • Step 4: The single-point energies and total energies of all species and the energy barriers of each reaction pathway were calculated on the CCSD(T)/6-311++G(d,p) level. The rate constants were then calculated based on the energy barrier values and the frequency values.

All the above-mentioned works of density functional theory method and ab initio calculation were performed using Gaussian 09 software.

According to the formatting rules of the ChemKin software, the thermodynamic parameters CPo, ΔfHo, and So are expressed in the form of seven polynomial coefficients as follows a1a7:20,
CPoR=a1+a2T+a3T2+a4T3+a5T4,
(1)
ΔfHoRT=a1+a22T+a33T2+a44T3+a55T4+a6T,
(2)
SoR=a1lnT+a2T+a32T2+a43T3+a54T4+a7,
(3)
where the molar gas constant R = 8.31 J·mol−1·K−1, CPo=CVo+R, CVo and So can be directly obtained from the output files of Gaussian 09 software frequency calculations. ΔfHo can be computed employing the following atomization enthalpy method.21 
The standard enthalpy of formation ΔfH298o(CxHyOz) is defined as the sum of the enthalpy changes for the transformation of x moles of C(s), y2 moles of H2(g), and z2 moles of O2(g) through two steps, namely,
xC(s)+y2H2(g)+z2O2(g)ΔH1xC(g)+yH(g)+zO(g),
(4)
xC(g)+yH(g)+zO(g)ΔH2CxHyOz,
(5)
ΔfH298o(CxHyOz)=ΔH1+ΔH2.
(6)
The formula for calculating ΔH1
ΔH1=xΔfH298o(C)+yΔfH298o(H)+zΔfH298o(O).
(7)
In this study, ΔfH298o(C)=171.29kcalmol1,ΔfH298o(H)=52.103kcalmol1, and ΔfH298o(O)=59.55kcalmol1 are taken from experimental values provided in the NIST-JANAF22 thermochemical table.
The formula for calculating ΔH2
ΔH2=H298o(CxHyOz)xH298o(C)yH298o(H)zH298o(O),
(8)
where H298o(CxHyOz),H298o(C),H298o(H),andH298o(O), respectively, represent the standard enthalpies for the CxHyOz molecule and C, H, and O atoms, which can be directly obtained from the output files of Gaussian 09 software frequency calculations.
Similarly, the enthalpy of the formation of the molecule CxHyOz at different temperatures can also be obtained using the above-mentioned method,
ΔfHTo(CxHyOz)=ΔH1(T)+ΔH2(T).
(9)
The calculation of ΔH1(T) at different temperatures is modified to
ΔH1(T)=ΔH1=xΔfH298o(C)+yΔfH298o(H)+zΔfH298o(O).
(10)
The calculation of ΔH2(T) at different temperatures is modified to
ΔH2(T)=HTo(CxHyOz)xHTo(C)yHTo(H)zHTo(O).
(11)

After calculating CPo, ΔfHo, and So at different temperatures, the values of a1a7 are then fitted by the least squares principle. See the detailed description of the fitting method in Ref. 23, and the reliability of this fitting method has been validated in our previous work in Refs. 23–25.

According to transition state theory (TS), for a bimolecular system, the temperature-dependent rate constant calculation formula can be expressed as26 
k(T)=kbThQ(T)QA(T)QB(T)eΔEkbT,
(12)
where the Boltzmann constant kb = 1.38 × 10−23 J·K−1, the Planck constant h = 6.63 × 10−34 J·s, ΔE represents the energy barrier, Q(T), QA(T), QB(T) represent the partition functions of the transition state (abbreviated as TS), the reactant A, and the reactant B, respectively.
According to the definition of the Yao–Lin (YL) method,27,28 the partition function of anharmonic vibrations is calculated using the Morse oscillator model. The partition function for the ith vibrational mode is given by
Qi(T)=zizimeEzikbT.
(13)
The energy for the ith vibrational mode is given as
Ezi=zi+12h2πωixizi+122h2πωi.
(14)
In Eqs. (13) and (14), ωi is the vibrational frequency, and zi and zim represent the vibrational quantum number and its maximum value, respectively.

The harmonic and anharmonic rate constants of the reaction system can be solved by substituting the results of harmonic frequency and anharmonic frequency calculations with the reaction channel energy barrier values into the program written by the YL method, respectively. The YL method has been applied to several reaction systems such as NO3-related reactions,24 PxOy (x = 1,2 and y = 1–5) related reactions,25 N2O-related reactions,26 ethylene dissociation,27 CF3CCl2O radical decomposition,29 NOx + H2O,30 C2H3Cl + OH,31 and the reliability of the method has been verified.

Following the Arrhenius equation, the reaction rate k(T) can be expressed in the form of three polynomial coefficients (A, n, E),20,23,24
k(T)=ATneERT.
(15)

After calculating k(T) at different temperatures, the values of A, n, and E are then fitted using the least squares principle. See the detailed description of the fitting method in Ref. 23. The reliability of this fitting method has been validated in our previous work in Refs. 23, 25, 26, and 32.

The presence of the –OH group breaks the symmetry of the carbon chain structure in the 3M1B molecule, resulting in five different types of H atoms. As a result, there are five possible reaction paths (R1–R5) in the H extraction reaction between 3M1B and the OH radical. (refer to Fig. 1). Fig. S1 in the supplementary material displays the geometric configurations resulting from the optimization of all species for the 3M1B + OH reaction at the M062X/6-311++G(d,p) level. Figure 2 presents the relative energy information calculated for all species involved in the 3M1B + OH reaction on the CCSD(T)/6-311++G(d,p) level. The analysis of Figs. 1 and 2 and S1 reveals that in the reaction of 3M1B with OH, the OH radical initially adds to the 3M1B molecule, resulting in the formation of the reactant complex RC1, which is 7.2 kcal·mol−1 below the energy of the reactant 3M1B + OH, indicating an exothermic reaction with no energy barrier. From RC1, transition states TS1–TS5 lead to the formation of product complexes PC1–PC5. These complexes eventually decompose to produce products P1–P5 and H2O.

FIG. 1.

The pathways of 3M1B + OH hydrogen abstraction reaction.

FIG. 1.

The pathways of 3M1B + OH hydrogen abstraction reaction.

Close modal
FIG. 2.

Energy barrier diagram calculated for the 3M1B + OH reaction system on CCSD(T)/6-311++G(d,p)//M062X/6-311++G(d,p) level.

FIG. 2.

Energy barrier diagram calculated for the 3M1B + OH reaction system on CCSD(T)/6-311++G(d,p)//M062X/6-311++G(d,p) level.

Close modal

1. Reaction pathway R1

Starting from the reactant complex RC1, the OH radical abstracts the H6 atom on the C1 (–CH2 group) atom to form the product complex PC1 via the transition state TS1. In this reaction step, the bond lengths of the C1–H6 bond in RC1, TS1, and PC1 are 1.091, 1.168, and 2.701 Å, respectively, and the H6–O19 bond lengths in TS1 and PC1 are 1.446 and 0.978 Å, respectively. In the following step, the product complex PC1 cleaves to generate C·H(OH)CH2CH(CH3)2 (referred to as P1) radical and H2O molecule. According to the analysis of the relative energy calculations, the energy barrier between TS1 and RC1 is ∼9.7 kcal mol−1, and the energy of the products P1 + H2O is 13.7 kcal mol−1 lower than that of the reactants 3M1B + OH, which suggests that the reaction pathway R1 is a fast exothermic process with a low energy barrier.

2. Reaction pathway R2

Starting from the reaction complex RC1, the OH radical abstracts the H8 atom on the C2 atom (similar to the reaction path R1, which also abstracts the hydrogen atom on the –CH2 group) to form the product complex PC2 via the transition state TS2. Comparing the configurations of RC1, TS2, and PC2, it is clear that the bond lengths of the C2–H8 bond in RC1, TS2, and PC2 are 1.093, 1.229, and 2.784 Å, respectively, and the H8–O19 bond lengths in TS2 and PC2 are 1.310 and 0.968 Å, respectively. In the next step, the product complex PC2 dissociates to produce the CH2(OH)C · HCH(CH3)2 (referred to as P2) radical and H2O. The energy barrier of TS2 relative to RC1 is 9.5 kcal mol−1, and the relative energy values of the products P2 + H2O and the reactants 3M1B + OH are −9.6 kcal mol−1, indicating that this reaction pathway is a fast exothermic process with a low energy barrier.

3. Reaction pathway R3

Comparing the configurations of RC1, TS3, and PC3, it is evident that the H10 atom in the reaction complex RC1 breaks away from the C3 (–CH group) atom while moving closer to the O19 atom to form the product complex PC3 via the transition state TS3. The bond lengths of the C3–H10 bond in RC1, TS3, and PC3 are 1.095, 1.193, and 2.769 Å, respectively, and the H10–O19 bond lengths in TS3 and PC3 are 1.362 and 0.968 Å, respectively. In the following step, the product complex PC3 dissociates to form the products CH2(OH)CH2C · (CH3)2 (referred to as P3) and H2O. Based on the relative energy calculations, the energy barrier of the TS3 is 5.4 kcal·mol−1, and the generation of the products P3 + H2O is exothermic at 14.3 kcal·mol−1, which suggests that the reaction pathway R3 is a fast exothermic process with a low energy barrier.

4. Reaction pathway R4

Starting from the reactant complex RC1, the OH radical first abstracts the H14 atom on the C5 (–CH3 group) to form the product complex PC4 via transition state TS4. Comparing the configurations of RC1, TS4, and PC4, it is clear that the bond lengths of the C5–H14 bond in RC1, TS4, and PC4 are 1.091, 1.203, and 2.264 Å, respectively, and the H14–O19 bond lengths in TS4 and PC4 are 1.351 and 0.974 Å, respectively. In the following step, PC4 dissociates to form the products CH2(OH)CH2CH(CH3)C · H2 (referred to as P4) and H2O. Based on the relative energy calculations, the energy barrier of TS4 relative to RC1 is ∼13.2 kcal mol−1, and the relative energy values of the products P4 + H2O and the reactants 3M1B + OH are −7.7 kcal mol−1, indicating that this reaction pathway is a fast exothermic process with a low energy barrier.

5. Reaction pathway R5

Comparing the configurations of RC1, TS5, and PC5, it is evident that the H18 atom in the reaction complex RC1 separates from the O17 atom (–OH group) as it approaches the O19 atom. The bond lengths of the O17–H18 bond in RC1, TS5, and PC5 are 0.968, 1.074, and 1.942 Å, respectively, and the H18–O19 bond lengths in TS5 and PC5 are 1.308 and 0.975 Å, respectively. Next, PC5 dissociates to form the products CH2(O) · CH2CH(CH3)2 (referred to as P5) radical and H2O molecule. Based on the relative energy calculations, the energy barrier of the TS5 is ∼11.7 kcal·mol−1, and the generation of the products P5 + H2O is exothermic by 9.5 kcal·mol−1, which suggests that the reaction pathway R3 is a fast exothermic process with a low energy barrier.

To verify the reliability of the thermodynamic parameter calculation results and methods in this study, Table I lists the ΔfH298o, S298o, (300 K) of reactants 3M1B, OH, and products P1, P2, P3, P4, P5, and H2O calculated on the CBS-QB3 level, along with corresponding reference data that can be consulted. From Table I, the standard enthalpy of formation ΔfH298o of 3M1B calculated in this paper is −71.88 kcal·mol−1, which is only 0.11% different from that of Markovnik33 (−71.8 kcal·mol−1). The ΔfH298o of OH is obtained as 8.93 kcal·mol−1 in this study, compared to Goldsmith’s et al.34 result of 8.9 kcal·mol−1 and Chase’s22 result of 9.3 kcal·mol−1. This paper has a relative deviation of 0.3% from Goldsmith’s results and 3.9% from Chase’s results. The ΔfH298o of H2O in this study is calculated as −58.10 kcal·mol−1, which is comparable to Goldsmith’s et al.34 result of −58.0 kcal·mol−1 and Chase’s22 result of −57.8 kcal·mol−1, with relative deviations of only 0.17% and 0.52%, respectively. The standard entropy S298o of OH is calculated to be 42.94 cal·mol−1·K−1, whereas both Goldsmith et al.34 and Chase22 reported a result of 43.9 cal·mol−1·K−1. The relative deviation of the calculated result in this study from the literature reference values is 2.1%. The S298o of H2O is calculated as 45.16 cal·mol−1·K−1 in this study, and the relative deviation is within 0.36% compared to the results of Goldsmith et al.34 and Chase.22 The molar heat capacity at constant pressure CPo (300 K) of OH and H2O at 300 K are calculated as 6.96 and 8.00 J·mol−1·K−1 in this study, respectively, and the relative deviation is within 0.87% compared to the results of Goldsmith et al.34 The overall comparison from Table I indicates that the ΔfH298o, S298o, and CPo (300 K) calculated in this study align well with existing reference data. This indicates that the method used to calculate thermodynamic parameters is accurate and reliable and can be applied to species without reference data.

TABLE I.

Standard enthalpy of formation ΔfH298o, entropy S298o, and constant pressure molar heat capacity CPo (300 K) on the CBS-QB3 level.

SpeciesΔfH298o kcal·mol−1S298o cal·mol−1·K−1CPo (300 K) J·mol−1·K−1
This workRef. valuesThis workRef. valuesThis workRef. values
3M1B −71.88 −71.8a 86.92 ⋯ 30.82 ⋯ 
OH 8.93 8.9b(9.3c42.94 43.9b(43.9c6.96 6.9b 
H2−58.10 −58.0b(−57.8c45.16 45.0b(45.1c8.00 8.0b 
P1 −28.91 ⋯ 87.98 ⋯ 31.13 ⋯ 
P2 −23.46 ⋯ 90.70 ⋯ 31.58 ⋯ 
P3 −26.02 ⋯ 90.39 ⋯ 31.08 ⋯ 
P4 −21.41 ⋯ 89.07 ⋯ 31.75 ⋯ 
P5 −18.13 ⋯ 86.76 ⋯ 29.83 ⋯ 
SpeciesΔfH298o kcal·mol−1S298o cal·mol−1·K−1CPo (300 K) J·mol−1·K−1
This workRef. valuesThis workRef. valuesThis workRef. values
3M1B −71.88 −71.8a 86.92 ⋯ 30.82 ⋯ 
OH 8.93 8.9b(9.3c42.94 43.9b(43.9c6.96 6.9b 
H2−58.10 −58.0b(−57.8c45.16 45.0b(45.1c8.00 8.0b 
P1 −28.91 ⋯ 87.98 ⋯ 31.13 ⋯ 
P2 −23.46 ⋯ 90.70 ⋯ 31.58 ⋯ 
P3 −26.02 ⋯ 90.39 ⋯ 31.08 ⋯ 
P4 −21.41 ⋯ 89.07 ⋯ 31.75 ⋯ 
P5 −18.13 ⋯ 86.76 ⋯ 29.83 ⋯ 
a

From Ref. 33.

b

From Ref. 34.

c

From Ref. 22.

Subsequently, the ΔfHo, So, and CPo of all species associated with the titled reaction were computed within the temperature range of 298–5000 K. The results were then substituted into formulas (1)(3), and the temperature-dependent thermodynamic polynomial coefficients (a1a7) were fitted using the principle of least squares. Here, the input thermodynamics file of CHEMKIN defines 1000 K as the critical point between low and high temperatures. The results of fitting thermodynamic polynomial coefficients for the low-temperature (fitted temperatures in the range of 300–1000 K) are shown in Table II, and the results of fitting thermodynamic polynomial coefficients for the high-temperature (fitted temperatures in the range of 1000–5000 K) are shown in Table III.

TABLE II.

The fitted values of thermodynamic parameters in the low-temperature zone for the reaction mechanism.

Speciesa1a2a3a4a5a6a7
3M1B 2.01 4.11 × 10−2 2.79 × 10−5 −5.90 × 10−8 2.47 × 10−11 −3.87 × 104 19.2 
OH 3.43 5.77 × 10−4 −1.76 × 10−6 2.15 × 10−9 −7.58 × 10−13 3.46 × 103 1.76 
P1 1.72 4.76 × 10−2 5.07 × 10−6 −3.64 × 10−8 1.70 × 10−11 −1.70 × 104 20.3 
P2 2.58 4.39 × 10−2 1.20 × 10−5 −4.21 × 10−8 1.89 × 10−11 −1.45 × 104 17.6 
P3 2.58 4.39 × 10−2 1.20 × 10−5 −4.21 × 10−8 1.89 × 10−11 −1.59 × 104 17.6 
P4 2.20 4.69 × 10−2 5.85 × 10−6 −3.71 × 10−8 1.73 × 10−11 −1.34 × 104 18.3 
P5 1.41 4.40 × 10−2 1.64 × 10−5 −4.72 × 10−8 2.06 × 10−11 −1.55 × 104 22.1 
H24.20 −2.14 × 10−3 6.70 × 10−6 −5.72 × 10−9 1.85 × 10−12 −3.04 × 103 −0.858 
Speciesa1a2a3a4a5a6a7
3M1B 2.01 4.11 × 10−2 2.79 × 10−5 −5.90 × 10−8 2.47 × 10−11 −3.87 × 104 19.2 
OH 3.43 5.77 × 10−4 −1.76 × 10−6 2.15 × 10−9 −7.58 × 10−13 3.46 × 103 1.76 
P1 1.72 4.76 × 10−2 5.07 × 10−6 −3.64 × 10−8 1.70 × 10−11 −1.70 × 104 20.3 
P2 2.58 4.39 × 10−2 1.20 × 10−5 −4.21 × 10−8 1.89 × 10−11 −1.45 × 104 17.6 
P3 2.58 4.39 × 10−2 1.20 × 10−5 −4.21 × 10−8 1.89 × 10−11 −1.59 × 104 17.6 
P4 2.20 4.69 × 10−2 5.85 × 10−6 −3.71 × 10−8 1.73 × 10−11 −1.34 × 104 18.3 
P5 1.41 4.40 × 10−2 1.64 × 10−5 −4.72 × 10−8 2.06 × 10−11 −1.55 × 104 22.1 
H24.20 −2.14 × 10−3 6.70 × 10−6 −5.72 × 10−9 1.85 × 10−12 −3.04 × 103 −0.858 
TABLE III.

The fitted values of thermodynamic parameters in the high-temperature zone for the reaction mechanism.

Speciesa1a2a3a4a5a6a7
3M1B 11.1 3.80 × 10−2 −1.48 × 10−5 2.64 × 10−9 −1.78 × 10−13 −4.22 × 104 −33.6 
OH 2.84 1.02 × 10−3 −2.55 × 10−7 2.79 × 10−11 −1.02 × 10−15 3.72 × 103 5.17 
P1 5.67 4.78 × 10−2 −2.35 × 10−5 5.60 × 10−9 −5.25 × 10−13 −1.84 × 104 −2.49 
P2 5.67 4.79 × 10−2 −2.35 × 10−5 5.62 × 10−9 −5.28 × 10−13 −1.57 × 104 −1.62 
P3 5.76 4.79 × 10−2 −2.35 × 10−5 5.62 × 10−9 −5.28 × 10−13 −1.71 × 104 −1.62 
P4 6.13 4.72 × 10−2 −2.31 × 10−5 5.50 × 10−9 −5.16 × 10−13 −1.48 × 104 −4.38 
P5 4.20 5.08 × 10−2 −2.54 × 10−5 6.15 × 10−9 −5.83 × 10−13 −1.27 × 104 4.46 
H22.66 2.97 × 10−3 −8.74 × 10−7 1.22 × 10−10 −6.54 × 10−15 −3.00 × 104 6.96 
Speciesa1a2a3a4a5a6a7
3M1B 11.1 3.80 × 10−2 −1.48 × 10−5 2.64 × 10−9 −1.78 × 10−13 −4.22 × 104 −33.6 
OH 2.84 1.02 × 10−3 −2.55 × 10−7 2.79 × 10−11 −1.02 × 10−15 3.72 × 103 5.17 
P1 5.67 4.78 × 10−2 −2.35 × 10−5 5.60 × 10−9 −5.25 × 10−13 −1.84 × 104 −2.49 
P2 5.67 4.79 × 10−2 −2.35 × 10−5 5.62 × 10−9 −5.28 × 10−13 −1.57 × 104 −1.62 
P3 5.76 4.79 × 10−2 −2.35 × 10−5 5.62 × 10−9 −5.28 × 10−13 −1.71 × 104 −1.62 
P4 6.13 4.72 × 10−2 −2.31 × 10−5 5.50 × 10−9 −5.16 × 10−13 −1.48 × 104 −4.38 
P5 4.20 5.08 × 10−2 −2.54 × 10−5 6.15 × 10−9 −5.83 × 10−13 −1.27 × 104 4.46 
H22.66 2.97 × 10−3 −8.74 × 10−7 1.22 × 10−10 −6.54 × 10−15 −3.00 × 104 6.96 

In view of investigating the kinetic characteristics of the 3M1B + OH hydrogen abstraction reaction system and the influence of anharmonic effects on kinetic parameters, this study computed the harmonic rate constants kR1(Harm)–kR5(Harm) and anharmonic rate constants kR1(Anharm)–kR5(Anharm) of the reaction pathways R1–R5 within the temperature scale of 223–4000 K (results shown in Figs. 37).

FIG. 3.

Temperature-dependent reaction rate constant curves for reaction channel R1.

FIG. 3.

Temperature-dependent reaction rate constant curves for reaction channel R1.

Close modal
FIG. 4.

Temperature-dependent reaction rate constant curves for reaction channel R2.

FIG. 4.

Temperature-dependent reaction rate constant curves for reaction channel R2.

Close modal
FIG. 5.

Temperature-dependent reaction rate constant curves for reaction channel R3.

FIG. 5.

Temperature-dependent reaction rate constant curves for reaction channel R3.

Close modal
FIG. 6.

Temperature-dependent reaction rate constant curves for reaction channel R4.

FIG. 6.

Temperature-dependent reaction rate constant curves for reaction channel R4.

Close modal
FIG. 7.

Temperature-dependent reaction rate constant curves for reaction channel R5.

FIG. 7.

Temperature-dependent reaction rate constant curves for reaction channel R5.

Close modal

1. Reaction path R1

As depicted in Fig. 3, at temperatures in the 223–4000 K region, the harmonic rate constant kR1(Harm) grows increasingly larger with temperature, and the anharmonic rate constant kR1(Anharm) increases with temperature below 2000 K and decreases slowly with increasing temperature above 2000 K. Moreover, the kR1(Harm) consistently exceeds that of the kR1(Anharm) across the entire temperature scale, and the influence of anharmonicity on the rate constant becomes more pronounced with increasing temperature. For instance, when T = 223 K, kR1(Harm) (2.30 × 103 cm3·mol−1·s−1) is ∼1.31 times equal to kR1(Anharm) (1.75 × 103 cm3·mol−1·s−1), when T = 1000 K, kR1(Harm) (1.73 × 1011 cm3·mol−1·s−1) is ∼26.2 times equal to kR1(Anharm) (6.59 × 109 cm3·mol−1·s−1), when T = 2000 K, kR1(Harm) (2.91 × 1012 cm3·mol−1·s−1) is ∼1.12 × 102 times equal to kR1(Anharm) (2.59 × 1010 cm3·mol−1·s−1), when T = 3000 K, kR1(Harm) (7.78 × 1012 cm3·mol−1·s−1) is ∼2.89 × 102 times equal to kR1(Anharm) (2.69 × 1010 cm3·mol−1·s−1), and when T = 4000 K, kR1(Harm) (1.28 × 1013 cm3·mol−1·s−1) is ∼5.82 × 102 times equal to kR1(Anharm) (2.20 × 1010 cm3·mol−1·s−1).

2. Reaction path R2

As illustrated in Fig. 4, at temperatures in the 223–4000 K region, both the harmonic rate constant kR2(Harm) and the anharmonic rate constant kR2(Anharm) grow increasingly larger with temperature. When 223 K T < 1000 K, the kR1(Harm) consistently remains slightly above the kR1(Anharm), albeit with minimal disparity. However, when 1000 K ≤ T ≤ 4000 K, the kR1(Anharm) is higher than the kR1(Harm), and this difference becomes progressively larger with increasing temperature. For example, when T = 223 K, kR2(Harm) (6.88 × 102 cm3·mol−1·s−1) is ∼2.15 times greater than kR2(Anharm) (3.21 × 102 cm3·mol−1·s−1), when T = 1000 K, kR2(Anharm) (2.46 × 1010 cm3·mol−1·s−1) is ∼1.19 times greater than kR2(Harm) (2.07 × 1010 cm3·mol−1·s−1), when T = 2000 K, kR2(Anharm) (1.33 × 1012 cm3·mol−1·s−1) is ∼4.28 times greater than kR2(Harm) (3.11 × 1011 cm3·mol−1·s−1), when T = 3000 K, kR2(Anharm) (6.89 × 1012 cm3·mol−1·s−1) is ∼8.59 times greater than kR2(Harm) (8.02 × 1011 cm3·mol−1·s−1), when T = 4000 K, kR2(Anharm) (1.80 × 1013 cm3·mol−1·s−1) is ∼13.8 times greater than kR2(Harm) (1.30 × 1012 cm3·mol−1·s−1).

3. Reaction path R3

As depicted in Fig. 5, at temperatures in the 223–4000 K region, the harmonic rate constant kR3(Harm) grows increasingly larger with temperature, and the anharmonic rate constant kR3(Anharm) increases with temperature below 2000 K and decreases slowly with increasing temperature above 2000 K. Additionally, the value of the kR3(Harm) consistently exceeds that of the kR3(Anharm) throughout the entire temperature scale, and the influence of anharmonicity on the rate constant becomes more pronounced with increasing temperature. For instance, when T = 223 K, kR3(Harm) (5.84 × 106 cm3·mol−1·s−1) is approximately equal to 1.25 times kR3(Anharm) (4.69 × 106 cm3·mol−1·s−1), when T = 1000 K, kR3(Harm) (1.27 × 1011 cm3·mol−1·s−1) is approximately equal to 2.75 times kR3(Anharm) (4.61 × 1010 cm3·mol−1·s−1), when T = 2000 K, kR3(Harm) (6.73 × 1011 cm3·mol−1·s−1) is approximately equal to 7.01 times kR3(Anharm) (9.65 × 1010 cm3·mol−1·s−1), when T = 3000 K, kR3(Harm) (1.23 × 1012 cm3·mol−1·s−1) is approximately equal to 15.6 times kR3(Anharm) (7.86 × 1010 cm3·mol−1·s−1), and when T = 4000 K, kR3(Harm) (1.68 × 1012 cm3·mol−1·s−1) is approximately equal to 30.7 times kR3(Anharm) (5.46 × 1010 cm3·mol−1·s−1).

4. Reaction path R4

As illustrated in Fig. 6, at temperatures in the 223–4000 K region, both the harmonic rate constant kR4(Harm) and the anharmonic rate constant kR4(Anharm) grow increasingly larger with temperature. Furthermore, the value of the kR4(Harm) slightly exceeds that of the kR4(Anharm) throughout the entire temperature scale, and the impact of anharmonicity on the rate constant is insignificant. For instance, at T = 223 K, kR4(Harm) (0.344 cm3·mol−1·s−1) is ∼1.53 times greater than kR4(Anharm) (0.225 cm3·mol−1·s−1), at T = 1000 K, kR4(Harm) (1.36 × 1010 cm3·mol−1·s−1) is ∼2.98 times greater than kR4(Anharm) (4.55 × 109 cm3·mol−1·s−1), at T = 2000 K, kR4(Harm) (6.10 × 1011 cm3·mol−1·s−1) is ∼2.14 times greater than kR4(Anharm) (2.85 × 1011 cm3·mol−1·s−1), at T = 3000 K, kR4(Harm) (2.28 × 1012 cm3·mol−1·s−1) is ∼1.59 times greater than kR4(Anharm) (1.44 × 1012 cm3·mol−1·s−1), and at T = 4000 K, kR4(Harm) (4.47 × 1012 cm3·mol−1·s−1) is ∼1.29 times greater than kR4(Anharm) (3.46 × 1012 cm3·mol−1·s−1).

5. Reaction path R5

As illustrated in Fig. 7, at temperatures in the 223–4000 K region, the harmonic rate constant kR5(Harm) grows increasingly larger with temperature. and the anharmonic rate constant kR5(Anharm) increases with temperature below 2000 K and decreases slowly with increasing temperature above 2000 K. Additionally, the value of the kR5(Harm) consistently exceeds that of the kR5(Anharm) throughout the entire temperature scale, and the impact of anharmonicity on the rate constant is insignificant. For instance, when T = 223 K, kR5(Harm) (12.2 cm3·mol−1·s−1) is ∼1.23 times equal to kR5(Anharm) (9.92 cm3·mol−1·s−1), when T = 1000 K, kR5(Harm) (2.26 × 1010 cm3·mol−1·s−1) is ∼3.58 times equal to kR5(Anharm) (6.33 × 109 cm3·mol−1·s−1), when T = 2000 K, kR5(Harm) (5.59 × 1011 cm3·mol−1·s−1) is ∼16.9 times equal to kR5(Anharm) (3.30 × 1010 cm3·mol−1·s−1), when T = 3000 K, kR5(Harm) (1.70 × 1012 cm3·mol−1·s−1) is ∼66.9 times equal to kR5(Anharm) (2.54 × 1010 cm3·mol−1·s−1), and when T = 4000 K, kR5(Harm) (3.00 × 1012 cm3·mol−1·s−1) is ∼2.18 × 102 times equal to kR5(Anharm) (1.38 × 1010 cm3·mol−1·s−1).

Based on the harmonic and anharmonic rate constants obtained from Figs. 37, the values of the kinetic polynomial coefficients A, n, and E for each reaction path were fitted using the principle of least squares, as shown in Table IV. The fitting results indicate that the fitted E values are close to the reaction barriers calculated by the CCSD(T) method for the relevant reactions, demonstrating that the method employed in this study for calculating kinetic parameters is accurate and reliable. Hence, this method can be applied to compute and evaluate the kinetic mechanisms of reaction paths without reference data.

TABLE IV.

The fitted values of kinetic parameters for the reaction mechanism.

PathsHarmAnharmBarrier
A cm3·mol−1·s−1nE kcal·mol−1A cm3·mol−1·s−1nE kcal·mol−1E kcal·mol−1
R1 1.73 × 1012 0.39 10.0 6.53 × 1016 −1.91 9.93 9.69 
R2 1.31 × 1011 0.42 9.46 2.61 × 104 2.59 8.91 9.54 
R3 1.04 × 1011 0.42 5.35 7.96 × 1016 −1.59 6.69 5.42 
R4 2.88 × 1011 0.54 13.5 2.61 × 104 2.59 13.0 13.2 
R5 1.37 × 1012 0.28 11.9 7.96 × 1015 −1.58 11.8 11.7 
PathsHarmAnharmBarrier
A cm3·mol−1·s−1nE kcal·mol−1A cm3·mol−1·s−1nE kcal·mol−1E kcal·mol−1
R1 1.73 × 1012 0.39 10.0 6.53 × 1016 −1.91 9.93 9.69 
R2 1.31 × 1011 0.42 9.46 2.61 × 104 2.59 8.91 9.54 
R3 1.04 × 1011 0.42 5.35 7.96 × 1016 −1.59 6.69 5.42 
R4 2.88 × 1011 0.54 13.5 2.61 × 104 2.59 13.0 13.2 
R5 1.37 × 1012 0.28 11.9 7.96 × 1015 −1.58 11.8 11.7 

This work provides a detailed description of the hydrogen abstraction reaction of 3M1B with OH, including the structures and energy information of all reactant species. Thermodynamic and kinetic parameters for each reaction pathway were calculated, reaching the below conclusions:

  1. The hydrogen abstraction reaction of 3M1B with OH involves five reaction pathways, denoted as R1–R5, leading to the formation of products P1 + H2O, P2 + H2O, P3 + H2O, P4 + H2O, and P5 + H2O, respectively. Based on the relative energy calculations, it is evident that all five reaction pathways are exothermic reactions with lower energy barriers. Among them, pathway R3 exhibits the lowest energy barrier, indicating a significant competitive advantage. Pathways R1 and R2 follow with moderate competitive advantages, while pathways R4 and R5 have higher energy barriers and are relatively less competitive.

  2. The thermochemical parameters Cpo, ΔfHo, and So of all reactants and products have been obtained at the CBS-QB3 level within the temperature scale of 298–5000 K. The calculations presented in this paper are in good agreement with the available experimental data, indicating the accuracy and reliability of the method used for calculating and evaluating the thermodynamic parameters of species for which no reference data are available. In addition, the least-squares method has been applied to fit the values of the polynomial coefficients a1a7 of the thermodynamic parameters in the low-temperature (300–1000 K) and high-temperature (1000–5000 K), respectively. These parameters can be directly utilized to establish chemical reaction mechanism models, providing the thermodynamic parameters of reaction mechanism models for subsequent numerical simulation studies.

  3. The harmonic and anharmonic rate constants for reaction pathways R1–R5 have been computed on CCSD(T)/6-311++G(d,p) level within the temperature range of 223–4000 K. The harmonic rate constants grow increasingly larger with temperature, but the anharmonic rate constants of some reaction pathways (R1, R3, R5) decrease slowly with the increase in temperature (when T > 2000 K), which shows a certain negative temperature effect. Specifically, the impact of anharmonicity on the rate constants of the pathways R1, R3, and R5 is significant. Therefore, it is important to consider anharmonic effects when studying the mechanism of the 3M1B + OH hydrogen extraction reaction. Furthermore, the polynomial coefficients A, n, and E of the kinetic parameters for reaction paths R1–R5 were fitted using the principle of least squares. The value of the fitted E closely approximates the reaction barriers computed by the CCSD(T) method. This suggests that the calculation method used in this paper for determining the kinetic parameters is accurate and reliable. As a result, these parameters can be directly applied to establish a chemical reaction mechanism model, provide kinetic parameters for the reaction mechanism model, and conduct relevant numerical simulation studies.

The supplementary material is on theoretical studies and anharmonic effect analysis on the reaction mechanism of 3-methyl-1-butanol with OH radical, which is the optimized geometric configurations on M062X/6-311++G(d,p) level for all species of the title reaction.

This work was supported by the Scientific Research Foundation of the Education Department of Liaoning Province (Grant Nos. L2020006 and LJKMZ20221858).

The authors have no conflicts to disclose.

Li Wang: Formal Analysis, Writing - Original Draft; Yiwei Chen: Review & Editing; Li Yao (Corresponding Author): Conceptualization, Resources, Supervision, Review & Editing. All authors reviewed the paper.

Li Wang: Writing – original draft (equal). Yiwei Chen: Writing – review & editing (equal). Li Yao: Supervision (equal).

The authors confirm that the data and materials supporting the findings of this study are available within the article. More research data and materials are available on request from the corresponding author, upon reasonable request.

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