Computational study on the mechanism and kinetics for the reaction between HO₂ and n-propyl peroxy radical

Abstract

The n-propyl peroxy radical (n-C₃H₇O₂) is the key intermediate during atmospheric oxidation of propane (C₃H₈) which plays an important role in the carbon and nitrogen cycles in the troposphere. In this paper, a comprehensive theoretical study on the reaction mechanism and kinetics of the reaction between HO₂ and n-C₃H₇O₂ was performed at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d,p) level of theory. Computational results show that the HO₂ + n-C₃H₇O₂ reaction proceeds on both singlet and triplet potential energy surfaces (PESs). From an energetic point of view, the formation of C₃H₇O₂H and ³O₂ via triplet hydrogen abstraction is the most favorable channel while other product channels are negligible. In addition, the calculated rate constants for the title reaction over the temperature range of 238–398 K were calculated by the multiconformer transition state theory (MC-TST), and the calculated rate constants show a negative temperature dependence. The contributions of the other four reaction channels to the total rate constant are negligible.

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1. Introduction

Propane (C₃H₈) is one of the most important nonmethane hydrocarbons (NMHCs) with a lifetime of about 14 days and its global emissions are estimated to be 15–20 Tg per year.^1,2 For decades, propane oxidation has been of great interest, and the n-propyl peroxy radical (n-C₃H₇O₂) is one of the key intermediates during propane oxidation.^3–6

In clean environments where NO_x concentrations are low, the reactions of HO₂ with organic peroxy radicals (RO₂) are generally considered as an important sink.^7–11 The reaction mechanisms and kinetic data of HO₂ + RO₂ reactions have not yet been well-established mainly because of inherent problems in exploring radical–radical reactions.¹² Besides, to the best of our knowledge, only a few studies for both kinetics and mechanism of the HO₂ + n-C₃H₇O₂ reaction have been reported. One of the difficulties is that the n-C₃H₇O₂ radical is more complex than CH₃O₂ and C₂H₅O₂ due to its rich conformational variety. It has been reported that the n-C₃H₇O₂ radical has five different conformers: G₁G₂, G₁T₂, T₁G₂ and T₁T₂ (see Fig. S1 in the ESI†).^13–15

Hou and co-workers have developed a structure–activity relationships (SAR) model to study structure–activity relationships and the characteristics of the HO₂ + RO₂ reactions.¹⁰ They reported the calculated rate constant for HO₂ + C₃H₇O₂ reaction as 9.12 × 10⁻¹² cm³ per molecule per s. However, the detailed reaction mechanism and kinetic data of HO₂ + n-C₃H₇O₂ reaction are still unclear. To better understanding of this issue, a systematic theoretical investigation on the HO₂ + n-C₃H₇O₂ reaction is required. In this work, quantum chemistry calculations have been performed to explore the detailed reaction mechanism of HO₂ + n-C₃H₇O₂ reaction both on the singlet and triplet potential energy surfaces. Then the rate constant of the title reaction was calculated using the multiconformer transition state theory (MC-TST) which considered that the n-C₃H₇O₂ radical has multiple conformers.

2. Computational methods

The geometries of the reactants, intermediates, transitions states and products in the HO₂ + n-C₃H₇O₂ reaction were fully optimized by Density Functional Theory (DFT) method at the B3LYP/6-311G(d,p) level of theory.^16,17 Harmonic vibrational frequencies were calculated at the same level to confirm that all minima are real frequencies, and transition states have only a single imaginary frequency. Vibrational frequencies and coordinates of all stationary points in the title reaction have been summarized Tables S1 and S2,† respectively (see ESI†). In addition, the intrinsic reaction coordinate (IRC) calculations were also carried out to verify that the transition states structures can be connected to the corresponding reactants and products.^18–21 The zero-point energies (ZPEs) and the thermodynamic corrections at the temperature of 298.15 K and pressure of 1 atm were evaluated at the B3LYP/6-311G(d,p) level of theory and were incorporated in to the final energy barrier, enthalpy and Gibbs free energy. To get more reliable energy information, single point energy calculations were carried out at CCSD(T)/aug-cc-pVDZ level of theory.²² In CCSD (T) calculation, T₁ diagnostic is thought to assess the reliability of the methods with respect to a possible multireference feature of the wave functions. For open-shell systems, if the T₁ diagnostic value do not exceed 0.044, the wave functions of CCSD are considered to be reliable.^23–26 The T₁ diagnostic values of the stationary points are presented in Table S3 (ESI†). T1 diagnostic values of the stationary points except for G₁G₂-³TS1, G₁T₂-³TS1, are less than 0.044 from Table S3,† revealing that the CCSD wave function could be reliable. All the computations were performed with Gaussian 09 program package.²⁷ The CCSD(T) single point energy computations were carried out by Molpro package.^28,29

Since that the n-C₃H₇O₂ has multiple conformers, such complexity should be taken account into the rate constant formula, multiconformer transition state theory (MC-TST) method were carried out for rate constant calculations.^30–33 Within the framework of the conventional transition state theory (TST),^34–36 the MC-TST expression for a rate constant k at temperature T can be written as

Here κ is the Eckart tunneling correction³⁷ factor associated with the lowest energy transition state. k_B and h are Boltzmann's constant and Planck's constant, respectively. ΔE_i represents the difference in zero-point corrected energy between the transition state conformer i and the lowest energy transition state conformer, and Q_TS,i represents the total partition function of the transition state conformer i. ΔE_j denotes zero-point corrected energy of reactant conformer j relative to the lowest energy reactant conformer, and Q_R,j represents the partition function of reactant conformer j. E_TS,0 and E_R,0 represent the zero-point corrected energy of the lowest energy conformer of the transition state and reactant, respectively. The energies in the MC-TST expression were computed at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d,p) level of theory and the partition functions were obtained at the B3LYP/6-311G(d,p) level of theory.

3. Results and discussion

The scheme of the possible reaction routes for the HO₂ + n-C₃H₇O₂ reaction has been showed in Fig. 1. In this section, the reaction mechanism and kinetics of the HO₂ + n-C₃H₇O₂ reaction have been discussed. For simplicity, we first focus on the reaction mechanism of HO₂ and the most stable G₁G₂ conformer reaction in the following parts. The HO₂ + G₁T₂, T₁G₂ and T₁T₂ reactions are compared with the HO₂ + G₁G₂ reaction. The schematic energy diagram of the HO₂ + G₁G₂ reaction is depicted in Fig. 2, whereas the corresponding profiles of the schematic energy diagram are shown schematically in Fig. S2–S5† for the HO₂ + G₁T₂, T₁G₂ and T₁T₂ reactions (ESI†), respectively. The selected geometric structures of the five reactions are displayed in Fig. 3 and S6–S9,† respectively. In what follows, energies of the HO₂ + G₁G₂, G₁T₂, T₁G₂ and T₁T₂ reactions are shown in Tables 1 and S4–S7,† respectively. Besides, to study the relative importance of various products in the HO₂ + n-C₃H₇O₂, the rate constants of the most favorable channel for the five different reactions have been discussed. Finally, Arrhenius plot for the triplet channel of HO₂ + n-C₃H₇O₂ reaction is displayed in Fig. 4 and the calculated rate constants are fitted into Arrhenius three parameter equation.

Fig. 1 The scheme of possible reaction routes of HO₂ + n-C₃H₇O₂ reaction on both the singlet and triplet potential energy surfaces.

Fig. 2 Schematic energy diagram of HO₂ + G₁G₂ reaction computed at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d,p) level of theory on both the singlet and triplet potential energy surfaces. Energies are in units of kcal mol⁻¹.

Fig. 3 Selected geometric structures of the reactants, intermediates and transition states of HO₂ + G₁G₂ reaction computed at the B3LYP/6-311G(d,p) level of theory on both the singlet and triplet potential energy surfaces. Bond distances are given in angstroms.

Table 1 Zero point energies (ZPE), relative energies (ΔE_{298 K}), reaction enthalpies (ΔH_{298 K}) and Gibbs free energies (ΔG_{298 K}) of the stationary points involved in HO₂ + G₁G₂ reaction. Energies are computed at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d,p) level of theory. Energy values are given in kcal mol⁻¹

Compound	ZPE	ΔE298 K	ΔH298 K	ΔG298 K
G1G2 + HO2	71.62	0.00	0.00	0.00
G1G2-^3IM1	73.23	−6.78	−7.37	1.82
G1G2-^3TS1	70.85	−2.47	−3.06	7.59
G1G2-C3H7O2H + ^3O2	72.27	−35.88	−35.88	−34.48
G1G2-TS2	72.41	9.96	9.36	20.45
G1G2-C3H7O2H + ^1O2	72.25	−4.93	−4.93	−2.88
G1G2-IM2	74.18	−12.02	−12.61	−0.41
G1G2-TS3	71.22	8.76	8.17	21.28
G1G2-C3H7OH + O3	72.58	−14.26	−14.26	−13.41
G1G2-IM3	73.98	−10.77	−11.36	0.85
G1G2-TS4	69.91	3.58	2.99	15.51
G1G2-IM4	72.52	−34.70	−35.29	−24.64
G1G2-C2H5CHO + HO2 + OH	66.88	−26.53	−25.94	−36.40
G1G2-IM5	74.07	−10.94	−11.53	1.28
G1G2-TS5	68.74	6.10	5.51	15.13
G1G2-C2H5CHO + HO3H	71.73	−55.18	−55.18	−54.90

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Fig. 4 Arrhenius plot of calculated rate coefficients for G₁G₂-C₃H₇O₂H + ³O₂ formation in HO₂ + n-C₃H₇O₂ reaction within the temperature range of 238–398 K at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d,p) level of theory.

Throughout the discussions, the transition states and intermediates in each reaction are denoted by “TS’’ and “IM”, respectively, followed by a number. The optimized geometries involved in the five reactions are designated by the prefix G₁G₂, G₁T₂, T₁G₂ and T₁T₂, respectively, followed by the “TS’’ or “IM”.

3.1 Mechanism of the HO₂ + n-C₃H₇O₂ reaction

3.1.1 Reaction mechanism on triplet PES. A schematic presentation of triplet potential energy surfaces for the reaction between HO₂ and individual n-C₃H₇O₂ conformer have been computed at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d,p) level of theory. For example, in the case of the HO₂ and G₁G₂ conformer reaction, schematic energy diagram of the reaction is shown in Fig. 2 and the geometric structures of reactants, intermediates, transition states and products are depicted in Fig. 3. For the triplet potential energy surface, our calculations show one possible reaction pathway proceeding through a pre-reaction complex G₁G₂-³IM1 and a transition state G₁G₂-³TS1 to produce G₁G₂-C₃H₇O₂H and triplet O₂. This pathway is a hydrogen abstraction process by the H atom on the HO₂ radical migrates to the terminal oxygen of G₁G₂. In G₁G₂-³IM1, the length of hydrogen bond between the terminal oxygen atom of G₁G₂ and the hydrogen atom of HO₂ is 1.801 Å, which is 0.408 Å longer than that in the G₁G₂-³TS1. It is stabilized by the hydrogen bond interaction with a binding energy of −7.35 kcal mol⁻¹ relative to the HO₂ + G₁G₂ reactants. From the equilibrium structure of G₁G₂-³TS1 shown in Fig. 3, the breaking H–O and the forming O–H bonds are 1.064 and 1.393 Å, respectively. The breaking H–O bond is only slightly longer by 0.089 Å compared to the equilibrium of H–O bond in HO₂ radical. The O⋯H⋯O bond angle is nearly linear with a value of approximately 171.93°. The barrier of G₁G₂-³TS1 is −2.48 kcal mol⁻¹. G₁G₂-³TS1 is an early barrier compared to other different channels in the reaction of HO₂ + G₁G₂.

For the triplet hydrogen abstraction process, the HO₂ + G₁T₂, T₁G₂ and T₁T₂ four reactions are also identified to be kinetically favorable pathways via the same reaction mechanism as that of HO₂ + G₁G₂ reaction (see Fig. S2–S5†). The selected geometric structures for the reactants, intermediates, transition states and products of the four reactions were shown in Fig. S6–S9,† respectively. As shown in Fig. S2–S5,† all the four reactions take place on the triplet surfaces from the reactants via intermediates (G₁T₂-³IM1, T₁G₂-³IM1 and T₁T₂-³IM1) and transition states (G₁T₂-³TS1, T₁G₂-³TS1 and T₁T₂-³TS1) to produce the C₃H₇O₂H and triplet O₂. The four intermediates are hydrogen bond complexes. The binding energies of four intermediates are −6.83 kcal mol⁻¹ (G₁T₂-³IM1), −6.73 kcal mol⁻¹ −6.81 kcal mol⁻¹ (T₁G₂-³IM1) and −6.79 kcal mol⁻¹ (T₁T₂-³IM1) kcal mol⁻¹, respectively. In the structure of G₁G₂-³IM1, the binding energy is −7.35 kcal mol⁻¹, which is close to that in the four intermediates above. The four corresponding transition states involve nearly linear O⋯H⋯O bond angles and are early barriers. The average distances of the breaking H–O bonds and forming O–H bonds are 1.041 and 1.466 Å, respectively. The barrier heights of the G₁T₂-³TS1, T₁G₂-³TS1 and T₁T₂-³TS1 are close to each other (−3.26, −2.15, −3.85 vs. −3.90 kcal mol⁻¹). The average barrier height of the four transition states is −3.29 kcal mol⁻¹, which is only 0.81 kcal mol⁻¹ lower than G₁G₂-³TS1. Evidently, G₁G₂-³TS1, G₁T₂-³TS1, T₁G₂-³TS1 and T₁T₂-³TS1 are all early barriers. The reactions of HO₂ with the five different conformers (G₁G₂, G₁T₂, T₁G₂ and T₁T₂) have same reaction mechanism and have simpler triplet potential energy surfaces via hydrogen abstraction routes to form C₃H₇O₂H + ³O₂ molecule.

3.1.2 Reaction mechanism on singlet PES. It can be seen in Fig. 2, the HO₂ + G₁G₂ reaction has a more complicated singlet potential energy surface. In singlet reaction, there are four different reaction pathways in where products are G₁G₂-C₃H₇O₂H + ¹O₂, G₁G₂-C₃H₇OH + O₃, G₁G₂-C₂H₅CHO + HO₂ + OH and G₁G₂-C₂H₅CHO + HO₃H. The detailed reaction mechanisms of the HO₂ + G₁G₂ reaction are discussed in the following parts.

The formation of G₁G₂-C₃H₇O₂H + ¹O₂ proceeds directly through one transition state G₁G₂-TS2 by abstracting the hydrogen atom of HO₂ to the terminal O atom of G₁G₂, which has been shown in Fig. 2. The barrier height of G₁G₂-TS2 is calculated to be 9.81 kcal mol⁻¹ higher than that of the initial HO₂ + G₁G₂ reactants. This product channel is a hydrogen abstraction process, which is different from the hydrogen abstraction on the triplet surface. In summary, the singlet hydrogen abstraction process is distinct from the triplet one in three respects. Firstly, hydrogen abstraction process on the singlet potential energy surface may undergo directly through the transition state G₁G₂-TS2 producing G₁G₂-C₃H₇O₂H and singlet O₂ molecule, while the triplet one proceeds the intermediate G₁G₂-³IM1 prior to the transition state G₁G₂-³TS1 producing G₁G₂-C₃H₇O₂H and triplet O₂ molecule. Secondly, the O⋯H⋯O bond angle in G₁G₂-TS2 is much more bent (i.e., 107.77° in G₁G₂-TS2 vs. 171.93° in G₁G₂-³TS1). Thirdly, our calculation shows the barrier for G₁G₂-TS2 is much higher than that for G₁G₂-³TS1 by about 12.29 kcal mol⁻¹. The G₁G₂-C₃H₇O₂H + ¹O₂ formation channel is of minor importance due to the high barrier height.

On the singlet potential energy surface, except for direct hydrogen abstraction mechanism described above, addition–elimination mechanism is located as well. The remaining three reaction pathways precede via an addition–elimination mechanism. As shown in Fig. 2, HO₂ + G₁G₂ → G₁G₂-IM2 → G₁G₂-TS3 → G₁G₂-C₃H₇OH + O₃, this channel involves a rather high barrier and is exothermic. The structures of G₁G₂-IM2 and G₁G₂-TS3 are shown in Fig. 3. The lengths of three O–O bonds of G₁G₂-IM2 are about 1.4 Å. G₁G₂-IM2 is −11.92 kcal mol⁻¹ with respect to the initial HO₂ + G₁G₂ reactants. G₁G₂-TS3 is a five-membered ring structure. With respect to the HO₂ + G₁G₂ reactants, the barrier of G₁G₂-TS3 is as high as 9.27 kcal mol⁻¹. Compared with other pathways, the formations of G₁G₂-C₃H₇OH + O₃ might be negligible because of the high barrier height.

The formation of G₁G₂-TS4 from the reactants HO₂ + G₁G₂ radicals could also occur via G₁G₂-IM3. Similar to G₁G₂-IM2, G₁G₂-IM3 also has three OO bonds and the bond lengths are about 1.4 Å. The computed binding energy for G₁G₂-IM3 are −10.67 kcal mol⁻¹. In G₁G₂-TS4, the hydrogen atom migrates from the C to O to form HO₂, while the two O–O bonds cleavage to form post-reaction complex G₁G₂-IM4. The barrier for G₁G₂-TS4 is relatively higher than that for G₁G₂-³TS1 by about 6.18 kcal mol⁻¹. After G₁G₂-TS4, this product channel proceeds through G₁G₂-IM4 complex to form G₁G₂-C₂H₅CHO + HO₂ + OH products. It is found that the calculated relative energy of the G₁G₂-IM4 to the reactants HO₂ + G₁G₂ is −35.29 kcal mol⁻¹, which is lower than the products. It's worth noting that the reaction pathway of G₁G₂-C₂H₅CHO + HO₂ + OH formation could be viewed as a HO₂-mediated dissociation process of G₁G₂ because the HO₂ radical is also reproduced in the final products.

The last channel examined on the singlet potential energy surface is the formation of G₁G₂-C₂H₅CHO and HO₃H. As shown in Fig. 2, HO₂ + G₁G₂→ G₁G₂-IM5 → G₁G₂-TS5 →G₁G₂-C₂H₅CHO + HO₃H, this pathway involves a high barrier and is extremely exothermic. Analogous to the energies of G₁G₂-IM2 and G₁G₂-IM3, the binding energy for G₁G₂-IM5 is −10.70 kcal mol⁻¹. G₁G₂-IM5 also has three OO bonds, all of which are about 1.4 Å in length. The barrier height for G₁G₂-TS5 is about 5.62 kcal mol⁻¹ with respect to the reactants HO₂ + G₁G₂. Clearly, the formation of G₁G₂-C₂H₅CHO and HO₃H via G₁G₂-TS5 involves significant barrier and is the most exothermic pathway on the both triplet and singlet potential energy surfaces.

From the Fig. S2–S5 in the ESI,† we can see that the singlet potential energy surfaces for the HO₂ + G₁T₂, T₁G₂ and T₁T₂ four reactions, as well as the HO₂ + G₁G₂ reaction proceed on the similar reaction mechanism which has been discussed above in detail in the present work. The formations of C₃H₇O₂H + ¹O₂, C₃H₇OH + O₃ and C₂H₅CHO + HO₂ + OH in HO₂ + G₁T₂, T₁G₂ and T₁T₂ four reactions have similar energetic data as that of the HO₂ + G₁G₂ reaction. For example, in the C₃H₇O₂H + ¹O₂ formation pathway, the barrier heights of the four transition states G₁T₂-TS2, T₁G₂-TS2 and T₁T₂-TS2 are generally consistent with each other (9.82, 9.51, 9.53 vs. 9.52 kcal mol⁻¹). The calculated barrier height for G₁G₂-TS2 is about 9.81 kcal mol⁻¹. By comparison, we can conclude that the energy barriers of the above three channels in the five reactions of HO₂ + G₁G₂, G₁T₂, T₁G₂ and T₁T₂ have little difference. However, in the C₂H₅CHO and HO₃H formation pathways, the average barrier height for the four transition states (G₁T₂-TS5, T₁G₂-TS5 and T₁T₂-TS5) is 14.80 kcal mol⁻¹, which is 9.18 kcal mol⁻¹ higher than G₁G₂-TS5. As a result, for HO₂ + G₁G₂ reaction, the C₃H₇O₂H + ¹O₂ formation pathway is the highest barrier height, while C₂H₅CHO and HO₃H formation pathways are the highest barrier heights in the other four reactions. Compared with the energetically favorable triplet reactions, all the singlet reactions involve relatively high barriers.

In summary, the reactions of HO₂ with the five different conformers (G₁G₂, G₁T₂, T₁G₂ and T₁T₂) have simpler triplet potential energy surfaces via hydrogen abstraction routes to form C₃H₇O₂H + ³O₂ molecule and more complicated singlet surfaces via direct hydrogen abstraction and addition–elimination mechanisms form various products. From the mechanism discussed above, we can conclude that the pathway of formation of C₃H₇O₂H + ³O₂ is the most important reaction channel and other channels can be negligible in the n-C₃H₇O₂ + HO₂ reaction.

3.2 Kinetics of the HO₂ + n-C₃H₇O₂reaction

Based on the singlet and triplet potential energy surfaces, the rate constants of different reaction pathways for the individual conformer have been evaluated using the conventional transition-state theory (TST) over the temperature range of 238–398 K. For example, in the case of the lowest energy conformer HO₂ + G₁G₂ reaction, the calculated rate constants for individual channel are listed in Table 2. As can be seen from Table 2, results show that the rate constants for the triplet hydrogen abstraction reaction contributes significantly to the overall rate constants. The rate constant of triplet channel is at least four orders of magnitude higher than that of singlet ones over the temperature range. This indicates that the triplet hydrogen abstraction channel for formation of G₁G₂-C₃H₇O₂H + ³O₂ products is the major channel, while the singlet channels can be negligible. The reactions of HO₂ with the other conformers (G₁T₂, T₁G₂ and T₁T₂) have similar reaction mechanism and kinetic behavior as the HO₂ + G₁G₂ reaction. Thus, only the rate constants of each individual triplet hydrogen abstraction channel are considered in the total rate constants calculations of the HO₂ + n-C₃H₇O₂ reaction. The triplet channels for each n-C₃H₇O₂ conformer are displayed in Table 3. It is clear that rate constants for each triplet hydrogen abstraction channel give the total rate constants for the HO₂ + n-C₃H₇O₂ reaction. Considering that n-C₃H₇O₂ has multiple conformers, the total rate constants for HO₂ with n-C₃H₇O₂ reaction are obtained by MC-TST method. Overview of triplet channels for the reactions of HO₂ with the five conformers (G₁G₂, G₁T₂, T₁G₂ and T₁T₂) showing the individual conformer of the reactants, intermediates, transition states, and products are shown in the Fig. 5. The MC-TST rate constant can be regarded as a sum of the individual TST reaction rate constants which weighted by the Boltzmann population of the corresponding n-C₃H₇O₂ conformers. The overall calculated rate constant of the HO₂ + n-C₃H₇O₂ reaction over the temperature range of 238–398 K are listed in Table 4. Moreover, the calculated rate constants are fitted into Arrhenius three parameter equation as follows:

Table 2 Theoretical rate coefficients (cm³ per molecule per s) for HO₂ + G₁G₂ reaction within the temperature range of 238–398 K at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d,p) level of theory. ³O₂, ¹O₂, O₃, OH and HO₃H denote the rate constant of product channel G₁G₂-C₃H₇O₂H + ³O₂, G₁G₂-C₃H₇O₂H + ¹O₂, G₁G₂-C₃H₇OH + O₃, G₁G₂-C₂H₅CHO + HO₂ + OH and G₁G₂-C₂H₅CHO + HO₃H for the reaction, respectively

T (K)	^3O2	^1O2	O3	OH	HO3H
238	3.44 × 10^−12	4.70 × 10^−24	9.71 × 10^−22	6.18 × 10^−19	2.57 × 10^−19
258	2.22 × 10^−12	2.43 × 10^−23	8.96 × 10^−22	9.85 × 10^−19	6.70 × 10^−19
278	1.56 × 10^−12	1.01 × 10^−22	1.08 × 10^−21	1.52 × 10^−18	1.56 × 10^−18
298	1.16 × 10^−12	3.49 × 10^−22	1.52 × 10^−21	2.27 × 10^−18	3.30 × 10^−18
318	9.13 × 10^−13	1.05 × 10^−21	2.35 × 10^−21	3.28 × 10^−18	6.47 × 10^−18
338	7.45 × 10^−13	2.79 × 10^−21	3.78 × 10^−21	4.62 × 10^−18	1.19 × 10^−17
358	6.27 × 10^−13	6.73 × 10^−21	6.14 × 10^−21	6.35 × 10^−18	2.07 × 10^−17
378	5.42 × 10^−13	1.49 × 10^−20	9.91 × 10^−21	8.53 × 10^−18	3.43 × 10^−17
398	4.80 × 10^−13	3.06 × 10^−20	1.57 × 10^−20	1.12 × 10^−17	5.47 × 10^−17

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Table 3 Theoretical rate coefficients (cm³ per molecule per s) of the triplet channel for the five reactions within the temperature range of 238–398 K at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d,p) level of theory

T (K)	HO2 + G1G2	HO2 + G1T2		HO2 + T1G2	HO2 + T1T2
238	3.44 × 10^−12	1.05 × 10^−11	1.12 × 10^−12	2.83 × 10^−11	4.61 × 10^−11
258	2.22 × 10^−12	6.30 × 10^−12	8.27 × 10^−13	1.57 × 10^−11	2.53 × 10^−11
278	1.56 × 10^−12	4.11 × 10^−12	6.45 × 10^−13	9.57 × 10^−12	1.53 × 10^−11
298	1.16 × 10^−12	2.87 × 10^−12	5.27 × 10^−13	6.31 × 10^−12	1.00 × 10^−11
318	9.13 × 10^−13	2.12 × 10^−12	4.45 × 10^−13	4.42 × 10^−12	7.00 × 10^−12
338	7.44 × 10^−13	1.64 × 10^−12	3.87 × 10^−13	3.26 × 10^−12	5.14 × 10^−12
358	6.27 × 10^−13	1.31 × 10^−12	3.44 × 10^−13	2.50 × 10^−12	3.93 × 10^−12
378	5.42 × 10^−13	1.08 × 10^−12	3.12 × 10^−13	1.99 × 10^−12	3.11 × 10^−12
398	4.80 × 10^−13	9.19 × 10^−13	2.88 × 10^−13	1.63 × 10^−12	2.54 × 10^−12

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Fig. 5 In the multiconformer system, diagram showing triplet channels for the reactions of HO₂ radical with the five conformers (G₁G₂, G₁T₂, T₁G₂ and T₁T₂). All the energies (Δ(E + ZPE)) are relative to the energies of HO₂ + G₁G₂.

Table 4 The overall rate constants (cm³ per molecule per s) within the temperature range 238–398 K for the HO₂ + n-C₃H₇O₂ reaction at CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d,p) level of theory

T (K)	ktotal
238	2.30 × 10^−11
258	1.38 × 10^−11
278	8.98 × 10^−12
298	6.27 × 10^−12
318	4.64 × 10^−12
338	3.58 × 10^−12
358	2.88 × 10^−12
378	2.38 × 10^−12
398	2.02 × 10^−12

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The Arrhenius plot for the reaction of HO₂ and n-C₃H₇O₂ is shown in Fig. 4. From the Arrhenius plot, it can be seen clearly that the negative temperature dependence for the title reaction in lower temperature regime (e.g. T < 400 K). This can be attributed to the formation of the pre-reaction complexes with negative barriers in the triplet channels of the title reaction. For example, in the triplet channel of HO₂ + G₁G₂ reaction, the values of the rate coefficients of reverse process (G₁G₂-³IM1 to HO₂ and G₁G₂) increases with the rising temperature, which reduces the value of the equilibrium constant. It can be said that when the reaction reaches equilibrium, the macroscopic rate coefficient decreases. This downward trend can be seen in the other four reactions of HO₂ with the different conformers (G₁T₂, T₁G₂ and T₁T₂). Thus, the overall rate coefficient of the title reaction shows negative temperature dependence. The calculated rate constants for HO₂ + n-C₃H₇O₂ reaction is predicted to be 6.27 × 10⁻¹² cm³ per molecule per s at 298 K. The kinetic results shown good agreement with the value 9.12 × 10⁻¹² cm³ per molecule per s reported by Hou and his co-workers using structure–activity relationships (SAR) analysis.¹⁰ It shows that our CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(d,p) calculated rate constants are in good agreement with the available recent theoretical result in the related reference.

4. Summary and conclusions

In present study, the detailed mechanism and kinetics of the reaction of HO₂ and n-C₃H₇O₂ (including five conformers G₁G₂, G₁T₂, T₁G₂ and T₁T₂) have been investigated by quantum chemistry and MC-TST method. The mechanism for the reaction between HO₂ and n-C₃H₇O₂ radical on both singlet and triplet potential energy surfaces mainly includes hydrogen abstraction and addition–elimination mechanisms. The energy barriers show the main products are C₃H₇O₂H and ³O₂ on the triplet potential energy surface via the hydrogen abstraction mechanism. In addition, the rate constants of HO₂ + n-C₃H₇O₂ reaction were further studied over the temperature range of 238–398 K which show a negative temperature dependent. The kinetic calculations indicate that the formation of C₃H₇O₂H + ³O₂ channel is most kinetically favorable since that the rate constant of which is at least four orders of magnitude larger than that of the other channels at the studied temperature range. The calculated rate constant for HO₂ + n-C₃H₇O₂ reaction is predicted to be 6.27 × 10⁻¹² cm³ per molecule per s at 298 K, which match good with the results from SAR analysis.¹⁰ The theoretical results can be helpful to deeply understand the chemical behaviors of HO₂ + n-C₃H₇O₂ reaction.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We would like to thank financial support from the National Natural Science Foundation of China (91544228, 41605102, 21876177, and 41575125), the National Key Research and Development Program of China (2016YFC0202205, 2017YFC0209401), the Youth Innovation Promotion Association CAS (2019439), and the Science and Technology Foundation of Guizhou Province, China ([2019]5648 and [2018]1080).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9ra07503h

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