Rapid Hydrogen Shift Reactions in Acyl Peroxy Radicals - The Journal

Feb 1, 2017 - The HO2 concentration is here kept constant at 55 ppt in our calculation. ... reaction rate constant is significantly faster than the bi...
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Rapid Hydrogen Shift Reactions in Acyl Peroxy Radicals Hasse C. Knap and Solvejg Jørgensen* Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen O, Denmark S Supporting Information *

ABSTRACT: We have used quantum mechanical chemical calculations (CCSD(T)F12a/cc-pVDZ-F12//M06-2X/aug-cc-pVTZ) to investigate the hydrogen shift (Hshift) reactions in acyl peroxy and hydroperoxy acyl peroxy radicals. We have focused on the H-shift reactions from a hydroperoxy group (OOH) (1,X-OOH H-shift with X = 6, 7, 8, or 9) in the hydroperoxy acyl peroxy radicals, this H-shift is a reversible reaction and it scrambles between two peroxides, hydroperoxy acyl peroxy and peroxy peroxoic acid radicals. The forward reaction rate constants of the 1,X-OOH H-shift reactions are estimated to be above 103 s−1 with transition state theory corrected with Eckart quantum tunnelling correction. The ratio between the forward and reverse reaction rate constant of the 1,X-OOH H-shift reactions is around ∼105. Therefore, the equilibrium is pushed toward the production of peroxy peroxoic acid radicals. These very fast 1,X-OOH H-shift reactions are much faster than the reactions with NO and HO2 under most atmospheric conditions and must be included in the atmospheric models when hydroperoxy acyl peroxy radicals are oxidized. Finally, we have observed that H-shift reactions in a pentane acyl peroxy radical (C5-AOO) is fast (>1 s−1); this can have a significant influence on the possible formation of large acyl peroxy nitrate molecules.

1. INTRODUCTION Acyl peroxy (R-CH2−C(O)OO) radicals are important for the understanding of the atmospheric NOx (NOx = NO, NO2) cycle, because the acyl peroxy radical can react with NO2 and produce the long-lived acyl peroxy nitrate (R-CH2−C(O)OONO2, APN).1−3 The APN molecule is produced through a thermal equilibrium between the acyl peroxy radical and NO2 with the presence of third body M for example N2, O2, given as

Scheme 1. Acyl Peroxy (AP) Radicals Formed Directly through Photolysis/Oxidation and Hydroperoxy Acyl Peroxy Radicals Formed Indirectly through Autoxidation Initiated by OH Oxidation Leading to Hydroperoxy Acyl Peroxy Radical Denoted R-2OOH_AOOa

R‐CH 2C(O)OO + NO2 + M ↔ R‐CH 2C(O)OONO2 + M

APN is known to be a reservoir species in the troposphere, where it contributes to the long-range transport of NOx to unpolluted regions.4 The simplest APN is the acetyl peroxy nitrate (CH3C(O)OONO2, or PAN), which is the most abundant APN species in the troposphere. PAN accounts at a single location in a remote forest region of about 90% of the total APN yield.5 PAN is produced by direct oxidation or photolysis of acetaldehyde (CH3CHO) and methylglyoxal (CH3C(O)CHO). The acyl peroxy radicals are typically produced from nonmethane volatile organic compounds (NMVOCs) containing an aldehyde as shown in Scheme 1. For the larger aldehydes, the reaction with the OH radical is the most important.6 NMVOCs (including aldehydes) are emitted in high amounts to the atmosphere by both anthropogenic sources (∼100 Tg per year)7 and natural sources (∼1000 Tg per year).8 Aldehydes are a key component in the atmospheric degradation of NMVOCs.9 In the oxidation of an aldehyde the acyl peroxy radical can be formed directly or indirectly. In the direct route the hydrogen atom in the −CHO group is removed either by photolysis or by an OH radical abstraction © 2017 American Chemical Society

a

R-2OOH_AOO is produced from the RO2 through an aldehyde Hshift reaction and a subsequent O2 addition reaction.

leading to the formation of an alkyl radical. The acyl radical reacts with molecular oxygen O2 leading to an acyl peroxy radical.9 Received: December 20, 2016 Revised: February 1, 2017 Published: February 1, 2017 1470

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lowest B3LYP/6-31+G(d,p) energy are refined by a M062X optimization. All M062X open-shell radicals are checked for spin contamination, before and after spin annihilation. None of the open-shell M062X calculations have spin contamination; all the radicals have ⟨S2⟩ below 0.77 before spin annihilation. Finally, a ROHF-UCCSD(T)-F12a/cc-pVDZ-F1233−36 (F12) single-point energy is calculated on the conformer with the lowest zero-point-corrected M062X energy. All F12 energies are ZPVE corrected with the values from the M062X calculations. The Molpro201237,38 program is used for all the F12 calculations. The geminal Slater coefficient is set to 0.934 and the triplet contribution in the F12 method is scaled as recommended by Marchetti and Werner.39 In all single-point F12 calculations the T1-diagnostic value is checked. The T1diagnostic value needs to be below 0.045 to be an acceptable represent for the single reference F12 wave function of an open-shell species.40 A high T1-diagnostic value (T1 ∼ 0.05) is observed for the transition state for the 1,9-OOH H-shift reaction in the 5-peroxypentaneperoxoic acid radical. All other F12 calculations have T1-diagnostic values below 0.04. We use the transition state theory41 (TST) and the multiconformer transition state theory (MC-TST) to calculate the H-shift reaction rate constants. The MC-TST calculated reaction rate constants are given in the Supporting Information.

The hydroperoxy acyl peroxy radical (an acyl peroxy radical with an OOH substituent) can also be formed indirectly through an autoxidation reaction mechanism.10−12 The autoxidation is initiated by the OH radical, which abstracts a hydrogen atom on the R-chain followed by O2 addition leading to formation of a peroxy radical (RO2). In the atmosphere the RO2 radical can either undergo hydrogen shift reactions (Hshift) or react with NOx, HO2, or another RO2. In the H-shift reaction a hydrogen atom is moved internally to the peroxy group (OO) and produces an alkyl radical (usually denoted QOOH). The H-shift reaction in Scheme 1 is from the aldehyde group. Aldehyde H-shift reactions are generally found to be fast with a reaction rate constant of ∼1 s−1.13,14 The QOOH radical can either decompose into smaller molecules (an aldehyde with one less carbon, CO and OH) or react with O2 to produce the hydroperoxy acyl peroxy radical denoted as R-XOOH_AOO, with X denoting the position of the carbon atom with the hydroperoxy group. In Scheme 1, R2OOH_AOO reacts with NO, NO2, RO2, or HO2 or undergoes H-shift reactions. H-shift reactions in acyl peroxy radicals have only been investigated in a few cases.14,15 The Hshift reaction from the hydroperoxy group to the acyl peroxy radical (1,X-OOH) has to our knowledge not been investigated before. In the ozonolysis of the larger NMVOCs, like α-pinene, cyclohexene, 1-methylcyclohexene, and 4-methylcyclohexene, the autoxidation produces hydroperoxy acyl peroxy radicals.14,16−18 Furthermore, the autoxidation mechanism can introduce a large amount of hydroperoxy (OOH) groups into the secondary oxidation products of NMVOC.14,18−21 These secondary oxidation products can most likely explain the gasphase conversion of NMVOCs into secondary organic aerosols (SOA).14,19 Recently, 1,X-OOH H-shift reactions in hydroperoxy substituted peroxy radical derived from the oxidation of 1-pentene (C5-XOOH_OO) contribute significantly to the complexity of the secondary NMVOC oxidation products by scrambling the peroxy radical pool.22 A similar peroxy radical scrambling might be possible in the hydroperoxy acyl peroxy radical (R-2OOH_AOO).

k TST = κEckart

⎛ −E ⎞ k bT QTS exp⎜ F ⎟ h QR ⎝ k bT ⎠

(1)

Here kb is the Boltzmann constant, h is the Planck constant, κEckart is the quantum42 tunnelling correction, and EF is the F12 ZPVE-corrected energy difference between the conformer of the transition state and the reactant with the lowest energy. QTS and QR are the partition functions of the transition state and reactant, respectively, calculated with the M062X method. The harmonic oscillator and rigid-rotor approximation are used to calculate the partition functions. The Eckart quantum tunnelling correction is estimated from an asymmetric potential, where the forward and reverse barrier heights define the potential heights and the imaginary frequency at the transition state defines the potential width. For H-shift reactions the Eckart quantum tunnelling correction has been shown to overestimate the tunnelling correction by a factor of 1.5 at ambient temperatures.43−45 The hindered rotational effects in H-shift reactions have been shown to only decrease the forward and reverse H-shift reaction rate constants by a factor of 6 compared to noncorrected H-shift reaction rate constants.14 We have not included hindered rotational effects in our investigation.

2. COMPUTATIONAL DETAILS We use the following computational strategy to find the lowest energy structure for the H-shift reactions. First, we locate the transition state (TS) structure with the B3LYP/6-31+G(d,p)23−25 method. Subsequently, the B3LYP/6-31+G(d,p) method is used to calculate an intrinsic reaction coordinate (IRC),26,27 which enables us to locate the reactant and product structures. All IRC calculations are calculated with 50 points in each direction with the default step-size. The B3LYP/631+G(d,p) optimized structures are hereafter optimized with the M06-2X/aug-cc-pVTZ28,29 (M062X) method. The M062X/aug-cc-pVTZ method has been shown to calculate good barrier heights for H-shift reactions.30 The M062X optimized structures are used to generate a set of conformers with the SYBYL force field method in Spartan’10 program.31 We calculate a single-point energy on all of the generated conformers with the B3LYP/6-31+G(d) method. The conformers which are energetically close (10 kcal/mol) to the energy of the conformer with the lowest B3LYP/6-31+G(d) energy are optimized and frequencies are calculated with the B3LYP/6-31+G(d,p) method using the Gaussian09 program.32 The conformers with zero-point vibrational energy (ZPVE)corrected energy within 2 kcal/mol of the conformer with the

3. RESULTS AND DISCUSSION In this article we focus on the H-shift reactions in the acyl peroxy radicals produced from either the direct or the indirect reaction mechanism (Scheme 1). First, the hydrogen shift reactions from a hydroperoxy group to the acyl peroxy radical (1,X-OOH) are investigated. The first section investigate the 1,6-OOH H-shift reaction when the carbon backbone is increased from R = H to R = CH3CH2CH2 in R-2OOH_AOO. In the second section, the 1,X-OOH H-shift reactions in four different OOH substituted acyl peroxy radicals are investigated (C5-XOOH_AOO). Here, the H-shift ring size is increased from a 1,6-OOH to a 1,9-OOH H-shift reaction. In section 3.3, the reaction pathways for four C5-XOOH_AOO ↔ C5XOO_AOOH cycles are investigated, with X = 2, 3, 4, or 5. All 1471

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the transition state in the 1,6-OOH H-shift in a hydroperoxy substituted peroxy radical derived from the oxidation of 1pentene.22 The short distance between the two OO groups results in a narrow potential energy surface around the transition state for the 1,6-OOH H-shift reaction leading to high imaginary frequency. 3.2. 1,X-OOH H-Shift Reaction in Hydroperoxy Acyl Peroxy Radicals. In this section we consider the 1,X-OOH Hshift in hydroperoxy acyl peroxy radical denoted C5XOOH_AOO and the possible H-shift reactions in 1peroxypentane (C5-OO) and pentane acyl peroxy radical (C5-AOO). First, the 1,8-OOH H-shift in 4-hydroperoxy acyl peroxy radical, C5-4OOH_AOO is shown in Scheme 3. The carbon atom with the acyl peroxy group is labeled as 1, and the carbon atom at the α-position to the acyl peroxy group is labeled as 2 etc. We have substituted an OOH group on the carbon atoms labeled 2, 3, 4, or 5. The symbol X in C5-XOOH_AOO denotes the position of the OOH group. The F12 calculated TST forward and reverse 1,X-OOH Hshift reaction rate constants in the four C5-XOOH_AOO are shown in Table 2. The forward 1,X-OOH H-shift reactions in the four C5-XOOH_AOO are rapid with reaction rate constants of around 105−106 s−1. The reaction rate constants of the reverse 1,X-OOH H-shift reaction are in the range from 10−1 to 10−3 s−1. The forward 1,X-OOH H-shift reaction rate constants are more than a factor of 106 faster than the reverse 1,X-OOH H-shift reaction rate constants. Therefore, C5XOOH_AOO is rapidly converted to C5-XOO_AOOH, thus the C5-XOOH_AOO ↔ C5-XOO_AOOH cycles are significantly pushed toward the production of C5XOO_AOOH. This implies that the 1,X-OOH H-shift reactions need to be investigated to correctly determine the autoxidation of hydroperoxy acyl peroxy radicals. The reverse 1,6-OOH H-shift reaction is almost 102 times faster than the other three reverse 1,X-OOH H-shift reactions. This is mainly due to a higher Eckart quantum tunnelling correction arising from a higher imaginary frequency and a higher forward barrier height for the 1,6-OOH H-shift reaction compared to the three other 1,X-OOH H-shift reactions. The forward barrier height of the 1,6-OOH H-shift reaction is about 4 kcal/mol higher than the forward 1,7-OOH, 1,8-OOH and 1,9-OOH H-shift barrier heights. All 1,X-OOH H-shift reactions are exothermic. The aldehyde group (−CO) on the same carbon as the OO group leads to a significant change in both the forward and reverse rate constants compared to the hydroperoxy-substituted peroxy radical derived from the oxidation of 1-pentene (denoted C5-XOOH_OO) where the OO group is sitting on a secondary carbon.22 The forward 1,X-OOH H-shift reactions in C5-XOOH_AOO are faster than the forward 1,X-OOH Hshift reaction in C5-XOOH_OO whereas the opposite trend is observed for reaction rate constant of the reverse 1,X-OOH Hshift reaction. The F12 calculated MC-TST 1,X-OOH H-shift reaction rate constants are within a factor of 6 of the TST calculated reaction rate constant (Table S2 in the Supporting Information). We have also calculated the H-shift reactions in the 1peroxypentane (C5-OO) and pentane acyl peroxy radical (C5AOO). The two radicals have the peroxy group located on the terminal carbon atom and both can undergo 1,4-CH, 1,5-CH, 1,6-CH, and 1,7-CH H-shift reactions. The F12 calculated TST forward and reverse H-shift reaction rate constants are shown

H-shift reactions in C5-XOOH_AOO and C5-XOO_AOOH are compared with the bimolecular reactions with NO and HO2 to assess the atmospheric impact when the new rapid 1,X-OOH H-shift reaction is included in the autoxidation. Finally, the 1,XOOH reactions are investigated in the autoxidation initialized by the ozonolysis of cyclohexene. 3.1. 1,6-OOH H-Shift in Hydroperoxy Acyl Peroxy Radicals. In this section, we will focus on the forward and reverse 1,6-OOH H-shift reaction in the hydroperoxy acyl peroxy radicals, R-2OOH_AOO. In the 1,6-OOH H-shift reaction, the hydrogen atom is shifted from the hydroperoxy (−OOH) group to an acyl peroxy radical (−C(O)OO) as shown in Scheme 2. We consider four different R-groups: H, CH3, CH3CH2, and CH3CH2CH2. Scheme 2. 1,6-OOH H-Shift Reaction in Hydroperoxy Acyl Peroxy Radical R-2OOH_AOO Leading to 2-Peroxy Peroxoic Acid Radicals R-2OO_AOOH, Where R = H, CH3, CH3CH2, or CH3CH2CH2

We have only performed a conformer search on the reactant, product, and transition state for the 1,6-OOH H-shift reaction in CH3CH2CH2-2OOH_AOO. The conformers with the lowest energy of CH3CH2CH2-2OOH_AOO, CH3CH2CH22OO_AOOH, and the transition state have been used to generate the species involved in the 1,6-OOH H-shift reaction in H-2OOH_AOO, CH3-2OOH_AOO, and CH3CH2-2OOH_AOO. The forward and reverse F12 calculated 1,6-OOH H-shift TST reaction rate constants, Eckart quantum tunnelling correction, imaginary frequencies, and the barrier heights for the four R-2OOH_AOO radicals are shown in Table 1. In all four R-2OOH_AOO radicals, the forward 1,6-OOH H-shift reaction rate constants are calculated to be around 103−105 s−1 whereas the reverse 1,6-OOH H-shift reaction rate constants are approximately 10−1 s−1. The forward 1,6-OOH H-shift reaction rate constants are more than a factor of 105 (kF/kR) faster than the reverse H-shift reaction rate constant; hence, R2OOH_AOO will rapidly be converted to R-2OO_AOOH. If the OOH group is located on a primary carbon (R = H), then the forward H-shift reaction rate constant is about a factor of 10 lower compared to the ones where the OOH is located on the secondary carbon atom (R = CH3, CH2CH3, or CH2CH2CH3). The forward 1,6-OOH barrier height is 2 kcal/ mol higher when the OOH group is located on a primary carbon (R = H) compared to a secondary carbon (R = CH3, CH3CH2, or CH3CH2CH2). The reverse H-shift barrier heights are approximately 24 kcal/mol for all the 1,6-OOH H-shift reactions in R-2OOH_AOO. All the 1,6-OOH H-shift reactions have a high Eckart quantum tunnelling correction (around 104). The high Eckart quantum tunnelling corrections are due to a high imaginary frequency of ∼2600i cm−1 in the transition state. The distance between the two OO groups (O···H···O) in the 1,6-OOH transition state is about 2.3 Å, which is similar to the distance in 1472

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Table 1. Parameters for the 1,6-OOH H-Shift Reactions in the 2-Hydroperoxy Acyl Peroxy Radical (R-CH2−CH(OOH)− CO(OO), R-2OOH_AOO) Calculated with the ROHF-UCCSD(T)-F12a/cc-pVDZ-F12//M06-2X/aug-cc-pVTZ Method

Forward H-shift barrier height with zero-pointed correction in kcal mol−1. bReverse H-shift barrier height with zero-pointed correction in kcal mol−1. cImaginary frequency of the transition state in cm−1. dEckart quantum tunnelling correction. eForward TST reaction rate constant in s−1. f Reverse TST reaction rate constant in s−1. a

shift reaction is fast enough to compete with the pseudo-firstorder reaction rate constant of C5-OO with NO ([NO] = 0.1 ppb) and HO2 ([HO2] = 55 ppt). The H-shift reaction rate constants in C5-OO are comparable to the H-shift reactions in the peroxy radical derived from the oxidation of 1-pentene.22 The peroxy group is located on a primary (terminal) carbon in C5-OO but on a secondary carbon in the 1-pentene derived peroxy radical.22 The 1,4-CH H-shift reaction rate constant in C5-AOO radical is around 10−3 s−1, thus also too slow to compete with the pseudo-first-order reaction rate constant of C5-AOO with NO/HO2 at the same concentrations. The larger H-shift reaction rate constants 1,5-CH, 1,6-CH, and 1,7-CH in C5-AOO are much faster (∼1−10 s−1) than the 1,4-CH and will dominate over the bimolecular reactions. The QOOH radicals produced from C5-AOO will all attach an O2 to produce an OOQOOH radical, because all reverse H-shift reactions are below 102 s−1.

Scheme 3. Structure of the 4-Hydroperoxy Acyl Peroxy Radical (C5-4OOH_AOO) and the 4-Peroxy Pentaneperoxoic Acid Radical (C5-4OO_AOOH)

in Tables S8 and S9. We have used the reactant, transition state, and product conformer of C5-2OOH_AOO with the lowest zero-point-corrected M062X energy to generate the reactant, transition state, and product of C5-AOO and C5-OO. All the forward H-shift reaction rate constants in C5-AOO are a factor of about 103 faster than the corresponding forward H-shift reactions in C5-OO. For C5-OO, only the 1,5-CH H1473

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Table 2. Parameters for the 1,X-OOH H-Shift Reactions in the C5-XOOH_AOO Radicals Calculated with the ROHFUCCSD(T)-F12a/cc-pVDZ-F12//M06-2X/aug-cc-pVTZ Method

Forward H-shift barrier height with zero-pointed correction in kcal mol−1. bReverse H-shift barrier height with zero-pointed correction in kcal mol−1. cImaginary frequency of the transition state in cm−1. dEckart quantum tunnelling correction. eForward TST reaction rate constant in s−1. f Reverse TST reaction rate constant in s−1. a

further autoxidation of the large acyl peroxy radicals in the atmosphere. The ongoing autoxidation of the larger acyl peroxy radicals might therefore alter the atmospheric NOx distribution and O3 production because only the small acyl peroxy radicals are able to produce APN. However, more research is needed to establish the atmospheric importance of the fast autoxidation of large acyl peroxy radicals. 3.3. Atmospheric Impact of the 1,X-OOH H-Shift Reaction in Hydroperoxy Acyl Peroxy Radicals. In this section we will focus on the atmospheric impact of including the C5-XOOH_AOO ↔ C5-XOO_AOOH cycle in atmospheric modeling. We have included the H-shift from both C5XOOH_AOO and C5-XOO_AOOH radical in our model. We

In smaller acyl peroxy radicals (like the acetyl peroxy radical) only the small H-shift reactions are possible (e.g., the acetyl peroxy radical can only undergo a 1,4 H-shift reaction). The 1,4-CH H-shift reaction is here observed to be very slow in C5AOO. Thus, H-shift reactions in small acyl peroxy radicals are suggested to be of minor importance in the atmosphere. In larger acyl peroxy radicals, however, the H-shift reactions are much more important, because they can make 1,5-CH, 1,6-CH, and 1,7-CH H-shift reactions, which have much higher reaction rate constants (above 1 s−1). The possible fast H-shift reaction in C5-AOO and related large acyl peroxy radicals will compete with the formation of APN species. The fast H-shift reaction in C5-AOO and related large acyl peroxy radicals will favor the 1474

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Scheme 4. 1,8-OOH H-Shift Reaction in C5-4OOH_AOO and the Subsequent Reactions with NO or HO2 or a H-Shifta

a

Only the most important H-shift reactions are shown. The TST reaction rate constants are calculated with the ROHF-UCCSD(T)-F12a/cc-pVDZF12//M06-2X/aug-cc-pVTZ method.

Figure 1. Branching ratio in the C5-4OOH_AOO ↔ C5-4OO_AOOH mechanism as a function of the NO concentration. The HO2 concentration is kept constant (55 ppt). Figure A shows the branching ratio when the 1,8-OOH H-shift reaction is left out. Figure B shows the branching ratio when the 1,8-OOH H-shift reaction is included together with the subsequent H-shift reactions in C5-4OO_AOOH. Note that the NO concentration in (A) is in ppm, and in (B) it is in ppb. The TST reaction rate constants are calculated with the ROHF-UCCSD(T)-F12a/cc-pVDZ-F12//M062X/aug-cc-pVTZ method.

(>CH(OOH)) with the OOH group attached, the reaction rate constants are in the range from 10−1 to 102 s−1. In C52OOH_AOO the 1,6-CH H-shift reaction is the fastest with a reaction rate constant of ∼101 s−1. The 1,7-CH H-shift reaction rate constants in all four C5-XOOH_AOO is close to the reaction rate constant of the 1,5-CH and 1,6-CH H-shift reactions. The F12 calculated MC-TST reaction rate constants deviate from the F12 calculated TST reaction rate constants by less than a factor of 10 (Tables S3 and S4 in the Supporting Information).

solve the coupled differential equations for all the species in the C5-XOOH_AOO ↔ C5-XOO_AOOH cycle. The F12 calculated TST reaction rate constants for the Hshift reaction are shown in Table S4 in the Supporting Information. For all four C5-XOO_AOOH, the 1,5-CH H-shift reactions are the fastest with reaction rate constants in the range from 10−3 to 10−1 s−1. The 1,4-CH H-shift reactions in C5-XOO_AOOH are very slow with reaction rate constants below 10−7 s−1. The fastest CH H-shift reactions in C53OOH_AOO, C5-4OOH_AOO, and C5-5OOH_AOO are the H-shift reaction of the hydrogen atom on the carbon atom 1475

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shift reaction is a factor of 50 slower than the 1,5 H-shift reaction in C5-4OO_AOOH. The reverse 1,5 H-shift reaction is much slower than the bimolecular reaction between the 1,5 H-shift produced QOOH radical and O2, which is estimated to be ∼107 s−1. Only H-shift reactions from C5-4OO_AOOH are observed in the atmospheric model (red dotted line in Figure 1B) for the C5-4OOH_AOO ↔ C5-4OO_AOOH cycle. We observed no significant products from C5-4OOH_AOO, green dotted line in Figure 1B. At moderate concentration of NO (0.1 ppb) and high concentration of HO2 (55 ppt), the production ratios of PO (produced from C5-4OO_AOOH), POH (produced from C5-4OO_AOOH reaction with HO2), and P4-C2 are around 0.25, 0.26, and 0.49, respectively. The C5-2OOH_AOO ↔ C5-2OO_AOOH cycle resembles the C5-4OOH_AOO ↔ C5-4OO_AOOH cycle, Figure S1 in the Supporting Information. Thus, in the C5-2OOH_AOO ↔ C5-2OO_AOOH cycle a decrease of the total H-shift branching ratio is also observed when the 1,6-OOH H-shift and the subsequent reactions of C5-2OO_AOOH are included in the C5-2OOH_AOO ↔ C5-2OO_AOOH cycle. Furthermore, all of the produced products originate from C52OO_AOOH. In both the C5-3OOH_AOO ↔ C5-3OO_AOOH cycle and the C5-5OOH_AOO ↔ C5-5OO_AOOH cycle the H-shift branching ratio is very close to zero; this implies that the C5XOOH_AOO ↔ C5-XOO_AOOH cycle eliminates the possible H-shift reactions and the reaction with NO dominates (Figure S2 and S3 in the Supporting Information, respectively). These observation can be explained by the fact that the 1,XOOH H-shift reactions are highly pushed toward C5XOO_AOOH, the H-shift reactions in C5-XOO_AOOH are slower than the pseudo-first-order reaction with NO (or HO2). The total H-shift branching ratio is below 0.1 for the C53OOH_AOO ↔ C5-3OO_AOOH cycle, when the NO and HO2 concentrations are set to 0.1 ppb and 55 ppt, respectively. With the same NO and HO2 concentrations, the total H-shift branching ratio in the C5-5OOH_AOO ↔ C5-5OO_AOOH cycle is 0.1 with the 1,5 and 1,6 H-shift reactions in C55OO_AOOH as the only contributors. The branching ratio for C5-5OO_AOOH + NO is 0.48 whereas for C5-5OO_AOOH + HO2 it is 0.51. Generally, the C5-XOOH_AOO ↔ C5-XOO_AOOH cycle suppresses the overall H-shift branching ratio. Due to the large equilibrium constant (kF/kR > 106) for the C5-XOOH_AOO ↔ C5-XOO_AOOH cycles, C5-XOOH_AOO will rapidly be transformed into C5-XOO_AOOH. We have also observed that the rapid 1,X-OOH H-shift reaction blocks for all the possible H-shift reactions in the four C5-XOOH_AOO. Furthermore, one consequence of the rapid 1,X-OOH H-shift reaction is that the autoxidation can be stopped if the H-shift reactions from the peroxy peroxoic acid (C5-XOO_AOOH) are too slow to compete with the bimolecular reaction with NO and HO2. All of this emphasizes that these rapid 1,X-OOH Hshift reactions must be included when studying the atmospheric fate of hydroperoxy acyl peroxy radicals in the atmosphere and that they are important in all autoxidation reactions where hydroperoxy acyl peroxy radicals are invariably formed. 3.4. Influence of the XOOH_AOO ↔ XOO_AOOH Cycle in the C6H9O6 Hydroperoxy Acyl Peroxy Radical. In the ozonolysis of cyclohexene, the autoxidation produces a C6H9O6 hydroperoxy acyl peroxy radical (C(O)OO−CH2−CH2− CH2−CH(OOH)−CHO) denoted as XOOH_AOO.14 The XOOH_AOO radical is here suggested to undergo a series of

In Scheme 4, the atmospheric oxidation of C5-4OOH_AOO and C5-4OO_AOOH is shown. Here, only the 1,6 H-shift reaction in C5-4OOH_AOO, the 1,5 H-shift reaction in C54OO_AOOH, and the forward/reverse 1,8-OOH H-shift reactions are shown, because these reactions are much faster than the other H-shift reactions. The 1,6-CH H-shift reaction in C5-4OOH_AOO leads to a decomposition giving the products P4-C4 and OH. The 1,5-CH H-shift reaction in C54OO_AOOH leads to the product P4-C2 after an O2 addition to the QOOH radical. All the reverse CH H-shift reactions are much slower than the reaction with O2 (∼107 s−1), when a bimolecular reaction rate constant of 2.3 × 10−12 cm3 molecules−1 s−1 and an O2 concentration of 5.2 × 1018 molecules cm−3 are used.46 C54OOH_AOO and C5-4OO_AOOH are assumed to react with HO2 and NO with reaction rate constants of kHO2 = 1.7 × 10−11 cm3 molecules−1 s−1 and kNO = 8.8 × 10−12 cm3 molecules−1 s−1, respectively.46,47 The reaction between C5-XOOH_AOO and NO2 is not included in the calculation, because the equilibrium is highly shifted toward the reactants, C5XOOH_AOO and NO2 at 298 K and 760 Torr.48 In eq 2, the total H-shift branching ratio ΓH‑shift as a function of NO is shown. ΓH‐shift =

∑ kH‐shift

∑ kH‐shift + ∑ kNO[NO] + ∑ kHO2[HO2 ]

(2)

kH‑shift is the reaction rate constant of each H-shift reaction (excluding the forward and reverse 1,X-OOH H-shift reaction). The HO2 concentration is here kept constant at 55 ppt in our calculation. In Figure 1 the H-shift branching ratio ΓH‑shift is plotted as a function of the NO concentrations with and without the 4OOH_AOO ↔ 4OO_AOOH cycle. The total H-shift reaction branching ratio in the C54OOH_AOO ↔ C5-4OO_AOOH cycle is shown as the black line in Figure 1A,B, and the green and red dotted lines in Figure 1B are the total H-shift branching ratio from C54OOH_AOO and C5-4OO_AOOH, respectively. First, we consider the atmospheric model where the C5-4OOH_AOO ↔ C5-4OO_AOOH cycle is not included and thereby only the CH H-shift reactions in the C5-4OOH_AOO are included in Figure 1A. The 1,6-CH H-shift reaction in C5-4OOH_AOO is competitive with the bimolecular reaction between C54OOH_AOO and NO for NO concentration below 0.5 ppm. The 1,6-CH H-shift reaction rate constant is significantly faster than the bimolecular reaction rate constants of C54OOH_AOO with HO2 for a HO2 concentration at 55 ppt. Thus, a large total H-shift branching ratio is observed when the C5-4OOH_AOO ↔ C5-4OO_AOOH cycle is not included in the atmospheric model. If we include the C5-4OOH_AOO ↔ C5-4OO_AOOH cycle, then the total H-shift branching ratio is decreased significantly (Figure 1B). The decrease in the total H-shift branching ratio is due to a range of factors. First, this occurs because the rapid 1,8-OOH H-shift reaction in C54OOH_AOO is much faster than the 1,6 H-shift reaction in C5-4OOH_AOO (a factor of ∼2000 faster). Second, the equilibrium C5-4OOH_AOO ↔ C5-4OO_AOOH is pushed toward C5-4OO_AOOH (the equilibrium constant is kF/kR = ∼108). Thus, all of C5-4OOH_AOO will rapidly be converted to C5-4OO_AOOH. Third, the 1,5 H-shift reactions in C54OO_AOOH are a factor of 103 slower than the 1,6 H-shift reaction in C5-4OOH_AOO. Finally, the reverse 1,8-OOH H1476

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Scheme 5. Rapid XOOH_AOO ↔ XOO_AOOH Cycle in the Autoxidation of the C6H9O6 Hydroperoxy Acyl Peroxy Radical Produced in the Ozonolysis of Cyclohexenea

a

The TST reaction rate constants are calculated with the ROHF-UCCSD(T)-F12a/cc-pVDZ-F12//M06-2X/aug-cc-pVTZ method.

H-shift reactions.14 The rapid 1,9-OOH H-shift reaction in XOOH_AOO to form XOO_AOOH is not included in their investigation. We will now investigate the effect of the rapid XOOH_AOO ↔ XOO_AOOH cycle. The F12 calculated TST reaction rate constants are shown in Scheme 5. We have solved the coupled differential equations for all the species in the XOOH_AOO ↔ XOO_AOOH cycle and the subsequent H-shift reactions as in section 3.3. The concentration of NO and HO2 are fixed at 0.1 ppb and 55 ppt, respectively. We observe that the major reaction pathway (>99%) of XOOH_AOO is through the 1,9-OOH H-shift reaction, leading to the production of XOO_AOOH, subsequently, XOO_AOOH undergoes a 1,4 aldehyde H-shift reaction leading to the acyl-C6H9O6 radical. The 1,7 and 1,8 aldehyde H-shift reactions in XOOH_AOO are minor reaction pathways with product yields below CH(OOH) group in XOOH_AOO), because the

XOO_AOOH radical is unable to make this elimination reaction. This clearly shows the importance of including the XOOH_AOO ↔ XOO_AOOH cycle in the autoxidation of NMVOCs. In the ozonolysis of cyclohexene, the same peroxy group can be regenerated, because the acyl peroxy radical undergoes rapid H-shift reactions from the OOH group. In the autoxidation of cyclohexene, the same peroxy group can undergo up to three H-shift reactions illustrated in reaction Scheme S5 in the Supporting Information. The consequence of the peroxy radical regeneration is that the elimination reaction (the H-shift where a hydrogen is abstracted from a >CH(OOH) group) will occur later, thus favoring a production of secondary NMVOC oxidation products with a high O:C ratio.

4. CONCLUSION We have studied the H-shift reaction in the acyl peroxy radicals produced from either the direct or the indirect reaction mechanism (Scheme 1). We have considered the 1,X-OOH Hshift in hydroperoxy acyl peroxy radical (denoted XOOH_AOO). We observe that the forward 1,X-OOH H-shift reactions in the hydroperoxy acyl peroxy radicals are rapid with reaction rate constants in the range from 103 to 105 s−1. Further, the XOOH_AOO ↔ XOOH_AOO equilibrium is highly (kF/kR > 105) pushed toward the XOO_AOOH radical. We have also observed that the rapid 1,X-OOH H-shift reaction will block the possible H-shift reactions in the hydroperoxy acyl peroxy radical XOOH_AOO and often also the bimolecular reaction with NO. The atmospheric chemistry of the newly formed peroxy peroxoic acid radical XOOH_AOO must therefore be studied. The XOOH_AOO ↔ XOOH_AOO cycle must be included in the studies of the atmospheric oxidation of hydroperoxy acyl peroxy radicals, because it is a likely important reaction mechanism in the autoxidation where acyl peroxy radicals are invariably formed. We have also observed that the H-shift reactions in a large acyl peroxy radical (C5-AOO) without a hydroperoxy group can undergo fast H-shift reactions which might influence the atmospheric NOx distribution and O3 1477

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(8) Guenther, A. B.; Jiang, X.; Heald, C. L.; Sakulyanontvittaya, T.; Duhl, T.; Emmons, L. K.; Wang, X. The model of emissions of gases and aerosols from nature version 2.1 (MEGAN2.1): An extended and updated framework for modeling biogenic emissions. Geosci. Model Dev. 2012, 5, 1471−1492. (9) Atkinson, R.; Arey, J. Atmospheric degradation of volatile organic compounds. Chem. Rev. 2003, 103, 4605−4638. (10) Cox, R. A.; Cole, J. A. Chemical aspects of the autoignition of hydrocarbon-air mixtures. Combust. Flame 1985, 60, 109−123. (11) Zador, J.; Taatjes, C. A.; Fernandes, R. X. Kinetics of elementary reactions in low-temperature autoignition chemistry. Prog. Energy Combust. Sci. 2011, 37, 371−421. (12) Crounse, J. D.; Nielsen, L. B.; Jørgensen, S.; Kjaergaard, H. G.; Wennberg, P. O. Autoxidation of organic compounds in the atmosphere. J. Phys. Chem. Lett. 2013, 4, 3513−3520. (13) Crounse, J. D.; Knap, H. C.; Ornso, K. B.; Jørgensen, S.; Paulot, F.; Kjaergaard, H. G.; Wennberg, P. O. Atmospheric fate of methacrolein. 1. Peroxy radical isomerization following addition of OH and O2. J. Phys. Chem. A 2012, 116, 5756−5762. (14) Rissanen, M. P.; Kurten, T.; Sipila, M.; Thornton, J. A.; Kangasluoma, J.; Sarnela, N.; Junninen, H.; Jørgensen, S.; Schallhart, S.; Kajos, M. K.; et al. The formation of highly oxidized multifunctional products in the ozonolysis of cyclohexene. J. Am. Chem. Soc. 2014, 136, 15596−15606. (15) Peeters, J.; Muller, J. F. HOx radical regeneration in isoprene oxidation via peroxy radical isomerisations. II: Experimental evidence and global impact. Phys. Chem. Chem. Phys. 2010, 12, 14227−14235. (16) Kurten, T.; Rissanen, M. P.; Mackeprang, K.; Thornton, J. A.; Hyttinen, N.; Jorgensen, S.; Ehn, M.; Kjaergaard, H. G. Computational study of hydrogen shifts and ring-opening mechanisms in alpha-pinene ozonolysis products. J. Phys. Chem. A 2015, 119, 11366−11375. (17) Berndt, T.; Richters, S.; Kaethner, R.; Voigtlaender, J.; Stratmann, F.; Sipilae, M.; Kulmala, M.; Herrmann, H. Gas-phase ozonolysis of cycloalkenes: Formation of highly oxidized RO2 radicals and their reactions with NO, NO2, SO2, and other RO2 adicals. J. Phys. Chem. A 2015, 119, 10336−10348. (18) Rissanen, M. P.; Kurten, T.; Sipila, M.; Thornton, J. A.; Kausiala, O.; Garmash, O.; Kjaergaard, H. G.; Petaja, T.; Worsnop, D. R.; Ehn, M.; et al. Effects of chemical complexity on the autoxidation mechanisms of endocyclic alkene ozonolysis products: From methylcyclohexenes toward understanding alpha-pinene. J. Phys. Chem. A 2015, 119, 4633−4650. (19) Ehn, M.; Thornton, J. A.; Kleist, E.; Sipila, M.; Junninen, H.; Pullinen, I.; Springer, M.; Rubach, F.; Tillmann, R.; Lee, B.; et al. A large source of low-volatility secondary organic aerosol. Nature 2014, 506, 476−479. (20) Wang, S. N.; Wang, L. M. The atmospheric oxidation of dimethyl, diethyl, and diisopropyl ethers. The role of the intramolecular hydrogen shift in peroxy radicals. Phys. Chem. Chem. Phys. 2016, 18, 7707−7714. (21) Jokinen, T.; Sipila, M.; Richters, S.; Kerminen, V. M.; Paasonen, P.; Stratmann, F.; Worsnop, D.; Kulmala, M.; Ehn, M.; Herrmann, H.; et al. Rapid autoxidation forms highly oxidized RO2 radicals in the atmosphere. Angew. Chem., Int. Ed. 2014, 53, 14596−14600. (22) Jørgensen, S.; Knap, H. C.; Otkjær, R. V.; Jensen, A. M.; Kjeldsen, M. L. H.; Wennberg, P. O.; Kjaergaard, H. G. Rapid hydrogen shift scrambling in hydroperoxy substituted organic peroxy radicals. J. Phys. Chem. A 2016, 120, 266−275. (23) Lee, C. T.; Yang, W. T.; Parr, R. G. Development of the ColleSalvetti correlation-energy formula into a function of the electrondensity. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785−789. (24) Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic-behavior. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 38, 3098−3100. (25) Frisch, M. J.; Pople, J. A.; Binkley, J. S. Self-consistent molecular-orbital methods. 25. Supplementary functions for gaussianbasis sets. J. Chem. Phys. 1984, 80, 3265−3269. (26) Gonzalez, C.; Schlegel, H. B. An improved algorithm for reaction-path following. J. Chem. Phys. 1989, 90, 2154−2161.

production. Finally, we suggest that a peroxy radical can be regenerated in the autoxidation of aldehydes through the 1,XOOH H-shift reaction. This peroxy radical regeneration favors a production of secondary NMVOC oxidation products with a high O:C ratio, because the termination occurs later in the autoxidation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b12787. Detailed information on the H-shift reactions in the R2OOH_AOO ↔ R-2OO_AOOH cycles, C5-XOOH_AOO ↔ C5-XOO_AOO cycles, C6H9O6 acyl peroxy ↔ C6H9O6 peroxy cycle, 1-peroxypentane and pentane acyl peroxy radical (energetics and rate constants, branching ratios vs NO concentration, the expectation value of the total spin, T1-diagnostic values, and xyzcoordinates of the conformer with lowest zero-pointcorrected energy for the reactant, transition state, and product) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*S. Jørgensen. E-mail: [email protected]. ORCID

Hasse C. Knap: 0000-0002-8240-9496 Solvejg Jørgensen: 0000-0002-0255-1338 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Henrik G. Kjaergaard for helpful discussions. We thank the Danish Center for Scientific Computing (DCSC) for funding.

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REFERENCES

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