Unimolecular HO2 Loss from Peroxy Radicals Formed in Autoxidation

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Unimolecular HO Loss from Peroxy Radicals Formed in Autoxidation is Unlikely under Atmospheric Conditions Noora Hyttinen, Hasse C. Knap, Matti P. Rissanen, Solvejg Jørgensen, Henrik G. Kjaergaard, and Theo Kurtén J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b02281 • Publication Date (Web): 10 May 2016 Downloaded from http://pubs.acs.org on May 15, 2016

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The Journal of Physical Chemistry

Unimolecular HO2 Loss from Peroxy Radicals Formed in Autoxidation is Unlikely under Atmospheric Conditions Noora Hyttinen,a Hasse C. Knap,b Matti P. Rissanen, c Solvejg Jørgensen, b Henrik G. Kjaergaard, b Theo Kurténa,* a

b

Department of Chemistry, University of Helsinki, P.O. BOX 55, FI-00014, Finland

Department of Chemistry, DK-2100 Copenhagen Ø, University of Copenhagen, Copenhagen, Denmark c

Department of Physics, University of Helsinki, P.O. BOX 64, FI-00014, Finland

ABSTRACT. A concerted HO2 loss reaction from a peroxy radical (RO2), formed from the addition of O2 to an alkyl radical, has been proposed as a mechanism to form closed shell products in the atmospheric oxidation of organic molecules. We investigate this reaction computationally with four progressively oxidized radicals. Potential energy surfaces of the O2 addition

and

HO2

loss

reactions

were

calculated

at

ROHF-RCCSD(T)-F12a/VDZ-

F12//ωB97xD/aug-cc-pVTZ level of theory and the Master Equation Solver for Multi-Energy well Reactions (MESMER) was used to calculate Bartis-Widom phenomenological rate

ACS Paragon Plus Environment

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coefficients. The rate coefficients were also compared with the unimolecular rate coefficients of the HO2 loss reaction calculated with Transition State Theory (TST) at atmospheric temperature and pressure. Based on our calculations the unimolecular concerted HO2 loss is unlikely to be a major pathway in the formation of highly oxidized closed-shell molecules in the atmosphere.

INTRODUCTION Organic molecules contribute significantly to atmospheric new particle formation and aerosol growth.1-4 Volatile organic compounds are emitted to the atmosphere by both anthropogenic and biogenic sources and oxidized in the gas phase, yielding a complex mixture of reaction products with a large range of volatilities. The least volatile of these products, denoted ELVOC (Extremely Low-Volatility Organic Compounds), have short lifetimes and low ambient concentrations, and are therefore difficult to characterize experimentally. For this reason, the molecular-level formation mechanisms and precise chemical composition of these highly oxidized species have been studied mostly with computational methods. The atmospheric oxidation of different organic compounds has been widely studied for decades. The recent observations of surprisingly highly oxidized organic molecules in the ambient air5 has focused attention on a process called autoxidation.6-9 In autoxidation only one oxidant, such as O3, OH or NO3, is needed to initiate the chain reaction of O2 additions and hydrogen shifts (H-shifts) to produce highly oxidized products. Compared to autoxidation, normal oxidation reactions typically need an oxidant for each oxygen addition step, making the formation of highly oxidized products very slow. Autoxidation is well-known in e.g. combustion chemistry,10 but has only recently been highlighted as a potentially important mechanism in atmospheric oxidation.9,11-13


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In the autoxidation of endocyclic alkenes initiated by O3, the double bond of the alkene breaks, leaving (after unimolecular isomerization, OH loss and O2 addition6) a peroxy radical (RO2) with two keto-/aldehyde groups. Throughout the following chain of H-shifts and O2 additions, the RO2 radical intermediates thus always contain an even number of oxygen atoms. Unimolecular OH elimination from the “QOOH” products, which arise in RO2 H-shifts, is presumed to explain the formation of closed-shell products with an odd number of oxygen atoms.6 Mentel et al.8 explained the observation of closed-shell products with an even number of oxygen atoms by bimolecular propagation or termination reactions. Propagation reactions include alkoxy radical (RO) formation, e.g. via RO2 + NO → RO + NO2. These are likely followed by rapid H-shifts of the alkoxy radical RO, and subsequent O2 addition to yield a hydroxy-RO2 with an odd number of oxygen atoms. This would then lead to a closed-shell product with an even number of oxygen atoms through a rapid OH loss reaction. Bimolecular termination reactions such as RO2 + HO2 → ROOH + O2 can also explain the formation of products with an even number of oxygen atoms. However, the possible existence of pseudo-unimolecular (i.e. involving no bimolecular steps apart from O2 addition reactions) mechanisms to create closed-shell molecules with an even number of oxygen atoms from ozone-initiated autoxidation of endocyclic alkenes is still uncertain. Rissanen et al.6 suggested that the mechanism for the unimolecular formation of C6H8O8 products in the cyclohexene + O3 system could be a concerted HO2 elimination from an RO2 radical, resulting in an alkene product. The pseudo first order rate coefficients for different bimolecular sinks competing with the unimolecular sink in the atmosphere at atmospheric pressure are roughly on the order of 10-2 s-1 for peroxy radical + HO2 under pristine conditions and 1 s-1 or higher for peroxy radical + NO in polluted areas.14 For the concerted HO2 loss to be a


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feasible candidate to give high yields of closed shell products, the reaction would have to occur on the same time scale or faster than the competing bimolecular sink reactions. The concerted HO2 elimination reaction in the gas-phase has previously been studied for many different compounds, with focus on combustion chemistry15-20 and atmospheric HO2 loss from nitrogen containing radicals.21-23 Kaiser17 studied the oxidation reaction C2H5 + O2 experimentally at several temperatures and pressures, including tropospheric conditions, and concluded that the yield of the product C2H4 is extremely low (< 1 %) at atmospheric temperature and pressure. This experiment did not distinguish between two different HO2 elimination mechanisms in the formation of C2H4: i) the concerted HO2 loss (one-step reaction mechanism) and ii) a H-shift followed by an HO2 loss (two-step reaction mechanism). Note that while the concerted HO2 loss mechanism can also be defined as a H-shift, the H-C and O-C bonds break simultaneously in this mechanism, which involves only one transition state. In contrast, the “H-shift” mechanism involves two transition states: one for the H-shift, and another for the breaking of the HOO-C bond. A computational study on the same C2H5 + O2 reaction showed that the concerted HO2 loss is the most favorable out of five different reaction paths, with the CCSD(T) level transition state energy only 0.2 kcal/mol above the C2H5 + O2 reactants, and 30.5 kcal/mol above the C2H5OO radical.19 Similar calculations were also done on propyl + O2 and butyl + O2, where the transition state of the concerted HO2 loss was found to be 4.3 kcal/mol below the reactants.20 For ethyl-, propyl-, and butyl-O2 systems the QCISD(T) based energy barrier of the HO2 loss transition state with respect to the RO2 radical is consistent, varying only ~1 kcal/mol around an average value of 30.5 kcal/mol.20 Larger alkanes have more secondary and tertiary hydrogens that are easier to abstract, and the intramolecular H-shifts have larger rings in the transition states, making the H-shift reaction more competitive with the


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concerted HO2 loss reaction.24 An experimental study found that the concerted HO2 loss is a dominating reaction in the oxidation of cyclic ketones at higher temperatures and lower pressures.25 In nitrogen containing radicals, concerted HO2 loss has been experimentally and theoretically determined to be a major reaction path, for instance in the atmospheric oxidation of NH2CO23, and CH2NH2 and CH3CHNH2.26 In that case, the hydrogen is abstracted from the NH2 group, forming a double bond between a carbon and a nitrogen atom. Computationally, at the G3X-K level of theory, the well depth of the addition of O2 to NH2CO is 36.9 kcal/mol and the transition state for the HO2 loss is 17.9 kcal/mol below the NH2CO + O2 reactants.23 This reaction gave computationally a 100 % yield under tropospheric conditions.23 For these smaller molecules with relatively few vibrational degrees of freedom, it is possible that the energy-rich RO2 radical formed in the alkyl radical + O2 reaction is not collisionally stabilized, but instead reacts promptly to form the HO2 and alkene products. In this case, the rate coefficient mainly depends on the energy difference between the alkyl + O2 reactants and the transition state. Larger RO2 radicals have more vibrational degrees of freedom. Larger energetically excited RO2 radicals will thus have longer lifetimes and are, at atmospheric pressure, more likely to collisionally stabilize before reacting. With collisional stabilization, the rate coefficient mainly depends on the energy difference between the transition state and the RO2 radical. In this study, we calculate the potential energy surfaces and rate coefficients of the concerted HO2 loss process starting from selected alkyl radicals. Energies of the alternative two-step HO2 loss reaction path that goes through two transition states (H-shift and HO2 loss) and a QOOH radical are also computed. In Rissanen et al.,6 the concerted HO2 loss reaction was suggested for an RO2 radical with two peroxy acid groups and one hydroperoxide group. The ozonolysis of


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endocyclic alkenes forms a peroxy radical with two carbonyl groups. If they are aldehyde groups, autoxidation by subsequent H-shifts and O2 additions is likely to convert them into peroxy acid groups.27 For this reason, the rate coefficients are calculated for RO2 radicals derived from the oxidation of four different sec-butyl radicals allowing for peroxy acid substitutions at the ends of the carbon chain. The aim is to find out if the HO2 loss reaction is relevant (i.e. able to compete with other sink reactions) for RO2 radicals produced by autoxidation under any atmospheric conditions, and to determine how peroxy acid group substituents affect the rate coefficients.

METHODOLOGY Figure 1 shows the alkyl reactants that were studied. For the purpose of studying the concerted HO2 loss reaction from RO2 radicals formed in autoxidation, we used four different sec-butyl radicals that have zero (Figure 1a), one (Figures 1b and 1c) or two (Figure 1d) peroxy acid substituents at the ends of the carbon chain. By comparing the rate coefficients of the different radicals we can see the effects of the peroxy acid groups in different positions in relation to the radical center and the H-abstraction site.

Figure 1 The alkyl reactants. a has no peroxy acid groups, b has one peroxy acid group next to the hydrogen abstraction site, c has one on the carbon next to the radical center, and d has peroxy acid groups on both ends of the carbon chain.


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The concerted HO2 reaction is shown in Figure 2. First the O2 is added to the radical center of the alkyl radical to form a peroxy radical (RO2). After that, a 1,4-H-shift leads to the concerted HO2 loss, forming a double bond in the carbon chain. A transition state can be found between the peroxy radical and the alkene product, where the two carbon atoms form a 5-membered ring structure with the leaving HO2-group. Depending on the orientation of the carbon chain in the RO2 radical, the transition state and the product can be either cis- or trans-isomers. Figure 2 shows the transition state and product in the trans-isomer form.

Figure 2 Reaction mechanism illustrating the addition of O2 to an alkyl radical, the formation of a peroxy radical (RO2), and the subsequent H-shift and HO2 loss leading to alkene product formation. QUANTUM CHEMICAL CALCULATIONS The quantum chemical calculations were done with a scheme similar to that previously used by Rissanen et al.6 The conformational sampling of the different molecules (alkyl reactants, peroxy radicals, transition states and alkene products) was done with the MMFF force field using Spartan ’14.28 For the smallest system (the sec-butyl radical with no peroxy acid groups) with the fewest torsional angles, the sampling stage was omitted, and all possible torsional combinations were included in the initial optimizations. The initial B3LYP/6-31+G* level optimizations were also done with Spartan ’14, except for the transition states, as described below. Conformers with B3LYP/6-31+G* energies within 3 kcal/mol of the lowest-energy conformer at the B3LYP/631+G* level were selected for subsequent higher-level optimization.29 This approach reduced the


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number of conformers to less than 20 for each system. For all of these conformers, the final optimizations were done at the ωB97xD/aug-cc-pVTZ level using Gaussian 09,30 with default convergence criteria and the ultrafine integration grid. The final ROHF-RCCSD(T)-F12a/VDZF12 level single-point energy calculations were done using Molpro version 2012.131 with all of the D1 and T1 values of the calculations being less than 0.14 and 0.03, respectively. The zeropoint potential energy surface for the reactions was calculated from the ROHF-RCCSD(T)F12a/VDZ-F12 level coupled cluster energies together with the ωB97xD/aug-cc-pVTZ level zero-point vibrational energy corrections. For the conformational sampling of the transition states, the geometry of the transition state was first optimized at the B3LYP/6-31+G* level for one arbitrary conformer using Gaussian 09. In the subsequent MMFF conformational sampling on Spartan ‘14, the distances and some dihedrals between the atoms involved in the reaction (i.e. the two C atoms, the two O atoms and the H atom being abstracted) were frozen. In the initial B3LYP/6-31+G* and the final ωB97xD/aug-cc-pVTZ optimizations, both done using Gaussian 09, these constraints were removed, and the structures of the transition states were optimized. (Note that this differs slightly from the approach used in Rissanen et al.,6 where the initial optimizations of the transition states were carried out as constrained minimizations.) Intrinsic reaction coordinate (IRC) scans were performed with default step size, at the ωB97xD/aug-cc-pVTZ level of theory, for the minimum energy transition states to confirm that the transition state connected the right RO2 radical and alkene product. The rate coefficient calculations were performed using only the lowest-energy conformers of the alkyl reactant, RO2 radical, transition state and product. Our sensitivity analysis indicated that including multiple conformers in the rate coefficient calculation affects the rate coefficient by less than a factor 2 for the systems studied here, mainly due to the


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relatively large energy differences between the two lowest-energy transition-state conformers of each system.

RATE COEFFICIENT CALCULATIONS The Master Equation Solver for Multi-Energy well Reactions (MESMER32) was used to calculate Bartis-Widom33 phenomenological rate coefficients for the concerted HO2 elimination reactions from RO2 radicals. In addition to data from the quantum chemical calculations, MESMER needs values for various parameters, such as the Lennard-Jones coefficients for the reacting molecules and the bath gas, and the average downward energy transfer (∆Edown) used in the collisional energy transfer model. The exponential-down model34 was used to describe the collisional energy transfer. The Lennard-Jones coefficients σ(Å) and ε(K) were estimated from literature values35-37 of similar compounds. The σ (Å) values for the RO2 radicals of a, b, c, and d were thus set to 4.0, 4.5, 4.5, and 5.0, and the ε (K) values to 450, 500, 500, and 550, respectively. Additional sensitivity analysis was performed to see how the rate coefficients are affected by changes in the Lennard-Jones coefficients. Nitrogen (N2) was used as a bath gas, with Lennard-Jones coefficients σ = 3.919 Å and ε = 91.85 K.38 The recommended value for the average downward collisional energy transfer (∆Edown) in the MESMER program39 when using the exponential-down model and N2 as bath gas varies between 175 and 275 cm-1 depending on the reacting molecule, but the exact value cannot be determined without experimental results. The value used in the calculations was 225 cm-1, but other values were also tested. The size of the energy grain and the span of energy grains above the highest stationary point were set to 15 cm-1 and 50 kbT, respectively, where kb is the


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Boltzmann constant. Test calculations were performed to ensure that the obtained phenomenological rate coefficients are converged with respect to these parameters. The rate coefficients were first calculated for atmospheric conditions with the temperature (T) set to T = 298 K and the bath gas pressure (p) to p = 1 atm. Lower bath gas pressures were tested to find out at what bath gas pressure the collisional stabilization becomes imperfect, and to calculate the timescale of the product formation at low pressures without collisional stabilization. Higher temperatures were tested to find the temperature where the rate coefficients are above 102 -1

s . The MesmerILT method was used for the reversible alkyl reactant + O2 association, for which

we did not find a saddle point. The Arrhenius parameters used in the MesmerILT method were a pre-exponential factor of 6×10-12 cm3 molec-1 s-1 (which is roughly the same magnitude as the experimental values of alkyl + O2 reactions at 298 K40), an activation energy of 0 kcal/mol, and a modified Arrhenius parameter of -0.5. This implies that at atmospheric sea-level O2 concentrations, the initial RO2 formation occurs on the timescale of some tens of nanoseconds. The alkyl radical + O2 reaction was treated as a pseudo first order reaction (with O2 as the excess reactant), since the O2 concentration is many orders of magnitude higher than the alkyl radical concentration. As the purpose of this study is to investigate whether or not the RO2 → alkene + HO2 reaction is fast enough to compete with other RO2 sink reactions, the details of the alkyl + O2 reaction are relatively unimportant. The only reason for explicitly including the alkyl + O2 step in the MESMER simulations is to create a realistic energy distribution for the initially formed (non-thermalized) RO2 radicals. For this reason, the concentration of O2 was kept fixed at the atmospheric value at ground level, 5.16×1018 molec cm-3 irrespective of the bath gas pressure (note that any sufficiently high value for [O2] would have served the same purpose, and that the


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O2 concentration is not used in the collisional energy transfer calculations). This may seem counterintuitive, as varying the O2 concentration will naturally affect the rate of the overall alkyl radical + O2 → alkene + HO2 reaction. For example, in the upper troposphere the formation of RO2 from alkyl radicals and O2 might take hundreds rather than tens of nanoseconds, and in the stratosphere it might even take microseconds. However, the timescale for the initial RO2 formation is irrelevant to the subsequent fate of the RO2, which is the focus of this study. Within MESMER, we used the simple RRKM method for the irreversible concerted HO2 loss reaction, for which transition states could be found. Eckart tunneling was used to calculate the tunneling factor of this reaction. Test calculations of the ring polymer instanton method41 on a smaller test molecule show that the Eckart tunneling factors are on the same order-of-magnitude with this multidimensional tunneling factor (unpublished results). At high enough pressures, the RO2 radical is collisionally stabilized, and the rate coefficient for the HO2 loss reaction depends on the energy difference between the transition state and the RO2 radical. At lower pressures, collisional stabilization becomes imperfect, and some of the nascent RO2 radicals formed in the alkyl radical + O2 reaction form the alkene + HO2 products directly, without thermalization. At low enough pressures with no collisional stabilization, the total rate coefficient depends only on the energy difference between the alkyl radical + O2 and the transition state. MESMER calculates Bartis-Widom phenomenological rate coefficients that are not reliable when the rate of the reaction is faster than the collisional stabilization of the species, and can thus only be used to calculate rate coefficients with complete collisional stabilization of the RO2 radical.42 At intermediate pressure regions where collisional stabilization is significant but incomplete (in the sense that the fractions of products formed directly and via thermalized RO2 are both


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significant), part of the products are formed extremely rapidly (on a timescale characteristic of the low-pressure rate coefficient), while part is formed slowly (on a timescale characteristic of the high-pressure rate coefficient). The Bartis-Widom phenomenological rate coefficients are also compared with rate coefficients of the RO2 dissociation reaction calculated from transition state theory43 ்݇ௌ் = ߢ

௞್ ் ொ೅ೄ ௛

ொೃ

݁‫ ݌ݔ‬ቀ−

ா೅ೄ ିாೃ ௞್ ்

ቁ

(1)

where ߢ is Eckart44 tunneling factor, kb is the Boltzmann constant, h is the Planck constant and T is the temperature. The energy barrier between the transition state and the RO2 radical (ETS-ER) is the ωB97xD/aug-cc-pVTZ zero-point vibrational energy corrected ROHF-RCCSD(T)F12a/VDZ-F12 energy. The same RO2 radical, transition state, and alkene product energies, and the imaginary frequency and reduced mass from the ωB97xD/aug-cc-pVTZ frequency calculation of the transition state are used in the Eckart tunneling factor calculation. Based on single-point CCSD(T)-F12a/VDZ-F12 calculations along a ωB97xD/aug-cc-pVTZ IRC path for a H-shift reaction, the ωB97xD/aug-cc-pVTZ potential energy surface has been found to be in good agreement with the CCSD(T)-F12a/VDZ-F12 surface. This means that the computed imaginary frequencies likely correspond to the curvature of the “true” potential energy surface.45 For consistency, the product energy required in the Eckart tunneling factor calculation (in both MESMER and Equation 1) was computed using the separated alkene and HO2 products, even for the one system where a product complex was present on the IRC path. The difference between tunneling factors computed using the product complex and the separated products was less than 4%. The partition functions (Q) are calculated using the ωB97xD/aug-cc-pVTZ moments of inertia and harmonic vibrational frequencies. The rate coefficients are calculated with the lowest energy reactant, TS, and product.


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RESULTS AND DISCUSSION The optimized structures of the concerted HO2 loss transition states of molecules a-d are shown in Figure 3 a-d, respectively. The biggest differences between the transition state geometries originate from the peroxy acid groups next to the hydrogen abstraction sites in molecules b and d, which make the distance between the carbon and the leaving hydrogen longer, and the distance between the carbon and the leaving oxygen shorter.

Figure 3 The minimum energy conformers of the transition states, and the bond distances (Ångström) and angles (degrees) of the transition states obtained at the ωB97xD/aug-cc-pVTZ level. Color coding: grey = carbon, red = oxygen, and white = hydrogen. Figure 4 shows the potential energy diagram of the O2 addition and concerted HO2 loss reactions (Figure 2) starting from the alkyl reactants presented in Figure 1. The energies of all


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products are lower than the energies of the alkyl radical + O2 reactants, but higher than the energies of the RO2 radicals. Both c and d have transition states that are higher in energy than the alkyl radical + O2 reactants. A product complex along the IRC was found only for molecule a. For the other molecules, it is possible that the leaving HO2 could form a product complex with a peroxy acid group of the alkene product, but such product complexes were not located on the IRC paths. (The product complexes were not included in this study for any of the reactions.)

Figure 4

Zero-point

corrected ROHF-RCCSD(T)-F12a/VDZ-F12//ωB97xD/aug-cc-pVTZ

potential energies of the stationary points on the reaction path that lead to trans-isomer products. Adding a peroxy acid group next to the carbon radical center (a versus c and b versus d) reduces both the well-depth of the O2 addition reaction and the energy barrier of the HO2 loss reaction with respect to the RO2 radical. On the other hand, the barrier with respect to the alkyl radical + O2 reactants is increased by the addition of a peroxy acid group next to the carbon radical center. Thus, this substitution should make the high-pressure rate coefficient higher, but the low-pressure rate coefficient lower. Adding a peroxy acid group next to the H abstraction site (a versus b and c versus d) lowers the energy barrier of the transition state with respect to both the RO2 radical, and the alkyl radical + O2 reactants. This substitution should thus make the


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reaction faster at all bath gas pressures. The addition of a peroxy acid group to either position (a versus b and a versus c) lowers the energy barrier of the transition state relative to the RO2 radical by roughly the same amount. At low bath gas pressure (i.e. in the absence of collisional stabilization of the RO2 radical), molecule b should have the fastest reaction, because it has the lowest transition state relative to the alkyl radical + O2 reactants. All of the minimum-energy transition state conformers (shown in Figure 3) and product conformers are trans-isomers, with the R1 and R2 groups (Figure 2) located on opposite sides of the C=C bond formed in the reaction. In the cis-isomers, the R1 and R2 groups (Figure 2) are located on the same side of the C=C bond. This will, especially in the molecules with peroxy acid groups, create steric strain in the molecule. The zero-point corrected energy differences between the lowest-energy cis and trans conformers of the transition states are 0.72, 3.35, 1.89, and 5.51 kcal/mol for molecules a, b, c, and d, respectively. The ROHF-RCCSD(T)-F12a/VDZF12//ωB97xD/aug-cc-pVTZ zero-point corrected energies of the minimum energy conformers, including the cis-isomers, relative to the RO2 radicals are presented in Table 1. Table

1

Zero-point

corrected

ROHF-RCCSD(T)-F12a/VDZ-F12//ωB97xD/aug-cc-pVTZ

energies relative to the RO2 radical of both trans- and cis-isomers, in kcal/mol.

Alkyl radical + O2 Molecule a b c d

34.52 32.81 22.41 21.33

RO2 radical

0.00 0.00 0.00 0.00

Transition state Trans 30.75 25.59 25.28 22.87

Cis 31.47 28.95 27.17 28.56

Alkene···HO2 product complex Trans Cis 14.21 15.49 -

Alkene + HO2 Trans 19.18 15.92 10.11 11.72

Cis 20.41 17.65 11.84 16.62

The transition state energies for the H-shift forming a QOOH radical are all higher than those of the concerted HO2 loss. The barrier heights relative to the RO2 radical are 32.85, 34.23, 32.71


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and 35.42 kcal/mol for molecules a, b, c, and d, respectively. We can see that adding peroxy acid groups to the RO2 radical does not significantly affect the barrier height of this H-shift relative to the RO2 radical. The difference between the concerted HO2 loss barrier and the H-shift barrier for molecule a is only 2.09 kcal/mol, making the two-step H-shift reaction path potentially competitive for molecule a. For the other molecules the difference is several kcal/mol, making the two-step reaction path much less favorable than the concerted loss. The potential energy surfaces of the two-step reactions (Figure S1) and the absolute energies (Table S1) can be found in the SI. When the lowest-energy conformers of the trans-isomers were used in MESMER simulations using atmospheric pressure and a temperature of 298 K, the Bartis-Widom phenomenological rate coefficients of the concerted HO2 loss from peroxy radicals a, b, c and d are 4.57×10-10 s-1, 8.45×10-7 s-1, 2.16×10-6 s-1, and 1.05×10-4 s-1 respectively (see Table 2). The rate coefficients calculated by transition state theory are very close to the phenomenological rate coefficients computed by MESMER. Looking at the time profiles of each of the species in the reactions, we can also see that all four RO2 radicals are perfectly collisionally stabilized before the concerted HO2 loss reaction has time to occur, and the concerted HO2 loss reaction, and the two-step HO2 loss reaction, are thus far too slow to matter in the atmosphere at 298 K and 1 atm. Table 2 The Bartis-Widom phenomenological rate coefficients at 298 K and 1 atm, calculated with MESMER (kM), and the rate coefficients calculated using transition state theory (kTST). Molecule

a

b

c

d

kM (s-1)

4.57×10-10

8.45×10-7

2.16×10-6

1.05×10-4

kTST (s-1)

4.55×10-10

8.22×10-7

2.67×10-6

1.23×10-4


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The effects of the parameters in the MESMER simulations were further tested for molecule d, as it has the fastest reaction at atmospheric pressure, to see if varying the parameters within reasonable limits could lead to rate coefficients fast enough to be relevant (i.e. compete with bimolecular sinks) in the atmosphere. The rate coefficients increase with temperature, indicating that HO2 loss is the rate-limiting step of the overall reaction. The rate coefficient of HO2 loss starting from radical d + O2 reaches a value of 10-2 s-1 at a temperature around 340 K. Thus, this reaction could possibly play a minor role in very clean tropical boundary layer air, but not elsewhere in the atmosphere. The other molecules need even higher temperatures for the reaction to occur at comparable rate coefficients. The RO2 radicals derived from the oxidation of radicals a-d collisionally stabilize perfectly (i.e. the promptly reacted fraction is < 1 %) at bath gas pressures above around 10-2 atm, 10-1 atm, 10-6 atm, and 10-5 atm, respectively (Figure 5). Thus, a non-negligible fraction of RO2 radicals a and b might react promptly in e.g. stratospheric conditions, or low-pressure laboratory experiments. In the troposphere, where the total pressure is always above about 0.2 atm, the promptly reacted fraction is far too small to make HO2 loss a significant sink reaction. For molecules a and b, that have transition state energies below the alkyl radical + O2 reactants, from MESMER the order-of-magnitude of the timescale of product formation without collisional stabilization is 10-5 s and for molecules c and d, with transition state energies above the reactants, the timescale is 10-1 s.


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Figure 5 Fraction of the alkene product that forms promptly without collisional stabilization of the RO2 radical at 298 K. In order to test the effect of uncertainties in the energy calculations on the rate coefficient, at 298 K and 1 atm, the height of the transition state energy barrier was varied within 5 kcal/mol of the calculated barrier height. The rate coefficient changed with a factor of 5 for each 1 kcal/mol change in barrier height. The barrier height of the concerted HO2 loss of molecule d would have to be about 3 kcal/mol lower, for the rate coefficient to be above 10-2 s-1 at 298 K and 1 atm. This is much higher than the likely error margin of the CCSD(T)-F12 energy calculations. The Eckart tunneling factor is calculated from the forward and reverse barrier heights, and the imaginary frequency of the transition state. Increasing the reverse barrier height by 1 kcal/mol gave an increase of less than 2 % in the rate coefficient. The calculated ωB97xD/aug-cc-pVTZ level imaginary frequency of the concerted HO2 loss reaction transition state is for all the molecules around 1000 cm-1. Increasing the imaginary frequency of molecule d by 100 cm-1 gave around a 40 % increase in the rate coefficient. To get a rate coefficient of above 10-2 s-1 the imaginary frequency would have to be at least 1000 cm-1 higher than what has been calculated


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here. Such a large change is unlikely with calculations at the ωB97xD/aug-cc-pVTZ level, which give reaction profiles similar to the CCSD(T)-F12 calculations.45 A sensitivity analysis was also done on the Lennard-Jones coefficients and the ∆Edown value of the energy transfer model for molecule d. There was only a small change ( 90 %). Only molecule c has a faster HO2 loss reaction from the QOOH radical than the reverse reaction back to the RO2 radical, but the forward H-shift reaction from RO2 to QOOH (1.20×10-7 s-1) is much slower than the concerted HO2 loss reaction (2.16×10-6 s-1). The two-step HO2 loss phenomenological rate coefficients of the all the molecules are presented in Table S2 of the SI.

CONCLUSIONS We investigated the effect of peroxy acid groups on the phenomenological rate coefficients of HO2 loss from peroxy radicals (RO2). The presence of peroxy acid groups was found to lower the forward barrier of the concerted HO2 loss reaction with respect to the RO2 radical, but even with two peroxy acid groups present, the reaction is very slow under atmospheric conditions. The location of the peroxy acid groups in the molecules that were investigated here does not significantly affect the barrier height relative to the RO2 radical, but has a significant effect on the well-depth of the O2 addition (i.e. the formation energy of the RO2), and thus on the barrier height relative to the alkyl radical + O2 reactants. The well-depth of the O2 addition is larger if there is no peroxy acid group next to the carbon radical center of the alkyl radicals. Based on our MESMER simulations, the studied RO2 radicals, formed from the reactions of substituted sec-butyl radicals + O2, are all collisionally stabilized at pressures relevant to the troposphere. This implies that the rate coefficient for HO2 loss from these and larger RO2 radicals


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(such as those derived from the oxidation of biogenic hydrocarbons) is mainly controlled by the energy difference between the RO2 radical and the HO2 loss transition state, with the energy of the alkyl radical + O2 reaction playing a negligible role. The computed concerted HO2 loss rate coefficients at 298 K and 1 atm pressure are well below 10-3 s-1, and the two-step HO2 loss reaction is even slower, for all studied radicals. Either high temperatures (over 340 K even for the most reactive system in this study) or very low bath gas pressures are needed to increase the rate coefficient to 10-2 s-1. For all the studied systems, the fraction of RO2 radicals reacting promptly (and thus permitting HO2 loss on a sub-second timescale) is less than 1 % for any pressures encountered in the troposphere. Alternatively, the computed ROHF-RCCSD(T)F12a/VDZ-F12//ωB97xD/aug-cc-pVTZ barrier heights would need to be over 3 kcal/mol too high for the reaction to be competitive under atmospheric conditions. It therefore seems unlikely that the concerted HO2 loss reaction would be a significant reaction route for peroxy radicals formed in atmospheric autoxidation reactions from hydrocarbons with four or more carbon atoms.

ASSOCIATED CONTENT Supporting Information. Table S3. ωB97xD/aug-cc-pVTZ and ROHF-RCCSD(T)F12a/VDZ-F12 electronic energies and ωB97xD/aug-cc-pVTZ zero-point corrections of all minimum energy conformers and the cis-isomer transition state and product. Figure S1. Zeropoint corrected ROHF-RCCSD(T)-F12a/VDZ-F12//ωB97xD/aug-cc-pVTZ potential energies of the stationary points on the reaction path of the alternative HO2 loss. Table S2. Bartis-Widom rate coefficients of the two-step HO2 loss reaction under atmospheric conditions. Output files of


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ωB97xD/aug-cc-pVTZ optimizations and ROHF-RCCSD(T)-F12a/VDZ-F12 single-point calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Tel: +358 50 526 0123. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT We thank the Academy of Finland for funding. We thank CSC-IT Center for Science in Espoo, Finland, for computing time. REFERENCES (1) Zhang, R.; Suh, I.; Zhao, J.; Zhang, D.; Fortner, E. C.; Tie, X.; Molina, L. T.; Molina, M. J. Atmospheric New Particle Formation Enhanced by Organic Acids. Science 2004, 304, 14871490. (2) Paasonen, P.; Nieminen, T.; Asmi, E.; Manninen, H. E.; Petäjä, T.; Plass-Dülmer, C.; Flentje, H.; Birmili, W.; Wiedensohler, A.; Hõrrak, U.; et al. On the Roles of Sulphuric Acid and Low-Volatility Organic Vapours in the Initial Steps of Atmospheric New Particle Formation. Atmos. Chem. Phys. 2010, 10, 11223-11242.


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Table of Contents Graphic


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Figure 1 33x16mm (600 x 600 DPI)


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Figure 2 20x3mm (600 x 600 DPI)



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Figure 3 177x107mm (300 x 300 DPI)


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Figure 4 287x199mm (300 x 300 DPI)



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Figure 5 287x199mm (300 x 300 DPI)


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Page 35 of 35 The Journal of Physical Chemistry

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Unimolecular HO2 Loss from Peroxy Radicals Formed in Autoxidation

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