Reaction between Peroxy and Alkoxy Radicals Can Form Stable Adducts

Peroxy (RO2) and alkoxy (RO) radicals are prototypical intermediates in any hydrocarbon oxidation. In this work, we use computational methods to (1) study the mechanism and kinetics of the RO2 + OH reaction for previously unexplored “R” structures (R = CH(O)CH2 and R = CH3C(O)) and (2) investigate a hitherto unaccounted channel of molecular growth, R′O2 + RO. On the singlet surface, these reactions rapidly form ROOOH and R′OOOR adducts, respectively. The former decomposes to RO + HO2 and R(O)OH + O2 products, while the main decomposition channel for the latter is back to the reactant radicals. Decomposition rates of R′OOOR adducts varied between 103 and 0.015 s–1 at 298 K and 1 atm. The most long-lived R′OOOR adducts likely account for some fraction of the elemental compositions detected in the atmosphere that are commonly assigned to stable covalently bound dimers.

O rganic peroxy radicals (RO 2 ) produced from the oxidation of volatile organic compounds (VOCs) are known to play an important role in, for example, trace gas removal, generation of ozone, and the formation of secondary organic aerosol (SOA) in the atmosphere. 1−4 An important sink pathway of RO 2 in polluted environments is the reaction with NO, which leads to the formation of NO 2 . NO 2 subsequently photolyzes in the atmosphere and leads to the net formation of one ozone (O 3 ) molecule. In unpolluted areas, RO 2 is mainly lost to reactions with the hydroperoxy radical (HO 2 ) and with other peroxy radicals. Unimolecular H-shift isomerization reactions can outcompete these bimolecular reactions for certain RO 2 . 5,6 Alkoxy radicals (RO) are products of RO 2 + RO 2 and RO 2 + NO reactions. An additional RO source is the photolysis of peroxides. 7 Sink pathways of alkoxy radicals in the atmosphere include reaction with O 2 , leading to the formation of a carbonyl compound and HO 2 , isomerization via intramolecular hydrogen shifts, and decomposition via bond fission.
Recently, multiple theoretical and experimental studies have reported that the RO 2 + OH (hydroxy radical) reaction could be a significant sink channel for peroxy radicals under remote conditions, such as in the marine boundary layer. 8−16 This reaction for methyl peroxy radical is reportedly quick, with a rate coefficient of 1.6 × 10 −10 cm 3 s −1 at 295 K. 11 The fast reaction rate partially compensates for the relatively lower concentrations of OH compared to the HO 2 radical, and the RO 2 + OH reaction may thus compete with the RO 2 + HO 2 reaction whenever the HO 2 /OH ratio is low. Studies on larger C 2 to C 4 alkyl peroxy radicals found the RO 2 + OH reaction rate coefficient to be 1.3− 1.5 × 10 −10 cm 3 s −1 . 17 Studies on CH 3 O 2 + OH 13,14 and C 2 H 5 O 2 + OH 15 show that these reactions proceed almost exclusively via the barrierless formation of a ROOOH trioxide intermediate on the singlet surface, with RO + HO 2 being the lowest-energy fragmentation channel. This is in agreement with the observed 80% HO 2 yield for the CH 3 O 2 + OH reaction. 18 For peroxy radicals CH 3 OO, CH 3 CH 2 OO, CH 3 CH 2 CH 2 OO, and CH 3 CH 2 CH 2 CH 2 OO, the increase in the "R" size corresponded to a decrease in HO 2 yield (0.9, 0.75, 0.41, and 0.15, respectively) in the experimental study of the RO 2 + OH reaction reported by Assaf et al. 19 This points to more efficient stabilization of the larger ROOOH intermediates. Similar mechanistic studies for nonalkyl peroxy radical types have not been carried out. In this work, the kinetics of the RO 2 + OH reactions are inspected also for the carbonyl containing acetyl and β-oxo peroxy radicals. Differences in RO 2 structures have previously been observed to significantly alter product branching ratios. Hasson et al., 20 for example, reported a strong structure dependence for the different product channels of the RO 2 + HO 2 reaction, where "R" is either an alkyl, acetonyl, or acetyl group.
Like RO 2 and HO 2 , RO and OH often have similar or analogous reactivities, and one can postulate that the R′O 2 + RO reaction should go through a similar trioxide adduct (R′OOOR in this case) as the RO 2 + OH reaction. The atmospheric importance of the R′O 2 + RO reaction depends on the steadystate RO concentration, which is generally assumed to be small due to the high loss rates of alkoxy radicals. Considering an effective RO loss rate between 1 × 10 6 and 1 × 10 3 s −1 , together with atmospherically representative values for the RO source terms, we obtain an ambient RO concentration range from 2 to 1 × 10 5 molecules cm −3 (see section S6 for details). If the formation of the R′OOOR adducts is fast and they are sufficiently stable, they could thus constitute a fraction of the low-volatility organic compounds in the atmosphere referred to as dimers. 1,21,22 Recently, R′OOOR formed via a R′O 2 + RO reaction was tentatively suggested 23 as the mechanism involved in the formation of C 19 H 28 O 11 , a major dimer peak reported in multiple nitrate chemical ionization mass spectrometry-based laboratory and ambient studies of α-pinene ozonolysis. 1,24−27 Additionally, the R′O 2 + RO reaction along the triplet surface could potentially lead to low barrier product channels, forming, for example, Criegee intermediates (CI; denoted by R −H ′ • OO • in reaction 2) that play a critical role in the oxidative capacity of the atmosphere and in SOA formation. 28−31 The possible reaction channels of R′O 2 + RO are We considered 2-carbon CH 3 CH 2 OO, CH(O)CH 2 OO, and CH 3 C(O)OO peroxy/alkoxy radicals (see Figure 1 for the RO 2 systems; the RO systems were identical except for an oxy radical group instead of a peroxy radical group). For the RO 2 + OH reaction, only CH(O)CH 2 OO and CH 3 C(O)OO systems were studied here as CH 3 CH 2 OO has already been investigated in detail previously. 15 On the singlet surface, the decomposition of the β-oxo CH(O)CH 2 OOOH adduct primarily follows the CH(O)CH 2 O + HO 2 channel (see section S1 for details), which is analogous to the previously studied alkyl CH 3 CH 2 OOOH. 15,18,19 However, the acetyl CH 3 C(O)OOOH adduct will rather decompose into CH 3 C(O)OH + 1 O 2 as this channel has a low barrier. Total firstorder decomposition rates of CH(O)CH 2 OOOH and CH 3 C-(O)OOOH adducts were calculated using the master equation solver for multienergy well reactions (MESMER) program and were found to be 2.7 × 10 −3 and 1.9 × 10 3 s −1 , respectively.
Formation of the adducts is unfavorable on the triplet surface for both sets of reactions (see Figure S5). The reaction stationary points with the energies of the different breakup channels on the singlet and triplet surfaces and the MESMER-simulated pressure and temperature dependencies of the ROOOH formation rate coefficients are provided in section S1.
Similarly to the RO 2 + OH reaction, R′O 2 + RO also forms a trioxide adduct (R′OOOR, in this case) on the singlet surface for the studied systems. A relaxed scan over the R′OO···OR bond showed that this reaction is barrierless, at least at the ωB97X-D/ 6-31+G(d) level of theory (see section S8 for details). The adduct can then decompose in four ways, illustrated in reactions 1 (back to parent reactants), 2, 3, and 4 (the possible product channels). Figure 2 shows the stationary points of the R′O 2 + RO reaction on the singlet surface. The reactants can also form a CI and an alcohol directly. However, this reaction has a barrier of ∼2 kcal/mol and higher in zero-point-corrected energy (∼12 kcal/mol in free energy) for the studied systems and is therefore unlikely to compete with the formation of the R′OOOR adduct. Details of this reaction are provided in section S2. We note that CH(O)CH 2 OO will undergo a fast 1,4-aldehydic H-shift 6 and that the decomposition of the CH 3 C(O)O acetyloxy radical to form CH 3 and CO 2 has a very small barrier. 7 Especially the CH 3 C(O)O radical will therefore not live long enough to undergo bimolecular reactions in the atmosphere. The two systems are nevertheless included here for completeness and to demonstrate the effect of reactant structure on the product channels. Other β-oxo peroxy and acetyloxy radicals could have longer lifetimes, and their participation in bimolecular reactions cannot be ruled out.
The R′OOOR adducts are significantly lower in energy relative to the reactants on the singlet surface. Considering the high reactivity of RO radicals and that the reaction was found to be barrierless, the formation of the R′OOOR adduct is likely facile for all atmospherically relevant RO + RO 2 combinations. While the decomposition channels of the ROOOH adduct had barriers that were mostly below the reactant energies (and therefore more likely to be competitive; see Figure S1), the transition state energies connecting the two breakup channels of R′OOOR illustrated in reactions 2 and 3 were above the reactant energy for all cases (except for the β-oxo-acetyl case, which had a barrier of −0.5 kcal/mol relative to the reactants for reaction 2; see Figure 2b). The barrier heights for reactions 2 and 3 are ∼23−32 and ∼33−37 kcal/mol above the R′OOOR intermediate, respectively, for all studied systems. These are therefore not competitive with decomposition back into R′O 2 + RO (or R′O + RO 2 ). The Criegee-forming channel via the trioxide intermediate (reaction 2) was found to have a relatively low barrier (23−24 kcal/mol relative to the trioxide

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Letter intermediate) for the acetyl-β-oxo and acetyl-alkyl systems. This is due to the added flexibility afforded by the carbonyl oxygen of the acetyl molecule to the H-shift transition state geometry (see Figure S8). The transition state corresponding to reaction 3 requires contortion of the trioxide group, and the barrier involved is significantly higher.
The MESMER-simulated total first-order R′OOOR loss rate coefficients and the likely decomposition channels are shown in   Figure 3. RO 2 was assigned as the excess reactant and given a value of 1 × 10 9 molecules cm −3 in the simulations as this was calculated to be a roughly representative steady-state peroxy radical concentration in both pristine and polluted conditions (see section S6 for details). Figure 4 shows the first-order R′OOOR decomposition rate coefficients via the different possible channels. The pressureand temperature-dependent formation rate coefficient of the   Figure 5. Similar plots for the remaining studied systems are provided in section S2. The stationary points on the triplet surface for the studied systems are shown in section S5. Analogous to ROOOH, the formation of R′OOOR adducts was found to be highly unfavorable on the triplet surface.

R′OOOR intermediate for the CH(O)CH 2 OO + CH(O)-CH 2 O system is shown in
Of the studied cases, the fastest R′OOOR decomposition rates corresponded to systems where one of the reacting radicals is of the acetyl type and the other is of either an alkyl or β-oxo type (see Table 1). In these cases, the stability of the R′OOOR intermediate is relatively low, leading to rapid decomposition back into R′O 2 + RO (or R′O + RO 2 ) (see Figure 2a,b and Table  1). This is likely due to the resonance stabilization of the acetyloxy radical, which lowers the energy of this product channel. When both reactant radicals are of the acetyl type, the only decomposition channel possible for the R′OOOR intermediate is back into the parent reactants (shown in Figure  2c) as the acetyl RO 2 can form neither a CI nor an aldehyde (due to the lack of H-atoms on the carbon atom containing the radical group). Note that CH 3 C(O)OO + CH 3 C(O)O will never occur in the atmosphere as the barrier for the decomposition of this acetyloxy radical into CH 3 and CO 2 has a barrier of only about ∼3 kcal/mol in zero-point corrected energies. 7 The R′OOOR formed from the homo and hetero alkyl/β-oxo systems (see Figure 2d−f) is significantly more stable, and the rate of decomposition back to R′O 2 + RO (or R′O + RO 2 ) is accordingly slower (see Table 1). The most stable R′OOOR intermediate was found for the β-oxo-β-oxo system, which has a decomposition rate (at 298 K and 1 atm) of 1.5 × 10 −2 s −1 . The stability of R′OOOR adducts is thus in line with that of the analogous species R′OOR and R′OOOOR. While reactive, the former can have room-temperature lifetimes on the order of weeks or more, whereas the latter have been postulated since 1957 to be intermediates of RO 2 + RO 2 reactions but have such short lifetimes that they have, to our knowledge, never been experimentally detected. 32,33 On the triplet surface, the R′O 2 + RO product channels have significant barriers (see section S5). Similarly to the RO 2 + OH reaction (section S1), reactions on the triplet surface would need to be essentially barrierless to be competitive with the rapid formation of the trioxide intermediates on the singlet surface. Given the calculated barrier heights reported here (several kcal/ mol in zero-point corrected energy and over 10 kcal/mol in free energy), none of the studied product channels on the triplet surface are likely competitive.
Our results indicate that the R′O 2 + RO reaction is a source of stable R′OOOR adducts. We estimated that the ambient steadystate concentrations of the adducts can range from 30 to 3 × 10 4 molecules cm −3 (see Table S5). Their stability was found to be strongly dependent on the structure of the reacting radicals that were considered, with decomposition rates ranging from a high of ∼50−100 s −1 for acetyl-alkyl and acetyl-β-oxo systems, respectively, and a low of ∼0.2−0.02 s −1 for the others. The binding energies (relative to R′O + RO 2 and RO + R′O 2 ) of R′OOOR adducts were computed at the ωB97X-D/6-31+G(d) level for a series of larger (4−10 C-atoms) RO and RO 2 generated in the oxidation of representative anthropogenic and biogenic VOC molecules (see section S7). The computed R′OOOR stabilities were similar to those for the systems studied here (recomputed at the same level), indicating that the lifetimes of larger R′OOOR are also likely to be on the order of 10−100 s, in some cases (e.g., cyclohexene ozonolysis) possibly even higher. These stabilized adducts could therefore constitute a fraction of the low-volatile dimer compositions reported in ambient mass spectrometry measurements and are consequently important in SOA formation.

Quantum Chemical Calculations.
To calculate the stationary points of the studied reactions, a systematic conformer search was performed for each system using MMFF 34−39 implemented in the Spartan '14 program. 40 For the reactant and product systems in the RO 2 + OH reaction, all conformers were optimized directly using density functional theory (DFT) at the ωB97X-D/aug-cc-pVTZ 41−43 level due to the limited number of available conformers. For the R′OOOR intermediate complexes of the R′O 2 + RO reaction, however, the conformers were first optimized at the lower DFT B3LYP/6-31+G(d) level, 44−48 and those within 2 kcal/mol in relative electronic energies were selected for the higher-level optimization at the ωB97X-D/augcc-pVTZ level with the ultrafine integration grid. The transition state geometries connecting the different product channels studied here were found by performing a relaxed scan over the bond lengths of the appropriate atoms at the B3LYP/6-31+G(d) level of theory. The initial transition state optimization, as well as the intrinsic reaction coordinate

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Letter (IRC) calculations to confirm that the transition states connected to the correct product channels, were performed at the same level. The transition states were subsequently reoptimized at the ωB97X-D/aug-cc-pVTZ level of theory. The electronic energies of the lowest-energy conformers of all reactants, intermediates, transition states, and products were corrected using ROHF-RCCSD(T)-F12a/VDZ-F12 singlepoint energies calculated with the Molpro program. 49 We note that the ROHF-RCCSD(T)-F12a/VDZ-F12 correction to the formation energies of ROOOH and R′OOOR adducts were significant, making their formation more exergonic by ∼4 and ∼7−8 kcal/mol, respectively, relative to pure DFT energies.
RRKM Calculations. The master equation solver for multienergy well reactions (MESMER) program 50