Molecular rearrangement of bicyclic peroxy radicals is a key route to aerosol from aromatics

Domain: earth_science
Published: 2023-08-17
Editorial outcome: accept

Abstract
The oxidation of aromatics contributes significantly to the formation of atmospheric aerosol. Using toluene as an example, we demonstrate the existence of a molecular rearrangement channel in the oxidation mechanism. Based on both flow reactor experiments and quantum chemical calculations, we show that the bicyclic peroxy radicals (BPRs) formed in OH-initiated aromatic oxidation are much less stable than previously thought, and in the case of the toluene derived ipso-BPRs, lead to aerosol-forming low-volatility products with up to 9 oxygen atoms on sub-second timescales. Similar results are predicted for ipso-BPRs formed from many other aromatic compounds. This reaction class is likely a key route for atmospheric aerosol formation, and including the molecular rearrangement of BPRs may be vital for accurate chemical modeling of the atmosphere.

Introduction
Aromatic hydrocarbons are an important class of atmospheric trace gases. The global emissions of the most important aromatic molecules, benzene, toluene, ethylbenzene and xylenes (collectively known as BTEX), account for 23% of the global anthropogenic non-methane hydrocarbons on a per-carbon basis1 and up to 60% of the urban emissions2,3. Their sources are primarily anthropogenic, such as from incomplete combustion, industrial processes, and solvent evaporation4–9. Recent studies have shown that biogenic sources of BTEX, such as from terrestrial vegetation and from marine phytoplanktons, are also important10–12, and they have even been measured in the remote Southern ocean and in the arctic13,14. Aromatic hydrocarbons in the gas phase pose serious health risks directly15–18 and also indirectly as their secondary chemistry can lead to tropospheric ozone and secondary organic aerosol (SOA) production19–23. The latter can have implications on the planet’s radiative balance by affecting the formation and properties of clouds, but significant uncertainties remain regarding the extent of these radiative effects24–26.

In order to form SOA, participating vapors need to have sufficiently low volatility, which in practice implies molecules with multiple oxygen-containing polar functional groups. Autoxidation27 has been shown to efficiently form SOA from various aliphatic VOCs, and the molecular level mechanism has been fairly well established for a few key aliphatics28–31. Laboratory studies show that aromatics also autoxidize and form SOA efficiently22, but all presented molecular level aromatic oxidation mechanisms are far too slow to explain observations. This is a problem because the accurate modeling of SOA from aromatics requires accurately predicting the paths that lead to SOA.

The oxidative chemistry of aromatic hydrocarbons is mainly initiated by OH radicals. In a majority of cases, the reaction of OH with BTEX molecules involves addition to the aromatic ring, with H-atom abstraction playing a minor role at atmospherically relevant temperatures32. For toluene, OH addition to the ortho position accounts for 69.8%, followed by ipso, para and meta additions (7.3%, 5.1%, 5.1%, respectively)33. The addition reaction leads to the formation of the bridged bicyclic peroxy radical (BPR34) as a major product. The critical early steps of toluene oxidation by OH addition are described in Supplementary Section 2. The formation of the BPR from toluene oxidation is considered to be a mechanistic branching point as it has so far been thought to require bimolecular reaction partners to further oxidize due to slow unimolecular reaction rate coefficients (<0.03 s−1 35). This is due to the double-ringed structure that sterically hinders both intramolecular H-shift and ring closure reactions forming endoperoxides. In contrast to this mechanistic understanding, flow reactor measurements at 7.9 s reaction time show that the initially formed BPR will quickly add several more oxygen atoms to form peroxy radicals with up to 9 oxygen atoms35. These discrepancies suggest an alternative unimolecular fate of the BPR that is both rapid and completely neglected in previous studies.

In this work, we conclusively demonstrate that the toluene derived ipso BPR (i-BPR) is unstable under atmospheric conditions, and undergoes spontaneous molecular rearrangement. This reaction leads to completely ring broken RO2s, a prerequisite for efficient autoxidation, at rates competitive with bimolecular reactions with NO even under polluted conditions. Intriguingly, several of the organo nitrates and other closed shell products derived from the i-BPR are likewise unstable and decompose on regional atmospheric transport timescales. This could provide, e.g., a transport reservoir for NOx similar to peroxyacyl nitrates (PAN). Using quantum chemical calculations and master equation simulations that account for energy non-accommodation, we elucidate the molecular level mechanism of the subsequent autoxidation of the ring broken RO2s that leads rapidly to the highly oxygenated SOA precursor molecules with up to nine oxygen atoms in sub-second timescales. Furthermore, using targeted flow reactor experiments of the OH reaction of toluene and partially deuterated toluene with nitrate chemical ionization mass spectrometry (NO3-CIMS) detection, we corroborate the proposed mechanism. This is the only unambiguous reaction pathway to toluene derived SOA precursors reported to date.

Results
Spontaneous molecular rearrangement of i-BPR
The rearrangement of i-BPR occurs by the concomitant cleavage of a C-C bond and the O-O bond, along with an H-shift (see Fig. 1a) to lead to a completely ring broken RO2 with two carbonyl (=O) groups and one hydroxyl (−OH) group. Two rearrangement pathways are possible, C1 and C2, depending on which of the two C-C bonds are broken. Relative to the i-BPR, the energy barriers for C1 and C2 are 18.8 kcal/mol and 17.9 kcal/mol, respectively, and the energies of the ring broken RO2s, P-C1 and P-C2, are −51.7 kcal/mol and −49.4 kcal/mol, respectively. All energies reported here are zero-point corrected energies. At P = 1 atm and T = 300 K, the unimolecular rate coefficients of the two pathways are 0.16 s−1 and 0.59 s−1, respectively, which are competitive with RO2 bimolecular reactions with NO even under heavily polluted conditions. The predicted rate coefficients as a function of temperature are shown in Fig. 1b. Toluene derived BPRs with OH in the ortho, meta and para positions can also undergo the two rearrangement mechanisms, but they are significantly slower and follow the trend of ipso > meta > para > ortho. The rearrangement rate coefficients for meta, para and ortho BPRs are provided in Supplementary Table 7. In addition to being an order-of-magnitude faster than any previously reported isomerization reaction of a toluene derived BPR, the significant exothermicity of the formation of the products mean that the rearrangement reactions are irreversible. This is important since some of those previously reported isomerization reactions of BPR, specifically H-shift reactions, were reversible with reverse rate coefficients that are competitive with the bimolecular recombination reactions with O2 under atmospheric conditions35.

Subsequent autoxidation of ring broken peroxy radicals from i-BPR
Both molecular rearrangement mechanisms of i-BPR are expected to occur, leading to the two ring broken RO2s from i-BPR, P-C1 and P-C2. These will subsequently autoxidize rapidly in the absence of the steric hindrance of structural rings, as we have shown previously for the α-pinene ozonolysis system28. Master equation simulations also show that the excess energy carried by P-C1 and P-C2 allows them to access multiple autoxidation pathways simultaneously. Figure 2 shows the master equation simulation derived initial yields of P-C1 and P-C2, and the yields of the three intermediates formed from the lowest energy barrier autoxidation pathways of P-C2: R1, R2 and R3. The corresponding intermediates from P-C1 were also included in the master equation simulation, but are excluded in Fig. 2. The three autoxidation pathways of P-C2 are shown with differently colored arrows for clarity. Green is the dominant pathway (59%) because the 1,6 H-shift leading to the alkyl radical R1 has the lowest energy barrier. R1 can either react with O2 to lose HO2 and form the carbonyl compound C7H8O5, or add an O2 to form the peroxy radical R1b-RO2. R1b-RO2 will isomerize via a 1,6 H-shift to form the R1b-OOH-vinoxy radical, that subsequently adds an O2 to form the O9-RO2 C7H9O9. The branching between the carbonyl and peroxy radical pathways is estimated in Supplementary Section 8. The pathway indicated by blue arrows has the next highest yield (16%), and can lead to the O9-RO2 C7H9O9. Finally, the pathway with red arrows has the lowest initial yield, but can subsequently isomerize rapidly to form the O7-RO2 C7H9O7 (R3-Epo-RO2), followed by a 1,5 H-shift with a relatively slower rate coefficient to form the O9-RO2 (R3-Epo-OOH-R"O). R2 and R3-Epo-R’ both have small reverse barriers, but the yield of R3-Epo-RO2 is nevertheless likely to be high due to the excess energy of P-C2 as shown in our simulations (see Supplementary Section 12). Note that the last radical intermediates shown for each of the three pathways can continue to autoxidize to form even higher oxygenated products. Due to difficulties in accurately treating the transition states of H-shift reactions from hydroxy groups computationally (see Methods and ref. 31), the yield of R3 was calculated at a lower level of theory. Therefore, the final yields of R1, R2 and R3 shown in Fig. 2 likely have high uncertainties.

Experimental results
NO3-CIMS coupled to a flow reactor was used to explore the formation of the oxidized products from the reaction of OH with toluene and the partially deuterated CD3-toluene, where the methyl H-atoms are substituted with D-atoms. Experiments carried out at the short residence times (RT) of 0.8–3.7 s, show that C7H9O9 (O9-RO2) with the nominal mass-to-charge ratio of 299 Th is rapidly formed. It is the dominant product peak already at 1.5 s RT, likely due to a combination of two factors: 1) its accumulation at short residence times and 2) the higher sensitivity of the NO3-CIMS for the higher oxygenated products36. The recorded spectra and product signals during the 0.8 and 1.5 s RT experiments are shown in Supplementary Figs. 1, 2, while Fig. 3 shows the same during the 3.7 s RT experiment. Even higher oxygenated C7H9O11 RO2 was also detected at this RT, albeit at much lower signal.

The rapid formation of O9-RO2 agrees with the proposed mechanism from our quantum chemical calculations. Identical results are observed for the partially deuterated CD3-toluene system, which is in line with the proposed mechanism where the methyl group plays no role in the formation of the oxidized products. This is in disagreement with the previous mechanistic understanding where Wang et al. showed that the only unimolecular reaction that could potentially be competitive under atmospheric conditions is the H-abstraction from the methyl group for the toluene derived BPR with OH in the para position35. They also reported that the subsequent peroxy radical will quickly lose the abstracted methyl H-atom to OH loss with a rate coefficient of 8 s−1 at 298 K, forming a closed-shell carbonyl compound. However, their computed rate coefficient of 0.026 s−1 for the H-abstraction would indicate that bimolecular reactions with NO is likely the dominant sink of the BPR. It is also not sufficiently fast to completely explain their measurement of the 9-oxygen containing RO2 (O9-RO2) from toluene + OH at their 7.9 s experimental residence time. Nevertheless, if this is the dominant fate of the toluene + OH system in our experiments, it would compete with the mechanism proposed in this study. However, our CD3-toluene experiments showed that the dominant closed-shell and peroxy radical products detected contained all three D atoms (see Supplementary Fig. 11), indicating that the mechanism proposed in this work is likely to be the dominant unimolecular pathway to the SOA precursors that we detect. Note that D-shift rates are slower than H-shift rates due to isotope effects, in particular lower tunneling factors, so the use of CD3-toluene will to an extent underestimate the role of H-shift from the methyl group. However, we observe that the mass spectra for toluene and CD3-toluene are near identical, indicating that H-shift from the methyl group is unlikely to play a major role in our experiments. Nevertheless, this pathway might well be important under certain atmospheric conditions. The methyl H-abstraction pathway reported in ref. 35 and the rearrangement pathway reported here do not compete with each other but depend on the site of the initial OH addition to toluene (para vs ipso relative to the methyl substituent). D2O experiments revealed that the dominant peak corresponding to O9-RO2 contains only two exchangeable H-atoms. This is more consistent with the mechanism we propose because the formed O9-RO2 via the dominant green pathway in Fig. 2 has two groups with exchangeable H-atoms. Following the previously proposed mechanism, RO2 with three exchangeable H-atoms should form, which is not the case. The blue pathway in Fig. 2 does lead to a O9-RO2 with three exchangeable H-atoms, but likely due to its fast isomerization reaction (~230 s−1) rapidly forms O11-RO2, and is not measured. In addition, the D2O experiments also indicated two isomers of the O7-RO2, with one and two D-atoms, respectively (see Supplementary Figs 14, 15). While the latter is expected in previous and in our mechanisms, the former can occur if the autoxidation follows the red pathway in Fig. 2 that leads to an O7-RO2 with one exchangeable H-atom. Note that autoxidation is known to produce many isomers and the pathways shown in Fig. 2 are not the only autoxidation pathways occurring in our measurements. However, these are the only pathways that can currently explain the observed H-to-D shifts in the isomers we measure. Details of the D2O experiments are provided in Supplementary Section 5.

To confirm that these compounds are in fact peroxy radicals, NO was added to form the corresponding organo nitrate (RONO2) products. These experiments clearly illustrated the occurrence of the expected organo nitrates (see Supplementary Figs 12, 13). Reactions of peroxy radicals with NO can also lead to alkoxy radicals and the molecule can continue to oxidize via the alkoxy-peroxy autoxidation pathway. However, the resulting peroxy radicals will have an even number of oxygen atoms and not odd as the peroxy radicals involved in the formation of the organo nitrates reported in this study. The peroxy radicals are unlikely to undergo two NO reactions to revert to an odd number of oxygen atoms followed by a third NO reaction to produce the organo nitrates we detect under the short residence time conditions of our experiments.

The evolution of the oxidation products in the flow tube measurements was also modeled using the Aerosol Dynamics gas- and particle-phase chemistry model for laboratory CHAMber (ADCHAM) studies37. This model couples the i-BPR rearrangement pathways described in this work with the conventional Master Chemical Mechanism chemistry of toluene, and achieves a reasonable agreement with the flow reactor data despite the usage of lumped rate coefficients and uncertain branching ratios for the different pathways in toluene oxidation. Details are provided in Supplementary Section 9.

Universal rearrangement mechanism of aromatics
Quantum chemical calculations indicate that similar rearrangement mechanisms are key players in aromatic oxidation in general. Figure 4 shows the rate coefficients of the fastest of the two possible rearrangement mechanisms, C1 and C2 as shown in Fig. 1a, for select key aromatics. Like toluene, the rearrangement mechanism for the other studied aromatic molecules is fastest for i-BPRs, and for molecules, such as meta-xylene and isopropylbenzene, the rate coefficient is in excess of 1 s−1. For all studied aromatic molecules, the rearrangement mechanism of i-BPRs is their dominant loss process under most atmospheric conditions, and will lead to ring broken RO2s that carry significant excess energy. The subsequent autoxidation of such RO2s will be different from what is currently known, as has been demonstrated here for toluene. Modeling the SOA formation from these aromatic molecules will therefore necessitate the study of their molecular rearrangement mechanisms, and the role of excess energy in their autoxidation. The findings of this study will be a crucial starting point for similar studies on the oxidation of other aromatic molecules, and also for other VOC systems containing structures that could be prone to similar rearrangements (e.g., biogenic terpenes with several cyclic structures and unsaturated sites).

Atmospheric perspective of the molecular rearrangement mechanism
Field and laboratory measurements show that the oxidation processes of aromatic molecules in general, and toluene in particular, yield SOA. However, the autoxidation mechanism leading unambiguously from toluene+OH to SOA precursors has not been reported thus far. A key challenge for establishing such a mechanism is that bicyclic peroxy radicals from toluene are sterically prevented from taking part in autoxidation. The molecular rearrangement mechanism is the dominant fate of toluene derived i-BPR, and leads directly, and in substantial yield, to hitherto undiscovered peroxy radicals P-C1 and P-C2 without steric constraints. These peroxy radicals have access to fast unimolecular reaction channels, and to significant excess energy, allowing them to form peroxy radicals with up to nine oxygen atoms in sub-second timescales and via multiple concurrent autoxidation channels.

Our calculations also show that the molecular rearrangement mechanism is operative for bicyclic organo nitrates, and lead to organo nitrates that are completely ring broken (see Supplementary Section 7). In some cases, they can subsequently lose NO2 and convert back to a radical. This could re-initiate autoxidation and provide a transport mechanism for NOx, similarly as PAN do.

The molecular rearrangement mechanism reported in this work explains the rapid formation of highly oxidized organic products in one of the most important urban SOA-forming systems, toluene+OH, with potential relevance also for other atmospherically abundant aromatic molecules.

Methods
Systematic conformer sampling of the reactants, intermediates, transition states and products studied here were performed using the MMFF method in Spartan’18 (Wavefunction, Inc.) program. Radical oxygen and carbon atoms in open-shell systems were assigned as uncharged by using the keyword FFHINTOn=+-0 for oxygen atoms and FFHINTCn=+-0, respectively, where n is the atomic label of the relevant O or C atoms. For the non-transition state systems, the initial geometry optimization was carried out using the density functional theory (DFT) method B3LYP/6-31+G(d). For the ring broken systems with many tens to hundreds of possible conformers, a single-point energy calculation was carried out using the B3LYP/6-31+G(d) method, and conformers within 5 kcal/mol in relative electronic energies of the lowest-energy conformers were carried over for the geometry optimization step at the same level of theory. Conformers within 2 kcal/mol in relative electronic energies after the geometry optimization step at B3LYP/6-31+G(d) were re-optimized at the higher ωB97X-D/aug-cc-pVTZ level of theory. Frequencies were also calculated using this method. These computations were performed with the ultrafine grid using the Gaussian 16 program38. Finally, only a single lowest energy conformer for each reactant, intermediate, and product was taken for the final energy refinement step at the ROHF-ROCCSD(T)-F12a/VDZ-F12 level performed using the Molpro 2021.2 and Molpro 2022.2.2 programs39.

For the transition states (TS), the geometries were first optimized with the bonds relevant for the TS constrained at approximate distances, followed by unconstrained transition state calculations. Both calculations were carried out at the B3LYP/6-31+G(d) level of theory. Once the TS geometry was found, the structure was taken to Spartan’18 (Wavefunction Inc.). Partial bonds were added to the TS relevant bonds and the distances constrained, and a conformer sampling step was performed using the MMFF method. If the number of conformers numbered in the tens, the single-point energy calculation at the B3LYP/6-31+G(d) was performed, and structures within 5 kcal/mol in relative electronic energies were taken for the optimization step. The constrained and unconstrained TS optimizations were repeated, this time for multiple conformers, at the B3LYP/6-31+G(d) level of theory. Transition state conformers within 2 kcal/mol in relative electronic energies were carried over for TS optimization at the ωB97X-D/aug-cc-pVTZ level of theory. For each studied TS, the energy of the lowest energy conformer was refined at the ROHF-ROCCSD(T)-F12a/VDZ-F12 (abbreviated F12) level of theory.

Rate calculations using multi-conformer transition state theory (MC-TST)
The rate-coefficients of the autoxidation steps of the ring broken peroxy radicals were calculated using the MC-TST method with Eckart tunneling40,41. The MC-TST expression is given by the following:

k = \kappa \frac{k_B T}{h} \frac{\sum_i Q_{TS,i} \exp(-\Delta E_i / k_B T)}{\sum_j Q_{R,j} \exp(-\Delta E_j / k_B T)} \exp(-E_R / k_B T) (1)

Here, κ is the quantum-mechanical tunneling coefficient, T is the absolute temperature (=298.15 K), kB is the Boltzmann’s constant and h is the planck’s constant. QR,j and QTS,i are the partition functions of the reactant and transition state conformers j and i, respectively, and ΔEj and ΔEi are the zero-point corrected electronic energies of the reactant and transition state conformers relative to the lowest energy conformers, respectively. ER and ETS are the zero-point corrected electronic energies of the lowest energy reactant and transition state conformers. Partition functions were calculated using DFT at the ωB97X-D/aug-cc-pVTZ level of theory, while the reaction barrier (ETS-ER) includes the F12 correction. Only those conformers that are within 2 kcal/mol of the lowest energy conformer at B3LYP/6-31+G(d) level of theory are included in the summations in the numerator and denominator, which has been reported to be adequate40.

The Eckart approach was used to calculate the tunneling coefficient κ40,41. Briefly, it is based on the conformers connected to the lowest energy TS conformer by an intrinsic reaction coordinate. Barriers are calculated at the F12 level of theory, while the imaginary frequency of the TS is calculated at the ωB97X-D/aug-cc-pVTZ level of theory. Because of issues with the HF calculations converging to different possible solutions, transition state energies for H atom abstraction from -OH and -OOH groups were calculated at the ωB97X-D/aug-cc-pVTZ level of theory (without F12 corrections). Møller et al.31 estimate that the uncertainty in the rate coefficients would increase to a factor of 100 without the F12 single-point energy corrections. This is relevant for the rate coefficients of the H-abstractions leading to intermediates R1b-OOH-vinoxy, R2b-RO2, and R3 in Fig. 2.

Wavefunction stability
The stabilities of the wavefunctions of the two molecular rearrangement transition states of toluene derived i-BPR were checked at the CCSD(T) stage. This was done to ensure that the lowest lying wavefunction was found. First, a CASSCF calculation was carried out with the MINAO basis set, and with the 1s and 2s orbitals of the heavy (non-H) atoms frozen. Included in the active space were, all occupied p-orbitals/electrons of H atoms, the one half-occupied orbitals for radicals, and one virtual (unoccupied) orbital to allow for rotations within the active space. This is then used as input for the RHF calculation with the larger desired basis set. These calculations were carried out with the Molpro 2022.2.2 program39. This is a much more robust approach for checking wavefunction stability than e.g., the standard Stable=Opt check in Gaussian. An example input file is provided in the supplementary files.

Master equation simulations
The master equation solver for multi-energy well reactions (MESMER) program42 was used to carry out the master equation simulations. The Simple RRKM method with Eckart tunneling was used to calculate the rate coefficients of the rearrangement reactions, C1 and C2, of toluene and the other aromatics derived i-BPRs. In a separate MESMER simulation, the first isomerization intermediates of the ring broken intermediates P-C1 and P-C2 were included to calculate the final yields. Lennard-Jones parameters for the toluene derived species: σ = 5.92 Å and ϵ = 410 K, which are the values for toluene43,44. The exponential energy decay with an average energy transfer per collision, ΔEdown, was given a value of 278.89 cm−1, which is based on experimental results for toluene with N2 bath gas43. Grain size = 100 cm−1 and numerical precision = dd. In the simulations where the yields of the different pathways were calculated, temperature and pressure were given values of 298.15 and 760 Torr, respectively. The temperature was also varied to derive the temperature dependent rates of the two rearrangement reactions C1 and C2 of toluene derived i-BPR.

In the MESMER simulations, the hindered rotors were treated by performing computations using Gaussian 16 to identify the hindered rotors, and to calculate the corresponding periodicities and barriers using the Freq=HinderedRotor keyword at the ω97X-D/aug-cc-pVTZ level of theory. For the subsequent MESMER simulation, the HinderedRotorQM1D method was used, which requires the Gaussian derived periodicities and barriers, the bonds corresponding to the hindered rotors and the removal of corresponding harmonic frequencies.

The MESMER input file used for calculating the yields of the different pathways following the rearrangement of toluene derived i-BPR is provided in the supplementary files.

Mass spectrometry experiments
Toluene and CD3-toluene were mixed with OH generated by reacting ozone with tetramethylethylene in a quartz flow reactor. The products were subsequently detected by a nitrate-based chemical ionization mass spectrometer (CIMS). The reaction time was controlled by directing the toluene and CD3-toluene flow through an injector tube within the flow reactor, limiting their residence time with OH from 3.7 s to 1.5 s and 0.8 s. For a given OH concentration, the concentrations of toluene and CD3-toluene were varied to observe the changes in product signals. For the NO experiments, toluene/CD3-toluene and OH concentrations were kept constant, while the NO concentration was varied. For the D2O experiments, N2 was bubbled through a D2O reservoir to introduce it into the flow reactor, where it was allowed to mix with the reactants and the oxidation products. The experiments were conducted under atmospheric conditions.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript presents quantum chemical, statistical rate theory, and flow reactor-mass spectrometric results to establish a new mechanism for the generation of secondary organic aerosol (SOA) precursors in the OH-initiated oxidation of aromatics. The novel reaction being proposed is a concerted rearrangement of bicyclic peroxy radicals in which C-C homolysis, O-O homolysis, and transfer of the H atom from the OH to one of the incipient alkoxy O atoms all happen at one transition state. The manuscript is technically solid, the major results are presented clearly, and the discoveries are highly significant for the area of atmospheric chemistry. I recommend its publication after a few minor issues are addressed:\n* The labels within Figure 2 are a little hard to read. Please print this figure as large as possible.\n* In the caption to Figure 2, the reference to \"P-S<sub>2</sub>\" should probably be to P-C<sub>2</sub>.\n* One of the O<sub>2</sub> addition barriers reported in Supplementary Section 8 is negative. The same is true in Supplementary Section 2. This does not impede the MESMER simulations based on the quantum chemical data, nor does it render the predicted O<sub>2</sub> addition branching ratios invalid. Still, the authors should acknowledge that this is a technical problem that adds uncertainty to the predicted branching ratios.\n* On p. 10 and in Figure 4, there is a consideration of \"the fastest of the two possible rearrangements for select key aromatics.\" I am pretty sure that the authors are referring to the rearrangements depicted in Figure 1, but the authors should be explicit about this.\n* The ends of the two paragraphs in the Atmospheric perspective of the molecular rearrangement mechanism section are somewhat redundant.", "reviewer_2": "On NCOMMS-23-12910-T, “Molecular rearrangement of bicyclic peroxy radicals: key route to aerosol from aromatics”, by Iyer et al.\nThis manuscript proposed a new rearrangement of ipso-BPRs and also the bicyclic hydroperoxides and nitrates in oxidation of aromatics. The study suggested a new route for formation of highly oxygenated molecules (HOMs) with supports from quantum chemical and kinetic calculations and mass spectrometric observations. Deuterated toluene and D2O were used to probe the reaction pathways and to check the exchangeable protons in the products. Calculations were done at adequate levels, and the experiments were designed carefully to sort support for the proposed mechanism.\nThe finding here might be a significant improvement on our understanding in mechanism of HOMs and thereafter the mechanism of SOA formation.\nComments:\n# Line 119 \"potentially reversible\": The reversible H-shifts here should be slow as well, and is much slower than the bimolecular recombination with O2. Therefore should \"also be virtually irreversible\".\n# On reaction of C6H5CD3: There is an issue of isotope effect and tunneling correction here when changing from –CH3 to –CD3. Obviously, the H-shifts here should be much faster than the D-shifts. This might be part of the reason for the low signal for C7D2H6O6 in Fig S11, and probably for C7D2H6O8 as well. Using –CD3 might underestimate the role of H shifts in Ref 35 (Wang et al., EST, 51, 8442, 2017).\n# Fig S16, RONO2: BPR + NO forms ROONO first, which might decompose to RO + ONO or isomerize to RONO2. Even though barrier for rearrangement of RONO2 is lower than RO + NO2, the scheme here seems to exaggerate the role of rearrangement. RONO2s were missing in Fig S16 and Table S9.\n# D2O Experiments:\n(1) Presumably, C7H9O9 and C7D2H7O9 were from reaction of C6H5CH3, and C7D3H6O9 and C7D5H4O9 were from reaction of C6H5CD3 (Table S6). So the C7H9O9 contains only two exchangeable H-atoms, insetad “two, three and four” (Page S14). Please confirm or explain.\n(2) In Fig 2, three C9H9O9 isomers were given as R3-Epo-OOH-R”O2 (containing one exchangeable H), R2b-OOH-R’2O2 (containing three exchangeable Hs), and the green C7H9O9 (lower left corner, containing two exchangeable Hs). But R2b-OOH-R’2O2 has a fast isomerization rate of ~230 s-1, and the last isomer would have a fast H shift (from the aldehyde H). Alternative isomers of C7H9O9 might be needed to account for the observed signal.\n(3) Page S14, “… Fig S11 shows the time series of the normalized signals …”: The figure cannot be found.\n# Kinetics of R1 (as in Fig S17 and S18): It should be noticed that the two additions of O2 are both reversible, particularly for R1a-RO2 and when R1 contains excess energy. The usual “+ O2 – HO2” process in alpha-hydroxyl alkyl radicals may be limited by the 1,4 H-shift because the addition of O2 to R1a-RO2 is much less exothermic (only ~7 kcal/mol here) than the addition to normal alkyl radicals such as CH3CHOH radical (exothermic by ~30 kcal/mol).\n# Flow tube simulations: Could typical concentrations of OH radical and RO2 be given here? These quantities are essential in assessing the competition between unimolecular and bimolecular reactions for peroxy radicals.\nMinors:\n# Page S9, the 4th line from Bottom: “Fig S4” should be “Fig S9”; Page S10, “Fig S5” should be “Fig S10”; Page S11: “Fig S6” should be “S11”; …", "reviewer_3": "This manuscripts describes a pathway in the atmospheric oxidation of aromatics that appears to be the missing link between the traditional chemistry and the unexplained HOM formation from these compounds. By combining theoretical kinetic calculations, a kinetic model, and experimental observations, the authors make a case that inclusion of this pathway leads to predictions that are consistent with the observations. The research is timely, as there is a lot of interest in HOM and aerosol formation, and the role of aromatics in urban air quality. The methodologies used are of high level and appropriate for the topic, leading to robust results. This paper describes a high-impact result that has the potential to solve a long-standing conundrum. I support publication of this manuscript.\nReviewing the experimental section is outside my field of expertise.\nMost of my comments are minor, but I do have 2 main comments that I urge the authors to consider.\nMain comments\nTo me, it feels that the authors did not do due diligence to the literature. While I recognize that space and number of references are limited in the main text, the supporting information contains extensive descriptions of mechanistic steps without any referencing at all. Most of this even seems to be based on a single paper (Wang and coworkers), which does not acknowledge the vast effort that the community has put into elucidating aromatics oxidation mechanisms to establish a base upon which the current study can to add its contribution. The paper also generalizes to aromatics beyond toluene, which is certainly not covered by a single reference to Wang et al.\nReviewing the aromatics literature is daunting and I understand that this is not the manuscript to do this in full, but at the very least some key papers should be cited, as well as mechanistic reviews (e.g. Vereecken 2019, Vereecken and Francisco 2012, Atkinson 2003, Calvert 2002,...). These, and perhaps some additional references to SARs, will also support some of the calculations in the SI that were only done using low-level methodologies. Below, I will not list all places where literature citations are needed, as it is pervasive.\nOne should be weary about presenting the experiments as proof of the contribution of the characterized pathway. The experiments show that an autoxidation chemistry exists, but does not establish that the molecules observed are those predicted by the theoretical analysis; autoxidation is known to generate many isomers. While the results seems consistent, there remain uncertainties on the theoretical predictions and the experimental observations, and the latter only span a small range of reaction conditions that may be insufficient to discriminate between distinct reaction mechanism. Likewise, the authors do not establish that the proposed mechanism is also consist with the observations available in the literature.\nRelated to this is that, at first glance, the mechanism seems to miss some pathways, or at least does not discuss their contribution as far as I could find. This includes e.g. the reversibility of the epoxidation in R3 (competitive against O2 addition), the H-migration from -OOH to -O-radical in R3 (with a literature rate ~1E10 s-1), or H-scrambling and ring closure in R2b-OOH-R'2O2, all of which represent reactions classes known to be fast. The kinetic calculations also do not seem to account for the impact of fast H-scrambling across OOH/OO groups on the rate coefficient, as well-documented in the literature. It is unclear whether any of this would affect the predictions, but perhaps the mechanism is not fully robust yet.\nMinor comments\np. 3 line 79: \"finite timescales\"\ndefine \"finite\", in this context probably relative to atmospheric transport time scales (regional, continental, hemisphere, global ?)\np. 4 lines 90-105:\nThis would be significantly easier to understand with a graphical inset with a Lewis-structure representation of an example.\np. 5 fig 1:\nTop: One can not really see what the rearrangement is, due to the use of ball-and-stick graphics. See also remark above.\nBottom: Perhaps an Arrhenius plot with x-axis in 1000K/T ? Then again, Nat.Comm is not a kinetics journal.\np 7 fig 2:\n- Caption: \"autoxdation\" -> autoxidation\n- The intermediates must not be represented as trans-alkenes but strictly as cis-isomers or unspecified (where allylic rotation is possible). Trans-stereoisomers are not what was calculated (sampling a few of the log files shows as much), are not what is expected for the parent molecule decomposition, and would prevent some of the chemistry to happen (e.g. the H-shift in R2b-RO2)\n- The fates for P-C2 do not sum to 100%\np. 9 line 183: \" indicating that the mechanism proposed in this work is the dominant unimolecular pathway to the SOA precursors that we detect.\"\n\"is\" -> is likely to be / is consistent with / ...\np. 12, fig 4 : perhaps remove the minor grid lines to lighten the plot\np. 13, line 246: \"This could re-initiate autoxidation and provide a long range transport mechanism for NOx\"\nIt is unclear how prompt decomposition losing NO2 could be useful for long-range NOx transport, as the NO2 is then lost before it can be transported?\np. 16, wave function stability\nWhat do the CASSCF calculations show for multi-reference effects on the biradical O-O bond breaking? Is the active space (1 virtual orbital) large enough to accommodate such multi-reference effects ?\np. 17, line 341 \"In the MESMER simulations, the harmonic frequencies were treated as hindered rotors\"\nI assume the authors mean that only those internal modes corresponding to internal rotations were removed from the vibrational frequencies and treated as hindered rotors.\np S9, top, ring opening in B-alkyl\nThere are much better discussions of this channel available that should be cited, e.g. Glowacki et al. 2009, Vereecken 2018, Vereecken 2019, as well as experimental evidence of its lack of importance by the Wennberg group (Xu et al. 2020)\np. S12, NO experiments.\nNO can lead to autoxidation proceeding through different pathways (so-called alkoxy-peroxy autoxidation steps). They may form different isomers of the same mass, and a mass spectrum won't reveal mechanistic changes. Alkoxy-peroxy autoxidation is also implicated as a key step in ring breaking HOM formation in some VOC (e.g. Shen et al. 2022, Guo et al. 2022). Furthermore, Vereecken (2018, 2019) points out the role of NO in changing the early stage aromatic oxidation mechanism, based on available literature data. These experiments may thus not as straightforward to interpret as the authors imply.\np. S17, top: \"the rearrangement mechanism is also possible for other aromatic derived bicyclic molecules. Table S8 \"\nWithout context, it is not clear which rearrangement mechanism is meant. The bicyclic alkyl radicals have very different rearrangement mechanism reported (ring retaining with epoxide-alkoxy) than given in this work for bicyclic peroxy radicals (ring opening with H-shift and carbonyl formation).\np. S19, bottom\n- Mention \"site-specific O2 addition\" at the start of the last paragraph\n- \"H-abstraction by O2 to form C7H8O5 is not direct but follows the initial addition of O2 to the C(OH) carbon.\"\nThis needs specific literature citations\n- \"These transition states were calculated to be -0.7 kcal/mol and 1.9 kcal/mol, respectively, above R1 at F12 level of theory.\" -> \"...relative to R1 at the F12 level of theory.\"\n- \" the potential energy surface shown in Fig. S12 was used as input in a MESMER simulation to account for the excess energy of R1.\"\nThis glosses over a lot of details. At the very least refer explicitly to the Mesmer input files in the Zenodo archive, but preferable document this more thoroughly.\np. S20, bottom \" the analytical solution is represented by its Taylor expansion\"\nThe analytical solution to what? The MCM ?\np. S21, middle \"The likely reason for this is the less reactive TME RO2s.\"\nWhy are they less reactive ? Is literature data available ?\np. S22, ref 1: remove \"Vertiotie.4P\"\nReferences (Alph.)\nAtkinson, R. and Arey, J.: Atmospheric Degradation of Volatile Organic Compounds, Chem. Rev., 103, 4605–4638, https://doi.org/10.1021/cr0206420, 2003.\nCalvert, J. G., Atkinson, R., Becker, K. H., Kamens, R. M., Seinfeld, J. H., Wallington, T. J., and Yarwood, G.: The mechanisms of atmospheric oxidation of aromatic hydrocarbons, Oxford University Press, Oxford, New York, 566 pp., 2002.\nGlowacki, D. R., Wang, L., and Pilling, M. J.: Evidence of Formation of Bicyclic Species in the Early Stages of Atmospheric Benzene Oxidation, J. Phys. Chem. A, 113, 5385–5396, https://doi.org/10.1021/jp9001466, 2009.\nGuo, Y., Shen, H., Pullinen, I., Luo, H., Kang, S., Vereecken, L., Fuchs, H., Hallquist, M., Acir, I.-H., Tillmann, R., Rohrer, F., Wildt, J., Kiendler-Scharr, A., Wahner, A., Zhao, D., and Mentel, T. F.: Identification of highly oxygenated organic molecules and their role in aerosol formation in the reaction of limonene with nitrate radical, Atmos. Chem. Phys., 22, 11323–11346, https://doi.org/10.5194/acp-22-11323-2022, 2022.\nShen, H., Vereecken, L., Kang, S., Pullinen, I., Fuchs, H., Zhao, D., and Mentel, T. F.: Unexpected significance of a minor reaction pathway in daytime formation of biogenic highly oxygenated organic compounds, Sci. Adv., 8, eabp8702, https://doi.org/10.1126/sciadv.abp8702, 2022.\nVereecken, L.: Reaction mechanisms for the atmospheric oxidation of monocyclic aromatic compounds, in: Advances in Atmospheric Chemistry: Volume 2: Organic Oxidation and Multiphase Chemistry, edited by: Barker, J. R., Steiner, A. L., and Wallington, T. J., World Scientific Publishing Co. Pte. Ltd., Singapore, 377–527, https://doi.org/10.1142/9789813271838_0006, 2019.\nVereecken, L.: The mechanism of aromatic oxidation: thoughts based on theoretical and experimental data, with alternative reduced mechanism, Gases/Atmospheric Modelling/Troposphere/Chemistry (chemical composition and reactions)/acp-2018-146, https://doi.org/10.5194/acp-2018-146-SC1, 2018.\nVereecken, L. and Francisco, J. S.: Theoretical studies of atmospheric reaction mechanisms in the troposphere, Chem. Soc. Rev., 41, 6259–6293, https://doi.org/10.1039/c2cs35070j, 2012.\nXu, L., Møller, K. H., Crounse, J. D., Kjaergaard, H. G., and Wennberg, P. O.: New Insights into the Radical Chemistry and Product Distribution in the OH-Initiated Oxidation of Benzene, Environ. Sci. Technol., 54, 13467–13477, https://doi.org/10.1021/acs.est.0c04780, 2020."}, "author_response": "We thank all reviewers for their valuable input that helped improve the manuscript.\nReviewer 1:\nGeneral comment: This manuscript presents quantum chemical, statistical rate theory, and flow reactor-mass spectrometric results to establish a new mechanism for the generation of secondary organic aerosol (SOA) precursors in the OH-initiated oxidation of aromatics. The novel reaction being proposed is a concerted rearrangement of bicyclic peroxy radicals in which C-C homolysis, O-O homolysis, and transfer of the H atom from the OH to one of the incipient alkoxy O atoms all happen at one transition state. The manuscript is technically solid, the major results are presented clearly, and the discoveries are highly significant for the area of atmospheric chemistry. I recommend its publication after a few minor issues are addressed:\nAuthor comment: We thank the reviewer for their comments and their recommendation for publication of our manuscript.\n1. The labels within Figure 2 are a little hard to read. Please print this figure as large as possible.\nAuthor comment: We have now increased the font size of the labels in Figure 2.\nChanges to manuscript: A larger font size is used for the labels in Fig. 2 of the main manuscript.\n2. In the caption to Figure 2, the reference to \"P-S \" should probably be to P-C .\n2 2\nAuthor comment: Thank you for pointing this out. This has now been corrected.\nChanges to manuscript: “P-S ” in Figure 2 caption corrected to “P-C ”.\n2 2\n3. One of the O addition barriers reported in Supplementary Section 8 is negative. The\n2\nsame is true in Supplementary Section 2. This does not impede the MESMER\nsimulations based on the quantum chemical data, nor does it render the predicted\nO addition branching ratios invalid. Still, the authors should acknowledge that this is\n2\na technical problem that adds uncertainty to the predicted branching ratios.\nAuthor comment: We agree. This is now acknowledged in Supplementary Section 8.\nRegarding Supplementary Section 2, we suspect that the reviewer is indicating this line in\npage S6: “This corroborates with the energy barriers for the syn and anti O2 additions we\ncalculated at the F12 level of theory - 2.5 kcal/mol and 3.4 kcal/mol, respectively.” If so, both\nbarriers are in fact positive (+2.5 kcal/mol and +3.4 kcal/mol), and our use of the hyphen is\ninjudicious here. The hyphen (-) has now been changed to a colon (:) for clarity.\nChanges to supplementary:\nSupplementary Section 8: “Note that the F12 correction causes TS to be slightly negative,\ni\nand while this does not impede the MESMER simulations, it does add some uncertainty to\nthe predicted branching ratios”. Supplementary section 2, page S6: “-“ => “:”.\n4. On p. 10 and in Figure 4, there is a consideration of \"the fastest of the two possible\nrearrangements for select key aromatics.\" I am pretty sure that the authors are\nreferring to the rearrangements depicted in Figure 1, but the authors should be\nexplicit about this.\nAuthor comment: We agree that this should be more clearly acknowledged. The text on p.\n10 of the main manuscript has been modified to make this clear.\nChanges to manuscript: Sentence in p. 10 of the main manuscript changed to: “Fig. 4 shows\nthe rate coefficients of the fastest of the two possible rearrangement mechanisms, C and C\n1 2\nas shown in Fig. 1 A, for select key aromatics.”\n5. The ends of the two paragraphs in the Atmospheric perspective of the\nmolecular\nrearrangement mechanism section are somewhat redundant.\nAuthor comment: Thank you for pointing this out, and we agree. We have decided to\ncombine the two paragraphs and modify the last summary sentence.\nChanges to manuscript: The two paragraphs in the “Atmospheric perspective of the\nmolecular rearrangement mechanism” section have been combined and this modified final\nsummary sentence has been added: “The novel molecular rearrangement mechanism\nreported in this work explains the rapid formation of highly oxidized organic products in one\nof the most important urban SOA-forming systems, toluene + OH, with potential relevance\nalso for other atmospherically abundant aromatic molecules.”\nReviewer 2:\nGeneral comment: This manuscript proposed a new rearrangement of ipso-BPRs and also\nthe bicyclic hydroperoxides and nitrates in oxidation of aromatics. The study suggested a\nnew route for formation of highly oxygenated molecules (HOMs) with supports from\nquantum chemical and kinetic calculations and mass spectrometric observations.\nDeuterated toluene and D2O were used to probe the reaction pathways and to check the\nexchangeable protons in the products. Calculations were done at adequate levels, and the\nexperiments were designed carefully to sort support for the proposed mechanism.\nThe finding here might be a significant improvement on our understanding in mechanism of\nHOMs and thereafter the mechanism of SOA formation.\nAuthor comment: We thank the reviewer for their comments.\n1. # Line 119 \"potentially reversible\": The reversible H-shifts here should be slow as\nwell, and is much slower than the bimolecular recombination with O2. Therefore\nshould \"also be virtually irreversible\".\nAuthor comment: In their 2017 paper, Wang et al. (Wang et al. Environ. Sci. Technol. 2017,\n51, 15, 8442–8449) report in Table 1 reverse rates for H-migrations in toluene derived BPRs\nof 1.9´106 s-1 and 2.8´108 s-1, which are competitive with bimolecular recombination\nreactions with O under atmospheric conditions. These are for H-migration reactions of\nvirtually irreversible H-migration reactions for the BPR with OH in the para position. We\nhave now modified our text to say that only some of the reported isomerization reactions of\nBPR are irreversible.\nChanges to manuscript: Sentence in the main manuscript modified to: “This is important\nsince some of those previously reported isomerization reactions of BPR, specifically H-shift\nreactions, were reversible with reverse rate coefficients that are competitive with the\nbimolecular recombination reactions with O under atmospheric conditions.”\n2\n2. # On reaction of C6H5CD3: There is an issue of isotope effect and tunneling\ncorrection here when changing from –CH3 to –CD3. Obviously, the H-shifts here\nshould be much faster than the D-shifts. This might be part of the reason for the low\nsignal for C7D2H6O6 in Fig S11, and probably for C7D2H6O8 as well. Using –CD3\nmight underestimate the role of H shifts in Ref 35 (Wang et al., EST, 51, 8442, 2017).\nAuthor comment: We agree that the slower -CD shift rate could be part of the reason for\n3\nthe observed low C D H O signals. If the methyl H-shift was a dominant reaction in our\n7 2 6 6\nC H CH measurements and missing in our C H CD measurements, the observed mass\n6 5 3 6 5 3\nspectra for the two precursors would be expected to be different. However, we observe\nthat the produced mass spectra are near identical (Figs. S12 to S15). We now include the\nsignals of the closed-shell products from the C H CH experiment (Fig. S11 B) in the\n6 5 3\nsupplementary. These signals are also low, indicating that the methyl H-shift is unlikely to\nplay a major role under our experimental conditions. We agree that the isotope effect\nshould nevertheless be noted. We now note it in the manuscript and supplementary text.\nChanges to manuscript: We have noted in the manuscript that the use of CD -toluene might\n3\nunderestimate the role of methyl H-shifts. “Note that D-shift rates are slower than H-shift\nrates due to isotope effects, in particular lower tunneling factors, so the use of CD -toluene\n3\nwill to an extent underestimate the role of H-shift from the methyl group. We observe that\nthe mass spectra for toluene and CD -toluene are near identical, indicating that H-shift from\n3\nthe methyl group is unlikely to play a major role.”\nChanges to supplementary: “While D-shift reactions are known to be slower than H-shifts,\nand the CD -toluene experiments could underestimate the role of methyl H-shifts, we also\n3\nmeasured low signals of the closed-shell species from the CH -toluene experiments (Fig. S11\nconditions.”\nFig. S11 caption: Fig. S11 B added that shows the signals of the closed-shell species from the\nCH -toluene experiment. Text added to Fig. S11 caption: “The closed-shell species are also low\n3\nin the CH3-toluene experiment, indicating that H-shift from the methyl carbon is playing an\ninsignificant role under our experimental conditions.”\n3. Fig S16, RONO2: BPR + NO forms ROONO first, which might decompose to RO + ONO\nor isomerize to RONO2. Even though barrier for rearrangement of RONO2 is lower\nthan RO + NO2, the scheme here seems to exaggerate the role of rearrangement.\nRONO2s were missing in Fig S16 and Table S9.\nAuthor comment: We agree that BPR + NO would form ROONO first, that might directly\ndecompose to RO + ONO or isomerize to the more stable RONO . However, that is not the\n2\nfocus of our work. Our focus is on the eventual fate of the fraction of RO + NO reactions\n2\nthat lead to the more stable RONO organo nitrate. This is why the PES in Fig. S16 and Table\nnot RONO in their comment?). Additionally, we should have noticed (and mentioned) that\n2\nthe rearrangement rates in Table S9 are of thermalized RONO s as is probably obvious from\n2\nthe rates and the corresponding lifetimes of tens of minutes to hours. We acknowledge that\nshowing the PES in Fig. S16 starting from reactants RO + NO without clarifying the lack of\n2\nrole of excess energy in the rearrangement rates is misleading. If excess energy played a role\nin the rearrangement of RONO , then we agree with the reviewer that including the ROONO\n2\nintermediate in the PES would have been necessary. Fortunately, the rearrangement is in\nfact thermal, and we can therefore avoid computing the complex PES involved in the\nisomerization of ROONO to RONO . We now state explicitly that 1) the RONO\n2 2\nrearrangement reaction is thermal and 2) that the general PES of RO + NO includes the\nconsider the fate of the more stable RONO .\n2\nis mentioned and discussed in the supplementary text and in Fig. S16 caption.\n“The previous mechanistic understanding of aromatic oxidation was that the primary fate of\nBPRs under polluted conditions is bimolecular reactions with NO to form B-ROONO\nintermediates that can either decompose into alkoxy radicals or isomerize to form organo\nnitrates (B-RONO ; BPR + NO => B-RONO ; B = bicyclic). While only some fraction of BPR +\n2 2\nNO reactions will lead to B-RONO , these organo nitrates are thought to be stable once\n2\nformed.”\n“MESMER simulations indicate that even when the B-ROONO intermediates are neglected,\nexcess energy from RO + NO => B-RONO step does not affect the B-RONO dissociation\n2 2 2\nrates: the dissociation reactions are fully thermal.”\n“Similarly, the atmospheric lifetimes of Tol-meta-B-RONO and Tol-para-B-RONO are about\n2 2\n28 minutes and 3 hours, respectively.”\nFig. S16 caption: “Note that BPR + NO will first lead to a ROONO intermediate and only a\nfraction will subsequently isomerize to the more stable RONO2 isomer (the rest directly\ndecomposing into RO + NO ). We only include RONO here as we are interested in the fate of\n2 2\nthe intermediate that is generally considered to be stable under atmospheric conditions.”\n4. Presumably, C7H9O9 and C7D2H7O9 were from reaction of C6H5CH3, and\nC7D3H6O9 and C7D5H4O9 were from reaction of C6H5CD3 (Table S6). So the\nC7H9O9 contains only two exchangeable H-atoms, insetad “two, three and four”\n(Page S14). Please confirm or explain.\nAuthor comments: It is correct that the dominant C H O signal has two exchangeable H-\n7 9 9\natoms, and we indicate this in the original supplementary text as follows: “Similarly, the\nproposed autoxidation mechanism points to the C H O peroxy radical isomer with two\n7 9 9\nacidic functional groups that forms rapidly and is likely the dominant signal. This is\ncorroborated by the D O experiment.” When we note the two, three and four H->D\n2\nexchanges, it is for the C H O peroxy radical, as noted in the original supplementary text.\n7 9 11\nWe have now modified the sentence to say 11-oxygen containing C H O peroxy radical to\n7 9 11\nmake it clear that we are talking about the O peroxy radical.\n7 9 11\nD O experiments also indicate three isomers for the 11-oxygen containing C H O peroxy\n2 7 9 11\nradical with two, three and four H->D exchanges.”\n5. In Fig 2, three C9H9O9 isomers were given as R3-Epo-OOH-R”O2 (containing one\nexchangeable H), R2b-OOH-R’2O2 (containing three exchangeable Hs), and the green\nC7H9O9 (lower left corner, containing two exchangeable Hs). But R2b-OOH-R’2O2\nhas a fast isomerization rate of ~230 s-1, and the last isomer would have a fast H\nshift (from the aldehyde H). Alternative isomers of C7H9O9 might be needed to\naccount for the observed signal.\nAuthor comments: We agree that R -OOH-R’ O is unlikely to accumulate due to its fast\n2b 2 2\nisomerization rates. This could at least partially explain why we do not see C H O isomers\n7 9 9\nwith 3 exchangeable H-atoms (see Fig. S14 and S15 where the isomer with 2 exchangeable H\natoms is clearly the dominant peak). We also note in the manuscript that we measure\nC H O with two exchangeable H-atoms (this sentence is slightly modified to note that the\n7 9 9\ndominant peak corresponding to C H O has two exchangeable atoms as some small\n7 9 9\ncontribution of a peroxy radical isomer with three exchangeable H-atoms cannot be ruled\nout). It is a good idea to explicitly acknowledge that the blue pathway is not a source of the\nC H O peroxy radical exactly for the reason the reviewer suggests. We now note that in the\n7 9 9\nmanuscript.\nChanges to manuscript: Section Experimental results, 1) “This is more consistent with the\nmechanism we propose because the formed O -RO via the dominant green pathway in Fig.\n9 2\n2…” 2) “The blue pathway in Fig. 2 does lead to a O -RO with three exchangeable H-atoms,\n9 2\nbut likely due to its fast isomerization reaction (~230 s-1) rapidly forms O -RO , and is not\n11 2\nmeasured.”\n6. Page S14, “… Fig S11 shows the time series of the normalized signals …”: The figure\ncannot be found.\nAuthor comments: Thank you for pointing this out. We initially included and later deleted\nthe time series plot for the D O experiments, but then neglected to remove our reference to\n2\nit in the supplementary text. We decided that the figure was too complicated while adding\nlittle value. The figure is below:\nWe will remove the reference to the missing figure in the supplementary text. Alternatively,\nif the reviewer suggests that the plot should be included, we will add it to the\nsupplementary text.\nChanges to supplemantary: Removed the reference to Fig. S11 in the supplementary text.\n7. Kinetics of R1 (as in Fig S17 and S18): It should be noticed that the two additions of\nO2 are both reversible, particularly for R1a-RO2 and when R1 contains excess\nenergy. The usual “+ O2 – HO2” process in alpha-hydroxyl alkyl radicals may be\nlimited by the 1,4 H-shift because the addition of O2 to R1a-RO2 is much less\nexothermic (only ~7 kcal/mol here) than the addition to normal alkyl radicals such as\nCH3CHOH radical (exothermic by ~30 kcal/mol).\nAuthor comments: We agree that the reversibility of the O addition reactions should be\n2\nnoted. The lower exothermicity of the formation of R -RO will also likely favor the\n1a 2\nformation of R -RO , making the green channel in Fig. 2 more important. This is now noted\n1b 2\nin the supplementary text. In addition, we included R -RO + NO => R -ROONO and R -RO\n1a 2 1a 1b 2\n+ NO => R -ROONO sink reactions with rate coefficients of 1 s-1 to include the reverse\n1b\nreactions of R -RO and R -RO in the MESMER simulation. The ROONO was a model\n1a 2 1b 2\nsystem generated without a conformer sampling step and computed at the B3LYP/6-\n31+G(d) level. The exothermicity of the formation of ROONO was arbitrarily set to -15\nkcal/mol relative to the RO s. If no sink reactions are added and R -RO and R -RO are\n2 1a 2 1b 2\nsimply treated as “modelled” to account for the reverse reactions, then the product that is\nthermodynamically the most stable is formed with a 100% yield. Therefore, a sink with an\napproximately correct timescale to correctly model the effect of reversibility is needed. A\nmore accurate description of the ROONO sink was considered unnecessary as long as the\ntimescale is correct. The rate of conversion of RO to ROONO was set at 1 s-1 by giving a NO\n2\nconcentration of 5´1010 molecules/cm3 and a reaction rate coefficient of 2´10-11\ncm3/molecule/s. This simulation produced a 100% yield of R -ROONO, indicating a larger\n1b\nyield of R -RO when the low exothermicity of R -RO formation and consequently the\n1b 2 1a 2\nreversibility of the two O addition reactions are accounted for.\ntransition states and these reactions were treated using the SimpleRRKM method with\nEckart tunneling. The intermediates P-C and R were treated as “modelled” and R -RO and\n2 1 1a 2\nR -RO as sinks in the simulation. The MESMER input file is provided in the data archive. This\n1b 2\nresulted in a 20% yield for R -RO . Note that the F12 correction causes TSi to be slightly\n1b 2\nnegative, and while this does not impede the MESMER simulations, it does add some\nuncertainty to the predicted branching ratios. Also, the two O addition reactions are\n2\nreversible, which is especially important for R -RO given that its formation is less\n1a 2\nexothermic and R contains excess energy. We accounted for the reverse reactions of R -RO\n1 1a 2\nand R -RO by including a RO + NO => ROONO channel with a loss rate of 1 s-1. This was\n1b 2 2\ndone by adding a model ROONO sink to R -RO and R -RO using the\n1a 2 1b 2\nSimpleBimolecularSink method in MESMER with NO concentration of 5´1010 molecules/cm3\nand a reaction rate coefficient of 2´10-11 cm3/molecule/s. R -RO and R -RO were treated\n1a 2 1b 2\nas “modelled” to account for their reverse reactions. If no sink reactions are added and R -\n1a\nRO and R -RO are simply treated as “modelled” to account for reverse reactions, then the\n2 1b 2\nproduct that is thermodynamically the most stable is formed with a 100% yield. Therefore, a\nsink with an approximately correct timescale to correctly model the effect of reversibility is\nneeded. The precise details of the sink do not matter as long as the timescale is correct.\nTherefore, a model ROONO system computed at the B3LYP/6-31+G(d) level was used with an\neffective rate of 1 s-1. The MESMER input PES is shown in Fig. S19 and the input file is\nprovided in the data archive. This resulted in 100% yield of R -ROONO, indicating a larger\n1b\nyield of R1b-RO2 when low exothermicity of R1a-RO formation is accounted for.”\n2\n8. Flow tube simulations: Could typical concentrations of OH radical and RO2 be given\nhere? These quantities are essential in assessing the competition between\nunimolecular and bimolecular reactions for peroxy radicals.\nAuthor comments: These are now included in the supplementary. The OH concentrations\nare ~7´107 molecules cm-3 and RO concentrations are ~9´109 – ~1´1010 molecules cm-3 for\n2\nthe flow tube simulations with reaction times of 0.8 s, 1.5 s and 3.7 s.\nChanges to supplementary: Typical concentrations of OH radical and RO now provided in\n9. Minor comments: # Page S9, the 4th line from Bottom: “Fig S4” should be “Fig S9”;\nPage S10, “Fig S5” should be “Fig S10”; Page S11: “Fig S6” should be “S11”; …\nAuthor comments: Thank you for pointing these out. They have now been corrected.\nChanges to supplemenatry: Corrections have been made to the supplementary.\nReviewer 3:\nGeneral comment: This manuscripts describes a pathway in the atmospheric oxidation\nof aromatics that appears to be the missing link between the traditional chemistry and\nthe unexplained HOM formation from these compounds. By combining theoretical\nkinetic calculations, a kinetic model, and experimental observations, the authors make a\ncase that inclusion of this pathway leads to predictions that are consistent with the\nobservations. The research is timely, as there is a lot of interest in HOM and aerosol\nformation, and the role of aromatics in urban air quality. The methodologies used are of\nhigh level and appropriate for the topic, leading to robust results. This paper describes a\nhigh-impact result that has the potential to solve a long-standing conundrum. I support\npublication of this manuscript.\nAuthor comment: We thank the reviewer for their positive comment and their support\nfor the publication of the manuscript.\nFirst main comment: To me, it feels that the authors did not do due diligence to the\nliterature. While I recognize that space and number of references are limited in the main\ntext, the supporting information contains extensive descriptions of mechanistic steps\nwithout any referencing at all. Most of this even seems to be based on a single paper\n(Wang and coworkers), which does not acknowledge the vast effort that the\ncommunity has put into elucidating aromatics oxidation mechanisms to establish a base upon which\nthe current study can to add its contribution. The paper also generalizes to aromatics\nbeyond toluene, which is certainly not covered by a single reference to Wang et al.\nReviewing the aromatics literature is daunting and I understand that this is not the\nmanuscript to do this in full, but at the very least some key papers should be cited, as\nwell as mechanistic reviews (e.g. Vereecken 2019, Vereecken and Francisco 2012,\nAtkinson 2003, Calvert 2002,...). These, and perhaps some additional references to SARs,\nwill also support some of the calculations in the SI that were only done using low-level\nmethodologies. Below, I will not list all places where literature citations are needed, as it\nis pervasive.\nAuthor comments: We acknowledge that the aromatic oxidation mechanisms in the\nsupplementary should have been better cited. Key papers suggested by the reviewer are\nnow cited where appropriate.\nChanges to supplementary: Papers are cited in supplementary. Page S4: “The initial\nsteps of OH addition to toluene is shown in Fig. S4 and have been discussed in detail in\nprevious works (16-19).”\nSecond main comment: One should be weary about presenting the experiments as proof of\nthe contribution of the characterized pathway. The experiments show that an autoxidation\nchemistry exists, but does not establish that the molecules observed are those predicted by\nthe theoretical analysis; autoxidation is known to generate many isomers. While the results\nseems consistent, there remain uncertainties on the theoretical predictions and the\nexperimental observations, and the latter only span a small range of reaction conditions\nthat may be insufficient to discriminate between distinct reaction mechanism. Likewise, the\nauthors do not establish that the proposed mechanism is also consist with the\nobservations available in the literature.\nRelated to this is that, at first glance, the mechanism seems to miss some pathways, or at\nleast does not discuss their contribution as far as I could find. This includes e.g. the\nreversibility of the epoxidation in R3 (competitive against O2 addition), the H-migration\nfrom -OOH to -O-radical in R3 (with a literature rate ~1E10 s-1), or H-scrambling and ring\nclosure in R2b-OOH-R'2O2, all of which represent reactions classes known to be fast. The\nkinetic calculations also do not seem to account for the impact of fast H-scrambling across\nOOH/OO groups on the rate coefficient, as well-documented in the literature. It is unclear\nwhether any of this would affect the predictions, but perhaps the mechanism is not fully\nrobust yet.\nAuthor comment: We agree that we must be careful when assigning peaks from\nexperimental spectra to one theoretically predicted mechanism and we acknowledge that\nthe proposed mechanism does not represent the entire autoxidation chemistry of toluene.\nIt is in fact impossible for it to do so given that we have not explored all the autoxidation\nchannels even in the mechanism we propose (i.e., the autoxidation of the P-C peroxy\n1\nradical). Our choice to discuss the experimental results in relation to our mechanism were to\n1) offer mechanistic insights on the autoxidation products of toluene + OH we measure that\nare formed under the rapid reaction time conditions of our experiments, and 2) highlight\nthat multiple autoxidation pathways can occur concurrently, as predicted by our\nmechanism. Regarding 1) the only experimental observation available in literature carried\nout under the reaction time conditions that are close to our study is Wang et al. 2017, and\nwe have compared our result to theirs extensively. Our D O experiments that indicate the\n2\nnumber of -OH and -OOH functional groups are not in disagreement with the RO isomers\n2\nfrom our mechanism, and this adds credence to our mechanism. Regarding 2) This result is\nnon-trivial as no previous work has shown that excess energy from the formation of an RO\n2\nleads to multiple autoxidation pathways. Specifically, the two isomers of O -RO , one with\n7 2\none labile H-atom and another with two labile H-atoms shows that multiple autoxidation\npaths occur concurrently, and this is not in disagreement with the green and red pathways\nin Fig. 2.\nWe acknowledge that the proposed pathways provide one explanation and possible\nstructures of the observed highly oxidized RO s. We agree that there could be other\n2\nautoxidation pathways not considered in this study that can also lead to the RO s we detect.\nRegarding the red channel in Fig. 2 and the issues the reviewer raises about 1) reversibility\nof R -Epo-R’ and 2) H-migration from -OOH to -O radical, which is essentially the reverse\n3\nreaction of R back to P-C . We ran a MESMER simulation along the R , R and R pathways\n3 2 1 2 3\nof P-C with parameters calculated at the wB97X-D/aug-cc-pVTZ level. The lower level of\n2\ntheory is to use the same methodology as what is used for computing the TS to R for which\n1 7 8 5\nchannel and assigned the formation of R -RO as the direct sink of R (+ O ). The simulation\n1b 2 1 2\nshows that R -Epo-RO is a significant product (36% yield). While the reverse reactions have\n3 2\nlow barriers, the excess energy of P-C likely drives the formation of the R -Epo-R’O .\n2 3 2\nOther pathways available to R -OOH-R’ O such as H-scrambling could be competitive with\n2b 2 2\nthe vinoxy forming channel shown in Fig. 2, but these do not directly lead to the next O\n2\naddition. The -OH H-atom is likely still very labile, and abstraction of that H-atom by the H-\nscrambled RO would still lead to the same R -OOH-vinoxy. The ring closure reactions are\n2 2b\nunlikely to be competitive with H-shifts from -OH and -OOH groups as our previous\ncalculations, e.g., ring closure reactions of R -RO , indicate that these have much larger\n2a 2\nbarriers. We completely agree with the reviewer that the mechanism is not robust yet. We\nnow make that clear in the manuscript text.\nChanges to manuscript: Pg. 5: “R and R -Epo-Rʹ both have small reverse barriers, but the\n3 3\nyield of R -Epo-RO is nevertheless likely to be high due to the excess energy of P-C\n3 2 2\nas shown in our simulations (see supplementary section S12).”\nPg. 5. “Note that autoxidation is known to produce many isomers and the pathways shown\nin Fig. 2 are not the only autoxidation pathways occurring in our measurements. However,\nthese are the only pathways that can currently explain the observed H-to-D shifts in the\nisomers we measure.”\nChanges to supplementary: New supplementary section S12 added that describes the\nfavorability of the formation of R -Epo-RO .\n3 2\nMinor comments:\n1. p. 3 line 79: \"finite timescales\"\ndefine \"finite\", in this context probably relative to atmospheric transport time scales\n(regional, continental, hemisphere, global ?)\nAuthor comment: Thank you, we agree that the word “finite” is somewhat ambiguous in\nthis context. We have now changed it to regional atmospheric transport timescales.\nChanges to manuscript: Pg. 2: “Intriguingly, several of the organo nitrates and other closed\nshell products derived from the i-BPR are likewise unstable and decompose on regional\natmospheric transport timescales.”\n2. p. 4 lines 90-105:\nThis would be significantly easier to understand with a graphical inset with a Lewis-\nstructure representation of an example.\nAuthor comment: We have now included a 2-D schematic of the rearrangement reaction in\nFig. 1.\nChanges to manuscript: A 2-D schematic of the rearrangement reaction is included as Fig. 1\nA.\n3. p. 5 fig 1:\nTop: One can not really see what the rearrangement is, due to the use of ball-and-\nstick graphics. See also remark above.\nBottom: Perhaps an Arrhenius plot with x-axis in 1000K/T ? Then again, Nat.Comm is\nnot a kinetics journal.\nAuthor comment: Regarding top: we have now included a 2-D schematic of the\nrearrangement reaction in Fig. 1 A. Regarding bottom: We decided to show an easier to\nread temperature relation plot for modelers. The Arrhenius form of the plot is now included\nin the supplementary (Fig. S22).\nChanges to supplementary: The Arrhenius plot of the rearrangement reactions of toluene\nderived i-BPR is provided in the supplementary (Fig. S22).\n4. p 7 fig 2:\n- Caption: \"autoxdation\" -> autoxidation\n- The intermediates must not be represented as trans-alkenes but strictly as cis-\nisomers or unspecified (where allylic rotation is possible). Trans-stereoisomers are\nnot what was calculated (sampling a few of the log files shows as much), are not\nwhat is expected for the parent molecule decomposition, and would prevent some\nof the chemistry to happen (e.g. the H-shift in R2b-RO2)\n- The fates for P-C2 do not sum to 100%\nAuthor comment:\n- Typo in caption corrected.\n- The intermediates in Fig. 2 are now represented as cis-isomers.\n- The fates of P-C should sum up to 79% as the remaining is the yield of P-C . We\n2 1\nacknowledge that this might not be clear from the figure, and we now make a note\nto this effect in the figure caption.\nChanges to manuscript:\n- Typo corrected.\n- Fig. 2 modified to show intermediates as cis-isomers.\n- Text added to Fig. 2 caption noting that the yield of P-C is 79% and that the fates of\n2\n5. p. 9 line 183: \" indicating that the mechanism proposed in this work is the dominant\nunimolecular pathway to the SOA precursors that we detect.\"\n\"is\" -> is likely to be / is consistent with / ...\nAuthor comment: We agree with the reviewer’s correction to this sentence. The text now\nreads “…indicating that the mechanism proposed in this work is likely to be the dominant\nunimolecular pathway to the SOA precursors that we detect.”\nChanges to manuscript: The text now reads “…indicating that the mechanism proposed in\nthis work is likely to be the dominant unimolecular pathway to the SOA precursors that we\ndetect.”\n6. p. 12, fig 4 : perhaps remove the minor grid lines to lighten the plot\nAuthor comment: The minor grid lines have been removed from Fig. 4.\nChanges to manuscript: Minor grid lines in Fig. 4 have been removed.\n7. p. 13, line 246: \"This could re-initiate autoxidation and provide a long range\ntransport mechanism for NOx\"\nIt is unclear how prompt decomposition losing NO2 could be useful for long-range\nNOx transport, as the NO2 is then lost before it can be transported?\nAuthor comment: While the decomposition of the ipso-RONO is prompt, the lifetimes\n2\norders of tens of minutes to hours as indicated by their decomposition rates in the last row\nof Table S9. However, we agree that these timescales are too short for long-range transport,\nso we have decided to omit “long-range” and only say “transport” instead.\nChanges to supplementary: “The relatively fast conversion of the benzene derived B-RONO\n2\nto RB-RO + NO is significant as it corresponds to an atmospheric lifetime of Ben-B-RONO of\n2 2\nabout 34 minutes. Similarly, the atmospheric lifetimes of Tol-meta-B-RONO and Tol-para-B-\n(conclusion).\n8. p. 16, wave function stability\nWhat do the CASSCF calculations show for multi-reference effects on the biradical O-\nO bond breaking? Is the active space (1 virtual orbital) large enough to accommodate\nsuch multi-reference effects ?\nAuthor comment: The wave function stability calculations were only carried to ensure that\nthe initial Hartree-Fock calculation before CCSD(T) converged to the correct minima and not\nto check for multi-reference effects. But we acknowledge that we should have noted the\npossibility of multi-reference effects in the rearrangement mechanism. We now provide the\nT1 diagnostic numbers of the T-C and T-C rearrangement transition states in the\n1 2\nsupplementary. Note that these are within 0.025 and under the accepted threshold for\nopen-shell systems. In addition, the triples contribution to the total atomization energy\n%TAE(T) value was calculated for T-C and found to be 2.7%, indicating minor static\n1\ncorrelation effects.\nChanges to supplementary: The T1 diagnostic and %TAE(T) numbers are now provided in\nSection 11 of the supplementary.\n9. p. 17, line 341 \"In the MESMER simulations, the harmonic frequencies were treated\nas hindered rotors\"\nI assume the authors mean that only those internal modes corresponding to internal\nrotations were removed from the vibrational frequencies and treated as hindered\nrotors.\nAuthor response: The reviewer is correct. The modified text now reflects the reviewer’s\ndescription.\nChanges to manuscript: “In the MESMER simulations, the internal modes corresponding to\ninternal rotations were removed from the vibrational frequencies and treated as hindered\nrotors. This was performed…”\n10. p S9, top, ring opening in B-alkyl\nThere are much better discussions of this channel available that should be cited, e.g.\nGlowacki et al. 2009, Vereecken 2018, Vereecken 2019, as well as experimental\nevidence of its lack of importance by the Wennberg group (Xu et al. 2020)\nAuthor response: Thank you. The suggested papers are now cited.\nChanges to supplementary: The suggested papers on the ring opening of B-alkyl are now\ncited in the supplementary. “In addition to adding an O to form BPR, B-alkyl can undergo an\n2\nisomerization reaction to form B-oxy (see Fig. S8 (2-4)). This path has been shown to be\nunimportant for the benzene derived BPR(6).”\n11. p. S12, NO experiments.\nNO can lead to autoxidation proceeding through different pathways (so-called\nalkoxy-peroxy autoxidation steps). They may form different isomers of the same\nmass, and a mass spectrum won't reveal mechanistic changes. Alkoxy-peroxy\nautoxidation is also implicated as a key step in ring breaking HOM formation in some\nVOC (e.g. Shen et al. 2022, Guo et al. 2022). Furthermore, Vereecken (2018, 2019)\npoints out the role of NO in changing the early stage aromatic oxidation mechanism,\nbased on available literature data. These experiments may thus not as\nstraightforward to interpret as the authors imply.\nAuthor comment: We agree with the reviewer that the formation of organo nitrates is not\nthe only possible pathway for RO + NO. Alkoxy-peroxy autoxidation steps are indeed\n2\nimportant in many cases but are expected to lead to products with one less O-atom. In our\ncase, this would lead to peroxy radicals with even number of oxygen atoms, not odd as\nmeasured. It is unlikely that the peroxy radicals will react with NO two times to produce odd\nnumber of O-atoms and react with NO a third time to produce the organo nitrates we\ndetect under the 3.7 s reaction time conditions of our experiments.\nChanges to manuscript: “Reactions of peroxy radicals with NO can also lead to alkoxy\nradicals and the molecule can continue to oxidize via the alkoxy-peroxy autoxidation\npathway. However, the resulting peroxy radicals will have an even number of oxygen atoms\nand not odd as the peroxy radicals involved in the formation of the organo nitrates reported\nin this study. The peroxy radicals are unlikely to undergo two NO reactions to revert to an\nodd number of oxygen atoms followed by a third NO reaction to produce the organo nitrates\nwe detect under the short residence time conditions of our experiments.”\n12. p. S17, top: \"the rearrangement mechanism is also possible for other aromatic\nderived bicyclic molecules. Table S8 \"\nWithout context, it is not clear which rearrangement mechanism is meant. The\nbicyclic alkyl radicals have very different rearrangement mechanism reported (ring\nretaining with epoxide-alkoxy) than given in this work for bicyclic peroxy radicals\n(ring opening with H-shift and carbonyl formation).\nAuthor comment: We agree that additional clarification is needed here. We now explicitly\nmention that the rearrangement mechanism we discuss is the one reported in this work.\nChanges to supplementary: The text in the supplementary is modified to show that the\nrearrangement mechanism described is the one reported in this work. “In addition to BPRs,\nthe rearrangement mechanism described in this work is also possible for other aromatic\nderived bicyclic molecules.”\n13. p. S19, bottom\n- Mention \"site-specific O2 addition\" at the start of the last paragraph\n- \"H-abstraction by O2 to form C7H8O5 is not direct but follows the initial addition of\nO2 to the C(OH) carbon.\"\nThis needs specific literature citations\n- \"These transition states were calculated to be -0.7 kcal/mol and 1.9 kcal/mol,\nrespectively, above R1 at F12 level of theory.\" -> \"...relative to R1 at the F12 level of\ntheory.\"\n- \" the potential energy surface shown in Fig. S12 was used as input in a MESMER\nsimulation to account for the excess energy of R1.\"\nThis glosses over a lot of details. At the very least refer explicitly to the Mesmer input\nfiles in the Zenodo archive, but preferable document this more thoroughly.\nAuthor response:\n- Thank you, we now mention this.\n- This was a result from our calculations. Intrinsic reaction coordinate calculations on\nthe transition state structure corresponding to the H-abstraction by O showed that\n2\nthe reactant well structure has O on the C(OH) carbon. We now make this clear in\n2\nthe supplementary text.\n- We have incorporated this correction.\n- Additional details are added and the MESMER input is added to the Zenodo archive.\nChanges to supplementary: Pg. S19: “Due to site specific O addition…”\n2\n“Transition state calculations followed by intrinsic reaction coordinate calculations indicated\nthat the H-abstraction by O to form C H O is not direct but follows the initial addition of O\n2 7 8 5 2\nto the C(OH) carbon.”\n“The formation of all intermediates in Fig. S18 are preceded by transition states and these\nreactions were treated using the SimpleRRKM method with Eckart tunneling. The\nintermediates P-C and R were treated as “modelled” and R -RO and R -RO as sinks in\n2 1 1a 2 1b 2\nthe simulation. The MESMER input file is provided in the data archive.”\n14. p. S20, bottom \" the analytical solution is represented by its Taylor expansion\"\nThe analytical solution to what? The MCM ?\nAuthor response: The analytical solution for diffusion of chemical species in a laminar flow\nfield of a tube, as it is provided by Ingham (D. B. Ingham, Journal of Aerosol Science 6, 125-\n132 (1975)), is not a good representation if there are sources/sinks of those molecules (we\ngot sources: the chemical reactions). As a consequence, we expanded this analytical solution\ninto its Taylor-representation (the same is done in the referenced article: Pichelstorfer &\nHofmann, 2017 - Pichelstorfer, L. and Hofmann, W., Aerosol Science and Technology 51,\n1419-1428 (2017)).\nChanges to supplementary: “…the analytical solution for diffusion of chemical species in a\nlaminar flow field of the tube is represented by its Taylor expansion”.\n15. p. S21, middle \"The likely reason for this is the less reactive TME RO2s.\"\nWhy are they less reactive ? Is literature data available ?\nAuthor response: The sentence was added in error, it has now been removed.\nChanges to supplementary: Sentence “The likely reason for this is the less reactive TME\nRO2s” removed in the supplementary.\n16. p. S22, ref 1: remove \"Vertiotie.4P\"\nAuthor response: Thank you for pointing out the typo. This has now been removed.\nChanges to supplementary: Typo removed from supplementary.\nReviewers' Comments:\nReviewer #2:\nRemarks to the Author:\nComments on NCOMMS-23-12910A, “Molecular rearrangement of bicyclic peroxy radicals: key route to\naerosol from aromatics”, by Iyer et al.\nThe revision here provides more evidence on the proposed new mechanism. The oxidation\nmechanisms are always complex, and search for new reaction pathways is desired all the time. The\nfinding here provides additional information on the formation of highly oxidized products and SOAs.\nComments:\n1. It should be noticed that the rearrangement of BPRs from ipso-addition in this study and the H shift\nof BPRs from para-addition from Wang et al. are parallel and independent reaction pathways. Under\ndifferent conditions (particularly the residual time), pathways with different rates show different\nproduct formation. These two pathways do not compete with each other. Under the atmospheric\nconditions, there is enough time for the reaction to complete and both pathways should exist and\ndifferent products are formed. When NO is low, both pathways are likely the dominant for ipso- and\npara-additions.\nWe agree the existence of the new reaction pathway, but the H shift mechanism in para-path should\nbe at least equally important in real atmosphere.\n2. On BPRs with NO: The existence if ROONO does not affect the kinetics of RONO2. I am satisfied\nwith the statement “… only some fraction of BPR + NO reactions will lead to B-RONO2”. Decomposition\nof x-B-RONO2 is fully thermal, so the RRKM-ME modeling does not need the entry “x-BPR + NO” as\nshown in S16.\nReviewer #3:\nRemarks to the Author:\nThis manuscripts describes a pathway in the atmospheric oxidation of aromatics that, based on the\npresented theoretical and experimental data, is likely to be the source of the unexplained HOM\nformation from such compounds. The theoretical methodologies used are expected to yield robust\nresults, and are supported by a thoughtful interpretation of experimental data.\nThe research is important and timely, as there is a lot of interest in HOM and aerosol formation, and\nthe role of aromatics in urban air quality. This pathway is likely to receive a lot of further attention,\nand will be included in atmospheric kinetic and air quality models.\nThe authors have addressed all questions and comments raised in the referees comments, and I have\nno further suggestions for improvement. I support publication of this manuscript as is.\nWe thank the reviewers once again for their time and feedback.\nReviewer 2:\nGeneral comment: The revision here provides more evidence on the proposed new\nmechanism. The oxidation mechanisms are always complex, and search for new reaction\npathways is desired all the time. The finding here provides additional information on the\nformation of highly oxidized products and SOAs.\nAuthor comment: We thank the reviewer for their positive comment.\n1. It should be noticed that the rearrangement of BPRs from ipso-addition in this study\nand the H shift of BPRs from para-addition from Wang et al. are parallel and\nindependent reaction pathways. Under different conditions (particularly the residual\ntime), pathways with different rates show different product formation. These two\npathways do not compete with each other. Under the atmospheric conditions, there\nis enough time for the reaction to complete and both pathways should exist and\ndifferent products are formed. When NO is low, both pathways are likely the\ndominant for ipso- and para-additions.\nWe agree the existence of the new reaction pathway, but the H shift mechanism in\npara-path should be at least equally important in real atmosphere.\nAuthor comment: We agree that the pathway described in the Wang et al. 2017 paper,\ndespite not being observed in our experiments, could nevertheless be important under\ncertain atmospheric conditions. We now note this in the manuscript.\nChanges to manuscript: Page 3 - Nevertheless, if this is the dominant fate of the toluene +\nOH system in our experiments,…\nPage 3 - However, we observe that the mass spectra for toluene and CD -toluene are near\n3\nidentical, indicating that H-shift from the methyl group is unlikely to play a major role in our\nexperiments. Nevertheless, this pathway might well be important under certain atmospheric\nconditions. The methyl H-abstraction pathway reported in Wang et al. and the\nrearrangement pathway reported here do not compete with each other but depend on the\nsite of the initial OH addition to toluene (para vs ipso relative to the methyl substituent).\n2. On BPRs with NO: The existence if ROONO does not affect the kinetics of RONO2. I\nam satisfied with the statement “… only some fraction of BPR + NO reactions will\nlead to B-RONO2”. Decomposition of x-B-RONO2 is fully thermal, so the RRKM-ME\nmodeling does not need the entry “x-BPR + NO” as shown in S16.\nAuthor comment: We agree that Supplementary Figure 16 does not need the reactants x-\nBPR + NO. This has now been corrected.\nChanges to supplementary: Supplementary Figure 16 modified to start the PES from x-\nRONO instead of x-BPR + NO. Supplementary Table 9 has also been similarly modified.\nGeneral comment: This manuscripts describes a pathway in the atmospheric oxidation of\naromatics that, based on the presented theoretical and experimental data, is likely to be the\nsource of the unexplained HOM formation from such compounds. The theoretical\nmethodologies used are expected to yield robust results, and are supported by a thoughtful\ninterpretation of experimental data.\nThe research is important and timely, as there is a lot of interest in HOM and aerosol\nformation, and the role of aromatics in urban air quality. This pathway is likely to receive a\nlot of further attention, and will be included in atmospheric kinetic and air quality models.\nThe authors have addressed all questions and comments raised in the referees comments,\nand I have no further suggestions for improvement. I support publication of this manuscript\nas is.\nAuthor comment: We thank the reviewer for their positive comment."}]

Decision letter