Reactivity of Benzoylperoxy Radicals with Monoterpenes: One-Step Reaction to Form Low-Volatility Organic Compounds

Supporting information for Reactivity of Benzoylperoxy Radicals with Monoterpenes: one-step reaction to form low-volatility organic compounds Dominika Pasik1,2, Noora Hyttinen3, Siddharth Iyer4, and Nanna Myllys1,2 1Department of Chemistry, University of Helsinki, Helsinki, 00014, Finland 2Institute for Atmospheric and Earth System Research, University of Helsinki, Helsinki, 00014, Finland 3Atmospheric Research Centre of Eastern Finland, Finnish Meteorological Institute, Kuopio, 70211, Finland 4Aerosol Physics Laboratory, Tampere University, Tampere, 33014, Finland Corresponding authors: [email protected],[email protected] Summary of supporting information •Number of pages: 10 •Figures S1-S5 •Tables S1-S6 S1 Contents S1 β-scission reaction rates S3 S2 Tunneling coefficient for IM7 H-shift-3 S4 S3 H-shifts sabinene-IM2 S4 S4 Saturation vapour pressures S5 S5 Alkyl radical ring-opening reactions for sabinene-NO3derived systems S6 S6 Lennard-Jones parameters for RRKM-ME calculations S7 7 Addition of C6H5C(O)OO ·to double bond in monoterpenes S7 S8 Estimation of C6H5C(O)OO ·concentration in the atmosphere S8 S9 APR+MT reaction energetics S9 References S10 S2 S1 β-scission reaction rates For monterpene+benzoyl peroxy radical-derived alkoxy radicals we calculated β -scission rearrangement reaction rate coefficients. FigurS1 presents considered structures and obtained results are presented in Table S1. Figure S1: Molecular structures of examined acetyl-alkoxyl stereoisomers of limonene, α -pinene and sabinene (left side). Reaction labeling for alkoxy scissions reactions (right side). Results presented in Table S1 align with findings obtained by Pasik et al. (2025). For α -pinene and limonene we observe that β -scissions towards the right-side are favored with a 100% yield for all stereoisomers. For two sabinene-alkoxy stereosimers, we observe different β -scission yields. R-alkoxy favours R β 3 scission (70%), while S-alkoxy prefers R β 1 (71%). Left-side scissions were not considered for sabinene, as previous studies by Pasik et al.(2025) reported a 0% yield for this reaction pathway. Table S1: Zero-point corrected barrier heights (∆E) for considered acetyl–alkoxy β -scission reactions, corresponding MC-TST rate coefficients and product yields. monoterpene ∆E [kcal/mol] kT ST [1/s] Yield [%] Rβ1 Rβ2 Rβ3 Rβ1 Rβ2 Rβ3 Rβ1 Rβ2 Rβ3 sabinene-1-R 10.5 x 10.1 8×104x 2×10530 x 70 sabinene-1-S 9.6 x 9.9 6×105x 4×10571 x 29 limonene-1-RR 7.3 13.5 x 6.2×1062.9×102x 100 0 x limonene-1-RS 6.3 12.6 x 1.3×1083.8×103x 100 0 x limonene-1-SR 7.1 14.4 4.3×1074.3×107x 100 0 x limonene-1-SS 7.4 12.5 x 3.6×1073.1×103x 100 0 x α-pinene-1-RR 8.2 12.0 x 1.8×1066.7×103x 100 0 x α-pinene-1-SR 6.5 11.6 x 1.5×1084.7×104x 100 0 x S3 S2 Tunneling coefficient for IM7 H-shift-3 In Section 3.3 of the main text, we calculated unimolecular reactions for the sabinene-derived peroxy radical, referred to as IM7. H-shift-3 reaction leads to formation of α -QOOR radical which decomposes. We were unable to optimize the product of only H-shift reaction (without decomposition). To estimate the Eckart tunneling factor we took electronic energies from potential energy surface obtained in IRC calculations. For structure S1 the forward barrier was 16 kcal/mol and tunneling factor was 536. For point S2, the forward barrier was 27 kcal/mol, and the tunneling coefficient was 3227. This discrepancy affects the reaction rate coefficient for H-shift-3 by approximately one order of magnitude, meaning the kfor this reaction is around 10 −3 –10 −2 1/s. Optimized decomposed product has around 64 kcal/mol lower energy than the transition state. The potential energy surface obtained from IRC calculations is presented in Figure S2. Figure S2: Potential energy surface for H-shift-3 reaction for IM7 taken from IRC calculations. Tunneling factors were calculated for structures S1 and S2. TS stands for transition state, Rreactant and Pproduct. O-O distance in TS structure is 1.43 Å. S3 H-shifts sabinene-IM2 In oxidation pathaway of sabinene proposed in the main text, RC1 compound undergoes ringopening reaction or O2 -addition. In the case of the latter, it would form the compound shown in Figure S3 denoted as IM2. For this system we considered H-shift reactions. Results are presented in the Table S2. The fastest reaction is H-shift-4 and it leads to the formation of α -QOOH radical. α -QOOH radicals are known to be unstable and decompose to a closed-shell product and OH radical. S4 Figure S3: Labeling for H-shift reactions of sabinene peroxy radical IM2. The numbers on the scheme correspond to the numbering in the Table S2. Table S2: Energy barrier heights [kcal/mol] and calculated MC-TST reaction rate coefficients [ kMC−T ST 1/s] for studied H-shift reactions of sabinene-derived peroxyl radical. *H-shift-6 reaction leads to immediate decomposition of a product, for which we could not find optimized structure, thus calculating reliable tunneling factor was impossible. However barrier for this reaction is too high to be competitive and lack of tunneling correction does not impact overall result. pathway barrier kMC−T ST Eckart tunneling factor H-shift-1 35.0 5×10−97919 H-shift-2 26.4 5×10−83 H-shift-3 22.0 3×10−322 H-shift-4 21.5 2 208 H-shift-5 25.5 7×10−631 H-shift-6* 31.8 3×10−12 decomposes S4 Saturation vapour pressures To ensure our calculations are reliable and correct, we estimated saturation vapour pressures for both radical (denoted as -OO · ) and closed-shell system (-OOH). Results from COSMOthem and machine learning models COSMO-ML are presented in Table S3. Table S3: COSMO-ML-Predicted and COSMOtherm-Estimated Saturation Vapor Pressures (p sat in Pa) of monoterpene(MT)+Benzoyl Peroxy Radical Oxidation Products at 298.15 K MT+ C6H5C(O)OO·molecular formula COSMO-ML, solid COSMO-ML, liquid COSMOtherm, liquid α-pinene-1-OO·C17H21O52.5×10−41.4×10−21.2×10−3 α-pinene-1-OOH C17H22O53.0×10−55.5×10−45.2×10−5 β-pinene-1-OO·C17H21O52.4×10−41.1×10−27.3×10−4 β-pinene-1-OOH C17H22O59.0×10−52.0×10−32.6×10−5 limonene-1-OO·C17H21O56.3×10−55.4×10−36.3×10−4 limonene-1-OOH C17H22O51.6×10−64.5×10−52.6×10−5 sabinene-1-OO·C17H21O53.1×10−52.4×10−38.0×10−4 sabinene-1-OOH C17H22O55.2×10−61.5×10−42.4×10−7 system RC0-OO·C17H21O68.7×10−61.5×10−41.7×10−4 RC0-OOH C17H22O67.3×10−77.4×10−62.6×10−5 IM4-OO·C17H21O81.9×10−67.2×10−62.4×10−9 IM4-OOH C17H22O86.2×10−11 1.3×10−10 1.5×10−13 sabinene-RC2-OO·C17H21O53.6×10−51.8×10−31.3×10−3 sabinene-RC2-OOH C17H22O53.6×10−68.1×10−53.9×10−5 IM7-OO·C17H21O72.4×10−67.3×10−54.6×10−4 IM7-OOH C17H22O72.6×10−81.7×10−71.4×10−7 S5 S5 Alkyl radical ring-opening reactions for sabineneNO3 - derived systems Since the 3-membered ring-opening reaction in the RC1 system (see Figure 5 in main text) leads to a new radical with less steric hindrance compared to the original RC1, thereby making further autoxidation more efficient, we consider analogous reactions for sabinene+ NO3 -derived intermediates. This serves as a continuation of the Draper et al. (2024) study, where the authors investigated ring-opening reactions and bond scissions of monoterpene+ NO3 -derived alkyl and alkoxy radicals. The schematic workflow, including calculated barriers and reaction rate coefficients, is shown in Figure S4. Figure S4: Proposed fate of sabinene+ NO3 . Mechanism within dashed box was adapted from Draper et al. (2024), whereas remaining reactions were calculated in this study. Energy barrier heights values [kcal/mol] are marked as ∆E and corresponding MC-TST reaction rate coefficients are denoted as k. We indeed observe similar reactivity of sabinene+ NO3 -derived radicals compared to the analogous APR-derived system (see Figure 5, starting from RC1). Beginning with the structure taken from Draper et al. (2024), we calculate an H-shift reaction for the formed peroxy radical, followed by a subsequent ring-opening reaction. We find the H-shift reaction to occur at a rate of approximately 1 s −1 , resulting in an alkyl radical with the radical center positioned near the 3-membered ring. Our calculations show that the ring opening proceeds about five orders of magnitude faster than the competing bimolecular reaction with oxygen (estimated based on literature values). This represents a novel pathway for the sabinene+ NO3 -derived system that may lead to more functionalized products. However, it is important to note that only around 14% of the original sabinene undergoes reactions that eventually lead to RC3, which was the starting point for our calculations. Nevertheless, NO3 -initiated reactions are of great importance, and even minor pathways can significantly impact the overall oxidation mechanism. For more details, please refer to Draper et al. (2024). S6 S6 Lennard-Jones parameters for RRKM-ME calculations Table S4: Lennard-Jones parameters σ and ϵ used for the alkyl radical formed in reaction with benzoyl peroxy radical (sab-APR), and the alkoxy radical formed from ring-opening rearrangement (RO-sab-APR) in RRKM-ME calculations. system σ(Å) ϵ/kB(K) sab-APR 8.81 714 RO-sab-APR 8.98 726 S7 Addition of C6H5C(O)OO ·to double bond in monoterpenes In Section 3.1 of the main text, we calculate rate coefficients for the addition reaction of the benzoyl peroxy radical to the double bond in monoterpenes. As shown in Table 1 in main text, some reactions yield negative electronic energy barriers. To address this, we calculate rate coefficients using Gibbs free energy barriers following the equation below. kMC-TST =kBT hpref nTS P i exp−GTSi −GRmin RT  nR P j exp− GRj −GRmin RT ,(S1) where kB is the Boltzmann constant, h is Planck’s constant, T is the temperature (298.15 K), and pref denotes the reference pressure. GRmin corresponds to the Gibbs free energy of the lowest-energy reactant conformer, R is the gas constant. The numerator accounts for all nTS transition state conformers ( i ) through their Gibbs free energies GTSi , referenced to GRmin . The denominator describes the Gibbs free energies of reactant conformers GRj relative to global minimum. As indicated in Table S5, all Gibbs free energy barriers are positive. When comparing the results, we find that the Gibbs free energy based rates ( kTSTG ) are comparable with the MC-TST rates based on electronic energies. S7 Table S5: Zero-point corrected energies [kcal/mol] for monoterpene + C6H5C(O)OO· accretion reaction barrier (∆ G ) calculated at DLPNO-CCSD(T)/aug-cc-pVTZ// ω B97X-D/6-31+G*. Corresponding reaction rate coefficients at 298 K for monoterpene + C6H5C(O)OO· accretion reaction ( kTSTG ) [cm 3 s −1 ] were calculated using Equation S1. Total reaction rate coefficient was calculated as a sum of all four (for α -pinene, β -pinene and sabinene) or six (limonene) reaction rate coefficients. monoterpene ∆G kTSTGktotal α-pinene-1 (a) 11.7 1.9×10−15 2.0×10−15 α-pinene-2 (a) 13.6 4.6×10−17 α-pinene-1 (b) 14.7 1.7×10−17 α-pinene-2 (b) 17.1 8.8×10−20 β-pinene-1 (a) 12.3 5.9×10−16 6.5×10−16 β-pinene-2 (a) 14.7 4.8×10−18 β-pinene-1 (b) 14.7 5.3×10−17 β-pinene-2 (b) 17.7 3.7×10−20 sabinene-1 (a) 11.6 1.5×10−15 3.0×10−15 sabinene-2 (a) 14.6 6.4×10−17 sabinene-1 (b) 12.2 1.4×10−15 sabinene-2 (b) 15.1 5.1×10−18 limonene-1 (a) 12.2 1.6×10−15 9.6×10−15 limonene-2 (a) 11.9 1.8×10−15 limonene-3 14.7 1.0×10−17 limonene-4 13.5 3.1×10−16 limonene-1 (b) 13.4 8.4×10−16 limonene-2 (b) 11.5 5.0×10−15 S8 Estimation of C6H5C(O)OO · concentration in the atmosphere We used steady state theory to estimate concentration of C6H5C(O)OO· under atmospheric conditions. Let’s assume that the main source of C6H5C(O)OO· is benzaldehyde reacting with OH radical, followed by oxygen addition. C6H5CHO + OH k1 −→ C6H5C(O) ·+H2O(S2) C6H5C(O) ·+O2(+M) k2 −→ C6H5C(O)O2·(S3) The kinetic limiting step here is formation of C6H5C(O)· that’s why we assume rapid oxygen addition and for simplicity don’t include it in steady state equation. As for the main sink of C6H5C(O)OO·we assume reaction with NOx C6H5C(O)O2·+NOx kNOx −−−→ products (S4) However, instead of using the explicit sink equation, for NO x we will use the loss rate, which can be expressed as kloss =1 τbi (S5) where τbi is the lifetime of RO 2 with respect to bimolecular reactions. Based on studies by Kenagy et al. (2024), this value is approximately 102s. Thus, kloss =1 τbi =1 102= 10−2s−1.(S6) S8 Steady state d[C6H5C(O)O2·] dt =k1[OH][C6H5CHO] −kloss[C6H5C(O)O2·]=0,(S7) ⇒[C6H5C(O)O2·]ss =k1[OH][C6H5CHO] kloss .(S8) Numerical substitution We use: •k1= 1.0×10−11 cm3molecule−1s−1, •[OH] = 1.0×106molecule cm−3, •kloss = 1.0×10−2s−1, •[C6H5CHO] = 1 ppb = 2.46 ×1010 molecule cm−3. Production rate: k1[OH][C6H5CHO] = (1.0×10−11)(1.0×106)[C6H5CHO] = 1 ×10−5∗[C6H5CHO]s−1. Steady-state concentration (1ppb benzaldehyde): [C6H5C(O)O2·]ss =2.46 ×105 1.0×10−2= 2.46 ×107molecule cm−3. Steady-state concentration (4ppb benzaldehyde): [C6H5C(O)O2·]ss =9.84 ×105 1.0×10−2= 9.84 ×107molecule cm−3. S9 APR+MT reaction energetics The reaction energetics of monoterpene + APR can be generally represented as shown in Figure S5. The separate reactants first form a reaction complex, and passage through a transition state is required to yield the accretion product. In Table S6, we present detailed reaction energetics for the studied systemsone for each monoterpene.As evident from the table, the calculated decomposition rates are on the order of 10 1 s 1 , which is approximately six orders of magnitude slower than the literature values for O2 addition to a radical center. For this reason, we consider decomposition not to be competitive in this case. Table S6: Zero-point corrected energies [kcal/mol] for the monoterpene + C6H5C(O)OO· accretion reaction barriers calculated at the DLPNO-CCSD(T)/aug-cc-pVTZ// ω B97X-D/6-31+G level.* ∆ ERC denotes the energy difference between the reaction complex (RC) and the transition state (TS). ∆ Eex represents the energy difference between the separated reactants and the addition product. ∆ Edecomp corresponds to the energy difference between the addition product (acting here as reactant) and the transition state of unimolecular decomposition with corresponding LC-TST reaction rate coefficient kdecomp [1/s]. monoterpene ∆ERC ∆Eex ∆Edecomp kdecomp α-pinene-1 (a) 3.2 16.5 15.9 1.8×101 β-pinene-1 (a) 6.9 15.6 15.7 2.4×101 limonene-1 (a) 8.0 16.4 15.2 2.3×101 sabinene-1 (a) 5.0 17.7 15.8 2.6×101 S9