The 2013 IPCC assessment report illustrates that the greatest source of uncertainty in global climate modeling comes from aerosol. 1 Particulate matter in the atmosphere can influence atmospheric radiative balance both directly by scattering or absorbing light and indirectly by affecting the formation, reflectivity, and lifetime of clouds, and it is therefore an important factor limiting our understanding of climate as a whole. Secondary organic aerosol (SOA), which forms through secondary reactions of gas-phase emissions such as oxidation of volatile organic compounds (VOCs), contributes a major fraction of the global submicron aerosol. 2 It has been shown through numerous field studies, laboratory measurements, and the occasional modeling study that NO3 radical oxidation of monoterpenes is a significant, though often overlooked, source of SOA. [3][4][5] For example, Pye et al. 4 incorporated NO3 + monoterpene chemistry into GEOS-Chem, parameterized using laboratory NO3 + β-pinene SOA yields. 6 They found that SOA from monoterpenes approximately doubled in regions where monoterpene chemistry is important, comparing to simulations where NO3 chemistry was omitted. However, the significance of this chemistry is complicated by the fact that while most abundantly emitted monoterpenes (e.g. β-pinene, Δ-3-carene, and limonene) have moderate-to-high SOA yields with NO3 radical, the single most abundantly emitted monoterpene (α-pinene) has a negligible SOA yield with NO3. 3,7 This presents a challenge to modelers, since most models don't consider NO3 chemistry and those that do are subject to uncertainties due to poorly understood terpene speciesdependence of SOA formation and corresponding poorly characterized regional variability of SOA precursors.
At a glance, the structural difference between α-pinene and other bicyclic monoterpenes that would lead to such large differences in condensable products is not obvious. Structures of two of the most prevalent monoterpenes, α-pinene and Δ-3-carene, are shown in Figure 1a, highlighting that these molecules differ only by the location and size of the small secondary ring structure.
Both of these molecules are expected to undergo the same known atmospheric oxidation pathways in the gas phase, which is summarized in Figure 1b, where products may contribute to SOA formation or growth through thermodynamic partitioning or reactive uptake. For NO3 radical-initiated oxidation, the NO3 radical adds to the double bond, forming an alkyl radical (R).
In the oxygen-rich atmosphere, oxygen rapidly adds to the alkyl radical, forming a peroxy radical (RO2). 8 The peroxy radical will likely undergo a bimolecular reaction with another radical species, which, at night when NO3 chemistry is most important, is predominantly NO3, HO2, or RO2. These reactions lead either to alkoxy radicals (RO), or to closed-shell products like hydroperoxides, alcohols, and aldehydes or ketones. 9 Under conditions where the RO2 lifetime is long enough (on the order of seconds), research in the last few years has demonstrated that peroxy radicals with suitable substituents are able to undergo internal hydrogen shifts, regenerating an alkyl radical, which subsequently forms a new peroxy radical, thus initiating a chain of "autoxidation." [10][11][12][13] Alkoxy radicals are short-lived, and can either react with oxygen, decompose, or isomerize. RO reactions often lead to closed shell products, though both decomposition and isomerization reactions can also lead to the formation of new alkyl radical, and subsequently peroxy radical, species. 14 Since multiple cycles of radical propagation reactions may occur before terminating to a closed shell product, we will differentiate between different peroxy or alkoxy radicals as different generations, with the counter triggered by a backward arrow to an RO2 in Figure 1b. We note that not all pathways are available to all VOCs and some pathways may only become available for later generations of chemistry. Kurtén et al. 15 used computational chemistry to compare rate constants for the 1 st generation radical (RO2 and RO) rearrangement reactions following NO3 oxidation of α-pinene and Δ-3carene. They found that the potential unimolecular reactions of the 1 st generation Δ-3-carene peroxy radicals were calculated to be too slow to contribute significantly to the final product distribution. Instead, they identified the 1 st generation NO3-substituted RO as the point where the mechanisms for these two monoterpenes diverge, likely explaining the large difference in SOA yields from the two. As shown in Figure 2, the α-pinene-derived O2NO-RO overwhelmingly favors the pathway leading to closed-shell pinonaldehyde, whereas the corresponding Δ-3carene-derived O2NO-RO is more likely to undergo the radical-retaining pathway, enabling further generations of RO2 and RO radical rearrangement reactions, which we expect to lead to condensable products. In this study, we expand upon the mechanism presented in Kurtén et al. 15 and calculate rate constants for various unimolecular reactions of the probable 2 nd generation RO2 and RO generated by Δ-3-carene + NO3 chemistry. We then use these rate constants to predict the most probable 2 nd generation reaction products. These predicted products are then compared to compounds observed in the gas phase during chamber experiments of Δ-3-carene + NO3 chemistry. expected to be competitive with the right scission due to the unfavorability of the alkyl radical on the strained ring. All other reactions (solid arrows) are expected to occur, with an approximate 50/50 branching for the two Δ-3-carene RO pathways. 15 Beginning from the radical endpoints from the Kurtén et al. 15 Δ-3-carene mechanism shown in Figure 3a (mechanism leading to these radical endpoints shown in black in Scheme 1), we developed a computational mechanism for the next generation of chemistry, surveying five different types of unimolecular reactions as shown in Figure 3b: internal RO2 and RO hydrogen shifts (H-shifts), RO2 and RO ring closing, and RO decomposition. Published structure activity relationships (SARs) exist for many, though not all, of the possible reaction pathways assessed in this study. 16,17 However, explicit calculations of reaction barriers and rate constants for case studies such as this are valuable for several reasons. First, SARs are not available for any RO2 reactions, and existing SARs for alkoxy reactions lack certain substituent effects like the influence of -ONO2 groups on RO H-shifts. 17 Additionally, while it has been observed that unimolecular reaction rates increase with increased functionalization, 10,13 this phenomenon has not been systematically quantified, so computing rate constants for case studies like the complex multifunctional compounds in this study (i.e. a C10 organonitrate) improves our understanding of these processes for more atmospherically relevant species. 12 Finally, results from this study can provide additional validation of the applicability of existing SARs to more complex molecules. Accounting for all plausible hydrogen shifts, we compute forward reaction barrier heights and rate constants for all relevant reactions using quantum chemical methods that include coupledcluster energy corrections. For a few reactions, higher-level calculations were omitted as the barrier heights computed at a lower level of theory indicated that they would not be competitive.
The resulting detailed mechanism could be applied to a kinetics model or used to develop a parameterization that can be implemented in regional or global models in order to improve estimates of SOA formation.
Since our mechanism includes predictions of the distribution of product isomers, the results of this study are important for the interpretation of experimental data. The widespread application of chemical ionization mass spectrometry (CIMS) measurements to atmospheric chemistry has enabled characterization of the multitude of oxidized organic molecules resulting from complex chemistry. However, while some techniques can be applied to obtain chemical information beyond molecular formula, such as the use of multiple reagent ions selective toward different functional groups, 18 mass spectra alone do not provide enough information to explain observed SOA formation. 19 Two molecules with the same formula can vary by orders of magnitude in vapor pressure, depending on the identity and location of functional groups. In this study we compare our computational mechanism to laboratory measurements of the gas phase products of NO3 oxidation of Δ-3-carene performed by CIMS using NO3 -reagent ion. Since NO3 -is selective toward highly oxidized organic species and only a small number of other molecules such as sulfuric acid, it is particularly suited to validate this mechanism focusing on autoxidation pathways. 13,20,21
The computational mechanism presented in this study was developed according to the methods described in Møller et al. 22 and incorporating many of the modifications described in Kurtén et al. 15 due to the size of the molecules studied here. Since our reactant RO2 structures are composed of 17 non-hydrogen atoms, use of the multi-conformer transition state theory (MC-TST) framework was prohibitively expensive at any reasonable level of theory. We therefore made some additional modifications to the computational approach and calculated all rate constants using the lowest-conformer transition state theory (LC-TST) framework. 22 These modifications lead to a much larger uncertainty for the absolute rate constants (approximately an order of magnitude) than the complete treatment prescribed in Møller et al. 22 However, we expect the uncertainty from each modification to systematically bias absolute rate constants in the same direction for each reaction. For example, MC-TST accounts for the full population of conformers, so only including the lowest energy conformer by calculating rate constants with LC-TST will bias the absolute rate constants high. Likewise, Møller et al. 22 showed that for these types of systems, increasing the level of theory decreases the calculated absolute rate constant. Therefore, this approach should provide reasonable relative rate constants, whichlikely overestimate the absolute rate constants, but are sufficient for comparative mechanism development. 15 Additionally, due to the size of our reactants, and thus computational cost, we have chosen to investigate only the S-nitroxy stereoisomer of (+)-Δ-3-carene since the (+)-Δ-3carene enantiomer was used in the experimental portion of this study. Given that the stereocenter is far from the peroxy/alkoxy group and is freely able to rotate (since the 6-membered ring in Δ-3-carene has already opened for both of our reactants), we do not expect qualitative differences in the overall mechanism for the R-nitroxy stereoisomer.
Systematic conformer sampling for all reactants and products was performed with the Spartan'16 (Wavefunction, Inc.) software using the MMFF force field and ensuring the correct neutral charge was applied to all radical centers using the FFHINT keyword. 22 MMFF conformer sampling for the transition state structures was performed using constrained optimizations, with the relevant bond lengths (and/or angles) constrained based on a B3LYP/6-31+G(d) transition state optimization of an arbitrary conformer using Gaussian 09 Rev. D.01. [23][24][25] Constraints for Hshift, C-C scission, and addition reactions are included in Table S1. In addition, partial bonds were drawn in Spartan to describe the breaking and/or forming bonds of the transition state. This improves the MMFF optimization of the conformer sampling and the resulting geometries are closer to the local energy minima than those from a conformer sampling where the bonds of the transition state are drawn according to either the reactant or the product. Following the MMFF conformer sampling for reactants, products, and transition states, we calculated B3LYP/6-31+G(d) single point energies for all conformers and applied a 5 kcal/mol cutoff at this stage, as suggested in Moller et al. 22 for larger molecules. The use of partial bonds was tested with an Hshift reaction between a hydroxy and a peroxy radical group of a model compound, and all of the unique transition state conformers (within 2 kcal/mol of the lowest energy conformer after the B3LYP/6-31+G(d) optimization) were found using a 5 kcal/mol energy cut-off after the B3LYP/6-31+G(d) single-point calculation. For reactants and products, we performed B3LYP/6-31+G(d) optimizations, and for transition states we performed B3LYP/6-31+G(d) constrained optimizations, using the constraints mentioned above, on all structures within 5 kcal/mol of the lowest single point energy. For transition state structures, we performed full transition state optimizations with frequency calculations on unique conformers (determined by energy and dipole moment) following the constrained optimizations. Intrinsic reaction coordinate (IRC) calculations were then performed on the lowest-energy transition states at the B3LYP/6-31+G(d) level to verify that they connect the desired reactants and products. Due to the high cost of heavier calculations for molecules of this size, optimization and frequency calculations at the ωB97X-D/aug-cc-pVTZ level [26][27][28] were only performed for the lowest-energy structures found in the B3LYP/6-31+G(d) optimizations.
While ωB97X-D yields reasonable geometries and frequencies, the single point energies should be corrected using a highly correlated wavefunction-based method, such as CCSD(T). 29 However, the computational cost of canonical coupled cluster scales exponentially with molecule size and therefore cannot be applied for the studied system sizes. Therefore, on top of the ωB97X-D/aug-cc-pVTZ structures, DLPNO-CCSD(T) single point energy calculations were performed using ORCA 4.0.1.2 instead of the prohibitively expensive canonical CCSD(T) calculations. 30,31 The DLPNO-CCSD(T) method scales nearly linearly with system size, while still keeping the accuracy of its canonical counterpart, and has therefore become a popular choice to correct electronic energies of large molecular systems. 31,32 In order to check whether a singlereference method can be used for these systems, we tested both restricted open-shell and unrestricted Hartree-Fock (ROHF and UHF, respectively) reference wave functions for the DLPNO-CCSD(T) calculations, and also studied the T1 and T2 diagnostics, as well as the relative difference in DPLNO-CCSD and DLPNO-CCSD(T) total atomization energies. We found that ROHF and UHF wave functions yield similar DLPNO-CCSD(T) single point energies, with a mean absolute error of 0.2 kcal/mol, and both T1 and T2 amplitudes and total atomization energies are within acceptable ranges (see Section S1), thus confirming that singlereference methods can safely be applied. The final single point energy corrections are therefore calculated using ROHF-DLPNO-CCSD(T)/aug-cc-pVTZ with tight pair natural orbital criteria. 33 In the final LC-TST calculations, tunneling was treated using the Eckart model. 34 This requires information on the energy differences (forward and reverse barriers) between the lowest-energy transition state, and the reactants and product connected by IRC paths to this transition statewhich may not be the lowest-energy reactants and products used in the overall LC-TST rate expression. Due to computational cost, the forward and reverse barriers needed for the tunneling calculation were estimated using a combination of approaches. Specifically, the ωB97X-D zeropoint corrected barriers (energy differences between the lowest-energy transition state and the lowest-energy reactant or product) was corrected by the B3LYP/6-31+G(d) energy difference between the lowest-energy conformer, and the conformer actually connected to the transition state via an IRC path.
We conducted chamber experiments to validate the computational mechanism. Experiments were performed in a 560 L stainless steel chamber, described in detail in De Haan, et al., 35 operating in flow-through mode with a 23 minute residence time. NO3 radical was formed in situ by combining O3 (~370 ppb) with NO2 (~200 ppb). Ozone was generated by irradiating purified air produced by a zero air generator (model 737-13, Aadco Instruments) with ultraviolet light produced by a PenRay lamp (model 97-0066-01, Analytik Jena). NO2 was provided by a commercially prepared gas cylinder (2.56 ppm in air, Airgas Corp.). The concentrations of these compounds in the chamber were monitored with commercial O3 (Model 106-L, 2B Technologies) and NOx (Model 405 nm, 2B Technologies) analyzers. While we did not have NO3 radical or N2O5 measurements available, we estimated steady state concentrations of N2O5 (~50 ppb) and NO3 (~0.6 ppb) using the home-built kinetics box model described in Draper et al. 36 Once the oxidants reached steady state, Δ-3-carene (~50 ppb) was added to the chamber for an approximate 1:1 Δ-3-carene to NO3 ratio (including both NO3 and N2O5). The Δ-3-carene source consisted of a home-prepared gas cylinder containing 23 ppm of (+)-Δ-3-carene (>90% purity, TCI America.) in nitrogen.. Particle number-size distribution in the chamber was monitored with a Scanning Mobility Particle Sizer (SMPS) consisting of a Differential Mobility Analyzer (Model 3081, TSI, Inc.) and Ultrafine Condensation Particle Counter (Model 3020, TSI, Inc.). Gas-phase products, specifically the highly oxidized molecules that are the focus of the computational mechanism, were measured by chemical ionization mass spectrometry with the NO3 -reagent ion (NO3 -CIMS). This instrument employs a commercial CIMS inlet (Aerodyne, Corp.) based on the design by Eisele and Tanner 37 coupled to a high resolution timeof-flight mass spectrometer (LTOF analyzer, Tofwerk AG). Kinetics modeling confirmed that >98% of oxidation was NO3 radical-initiated, and comparison with an experiment conducted using only O3 and Δ-3-carene confirmed that the product distribution for the NO3 experiment did not have any significant contribution from O3 + Δ-3-carene products (see Section S2).
NO3 -CIMS mass spectra were analyzed in Igor Pro 6.3 (WaveMetrics, Inc.) using the Tofware analysis platform. Mass spectral data from m/z 4 to m/z 800 were processed, with most peaks >1000 ion counts identified and fit using high resolution peak fitting. Isotopes were constrained during peak fitting and accounted for when determining parent peak concentrations. The minimum detection limit is taken as 3 standard deviations above the baseline.
Log files from calculations and processed data from these experiments are publicly available and archived on the University of California Dash data publication service. 38
A summary of the dominant pathways in the Δ-3-carene + NO3 mechanism leading to the 3 rd generation of peroxy radicals is shown in Scheme 1. The complete Δ-3-carene + NO3 mechanism including minor channels and all reactions calculated in this study is included in Scheme S1.
Black colored structures are reproduced from Kurtén et al., 15 15 which serve as the "reactants" in this study. Green and purple structures and arrows indicate reactions calculated in this study originating from Reactant 1 and Reactant 2, respectively. For complete mechanism, including all pathways assessed in this study, refer to Scheme S1.
Starting with Reactant 1 and Reactant 2, we began by surveying the pathways available to these RO2 radicals. Since our mechanism explicitly calculates only the unimolecular reaction rate constants, we have estimated the pseudo-1st order rate constant for bimolecular reactions to be of order 10 -2 s -1 based on literature rate constants (k RO2+RO2 ~10 -12 cm 3 molec -1 s -1 and k RO2+NO3 = 2 × 10 -12 cm 3 molec -1 s -1 ) 9,21 and radical concentrations representative of the chamber experiments in this study ([RO2] ≈ 0.7 ppb, [NO3] ≈ 0.4 ppb) (see Figure S4).
Incidentally, this is a reasonable estimate under certain ambient conditions as well since HO2 is a significant bimolecular sink for RO2 in the atmosphere (assuming a "typical" ambient
[HO2]~100 ppt and k RO2+HO2 = 2 × 10 -11 cm 3 molec -1 s -1 ), 9,39 but [HO2] is assumed to be negligible in these chamber experiments. Therefore, to be competitive, RO2 unimolecular rate constants must be comparable to or faster than 10 -2 s -1 .
Hydrogen shifts were calculated for all unique hydrogens greater than a 1,4-H-shift apart, with the exception of methyl hydrogens, which have been shown to be slow in other studies, 11 and hydrogens on the strained 3-membered ring, which were shown in Kurtén et al. 15 to lead to a highly unstable alkyl radical. This includes all hydrogens labeled in Figure 3a except for rH0 and rH8. The fastest RO2 H-shifts in each reactant were for the hydrogen α to the -ONO2 group and β to the =O group (H7 and rH7). These H-shifts are of order 10 -2 s -1 and therefore are competitive with bimolecular reaction. However, the alkyl radical at this site leads to rapid loss of NO2 and termination of the radical as a carbonyl group, so while this pathway contributes to the final product distribution, it does not lead to further oxidation. 11 The remaining RO2 H-shifts range from approximately 10 -13 -10 -4 s -1 and therefore are too slow to contribute significantly to the final product distribution.
While the majority of these rate constants are too slow to be competitive, it is instructive to look at which of these H-shifts are more favorable than others for this complex, multifunctional molecule. Although a SAR does not currently exist for RO2 H-shifts, Otkjaer et al. 11
Reactant 1 arises from the opening of the 3-membered ring, which forms a new double bond.
We therefore tested whether the peroxy radical is able to add to the double bond, forming a 6membered endoperoxide ring. While it is also possible to add to the other side of the double bond, forming a 5-membered ring, this scenario results in a smaller ring and a primary alkyl radical, so we would expect this pathway to be slower than formation of the 6-membered endoperoxide. This type of endoperoxide formation reaction has been suggested to occur fairly rapidly (up to ~1 s -1 ) in the ozonolysis of a cyclodiene as well as in the photooxidation of αpinene. 40,41 As with the more well-known H-shift reactions, this reaction results in a similar autoxidation process, with O2 adding to the newly formed alkyl radical. We calculated this ring closing reaction to have a rate constant of approximately 5 × 10 -2 s -1 for Reactant 1, making it competitive with bimolecular reaction, and consistent with the α-pinene endoperoxide formation reactions in Xu et al. 41 that result in secondary radicals, which are somewhat slower than those leading to tertiary radicals.
Based on the calculated rate constants described above for RO2 unimolecular reactions, we expect that the product distribution from Reactant 1 will have some contribution from the endoperoxide channel as well as some closed-shell C10H16O4 from the H7 H-shift, but a significant amount of these RO2 will undergo bimolecular reaction and become RO radicals. For Reactant 2, which does not have an endoperoxide channel available to it, some C10H16O4 from the rH7 H-shift will form, and the significant remainder will be converted to RO by bimolecular reactions. We therefore assess the unimolecular reaction pathways available to these alkoxy radical products, including H-shifts, decomposition, and ring closing. Since published SARs are available for both alkoxy H-shifts and alkoxy bond scissions, 16,17 we started by implementing those to estimate which RO pathways are likely to be competitive for the Reactant 1 and Reactant 2 RO radicals.
Alkoxy scission reactions are influenced most strongly by the substituents on the α and β carbons, so any further substituents can be neglected when applying the SAR. 16 The alkoxy radical formed from Reactant 1 has two alkyl groups on each the α and β carbons, which reduce the overall SAR-predicted reaction barrier to 6.5 kcal/mol, compared to the 17.9 kcal/mol "baseline" forward barrier for the unsubstituted RO CH3CH2O. Reactant 2, on the other hand, has no substituents on the α carbon and a cyclopropyl ring on the β carbon. Scission of a C-C bond adjacent to a cyclopropyl ring leads to an alkyl radical on a highly strained ring, so this substituent results in an increase of the overall reaction barrier to 20.3 kcal/mol. H-shift favorability relies heavily on the structure of a molecule as a whole, since H-shifts can take place between carbons at different distances from the radical center (span) and are impacted by the location of functional groups (substituents). 17 Due to the wider range of span and substituent permutations, this SAR is less complete, for example lacking effects from -ONO2 groups, so we calculated these SAR-predicted rate constants assuming missing substituents would have a negligible effect. SAR-predicted forward energy barriers for alkoxy scission reactions and rate constants for alkoxy H-shift reactions are included in Table 2.
*Range of SAR-predicted k values come from structures with H-shifts not easily described by the SAR and therefore calculated using two different assumptions. **Note: these barriers were calculated for an arbitrary conformer at the B3LYP/6-31+G(d) level to confirm that the reaction would be slow relative to R1 C-C scission and thus unlikely to contribute to the final product distribution.
In spite of the increased uncertainty for the SAR-predicted H-shift rate constants due to missing substituents, the large predicted differences in barrier heights between the Reactant 1 and Reactant 2 alkoxy scission reactions makes it clear which pathway(s) will be favored by each reactant. We predict an extremely low barrier (6.5 kcal/mol) for the Reactant 1 RO scission, which we estimate to correspond to a rate constant of ~1 × 10 8 s -1 from similar alkoxy scission barriers in Kurtén et al. 15 SAR-predicted rate constants range from 10 -2 -20 s -1 for most available H-shifts in the Reactant 1 RO, with one notable exception. Following the qualitative trend of the RO2 radicals, the hydrogen α to the -ONO2 group and β to the =O group (H7) is predicted to have a rate constant of order 10 7 s -1 , which will be competitive with RO scission for this reactant. This H-shift leads to rapid loss of NO2 and termination of the radical to closed-shell C10H16O3, whereas the RO scission pathway will lead to continued radical propagation reactions, so we focus on the RO scission 1. In contrast, the predicted barrier for alkoxy scission for the Reactant 2 RO is quite high (20.3 kcal/mol) due to formation of a radical on the strained cyclopropyl ring. We can estimate this barrier to correspond to a rate constant of <10 -2 s -1 using the RO2 ring closing barrier/rate constant from Table 1 as an upper limit since neither the scission or ring closing reaction require significant tunneling corrections, unlike the H-shift reactions. Since SAR-predicted H-shift rate constants range from 10 -2 -10 6 s -1 , with the majority of hydrogens having rate constants above 10 5 s -1 , we can infer that the Reactant 2 RO will favor H-shifts over scission reactions. LC-TST calculated rate constants for alkoxy reactions are shown in Table 2. Alkoxy scission in Reactant 1 occurs at a calculated rate of 7 × 10 7 s -1 , confirming that H-shifts (except for H7) should be negligible in comparison. Rate constants for H-shift reactions in Reactant 2 alkoxy radicals were calculated for all hydrogens labeled in Figure 3a, this time also assessing whether methyl hydrogens with rate enhancing substituents at β positions (rH0 and rH8) might also be competitive, since RO chemistry is typically much faster than RO2 chemistry. Calculated rate constants range from 3 × 10 4 -2 × 10 7 s -1 . As expected from the trends observed in the RO2 Hshifts, rH4, rH5, and rH7 are among the fastest, with the methyl hydrogen rH0 being the slowest.
Unexpectedly, however, the fastest RO H-shift is from the methyl hydrogen rH8, likely due to a combination of a very favorable transition state geometry, as well as some additional stabilization due to the strained ring β to the subsequent alkyl radical. Barrier heights were also calculated for RO addition over the double bond in Reactant 1, but these calculations indicated that this ether-forming reaction is not competitive with the extremely fast RO scission or H-shift reactions. Since our calculated rate constants span many orders of magnitude, it is clear which pathways will dominate, but we note that the barriers for any of the fast RO reactions are quite low and therefore these rate constants calculated using transition state theory will have even larger absolute uncertainties than for the higher barrier RO2 reactions.
The LC-TST calculations confirmed the qualitative results of the SARs, with two H-shifts being 2-6 orders of magnitude faster than predicted by the SAR. The rate constants that deviated most significantly from the SAR predictions were those from methyl hydrogens that were seemingly better represented by the span and substituents included in the SAR. However, these deviations may have come from unincluded substituents like the cyclopropyl ring (rH8) and the fact that assumptions had to be made to combine substituent effects of the -C=O group at a 1,7 span (rH0). The SAR predicted rate constants well for the H-shifts where we had to assume that e.g. an -ONO2 group has a negligible effect.
From these results, it is evident that three dominant radical pathways emerge from Δ-3-carene + NO3 2 nd generation RO2 chemistry. Reactant 1 leads to radical products following RO2 addition to an internal double bond, as well as alkoxy radicals from bimolecular reaction, which subsequently undergo scission reactions leading predominantly to easily identifiable C7 radical intermediates. Reactant 2 proceeds straight to alkoxy radicals from bimolecular reaction, which predominantly undergo H-shift reactions, retaining their C10 backbone. These pathways are summarized in Scheme 1, and thus a complete mechanism through 2 nd generation products emerges that combines these results with those of Kurtén et al. 15 , along with inferred closed-shell products based on known oxidation chemistry (Scheme S1). Even though assessing the 3 rd generation of unimolecular chemistry for this system is computationally unfeasible, understanding the 2 nd generation of chemistry helps us understand the balance between bimolecular and unimolecular reactions in the atmosphere, which is a crucial link between known oxidation chemistry and experimental results.
Chamber experiments focused specifically on gas-phase NO3 -CIMS measurements to provide comparative measurements of the highly oxidized products formed from NO3 radical oxidation of Δ-3-carene. SMPS measurements showed new particle formation and subsequent particle growth during these experiments (see Figure S2), but particle-phase composition was outside the scope of this study. The complete table of identified products is included in Table S7, and Figures 4a and4c show a mass spectrum averaged over the duration of the experiment with structures assigned to the highest intensity peaks. When comparing a CIMS spectrum to the proposed mechanism, we must take into consideration which molecules will be detectable by the selected reagent ion chemistry. NO3 -CIMS will only detect molecules that have a larger binding energy with NO3 -than the binding energy of NO3 -with HNO3. Hyttinen et al. 20 showed that C6 molecules containing at least two hydrogen bond (H-bond) donors will bind with NO3 -, and are thus detectable by NO3 -CIMS, with increasing oxidation generally leading to stronger binding. While the products observed in this study seem to have a high enough oxidation state, many of these oxygens come from nitrate or carbonyl functionalities, so some pathways require multiple of chemistry to get even one H-bond donor. To ensure that we were assigning detectable structures to our NO3 -CIMS spectrum, we performed ion-clustering calculations on two expected products to investigate whether binding to NO3 -is, in fact, favorable. These results are shown in Section S3. For the highly oxidized compounds in this study (>O7), our results indicate that a single H-bond donor is sufficient to bind with NO3 -. Interestingly, despite not containing any H-bond donors, the dipole-dipole interactions in the RO2 formed following RO2 ring closing from Reactant 1 are sufficient to make clustering with NO3 -competitive with HNO3(NO3 -) cluster formation. M/z values reflect NO3 -adducts (M (NO3 -)) as detected, and labeled peaks reflect the product (M) alone. C7H11NO8 was not included in the mechanism in this study, but is expected to be a 3 rd generation product related to C7H10NO6. (b) Time series of the five highest intensity observed peaks as well as C7H11NO6 since it is the closed-shell product of one of our explicitly calculated intermediates. (c) Dimer region of mass spectrum with highest intensity peak formulas labeled.
Figure 4a shows that three of the five highest intensity observed peaks are consistent with products of the dominant reaction pathways identified in our computational mechanism. The highest intensity peak, C10H15NO7 most likely arises from Reactant 2 undergoing bimolecular reaction to produce RO, which undergoes one of several possible H-shifts with subsequent O2 addition. We then assume that the α-OH H-shift available to this new RO2 will be fast compared to other pathways and result in closed-shell C10H15NO7 by reaction with O2 and loss of HO2. The second highest intensity peak, C10H16NO8 must be a radical species given the even number of hydrogens and one nitrogen. This formula is consistent with the RO2 radical formed from the RO2 ring closing of Reactant 1 and subsequent O2 addition. It is somewhat surprising that we would measure this particular RO2 at such high intensity given that, as a radical intermediate, it is likely to react away relatively quickly. Additionally, the clustering calculations described above indicate NO3 -clustering with this radical may be competitive with HNO3, but not strongly, so we would expect to detect this species with lower sensitivity than others with more favorable interactions relative to HNO3. Looking at the time series of the species highlighted in Figure 4b, however, we see this ion appears earlier than any of the products postulated to come from RO unimolecular reactions, consistent with the fact that it would form directly from unimolecular reactions of Reactant 1 or 2. Some products remain unexplained or unexplored by the proposed mechanism. For example, formation of a C9 species is difficult to understand from the chemical pathways considered.
Formation of dinitrate species (e.g. C10H16N2O10) was not explored computationally, but given that Reactant 1 and many of its subsequent products and intermediates contain a double bond, these are easily justified by a second NO3 addition reaction. Dimer formation (for example via RO2 + RO2 reactions) was outside the scope of this study, but as seen in Figure 4c, most observed dimers are consistent with predicted monomer building blocks.
The derived mechanism and experimental results in this study describe autoxidation processes and products in the gas-phase up to the formation of 2 nd generation products. This part of the mechanism provides valuable insights into the SOA forming potential of Δ-3-carene + NO3 and can be extrapolated to some of the other monoterpenes that form SOA from NO3 oxidation. To start, we observe a number of dimer species, which have been correlated to new particle formation rates for other chemical systems. 42,43 Since the dimers in our study are also likely to be the lowest volatility products, we assume that these are the products linked most strongly to initial particle formation and the earliest stages of growth. We have estimated vapor pressures for many of our expected closed-shell products using the SIMPOL.1 group contribution method 44 and tabulated these in Chart S1. For the monomer products with known structures, vapor pressures at 298 K range from 1.6 × 10 -2 torr for caronaldehyde (C10H16O2) to 5.1 × 10 -8 torr for C10H17NO7 multifunctional hydroperoxides. If we consider "semi-volatile" vapor pressures (defined liberally, encompassing volatility ranges between primarily gas-phase and primarily condensed-phase) as ranging from 7.6 × 10 -2 -7.6 × 10 -9 torr, 45 nearly all products in this mechanism would be expected to be able to partition into the particle-phase, at least to some degree. Caronaldehyde, analogous to pinonaldehyde in the α-pinene + NO3 system, is one of the few products that is too volatile to contribute significantly to the particle-phase under atmospherically-relevant aerosol mass loadings, 46 whereas many of the products arising from the unimolecular pathways explored in this study have estimated vapor pressures on the very low end of our defined semi-volatile range, and therefore will partition heavily into the particlephase. The abundance of low volatility, highly oxidized monomers is consistent with observations of relatively small particle number concentrations but fast growth rates in other chamber experiments probing this chemistry. 7,36
In this work, we have expanded upon the known 1 st generation chemistry of Δ-3-carene + NO3 to include five different unimolecular reactions available to 2 nd generation RO2 radicals. In doing so, we have also assessed some of the structural features hindering and enhancing unimolecular reactions for C10 multifunctional molecules. In contrast to some of the chemical systems identified in recent years to undergo rapid and accelerating H-shift and autoxidation reactions leading to very highly oxidized and often extremely low volatility products, 10,13 NO3 + monoterpene oxidation products have a much more modest and balanced contribution from both unimolecular and bimolecular radical reactions. This is likely due to the combination of a strained secondary ring, which inhibits H-abstraction or alkyl radical-forming reactions on carbons within that ring, as well as the -ONO2 group, which does not strongly enhance unimolecular reactions and is also prone to decomposing to NO2 and a closed-shell product, thus terminating radical propagation. However, we also observed an unexpected enhancement of the RO H-shift rate from a methyl H β to the strained cyclopropyl ring. Understanding this balance between gas-phase bimolecular and unimolecular oxidation pathways is valuable for many chemical systems that, like Δ-3-carene + NO3, produce SOA but do not necessarily have dominant autoxidation pathways available, whether due to structural features or due to decreased RO2 lifetimes in more polluted environments.