Rates and Yields of Unimolecular Reactions Producing Highly Oxidized Peroxy Radicals in the OH Induced Autoxidation of α-pinene, β-pinene and Limonene

Abstract

Recent ambient atmospheric measurements have detected highly oxygenated organic molecules (HOMs) at many sites and are a consequence of autoxidation processes occurring at ambient temperatures. Monoterpenes in particular have a propensity to autoxidize although they exhibit a wide range of HOM yields which may be due to a variety of reasons including reactions with different oxidants like OH and O₃, differing hydrogen (H) atom transfer or peroxy radical cyclization rates, numbers of available reaction pathways and/or energy loss processes for activated HO-monoterpene or O₃-monoterpene adducts. In this work, the autoxidation mechanisms of (+)-α-pinene, (+)-β-pinene and (+)-limonene following initial OH oxidation and three successive O₂ additions are examined using density functional theory (DFT) to understand what accounts for the disparity. Rates of different potential autoxidation pathways initiated by OH addition or abstraction reactions are quantified using transition state theory (TST) and master equation approaches using the lowest energy conformers. OH abstraction reactions do not appreciably influence HOM production in the pinenes and limit autoxidation for limonene because the subsequent autoxidation reactions are slow while OH addition reactions are found to be the main route to HOMs for all three monoterpenes. Generally, faster autoxidation rates are computed in later unimolecular reactions that produce RO₇ radicals after OH addition (~10 s⁻¹ or greater) than rates for RO₅ peroxy radical production (0.2-7 s⁻¹). Mechanistic pathways that form RO₇ peroxy radicals are similar for all three monoterpenes with a particular bicyclo RO₇ radical involving a five membered peroxide ring being favored for all three monoterpenes. The molar yields of RO₇ radicals are 4.6% (+10.0/−2.4), 3.8% (+9.1/−2.6), and 7.6% (+13.1/−4.9) for α-pinene, β-pinene and limonene respectively at 298 K and 1 ppb of NO and only significantly decline at NO concentrations exceeding 10 ppb. The higher yield for limonene relative to the pinenes is predominantly a consequence of the initial oxidation step: OH adducts of the bicyclic pinenes have to use the excess energy after OH addition to break one of the rings and make the molecule more flexible for autoxidation although this process is inefficient while one of the prominent OH adducts for monocyclic limonene does not have to do this and may add O₂ immediately before autoxidizing further. These insights may be used to guide a better representation of these processes in atmospheric models because they affect particulate matter (PM), NO_x and ozone concentrations via enhanced production of low volatility species, less early generation NO_x cycling and altered organic nitrate production.

Graphical Abstract

Introduction

Monoterpenes are an important class of isoprenoid oils found in a wide variety of trees, fruits, vegetables, herbs and spices. Their volatile nature enables plants to use them as both repellents and fragrances and they are expansively applied in cuisine and human health care products.¹ Monoterpenes like α-pinene (2,6,6-trimethylbicyclo-[3.1.1]-hept-2-ene), β-pinene (6,6-dimethyl-2-methylidebicyclo-[3.1.1]-heptane) and limonene (1-methyl-4-(prop-1-en-2-yl)-cyclohex-1-ene) shown in Figure 1 are also used in a variety of volatile chemical products to add fragrant notes to cleaning products.² Their volatility in such applications is significant and has been shown to affect the air quality in indoor environments.^3–4 Significant emissions of monoterpenes from vegetation adds to the atmospheric burden of organic compounds that may subsequently oxidize and affect the concentrations of known pollutants such as PM, NO_x and ozone. Many early laboratory and field studies have discerned monoterpene bimolecular oxidation mechanisms involving NO, HO₂ and RO₂.^5–7 Reactions of these species with peroxy radicals may produce a complex array of products albeit with several sequential oxidation steps each producing a stable closed shell species. This may limit the degree of oxidation if the atmospheric concentration of radicals is low or the bimolecular reaction barriers are too high.

Figure 1.

Chemical structures of (+) monoterpene isomers investigated. The (−) isomers are expected to proceed via the same stereospecific oxidation pathways with similar rates because achiral oxidizing agents are being used.

Recent laboratory studies have shown that highly oxygenated organic molecules (HOMs) may be produced rapidly even when concentrations of radicals such as NO and HO₂ are relatively low.^8–9 This has prompted a more substantial examination at the potential for organic compounds to autoxidize under atmospheric conditions. Autoxidation reactions are characterized by spontaneous oxidation at normal temperatures without a flame or spark ignition source and involve a free radical chain reaction mechanism of either uni- or bimolecular reactions that propagate via unstable peroxy or alkoxy radical intermediates until a termination reaction produces a stable closed shell product. Autoxidation was unexpected and only thought to occur at higher temperatures during combustion processes¹⁰ or in the liquid phase.¹¹ However, laboratory and computational studies have accounted for the rapid onset of highly oxidized species containing greater than six oxygen atoms.¹² Such species have been observed to occur during OH and O₃ oxidation reactions although the latter have generally shown higher HOM yields.¹² Both types of autoxidation produce peroxy radicals and are initiated via different processes with OH reactions commencing either by addition to an alkene or hydrogen (H) atom abstraction followed by O₂ addition while O₃ reactions produce highly energized and reactive Criegee intermediates that may release OH radicals in subsequent reactions. While the latter mechanisms may produce higher molar yields of HOMs, the initial ozone reactions with monoterpenes are slow and occur more readily with high ozone concentrations and later in the day when OH concentrations are depleted.¹³ However, OH radicals are highly reactive with monoterpenes in particular and subsequent autoxidation may therefore represent an important unimolecular oxidation pathway whose products may readily condense onto aerosol particles.

Unimolecular H atom shift and cyclization reactions of alkenes involving peroxy radicals are fundamentally responsible for the propagation mechanism of atmospheric autoxidation in monoterpenes^{9, 14–19} because the resulting carbon centered radicals produced will quickly absorb another oxygen molecule thereby forming a new peroxy radical that perpetuates the reaction chain. An illustration of these processes is shown in Figure 2. Cyclization reactions are labeled here as x-endo or x-exo where x denotes the size of the peroxy ring that is formed and endo and exo refer to whether the double bond being broken lies inside or outside the newly formed ring respectively. After an OH initiation reaction, two autoxidation reactions may occur yielding highly oxidized RO₇ peroxy radicals and may involve a mix of H shift and cyclization reactions. In this study, the generation number that produces a specific peroxy radical (RO₃, RO₅, RO₇ from OH addition reactions and RO₂, RO₄, RO₆ from OH abstraction reactions) is defined to be equivalent to the number of O₂ molecules that have bonded with the monoterpene. In order to compete with HO₂ and in particular NO bimolecular reactions, unimolecular processes need to be rapid (> 0.5 s⁻¹). Recent calculations of first generation autoxidation reactions by Xu et al.¹⁴ and Moller et al.¹⁵ indicate that such reactions may span 1 – 5 s⁻¹ for α-pinene, β-pinene and limonene.

Figure 2.

Illustration of H shift and cyclization reactions occuring after OH addition to monoterpenes that produce highly oxidized peroxy radicals (RO₇). Peroxy radicals (RO₃, RO₅ or RO₇) are labeled by the generation in which they are formed with second and third generations being produced via consecutive autoxidation processes involving either an H shift or cyclization reaction followed by O₂ addition. Similar autoxidation reactions may occur after an initial OH hydrogen atom abstraction reaction although the OH group will be absent

In addition to peroxy radicals and Criegee intermediates, alkoxy radicals may also participate in H-shift reactions although these reactions compete with fast fragmentation pathways.^20–22 Vereecken et al.²³ have compiled and conducted a comprehensive computational study that has quantified the H-shift rate constants between peroxy radicals and hydrogen atoms on or adjacent to a variety of functional groups. The rate constants span many orders of magnitude although they possess considerable uncertainties. Generally, 1,5 and 1,6 H-shifts are favorable because the transition states possess the least ring strain. Additionally, hydrogen atoms bonded to carbon at alcohol, aldehyde or allylic sites are easier to abstract. These characteristics severely limit the plausible reaction pathways particularly for larger hydrocarbons because reactions with NO or HO₂ may be quite rapid (0.01 – 5 s⁻¹) depending on atmospheric concentrations.²⁴

For monoterpenes, the number of autoxidation pathways are limited further by the existing ring strain in their chemical structures. For instance, α- and β-pinene are rigid bicyclic compounds making it difficult for the initial peroxy radicals to autoxidize. Berndt et al. proposed that the bicyclo ring of α-pinene has to break open in an activated process involving the energy released upon OH addition to the double bond before autoxidation may happen⁹ consistent with earlier studies that looked at α-pinene ozonolysis.²⁵ Other monoterpenes like limonene only contain one ring giving it more conformational flexibility and also possess two double bonds that may potentially open up more autoxidation pathways. It is therefore not surprising that limonene gives rise to relatively large HOM yields although experimental measurements of yields have shown great variability using different chemical ionization schemes⁹ and it is possible that experimental measurements may underestimate yields because of the difficulty in detecting highly oxygenated compounds that may be lost to chamber walls and sampling lines.²⁶ The purpose of this work is to explore the OH initiated autoxidation mechanism of three common monoterpenes (α-pinene, β-pinene and limonene) in detail to quantify H-shift and cyclization rate constants after initiation by either OH addition or abstraction, predict HOM peroxy radical (RO₇) yields and determine which autoxidation pathways dominate to produce RO₇ peroxy radicals. This study seeks to build upon laboratory and computational structure-activity studies that are hampered by uncertainties in HOM detection yields and reaction rate quantification respectively. Results may then be used to update the chemistry of monoterpenes in air quality models where they may play an essential role in closing the gap between measured and predicted PM yields.

Methods

To quantify autoxidation rate constants, electronic structure calculations are required to compute reaction barriers. For all calculations, the (+) monoterpene isomers were selected for consistency and it is anticipated that gas phase autoxidation reaction rates will be similar for the (−) isomers because the reactions do not involve chiral oxidizing agents. Density functional theory (DFT) was applied here using the ωB97X-D density functional developed by Chai and Head-Gordon which includes dispersion corrections.²⁷ The widely used M062x density functional²⁸ was also employed in first generation autoxidation reactions to compare with the ωB97X-D method. The density functionals were paired with either 6-311++G(d,p)²⁹ and aug-cc-pVTZ³⁰ basis sets in Gaussian 16 (Rev. B.01).³¹ The latter larger basis set has been used recently to examine the autoxidation of α-pinene with ozone³² while the former basis set will be shown to provide comparable consistency in computing rate constants at a reduced computational cost.

Multiple conformers for reactants, transition states and products were optimized to compute rate constants for 42 different H shift and cyclization reactions: 13 first generation autoxidation reactions involving RO₂ and RO₃ peroxy radicals and 29 second generation autoxidation reactions involving RO₄ and RO₅ peroxy radicals with both generations of peroxy radicals initiated by OH abstraction and addition respectively. In order to distinguish reactions, all species were named following the convention of Xu et al.¹⁴ using numbers on carbon atoms, stereocenter R and S labels (where applicable) and functional group designations to distinguish the numerous stereoisomers produced. Figure 3 displays the general structure of the first carbon-centered radical produced subsequent to OH addition (at three different locations for α-pinene, β-pinene and limonene) that may then proceed to autoxidize. For the pinenes, the structure in Figure 3 represents ring opened OH adducts that are capable of autoxidizing. The numbers are used to indicate the locations of substituents like -OH, -OO∙, -OOH and ROOR groups from cyclization reactions so that all species may be labelled. The conformational space of all species encompasses different chair conformers of the cyclic monoterpenes as well as different rotamers involving all substituents which proliferate in later generations of autoxidation. In computing conformers for all species, the largest substituent (isopropyl peroxy group) was placed in an equatorial position on the ring which gives rise to the least steric hindrance. This was verified with initial calculations on different ring conformers as shown in Figure S1 of the Supporting Information. A rotamer search was then performed using the systematic rotor search method and the Merck molecular force field (MMFF)^33–34 in Avogadro software.³⁵ Typically, 6-10 of the lowest energy rotamers for the reactants and 3-6 transition state rotamers were then optimized for every reaction using the ωB97X-D/6-311++G(d,p) DFT method. Less rotamers were required for transition state calculations because the structures were more rigid as they involved fixing substituents so that the peroxy radical may approach a reaction site in a ring structure. Generally, the lowest energy conformers possessed substituents in staggered rotational conformations and also maximized the number of hydrogen bonding interactions. In instances where the reactant and associated transition state have different chair ring conformations for the peroxy radical because of the necessity to bring it closer to the target hydrogen atom for transfer or alkene for cyclization, it is assumed that the barrier to switch ring conformations is lower than the H transfer or cyclization barriers and therefore it does not represent the rate determining step. This is a reasonable assumption because a typical low barrier H shift is approximately 15-20 kcal/mol²³ while a chair flip for cyclohexane has a barrier of about 10 kcal/mol.³⁶ Finally at the DFT level, structures that possessed the lowest Gibbs free energy were then used in rate constant calculations.

Figure 3.

OH adduct of α-pinene (blue), β-pinene (red) and limonene (green). Numbers are used to label substituents produced in subsequent autoxidation reactions so that isomers may be distinguished.

For all the H-shift and cyclization reactions considered in this study, transition state theory (TST) coupled with a tunneling method (for H-shift reactions) is sufficient to compute all the rate constants. TST was used to compute the rate constants for all cyclization reactions. For the H-shift reactions that require a tunneling correction as well as the OH addition reaction to pinenes that produce ring opened peroxy radicals crucial to autoxidation via nonequilibrium kinetics, the Master Equation Solver for Multi-Energy Well Reactions (MESMER v. 4.0) was implemented.³⁷ MESMER is capable of computing the kinetics over complex potential energy surfaces involving multiple wells by solving an energy grained master equation and producing microcanonical rate coefficients using RRKM theory that are then converted to phenomenological rate constants by applying a procedure by Bartis and Widom.³⁸ For simple single barrier reactions (like H shifts), the phenomenological rate coefficients output by MESMER are identical to results from transition state theory without tunneling. MESMER include an Eckart tunneling correction^39–40 which was applied to all H shift reactions to account for H atom tunneling. Piletic et al. recently described all of the parameters invoked in calculations of early generation isoprene H shift reactions²⁴ and were used similarly in this work (see Supporting Information). For O₂ addition reactions, the resulting peroxy radicals were treated as a simple bimolecular sink with a bimolecular loss rate constant of 1.4E-11 cm³ molecule⁻¹ s⁻¹ which corresponds to the value for cyclohexanyl + O₂.⁴¹ For cyclization reactions that did not involve tunneling, the rate constant was computed within the rigid rotor-harmonic oscillator approximation of transition state theory.

Results and Discussion

Many recent laboratory and computational studies have already deduced the product yields and rates of OH addition and first-generation autoxidation for the pinenes and limonene.^{9, 14–18, 42} Here, the chemistry is explored to quantify uncertainties in predicting radical intermediate yields which are crucial to compute the subsequent RO₇ peroxy radical yields and to validate the DFT methods that are used to calculate autoxidation rates. Experimental measurements that quantify the concentrations of the initial carbon centered HO adducts or the subsequent peroxy radicals are difficult to acquire because the radicals are highly reactive species for which there are no standards. Typically, analysis of the product distributions or computational chemistry are used to infer reaction mechanisms.²⁰

The first step in the OH initiated autoxidation of monoterpenes is either an H atom abstraction or an OH addition to a double bond. In the former case, OH radicals may abstract from the allylic site to create peroxy radicals for autoxidation, but this pathway is estimated to have a branching ratio of 10% relative to addition to the double bond for the pinenes.⁴³ For autoxidation to occur via this pathway, a significant fraction of the initial radical pool has to break one of the rings to make the molecule flexible enough for autoxidation to occur. Xu et al. have indicated that ring opening does not occur after an OH abstraction reaction for the pinenes.¹⁴ Furthermore even if some ring opening occurs, subsequent reactions may terminate the peroxy radicals thereby limiting the production of highly oxidized RO₇ radicals further. For these reasons, the highly oxidized peroxy radical yield from the abstraction pathway is assumed to be small and is not considered for the pinenes. However, limonene is predicted to have a branching ratio of up to 33% for H atom abstraction by OH at 298 K.⁴⁴ This pathway will therefore be explored in more detail below and be accounted for when computing the highly oxidized peroxy radical yields.

The initial OH and O₂ addition to the double bond(s) of the monoterpenes that give rise to RO₃ radicals that may autoxidize is depicted in Figure 4. For α- and β-pinene, the OH may add at one of the two alkene carbons although addition is favorable on the less substituted carbon which produces a more stable tertiary carbon centered radical.⁴⁵ The preference is starker for β-pinene because the less preferred addition produces an unstable primary radical instead of a secondary radical for α-pinene. Addition at this site is essential for autoxidation because it produces a tertiary radical that can cause the cyclobutyl ring to rupture. Additionally, OH addition is preferable in α-pinene on the side opposite the methyl groups on the cyclobutane because it is less sterically hindered. For this reason, detailed DFT calculations were conducted on the anti or 3R-OH peroxy radical isomer only. However for yield calculations, the 3S-OH isomer will be assumed to react like the 3R isomer except no 1,6-H shifts are expected to occur because the H atom at the hydroxyl group site is inaccessible to the peroxy radical on the opposite side of the ring. Calculations by Moller et al. on the first-generation autoxidation of the pinenes have shown that unimolecular H-shifts are not possible in the pinene peroxy radicals that have retained the bicyclo ring structure.¹⁵ In this case, only H shifts from non-functionalized hydrocarbon rings are possible which are unfavorable as demonstrated by Vereecken et al.²³ One of the least strained of these H shifts is the 1,5-H shift from the secondary carbon on the cyclobutane of the pinenes. At the ωB97X-D/aug-cc-pVTZ level, the reaction barrier for this H shift in α-pinene is relatively high (21.6 kcal/mol) and the resulting radical is also unstable at 18.7 kcal/mol making hydrogen tunneling less likely. For these reasons, only the ring opened HO-adducts of the pinenes are considered for autoxidation. The largest yielding RO₃ isomers that may subsequently participate in autoxidation for α- and β-pinene are displayed in Figure 4.

Figure 4.

Initial OH addition step that produces the hydroxy peroxy radical (RO₃) isomers that may subsequently autoxidize for (+)-α-pinene, (+)-β-pinene and (+)-limonene. DFT calculations were performed on the RO₃ peroxy radical isomers labeled in purple because they represent either the highest yielding or most reactive intermediates (see text). Subsequent yield calculations incorporated all stereoisomers shown.

For limonene, OH addition may occur at four sites on the two double bonds (sites 2, 7, 8, and 9 on the carbon skeleton in Figure 2) and produce 12 hydroxy-peroxy radicals. Moller et al. have calculated that only four of these isomers may autoxidize at appreciable rates and only involve OH addition at sites 8 and 9.¹⁵ The H shift rates of the peroxy radicals generated by OH addition at sites 2 and 7 are too slow to compete with bimolecular reactions. Additionally, the predicted yield of the OH adduct at site 8 is zero in the MCM because like β-pinene it would produce a highly unstable primary carbon centered radical. Figure 4 shows the two hydroxy-peroxy diastereomers of limonene that may autoxidize and give rise to substantial concentrations of RO₅ and RO₇ radicals. Consequently, only the 8R- and 8S-RO₂ diastereomers may autoxidize although the 8R-RO₂ peroxy radical is computed to have a faster initial autoxidation rate.^{15 15} As a result, comprehensive DFT calculations were performed on the 8R-RO₂ hydroxy peroxy radical isomer of limonene only although the yield calculations of the RO₇ radicals will consider the 8S-RO₂ radical by assuming that its RO₅ oxidation products will reactivities similar to the 8R-RO₂ products.

For the pinene OH adducts shown in Figure 4, it is crucial to quantify the yields of the ring-opened OH adducts in order to compute overall HOM radical yields. Vereecken et al. have calculated the yield for the hydroxy peroxy radical to be 22%⁴³ and this yield was used recently in simulations to model HOM production rates in different ambient environments.⁴⁶ However, the ring opened peroxy radical yield is 7.5% for both α- and β-pinene in the MCM.⁴⁵ Xu et al. estimated the yield for ring opened α- and β-pinene to be 97% and 34% respectively from the measured distribution of monoterpene hydroxy nitrates.¹⁴ This wide range of values warrants further study here because the yields are critical for quantifing HOMs produced from the OH initiated oxidation of the pinenes.

The mechanism of ring opening for the pinenes features chemically activated OH adducts.^{14, 43} An RRKM master equation analysis was conducted using ωB97X-D/aug-cc-pVTZ electronic structure calculations. Using the parameters specified in the Supporting Information in MESMER, the ring opened yields of the OH adducts for α-pinene and β-pinene were computed to be 19% and 14% respectively. These values are lower than those computed by Vereecken et al. (50% for α-pinene) and Xu et al. (33% and 44% for α- and β-pinene respectively). However, the yields are extremely sensitive to two parameters: ΔE_down and the barrier to ring dissociation. ΔE_down is a variable parameter used to compute collisional energy transition probabilities. It represents the average energy transferred per collision in a downward direction. The values may range from 50 – 300 cm⁻¹ for He bath gas to 200 - 500 cm⁻¹ for O₂ and N₂ bath gases.³⁷ Recent calculations by Xu et al. implemented ΔE_down = 225 cm⁻¹. Figure 5 displays the master equation calculations for α- and β-pinene OH oxidation by varying the ΔE_down parameter from 100 – 300 cm⁻¹. It is evident that the yields of the ring opened adduct are highly sensitive to this parameter and this will represent a significant uncertainty in computing RO₇ peroxy radical yields because it is the first step in a multistep reaction sequence. Additionally, an uncertainty in the ring opening barrier of ± 1 kcal/mol leads to uncertainty ranges in the ring opened adduct yields from 8-37% for α-pinene and 6-32% for β-pinene. It is therefore not surprising to see large variability of the reported yields in the literature and this represents a significant source of uncertainty in the HOM yields for the pinenes. Because limonene is a monocyclic monoterpene, the only uncertainty in producing the initial hydroxy peroxy RO₃ radical shown in Figure 4 is the branching ratio of OH addition at site 9. Here, the MCM value of 37% is adopted as the base case for further calculations. This value is reasonable because of the four OH addition sites, this along with site 7 represent the most favorable pathways because tertiary radicals are produced as products. However, the branching ratio of OH addition to site 9 will be varied by +/− 10% to estimate the yield uncertainties for limonene’s highly oxidized peroxy radicals (RO₇).

Figure 5.

RRKM master equation calculations of OH + pinene reaction leading to hydroxy peroxy radicals and ring opened products. The ΔE_down collisional energy transfer parameter was varied to portray the uncertainty in computed yields of ring opened HO adducts.

The rates of first generation autoxidation reactions in α- and β-pinene,¹⁴ and limonene¹⁵ have been computed recently using ωB97X-D/aug-cc-pVTZ accompanied by high level RO-CCSD(T)-F12a single point energy calculations which have demonstrated substantial improvements in basis set convergence.⁴⁷ The results have shown that the most relevant unimolecular reactions for all three monoterpenes are 1,5 and 1,6-H shifts and 6-exo cyclization reactions. The latter reaction refers to a cyclization that breaks the double bond outside a newly produced 6-membered peroxy ring and creates a bicyclo compound. The computed rate constants span 0.2 – 4.0 s⁻¹ and are generally faster than similar reactions in many small oxygenated organics derived from pentanone, hexanol and isoprene.^{12, 48} As a comparison, at 298 K and 1 ppb of NO and assuming a bimolecular rate constant of 9.0E-12 cm³ molecule⁻¹ s⁻¹, the effective first order rate of reaction is ~0.2 s⁻¹. Early autoxidation reactions involving first generation RO₃ radicals will therefore outpace NO bimolecular reactions even in more polluted environments.

Results by Xu et al.¹⁴ and Moller et al.¹⁵ have shown that the fastest unimolecular rates for the initial RO₃ peroxy radicals of the pinenes and limonene are 1,5-H shifts and 6-exo cyclizations. Similar calculations for these reactions were performed here using different density functionals and basis sets. Table 1 displays the computed rate constants in relation to published CCSD(T)-F12a calculations that invoked multiconformer transition state theory (MC-TST)⁴⁹ which has been shown to reproduce experimental measurements.⁵⁰ The M062x density functional predicts the fastest 1,5-H shift rates in comparison with the ωB97X-D or CCSD(T)-F12a methods although the variance is not surprising because different computational methods can produce a substantial range of values even at the CCSD(T) level.⁵¹ The ωB97X-D/6-311++G(d,p) method happens to closely track the intensive CCSD(T)-F12a calculations for both reactions and all monoterpenes. The DFT results in terms of absolute rate constant values and their ratio of α- to β-pinene are also in reasonable agreement with experimental results presented by Xu et al. which predicted unimolecular rates of 4 and 16 s⁻¹ for α- and β-pinene respectively. The agreement is likely due to a fortuitous cancelation of errors although the method provides a computationally efficient means to access later generation reactions that produce larger highly oxidized molecules that are less conducive to intensive quantum chemistry calculations. In contrast, predictions of 1,6-H shifts by ωB97X-D/6-311++G(d,p) were up to a factor of 10 higher than predicted by Xu et al.¹⁴ and Moller et al.¹⁵ although this does not affect the predicted RO₇ yields to a great extent because both the 1,5-H shifts and 1,6-H shifts produce similar numbers of highly oxidized species. If 1,6-H shift rates are increased, less HOMs will be produced by the 1,5-H shift pathway but more will be produced by the 1,6-H shift pathway and vice versa. Consequently, ωB97X-D/6-311++G(d,p) was used to compute second generation autoxidation rate constants for all relevant RO₅ radicals and the results were used to estimate highly oxidized peroxy radical yields which are expected to correlate with HOM production.

Table 1.

Comparison of rate constants for the two fastest first generation unimolecular reactions for the hydroxy peroxy RO3 radicals of α-, β-pinene and limonene displayed in Figure 3.

1,5-H shift rate constants (s−1)
	ω B97X-D/6-311++G**	ω B97X-D/aug-cc-pVTZ	M062x/aug-cc-pVTZ	CCSD(T)-F12a
α-pinene	2.3	3.1	11.9	1.1a
β-pinene	2.7	4.7	14.9	1.4a
limonene	6.4	7.8	15.8	4.0b
Exo-cyclization rate constants (s−1)
	ω B97X-D/6-311++G**	ω B97X-D/aug-cc-pVTZ	M062x/aug-cc-pVTZ	CCSD(T)-F12a
α-pinene	0.24	0.08	0.31	0.35a
β-pinene	6.1	1.8	2.2	4.0a
limonene	7.1	1.5	1.8	3.9b

The CCSD(T)-F12a calculations were recently conducted by

^(a)Xu et al.¹⁴ and

^(b)Moller et al.¹⁵

The reactions of Table 1 are explicitly shown in Figure 6 for α-pinene in addition to 1,6-H shifts. All expected stereoisomer products are shown in the figure which illustrates the diversity of products that are produced from just three unimolecular reactions. Similar figures for first generation autoxidation of all three monoterpenes are shown in the Supporting Information (Figures S2, S4 and S6). Of the thirteen products produced, five represent either a closed shell species (3 ketone, 8OOH) or bicyclo peroxy radicals (like 2S-RO₂, 3R-OH, 7OO8 ring) that are unlikely to participate in further unimolecular reactions because there are no labile hydrogen atoms available and the structure is less flexible. Ten first generation product species however may participate in further unimolecular chemistry albeit after a rapid hydrogen atom exchange between the peroxy and hydroperoxy groups. The change of allegiance by the hydrogen atom is necessary because the RO₅ peroxy radicals at sites other than 8 are unlikely to participate in further unimolecular reactions. For instance, 5-endo cyclizations of the initially generated RO₅ peroxy radicals at site 2 are unfavorable because they produce an endocyclic radical and are forbidden by Baldwin’s rules.⁵² Additionally, the only available 1,5-H shifts for RO₅ peroxy radicals like (2R-RO₂, 3R-OH, 8OOH) are from non-functionalized hydrocarbon sites and therefore unfavorable. 1,6-H shifts would involve the peroxy group abstracting an H atom on the exact opposite side of the ring. This necessarily involves a costly chair to boat conformational transition of the ring in order for the substituents to approach each other in the transition state. Reactions 35 and 36 in Table S5 of the Supporting Information reaffirm these hypotheses because of the large reaction barriers involved. The H atom exchange reactions between the peroxy and hydroperoxy groups (i.e. 1,7 – 1,9-H shifts in Figure 5) however are known to be rapid (~10² – 10⁴ s⁻¹)^{23, 53–54} and computed to be 3.7E4 s⁻¹ for the 1,9-H shift for the α-pinene derived (2R-RO₂, 3R-OH, 8OOH) isomer. Therefore such reactions are expected to lead to the most reactive RO₅ peroxy radical isomer as has been computed in reactions involving hydroxy peroxy radical isomers of isoprene.⁵⁵

Figure 6.

OH initiated oxidation of α-pinene leading to eight reactive first generation autoxidation products. The circles on the reactant structures (3R-OH, 8RO₂ and 3S-OH, 8RO₂) indicate targets for either H atom shifts or peroxy radical cyclizations involving alkenes. The molar yields of the RO₃ and RO₅ radicals that proceed to autoxidize further are listed. DFT calculations of subsequent reactions involving the RO₅ isomers labeled with a red asterisk were carried out although subsequent yield calculations incorporated all stereoisomers shown.

The same types of reactions occur for β-pinene and limonene although in these cases 6 and 12 active RO₅ peroxy radicals are produced respectively. β-pinene produces the least RO₅ species because they are derived from one RO₃ isomer instead of two for α-pinene and limonene. The reactions and structures of the anticipated RO₅ radicals for β-pinene and limonene are shown in Figures S4 and S6 of the Supporting Information. Figures 6, S4 and S6 all contain the yields of all RO₃ and RO₅ species capable of autoxidizing further. The RO₃ yields for the pinenes were computed via a product of the fraction of activated OH adducts that break the bicyclo ring (shown in Figure 5 for ΔE_down = 200 cm⁻¹) with the branching ratio between the OH addition (at sites 3 and 1 for α- and β-pinene respectively) versus OH addition at the other alkene carbon and the branching ratio of OH addition versus abstraction.⁴³ α-pinene is further complicated because OH addition may occur on the same side (syn) or on the opposite side (anti) of the methyl groups where the latter is favored because there is less stearic hindrance. For yield calculations, the anti addition is assumed to be favored by a 2:1 ratio. For limonene, the burden of breaking a bicyclo ring is absent and the RO₃ yield is simply given by the product of the branching ratio of OH addition at site 9 relative to sites 2, 7 and 8 (see Figure 2) with the branching ratio of the OH addition versus abstraction reaction. Sites 2, 7 and 8 either have minimal OH adduct yields (site 8)⁴⁵ or do not autoxidize at appreciable rates (sites 2 and 7) that can compete with bimolecular reactions.¹⁵ The RO₅ yields were calculated as the product of the RO₃ yield with a sum of the branching ratios of all first generation autoxidation reactions that produce RO₅ products that may autoxidize further with all unimolecular and bimolecular reactions with NO and HO₂ considered. Equations S1 and S2 in the Supporting Information describe the yield calculations in detail. Of the three monoterpenes considered, limonene has the greatest RO₅ yield for peroxy radicals that may autoxidize further. This is simply a consequence of the high RO₃ yield which in itself is because energy is not required to fracture a bicyclo ring. Limonene unlike the pinenes has a significant OH abstraction yield at 33%.⁴⁴ This could either enhance or hinder limonene’s autoxidation yields depending on the values of the unimolecular rate constants for the resulting RO₂ peroxy radicals. Table S6 in the Supporting Information displays rate constants for unimolecular H-shift and cyclization reactions involving limonene RO₂’s produced by OH abstraction. In all cases, the rate constants are several orders of magnitude slower than related RO₃ radicals produced by OH addition and are considered irrelevant. A likely possibility for the disparity in the autoxidation rates is that the peroxy group in RO₂ radicals are bonded to the cyclohexenyl ring and are therefore more restricted in their motion relative to the peroxy group in RO₃ radicals which are located on the isopropyl substituent. Therefore, less ideal transition state structures will form and give rise to larger reaction barriers as seen in Table S6. The abstraction pathways therefore inhibit limonene autoxidation yields by an estimated factor of 1.5. Even in this case, limonene still exhibits the largest highly oxidized peroxy radical yield out of the three monoterpenes.

As mentioned earlier, the initial autoxidation reactions shown in Figure 6 produce RO₅ peroxy radicals that cannot autoxidize further because only unfavorable unimolecular pathways are available. Succeeding rapid 1,7 – 1,9-H shifts between peroxy radicals and hydroperoxy groups must occur although are only possible if oxygen has added to the same side of the ring as the hydroperoxy group because of proximity requirements. If it adds on the opposite side, the peroxy radical is expected to be longer lived because there are not viable H shift or cyclization reactions to continue autoxidation. However, reaction 37 in Table S5 of the Supporting Information suggests that the O₂ addition is reversible with a potentially fast dissociation rate. This has been observed for isoprene peroxy radicals⁵⁵ and is due to the stability of the allylic radicals that would result from O₂ dissociation. As argued by Peeters et al. for the production of hydroperoxy aldehydes (HPALDs), this would ultimately funnel O₂ addition reactions towards peroxy RO₅ species that are the most reactive.⁵⁵ As will be shown below, generally the fastest reactions involving RO₅ radicals are second generation unimolecular reactions.

The autoxidation mechanism of RO₅ radicals for α-pinene, β-pinene and limonene is developed here considering the results of first generation pathways, structure activity relationships²³ and speculated pathways given by Xu et al.¹⁴ Figure 7 depicts the second generation autoxidation mechanism for α- pinene. Figures S5 and S7 show the analogous mechanisms for β-pinene and limonene respectively. Once again, the reaction landscape is dominated by 1,5- and 1,6-H shifts as well as 5-exo and 6-exo cyclizations. Termination reactions involve either abstractions of α-H atoms at -OH or -OOH sites giving rise to closed shell ketones. All propagation reactions are facilitated by the double bond which enables cyclizations and gives rise to labile H atoms at allylic sites.¹⁵ As previously stated, any 1,5- or 1,6-H shifts at non-functionalized hydrocarbon sites are deemed too slow to be of relevance.

Figure 7.

Second generation autoxidation reactions for α-pinene derived RO₅ radicals. The circles on the reactant structures indicate targets for either H atom shifts or peroxy radical cyclizations involving alkenes. The total molar yield of highly oxidized RO₇ peroxy radicals (some of which are shown in purple for these specific RO₅ isomers) are computed as a product of yields for reactions producing ring opened RO₃, autoxidizable RO₅ and RO₇ and are described in detail in the Supporting Information.

The unimolecular rate constants for all reactions in Figures 7, S5 and S7 were computed and the fastest three reactions for every monoterpene RO₅ are given in Table 2. All second generation unimolecular rate constants are reported in Tables S2–S4 of the Supporting Information. Most of the reactions shown in Table 2 produce highly oxidized RO₇ radicals while several produce RO₅ ketones. All computed first order rate constants are rapid and greater than 7.9 s⁻¹ which is faster than any of the calculated first generation autoxidation reactions. This result is expected given that the autoxidation process adds oxygen to organic compounds and creates new sites containing labile H atoms that may promote further chain propagation in the mechanism. The fastest rate is extremely rapid at 1.2E2 s⁻¹ for a 6-exo cyclization of a β-pinene RO₅ radical (1OH, 6R-OOH, 8RO₂). Interestingly, a common 5-exo cyclization reaction is auspicious for all three monoterpenes. In this case, it is favorable because the carbon centered radical is produced outside the ring (unlike reaction 36 in Table S5). 5-exo cyclizations have been observed in other organic synthesis applications where they have been found to drive regio- and stereoselectivity.⁵⁶ The lower barriers for second generation autoxidation reactions give rise to higher yields of RO₇ radicals because less precursor RO₅ radicals will participate in bimolecular reactions. This result also implies that the yields of RO₇ radicals for all three monoterpenes will be less sensitive to NO_x than previously thought.⁴⁶ Figure 8 shows that the RO₇ yield is fairly insensitive to NO up to approximately 10 ppb when NO bimolecular reactions take over. Models invoking slower autoxidation rates (0.28 s⁻¹) exhibit much quicker falloffs at about 0.1 ppb of NO.⁴⁶ The yields shown in Figure 8 consider all likely first and second generation autoxidation pathways by invoking specific branching ratios for every RO₇ radical produced. A full yield calculation analysis is detailed in the Supporting Information and is accompanied with error estimates that account for uncertainties associated with the calculation of the fraction of ring opened pinenes and unimolecular rate constants. At 1 ppb of NO and 30 ppt of HO₂, the estimated RO₇ yields are 4.6% (+10.0/−2.4), 3.8% (+9.1/−2.6), and 7.6% (+13.1/−4.9) for α-pinene, β-pinene and limonene respectively. Limonene has the largest highly oxidized RO₇ peroxy radical yield and yield calculations show that this is predominantly driven by the original high yield of RO₃ radicals (8(R+S)-RO₂, 9OH) that are able to propagate autoxidation. This result is consistent with experimental measurements of extremely low volatility organic compounds (ELVOCs) in the OH oxidation of limonene relative to other monoterpenes.⁵⁷ For the pinenes, these yields are hindered by the requirement that the bicyclo ring has to break using a specific OH adduct in order for further autoxidation to proceed. β-pinene has a lower RO₇ yield than α-pinene because its reactive RO₃ species (1OH, 8RO₂) has a favorable 6-exo cyclization pathway that terminates autoxidation after one generation (compare reactions 3 and 6 in Table S1). The predicted molar yields of RO₇ radicals shown in Figure 8 (3 – 8%) are significantly higher than measured molar yields of ELVOC (0.5 - 1%) obtained in OH oxidation experiments of the same monoterpenes.^{12, 57} The discrepancy may be due to measurements being biased low for HOM species detection and such species may more readily adsorb to walls and tubing in experimental setups.²⁶ Additionally, the fate of the RO₇ radicals described in this work is unknown and some pathways may involve the fragmentation of peroxide rings such as those produced by reactions 2-4, 6 and 8-9 in Table 2 that lead to smaller species containing fewer oxygen atoms.

Table 2.

Fastest computed rate constants for second generation autoxidation reactions for α-pinene, β-pinene and limonene

Figure 8.

Calculated yields of RO₇ peroxy radicals derived from α-pinene, β-pinene and limonene as a function of NO concentrations. 30 ppt of HO₂ is assumed for the yield curves.

As described in the Supporting Information, the RO₇ yields are ultimately a product of initiation, RO₃ and RO₅ reaction yields. Specific yields of products from second generation autoxidation reactions of RO₅ peroxy radicals were calculated for oxidized α-pinene, β-pinene and limonene as shown in Figures 7, S5 and S7 respectively. The bicyclo compound containing a 5-membered peroxy ring derived from a 5-exo cyclization reaction was found to be the dominant species for all three monoterpenes (see Tables S2–S4). Rapid cyclization rates were confirmed using the larger aug-cc-pVTZ basis set and CCSD calculations (Table S5) and transition states for their formation are shown in Figure 9. The specific yields of (2R-OOH, 3R-OH, 6OO8 ring, 7RO₂), (1OH, 2R-OOH, 6OO8 ring, 7RO₂) and (2S-OOH, 6OO8 ring, 7RO₂, 9OH) from α-pinene, β-pinene and limonene are 0.8%, 1.0% and 1.6% respectively. Most recent work has speculated that 6-exo cyclization reactions are responsible for a lot of the RO₇ yields.^{9, 14, 46} The calculations here suggest this alternative pathway is significant and may give rise to different HOMs than those derived from 6-exo cyclizations.

Figure 9.

Transition states of 5-exo cyclization reactions of RO₅ radicals leading to the highest yielding RO₇ species for all three monoterpenes.

The implications of all these results are significant in that autoxidation in monoterpenes may be more prominent than originally thought. A substantial fraction of monoterpene oxidation products yields highly oxidized peroxy radicals rapidly. This should affect PM concentrations because the highly oxidized species are expected to readily condense on particles. Even though NO does not affect the first two generations of autoxidation pathways to a great extent, it may enter into the chemistry of RO₇ radicals when the number of unimolecular pathways has dwindled. Questions arise as to what the branching ratio will be between the highly oxidized organic nitrates and NO₂ generating pathways that affect ozone concentrations because even in simpler systems the reaction dynamics are complex.⁵⁸ With further research, this chemistry may be effectively incorporated in air quality models because the reactions affect the concentrations of important pollutants such as PM, NO_x and ozone.

Conclusions

The yields of highly oxidized RO₇ peroxy radicals for α-pinene, β-pinene and limonene have been computed and range from 3 – 8%. While there are considerable uncertainties in these yields, the results establish that limonene gives rise to larger RO₇ HOM yields when compared with the pinenes for OH initiated autoxidation processes. The substantial yields are a consequence of autoxidation steps that are rapid and effectively minimize known atmospheric bimolecular reaction pathways for specific OH adducts for a wide range of conditions. In many instances, second generation autoxidation rate constants were found to be approximately an order of magnitude greater than first generation reactions. While the yields and rate constants were found to be distinct for the three monoterpenes, the autoxidation mechanisms were very similar for all three monoterpenes with a bicyclo RO₇ radical involving a five membered peroxide ring being the most dominant highly oxidized radical produced. This study paves the path to understand how HOMs from monoterpenes are produced and what their fate may be in atmospheric aerosols.