The Atmospheric Oxidation Mechanism of Sabinene Initiated by the

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The Atmospheric Oxidation Mechanism of Sabinene Initiated by the Hydroxyl Radicals Lingyu Wang, and Liming Wang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b06381 • Publication Date (Web): 12 Oct 2018 Downloaded from http://pubs.acs.org on October 13, 2018

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The Journal of Physical Chemistry

The Atmospheric Oxidation Mechanism of Sabinene Initiated by the Hydroxyl Radicals Lingyu Wanga and Liming Wang*a,b (a) School of Chemistry & Chemical Engineering, South China University of Technology, 381 Wushan Rd., Guangzhou, China 510640; (b) Guangdong Provincial Laboratory of Atmospheric Environment and Pollution Control, South China University of Technology, Guangzhou, China 510006.

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ABSTRACT The atmospheric oxidation mechanism of sabinene initiated by the OH radical has been studied using quantum chemistry calculations at CBS-QB3 level and reaction kinetic calculations using transition state theory and unimolecular rate theory coupled with collisional energy transfer. The oxidation is initiated by OH radical additions to the CH2=C< bond with a branching ratio of ~(92 – 96)%, while all the hydrogen atom abstractions count for ~(4 – 8)% of branching ratio, which was estimated by comparing the rate coefficients of the reactions of sabinene and sabinaketon with OH radical. Addition of OH to the =C< carbon forms radical adduct Ra, while addition of OH to the terminal CH2= carbon forms radical adduct Rb, which would break the three-membered ring promptly and almost completely to radical Re. RRKM-ME calculations obtained fractional yields of 0.40, 0.09, and 0.51 for radicals syn-Ra, anti-Ra, and Re, respectively, at 298 K and 760 Torr. In the atmosphere, the syn/anti-Ra radical would ultimately transform to sabinaketone in presence of ppbv level of NO; while in the transformation of the Re radical, both bimolecular reactions and unimolecular H-migrations could occur competitively for the peroxy radicals formed. The H-migrations in peroxy radicals result in the formation of unsaturated multifunctional compounds containing >C=O, –OH and/or –OOH groups. Formation of sabinaketone from syn- and anti-Ra and formation of acetone from Re are predicted with yields of ~0.37 and ~0.38 in the presence of high NO, being larger than while in reasonable agreement with the experimental values of 0.19–0.23 and of 0.21–0.27, respectively.


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1. Introduction Of the large amount of biogenic volatile organic compounds emitted into the atmosphere by terrestrial and marine vegetation, monoterpenes account for ~20% of the total BVOC emission, the second largest after isoprene.1 Oxidation of monoterpenes in the atmosphere is crucial in regulating the atmospheric oxidation capacity and in the formation and growth of secondary organic aerosols (SOA), which in turn affect the cloud formation processes. Even though SOA formation has been observed in all monoterpenes studied, the studies on the oxidation mechanism have mostly focused on the abundant isomers such as α-pinene, β-pinene, limonene, etc.; while the others have received less attention even though they have been detected extensively in the emissions. As an example, sabinene (Sab) has been found with abundant emissions from many natural sources.2-6 The reactions of sabinene likely play a role in the chemistry of forest and rural atmosphere. Laboratory and modelling study suggested that the photo-oxidation of sabinene might contribute significantly to SOA formation amongst the biogenic hydrocarbons.7 The atmospheric removal of Sab is initiated by its reactions with OH, NO3, and O3, for which Atkinson et al.8 obtained rate coefficients of 1.18 × 10–10, 1.01 × 10–11, and 8.07 × 10–17 cm3 molecule–1 s–1 at 296 ± 2 K, rendering atmospheric lifetimes of 2.7 h, 7 min, and 4.8 h with concentrations of 1.0 × 106, 2.5 × 108, and 7 × 1011 molecules cm–3 for OH, NO3, and O3, respectively.9 The main removal of sabinene in daytime, when its emission is at peak level, is due to its reaction with the OH radical, especially in remote areas. There have been a few mechanistic studies on the oxidation of Sab initiated by OH radical under typical atmospheric condition, identifying the products and quantifying their yields,10-13 and on the oxidation initiated by O3.11-12,14-19 In the OH-initiated oxidation, the identified gasphase products included formaldehyde, acetone, and sabinaketone, with molar yields in the ranges of 0.22–0.27, 0.21–0.27, and 0.19–0.23, respectively. No noticeable difference in yields was observed in the presence and absence of NOx in the system. Librando and Tringali13 also observed formation of sabinic acid and pinic acid with total yield of ~0.1%. The identified gas-


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phase products could only account for ~30% of carbon balance, and the rest products are likely partitioned into particle phase or condensed on the wall of reactors. Carrasco et al.20 also tried to predict the mechanism by quantum chemistry calculations at levels of B3LYP and MP2 with basis set of 6-31G(d,p). The calculations confirmed the formation of sabinaketone and formaldehyde from the decomposition of two β-hydroxyalkoxy radicals, which are formed from the sequential –OH and –OO addition to the >C=C< bond, followed by reactions of RO2 and NO. Scheme 1 shows the mechanism proposed by Carrasco et al. They proposed the formation of acetone via direct H-abstraction from the isopropyl group of sabinene (site h). The mechanism could not explain the low yields of sabinaketone and formaldehyde though the yields of formaldehyde and sabinaketone agreed closely. In this study, we re-examined the atmospheric oxidation mechanism of Sab initiated by the OH radicals using quantum chemistry and kinetic calculations. Our computational results showed significant discrepancies to previous studies on the atmospheric oxidation mechanism of sabinene. 2. Theoretical Methods The molecular structures were optimized and vibrational frequencies were calculated at M06– 2X/6-311++G(2df,2p) level,21 and the electronic energies were calculated using the complete basis set model chemistry with spin unrestricted wavefunction (UCBS-QB3)22 and spin restricted wavefunctions (ROCBS-QB3).22 The ground state of OH radical is 2Π3/2, and the spin-doublet is included in the calculations of its thermodynamic parameters. The values of T1-diagonistic in CCSD/6-31+G(d') calculations (part of CBS-QB3) were computed to check the reliability of correlation calculations based on single reference wave function. Discussion below is based on UCBS–QB3 energies unless otherwise specified. All the values of T1-diagnostic are smaller than 0.03, being slightly higher than the suggested value of 0.02 but still being reasonable to assure the reliability of CCSD(T) calculations based on single-reference wavefunctions.23-24 Gaussian 09 suit of programs25 were employed for all these calculations. The high-pressure-limit rate constants are estimated using the traditional transition state theory (TST),26-27


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() ∙ ∙ exp − () = ∙ ∙ ℎ ()

where is the Boltzmann constant, ℎ is the Planck constant, is the classical barrier height, is the reaction path degeneracy, () is the quasi-partition function for transition state (not including the vibrational degree of freedom corresponding to the reaction coordinate), () is

the partition function for reactant, and is the tunneling correction factor which is calculated using the asymmetric Eckart model.28

Fast unimolecular reactions may not reach their high-pressure-limit rates under the atmospheric pressure. Therefore we also modelled the reaction kinetics by the unimolecular rate calculations coupled with master equation (RRKM-ME) using the MESMER code.29-31 For reactions with defined transition state and barrier, the E-resolved microcanonical rates are calculated using RRKM theory; while for barrierless bimolecular association, the microcanonical rates of dissociation are obtained by the Inverse Laplace Transform (ILT) method with recombination constant , .30,32 The collisional energy transfer is modelled by the singleexponential down model with down = 250 cm–1, and the collisional parameters are estimated

according to Gilbert and Smith.33 For density of rotational states, we used the classical rotor model. Tunneling correction factors were included according to the method by Miller.31 In our RRKM-ME calculations, the internal rotations, when free in reactant while frozen in transition state, were treated as hindered rotor. As being implemented in MESMER, the energy levels of the internal rotations were obtained by numerically solving their Schrödinger equations using the Fourier Grid Hamiltonian (FGH) method,34 and were then used for the calculation of density of state of the species in RRKM calculations. 3. Results and Discussion 3.1 The Initial Additions and Hydrogen Abstractions Reaction of Sab with OH radical proceeds via addition to the unsaturated >C=C< double bond and H-abstraction from saturated carbon sites. The reaction starts with the formation of prereactant complexes (PRCs), in which the H-atom of the OH group pointing to the >C=C< double bond. Two PRCs were identified as syn- and anti-conformers, referring to the same and opposite directions of the OH group and the >CH2 group in three-membered ring with respect to the five-


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membered ring. PRCs serve as the intermediates for additions and possibly for certain Habstractions. Four transition states are available for additions and 14 for H-abstractions. We have obtained the transition states for all the additions and other H-abstractions at M06-2X level, and calculated their electronic energies at levels of UCBS-QB3 and ROCBS-QB3, except for the ones for H-abstractions from >CH2 and –CH3 groups. Table 1 lists the results for all these channels and Figure 1 shows the potential energy surface for additions and the ensuing steps. The PRCs are responsible for the negative barrier heights relative to the separated reactants for the additions though PRCs are higher in energy than the transition states for addition. Under the atmospheric conditions, the reaction of Sab and OH is clearly dominated by the addition of OH radical to the >C=C< double bond; while H-abstractions all together account for only a small fraction. The branching ratios could be inferred from the experimental rate coefficients. Experimental study had obtained the overall rate coefficient as 1.18 × 10–10 cm3 molecule–1 s–1 at 296 ± 2 K for reaction between Sab and OH radical8 and 7.1 × 10–12 cm3 molecule–1 s–1 for reaction of sabinaketone and OH radical.35 At room temperatures, reaction of sabinaketone and OH proceeds almost exclusively via H-abstraction. According to the structureactivity relationship by Kwok and Atkinson,36 rate coefficients for H-abstraction could be obtained as 4.4 and 6.3 × 10–12 cm3 molecule–1 s–1 for Sab and sabinaketone, respectively. Giving the agreement between SAR prediction and measurement on sabinaketone, we expect the rate coefficient for H-abstraction from Sab to be ~4.4 × 10–12 cm3 molecule–1 s–1. By correlating the experimental rate data to the C-H bond strengths, Vereeken and Peeters37 also estimated a set of rate coefficients for H-abstractions from different sites of (poly)alkenes by OH radical. With their parameters, a rate coefficient of (5.3 – 9.4) × 10–12 cm3 molecule–1 s–1 could be obtained for the reaction between Sab and OH radical, agreeing with while being slight higher than the SAR estimation by Kowk and Atkinson. Therefore, a branching ratio of (4 – 8)% might be assigned to the H-abstraction channels in the reaction of Sab and OH radical, and the rest to the addition channels. The Addition Channels Appropriate prediction of rate coefficient for OH addition to Sab might require some sophisticated theoretical treatment. Simply implementing a steady-state approximation for the concentrations of PRCs suggests an effective rate coefficient of addition as


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= /( + ) where k–1 and k2 are the unimolecular rates for decomposition of PRCs back to sabinene + OH and for isomerization to Sab-OH adducts, and k1 is the bimolecular rate coefficient of forming

PRCs. At the canonical level, the equation reduces to = / when assuming k–1 is much larger than k2, and the rate coefficient can be calculated as = ! ⁄ℎ ∙ exp(−∆$ ⁄) according to the traditional TST as if the PRCs do not exist. However, this assumption may be invalid for the addition between Sab and OH radical, giving the low barriers for isomerizations. Simple calculations based on this assumption result in unrealistically high rate coefficients of >10–9 cm3 molecule–1 s–1 at 298 K for the additions with barrier heights at either UCBS-QB3 or ROCBS-QB3 level. The sophisticated way to deal with this problem is to introduce a long-range outer transition

state between reactants and PRCs and to approximate steady-states at microcanonical level with E,J-resolved density of states.38 Using the long-range transition state theory,39 a capture rate for the formation of PRCs could be estimated as 2.6 × 10–10 cm3 molecule–1 s–1 at 298 K if assuming the capture is dominated by the dipole-dipole force (with dipole moments of 1.74 and 0.87 D for OH and sabinene at M06-2X level). The value is close to the experimental value of 1.18 × 10–10 cm3 molecule–1 s–1 at 296 ± 2 K.8 With the low inner transition states from PRCs to Sab-OH adducts, the reaction at 298 K is likely limited by the outer transition states while the inner ones might control the branching ratios for adducts.40 The capture rate for the formation of PRCs changes only slightly from 2.71 × 10–10 cm3 molecule–1 s–1 at 243 K to 2.56 × 10–10 cm3 molecule–1 s–1 at 343 K. As for the adducts formed when OH adds to α-pinene and β-pinene which contain a constrained a four-membered ring,41-44 radical Rb, with a more constrained three-membered ring, would also break the ring promptly and form radical Re,

Transition state for this isomerization was found with a barrier height of only 30.7 kJ/mol (Table 1, ∆E0K) at UCBS–QB3 level (31.1 kJ/mol at ROCBS-QB3 level or 36.6 kJ/mol at Gausian-3


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level). With the exothermicity of –119.6 kJ/mol for OH addition to Rb radical, the chemically activated Rb* radical would isomerize to Re radical promptly. Therefore, the addition channels could be modelled as

We carried out RRKM-ME calculations for this reaction scheme in the absence of O2. In RRKMME calculations, all the steps were set to be reversible even though the ring breakage of Rb and isomerizations from PRCs to Ra and Rb are virtually irreversible because of their high exothermicity. Microcanonical rates k(E) for barrierless decomposition from PRCs to Sab and OH were modelled by an Inverse Laplace Transformation with the predicted rate coefficient of 2.6 × 10–10 cm3 molecule–1 s–1 for association of Sab and OH at all temperature, and the k(E)'s for other steps by RRKM theory. Figure S1 shows the time profiles of OH decay and the formation yields of the four radicals at 243 K and 760 Torr, and the time profiles at temperatures up to 343 K are similar. With both UCBS-QB3 and ROCBS-QB3 reaction energies and barrier heights, the chemically activated Rb* was found to isomerize to Re promptly within 10–9 s. The prompt isomerization is too fast to allow the collisional stabilization of Rb* or to allow recombination of Rb with O2 in the atmosphere, which has an effect rate of ~5 × 107 s–1 if assuming a high-pressure-limit rate coefficient of ~10–11 cm3 molecule–1 s–1 for association with O2 as for other alkyl radicals.45 Besides, energy contained in Rb* would enhance the re-dissociation of RbOO*, resulting in a smaller effective recombination rate with O2. The predicted formation yield for the thermalized Rb radical is less than 1% in the temperature range of 243–343 K. Dependence of yields for syn-/anti-Ra and Re on temperatures is rather weak. From 243 K to 343 K, the molar yields of anti-Ra, syn-Ra, and Re remain as 0.39, 0.10, and 0.51 if using UCBS–QB3 energies, or 0.40, 0.09, and 0.51 if using ROCBS-QB3 energies. Further improvement in the reaction energies and barrier heights might result in better predictions of radical yields. However, the dominant formation of anti-Ra, syn-Ra, and Re radicals could be assured at a reasonable confidence.


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The Hydrogen Abstraction Channels H-abstraction from Ch forms water and sabinenyl radical Rh (Scheme 1), and similarly from other carbon sites to radical Rc, Rd, Rf, Rg, and Ri/Rj. SAR method by Kowk and Atkinson36 KA predicts a rate coefficient of ~4.4 × 10–12 cm3 molecule–1 s–1. The H-abstraction would be dominated by the inner transition states. The values from TST calculations are all higher than the SAR prediction. The SAR method predicts fractions of H-abstraction as 0.20, 0.17, 0.54, and 0.08 from Cf, Cg, Ch, and Ci/j; while TST predicts different fractions of 0.32, 0.32, and 0.31 from Cf, Cg, and Ch if using UCBS-QB3 barrier heights. The TST fraction of H-abstraction from Ci+Cj is only 1-2% using barrier heights at all levels of theory, being much smaller than SAR prediction. Therefore, only the fates of Rf, Rg, and Rh radicals are considered below for simplicity. Radicals Rf, Rg, and Rh are all highly strained due to the 3-membered ring. Radical Rg is stable due to the delocalized π-bond; while radicals Rf and Rh might be able to break the 3membered ring, forming less strained and more stable conformers as

Both processes were found to be exothermic with reaction energies (∆E0K) of –82.1 and –70.2 kJ/mol and barrier heights of only 24.0 and 3.7 kJ/mol for Rf and Rh, respectively (Table 1). The low barriers suggest fast ring-breakage even at room temperatures with high-pressure-limit (HPL) rates of 5.3 × 108 and >1012 s–1 at 298 K though these processes are unlikely to reach their HPLs under atmospheric pressures. RRKM-ME modelling indeed obtained unimolecular rates of ~1.5 × 108 and ~7 × 108 s–1 at 298 K and 760 Torr for Rf and Rh, respectively, compared to the effective bimolecular recombination rates of ~5 × 107 s–1 with O2 in the atmosphere if assuming kB of ~10–11 cm3 molecule–1 s–1 and [O2] of ~5 × 1018 molecules cm–3.46 Furthermore, H-abstractions from sites f, g, h, and i/j are highly exothermic with ∆E0K of – 90.9, –143.1, –96.5 kJ/mol, and –71.5 kJ/mol, respectively, in the reaction of Sab and OH. Therefore, these radicals should be formed with considerable amount of internal energy.


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Consequently, the energy-rich radicals Rf* and Rh* would break the 3-membered ring promptly at rates higher than the thermal rates. We modelled the isomerizations of Rf* and Rh* by simply assuming their nascent internal energy distribution as the microcanonical prior distributions, namely, the total available energies E are partitioned into the rovibrational states of Rf/Rh and H2O (E and E& ) and the relative translational energy between the two fragments (E − E −

E& ). The probability of Rf*/Rh* with rovibrational energy of E was then calculated as47 '(E ) ∝ ρ(E ) *

,,-

.

ρ(E& )(E − E − E& )/ dE&

in which the total available energy E is ~94 kJ/mol for Rf* and ~100 kJ/mol for Rh* in reactions of Sab + OH → Rf/Rh + H2O, ρ(E ) andρ(E& ) are the rovibrational density of states for Rf/Rh

and water. The rovibrational density of states of fragments were determined with the BeyerSwinehart direct count method for vibrational modes and classical rotor model for rotation,30 and

(E − E − E& )/ is the proportional factor for the density of states of translation motion. Figure S2 shows the time profiles of Rf radical from RRKM-ME modelling of Rf* with the prior distributions, showing that radical Rf* breaks the ring to Rf' within 10–9 s. The lifetime of Rf* is too short to be stabilized by collisions or be captured by O2 as for Rb*, and the conversion of Rf* to peroxy radicals Rf'-OO is virtually 100%. So does Rh* to Rh'-OO radical virtually 100%. Therefore, only the reactions of radicals Rf', Rg, and Rh' are discussed below. Our calculations here suggest that Rh radical is converted almost exclusively to peroxy radicals Rh'-OO. Carrasco et al.20 proposed that Rh would recombine with O2 and be converted eventually for acetone and a C7H9 radical (Scheme 1). Given branching ratios of 0.04~0.08 only for H-abstractions all together and rapid isomerization of Rh, the mechanism by Carrasco et al. is unlikely able to account for their measured yields of (0.21–0.27) for acetone. Alternative mechanism for acetone formation is required. 3.2 Fate of Radicals Syn-/Anti-Ra and Re In the atmosphere, syn-Ra, anti-Ra, and Re would recombine rapidly with oxygen, forming peroxy radicals (RO2). Current understanding is that RO2 will react with NOx in polluted regions and with HO2 radicals in pristine atmosphere.46 In addition, recent studies also found that in the oxidation of many important organic precursor compounds,48-58 the unimolecular H-migration in


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RO2 radicals could lead to autoxidation and formation of highly oxidized multifunctional products (HOMs) which contribute substantially to SOA formation, particularly under the lowNOx conditions. Therefore the intramolecular H-migration in RO2 radicals is also examined in this study. Bimolecular Reactions of Peroxy Radicals Bimolecular reactions of RO2 with NO usually dominate in the atmosphere, particularly in continental regions with anthropogenic NOx emissions. The reaction forms an alkoxy radical (RO) or an organonitrates (RONO2) as46 RO2 + NO → RO + NO2 RO2 + NO + M → RONO2 + M No experimental information is available on the RO2 radicals formed in the oxidation of Sab. Alternatively, an overall rate coefficient was assumed here as ~10–11 cm3 molecule–1 s–1.46 In pristine atmosphere, the effective rate of RO2 with NO/HO2/R'O2 could be very low, e.g., at ~0.025 s–1 with 100 pptv (~2.5 × 109 molecules cm–3) of NO/HO2/R'O2 altogether, letting chances for unimolecular isomerizations in RO2 radicals. It is difficult to estimate the RONO2 yields, e.g., molar yields of α-pinene nitrates ranged from (0.13 ± 0.035) to (0.26 ± 0.07).59-60 For the time being, a yield of ~0.20 at 298 K is assumed by referring to the values in α-pinene and other RO2 radicals of similar size. Yields of RONO2 would be higher at lower temperatures. These nitrates may contribute significantly to SOA formation.61 Reactions of RO2 with HO2/R'O2 are important in more pristine regions of the atmosphere, or even in the urban atmosphere in the afternoon when NO levels are extremely low (< 0.5 ppbv).62 No previous study is available on reaction of Sab-RO2 radicals with HO2. Again, overall rate coefficients can be assumed as ~10–11 cm3 molecule–1 s–1. At this moment, it is considerably difficult to predict the products from the reactions of Sab-RO2 radicals with HO2 because of different functional groups in Sab-RO2. For alkyl-RO2 radicals, we expect a high yield for ROOH and a small yield for ROH and O3; while for RO2 radicals containing –OH or >C=O group, we expect formation of ROOH, R'CHO, RC(O)OH + O3, and RO + OH radical etc., though no quantitative yields could be given here.46


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Unimolecular Reactions of Peroxy Radicals Scheme S1 shows the possible H-migrations in the RaOO radicals and the energies of radicals and transition states, and Scheme S2 for ReOO. Detailed energies are available in Table S1 in Supporting Information. RRKMME calculations were carried out for these processes. In both syn-RaOO and anti-RaOO, barriers for H-migrations are too high to allow significant fractions for these channels at the atmospheric temperatures, e.g., an overall rate of ~3.6 × 10–3 s–1 at 298 K could be obtained from RRKM-ME calculations. Therefore the RaOO radicals would be converted to alkoxy RaO and other products via bimolecular reactions. Note that the internal rotations in RaOO and ReOO are treated as hindered rotor in RRKM-ME calculations. On the other hand, H-migration from ReOO to RegQ would be possible,

With a barrier height of 79.0 kJ/mol at UCBS-QB3 level (79.8 kJ/mol, at ROCBS-QB3 level), the process would be fast enough to compete with the possible bimolecular reactions of ReOO with NO and HO2 in the atmosphere. This H-migration process is endothermic by ~7 kJ/mol only, therefore the process is virtually irreversible because of the high barrier (~72 kJ/mol) for the reversed process and the rapid recombination of RegQ with O2. RRKM-ME calculations obtained a rate of ~5 s–1 for the H-migration at 298 K, being equivalent to the bimolecular reaction with NO of ~20 ppbv. The Hmigration would be faster at higher temperatures, e.g., ~14 s–1 at 323 K as in hot summer, and be still fast enough at low temperatures, e.g. ~0.5 s–1 at 243 K as in cold winter. The effective rates fit an expression ()/s = 1.75 × 10 exp 6− 71.08 × 109 −

..:×.;
.

Therefore, both bimolecular and unimolecular reactions are important for ReOO radical. The peroxy radicals RegQOO might undergo a second H-migration as


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There are two structures of RegQOO with the –OOH and –OO groups at the same or opposite sides of the ring (syn or anti). Barrier heights for the second H-migrations are only 70.8 and 66.4 kJ/mol for the syn- and anti-configurations, resulting in rates of ~100 and ~170 s–1 at 298 K after correction for quantum tunneling effect (Table S1). For the syn-conformer, H-migration from the –OOH group is also possible with a lower barrier of 62.6 kJ/mol; however, this process should be negligible due to its endothermicity by 26.2 kJ/mol and therefore high reversibility at a rate of > 106 s–1 at 298 K. Under the conditions leading to considerable amount of RegQ formation (low NOx), the second H-migration in RegQOO would dominate over their possible bimolecular reactions, resulting in formation of a C10H16O5 product as shown above. Reactions of Alkoxy Radicals Alkoxy radicals RaO, ReO and RegQO are formed in the bimolecular reactions of RaOO, ReOO, and RegQOO, respectively. The two RaO conformers would decompose as

For syn-and anti-RaO, the decomposition would be extremely fast due to their low barriers of only 3~7 and ~29 kJ/mol (∆E0K, UCBS-QB3), leading to formation of formaldehyde and a C9H15O radical under the atmospheric conditions (Table S1). The range of barrier heights here is for different rotational conformers of RaO radical. The C9H15O radical would react with O2 or break the ring as


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The unimolecular reaction, with a barrier height of 40.2 kJ/mol and a HPL rate of ~1.9 × 106 s–1 at 298 K (Table S1), can unlikely compete with the bimolecular reaction at effective rate of ~5 × 107 s–1 (assuming a bimolecular rate coefficient of ~10–11 cm3 molecule–1 s–1 as for the reaction between CH2OH radical and O2).63 Therefore, RaO radical would be converted mainly to formaldehyde and sabinaketone with about the same formation yields. Radical ReO has two unimolecular channels as ring breakage and decomposition as

Barrier heights at UCBS-QB3 level are found to be 38.0, 41.5, and 33.9 kJ/mol for the ring scissions to Re2O and Re2O' and the decomposition, leading to HPL rates at 298 K of ~4.7 × 106, ~7.5

× 105, and ~3.8 × 107 s–1, respectively (Table S1). The decomposition process

dominates, and i-C3H7 fragment would be converted to acetone in the presence of NOx. This might be the route for acetone formation. The Re2O from ring scission would recombine with O2,

The addition of O2 to Re3OO-1 and Re3OO-2 would be reversible with ∆E0K of –71.5 and –88.9 kJ/mol (∆G298K of –24.4 and –40.1 kJ/mol), respectively. The H-migration in Re3OO-1 has a barrier height of 81.6 kJ/mol, with which a rate of ~3 s–1 at 298 K was estimated by simple TST calculation with tunneling correction (Table S1). The rate might be reduced by a factor of 2 – 3 if


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treating the three internal rotations as hindered rotors.54 The H-migration in Re3OO-2 has a barrier of 70.5 kJ/mol and a rate of > 100 s–1 at 298 K. Both H-migrations in Re3OO-1/-2 are much slower than their back-decomposition to Re2O + O2. Assuming steady state for the intermediate Re3OO-1/-2 radical, the effective rate coefficient for the formation of Re2Q1/Re2Q2 becomes ,?? = @A ∙

BCA BCA ≅ @A ∙ = E,F BCA BCA +

in which E,F is the equilibrium constant between Re2O + O2 and Re3OO-1/2. Obviously, the channel to Re2O2 is favored both thermodynamically and kinetically, altogether by ~5 orders of magnitude. Therefore, Re2O would be transformed to Re2Q2 almost exclusively in the atmosphere. The radical Re2Q2 would recombine rapidly with O2, forming another peroxy radical,

in which the barrier for H-migration in the peroxy radical Re2Q2-OO is only 55.5 kJ/mol, resulting a unimolecular rate of 2400 s–1 at 298 K from RRKM-ME calculations. The radical formed after H-migration would react rapidly with O2, forming a C10H16O6 compound. Note that the H-migrations in Re3OO-2 and Re2Q2-OO are fast enough to dominate over their possible bimolecular reactions with NO even up to tens of ppbv. Schemes 2 and 3 summarize the main product channels after the initial OH additions to the >C=C< bond. Under the high NO conditions as in the heavily polluted atmosphere or in some of the smog chamber studies, we would expect the formation of sabinaketone and formaldehyde from addition to Cb with primary yields of ~0.37, and the formation of a C7H10O2 product and acetone with primary yields of ~0.35 if assuming the yield of 0.2 for organonitrates in the


15


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reaction of C10H16-OH-OO and NO as for peroxy radicals of similar size.46 Under low NO conditions, the intramolecular H-migrations in ReOO radicals become important, forming a C10H16O5 product. In the atmosphere, the reaction with NO usually dominates the bimolecular reactions of peroxy radicals, while the reactions with HO2 and other peroxy radicals are slow due to their extremely low concentrations (usually less than 100 pptv). Therefore, formation of the C10H16O5 product from radical Re would prevail in the pristine atmosphere, while the reaction of ReOO with HO2 might be important in smog chamber studies in which OH is generated from photolysis of H2O2 and from the enhanced oxidation of organic compounds in the absence of NOx. Under high NOx conditions, our predicted yields of ~0.37, ~0.35, and ~0.37 for formaldehyde, acetone, and sabinaketone are all higher than but in reasonable agreement with the previously measured values of 0.22–0.27, 0.21–0.27, and 0.19–0.23, respectively.10-13 We suspect the experimental yields might be underestimated because the measured total yield of 0.4–0.5 for sabinaketone and acetone was much less than the fraction of addition channels. No detection of the C7H10O2 product was reported in previous studies. Carrasco et al.20 found no noticeable difference in product yields in the presence and absence of NOx in their simulation chamber studies, probably due to high concentration of HO2 radical in the system. In the measurements in the absence of NO, the OH radical was produced by photolysis of H2O2 using TUV lamps with an emission maximum at 254 nm. In the absence of NO, the RaOO and ReOO radicals would react with HO2, forming RaOOH or ReOOH, which would be photolyzed at least partially by the TUV light as RaOOH/ReOOH + hv → RaO/ReO + OH. The RaO and ReO radicals would also decompose to sabinaketone + CH2O and C7H10O2 + acetone as shown in Scheme 2. This might be the reason for the similar yields of sabinaketone, formaldehyde, and acetone in the presence and in the absence of NO. 3.3 Fate of Radicals Rf', Rg, and Rh' Radical Rf' Saninenyl-Rf' is a radical with delocalized π-bond. O2 can add to Ca- and Cc-positions of Rf' radical, forming Rf'-aOO and Rf'-cOO radicals at a rough ratio of 1:2 at 298 K as being estimated by TST calculations (Table S1). For Rf'-aOO, the


16

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intramolecular H-migration from CgH2 is much favoured due to the delocalized π-bond in transition state and in product radical Rf'-aQ,

The barrier height for H-migration in Rf'-aOO is 64.7 kJ/mol at UCBS-QB3 level. The estimated unimolecular rate for H-migration here is ~4 × 102 s–1 at 298 K, letting negligible chances for Rf'-aOO to react with NO and other radicals even in the highly polluted atmosphere. The radical Rf'-aQ is structurally similar to the cyclohexadienyl radical, c-C6H7, which reacts with O2 with a rate coefficient of ~5 × 10–14 cm3 molecule–1 s–1 at room temperature.64-65 Our calculations show that the reaction of c-C6H7 with O2 forms benzene and HO2 radical, and the reaction of 2-isopropyl-5-methyl cyclohexadienyl radical with O2 forms p-cymene, all with almost unit yield.66 We expect similar reaction products for Rf'-aQ radical as shown above. Similarly, Rf'-cOO radical has the following intramolecular H-migration,

The barrier height for H-migration in Rf'-cOO is 81.1 kJ/mol at UCBS-QB3 level, resulting in fast H-migration at ~5 s–1 at 298 K. Both unimolecular and bimolecular processes are important in Rf'-cOO radical. Radical Rf'-cQ recombines with O2, forming three peroxy radicals as Rf'-cQ-aOO, -eOO, and –gOO, of which only Rf'-cQ-aOO can have a reasonably fast H-migration as


17


Page 18 of 31

The process, with a barrier height of 67.2 kJ/mol, is fast enough to minimize its bimolecular reactions. We ignored the H-migration from the –OOH group in Rf'-cQ-aOO via an eight-membered-ring transition state. The other two peroxy radicals would react with NO and HO2, and the alkoxy radicals Rf'-cQ-eO/-gO formed would react as HOO

HOO + i-C3H7 O O C H O 7 8 3 Rf'-cQ-eO (Two Conformers)

HOO

HOO

O

O

O2 HO2

C10H14O3

Rf'-cQ-gO

For Rf'-cQ-eO, the barrier heights for decomposition are 29.1 and –3.8 kJ/mol for the two conformers at UCBS-QB3 level (31.7 and 24.9 kJ/mol at M06-2X level), resulting in formation of i-C3H7 and a C7H8O3 compound. Radical Rg Sabinenyl-g radical has a delocalized G-bond; therefore O2 can add to Ca and Cg positions with branching ratios of ~0.10 and ~0.90. The peroxy radicals formed have no sensible unimolecular channel at atmospheric temperatures with their barriers all higher than 110 kJ/mol (UCBS-QB3). Instead, the peroxy radical will react with NO and/or HO2/RO2 radicals. For addition of O2 to Ca, the transformation would be

While for addition to Cg, the alkoxy radical RgO would react with O2 at an effective rate of 104–105 s–1 or decompose as

Barrier heights were obtained as 34.7 and 37.5 kJ/mol for the two conformers of RgO, leading to HPL rates of ~2.6 × 106 and ~4.5 × 106 s–1 at 298 K. The unimolecular processes would dominate the fate of RgO radicals. The resulted radical Rg2 would


18

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further break the 3-membered ring to Rg3 with a marginal barrier of ~6 kJ/mol only (relative to Rg2) at UCBS-QB3 level. Therefore, radicals RgO would convert dominantly to Rg3, which would recombine with O2 as

where the peroxy radicals have H-migrations as

in which the barrier height for the first H-migration (H-Mig1) is 76.5 kJ/mol, resulting in a rate of ~3.6 s–1 at 298 K. After addition of another O2, the radical Rg3-aQOO also has H-migrations from Ca (H-Mig2) and Cd (H-Mig3) with barrier heights of 75.8 and 55.4 kJ/mol, respectively. H-Mig3 dominates, and further reaction of radical would lead to formation of HOMs. Similarly for Rg3-cOO radical,

where the barrier heights for the three H-migrations were obtained as 72.3, 67.5, and 61.4 kJ/mol, rendering rates of ~59, ~108, and ~1000 s–1 for H-Mig4, H-Mig5 and H-Mig6, respectively, at 298 K. Fast H-Mig4 and H-Mig6 result in the dominant formation of Rg3c2, which would be further transformed to HOMs in the atmosphere.


19


Page 20 of 31

Radical Rh' O2 can add to Ca- and Cc-positions of Rh' radical, forming Rh'-aOO and Rh'-cOO radicals with a rough ratio of 10:1 at 298 K from TST calculations. Possible intramolecular H-migration in Rh'-aOO is,

The H-migration here has a barrier height of 70.4 kJ/mol (Table S1), leading to fast isomerization to Rh'-aQ at a rate of ~130 s–1 at 298 K. Similarly Rh'-aQOO has O

OH OO

O

OH OOH

O OOH + OH

Rh'-aQOO

C10H14O3

This H-migration has a barrier height of 82.9 kJ/mol and a rate of ~1.6 s–1 at 298 K. Therefore, Rh'-aQOO would react more likely with NO and HO2. The alkoxy radical Rh'aQO would react with O2 as

The barrier height for the ring scission was found to be ~24 kJ/mol, resulting rapid rates of >108 s–1 at 298 K. Alkoxy radicals from Rh'-aQO2 would lead to the formation of the following products.

The H-migration in Rh'-cOO is hindered by high barrier of ~94 kJ/mol (Table S1). Therefore, Rh'-cOO would react with NO and HO2 in the atmosphere. The Rh'-cO radical would break the ring as


20

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O

O

O

O + O2 OO

OO Rh'-cO

Rh'-c1

Rh'-c2

The barrier height for the ring breakage is ~30 kJ/mol at UCBS-QB3 level, resulting in a unimolecular rate of >107 s–1 at 298 K. The alkoxy radicals from Rh'-c1/-c2 would lead to formation of the following products.

Scheme 5 summarizes the main degradation routes of the three radicals formed by Habstractions. Fast H-migrations are found for many of the peroxy radicals, resulting in formation of HOMs. 4. Conclusions Atmospheric oxidation of sabinene initiated by OH radical has been investigated by quantum chemistry and kinetic calculations. The reaction proceed by OH additions to the >C=C< bond with a branching ratio of ~(92 – 96)% and by H-abstractions from the alkane groups with a branching ratio of ~(4 – 8)% at 298 K. Radical formed from addition to Ca-site would break the 3-membered ring promptly, leading to formation of Re radicals. Radicals Rf and Rh formed from H-abstractions would also break the 3-membered ring promptly to Rf' and Rh' radicals. Schemes 2 and 3 summarize the proposed mechanism after OH additions, and Scheme 4 shows the mechanism after H-abstractions at 298 K. The predicted yields at high NO conditions are ~0.37, ~0.37, and ~0.35 for sabinaketone, formaldehyde, and acetone, being higher than while being in reasonable agreement with the experimental values of 0.19–0.23, 0.22–0.27, and 0.21–0.27, respectively. A C7H10O2 compound is also formed with the same yield of ~0.35 for acetone. A formation yield of ~0.19 is also expected for C10H16-OH-ONO2 nitrates. Our calculations here showed that acetone is formed through the ReOO radical channel, instead of the H-abstraction channel as being proposed by Carrasco et al.20 Scheme 4 summarizes the main degradation pathways of radicals Rf', Rg, and Rh' formed from H-abstraction. Fast H-migration


21


Page 22 of 31

was found for many of the peroxy radicals formed in the degradation. HOMs are expected from degradation of these radicals. ASSOCIATED CONTENT Supporting Information. Figures S1–S3, Schemes S1 and S2, and Tables S1 and S2. The file is available free of charge. AUTHOR INFORMATION Corresponding Author * Liming Wang, E-Mail: [email protected]; ORCID: 0000-0002-8953-250X. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources National Natural Science Foundation of China and Natural Science Foundation of Guangdong Province. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (No. 21477038 and

21677051),

the

2016A030311005),

and

Natural the

Science National

Foundation Key

of

Research

Guangdong &

Province

Development

(No.

Program

(2017YFC0212800).


22

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OH

H 2C HO HO

H2C HO

HO

Figure 1. Potential energy diagram for OH additions to sabinene. OO g a

f

i

b c

j

d

NO OH

e h

O2

H-Abstraction

HO

RbOO

OO H2C

... NO2

O + CH2O + HO2

HO RaOO O

+ Acetone

Rh

Scheme 1. Mechanism by Carrasco et al.20.

Scheme 2. Main products after OH addition under high-NO conditions


23


HO

HO

~5s + O2 OO

1

Page 24 of 31

O OO ~ 100 s 1 or OOH ~ 170 s 1

O2

HO2

OOH

OOH C10H16O5

Scheme 3. Main products after H-migration in ReOO radical

Scheme 4. Main degradation routes of radicals from H-abstraction in the atmosphere


24

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Table 1. Energies of reaction intermediates, products, and transition states for the reaction of sabinene and OH radical (a)(b) ΔE0K (c)

ΔE0K (d)

ΔE0K (e)

ΔE0K (e)

Sabinene---HO syn-PRC

–20.7

–7.9

–8.2

22.6

Sabinene + OH

0.0

0.0

0.0

0.0

Sabinene---HO anti-PRC

–22.2

–15.2

–15.1

18.3

TS (syn-PRC → syn-Ra)

–9.5

–15.2

–18.2

17.4

TS (syn-PRC →Rb)

–15.2

–15.3

–18.5

15.7

TS (anti-PRC → anti-Ra)

–15.7

–20.8

–20.4

11.5

TS (anti-PRC → Rb)

–17.4

–18.2

–20.9

12.8

Syn-Ra

–124.2

–121.1

–121.3

–83.6

Anti-Ra

–127.5

–125.5

–125.8

–87.7

Rb

–123.6

–119.1

–119.6

–85.8

TS (Rb → Re)

–75.4

–88.0

–88.9

–55.6

Re

–150.3

–150.4

–150.7

–118.3

TSc (Sabinene + OH → Rc + H2O)

4.5

3.4

1.9

35.4

TSd1 (Sabinene + OH → Rd + H2O)

4.0

3.8

2.4

34.8

TSd2 (Sabinene + OH → Rd + H2O)

7.5

6.0

4.7

36.6

TSf1 (Sabinene + OH → Rf + H2O)

0.7

–1.2

–2.2

26.8

TSf2 (Sabinene + OH → Rf + H2O)

2.0

0.4

–0.6

31.9

TSg1 (Sabinene + OH → Rg + H2O)

–5.9

–5.9

–7.6

25.8

TSg2 (Sabinene + OH → Rg + H2O)

5.3

3.3

1.7

32.7

TS (Sabinene + OH → Rh + H2O)

–3.5

–5.4

–6.3

26.6

TSi1 (Sabinene + OH → Ri + H2O)

7.7

7.4

6.5

38.6


7.2

8.1

6.8

40.4


4.6

4.8

3.5

37.6

Rc + H2O

–33.5

–34.6

–36.3

–41.4

Rd + H2O

–44.2

–45.1

–45.8

–50.7

Rf + H2O

–89.2

–90.5

–90.9

–96.1

Rf' + H2O

–157.7

–171.2

–173.0

–179.3

TS (Rf → Rf') + H2O

–44.9

–63.7

–66.9

–71.6

Rg + H2O

–132.8

–141.3

–143.1

–147.2

Rh + H2O

–96.2

–96.0

–96.5

–106.0

Rh' + H2O

–150.2

–165.4

–166.7

–174.1

TS (Rh→ Rh') + H2O

–73.6

–88.9

–92.8

–98.0

Ri + H2O

–71.2

–71.3

–71.5

–76.9

(a) Energies, in kJ/mol, are all relative to the separate Sabinene + OH; (b) All based on geometries and zero-point-energy corrections at M06-2X/6-311++G(2df,2p) level; (c) At M06-2X level; (d) At ROCBSQB3 level; (e) At UCBS-QB3 level


25


Page 26 of 31

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The Atmospheric Oxidation Mechanism of Sabinene Initiated by the

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