Atmospheric photooxidation and ozonolysis of ∆-carene and 3-caronaldehyde: Rate constants and product yields

The oxidation of ∆-carene and one of its main oxidation products, caronaldehyde, by the OH radical and O3 was investigated in the atmospheric simulation chamber SAPHIR under atmospheric conditions for NOx mixing ratios below 2 ppbv. Within this study, the rate constants of the reaction of ∆-carene with OH and O3, and of the reaction of caronaldehyde with OH were determined to be (8.0±0.5)×10−11 cm3s−1 at 304 K, (4.4±0.2)×10−17 cm3s−1 at 300 K and (4.6±1.6)× 10−11 cm3s−1 at 300 K, respectively, in agreement with previously published values. The yields of caronaldehyde from the 5 reaction of OH and ozone with ∆-carene were determined to be (0.30±0.05) and (0.06±0.02), respectively. Both values are in reasonably well agreement with reported literature values. An organic nitrate (RONO2) yield from the reaction of NO with RO2 derived from ∆-carene of (0.25± 0.04) was determined from the analysis of the reactive nitrogen species (NOy) in the SAPHIR chamber. The RONO2 yield of the reaction of NO with RO2 derived from the reaction of caronaldehyde with OH was found to be (0.10±0.02). The organic nitrate yields of ∆-carene and caronaldehyde oxidation with OH are reported here 10 for the first time in the gas phase. An OH yield of (0.65±0.10) was determined from the ozonolysis of ∆-carene. Calculations of production and destruction rates of the sum of hydroxyl and peroxy radicals (ROx = OH+HO2+RO2) demonstrated that there were no unaccounted production or loss processes of radicals in the oxidation of ∆-carene for conditions of the the chamber experiments. In an OH free experiment with added OH scavenger, the photolysis frequency of caronaldehyde was obtained from its photolytical decay. The experimental photolysis frequency was a factor of 7 higher than the value calculated 15 from the measured solar acintic flux density, an absorption cross section from the literature and an assumed effective quantum yield of unity for photodissociation. 1 https://doi.org/10.5194/acp-2021-340 Preprint. Discussion started: 30 April 2021 c © Author(s) 2021. CC BY 4.0 License.


Introduction
On a global scale, the emission of carbon from biogenic volatile organic compounds (BVOC) exceeds 1000 Tg per year (Guenther et al., 2012). Among all BVOC emissions, monoterpenes are the second most important class of species, contributing up 20 to 16 % to the total emissions. As they are unsaturated and highly reactive, knowledge of their atmospheric chemistry is crucial to understand the formation of secondary pollutants such as ozone (O 3 ) and particles (e.g Seinfeld and Pandis, 2006;Zhang et al., 2018).
Of the total global annual monoterpene emissions, ∆ 3 -carene contributes 4.5 % making it the 7 th most abundant monoterpene species (Geron et al., 2000). ∆ 3 -carene is primarily emitted by pine trees. Measured emission rates are up to (85 ± 25 17) ngg(dw) −1 h −1 (nanograms monoterpenes per gram dry weight (dw) of needles and hour) from Scots pines (Komenda and Koppmann, 2002) and 57 ngg(dw) −1 h −1 from maritime pine. Therefore, ∆ 3 -carene regionally gains in importance, for example in boreal forests and the mediterranean region. Hakola et al. (2012) measured the mixing ratios of monoterpenes over a boreal forest in Hyytialä, Finland, and found ∆ 3 -carene to be the second most abundant monoterpene after α-pinene. However, while the atmospheric chemistry of some monoterpenes such as α-pinene or β-pinene has been investigated in a number  (shutters closed) and sunlit (shutters opened) chamber. With the shutters opened, the chamber is exposed to sunlight, therefore time of the injections using a ∆ 3 -carene + OH reaction rate constant of 8.0 × 10 −11 cm 3 s −1 . The uncertainty of this calibration correction is given by the uncertainty in the ∆ 3 -carene + OH reaction rate constant and the uncertainty in the OH reactivity measurements that is 10 % (Fuchs et al., 2017a). Pinonaldehyde was used as a substituent to calibrate the instrument for caronaldehyde, as there is no calibration standard for caronaldehyde. The concentrations obtained from this calibration were in good agreement with the rise of the OH reactivity during caronaldehyde photooxidation experiments using a reaction 130 rate constant of 4.1 × 10 −11 cm 3 s −1 .
Formaldehyde (HCHO) was measured by a Hantzsch monitor (AL4021, AeroLaser GmbH) and with a cavity ring-down instrument (G2307, Picarro). On average, the concentrations measured by both instruments agreed within 15 % (Glowania et al., 2021). HONO concentrations were measured by a custom-built long path absorption photometer (LOPAP) (Kleffmann et al., 2002;Li et al., 2014). NO and NO 2 were measured using a chemiluminescence instrument (Eco Physics) equipped with a 135 blue-light photolytic converter for the conversion of NO 2 to NO. CO and water vapor was measured with a cavity ring-down instrument (G2401, Picarro) and O 3 with an UV absorption instrument (Ansyco). Total and diffuse spectral actinic flux densities measured by a spectral radiometer outside of the chamber were used to calculate photolysis frequencies (j) following Equation (1): with σ the absorption cross section, φ the quantum yield and F λ the mean spectral actinic flux density inside the chamber.
Absorption cross sections and quantum yields were taken from recommendations in literature. The actinic flux spectra within the chamber were calculated in a model using the spectral radiometer measurements as input. As explained in more detail in  and Bohn and Zilken (2005), this model takes into account chamber specific parameters such as the time-dependent effects of shadings of the chamber steel frame and the transmittance of the Teflon film. RO x radicals (OH,

OH reactivity and peroxy radical distribution
The OH reactivity measured in the SAPHIR chamber represents the sum of all species that react with OH. It can be separated 155 into a fraction attributed to inorganic species (NO, CO, NO 2 ) and formaldehyde (here named kOH inorg ), and a fraction contributed by VOC species (kOH VOC ). This allows to distinguish between reactions forming RO 2 and those that do not.
Equation 2 allows to calculate the fraction contributed by VOC by substracting kOH inorg from the total measured reactivity.
k OH+X represents the reaction rate constant of the respective compound X with OH.
Included in kOH VOC is the reactivity from ∆ 3 -carene, but also from reaction products like oxygenated VOCs (OVOCs).
kOH carene , the fraction of OH-reactivity from ∆ 3 -carene, can be calculated using its OH reaction rate constant and measured concentrations (Equation 3).
Since the RO 2 measurement is the sum of all RO 2 produced in the chamber, it can be assumed that the fraction of RO 2 165 radicals produced by ∆ 3 -carene to the total RO 2 concentration is equal to the ratio of OH-reactivity from the ∆ 3 -carene + OH reaction to the total measured OH reactivity, assuming that every VOC + OH reaction leads to the formation of an RO 2 radical, and that all RO 2 species have similar chemical lifetimes. The concentration of RO 2 formed by ∆ 3 -carene oxidation can therefore be estimated using Equation 4.
2.5 Determination of product yields -organic nitrate RONO 2 The yield of nitrates (RONO 2 ) from the reaction of RO 2,carene + NO can be determined from the analysis of the concentrations of reactive nitrogen species in the chamber. NO, NO 2 and HONO were directly measured in the experiments and their sum is called NO y * for the analysis in this work (Equation 5): The source of all reactive nitrogen species in the experiment is the chamber source of HONO in the sunlit chamber. Its variable source strength Q(HONO) depends on temperature, relative humidity and solar ultraviolet radiation .
HONO photolysis leads to the production of NO that is further oxidized to higher nitrogen oxides over the course of the experiment.
As HONO can be reformed by the reaction of NO with OH, a photostationary state between HONO, NO and OH is usually 195 reached within several minutes. Therefore, measurements of NO, OH, j HONO and HONO can be used to calculate the source strength of HONO (Equation 7).

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ical loss of NO y * in the chamber occurs due to the formation of RONO 2 (R6, Table 2) and HNO 3 (R2 , Table 2). Additionally, NO y * species are lost due to replenishment flow that compensates for chamber leakage and gas sampling of analytical instruments. The difference between the time-integrated production and loss terms can then be used to determine the concentration of NO y * at a given time t.
[NO y where L dil is the loss due to the replenishment flow, diluting the chamber air with the first order rate coefficient k d = 1.6 × 10 −5 s −1 . L dil is calculated by Equation 9.
With respect to analysis of total nitrogen oxide concentration in the chamber, Equation 8 assumes that HNO 3 and RONO 2 formation are effective sinks for NO x and that it does not play a role, if nitrates remain as HNO 3 or RONO 2 in the gas-phase 210 or if they are for example deposited on the chamber wall as long as neither NO nor NO 2 are reformed. Possible decomposition pathways could e.g. be due to photolysis, which would lead to a reformation of NO 2 . However, reported atmospheric lifetimes of RONO 2 species are in the range of several days due to their small absorption cross sections (Roberts and Fajer, 1989) much longer than the duration of the chamber experiment. NO 2 loss due the formation of nitrate radicals (NO 3 ) from the reaction of NO 2 with ozone is also neglected in Equation 6. For the experimental conditions in this work, the photolytic 215 backreactions, reforming NO 2 from NO 3 are fast enough that the NO 3 concentration in the sunlit chamber remains negligibly small. The formation of other oxidized nitrogen species such as acetyl peroxy nitrate (PAN) is also assumed to be negligible.
The thermally unstable PAN species are formed from reaction of acyl peroxy radicals with NO 2 . For experiments in the SAPHIR chamber with comparable temperature conditions, the mixing ratios of PAN formed in the oxidation of acetaldehyde emitted by chamber sources are typically less than 100 pptv. Combining Equations 5 and 8, the amount of RONO 2 formed 220 can be calculated as follows.
To proof this concept of calculating organic nitrate yields, reference experiments with CH 4 were performed. An upper limit of 0.001 was found for the nitrate yield. Within the uncertainty of the measurements this value is in good agreement with literature (Scholtens et al., 1999;Butkovskaya et al., 2012). To exclude possible errors in the analysis for larger molecules for which nitrate formation is significant, such as unknown chamber sources of reactive nitrate species, a similar analysis was performed 230 for an α-pinene experiment conducted in the SAPHIR chamber. For this experiment, an organic nitrate yield of (26 ± 3) % was found, which is in reasonable agreement with the reported literature values. A detailed description of the reference experiments with CH 4 and α-pinene will be given in a publication currently in preparation.

Determination of product yields 235
The experiments conducted in SAPHIR allow to determine the product yields of caronaldehyde from the reaction of ∆ 3 -carene with OH and O 3 . The product yield determination for caronaldehyde is done using measured caronaldehyde concentrations and relating them to the concentration of ∆ 3 -carene consumed by OH or O 3 . The concentrations of ∆ 3 -carene and caronaldehyde were measured by VOCUS-or PTR-TOF-MS. A correction was applied to the ∆ 3 -carene and caronaldehyde concentrations similar to corrections described by Galloway et al. (2011) and Kaminski et al. (2017). To derive the concentration of ∆ 3 -carene 240 that reacted with OH or O 3 , measured ∆ 3 -carene concentrations were corrected for dilution in the chamber and the reaction with O 3 or OH, respectively. The measured product concentrations of caronaldehyde were corrected for loss due to photolysis and dilution.

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The experiments performed in the SAPHIR chamber that investigated the OH oxidation of ∆ 3 -carene allow to calculate production and destruction rates of the total ROx concentration. The atmospheric lifetimes of the ROx radicals range from only a few seconds for the OH radical to minutes for HO 2 and RO 2 radicals. Therefore, steady state conditions of ROx concentrations can be assumed, so that radical production and destruction rates are always balanced for the timescale of the chamber experiments. If there are imbalances between the calculated production and destruction rates, chemical reactions 250 leading to the formation or destruction of radicals must be missing in the calculations. Table 2 gives an overview of the formation and loss reactions considered in the analysis including the respective reaction rate constants used. The reaction rate constants of the individual reactions were either taken from recent experimental studies, from measurements in this study or from calculations applying structure-activity relationship (SAR) as described in Jenkin et al. (2019).
The main ROx formation processes include the photolysis of ozone (Reaction R11), HONO (Reaction R12) and HCHO 255 (Reaction R13) as well as the ozonolysis of ∆ 3 -carene (Reaction R14). The formation of ROx radicals from the photolysis of caronaldehyde (R4) was also considered. The formation rate of ROx radicals P(ROx) can be calculated by Equation 11.
Φ X indicates the yield of the respective radical X from the given reaction. Loss processes include the reactions of radicals with NOx that lead to the formation of HONO from the reaction of OH with NO (Reaction R5), nitric acid (HNO 3 ) from 260 the reaction of OH with NO 2 (Reaction R6) or organic nitrates (RONO 2 ) from the reaction of RO 2,carene and NO (Reaction R10). Depending on the experimental conditions, radical loss through radical self-reactions become more important, leading to the formation of hydrogen peroxide (H 2 O 2 ) from the reaction of two HO 2 radicals (Reaction R7), the formation of peroxides (ROOH) from the reaction of HO 2 with RO 2 (Reaction R8) and the self-reaction of RO 2 (Reaction R9). The loss rate of ROx Direct measurements of all relevant species allow to calculate the total formation and loss rates for the ROx radicals. The error of the loss and production rates of the ROx radicals is determined by error propagation taking uncertainties in the measurements and kinetic parameters into account.
270 Table 2. Formation and loss reactions of the ROx radicals considered in the budget analysis (Fig. 11). Reaction rate constants are given for 298K and 1 atm. The reaction rate constants in the actual analysis are calculated using temperature and pressure data measured during the experiments in SAPHIR.

Ozonolysis of ∆ 3 -carene
The ozonolysis of ∆ 3 -carene was investigated in the dark SAPHIR chamber in two experiments in order to determine the rate constant (experiment E3) and OH yield (experiment E4) of the ozonolysis reaction, and the yield of caronaldehyde. Measured timeseries of O 3 , ∆ 3 -carene and caronaldehyde are shown in Fig. 2. In total, 6.5 ppbv of ∆ 3 -carene was consumed in exper-275 iment E3, and 7 ppbv in experiment E4. The roof of the chamber was closed for the whole duration of both experiments, to eliminate photolytical OH production. Since there was no OH scavenger present in experiment E3, the reaction system was also influenced by OH that is formed from ozonolysis (Sect. 3.1.2). OH concentrations were in the range of 1.0 to 2.0 × 10 6 cm −3 .
CO was injected into the chamber as an OH scavenger prior to the beginning of experiment E4.

Rate constant of the ozonolysis reaction of ∆ 3 -carene
Optimization of the ozonolysis reaction rate constants as described in Sect. 2.4 results in a value of (4.4 ± 0.2) × 10 −17 cm 3 s −1 . The stated error arises from the accuracy of the O 3 and ∆ 3 -carene measurements. The average temperature inside the SAPHIR chamber during the experiment was 300 K. The value reported in this study is slightly higher than values reported by Atkinson et al. (1990) and Chen et al. (2015), but still agrees within the stated errors (Table 3).

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Reaction rate constants determined by Atkinson et al. (1990) and Chen et al. (2015) were (4.05 ± 0.4) × 10 −17 cm 3 s −1 and (3.7 ± 0.4) × 10 −17 cm 3 s −1 , respectively. Both values were obtained from relative reaction rate measurements by comparing the rate of decay of ∆ 3 -carene from ozonolysis to the rate of decay of a well-known reference compound (α-pinene in Atkinson 290   2015)). Additionally both studies also determined the reaction rate constant with an absolute rate technique using a pseudo-first order approach. In Atkinson et al. (1990), reactive impurities in the used ∆ 3 -carene sample were reported, whose presence would reduce the initially measured reaction rate constant from the absolute technique from Data Evaluation recommend to use a value of (4.9 ± 0.2 × 10 −17 ) cm 3 s −1 (Atkinson et al., 2004), which is an average of the relative rate constants determined by Atkinson et al. (1990) and Witter et al. (2002) and is in good agreement with the value determined in this work. Using the SAR published by Jenkin et al. (2020) a reaction rate constant of 4.7 × 10 −17 cm 3 s −1 can be calculated. The value reported in this study is in relatively good agreement with this theory derived value.
3.1.2 Determination of the OH yield from the ozonolysis of ∆ 3 -carene

310
During experiment E3, when no OH scavenger was present, ∆ 3 -carene was not only consumed by O 3 , but also by OH that is produced from the ozonolysis reaction. Because OH production from the ozonolysis was the only OH source, the OH yield from ozonolysis of ∆ 3 -carene can be determined from this experiment. The chamber roof was closed for the whole experiment and there are no photolytic sources for OH formation. The reaction rate constant determined in the previous section for the period, when an OH scavenger was present in the SAPHIR chamber, is used in the box model to determine the OH yield of 315 the ozonolysis as explained in Sect. 2.4. The OH yield from ozonolysis is optimized until the measured decay of ∆ 3 -carene matches the modeled decay (Fig. 3).
The OH yield is found to be 0.65 ± 0.10 in the experiment in this work. The error is mainly due to the uncertainties in More recent investigations of the yield of cyclohexanol and cyclohexanone from the reaction of cyclohexane and OH indicate a larger of yield, 0.88 (Berndt et al., 2003), as compared to the value of 0.5 used by Atkinson et al. (1992). This higher value would reduce the OH yield in the ozonolysis of ∆ 3 -carene in the experiments by Atkinson et al. (1992) to 0.6, which would 330 agree well with the OH yield determined in this work and the value calculated by Wang et al. (2019).
The ozonolysis of ∆ 3 -carene is initiated by O 3 attacking the C-C double bond, forming an energy-rich primary ozonide (POZ).
Mostly, the energy retained in the POZ leads to a decomposition into Criegee intermediates, retaining one structure bearing a carbonyl functionality on one side of the molecule and the Criegee funcionality on the other. These Criegee intermediates

Caronaldehyde yield from ozonolysis
The caronaldehyde yield for the ∆ 3 -carene + O 3 reaction was determined from experiment E4, where an OH scavenger was injected into the chamber, so that caronaldehyde is exclusively formed form the ozonolysis reaction. The corrections described 345 in Sect. 2.5 were applied. Caronaldehyde was formed from the ozonolysis of ∆ 3 -carene with a yield of (5.5 ± 2) % as shown in Fig. 4. The uncertainty is derived from measurements and errors of the applied corrections (Section 2.6) for the respective experiment.
The determined caronaldehyde yields from this study and reported literature values are given in Table 5. The obtained value 350 is in reasonably good agreement with most of the reported literature values. Yu et al. (1999) reported a caronaldehyde yield of 8 %, using 2−butanol to scavenge OH radicals. Hakola et al. (1994) determined the caronaldehyde yield to be ≤ 8 % .
In the presence of cyclohexane as an OH scavenger, caronaldehyde was not detected in the ozonolysis of ∆ 3 -carene in the experiments conducted by Hakola et al. (1994). Ma et al. (2009) reported a caronaldehyde yield of (0.47 ± 0.05) % from filter samples, using cyclohexane, methanol or ethanol to scavenge OH radicals. However, due to its relatively high vapour pressure, 355  it is likely that caronaldehyde was mainly present in the gas phase, so that only a small fraction of the formed caronaldehyde was collected on the filters.
The formation of caronaldehyde from ∆ 3 -carene ozonolysis most likely results from the stabilization and subsequent reaction with water of one of the Criegee intermediates, the formation mechanism of caronaldehyde in the absence of water has yet 360 to be clarified (Ma et al., 2009). The stabilization of the Criegee intermediate is found to be a minor pathway by Wang et al.
(2019), possibly explaining the small caronaldehyde yield found for the ozonolysis of ∆ 3 -carene. Further reaction products that have not been measured in this study include a range of multifunctional organic acids according to studies conducted by e.g. Ma et al. (2009).

OH reaction of ∆ 3 -carene 365
The first oxidation steps of the OH-induced photochemical oxidation of ∆ 3 -carene relevant for this study are shown in Fig. 5 ( Colville and Griffin, 2004). The OH oxidation is initiated by addition of OH to the C-C double bond or by the abstraction of an H-atom rapidly followed by addition of O 2 . From the OH addition two peroxy radical isomers are formed. The branching ratios of the specific attack on the C-C double bond (Fig. 5) Figure 5. Simplified scheme of the first reaction steps of the OH photooxidation of ∆ 3 -carene (adapted from Colville and Griffin (2004).
Yields shown in black are from SAR by Jenkin et al. (2018). OH induced photooxidation of ∆ 3 -carene was investigated in the SAPHIR chamber during two experiments with NOx mixing ratios below 1 ppbv (Table 1). Figure 6 shows an overview of all measured species in experiment E1 that are representative for experiments at low NOx mixing ratios. Time series of concentration measurements for the other experiment is shown in the Supplement (Fig. S1). For all experiments, ∆ 3 -carene was injected three times into the chamber, increasing the mixing ratio 380 by approximately 5 ppbv each injection.

Rate constant of the OH + ∆ 3 -carene reaction
In order to determine the rate constant of the reaction of ∆ 3 -carene with OH, measured time series were compared to model results from a box model, in which OH and O 3 concentrations were constrained to the measurements. A reaction rate constant was determined from all experiments. The determined value represents the mean value from all experiments. On average, the 385 temperature inside the SAPHIR chamber was 304 K during the experiments. OH concentrations usually ranged from 5 to 8 × 10 6 cm −3 . Ozonolysis only played a minor role in the experiments contributing to a maximum of 5 % to the ∆ 3 -carene consumption. The reaction rate constant for the ozonolysis reaction was taken from this work (Section 3.1.1).
The optimized rate constant of the OH reaction with ∆ 3 -carene is (8.0 ± 0.5) × 10 −11 cm 3 s −1 as shown in Fig. 7.  rate constant of (8.1 ± 0.1) × 10 −11 cm 3 s −1 using an absolute rate approach and Atkinson et al. (1986) reported a value of (8.7 ± 0.4) × 10 −11 cm 3 s −1 at 294 K using a relative rate determination approach. From a site specific structure-activity rela-395 tionship (SAR) Peeters et al. (2007) predict the reaction rate constant to be 8.5 × 10 −11 cm 3 s −1 at 298 K. In this reaction rate constant, the contribution of H-abstraction is not considered.   Hakola et al. (1994) a yield of (34 ± 0.8) %. In both studies, caronaldehyde was quantified using GC-FID. Hakola et al. (1994) additionally used GC-MS and 1 H-NMR to verify the structure and purity of the measured compound.

405
As shown in Fig. 5, caronaldehyde is mainly formed from the decomposition of alkoxy radicals (RO). These alkoxy radicals are mainly formed from the reaction of RO 2 with NO. A similar RO radical is also formed from the RO 2 + RO 2 reaction, and from the photolysis of hydroperoxides (ROOH) that result from the RO 2 + HO 2 reaction. Since the RO 2 + NO reaction mainly leads to the formation of RO (the branching ratio of an alternative pathway is discussed in Sect. 3.2.3), yields of caronaldehyde as found in this and previous studies can be expected. Other reaction products of the ∆ 3 -carene + OH reaction determined in previous studies include formaldehyde with a yield of 20 % (Orlando et al., 2000) and acetone with a yield of 15 % (Reissell et al., 1999;Orlando et al., 2000). Caronic acid, hydroxy-caronic acid isomers and hydroxy-caronaldehyde isomers have additionally been found in the aerosol phase of smog chamber experiments investigating the ∆ 3 -carene + OH reaction by Larsen et al. (2001).

Determination of alkyl nitrate yield for the reaction of
Organic nitrates are formed from the reaction of RO 2 radicals with NO as shown in Fig. 5 for the reaction of the RO 2 formed in the first oxidation step of ∆ 3 -carene. An alternative pathway for the NO + RO 2 reaction is the formation of an alkoxy radical and NO 2 that ultimately leads to the formation of caronaldehyde (Section 3.2.2). The nitrate yield ΦRONO 2 for the reaction of ∆ 3 -carene + OH is determined following the procedure described in Sect. 2.4 using RO 2,carene . Figure 8 shows the accumulation of reactive NOy species over the course of the experiment E2. In total, 8.1 ppbv of reactive nitrogen species 420 were formed over the course of the experiment. The contributions of NO, NO 2 and HONO are almost constant with 2.2 ppbv, while the contributions of RONO 2 and HNO 3 increase continuously over the course of the experiments due to their continuous production from the reaction of RO 2,carene with NO and OH with NO 2 , respectively. The formation of HNO 3 and RONO 2 before the injection of ∆ 3 -carene is not relevant for the analysis and therefore not shown in Fig. 8.

425
An organic nitrate yield of (25 ± 4) % was found from experiments E1 and E2. To our knowledge, only one other study investigated the organic nitrate yield of ∆ 3 -carene. Based on RONO 2 measurements in the aerosol phase using a TD-LIF instrument (thermal dissosciation laser induced fluorescence), Rollins et al. (2010) calculated an organic nitrate yield of 25 % for the photooxidation of ∆ 3 -carene in experiments with high NOx conditions (100 ppbv of ∆ 3 -carene and 500 ppbv of NO). This yield represents the fraction of SOA molecules that are hydoxy-nitrates and Rollins et al. (2010) suggest that the organic nitrate 430 fraction of SOA molecules produced in photooxidation are similar to the total yield of RONO 2 from RO 2 + NO. The SAR by Jenkin et al. (2019) predicts an organic nitrate yield of 19 %. This calculation is based on the number of C-atoms in the peroxy radical, and therefore possibly has a relatively high uncertainty. The value obtained in this study for experiments with NO x mixing ratios below 1 ppbv is in good agreement with both the experimental and the SAR derived values. Due to their structural similarities, it can be assumed that organic nitrate yields for ∆ 3 -carene could be comparable to reported determined 435 organic nitrate yields of α-pinene. Noziere et al. (1999) report an organic nitrate yield of (18 ± 9) % and Rindelaub et al.
(2015) (26 ± 7) % for the reaction of α-pinene with OH. The organic nitrate yield of 1 % by Aschmann et al. (2002b) was not measured directly, but approximated from API-MS measurements. This leads to a high uncertainty, and likely explains the difference to the values by Noziere et al. (1999); Rindelaub et al. (2015). The nitrate yield obtained in this study for ∆ 3 -carene is in reasonable agreement with the values reported for α-pinene, as can be expected due to their structural similarities.
440 Figure 8. Determination of the organic nitrate yield for the ∆ 3 -carene + OH oxidation experiment E2. The red line shows teh time integrated HONO emission calculated as described in the text. NOx and HONO concentrations were measured, while the time integrated NO2 loss by HNO3 formation and time integrated NO loss by RONO2 formation are calculated as described in the text. The yield of (25 ± 4) % for alkyl nitrates is optimized such that the total NOy produced over the course of both experiments E1 and E2 is accounted for.

Photooxidation of caronaldehyde
A simplified reaction scheme for caronaldehyde degradation chemistry is shown in Fig. 9. Caronaldehyde can be oxidized by the reaction with OH, forming RO 2 radicals through H-abstraction and fast subsequent addition of O 2 . The formed peroxy radicals can then undergo reactions with NO, HO 2 and RO 2 , resulting in similar product species such as explained before.

445
Photolysis of caronaldehyde is an additional loss path. Due to their structural similarities, it can be assumed that caronaldehyde photolyses in a similar way like pinonaldehyde. Photolysis leads to the C-C bond scisson next to the aldehydic functional unit of the molecule, leading to the formation of HCO and an alkyl radical. Both species subsequently react with O 2 , forming CO, HO 2 and a peroxy radical.  Figure 9. Simplified scheme of the first reaction steps of the OH photooxidation of caronaldehyde, adapted from the oxidation mechanism of pinonaldehyde. Yields shown in black are from SAR by Jenkin et al. (2018). Additional reactions like e.g. the formation of carbonic acids from RO2 with HO2 are not shown in the scheme.
The reaction of caronaldehyde with OH was investigated in experiment E6. Caronaldehyde was injected twice into the chamber to reach mixing ratios of 5 ppbv directly after the first and 6 ppbv directly after the the second injection. The OH concentration was 7 × 10 6 cm −3 for the period after the first injection. Prior the second injection, 50 ppmv of CO was injected into the chamber as an OH scavenger to study the photolysis of caronaldehyde separately. The temperature in the chamber ranged from 295 K to 305 K during the experiment.

Photolysis frequency of caronaldehyde
As CO was injected into the chamber as an OH scavenger and wall loss was found to be negligible in the timeframe of the experiment, the decay of caronaldehyde measured can only be due to photolysis and dilution. The absorption spectrum of caronaldehyde was measured by Hallquist et al. (1997) in the range from 275 to 340 nm at 300 K. This spectrum and an assumed quantum yield for dissociation of one was used to calculate the photolysis frequency for the conditions of the 460 experiment in the sunlit chamber using Equation 1 (Section 2.2) resulting in a mean loss of caronaldehyde due to photolysis of 1.3 × 10 −5 s −1 . The calculated photolysis frequency was included in a model to compare the measured to the modeled decay.
The modeled decay was found to be too slow and requires a photolysis frequency that is larger by a factor of 7 to match the experimental decay. The absorption cross section by Hallquist et al. (1997) used in this work is the only reported measurement.
It was measured in a 0.48 m 3 borosilica reactor at low pressure. During their experiments, dichlormethane and methanol 465 solvents used in the synthesis of caronaldehyde were present in the reactor. Even though the authors corrected for possible interferences caused by these two species regarding the caronaldehyde concentration measured by IR spectroscopy, potential errors in the measurent of caronaldehyde concentrations might explain the discrepancy. Although there is no mechanistic explanation, it cannot be fully excluded that the faster decay observed in the experiments in this work compared to that by Hallquist et al. (1997) is the result of an alternative OH independant loss process occuring in the illuminated chamber. The 470 absorption cross sections that have to be applied to explain the decay of caronaldehyde in photolysis experiments in SAPHIR suggest further investigation of this reaction and the absorption cross section of caronaldehyde.

Rate constant of the caronaldehyde + OH reaction
The measured decay of caronaldehyde was compared to the results from the box model constraining the photolysis frequency to the value with a correction by a factor of 7 calculated as explained above. The temperature inside the SAPHIR chamber 475 was 300 K, the OH concentration was 8 × 10 6 cm −3 . The optimum OH reaction rate constant is (3.6 ± 0.7) × 10 −11 cm 3 s −1 .
The reaction rate constant was also optimized with the model constrained to the photolysis frequency as calculated with the absorption spectrum measured by Hallquist and a quantum yield of 1. This yields an OH reaction rate constant of (5.5±0.7)× 10 −11 cm 3 s −1 . Both values agree reasonably well with the reaction rate constant of (4.8 ± 0.8) × 10 −11 cm 3 s −1 measured by Alvarado et al. (1998) within the error. Structure activity relationship by Jenkin et al. (2018) predicts a total reaction rate 480 constant of 2.9 × 10 −11 cm 3 s −1 which is consistent with the two measured values within the uncertainty of SAR. Hallquist et al. (1997) also determined the reaction rate constant of caronaldehyde with OH resulting in a value of (12.1 ± 3.6) × 10 −11 cm 3 s −1 . This value is significantly higher than both values reported here and by Alvarado et al. (1998). Both Alvarado et al. (1998) and Hallquist et al. (1997) determined the reaction rate constant using a relative rate technique and both studies were performed in smaller reaction volumes than the 270 m 3 SAPHIR chamber. The measurements by Hallquist et al. (1997) were 485 performed in a 0.153 m 3 borosilica glass reactor, while the studies by Alvarado et al. (1998) were performed in an 7.9 m 3 Teflon chamber. Wall losses of caronaldehyde in the range of (4 − 7) × 10 −5 s −1 were observed in the borosilica chamber in the dark and further increased when the chamber was irradiated. Even though the determined reaction rate constant is corrected for the measured wall loss, it causes further uncertainty. Additionally, the initial caronaldehyde mixing ratio in the experiments in this work and the study performed by Alvarado et al. (1998) were significantly lower than those used by Hallquist et al. 490 (1997) (20 ppbv (this study), 113 ppbv (Alvarado et al., 1998), 3252 ppbv (Hallquist et al., 1997), respectively). The reason for the high reaction rate constant reported by Hallquist et al. (1997) is not entirely clear, but it may arise from enhanced wall losses in the irradiated chamber unaccounted for in the experiments by Hallquist et al. (1997).  Field studies in forested environments, were ∆ 3 -carene was one of the main monoterpenes emitted found that both measured OH and HO 2 concentrations can not be reproduced by models (Kim et al., 2013;Hens et al., 2014). The analysis of radical formation and loss recations for those environments revealed that a photolytic HO 2 source missing in the model calculations is one possible explanation for the observed discrepancies. In the following, radical formation and loss rates of the sum of radicals 510 (ROx) and their differences are determined according to Equation (6) and (7). The results of this analysis for experiment E1 with NOx mixing ratios below 1 ppbv are shown in Fig. 11.
The turnover rates in this experiment reach maximum values between 2 and 3 ppbvh −1 . The main radical formation process is HONO photolysis, contributing more than 70 % to the average formation rate. Assuming that the photolysis frequency is 515 higher by a factor of 7 (see Section 3.3.1), the formation of one HO 2 and one RO 2 radical per photolyzed caronaldehyde molecule would have a higher influence on the radical budgets of the ∆ 3 -carene + OH reaction than previuosly assumed. This may therefore help to reduce the discrepancies between measured and modeled HO 2 concentrations in field studies. The photolysis of caronaldehyde contributes on average 0.3 ppbvh −1 . 60 % of the average loss rate is due to the reaction of ROx with NOx species. The remaining ROx losses can be explained by radical self-reactions, as can be expected for the experimental 520 conditions because the reaction of the peroxy radical with HO 2 (35 %) or RO 2 radicals becomes competitive.
For experiments with NOx mixing ratios below 1 ppbv in the experiments in this work, the ROx budgets are closed within the uncertainty. It can therefore be assumed that there are no primary radical production or loss processes that are unaccounted for in this analysis. The contribution of the photolysis of caronaldehyde to the radical formation is in the range of the error of the analysis, and the loss and formation of radicals would also be closed if this process was not considered. In the scope of this 525 work, it is therefore not possible to distinguish whether the caronaldehyde photolysis will contribute significantly to reduce the previouly observed discrepancies between measured and modeled HO 2 concentration in field studies. Possible reaction pathways leading to the formation and loss of radicals in the ∆ 3 -carene oxidation are shown in Fig. 5. The reaction of RO 2 with HO 2 proceeds with a reaction rate constant of 1.9 × 10 −11 cm 3 molecule −1 s −1 (Jenkin et al., 2019) mainly leading the formation of hydroperoxide species ROOH. The reaction of RO 2 with RO 2 results in the formation of either a diol or an 530 alkoxy radical RO, which again most likely decomposes forming caronaldehyde. The reaction rate constant of this reaction is calculated to be 1.2 × 10 −13 cm 3 molecule −1 s −1 (Jenkin et al., 2019). In the experiments presented here, this reaction only contributes < 1 % to the loss of total ROx radicals. Isomerization reactions like intramolecular H-shifts as investigated by Vereecken and Noziere (2020) can form a new pathway to product formation from RO 2 . For the RO 2 described here, an intramolecular 1,5-H-shift from the OH functional group to the peroxy-radical unit -OO would be the fastest of the possible 535 isomerization reactions with a reaction rate constant of 3.5 × 10 −5 s −1 expected from the SAR in (Vereecken and Noziere, 2020). Compared to the other described RO 2 loss rates, especially the loss in the reaction with NO (0.07 s −1 at 0.3 ppbv NO) and HO 2 (1.9 × 10 −3 s −1 at 1.0 × 10 8 cm −3 HO 2 ), this isomerization reaction is too slow to be signficant for atmospheric conditions like in the experiments here.

540
The photooxidation of ∆ 3 -carene was investigated for NO x mixing ratios below 1.5 ppbv in the atmospheric simulation chamber SAPHIR. Photooxidation experiments were performed under atmospheric conditions with ∆ 3 -carene mixing ratios in the range of 5 to 7 ppbv. In this study, the gas-phase organic nitrate yield of the ∆ 3 -carene + OH reaction was determined for the first time and found to be (25 ± 4) %. The comparison of the obtained organic nitrate yield to yields obtained in the aerosol phase (Rollins et al., 2010) and to the organic nitrate yield of the structurally similar monoterpene α-pinene shows 545 that the determined value is in accordance with the reported values. The reaction rate constant of the reaction of ∆ 3 -carene with OH was determined to be (8.0 ± 0.5) × 10 −11 cm 3 s −1 using an absolute rate technique approach. The obtained value was found to be in good agreement with reaction rate constants reported in the literature within the stated error. Additionally, the ozonolysis of ∆ 3 carene was studied. A reaction rate constant of (4.4 ± 0.2) × 10 −17 cm 3 s −1 was found, with an OH yield of 0.65 ± 0.10. The yield of the oxidation products caronaldehyde was determined for the ∆ 3 -carene + OH and ∆ 3 -carene + O 3 reactions and found to be (0.33 ± 0.03) and (0.055 ± 0.02), respectively, in good agreement with reported literature values.
The photolysis and OH-induced photooxidation of caronaldehyde were also studied. The photolysis frequency was calculated using the absorption spectrum measured by Hallquist et al. (1997), but it was found that to explain the observed caronaldehyde decay the absorption cross section would need to be higher by a factor of 7 assuming a maximum quantum yield of 1. The caronaldehyde + OH reaction rate constant was found to be (3.6 ± 0.7) × 10 −11 cm 3 s −1 , in relatively good agreement with 555 reported literature values. The experimental budget analysis of the loss and production processes of ROx radicals for the ∆ 3carene + OH reaction shows that primary loss and production reactions are balanced within the uncertainty of the experiment of ±0.5 ppbvh −1 . The formation of HO 2 and RO 2 radicals from the photolysis of caronaldehyde was considered as an additional radical source with the photolysis frequency determined in this work. The contribution of the photolysis reaction to the radical formation was about 10 %. The fact that radical formation and loss reactions are well balanced indicates that there are no 560 primary formation or loss processes unaccounted for in this analysis.