Identiﬁcation of highly oxygenated organic molecules and their role in aerosol formation in the reaction of limonene with nitrate radical

. Nighttime NO 3 -initiated oxidation of biogenic volatile organic compounds (BVOCs) such as monoterpenes is important for the atmospheric formation and growth of secondary organic aerosol (SOA), which has signiﬁcant impact on climate, air quality, and human health. In such SOA formation and growth, highly oxygenated organic molecules (HOM) may be crucial, but their formation pathways and role in aerosol formation have yet to be clariﬁed. Among monoterpenes, limonene is of particular interest for its high emission globally and high SOA yield. In this work, HOM formation in the reaction of limonene with nitrate radical (NO 3 ) was investigated in the SAPHIR chamber (Simulation of Atmospheric PHotochemistry In a large Reaction chamber). About 280 HOM products were identiﬁed, grouped into 19 monomer families, 11 dimer families, and 3 trimer families. Both closed-shell products and open-shell peroxy radicals (RO (cid:113) 2 ) were observed, and many of them have not been reported previously. Monomers and dimers accounted for 47 % and 47 % of HOM concentrations, respectively, with trimers making up the remaining 6 %. In the most abundant monomer families, C 10 H 15 − 17 NO 6 − 14 , carbonyl products outnumbered hydroxyl products, indicating the importance of RO (cid:113) 2 termination by unimolecular disso-ciation. Both RO (cid:113) 2 autoxidation and alkoxy–peroxy pathways were found to be important processes leading to HOM. Time-dependent concentration proﬁles of monomer products containing nitrogen showed mainly second-generation formation patterns. Dimers were likely formed via the accretion reaction of two monomer RO (cid:113) 2 , and HOM-trimers via the accretion reaction between monomer RO (cid:113) 2 and dimer RO (cid:113) 2 . Trimers are suggested to play an important role in new particle formation (NPF) observed in our experiment. A HOM yield of 1 . 5% + 1 . 7% − 0 . 7% was estimated considering only ﬁrst-generation products. SOA mass growth could be reasonably explained


Introduction
The nitrate radical (NO 3 ) is an important nighttime oxidant in tropospheric chemistry, and can reach mixing ratios of several hundred pptv during nighttime (Seinfeld and Pandis, 2006). It can react with volatile organic compounds (VOCs) and is especially reactive to alkenes, where the nitrate radical can undergo an addition reaction to the C=C double bond (Finlayson-Pitts and Pitts, 1997;Seinfeld and Pandis, 2006). Biogenic monoterpenes (C 10 H 16 ) are a large contribution to the alkenes in the atmosphere (Klinger et al., 2002;Guenther et al., 2012), and their major nighttime loss pathway is reaction with NO 3 (Beaver et al., 2012;Rollins et al., 2012;Ayres et al., 2015;Fry et al., 2013). The chemistry of monoterpenes with NO 3 has implications on the cycle of reactive nitrogen and thus on ozone formation (Brown and Stutz, 2012). Furthermore, since the NO 3 radical is formed through the reaction of NO 2 with O 3 , it is considered to be of anthropogenic origin, and reactions of NO 3 with biogenic VOC (BVOC) thus represent an important interaction between biogenic emissions and anthropogenic emissions.
The reaction of NO 3 with monoterpenes can form secondary organic aerosols (SOAs), which can have a large impact on global climate, air quality, and human health (Hallquist et al., 2009;Shrivastava et al., 2017). Laboratory studies showed that monoterpenes have high SOA yields in the reaction with NO 3 due to the low volatility of oxidation products (Ng et al., 2008;Rollins et al., 2009;Fry et al., 2013Fry et al., , 2014Ayres et al., 2015;Jokinen et al., 2015;Zhou et al., 2015;Boyd et al., 2015;Nah et al., 2016;Boyd et al., 2017;Slade et al., 2017;Claflin and Ziemann, 2018;Bates et al., 2022;Dam et al., 2022). Field studies also showed that nighttime NO 3 -initiated oxidation of monoterpenes contributes significantly to SOA in forested regions influenced by anthropogenic emissions (Pye et al., 2010;Rollins et al., 2012;Fry et al., 2013;Ayres et al., 2015;Zhou et al., 2015;Xu et al., 2015;Lee et al., 2016;Zhang et al., 2018;Chen et al., 2020) and potentially in urban areas due to the extensive usage of so-called volatile chemical products (VCPs) (Nazaroff and Weschler, 2004;McDonald et al., 2018). For example, the Southern Oxidant and Aerosol Study (SOAS) showed that the BVOC+NO 3 reactions were a substantial source of SOA (Ayres et al., 2015;Xu et al., 2015;Lee et al., 2016;Massoli et al., 2018). Therefore, accurate predictions and evaluations of SOA concentration and thus its climate and environmental effects require a comprehensive understanding of the reactions of monoterpenes with NO 3 .
Recently, a class of organic compounds named highly oxygenated molecules (HOM) have been shown to be critical substances in the SOA formation from BVOC oxidation, particularly monoterpenes, featuring high O/C ratio and low to extremely low volatility Tröstl et al., 2016;Kirkby et al., 2016;Bianchi et al., 2019). HOM here refers to compounds formed in the gas phase via autoxidation which contain at least six oxygen atoms (Bianchi et al., 2019). Most HOM are classified as ULVOC/ELVOC or LVOC (Bianchi et al., 2019) according to the classification of atmospheric organics based on their volatility (saturation concentration, C * ) by Donahue et al. (2012) (extremely low volatility organic compounds, ELVOCs; low volatility organic compounds, LVOCs; semi-volatile organic compounds, SVOCs; intermediate volatility organic compounds, IVOCs; volatile organic compounds, VOCs), and a recent update by Schervish and Donahue (2020) (ultra-low volatility organic compounds, ULVOCs). Thus, HOM can be a substantial contribution to growth of SOA particles through gas-particle partitioning.
A better description of the HOM formation chemistry in the oxidation of monoterpenes by NO 3 will improve our understanding of the role of HOM in SOA formation, and the relationship between oxidation products, SOA formation, and reaction systems. Field observation campaigns and laboratory experiments have proven the important contribution of HOM in monoterpene +NO 3 SOA (Lee et al., 2016;Faxon et al., 2018). In the SOAS campaign, HOM-ON (organic nitrates) were identified in both gas and particle phase using a NO − 3 -chemical ionization time-of-flight mass spectrometer (CI-APi-TOF) and a high-resolution time-of-flight chemical ionization mass spectrometer (HR-ToF-CIMS) coupled to a Filter Inlet for Gases and AEROsols (FIGAERO). Species with the sum formula C 10 H 15,17, were observed, which are formed through the oxidation of monoterpenes by NO 3 (Lee et al., 2016;Massoli et al., 2018). In a campaign in a boreal forest in Hyytiälä, measurement using a NO − 3 -CI-APi-TOF and positive matrix factor (PMF) analysis showed a nighttime factor of HOM-ON formed via NO 3 oxidation of monoterpenes . Besides the observations at forested regions, monoterpene-derived HOM via NO 3 oxidation also contribute to organic aerosols in urban regions. For example, Liu et al. (2021) and Nie et al. (2022) have found that HOM derived from monoterpene nighttime chemistry are important in megacities in China, especially during summertime. A number of laboratory studies have reported HOM formation by the oxidation of monoterpenes with NO 3 . Boyd et al. (2015) observed C 10 H 17 NO 4/5 and C 10 H 15 NO 5/6 in the gas phase in β-pinene +NO 3 experiments using a quadrupole chemical ionization mass spectrometer with I − as the reagent ion (I − -CIMS). They proposed possible formation schemes of these ONs. Nah et al. (2016) further detected 5 and 41 HOM-ON in the NO 3 oxidation of α-pinene and β-pinene, respectively, such as C 10 H 15/17/19 NO 4−9 in the gas-and particle-phase using I − -FIGAERO HR-ToF-CIMS. Claflin and Ziemann (2018) provided formation mechanisms for HOM-ON via gas-phase and particle-phase reactions in the β-pinene +NO 3 reaction system, where particle-phase products were analyzed using reversed-phase high-performance liquid chromatography equipped with a UV-vis photodiode array detector (HPLC-UV), electron-ionization thermal desorption particle beam mass spectrometer (EI-TDPBMS), chemical ionization Finnigan PolarisQ ion trap mass spectrometer (CI-ITMS), and electrospray-ionization mass spectrometer (ESI-MS). Recently, Shen et al. (2021) found a large number of HOM (> 150 species) in the β-pinene +NO 3 reaction using NO − 3 -CI-APi-TOF. HOM formed in the reaction of four monoterpenes (α-pinene, β-pinene, -3-carene, and α-thujene) with NO 3 were also detected using NO − 3 -CI-APi-TOF by Dam et al. (2022). Bell et al. (2021) found that dimer dinitrates (C 20 H 32 N 2 O 8−13 ) contribute a large portion to SOA from α-pinene +NO 3 , and also detected monomer ON such as C 10 H 15 NO 5−10 and C 10 H 14,16 N 2 O 7−11 ) using FIGAERO-CIMS and an extractive electrospray ionization time-of-flight mass spectrometer (EESI-ToF-MS). However, the detailed speciation depends on analytical method to some extent. Moreover, the HOM composition in the particlephase was found to depend on aging time and reaction conditions such as dark versus light .
Among the monoterpenes, understanding the reaction system of limonene with NO 3 is of specific importance. The emission of limonene makes the fourth largest contribution with an estimated global emission of 11.4 Tg annually, preceded only by α-pinene, trans-β-ocimene, and β-pinene (Guenther et al., 2012). Besides its biogenic origin, limonene is also a common additive in cleaning products (Nazaroff and Weschler, 2004) and can even be used as a tracer for fragrances in some places . Several studies have shown adverse health effects due to indoor pollution caused by the ozonolysis of limonene (Clausen et al., 2001;Fan et al., 2003;Carslaw et al., 2012;Pagonis et al., 2019). Moreover, limonene stands out with its high reactivity towards the NO 3 radical (with a lifetime of 3 min at 298 K at 20 pptv NO 3 ) (Ziemann and Atkinson, 2012), and NO 3 oxidation of limonene has high SOA yield (SOA mass yield 15 % to 231 %) (Hallquist et al., 1999;Spittler et al., 2006;Fry et al., , 2014Boyd et al., 2017;Berkemeier et al., 2020;Mutzel et al., 2021). A number of earlier studies have provided valuable insights into the reaction of limonene with NO 3 regarding its main products and their formation pathways, the SOA yield, and the SOA physicochemical properties. For example, Hallquist et al. (1999) measured the SOA mass yield and revealed the dominance of organic nitrates (ONs) and carbonyl compounds in the products.  determined the organic nitrate yield and proposed a reaction scheme leading to the formation of ON and carbonyls, and Fry et al. (2014) compared the SOA and ON yields from the NO 3 oxidation of α-pinene, β-pinene, and limonene, and demonstrated why limonene +NO 3 leads to more SOA and ON than α-pinene from a structural perspective. Boyd et al. (2017) found a higher N : C ratio for limonene +NO 3 SOA than for β-pinene +NO 3 SOA. Finally, Peng et al. (2018) studied the optical properties of the limonene +NO 3 SOA.
Regarding the HOM formation in the reaction of limonene with NO 3 , Faxon et al. (2018) reported a series of HOM in the particle phase, including C 7−10 monomers with 3-11 oxygen atoms and C 11−20 dimers with 5-19 oxygen atoms using I − -FIGAERO HR-ToF-CIMS. However, identification of gas-phase HOM products in the limonene +NO 3 reaction is still lacking and their formation mechanisms remain unclear. Theoretical investigations have revealed that NO 3 addition on the endocyclic C=C double bond is more favorable than the exocyclic one due to a lower energy barrier (Jiang et al., 2009), and this endocyclic double bond of limonene thus tends to be attacked by NO 3 and leads to products including hydroxy-substituted ON or diketone products. The remaining exocyclic double bond can also be attacked by NO 3 in secondary chemistry, leading to more functionalized products .
The formation of HOM via autoxidation involves a sequence of multiple intramolecular H-shift and O 2 addition reactions, and results in highly oxygenated peroxy radicals (HOM-RO q 2 ) . These HOM-RO q 2 can react similarly to traditional RO q 2 (Bianchi et al., 2019). The bimolecular reactions of HOM-RO q 2 with RO q 2 , HO q 2 , and NO lead to highly oxidized closed shell products including carbonyls, hydroperoxides, alcohols, or organic nitrates as termination groups (Reactions R1 to R3), or form accretion products (Reaction R4) Mentel et al., 2015). Unimolecular termination reactions of HOM-RO q 2 lead to carbonyls or epoxides (reactions R5 to R6) (Crounse et al., 2013). On the other hand, reactions of HOM-RO q 2 with NO, RO q 2 , NO 3 at nighttime can lead to alkoxy radicals as chain propagating steps (reactions R7 to R9): If the reactive HOM-RO q products undergo an H-migration reaction, they will again form HOM-RO 2 radicals ("alkoxy-peroxy" pathway) (Mentel et al., 2015), continuing the autoxidation chain. Finally, the HOM-RO q may also fragment leading to small RO 2 radicals, isomerize leading to carbonyls (Bianchi et al., 2019), or react with O 2 to form carbonyls (Ziemann and Atkinson, 2012). In this study, HOM formation in the NO 3 oxidation of limonene was investigated. We report the identification of gas-phase HOM products, including monomers, dimers, and trimers. The formation pathways of dominant products in each category are proposed based on their time profiles in response to multiple additions of limonene in the experiment and on the information in literature. Based on this analysis, we estimated HOM yields, and discuss the role of HOM in nucleation and growth of SOA particles.

Experiment setup
The limonene +NO 3 experiment was performed in the atmospheric simulation chamber SAPHIR (Simulation of Atmospheric PHotochemistry In a large Reaction chamber) at the Forschungszentrum Jülich, Germany. SAPHIR is a 270 m 3 double-wall cylindrical Teflon chamber with a surface-tovolume ratio of ∼ 1 m 2 m −3 . Details of SAPHIR have been described before (Rohrer et al., 2005;Zhao et al., 2015a, b;Zhao et al., 2018) and are only summarized here. Detailed experimental procedures can be found in Fig. 1a. Before each experiment, SAPHIR was flushed for about 4 h at a flow rate of 370 m 3 h −1 with high-purity synthetic air (purity > 99.9999 % O 2 and N 2 ) in order to clean the chamber. To simulate nighttime conditions for the NO 3 chemistry, the chamber roof remained closed throughout the experiment. The experiment was performed under dry conditions (RH < 2 %) at a temperature of 302 ± 3 K. No seed aerosols were used in the experiments. A fan was used for active mixing in the chamber, leading to a typical mixing time of ∼ 1 min (Fuchs et al., 2013).
NO 3 radicals were generated via the reaction of ozone with nitrogen dioxide: Therefore, O 3 and NO 2 were first added to the chamber to form N 2 O 5 and NO 3 with mixing ratios of ∼ 2 and ∼ 0.15 ppbv, respectively. About 20 min later, 5 ppbv of limonene was added to start the organic chemistry. Five more additions of limonene followed, with added concentrations of about 3, 3, 2, 2, and finally 8 ppbv, which divided the experiment into six periods (P1 to P6) (Fig. 1a). For period P3 and P5, NO 2 and O 3 were also added to compensate for the loss of NO 3 and N 2 O 5 (Fig. 1a). The concentrations of NO 2 and O 3 were maintained around 20 to 70 ppbv throughout the experiment, ensuring the major loss of limonene was by reaction with NO 3 rather than with O 3 (Figs. S1). In the first 10 min of reaction (named period P1a hereafter, Fig. 1a), NO 3 accounted for 86 % of the chemical loss of limonene.

Instrumentation
Gas-phase HOM were detected by a chemical ionization time-of-flight mass spectrometer (CI-APi-TOF, Aerodyne Research Inc., USA) with a resolution (m/z)/( m/z) of ∼ 3800 using 15 NO − 3 as the reagent ion, which is capable of detecting organic molecules with high oxygen content (Eisele and Tanner, 1993;Jokinen et al., 2012). The mass spectra were analyzed using the software Tofware (Tofwerk/Aerodyne) in Igor Pro (WaveMetrics, Inc.). Peak identification was conducted by a high-resolution analysis (examples shown in Fig. S2). We observed several peaks which were obviously products from the isoprene +NO 3 reaction, such as C 5 H 10 N 2 O q 8 · 15 NO − 3 at m/z 289. Such peaks were present before the limonene oxidation reaction started, suggesting that these compounds preexisted in the chamber. These isoprene oxidation products were likely formed in an isoprene +NO 3 experiment performed 2 d before  and released slowly from chamber walls due to their semi-volatile character. Their total concentration is less than 1 ppt. All the isoprene-HOM observed (C 5 H 9 NO 7,10 , C 5 H 8 N 2 O 8−10 , C 5 H 10 N 2 O 8 , C 5 H 9 N 3 O 9,10 ) are saturated and do not contain C=C double bond. The isoprene-HOM will not influence the reaction of limonene with NO 3 in this study. Therefore, they are not discussed as products from the limonene oxidation in our experiment. (However, we cannot exclude that they were partly generated from fragmentation in the limonene +NO 3 reaction.) A set of instruments were used to measure other gasphase species, including VOC, NO x , O 3 , NO 3 , and N 2 O 5 (Shen et al., 2021). Concentrations of NO 3 and N 2 O 5 were measured in situ using a home-built diode laser-based, cavity ring-down spectrometer similar to the instrument described in the work by Wagner et al. (2011). The concentrations of limonene were measured using a proton transfer reaction time-of-flight mass spectrometer (PTR-TOF-MS, Ionicon Analytik, Austria). The SOA number concentration, surface concentration, and size distribution were detected by a scanning mobility particle sizer (SMPS, TSI DMA3081/TSI CPC3786) and a condensation particle counter (CPC, TSI3785). Temperature and relative humidity were continuously monitored throughout the experiment.

Determination of HOM concentration and "primary"
HOM yield HOM concentrations were obtained from the normalized signals to the total signals of the mass spectra (nc, normalized counts) by applying a calibration coefficient (C) of 2.5 × 10 10 molecule cm −3 nc −1 . C was determined using H 2 SO 4 as the charging efficiency of HOM and H 2 SO 4 are consid- ered to be equal Pullinen et al., 2020;Shen et al., 2021). The details of determination of the calibration coefficient are shown in Sect. S1 in the Supplement. A massindependent transmission efficiency was used according to our previous study, which causes an additional uncertainty of 14 % (Pullinen et al., 2020). In this previous study, the transmission efficiency curve of nitrate CI-APi-TOF was determined and found to monotonously decrease with increas-ing mass of ions but only slightly depend on the mass range (14 % change). As we used the same setting as our previous study, we have included the slight dependence of transmission on m/z in the uncertainties. The concentrations of HOM were corrected for chamber wall losses, which were determined for a number of HOM similar to our previous study (Zhao et al., 2018), with details described in the Supplement. When the chamber is actively mixed, the wall loss was deter-mined to be (2.2 ± 0.2) × 10 −3 s −1 . As the HOM yield was determined during the first 3 min of the experiment, we considered the wall loss rate to be constant (2.2 × 10 −3 s −1 ) during this period. Sensitivity analysis showed that the HOM yield in this study is not very sensitive to the wall loss rate and is changing by only +0.88 % and −0.44 % if the wall loss rate is varied by +100 % or −50 %.
The HOM yield was calculated as where [HOM] is the concentration of HOM, I (HOM) is the total signal intensity of HOM, C is the calibration factor, and [VOC] r and [N 2 O 5 ] r stand for the concentrations of limonene and N 2 O 5 reacted, respectively. We used the reacted concentration of N 2 O 5 rather than the measured reacted limonene concentration as a large fraction of limonene was already reacting away during the VOC injection before it was homogeneously mixed in the chamber. During this part of the experiment, the high limonene concentration resulted in a rapid loss of NO 3 , such that every NO 3 formed from the decomposition of N 2 O 5 reacted with limonene: The initial NO 3 concentration before the limonene injection was small compared to the time-integrated loss of N 2 O 5 , and other NO 3 loss processes were negligible right after the limonene injection, so that the observed decrease in the N 2 O 5 concentration equals indeed the consumption of limonene. The wall loss rate constant of N 2 O 5 in the SAPHIR chamber is 7.2 × 10 −5 s −1 . As the HOM yield determination is based on the first 3 min, the wall loss of N 2 O 5 can be ignored compared to the loss via the reaction of NO 3 with limonene. The uncertainty of the HOM yield was estimated to be −55 %/ + 117 % based on the combined uncertainties of the HOM-ON peak intensities (∼ 10 %), the limonene concentration (∼ 15 %), the transmission efficiency (−0 %/+14 %), and the calibration factor (−52 %/+101 %) using error propagation . The first 3 min after the injection of limonene were used to calculate the HOM yield, when most of the first-generation oxidation products were produced and negligible particles were formed. The HOM yield thus reflects the "primary" HOM yield.

Determination of HOM condensation on SOA
The SOA mass from the condensation of HOM was calculated to evaluate the role of HOM for the SOA mass growth. Detailed estimation methods are described in the Supplement, including the determination of particle wall loss and dilution loss rate (Sect. S2). In brief, the growth rate of SOA through HOM vapor condensation is based on the collision rate of vapor molecules with aerosols in the kinetic regime. The Fuchs-Sutugin approach is applied to describe the correction for transition from the kinetic to the diffusion regime (Fuchs and Sutugin, 1971;Ehn et al., 2014). Based on the volatility of HOM, we considered two scenarios for HOM condensation. In scenario 1, all HOM were assumed to irreversibly condense on the surface of particles leading to particle mass growth. In scenario 2, only the irreversible uptake of LVOC and ULVOC/ELVOC compounds were considered to contribute to the growth of SOA particles in order to examine the role of LVOC and ELVOC while IVOC and SVOC were not included, although they may also contribute to SOA.
where n C , n O , n N , and n H are the number of carbon, oxygen, nitrogen, and hydrogen atoms of the compound, respectively.

Simulations of the RO q 2 loss pathway based on the Master Chemical Mechanism (MCM)
The RO q 2 loss pathways were estimated based on MCM simulations (http://mcm.york.ac.uk/, last access: 14 November 2021). The gas-phase reactions of limonene +NO 3 under dark condition were simulated using iChamber, an opensource program (https://sites.google.com/view/wangsiyuan/ models?authuser=0, last access: 14 November 2021) (Wang and Pratt, 2017). The default chemistry of limonene +NO 3 in the MCM was applied in this study (Saunders et al., 2003). Photolysis reactions were excluded by setting the zenith angle to 90 • . Concentrations of O 3 , NO 3 , NO 2 and N 2 O 5 , and temperature and relative humidity were constrained to the experimental data with a time resolution of 1 min. The chamber dilution rate of 1.5×10 −5 s −1 was applied to all species. The P1 period was simulated using the above conditions, and the initial concentrations of limonene were added in the model according to the experimental procedures. The sum of all 140 RO q 2 in the limonene subset of MCM v3.3.1 were used in the usual way to estimate the loss rates of RO q 2 bimolecular reactions. The reaction rate constants are provided in Table S3 in the Supplement, and calculated loss rates are shown in Fig. S3. We note that the MCM reaction schemes do not include the accretion reactions between HOM-RO q 2 . Berndt et al. (2018a) determined the rate constant of accretion reaction of C 10 H 15 O q 4 formed via α-pinene ozonolysis to be ∼ 1 × 10 −11 cm 3 molecule −1 s −1 , which is of the same order as the upper limit for RO q 2 + RO q 2 reactions used in the MCM schemes for functionalized peroxy radicals such as acyl peroxy radicals (Jenkin et al., 1997;Saunders et al., 2003). However, currently we do not see a reliable updated set of rate coefficients that are applicable to the reaction system in this study. If the rate constants of some RO q 2 +RO q 2 reactions were higher than those used in MCM, the concentrations of RO q 2 would be lower and relative importance of RO q 2 +RO q 2 in RO q 2 fate would increase. Several simulation results are shown in Fig. S4, including NO 3 , N 2 O 5 , limonene, RO q 2 , reaction rate of limonene with NO 3 (k × limonene × NO 3 ), and examples of first-and second-generation RO q 2 . In the early stage of each period, RO q 2 mainly reacted with RO q 2 and NO 3 , although in the later stage the reaction with NO 2 also contributed to a significant fraction of RO q 2 loss (Fig. S3, showing period P1 as an example). During the period P1a which our peak assignment was based on, the RO q 2 loss was dominated by RO q 2 + RO q 2 and RO q 2 + NO 3 .

Experiment overview and observed HOM
After each limonene addition, the concentration of limonene rose first and then rapidly declined, while the concentrations of NO 3 and N 2 O 5 rapidly decreased due to the fast reaction between limonene and NO 3 , and gradually increased when limonene had been consumed (Fig. 1a). About 10 min after the first limonene addition, new particles had already formed and quickly grew in size (Fig. 1b). Therefore, we used the first 10 min reaction time (period P1a) to identify gas-phase HOM products, and the whole experiment to examine the contribution of HOM to SOA. During period P1, HOM were quickly formed. We identified about 280 HOM compounds, including monomers (C 7 -C 10 , ∼ 280-460 Th), dimers (C 17 -C 20 , ∼ 490-700 Th), and trimers (C 26 -C 30 , ∼ 720-960 Th) (Fig. 2a). Their detailed formulas can be found in Table S1. HOM on the horizontal lines of the Kendrick mass defect plot (O-based) (Figs. 3, S5, and S6) share the same number of C, N, and H atoms, with the number of oxygen atoms increasing from left to right. Such HOM compounds are defined as a family. We notice that most monomer peroxy radical families are each related to two monomer closed-shell product families, with one H atom more or one H atom less, which are the expected termination products of RO is not classified as series because the supposedly relevant families are not clearly identified. Compounds containing at least one nitrogen atom accounted for more than 90 % of the identified HOM products. We assume that compounds containing nitrogen atoms are organic nitrates, because other N-containing species such as amines or nitro compounds are very unlikely to be formed from the reaction of limonene with NO 3 . Organic nitrates formed in this study could be alkylnitrates, or (acyl)peroxynitrates formed via the reaction of RO q 2 with NO 2 . During period P1a, in the absence of particles, both HOM monomers and oligomers were observed, including monomers (47 %), dimers (47 %), and trimers (6 %) (Fig. 2a). Concentrations of gas-phase dimers and trimers decreased evidently after particle formation (Figs. 2b, 5, 6), indicating a fast gas-particle condensation and strong tendency of oligomers to condense on particles.
Based on their typical time series (Fig. 1c), products can be classified as first-generation or second-generation products. Generally, the concentrations of first-generation products, which result from the direct reaction of limonene with NO 3 , are expected to quickly increase after the limonene addition, followed by a steady decline due to wall loss or chemical reactions. Concentrations of typical secondgeneration products, which result from further reactions of first-generation products, are expected to show a gradually increasing concentration pattern after a limonene addition and reach their maximum concentration later than firstgeneration products. These general expectations are modified in our case, since the particle concentration increased in our experiment (Fig. 1b) and the condensational sink of HOM products became stronger over time. Thus, an increase in concentration suggests that the increasing condensational sink was exceeded by increasing production with time, i.e., from second-generation pathways.
To sum up, gas-phase HOM formed in the limonene +NO 3 system were dominated by HOM monomers and dimers. Time series patterns of the products indicate multiple generations of reaction pathways.

Overview of HOM monomers
A number of HOM monomer families were detected with an increasing oxygenation pattern at 16 Th intervals (Fig. 3). Such a pattern is attributed to autoxidation of RO q 2 (with 32 Th interval for each O 2 addition) plus the alkoxy-peroxy pathway (shifted by 16 Th compared with exclusive autoxidation) as discussed below. During period P1a, the most abundant HOM monomers are C 10 compounds (64 %), such as peroxy radicals C 10 H 16 NO q x and closed-shell products C 10 H 15 NO x and C 10 H 17 NO x , which are carbonyl compounds and hydroxyl or hydroperoxy compounds from the termination reactions of C 10 H 16 NO q x , respectively. Reaction (R14): According to the nitrogen atoms contained, C 10 -HOM monomers can be classified into 1N-, 2N-, 3N-monomers, and monomers without nitrogen atoms. While 1N-C 10 HOM monomers were likely formed by direct NO 3 addition to limonene, C 10 HOM monomers containing multiple N atoms were likely formed via multiple reaction steps. Besides C 10 HOM monomers, C 6−9 HOM monomers were also observed. These C 6−10 families are discussed below in the order of their contributions to HOM monomers.

1N-C 10 monomers
Among C 10 HOM monomers, the 1N-C 10 families were most abundant and included stable closed-shell products C 10 H 15 NO x (x = 7-13) and C 10 H 17 NO x (x = 9-14) and peroxy radicals C 10 H 16 NO q x (x = 6-14). The concentration of C 10 H 16 NO q 11 increased in the later phase of each limonene addition period (Fig. 1c), showing mostly a time profile of a second-generation product, similar as most of the other radicals in the C 10 H 16 NO q x family (Fig. S7). However, the time series of C 10 H 15 NO x compounds showed an overlaying pattern of first-and second-generation products dominated by a second-generation time profile with the exception of C 10 H 15 NO 9 (Fig. 1c). Due to sensitivity restrictions of CIMS, the primary peroxy radical C 10 H 16 NO q 5 was not detected, which was supposed to show first-generation pattern. The absence of first-generation characteristics of the time profile of most HOM peroxy radicals C 10 H 16 NO q x (x ≥ 6) may be attributed to two possible reasons. They either did not undergo efficient autoxidation, or they underwent immediate conversion including autoxidation and/or bimolecular reactions with other RO q 2 or NO 3 forming closed-shell products such as dimers or continuing the radical chain forming RO q . The instantaneous increase of 2N-dimers and trimers after the first limonene addition shown below suggests that C 10 H 16 NO q x (x ≥ 6) were indeed formed efficiently via autoxidation. Therefore, the latter reason is more likely. At this time, we do not have a reasonable explanation for the trend of C 10 H 15 NO 9 , though we should consider that there are many isomers at play, which may have very different chemical pathways (un)available.
Since the C 10 H 15 NO x family showed an overlaying pattern of the first-generation and second-generation products, they likely contained multiple isobaric substances produced through different pathways. Based on the literature, possible formation pathways of these products were tentatively proposed (Seinfeld and Pandis, 2006;Vereecken and Peeters, 2010;Mentel et al., 2015;Vereecken and Nozière, 2020). As an example of the pathways to form first-generation products, C 10 H 16 NO q 2x−1 (with an odd number of oxygen atom) and their corresponding termination products can be formed via autoxidation of the first peroxy radical C 10 H 16 NO q 5 (R1OO), showing C 10 H 16 NO q 9 (R3OO) as an example (scheme 1a, first-generation products). C 10 H 16 NO q 2x (with an even number of oxygen atom) can be formed via alkoxy-peroxy channels. For example, the ring-opening of the alkoxy radical C 10 H 16 NO q 4 (R1O), which was formed via the reaction of C 10 H 16 NO q 5 (R1OO) with another RO q 2 or NO 3 radical (scheme 1a, first-generation products). Ring-opening of R1O leads to C 10 H 16 NO q 6 (R4OO), which can undergo autoxidation forming C 10 H 16 NO q 2x . In addition, the alkoxy radical C 10 H 16 NO q 4 (R1O) is susceptible to ring-opening reactions (Novelli et al., 2021), which can lead to a first-generation stable product 3-isopropenyl-6-oxoheptanal (endolim, TP1) after C-C bond cleavage followed by the elimination of a NO 2 fragment (scheme 1b, second-generation products). Endolim (TP1) has been detected as a major product in previ-ous limonene +NO 3 studies (Hallquist et al., 1999;Spittler et al., 2006).
As an example of second-generation chemistry, the remaining double bond of endolim could react with NO 3 to form RO q 2 , followed by the autoxidation to form secondgeneration C 10 H 16 NO q x (with odd number of oxygen atoms). Similar to first-generation pathways, second-generation C 10 H 16 NO q x with even number of oxygen atoms can be formed via alkoxy-peroxy channel. From the time profile of C 10 H 15 NO x , the second-generation pathway (scheme 1b) was expected to play a more important role, in agreement with the theoretical result by Kurtén et al. (2017), in which the two bond-cleavage pathways of limonene-derived RO q radical were considered. It is worth mentioning that the reaction products of limonene with O 3 may also react with NO 3 , forming C 10 H 16 NO q x (scheme S1). However, as shown above, this was a minor pathway in our experiment (Sect. 2.1). We would like to note that to simplify the scheme, only the reaction of NO 3 with the endocyclic double bond is presented, since this reaction is faster than that with the exocyclic double bond (Jiang et al., 2009;. C 10 H 16 NO q x with both even and odd number of oxygen atoms and their termination products had comparable abundance, which suggests that the alkoxy-peroxy pathway was important for RO q 2 formation in this reaction. This finding is analogous to the findings in the reaction of a number of alkenes with O 3 and in the reaction of isoprene and β-pinene with NO 3 (Mentel et al., 2015;Zhao et al., 2021;Shen et al., 2021).
Among 1N-C 10 monomers, concentrations of carbonyl compounds were much higher than the sum of hydroxyand hydroperoxy-substituted compounds (Table 1). According to Hyttinen et al. (2015), for nitrate CI-APi-TOF, HOM containing two hydrogen bond donors (such as -OOH and -OH group) have strong binding energy with NO − 3 . Additional hydrogen bond donors only enhance the binding energy marginally. If we compare HOM carbonyl product (such as C 10 H 15 NO 10 ) with the corresponding hydroxy product (C 10 H 17 NO 10 ), they only differ in one functional group. As both are highly functionalized, it is likely that HOM carbonyl have a quite similar sensitivity with HOM alcohol. If the sensitivity of carbonyl HOM were lower, this would result in even more dominance of carbonyl HOM over hydroxyl HOM. Thus, we conclude that carbonylnitrates are more abundant than hydroxynitrates or hydroperoxynitrates. This finding is likely attributed to unimolecular termination reactions of RO q 2 , although reaction paths via RO q also cannot be excluded. Smaller unbranched RO q tend to react with O 2 forming carbonyl compounds, while for larger or branched RO q , isomerization can also form carbonyl compounds and is a more energetically favorable and thus faster pathway compared with the reaction with O 2 (Ziemann and Atkinson, 2012). The importance of unimolecular termination reactions of HOM-RO q 2 and the resulting high ratio of carbonyl compounds to hydroxyl/hydroperoxyl com-pounds has also been found in the reaction system of βpinene +NO 3 (Shen et al., 2021;Dam et al., 2022). This high ratio is also consistent with findings in the ozonolysis of alkenes (Mentel et al., 2015), where unimolecular termination reactions were also proposed to be the likely explanation (Crounse et al., 2013;Rissanen et al., 2014). As discussed in our previous study by Shen et al. (2021), this higher abundance of carbonylnitrates is not likely to be explained by the reaction of alkoxy RO q + O 2 forming carbonyls and HO q 2 , decomposition of β-nitrooxyperoxynitrate, or self-reactions of RO q 2 via the Bennett and Summers mechanism forming carbonyls and H 2 O 2 . Reactions between RO q 2 in general should produce overall equal amounts of carbonyl and hydroxyl compounds. The decomposition of βnitrooxyperoxynitrate is slow in the gas-phase. The reaction of alkoxy RO q with O 2 for large RO q is generally slower than isomerization and decomposition Peeters, 2009, 2010). Thus, the higher abundance of carbonylnitrates compared to hydroxynitrates may be attributed to unimolecular termination of HOM-RO q 2 . In addition, isomerization of RO q forming carbonyl compounds may also contribute to this finding. Our result thus further emphasizes that unimolecular termination reactions of RO 2 radicals are important pathways in the formation of HOM monomers derived from the reactions of monoterpenes with NO 3 (Shen et al., 2021). Scheme 1c shows this unimolecular termination process using a C 10 H 16 NO q 9 radical as an example. C 10 H 16 NO q 9 undergoes a 1,4-H-shift, and O 2 addition to form a C 10 H 16 NO q 11 radical. The C 10 H 16 NO q 11 radical further undergoes an Hshift of the α-OOH H-atom, which produces a carbonyl closed-shell product and an OH q radical.
For 1N-C 10 HOM monomers, the products detected in this study generally agree with previous laboratory and field studies on the reaction of limonene and other monoterpenes. Faxon et al. (2018) also observed C 10 H 15 NO x as the most prevalent products in the particle phase from limonene +NO 3 . In the SOAS campaign, both C 10 H 15 NO x and C 10 H 17 NO x products were detected and were believed to be products of nighttime chemistry (Lee et al., 2016). The high abundance of 1N-C 10 HOM monomers is consistent with the finding that C 10 H 15 NO x and C 10 H 17 NO x dominate the chemical composition of SOA formed via NO 3 oxidation of α-pinene and β-pinene, as shown in previous chamber studies (Takeuchi and Ng, 2019).
In summary, 1N-C 10 HOM monomers are mainly formed via second-generation pathways, and unimolecular termination of RO q 2 likely plays an important role leading to higher abundance of carbonyl HOM-ON (C 10 H 15 NO x ) than hydroxy/hydroperoxy HOM-ON (C 10 H 17 NO x ).

2N and 3N-C 10 monomers
C 10 monomers with 2 and 3 nitrogen atoms accounted for 27 % and 1 % of HOM monomers, respectively. They were likely formed via the reaction of a second attack of NO 3 to the first-generation products as the 1N-C 10 closed-shell products formed via the reactions shown in scheme 1a should contain a remaining limonene C=C double bond. Typical 2N-and 3N-HOM showed a secondgeneration time profile (Fig. 4). For clarity, only periods P1 to P3 are shown. This time profile is consistent with the pathways with multiple NO 3 attacks. Scheme 2 shows possible formation pathways of 2N-and 3N-C 10 monomers. 2N-C 10 HOM were likely to be formed from NO 3 oxidation of 1N-C 10 monomers (C 10 H 15 NO x and C 10 H 17 NO x ), resulting in C 10 H 15 N 2 O q x and C 10 H 17 N 2 O q x (scheme 2a, b). While C 10 H 15 N 2 O q x (x = 9-12) were observed, C 10 H 17 N 2 O q x could not be uniquely identified because the peaks of the C 10 H 17 N 2 O q x and C 10 H 15 NO x families are too close in the mass spectra to be separated based on the resolution of our mass spectrometer. 3N-C 10 monomers, C 10 H 17 N 3 O x , were expected to be formed from limonene via two steps of NO 3 oxidation to the double bonds and an addition of NO 2 to an RO 2 radical, leading to a peroxynitrate or peroxyacylnitrate. NO 2 addition reactions may also contribute to the formation of 2N-C 10 monomers. The addition of NO 2 to RO 2 radicals could occur either before (scheme 2d) or after (scheme 2c) the second NO 3 attack.

Formation pathways of C 10 monomers without
N-atoms and monomers with less than 10 C-atoms Besides C 10 products containing nitrogen atoms, HOM monomers without nitrogen atoms were also identified. Among these products, C 10 H 14 O x (x = 7-12) were the most prevalent family, which were also detected in limonene ozonolysis (Jokinen et al., 2015). The C 10 H 14 O x family showed a time series typical of first-generation products (Fig. S8). C 10 H 14 O x and C 10 H 16 O x could be formed from limonene +NO 3 with C 10 H 16 NO q x terminating their autoxidation by migration of the α-NO 3 H-atom, eliminating an NO 2 fragment (scheme S2) (Novelli et al., 2021). Alternatively, these products could be formed via the reaction of O 3 with limonene (scheme S2). Either way, C 10 H 14 O x and C 10 H 16 O x were formed via first-generation pathways.
We also observed monomers with carbon atom number less than 10. During the P1a period, C 9 monomer families were the most abundant contributors to C < 10 HOM monomers, followed by C 8 families. The majority of C 9 monomers were C 9 H 15 NO x (x = 7-13) (time series shown in Fig. S9) and C 9 H 13 NO x (x = 8-14). The loss of one carbon atom may follow the mechanism shown in scheme S3 Bianchi et al., 2019). The major product family in C 8 monomers is C 8 H 11 NO x (x = 6, 7, 9-13). While during period P1a C 8 H 11 NO x compounds could be hardly observed, their concentrations increased considerably in the later periods (Fig. S10). The gas-phase concentration of C 8 H 11 NO 7 was even the highest among all compounds in later periods (highest intensity signal in Fig. 2b). This is partly attributed to the relatively high volatility of C 8 compounds compared with C 10 HOM species and accretion products, which tend to condense on particles. The major family in C 7 monomers, C 7 H 9 NO x (x = 6-13), showed a time series pattern similar to C 8 H 11 NO x compounds (Fig. S11). Such a time profile indicates that C 7 and C 8 products were likely a result of multi-generation gas-phase reactions.

Dimers and their formation
Among dimers, C 20 products were the most abundant, followed by C 19 products. Among C 20 and C 19 dimers, the most prevalent families included C 20 H 32 N 2 O x (x = 9-20), C 20 H 33 N 3 O x (x = 12-20), C 20 H 31 NO x (x = 10-15), C 20 H 31 N 3 O x (x = 14-20), C 20 H 34 N 4 O x (x = 15-20), and C 19 H 30 N 2 O x (x = 10-18) (Fig. S5). The O/C ratio of dimers did not exceed one, while that of monomers was as high as two. This could be due to oxygen atom loss and participation of less oxygenated RO q 2 in the dimer formation as discussed below. Time series of dimers also showed different behavior compared to monomers. For example, compounds of the C 20 H 32 N 2 O x family only reached a considerable peak intensity in period P1 and decreased rapidly thereafter, while the signal intensity in periods P2 to P6 were low (Fig. 5). Generally, other dimers showed similar patterns (Figs. S12-S14), though the difference of their concentration between P2-P6 and P1 were not as large as for the C 20 H 32 N 2 O x family. The time when signals of several dimers (e.g., C 20 H 32 N 2 O x , C 20 H 33 N 3 O x , C 20 H 34 N 4 O x ) dropped substantially matched the time of new particle formation (NPF) and the onset of particle growth, indicating that some dimers were likely involved in the early growth of particles. Such a behavior is expected since dimers have a much lower volatility than monomers. This observation is consistent with the limonene +NO 3 laboratory study by Faxon et al. (2018) that found a significant fraction of HOM dimer derived in the particle phase.
In general, C 20 H 32 N 2 O x showed an overlaying time profile of first-and second-generation products (Fig. 5). C 20 H 32 N 2 O x were likely formed via the accretion reaction between two monomer RO q 2 (C 10 H 16 NO q x ): Since C 10 H 16 NO q x can be first-or second-generation products, the resulting dimers C 20 H 32 N 2 O x can also be firstor second-generation products. The time series shows that C 20 H 32 N 2 O x with lower O number presented more of a firstgeneration product time profile (Fig. 5), while the relative contribution of second-generation formation was observed to increase with oxygen number.
We compared the observed dimer formula with those expected based on accretion reactions of HOM-RO q 2 .
x in the C 20 H 32 N 2 O x observed was ≥ 9; however, according to the accretion mechanism and the observed C 10 H 16 NO q x (x ≥ 6), x in C 20 H 32 N 2 O x should be ≥ 10 (6+6−2 = 10). Moreover, as the most abundant RO q 2 within the C 10 H 16 NO q x family was C 10 H 16 NO q 10 (Table 1), the most abundant C 20 H 32 N 2 O x would have an oxygen number of 18 if they were exclusively formed by the accretion reaction of HOM RO q 2 . This contradicted the fact that the most abundant molecule among the C 20 H 32 N 2 O x family was C 20 H 32 N 2 O 13 . The findings above could only be explained by the participation of less oxygenated RO q 2 such as C 10 H 16 NO q 5,6 in the accretion reaction (Berndt et al., 2018a, b;McFiggans et al., 2019). C 10 H 16 NO q 5 was not detected by our CI-APi-TOF, which is attributed to the lower detection sensitivity of molecules with O number ≤ 5 in the NO − 3 -CIMS . Still, C 10 H 16 NO q 5 is the first RO 2 radical formed in the limonene +NO 3 reaction (scheme 1a) so a high mass flux has to pass through this RO q 2 . If we assume that the abundance of C 10 H 16 NO q 5 was high, and considering that the concentration of C 10 H 16 NO q 10 was the highest in the C 10 H 16 NO q x family, their accretion reaction (R16) could form C 20 H 32 N 2 O 13 and support that C 20 H 32 N 2 O 13 was the most abundant C 20 dimer product: For example, the C 20 H 31 NO x family were mainly firstgeneration products (Fig. S12), which may be formed via the following reaction: C 10 H 15 O q x were first-generation radicals (Sect. 3.2.4), while C 10 H 16 NO q x were mainly second-generation radicals. C 10 H 16 NO q x could also be formed via first-generation pathway as discussed above (scheme 1a), but that was not borne out by the time profile, suggesting a fast termination of first-generation C 10 H 16 NO q x radicals. Reaction (R17) could be one of the termination pathways of first-generation C 10 H 16 NO q x based on the first-generation time profile of C 20 H 31 NO x . In the study by Faxon et al. (2018), the formation of 1N-C 20 dimers was explained by a mechanism involving two 1N-RO 2 radicals which produced HNO 3 as a byproduct. However, C 10 RO 2 radicals without nitrogen atoms were identified in our study, which provided a direct formation pathway of 1N-C 20 dimers through reaction (R17).
On the other hand, C 20 H 33 N 3 O x and C 20 H 34 N 4 O x were mainly second-generation products (Figs. S13, S14). C 20 H 33 N 3 O x and C 20 H 34 N 4 O x were likely to be formed via NO 3 oxidation of dimers containing less nitrogen atoms, and were thus second-generation products. The related radicals were also detected, such as C 20 H 32 N 3 O q x (x = 16-19) and C 20 H 31 N 2 O q x (x = 13-16). Possible formation pathways of dominant oligomer families are displayed in Table 2. We cannot exclude that the formation pathway of C 20 H 33 NO x , C 20 H 34 N 4 O x , and C 19 H 31 NO x may also involve limonene oxidation by OH q (Table 2), which can be formed in the ozonolysis of limonene as a minor pathway. In addition, the high abundance of C 20 H 31 NO x (x = 10-15) among the dimers may be partly attributed to a contribution of the reaction of limonene with O 3 . The initial drop of the products (dimers and monomers) in Figs. 1, S8, and S12 during P1 (the characteristic time of the fastest decay was 15, 10, and 13 min, respectively) is attributed to the balance of their sources via the reaction of limonene with NO 3 , their wall loss, and their potential loss by the reaction with NO 3 . The characteristic time of the fastest decay of the HOM over the second limonene addition in Figs. 1, 4, 5, S12, and S13 are 4-8 min. These decays can be explained by the wall loss rate (characteristic time ∼ 8 min) and condensation sink of vapor loss to particles according to the study of Kulmala et al. (2012) (characteristic time ∼ 13 min). The characteristic times of the fastest decay of the HOM at the end of P2 in Figs. S12 and S13 are 1.4-3.4 min, which can also be well explained by the updated wall loss rate and condensation sink of vapor loss to particles at the end of P2 (characteristic time ∼ 1.4 min). In addition, for some HOM (e.g., C 10 H 15 NO 10 , Fig. 1; C 10 H 14 N 2 O 10 , Fig. 4; C 20 H 33 N 3 O 17 , Fig. S13; C 20 H 34 N 4 O 17 , Fig. S14), the times of limonene additions (except for the first time) matched the time when HOM signals dropped rapidly. This phenomenon implies a sudden decrease of the source of these HOM at limonene additions as sinks including the losses to walls and particles were largely invariant in such a short time. The decrease of the source may be attributed to the rapid depletion of NO 3 at limonene injections (Fig. 1). As many of these HOM are second-generation products, i.e., formed via the reactions of first-generation products with NO 3 , the depletion of NO 3 could lead to sudden decreases of the source of the second-generation HOM, which accounted for most HOM in the study.
In summary, HOM dimers are likely to be formed via accretion reactions of monomer RO q 2 , and some dimers can undergo secondary oxidation by NO 3 . Some dimers were likely involved in the early growth of SOA particles.

Trimers and their formation
Trimers (C 26−30 ) were dominated by C 30 compounds (Fig. S6, Table S1). To the best of our knowledge, this is the first study that identified gas-phase trimers in the limonene +NO 3 reaction. The O/C ratio of trimers was lower than that of monomers and dimers, suggesting possible multiple accretion reactions in their formation pathways, which lose 2 oxygen atoms in each reaction. As each accretion reaction terminates the peroxy radical chain, the observation of trimers also implies that some dimers could further react with NO 3 , creating dimer RO q 2 . The most prevalent product families were C 30 H 48 N 4 O x (x = 16-24) and C 30 H 47 N 3 O x (x = 18, 19, 21, 23, 24), which were likely formed via the most abundant monomer RO 2 radicals -C 10 H 16 NO q x and the most abundant dimer RO 2 radicals -C 20 H 32 N 3 O q x and C 20 H 31 N 2 O q x . Trimers from other monoterpenes +NO 3 have been observed in previous laboratory studies. For example,C 30 H 48 N 4 O 16 and C 30 H 47 N 3 O 16 were observed in the mass spectra of α-pinene +NO 3 SOA by C. Wu et al. (2021), and C 30 H 47 N 3 O 13 was identified in β-pinene +NO 3 SOA by Claflin and Ziemann (2018).
Similar to their precursors C 20 H 32 N 2 O x , C 30 H 48 N 4 O x showed negligible signal except in period P1, and presented an overlaying time profile of first-and second-generation product pattern (Fig. 6). For comparison, gas-phase trimer products were not observed in the β-pinene +NO 3 reaction (Shen et al., 2021), and the trimers observed in SOA from βpinene +NO 3 are likely formed via particle phase reactions (Claflin and Ziemann, 2018). An efficient gas-phase trimer production via subsequent accretion reactions between peroxy radicals requires that the precursor dimer has a high enough reactivity to create a dimer RO q 2 , e.g., via NO 3 reaction to a double bond. This suggests that the VOC containing at least two double bonds are likely more favorable to form trimers, which is consistent with our previous findings that trimers were formed in the NO 3 reaction with isoprene which also contains two double bonds , while they were not observed in the reaction of NO 3 with β-pinene which contains only one double bond (Shen et al., 2021).

"Primary" incremental HOM yields
We chose period P1 for the calculation of HOM yields in order to minimize the influence of the condensational sink on HOM concentration. However, both first-generation and second-generation products existed in this period, as discussed in Sect. 3.2 through Sect. 3.4 and supported by the time-behavior of the total HOM concentration (Fig. S15). Period P1 can be roughly divided into three phases based on the trends in HOM concentration. Shortly after the limonene injection, large quantities of HOM were produced (firstproduction phase) followed by a balanced intermediate phase when HOM concentrations stopped increasing. After the intermediate phase, HOM concentrations began to increase again (second-production phase). The first-production phase overlapped with the time span where limonene, NO 3 , and N 2 O 5 concentrations decreased, implying the dominance of first-generation HOM production process. During the second production period, wall loss was compensated by second-generation HOM formation, leading to another rise of the total HOM concentrations. Therefore, we use the firstproduction phase to estimate primary HOM production, determined over the first 3 min of the experiment. The calculated "primary" HOM molar yield is 1.5 % +1.7 % −0.7 % . This value is significantly lower than the HOM yield of 5 % to 17 % in earlier limonene ozonolysis experiments Jokinen et al., 2015;Pagonis et al., 2019). It should be emphasized that second-generation HOM, which contributed greatly to the limonene +NO 3 reaction system, is not included in this primary HOM yield.

Contribution of HOM to particle formation and growth
We observed nucleation and growth of SOA particles in the limonene +NO 3 reaction. We calculated the contribution of HOM to SOA formation and particle growth, and compared it to the measured particle growth (Fig. 7a). We assumed different scenarios of HOM uptake on aerosol particles, using the calculation methods described in the literature Seinfeld and Pandis, 2006;Nieminen et al., 2010). The assumption that all HOM irreversibly condense on the particles (scenario 1) resulted in a strong overestimation of particle mass growth (red markers in Fig. 7a Fig. 7a). While scenario 2a agreed quite well with the observations and only slightly overestimated SOA concentrations after 7 h by +11 %, scenario 2b underestimated the SOA concentration at the end by −53 %. The agreement between the modeled and observed SOA concentration suggests that HOM, and particularly LVOC-and ULVOC/ELVOC-HOM, play a major role in growth of SOA particles in this study. This is consistent with the work by Faxon et al. (2018) who found that many of the dimers are ELVOC, which is also supported by our calculation result based on the method of Mohr et al. (2019).
Since neither SO 2 nor H 2 SO 4 was added in our experiment, new particle formation (NPF) could be attributed to the nucleation initiated by HOM of low volatility. HOM trimers with as many as 30 carbon atoms were identified in the early stage of this study, and their sudden loss matched the onset of rapid formation of SOA. Trimers identified in our experiment are classified as ULVOC/ELVOC, with much lower volatility than monomers and dimers (Fig. 7b). Therefore, NPF in the current study can more likely be attributed to HOM trimers since they have the strongest potential of initiating nucleation, although we cannot rule out some contributions of dimers in the NPF. In contrast, in an earlier experiment investigating the NO 3 -initiated oxidation of β-pinene also conducted in the SAPHIR chamber under similar conditions, new particles were barely formed (< 20 cm −3 ) (Shen et al., 2021). As already mentioned above, no trimer HOM products were observed in that study, and only molecules with C ≤ 20 were detected (Sect. 3.4). Extremely low volatile organic vapors formed in α-pinene ozonolysis have been shown to induce nucleation and drive initial particle growth in the atmosphere Kirkby et al., 2016). Since our experiment of NO 3 oxidation of limonene was performed under near atmospheric conditions, such NPF events induced by the oxidation of limonene by NO 3 could also occur in the ambient atmosphere. Although monoterpene concentrations in this study (0-0.92 ppbv) are higher than in most ambient regions, they are still in the range of ambient concentrations (∼ 0.01-1 ppbv) (e.g., Wang et al., 2022), especially for forested regions (e.g., Xu et al., 2015;Kontkanen et al., 2016;Janson, 1992). Assuming that dimers react with NO 3 at a rate similar to limonene, and that they have a condensation sink similar to H 2 SO 4 (10 −3 -10 −1 s −1 ) (Dada et al., 2020), the lifetime with respect to NO 3 at an NO 3 concentration of 5-300 ppt and to condensation on particles are ∼ 0.1-10 and ∼ 0.1-20 min, respectively. Therefore, although aerosols may scavenge HOM dimers in the ambient atmosphere, dimers can still react with NO 3 at nighttime, forming trimers. Such reactions are particularly important when the ambient aerosol concentration is low. Several field observations have shown NPF events taking place at nighttime where biogenic emissions dominate (Kammer et al., 2018;Huang et al., 2019). The work by Ortega et al. (2012) demonstrated an important role of monoterpene ozonolysis products in nocturnal NPF events in chamber experiments. In a previous laboratory study, limonene +NO 3 appears more effective at initiating nucleation than the limonene +O 3 reaction (Fry et al., 2014), which supports that limonene +NO 3 can play a significant role in nighttime nucleation. Our study suggests that NO 3 oxidation of limonene could contribute to the nighttime NPF via HOM trimer formation. In contrast, we infer that NO 3 reactions with other monoterpenes containing only one double bond such as α-pinene and β-pinene are less likely candidates for nighttime NPF, because gas-phase trimers are not observed.

Conclusion and implications
HOM formation in the reaction of limonene with NO 3 was investigated in the SAPHIR chamber. About 280 gas-phase HOM products were identified, including monomers (C 6−10 , O 6−16 , N 0−3 ), dimers (C 17−20 , O 7−20 , N 0−4 ), and trimers (C 27−30 , O 16−25 , N 1−6 ). Nitrogen-containing products dominated the HOM, with compounds of the C 10 H 15−17 NO 6−14 series being the most prevalent. Dimers contributed 47 % in the early stage of the experiment when particle surface concentration was rather low (< 6 × 10 4 nm 2 cm −3 ), which was similar to monomers (47 %). Tentative formation pathways of major families were proposed in this work based on their time-dependent concentration profiles.
In HOM monomers, the abundance of carbonyl compounds significantly exceeded that of hydroxy or hydroperoxy compounds, indicating the significance of unimolecular termination of HOM-RO 2 radicals. Both RO q 2 autoxidation and alkoxy-peroxy pathways were found to be important in the formation of HOM monomers. Monomers with 1 nitrogen atom (1N-monomers) contained both first-and secondgeneration products, which could be formed via NO 3 oxidation of limonene and its first-generation products, with the latter being more important. Monomers with 2 nitrogen atoms were classified as second-generation products, which could be formed via NO 3 oxidation of the remaining C=C double bond of 1N-monomers.
Dimers showed both first-and second-generation time pattern. Dimers were mostly formed via accretion reactions between monomer RO 2 radicals, resulting in a decrease in O/C ratio compared to monomers. The initial less oxygenated RO q 2 , including the C 10 H 16 NO q 5 radical that cannot be observed in our instrument, likely played an important role in dimer formation, based on the comparison of measured dimers against expected dimer identity and concentrations according to accretion monomer RO q 2 reactions. Trimers were likely formed via accretion reactions between monomer RO 2 and dimer RO 2 radicals formed from secondary reactions of dimers with NO 3 . Trimer formation is thus linked to the presence of two double bonds in limonene, of which the first reacts with NO 3 leading to dimer products while the remaining C=C double bond provides a reactive site for further oxidation of the dimers by NO 3 , forming dimer RO 2 radicals.
A "primary" HOM molar yield of 1.5 % +1.7 % −0.7 % in the limonene +NO 3 reaction was estimated, including only the first-generation HOM. Second-generation HOM contributed greatly to monomers, dimers, and trimers, and hence the HOM yield we obtained is a lower limit of the total HOM yield, and is likewise much lower than the total HOM yield in the reaction of limonene with ozone (5 % to 17 %) Jokinen et al., 2015;Pagonis et al., 2019).
NPF observed in this work was likely related to the trimer formation due to much lower volatility of trimers compared to monomers and dimers. The SOA concentration in the limonene +NO 3 reaction could be explained by the condensation of the HOM belonging to LVOC and ULVOC/ELVOC classes assuming irreversible uptake, indicating an important role of HOM for growth of SOA particles in this reaction system. To our knowledge, this work is the first identifying trimer products from the limonene +NO 3 reaction system, suggesting that limonene +NO 3 is a possible crucial source of new particles formed in nighttime biogenic emission-dominated areas (Kammer et al., 2018;Huang et al., 2019). Our work highlights the need to consider the role of limonene +NO 3 in NPF in models simulating nighttime aerosols formation in biogenic-emission dominated areas, especially with large limonene emissions. In addition, comparison with the reactions of NO 3 with isoprene  and other monoterpenes (Shen et al., 2021) reveals a strong dependence of HOM products on the molecular structure of the VOC species in NO 3 -initiated chemistry.
The concentration of limonene and NO 3 in this study was on the order of few ppb and a few to 100 ppt, respectively, which are similar to the ambient levels in rural and forest regions affected by anthropogenic emissions (Brown and Stutz, 2012). The chemical lifetime of RO q 2 was of the order of 50 to 500 s, which is also similar to ambient conditions at nighttime (Fry et al., 2018). The RO q 2 loss pathway in our study was dominated by the reactions RO q 2 + NO 3 and RO q 2 + RO q 2 , which is relevant for the RO q 2 fate in urban areas and forested areas influenced by an urban plume at nighttime. However, in more pristine forested regions, the RO q 2 fate is mostly determined by RO q 2 + HO 2 and RO q 2 + RO q 2 , as shown by Bates et al. (2022) for the example of a Southeast US forest. As NO 3 concentration is generally enhanced with increased anthropogenic emissions, RO q 2 + NO 3 will become more important going from remote to urban areas. Therefore, the HOM products and their formation process in our study are relevant for rural and forested regions influenced by anthropogenic plumes and ambient urban regions with high volatile commercial products emissions, as limonene is a typical component of volatile chemical products (VCPs) (Nazaroff and Weschler, 2004). In these regions, HOM from monoterpene +NO 3 reactions can be major components of nighttime SOA. As nitrooxy-RO 2 fate can strongly affect the oxidation product distribution and SOA yield as shown for the reaction of α-pinene with NO 3 (Bates et al., 2022), more studies of HOM formation by NO 3 at various RO q 2 fates are needed to be representative of various environments, including (remote) forested regions.
This study also highlights the important role of secondgeneration chemistry in HOM formation, which needs to be further investigated and should be included in chemical mechanisms used in numerical models. Additional work is also needed to investigate the role of different HOM formed via NO 3 -initiated BVOC oxidation reactions in NPF and growth of SOA particles in order to better constrain the climatic and environmental effects of BVOC + NO 3 chemistry. Data availability. All the data in the figures and tables of this study are available upon request to the corresponding author (t.mentel@fz-juelich.de or dfzhao@fudan.edu.cn).
Author contributions. DZ, TFM, and HF designed the study. IP, HF, IHA, RT, FR, and DZ carried out instrument deployment and operation. YG analyzed the MS data and did the MCM simulation with the aid of DZ, HS, and HL. YG, DZ, TFM, and LV interpreted the compiled data set. LV examined the reaction schemes. YG, DZ, TFM, and LV wrote the paper and HS, IP, HL, SK, LV, HF edited the paper. All the co-authors discussed the results and commented on the paper.

Competing interests.
The contact author has declared that none of the authors has any competing interests.

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Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Review statement. This paper was edited by Sergey A. Nizkorodov and reviewed by two anonymous referees.