Highly oxygenated organic molecules ( HOM ) formation in the 1 isoprene oxidation by NO 3 radical 2

13 Highly oxygenated organic molecules (HOM) are found to play an important role in the formation and 14 growth of secondary organic aerosol (SOA). SOA is an important type of aerosol with significant impact on air 15 quality and climate. Compared with the oxidation of volatile organic compounds by O3 and OH, HOM formation in 16 the oxidation by NO3 radical, an important oxidant at night-time and dawn, has received less attention. In this study, 17 HOM formation in the reaction of isoprene with NO3 was investigated in the SAPHIR chamber (Simulation of 18 Atmospheric PHotochemistry In a large Reaction chamber). A large number of HOM including monomers (C5), 19 dimers (C10), and trimers (C15), both closed-shell compounds and open-shell peroxy radicals, were identified and 20 were classified into various series according to their formula. Their formation pathways were proposed based on the 21 peroxy radicals observed and known mechanisms in the literature, which were further constrained by the time profiles 22 of HOM after sequential isoprene addition to differentiate firstand second-generation products. HOM monomers 23 containing one to three N atoms (1-3N monomers) were formed, starting with NO3 addition to carbon double bond, 24 forming peroxy radicals (RO2), followed by autoxidation. 1N monomers were formed by both the direct reaction of 25 NO3 with isoprene and of NO3 with first-generation products. 2N-monomers (e.g. C5H8N2On (n=7-13), C5H10N2On (n=826 14)) were likely the termination products of C5H9N2On•, which was formed by the addition of NO3 to C527 hydroxynitrate (C5H9NO4), a first-generation product containing one carbon double bond. 2N-monomers, which were 28 second-generation products, dominated in monomers and accounted for ~34% of all HOM, indicating the important 29 role of second-generation oxidation in HOM formation in the isoprene+NO3 reaction under our experimental 30 conditions. H-shift of alkoxy radicals to form peroxy radicals and subsequent autoxidation (“alkoxy-peroxy” pathway) 31 was found to be an important pathway of HOM formation. HOM dimers were mostly formed by the accretion reaction 32 of various HOM monomer RO2 and via the termination reactions of dimer RO2 formed by further reaction of closed33 shell dimers with NO3 and possibly by the reaction of C5-RO2 with isoprene. HOM trimers were likely formed by 34 the accretion reaction of dimer RO2 with monomer RO2. The concentrations of different HOM showed distinct time 35 profiles during the reaction, which was linked to their formation pathway. HOM concentrations either showed a 36 typical time profile of first-generation products, or of second-generation products, or a combination of both, 37 indicating multiple formation pathways and/or multiple isomers. Total HOM molar yield was estimated to be 1.2% 38 +1.3% -0.7% , which corresponded to a SOA yield of ~3.6% assuming the molecular weight of C5H9NO6 as the lower limit. 39

of HOM after sequential isoprene addition to differentiate first-and second-generation products. HOM monomers 23 containing one to three N atoms (1-3N monomers) were formed, starting with NO 3 addition to carbon double bond, 24 forming peroxy radicals (RO 2 ), followed by autoxidation. 1N monomers were formed by both the direct reaction of 25 NO 3 with isoprene and of NO 3 with first-generation products. 2N-monomers (e.g. C 5 H 8 N 2 O n (n=7-13) , C 5 H 10 N 2 O n (n=8-26 14) ) were likely the termination products of C 5 H 9 N 2 O n •, which was formed by the addition of NO 3 to C5-27 hydroxynitrate (C 5 H 9 NO 4 ), a first-generation product containing one carbon double bond. 2N-monomers, which were 28 second-generation products, dominated in monomers and accounted for ~34% of all HOM, indicating the important 29 role of second-generation oxidation in HOM formation in the isoprene+NO 3 reaction under our experimental 30 conditions. H-shift of alkoxy radicals to form peroxy radicals and subsequent autoxidation ("alkoxy-peroxy" pathway) 31 was found to be an important pathway of HOM formation. HOM dimers were mostly formed by the accretion reaction 32 of various HOM monomer RO 2 and via the termination reactions of dimer RO 2 formed by further reaction of closed-33 shell dimers with NO 3 and possibly by the reaction of C5-RO 2 with isoprene. HOM trimers were likely formed by 34 the accretion reaction of dimer RO 2 with monomer RO 2 . The concentrations of different HOM showed distinct time 35 profiles during the reaction, which was linked to their formation pathway. HOM concentrations either showed a 36 typical time profile of first-generation products, or of second-generation products, or a combination of both, 37 indicating multiple formation pathways and/or multiple isomers. Total HOM molar yield was estimated to be 1.2% 38 +1.3% -0.7% , which corresponded to a SOA yield of ~3.6% assuming the molecular weight of C 5 H 9 NO 6 as the lower limit. 39

Introduction 42
Highly oxygenated organic molecules (HOM) are an important class of compounds formed in the oxidation 43 of volatile of organic compounds (VOC) including biogenic VOC (BVOC) and anthropogenic VOC (Crounse 44 et al., 2013;Ehn et al., 2014;Jokinen et al., 2014;Rissanen et al., 2014;Jokinen et al., 2015;Krechmer et al., 45 2015;Mentel et al., 2015;Rissanen et al., 2015;Kenseth et al., 2018;Molteni et al., 2018;Garmash et al., 2019;46 McFiggans et al., 2019;Molteni et al., 2019;Quelever et al., 2019). A number of recent studies have 47 demonstrated that HOM play a pivotal role in both nucleation and also particle growth of pre-existing particles, 48 thus contributing to secondary organic aerosol (SOA) Kirkby et al., 2016;Tröstl et al., 2016). 49 Particularly, in the early stage of aerosol growth, HOM may contribute a significant fraction of SOA mass 50 . 51 HOM are formed by the autoxidation of peroxy radicals (RO 2 ), which means they undergo intramolecular 52 H-shift forming alky radicals, followed by O 2 addition leading to formation of new RO 2 as shown below 53 (Vereecken et al., 2007;Crounse et al., 2013;Ehn et al., 2017;Bianchi et al., 2019;Møller et al., 2019;Nozière 54 and Vereecken, 2019;Vereecken and Nozière, 2020). 55 56 Besides autoxidation, the RO 2 can also react with HO 2 , RO 2 and NO 3 , either forming a series of termination 57 products (R1-3), including organic hydroxyperoxide, alcohol, and carbonyl, or forming alkoxy radicals (RO,  nitrate yield (57-95%) was found (Perring et al., 2009;Rollins et al., 2009;Kwan et al., 2012;Schwantes et al., 112 2015). Products in the particle phase such as C 10 dimers were also detected (Ng et al., 2008;Kwan et al., 2012;113 Schwantes et al., 2015). The SOA yield varies from 2% to 23.8% depending on the organic aerosol concentration 114 (Ng et al., 2008;Rollins et al., 2009). These studies have provided valuable insights in oxidation mechanism, 115 particle yield and composition. However, because HOM formation was not the focus of these studies, only a 116 limited number of products, mainly moderately oxygenated ones (oxygen number ≤2 in addition to NO 3 117 functional groups), were detected in the gas phase. The detailed mechanism of HOM formation and their yields 118 in the reaction of BVOC+NO 3 are still unclear. 119 In this study, we investigated the HOM formation in the oxidation of isoprene by NO 3 . We report the 120 identification of HOM, including HOM monomers, dimers, and trimers. According to the reaction products and 121 literature, we discuss the formation mechanism of these HOM. The formation mechanism of various HOM is 122 further constrained with time series of HOM upon repeated isoprene additions. We also provide an estimate of 123 HOM yield in the isoprene+NO 3 reaction and assess their roles in SOA formation. 124 2 Experimental 125

Chamber setup and experiments 126
Experiments investigating the reaction of isoprene with NO 3 were conducted in the SAPHIR chamber 127 (Simulation of Atmospheric PHotochemistry In a large Reaction chamber) at Forschungszentrum Jülich, 128 Germany. The details of the chamber have been described before (Rohrer et al., 2005;Zhao et al., 2015a;Zhao 129 et al., 2015b;Zhao et al., 2018). Briefly, SAPHIR is a Teflon chamber with a volume of 270 m 3 . It can utilize 130 natural sunlight for illumination and is equipped with a louvre system to switch between light and dark 131 conditions. In this study, the experiments were conducted in the dark with the louvres closed. 132 Temperature and relative humidity were continuously measured. Gas and particle phase species were 133 characterized using a comprehensive set of instruments with the details described before (Zhao et al., 2015b). 134 VOC were characterized using a Proton Transfer Reaction Time-of-Flight Mass Spectrometer 135 Ionicon Analytik, Austria). NO x and O 3 concentrations were measured using a chemiluminescence NO x analyzer 136 (ECO PHYSICS TR480) and an UV photometer O 3 analyzer (ANSYCO, model O341M), respectively. OH, 137 HO 2 and RO 2 concentrations were measured using a laser induced fluorescence system (LIF) (Fuchs et al., 2012). 138 NO 3 and N 2 O 5 were detected by a custom-built instrument based on cavity ring-down spectroscopy. The design 139 of the instrument is similar to that described by Wagner et al. (2011). NO 3 was directly detected in one cavity 140 by its absorption at 662 nm and the sum of NO 3 and N 2 O 5 in a second, heated cavity, which had a heated inlet 141 to thermally decompose N 2 O 5 to NO 3 . The sampling flow rate was 3 to 4 liters per minute. The detection by 142 cavity ring-down spectroscopy was achieved by a diode laser that was periodically switched on and off with a 143 repetition rate of 200 Hz. Ring-down events were observed by a digital oscilloscope PC card during the time 144 when the laser was switched off and were averaged over 1s. The zero-decay time that is needed to calculate the 145 concentration of NO 3 was measured every 20 s by chemically removing NO 3 in the reaction with excess nitric 146 oxide (NO) in the inlet system. The accuracy of measurements was limited by the uncertainty in the correction 147 for inlet losses of NO 3 and N 2 O 5 . In the case of N 2 O 5 a transmission of (85±10) % was achieved and in the case 148 of NO 3 of (50±30) %. 149 Before an experiment, the chamber was flushed with high purity synthetic air (purity>99.9999% O 2 and N 2 ). 150 Experiments were conducted under dry condition (RH<2 %) and temperature was at 302±3 K. NO 2 and O 3 were 151 added to the chamber first to form N 2 O 5 and NO 3 , reaching concentrations of ~60 ppb for NO 2 and ~100 ppb for O 3 . 152 After around half an hour, isoprene was sequentially added into the chamber for three times at intervals of ~1 h. 153 Around 40 min after the third isoprene injection, NO 2 was added to compensate the loss of NO 3 and N 2 O 5 . Afterwards, 154 three isoprene additions were repeated in the same way as before. O 3 was added before the fifth and the sixth isoprene 155 addition to compensate for its loss by reaction. The schematic for the experimental procedure is shown in Fig. S1. 156 Experiments were designed such that the chemical system was dominated by the reaction of isoprene with NO 3 and 157 the reaction of isoprene with O 3 did not play a major role (<3% of the isoprene consumption). Figure S2 shows the 158 relative contributions of the reaction of O 3 and NO 3 with isoprene to the total chemical loss of isoprene using the 159 NO 3 and O 3 concentrations measured. The reaction with NO 3 accounted for >95% of the isoprene consumption for 160 the whole experiments. The contribution of the reaction of isoprene with trace amount of OH, mainly produced in 161 the reaction of isoprene+O 3 via Criegee intermediates (Nguyen et al., 2016), is negligible as the OH yield is less than 162 one (Malkin et al., 2010) and thus its contribution is less than that of isoprene+O 3 . This is consistent with the 163 contribution determined using measured OH concentration, despite some uncertainty in measured OH concentration 164 due to the interference from NO 3 . In these experiments, RO 2 fate is estimated to be dominated by its reaction with 165 NO 3 according to the measured NO 3 , RO 2 , and HO 2 concentration and their rate constants for the reactions with RO 2 166 (MCM v3.2 (Jenkin et al., 1997;Jenkin et al., 2003;Saunders et al., 2003;Jenkin et al., 2015), via website: 167 http://mcm.leeds.ac.uk/MCM) despite uncertainties of the measured RO 2 and HO 2 concentration due to interference 168 from NO 3 . As a large portion of RO 2 is not measured by LIF (Vereecken et al., 2021) and thus RO 2 is underestimated, 169 we expected the reaction of RO 2 +RO 2 to be also important. Overall, we estimate that he RO 2 fate is dominated the 170 reaction RO 2 +NO 3 with significant contribution of RO 2 +RO 2 . 171

Characterization of HOM 172
In this study we refer to similar definition for HOM by Bianchi et al. (2019), i.e., HOM typically contain six or 173 more oxygen atoms formed via autoxidation and related chemistry of peroxy radicals. HOM were detected using a 174 Chemical Ionization time-of-flight Mass Spectrometer (Aerodyne Research Inc., USA) with nitrate as the reagent ion 175 (CIMS) (Eisele and Tanner, 1993;Jokinen et al., 2012). 15 N nitric acid was used to produce 15 NO 3in order to 176 distinguish the NO 3 group in target molecules formed in the reaction from the reagent ion. The details of the 177 instrument are described in our previous publications Mentel et al., 2015;Pullinen et al., 2020). 178 The CIMS has a mass resolution of ~4000 (m/dm). Examples of peak fitting are shown in Fig. S3. HOM 179 concentrations were estimated using the calibration coefficient of H 2 SO 4 as described by Pullinen et al. (2020) 180 because the charge efficiency of HOM and H 2 SO 4 can be assumed to be equal and close to the collision limit (Ehn et 181 al., 2014;Pullinen et al., 2020). The details of the calibration with H 2 SO 4 are provided in the supplement S1. Since 182 HOM contain more than six oxygen atoms and their clusters with nitrate ions are quite stable , the 183 charge efficiency of HOM is thus assumed to be equal to that of H 2 SO 4 , which is close to the collision limit (Viggiano 184 et al., 1997). If HOM do not charge with nitrate ions at their collision limit or the clusters formed break during the 185 short residence time in the charger, its concentration would be underestimated as pointed by Ehn et al. (2014). Thus, 186 our assumption provides a lower limit of the HOM concentration. The HOM yield was derived using the 187 concentration of the HOM produced, divided by the concentration of isoprene that was consumed by NO 3 . The 188 uncertainty of HOM yield was estimated to -55%/+103%. The loss of HOM to the chamber was corrected using a 189 wall loss rate of 6×10 -4 s -1 as quantified previously . HOM concentrations were also corrected for 190 dilution due to the replenishment flow needed to maintain a constant overpressure of the chamber (loss rate ~1×10 -6 191 s -1 ) (Zhao et al., 2015b). The influence of wall loss correction and dilution correction on HOM yield was ~12% and 192 <1%, respectively. Although the wall loss rate of vapors in this study might not be exactly the same as in our previous 193 photo-oxidation experiments , HOM yield is not sensitive to the vapor wall loss rate. An increase 194 of wall loss rate by 100% or a decrease by 50% only changes the HOM yield by 11% and -6%, respectively. 195 3 Results and discussion 196

Overview of HOM 197
The mass spectra of HOM in the gas phase formed in the oxidation of isoprene by NO 3 are shown in 198 with possibly few exceptions such as C 5 H 10 O 8 and C 5 H 8 O 11 with very minor peaks (<~1% of the maximum 200 peak). The reaction products can be roughly divided into three classes: monomers (C5, ~200-400 Th), dimers 201 (C10, ~400-600 Th), and trimers (C15, ~>600 Th), according to their mass to charge ratio (m/z). The detailed 202 peak assignment of monomers, dimers, and trimers is discussed in the following sections. 203

Overview of HOM monomers 205
HOM monomers showed a roughly repeating pattern in the mass spectrum at every 16 Th 206 (corresponding to the mass of oxygen) (Fig. 1a). Here a number of series of HOM monomers with continuously 207 increasing oxygenation were found, such as C 5 H 9 NO n , C 5 H 7 NO n , C 5 H 8 N 2 O n , C 5 H 10 N 2 O n ( Table 1, Table S1-2 208 and Fig. 2). These monomers included both stable closed-shell molecules and open-shell radicals, such as 209 C 5 H 8 NO n • and C 5 H 9 N 2 O n •. The open-shell molecules were likely RO 2 radicals because of their much longer life 210 time and hence higher concentrations compared with alkoxy radicals (RO) and alkyl radicals (R). Since the 211 observed stable products were mostly termination products of RO 2 reactions, we describe the stable products in 212 a RO 2 -oriented approach. It is worth noting that some of the termination products may contain multiple isomers 213 formed from different pathways. atoms that they contain. HOM without nitrogen atoms were barely observed except for very minor peaks (<~1% of 222 the maximum peak) possibly assigned to C 5 H 10 O 8 and C 5 H 8 O 11 . The contribution of 2N-monomers such as 223 C 5 H 10 N 2 O n and C 5 H 8 N 2 O n was higher than that of the 1N-HOM monomers, and that of 3N-monomers was the least 224 ( Fig. 1, inset). The most abundant monomers were C 5 H 10 N 2 O 8 , C 5 H 10 N 2 O 9 , and C 5 H 8 N 2 O 8 . The termination products 225 of C 5 H 9 NO 8 , C 5 H 9 NO 9 , and C 5 H 7 NO 8 also showed relatively high abundance. These limited number of compounds 226 dominated the HOM monomers. Since 2N-monomers were second-generation products as discussed below, the 227 higher abundance 2N-monomers indicate that the second-generation HOM play an important role in the reaction of 228 NO 3 with isoprene in the reaction conditions of our study, as also seen by Wu et al. (2020) . This is more evident for 229 the mass spectrum averaged over six isoprene addition periods (Fig. 1b), where the abundance of C 5 H 10 N 2 O n and 230 C 5 H 8 N 2 O n were more dominant. This observation is in contrast with the finding for the reaction of O 3 with BVOC 231 which contains only one double bond such as α-pinene , where HOM are mainly first-generation 232 products formed via autoxidation. The higher abundance of HOM 2N-monomers than 1N-monomers is likely because 233 HOM production rate via the autoxidation of 1N-monomer RO 2 following the reaction of isoprene with NO 3 may be 234 slower than that of the reaction of 1N-monomers (including both HOM and non-HOM monomers) with NO 3 . We 235 would like to note that some less oxygenated 1N-monomers such as C 5 H 9 NO 4/5 and C 5 H 7 NO 4 may have high 236 abundance but are not detected by NO 3 --CIMS and are not HOM and thus not included in HOM 1N-monomers.

1N-monomers 245
In our experiments we observed a C 5 H 8 NO n • (n=7-12) series (series M1), as well as its corresponding 246 termination products C 5 H 7 NO n-1 , C 5 H 9 NO n-1 , and C 5 H 9 NO n via the reactions with RO 2 and HO 2 , which contain 247 carbonyl, hydroxyl, and hydroperoxy group, respectively. Overall, the peak intensities of C 5 H 9 NO n and 248 C 5 H 7 NO n series first increased and then decreased as oxygen number increased (Fig. 2), with the peak intensity 249 of C 5 H 9 NO 8 and C 5 H 7 NO 8 being the highest within their respective series when averaged over the whole 250 experiment period. 251 C 5 H 10 NO n (n=8-9) R O 2 Isoprene +NO 3 +OH C 5 H 11 NO n (n=7-9) ROOH/ROH C 5 H 9 NO n (n=7-8) R = O a : RO 2 denotes peroxy radical and ROOH, ROH, R=O, and RO 2 NO 2 denote the termination products 253 containing hydroperoxy, hydroxyl, carbonyl group, and peroxynitrate, respectively. 254 b : Peak assignment of compounds with n=13,14 may be subject to uncertainties. 255

259
(b) 260 Scheme 1. The example pathways to form HOM RO 2 C 5 H 8 NO n • (n=7, 9, 11) series (a) and C 5 H 8 NO n • 261 (n=8, 10) series (b) in the reaction of isoprene with NO 3 . The detected products are in bold. 262 C 5 H 8 NO n • with odd number oxygen atoms (n=7, 9, 11, series M1a) were possibly formed by the attack 263 of NO 3 to one double bond (preferentially to C1 according to previous studies (Skov et al., 1992;Berndt and 264 Böge, 1997;Schwantes et al., 2015) and followed by autoxidation (Scheme 1a). We would like to note that 265 NO 3 --CIMS only observed HOM with oxygen numbers ≥ 6 in this study due to its selectivity of detection. 266 C 5 H 8 NO n • with even number oxygen atoms (n=8, 10, series M1b in Table 1) were possibly formed after H-shift 267 of an alkoxy radical formed in reaction R4 or R5 and subsequent O 2 addition ("alkoxy-peroxy" channel) 268 (Scheme 1b), where the alkoxy radicals can be formed both from the RO 2 +NO 3 and RO 2 +RO 2 reactions. The 269 hydroxyRO 2 formed can undergo further autoxidation adding two oxygen atoms after each H-shift. We would 270 like to note that the scheme and other schemes in this study only show example isomers and pathways to form these 271 Some HOM monomers may contain multiple isomers and be formed via different pathways. For 274 example, C 5 H 9 NO n can contain alcohols derived from RO 2 C 5 H 8 NO n+1 •, hydroperoxides derived from RO 2 275 C 5 H 8 NO n • or the ketones from RO 2 C 5 H 10 NO n+1 •. Some RO 2 C 5 H 8 NO n • may be formed via the reaction of first-276 generation products with NO 3 in addition to direct reaction of isoprene with NO 3 . For example, C 5 H 8 NO 7 • can 277 be formed by the reaction of NO 3 with C 5 H 8 O 2 , which is a first-generation product observed previously in the 278 reaction of isoprene with NO 3 or OH (Scheme S1b) (Kwan et al., 2012). Moreover, RO 2 C 5 H 8 NO n • can be 279 formed from C5-carbonylnitrate, a first-generation product, with OH (Scheme S1a). Trace amount of OH can 280 be produced in the reaction of isoprene with NO 3 (Kwan et al., 2012;Wennberg et al., 2018). OH can also be 281 formed via Criegee intermediates formed in the isoprene+O 3 reaction (Nguyen et al., 2016), but this OH source 282 was likely minor because the contribution of the isoprene+O 3 reaction to total isoprene loss was negligible (<5%, 283 Fig. S2). In addition, C 5 H 8 NO 8 • may also be formed by the reaction of NO 3 with C 5 H 8 O 3 , which is a first-284 generation product observed in the reaction of isoprene with OH (Kwan et al., 2012). The C 5 H 8 NO n • formed 285 via direct reaction of isoprene with NO 3 is a first-generation RO 2 while that formed via other indirect pathways 286 is a second-generation RO 2 . The time profile of the isomers from these two pathways, however, are expected to 287 be different as will be discussed below. 288 Time series of HOM can shed light on their formation mechanisms. It is expected that first-generation 289 products increase fast with isoprene addition and reach a maximum earlier in the presence of wall loss of organic 290 vapour, while second-generation products reach a maximum in the later stage or increase continuously if the 291 production rate is higher than the loss rate. As a reference to analyze the time profiles of HOM, the times profile 292 of isoprene, NO 3 , and N 2 O 5 are also shown (Fig. S4). After isoprene was added in each period, NO 3 and N 2 O 5 293 dropped dramatically and then gradually increased. We found that termination products within the same M1 294 series showed different time profiles. For example, in C 5 H 9 NO n series, C 5 H 9 NO 8 clearly increased 295 instantaneously with isoprene addition, and decreased fast afterwards (Fig. 3a), indicating that it was a first-296 generation product, which was expected according to the mechanism Scheme 1. C 5 H 9 NO 6 and C 5 H 9 NO 10 had a 297 general increasing trend with time. While C 5 H 9 NO 6 increased continuously with time, C 5 H 9 NO 10 reached 298 maximum intensity in the late phase of each isoprene addition period and then decreased naturally or after 299 isoprene addition. The faster loss of C 5 H 9 NO 10 than C 5 H 9 NO 6 may result from the faster wall loss due to its 300 lower volatility. C 5 H 9 NO 7 and C 5 H 9 NO 9 showed a mixing time profile with features of the former two kinds of 301 time profiles, increasing almost instantaneously with isoprene additions, especially in the first two periods, 302 while increasing continuously or decreasing first with isoprene additions and then increasing later in each period. 303 This kind of time series indicates that there were significant contributions from both first-and second-generation 304 products. 305 The second-generation products may be different isomers formed in pathways other than shown in 306 Scheme 1. Second-generation C 5 H 9 NO 6 can be formed via C 5 H 8 NO 7 •, which can also be formed by the reaction 307 of NO 3 and O 2 with C 5 H 8 O 2 as mentioned above (Scheme S2b), or by the reaction of OH with C 5 H 7 NO 4 (Scheme 308 S2a). The time profiles of C 5 H 8 NO 7 • did show more contribution of second-generation processes because it 309 continuously increased with time in general. If the pathways via the reaction of NO 3 and O 2 with C 5 H 8 O 2 and 310 the reaction of OH with C 5 H 7 NO 4 contribute most to C 5 H 9 NO 6 , C 5 H 9 NO 6 would show mostly a time profile of 311 second-generation products. Similarly, second-generation C 5 H 9 NO 7 can be formed via C 5 H 8 NO 7 • or C 5 H 8 NO 8 •. 312 The time series of C 5 H 8 NO 8 • did show the contribution of both the first-and second-generation processes, which 313 generally increased with time while also responding to isoprene addition (Fig. S5). Similar to C 5 H 9 NO 6 , the 314 second-generation pathway for C 5 H 9 NO 7 , C 5 H 9 NO 9 , and C 5 H 9 NO 10 are shown in Scheme S1, S3, S4. For the 315 RO 2 in C 5 H 8 NO n • series other than C 5 H 8 NO 7/8 •, the peak of C 5 H 8 NO n • overlaps with C 5 H 10 N 2 O n in the mass 316 spectra, which is a much larger peak, and thus cannot be differentiated from C 5 H 10 N 2 O n . Therefore, it is not 317 possible to obtain reliable separate time profiles in order to differentiate their major sources. It is worth noting 318 that nitrate CIMS may not be able to detect all isomers of C 5 H 9 NO 6 due to the sensitivity limitation. Therefore, 319 we cannot exclude the possibility that the absence of some first-generation isomers of C 5 H 9 NO 6 was due to the 320 low sensitivity of these isomers. Among the termination products of the 1N-monomer RO 2 , carbonyl and hydroxyl/hydroperoxide 330 species had comparable abundance in general (Table S1), suggesting that disproportionation reactions between 331 RO 2 and RO 2 forming hydroxy and carbonyl species (R1-2) was likely an important RO 2 termination pathway. 332 However, dependence of the exact ratio of carbonyl species to hydroxyl/hydroperoxide species on the number 333 of oxygen atoms did not show a clear trend (Table S1), suggesting that the reactions of HOM RO 2 depended on 334 their specific structure. There was no clear difference in the abundance between the termination products from 335 C 5 H 8 NO n • with odd and even number of oxygen atom in general, although the most abundant termination 336 product of C 5 H 8 NO n • , i.e. C 5 H 7 NO 8 , was likely formed from C 5 H 8 NO 9 • in series M1a. This fact indicates that 337 both the peroxy pathway and alkoxy-peroxy pathway were important for the HOM formation in the 338 isoprene+NO 3 reaction under our conditions, in agreement with the significant formation of alkoxy radicals 339 from the reaction of RO 2 with NO 3 and RO 2 . 340 In addition to the termination products of RO 2 M1, minor peaks of the RO 2 series C 5 H 10 NO n • (n=8-9) (M4, 341 Table 1) and their corresponding termination products including hydroperoxide, alcohol and carbonyl species were 342 detected (Table S3). C 5 H 10 NO n were likely formed by sequential addition of NO 3 and OH to two double bonds of 343 isoprene (Scheme S5). OH can react fast with isoprene or with the first-generation products of the reaction of isoprene 344 with NO 3 , thus forming C 5 H 10 NO n •. In addition, a few very minor but noticeable peaks of C 5 H 9 O n • and their 345 corresponding termination products C 5 H 10 O n and C 5 H 8 O n were also observed. These HOM may be formed by the 346 reactions of isoprene with trace amount of OH and with O 3 , although their contributions to reacted isoprene were 347 negligible. These HOM were also observed in the reaction of isoprene with O 3 with and without OH scavengers 348 (Jokinen et al., 2015). 349 Among 1N-monomer HOM, C 5 H 9 NO 7 has been observed in the particle phase using ESI-TOFMS by 350 Ng et al. (2008) while others have not been observed in previous laboratory studies of the reaction of isoprene 351 with NO 3 , to our knowledge. A number of C 5 organic nitrates have been observed in field studies. For example, 352 C 5 H 7-11 NO 4-9 have been observed in aerosol particles during the Southern Oxidant and Aerosol Study in rural 353 Alabama, US, where isoprene is abundant (Lee et al., 2016). Those compounds were also observed in chamber 354 experiments of the reaction of isoprene with OH in the presence of NO x (Lee et al., 2016). C 5 H x NO 4-9 and 355 C 5 H x NO 4-10 have been observed in the gas phase and particle, respectively, in a rural area in southwest Germany 356 (Huang et al., 2019). 357

2N-mononmers 358
The 2N-monomer RO 2 series C 5 H 9 N 2 O n •(n=8-14), were observed, as well as its likely termination 359 products, C 5 H 8 N 2 O n and C 5 H 10 N 2 O n , which contain a carbonyl and hydroxyl or hydroperoxide functional group, 360 respectively. The RO 2 series C 5 H 9 N 2 O n • with odd number of oxygen atoms (n=9, 11) (M2a in Table 1) were 361 likely formed from the first-generation product C 5 H 9 NO 4 (C5-hydroxynitrate) by adding NO 3 to the remaining 362 double bond, forming C 5 H 9 N 2 O 9 •, followed by autoxidation (Scheme 2a). This RO 2 series can also be formed 363 by the addition of NO 3 to the double bond of first-generation products (e.g. C 5 H 9 NO 5 , C5-364 nitrooxyhydroperoxide) and a subsequent alkoxy-peroxy step (Scheme 2b). C 5 H 9 N 2 O n • with even number of 365 oxygen atoms (n=8, 10, 12) (M2b in Table 1), can be formed by the addition of NO 3 to the double bond of 366 C 5 H 9 NO 5 followed by autoxidation (Scheme. 3a), or of C 5 H 9 NO 4 followed by an alkoxy-peroxy step (Scheme. 367 3b). The formation pathways of C 5 H 9 N 2 O 13/14 • and C 5 H 9 N 2 O 8 • cannot be well explained, as they contain too 368 many or too few oxygen atoms to be formed via the pathways in Scheme 2 or 3. In Scheme 2 and 3, we show the 369 reactions starting from 1-NO 3 -isoprene-4-OO as an example. In the supplement, we have also shown the pathways 370 starting from 1-NO 3 -isoprene-2-OO peroxy radicals, which is indicated in a recent study by Vereecken et al. (2021) 371 to be the dominant RO 2 in the reaction of isoprene with NO 3 . 372 Formation through either Scheme 2 or 3 means that C 5 H 8 N 2 O n and C 5 H 10 N 2 O n were second-generation 373 products. The time series of C 5 H 10 N 2 O n species clearly indicates that they were indeed second-generation 374 products. C 5 H 10 N 2 O n species generally did not increase immediately with isoprene addition (Fig. 3b), but 375 increased gradually with time and reached its maximum in the later stage of each period before decreasing with 376 time (in the period 1 and 6), or decreasing after the next isoprene addition (periods 2-5). This time profile can 377 be explained by the time series of the precursor of C 5 H 10 N 2 O n , C 5 H 9 N 2 O n • (RO 2 ) (Fig. S6). The changing rate 378 (production rate minus destruction rate) of C 5 H 10 N 2 O n concentration was dictated by the concentration of 379 C 5 H 9 N 2 O n • and the wall loss rate. During periods 2 to 5, C 5 H 9 N 2 O n • gradually increased but decreased sharply 380 after the isoprene additions, resulted from chemical reactions of C 5 H 9 N 2 O n • and additionally from wall loss. 381 When the rate of change of the C 5 H 10 N 2 O n concentration was positive, the concentration of C 5 H 10 N 2 O n increased 382 with time. After isoprene additions, the rate of change of the C 5 H 10 N 2 O n concentration decreased dramatically 383 to even negative, leading to decreasing concentrations. Similar to C 5 H 10 N 2 O n , the C 5 H 8 N 2 O n series did not 384 respond immediately to isoprene additions (Fig. S7), which is expected for second-generation products 385 according to the mechanism discussed above (Scheme 2-3). Particularly, the continuing increase of C 5 H 8 N 2 O n 386 even after isoprene was completely depleted (at ~21:40, Fig. S7) clearly indicates that these compounds were 387 second-generation products, although in the end they decreased due to wall loss. 388 According to the finding of Ng et al. (2008), C5-hydroxynitrate decays much faster than C5-402 nitrooxyhydroperoxides. Additionally, C5-hydroxynitrate concentration is expected to be higher than that of 403 nitrooxyhydroperoxides because RO 2 +RO 2 forming alcohol is likely more important than RO 2 +HO 2 forming 404 hydroperoxide in this study. Therefore, it is likely that C 5 H 9 N 2 O n • M2a series was mainly formed from C 5 H 9 NO 4 405 instead of C 5 H 9 NO 5 , while C 5 H 9 N 2 O n • M2b were formed from C 5 H 9 NO 4 followed by an alkoxy-peroxy step. 406

389
That is, Scheme 2a and 3b appear more likely. 407 Similar to C 5 H 8 NO n •, the intensity of carbonyl species from C 5 H 9 N 2 O n • was also comparable with that 408 of hydroxyl/hydroperoxide species, suggesting that RO 2 +RO 2 reaction forming ketone and alcohol was likely 409 an important pathway of HOM formation in the isoprene+NO 3 reaction. In general, the intensity of the 410 termination products from C 5 H 9 N 2 O n • with both even and odd oxygen numbers were comparable. This again 411 suggests that both peroxy and alkoxy-peroxy pathways were important for HOM formation in the isoprene+NO 3 412 reaction. The intensity of C 5 H 8 N 2 O n first increased and then decreased with oxygen number while C 5 H 10 N 2 O n 413 decreased with oxygen number, with C 5 H 10 N 2 O 8 and C 5 H 8 N 2 O 8 being the most abundant within their respective 414 series. 415 Some 2N-monomers have been detected in previous studies of the reaction of isoprene with NO 3 . 416 C 5 H 10 N 2 O 8 has been detected in the particle phase by Ng et al. (2008) and C 5 H 8 N 2 O 7 was detected in the gas 417 phase by Kwan et al. (2012). C 5 H 9 N 2 O 9 • has been proposed to be formed via the pathway as in Scheme 2a (Ng 418 et al., 2008), and it was directly detected in our study. C 5 H 8 N 2 O 7 species has been proposed to be a dinitrooxy 419 epoxide formed by the oxidation of nitrooxyhydroperoxide (Kwan et al., 2012), instead of being a dinitrooxy 420 ketone proposed in our study, a termination product of C 5 H 9 N 2 O 8 •. Admittedly, C 5 H 8 N 2 O 7 may contain both 421 isomers. In addition, Ng et al. (2008) detected C 5 H 8 N 2 O 6 in the gas phase, which was not detected in this study 422 likely due to the selectivity of NO 3 --CIMS. 423 One could suppose that C 5 H 7 N 2 O n • should also be formed since C5-nitrooxycarbonyl (C 5 H 7 NO 4 ) also 424 contains one double bond that can be attacked by NO 3 in a second oxidation step. However, concentrations of 425 C 5 H 7 N 2 O n were too low to assign molecular formulas with confidence except for C 5 H 7 N 2 O 9 •, clearly showing 426 that C 5 H 7 N 2 O n • was not important. This fact is consistent with the finding of Ng et al. (2008) that C5-427 nitrooxycarbonyls react slowly with NO 3 . Additionally, the peroxy radical formed in the reaction of C5-428 nitrooxycarbonyls with NO 3 likely leads to more fragmentation in H-shift as found in the OH oxidation of 429 methacrolein (Crounse et al., 2012), which may also contribute to the low abundance of C 5 H 7 N 2 O n . The presence of 430 HOM containing two N atoms is in line with the finding by Faxon et al. (2018) who detected products containing 431 two N atoms in the reaction of NO 3 with limonene, which also contain two carbon double bonds. It is anticipated 432 that for VOC with more than one double bond, NO 3 can add to all the double bonds as for isoprene and limonene. 433

3N-monomers 434
HOM containing three nitrogen atoms, C 5 H 9 N 3 O n (n=9-16), were observed. These compounds were 435 possibly peroxynitrates formed by the reaction of RO 2 (C 5 H 9 N 2 O n •) with NO 2 . The time series of C 5 H 9 N 3 O n 436 was examined to check whether they match such a mechanism. If C 5 H 9 N 3 O n were formed by the reaction of 437 C 5 H 9 N 2 O n-2 • with NO 2 , the concentration would be a function of the concentrations of C 5 H 9 N 2 O n-2 • and NO 2 as 438 follows: 439 5 9 3 n 5 9 2 2 2 a 5 9 constant and k wall is the wall loss rate. Because the products of C 5 H 9 N 2 O n-2 • and NO 2 were at their maximum at 442 the end of each period and decreased rapidly after isoprene addition (Fig. S8), the concentration should have its 443 maximum increasing rate at the end of each isoprene addition period. However, we found that only C 5 H 9 N 3 O 12, 444 15, 16 showed such a time profile (Fig. S9), while C 5 H 9 N 3 O 9, 10, 11, 13, 14 generally increased with time, different 445 from what one would expect based on the proposed pathway. Therefore, it is likely that C 5 H 9 N 3 O 12, 15, 16 were 446 mainly formed via the reaction of C 5 H 9 N 2 O n • with NO 2 , whereas C 5 H 9 N 3 O 9,10,11,13,14 were not. Moreover, 447 C 5 H 9 N 3 O 9 cannot be explained by the reaction C 5 H 9 N 2 O n • (n≥9) with NO 2 or NO 3 , because these reactions 448 would add at least one more oxygen atom. One possible pathway to form C 5 H 9 N 3 O 9 was the direct addition of 449 N 2 O 5 to the carbon double bond of C5-hydroxynitrate, forming a nitronitrate. Such a mechanism has been 450 proposed previously in the heterogeneous reaction of N 2 O 5 with 1-palmitoyl-2-oleoyl-sn-glycero-3-451 phosphocholine (POPC) because -NO 2 and -NO 3 groups were detected (Lai and Finlayson-Pitts, 1991). This 452 pathway generally matched the time series of C 5 H 9 N 3 O 9,10,11,13,14 typical of second-generation products since 453 C5-hydroxynitrate was a first-generation product. It is possible that the main pathway of C 5 H 9 N 3 O 9,10,11,13,14 was 454 the reaction of C 5 H 9 NO 4,5,6 with N 2 O 5 , although the reaction of N 2 O 5 with C=C double bonds in common alkenes 455 and unsaturated alcohols are believed to be not important (Japar and Niki, 1975;Pfrang et al., 2006). 456 3N-monomers, C 5 H 9 N 3 O 10 , has been observed in the particles formed in the isoprene+NO 3 reaction by 457 Ng et al. (2008). Here a complete series of C 5 H 9 N 3 O n were observed. C 5 H 9 N 3 O 10 was previously proposed to 458 be formed by another pathway, i.e. the reaction of RO 2 (C 5 H 9 N 2 O 9 •) and NO 3 (Ng et al., 2008). We further 459 examined the possibility of such a pathway in our study. Similar to NO 2 , if C 5 H 9 N 3 O n were formed by the 460 reaction of C 5 H 9 N 2 O n-2 • with NO 3 , the concentration would have its maximum increasing rate at the end of each 461 isoprene addition period. Among C 5 H 9 N 2 O n •, the precursors of C 5 H 9 N 3 O n , C 5 H 9 N 2 O 9, 10, 13, 14 • showed a 462 maximum increasing rate and a subsequent decrease after isoprene addition. The difference in oxygen number 463 between C 5 H 9 N 3 O 12, 15, 16 , the termination products, and C 5 H 9 N 2 O 9, 10, 13, 14 •, the corresponding RO 2 with the 464 consistent time profile is mostly two. Since the reaction of C 5 H 9 N 2 O n with NO 2 and NO 3 result an increased 465 oxygen number by two and by one, respectively, we infer that it is more likely that C 5 H 9 N 3 O 12, 15, 16 were formed 466 by the reaction of C 5 H 9 N 2 O 10, 13, 14 • with NO 2 rather than NO 3 , and thus they were likely peroxynitrates rather 467 than nitrates formed by the reaction of RO 2 with NO 3 . Since alkyl peroxynitrates decompose rapidly (Finlayson-468 Pitts and Pitts, 2000;Ziemann and Atkinson, 2012), it is possible that these compounds contained 469

peroxyacylnitrates. 470
Little attention has been paid to the RO 2 +NO 2 pathway in nighttime chemistry of isoprene in the 471 literature (Wennberg et al., 2018), which is likely due to the instability of the products. According to this 472 pathway, C 5 H 8 N 2 O n , which was proposed to be a ketone formed via C 5 H 9 N 2 O 9 • in the M2 series (Table 1) as 473 discussed above, can also comprise peroxynitrate formed by the reaction of C 5 H 8 NO n • (M1a RO 2 ) with NO 2 . 474 3N dimer such as C 5 H 9 N 3 O 10 as well as 2N-monomers such as C 5 H 8 N 2 O 8 and C 5 H 8 N 2 O 10 have been observed 475 in a recent field study in polluted cities in east China (Xu et al., 2021). 476 Similarly, C 10 H 18 N 2 O n (n=10-16) and C 10 H 15 N 3 O n (n=13-17) series (dimer 4, dimer 5, Table 2) were likely formed 494 from the accretion reaction between one M1 RO 2 and one M4 RO 2 , and between one M1 RO 2 and one M3 RO 2 495 (C 5 H 7 N 2 O 9 •). Other dimer series than dimer 1-5 were also present. However, they had quite low intensity (Fig. 4), 496 which was consistent with the low abundance of their parent monomer RO 2 . They can be formed from various 497 accretion reactions of monomer RO 2 . For example, C 10 H 19 N 3 O n can be formed by the accretion reaction of 498 C 5 H 9 N 2 O n • and C 5 H 10 NO n • (Table 2). 499

HOM dimers and their formation 477
Similar to monomers, a few species dominated in HOM dimers spectrum. The dominant dimer series were 500 C 10 H 17 N 3 O x and C 10 H 16 N 2 O x series, with C 10 H 17 N 3 O 12-14 and C 10 H 16 N 2 O 12-14 showing highest intensity among each 501 series (Fig. 4). In addition, the O/C ratio or oxidation state of HOM dimers were generally lower than that of 502 monomers (Fig. 2, Fig. 4), which resulted from the loss of two oxygen atoms in the accretion reaction of two 503 monomer RO 2 . 504 505 Figure 4. Kendrick mass defect plot for O of HOM dimers formed in the isoprene+NO 3 reaction. The size (area) 506 of circles is set to be proportional to the average peak intensity of each molecular formula during the first isoprene addition 507 period (P1). The molecular formula include the reagent ion 15 NO 3 -, which is not shown for simplicity. The species 508 labelled in grey (C 10  According to the mechanism above (R7-9), we attempt to explain the relative intensities of the dimers using 510 the signal intensities of monomer RO 2 . Assuming that the rate constant for each of HOM-RO 2 + HOM-RO 2 reaction 511 forming dimers is the same considering that all HOM-RO 2 are highly oxygenated with a number of functional groups, 512 it is expected that the dimer formed by the recombination between the most abundant RO 2 has the highest intensity. 513 The most abundant monomer RO 2 were C 5 H 9 N 2 O 9 • and C 5 H 9 N 2 O 10 • and thus the most abundant dimers are expected 514 to be C 10 H 16 (Fig. 4) attributed to the presence of less oxygenated RO 2 (with O≤5) that have a low detection sensitivity in the NO 3 -CIMS 517  due to their lower oxygenation compared with other HOM RO 2 shown above. These RO 2 may 518 react with C 5 H 9 N 2 O 9 • and C 5 H 9 N 2 O 10 •. For example, C 5 H 8 NO 5 • (RO 2 ) is proposed to be an important first-519 generation RO 2 in the oxidation of isoprene by NO 3 (Ng et al., 2008;Rollins et al., 2009;Kwan et al., 2012;520 Schwantes et al., 2015). Although C 5 H 8 NO 5 • showed very low signal in our mass spectra, it was likely to have high 521 abundance since it was the first RO 2 formed in the reaction of isoprene with NO 3 . Indeed, we found that the 522 termination products of C 5 H 8 NO 5 • such as C 5 H 9 NO 5 , C 5 H 7 NO 4 , and C 5 H 9 NO 4 had high abundance in another study, 523 indicating the high abundance of C 5 H 8 NO 5 •. The accretion reaction of C 5 H 8 NO 5 • with C 5 H 9 N 2 O 9-10 • and C 5 H 8 NO 9-524 10 • can explain the high abundance of C 10 H 17 N 3 O 12-14 and C 10 H 16 N 2 O 12-14 among all dimers. 525 Provided that C 5 H 8 NO 5 • is abundant, we still cannot explain the relative intensity of C 10 H 17 N 3 O 12 , 526 C 10 H 17 N 3 O 13 , and C 10 H 17 N 3 O 14 that were all formed by the accretion reaction with C 5 H 8 NO 5 •. C 10 H 17 N 3 O 12 should 527 have the highest intensity among C 10 H 17 N 3 O 12-14 as its precursor RO 2 , C 5 H 9 N 2 O 9 •, is the most abundant. This 528 suggests that accretion reactions other than those of C 5 H 8 NO 5 • with C 5 H 9 N 2 O 9-10 • also contributed to C 10 H 17 N 3 O 12-529 14 . Admittedly, the assumption of different RO 2 having similar rate constants in accretion reactions may not be valid. 530 For example, self-reaction of tertiary RO 2 is slower than secondary and primary RO 2 (Jenkin et al., 1998;Finlayson-531 Pitts and Pitts, 2000). Different rate constants may also lead to the observation that the most abundant dimers could 532 not be explained the most abundant RO 2 . 533  The time profiles of C 10 H 16 N 2 O n indicate contributions of both the first-and second-generation products. 539 The dominance of the first-or second-generation products depended on the specific compounds. Most C 10 H 16 N 2 O n 540 compounds increased instantaneously after isoprene additions, indicating significant contributions of first-generation 541 products. Since the formation of C 10 H 16 N 2 O n likely involved C 5 H 8 NO 5 • as discussed above, the instantaneous 542 increase may result from the increase of C 5 H 8 NO 5 • as well as other first-generation RO 2 . After the initial increase, 543 C 10 H 16 N 2 O 10-12 then decayed with time (Fig. 5) while C 10 H 16 N 2 O 13-15 increased again in the later phase of a period 544 and when NO 2 and O 3 were added. The second increase indicated that C 10 H 16 N 2 O 13-15 may contain more than one 545 isomer, which had different production pathways. As discussed above, C 5 H 8 NO n • can be either a first-generation 546 RO 2 formed directly via the reaction of isoprene with NO 3 and autoxidation, or a second-generation RO 2 , e.g. formed 547 via the reaction of with C 5 H 8 O 2 with NO 3 . Therefore the second increase of C 10 H 16 N 2 O 13-15 may result from the 548 reaction of two first-generation RO 2 and of two second-generation RO 2 or between one first-generation and one 549 second-generation RO 2 . The increase of C 10 H 16 N 2 O 14-15 after isoprene addition was not large, indicating the 550 larger contributions from second-generation products compared with other C 10 H 16 N 2 O n . Overall, as the number 551 of oxygen increased, the contribution of second-generation products to C 10 H 16 N 2 O n increased. 552 In contrast to C 10 H 16 N 2 O n series, C 10 H 18 N 4 O n increased gradually after each isoprene addition and then 553 decreased afterward (Fig. 6), either naturally or after isoprene additions, which is typical for second-generation 554 products. Since C 10 H 18 N 4 O n was likely formed by the accretion reaction of C 5 H 9 N 2 O n • (RO 2 ), the time profile 555 of C 10 H 18 N 4 O n was as expected since C 5 H 9 N 2 O n • was formed via the reaction of NO 3 with first-generation 556 products C 5 H 9 NO n . The C 10 H 18 N 4 O n concentration depended on the product of the concentrations of two 557 C 5 H 9 N 2 O n •. Taking C 10 H 18 N 4 O 16 as an example, its concentration can be expressed as follows: 558 10 18 4 16 5 9 2 9 5 9 2 9 10 18 4 16 When the concentration of C 5 H 9 N 2 O 9 • increased, the changing rate of C 10 H 18 N 4 O 16 was positive and increased 560 and thus the concentration of C 10 H 18 N 4 O 16 increased. When the concentration C 5 H 9 N 2 O 9 • decreased sharply 561 after isoprene additions, the changing rate of C 10 H 18 N 4 O 16 decreased and even became negative values, and thus 562 the concentration of C 10 H 18 N 4 O 16 decreased after isoprene addition. 563 Similar to the C 10 H 16 N 2 O n series, while C 10 H 17 N 3 O n first increased instantaneously with isoprene 564 addition, it increased again during the later stage of each period (Fig. S10), showing a mixed behavior of the 565 first-generation products and second-generation products. The time series of C 10 H 17 N 3 O n was as expected in 566 general because C 10 H 17 N 3 O n was likely formed via the accretion reaction of C 5 H 8 NO n • (M1 RO 2 ) and 567 C 5 H 9 N 2 O n • (M2 RO 2 ), which were first-or second-generation, and second-generation RO 2 , respectively, 568 Some dimers that cannot be explained by accretion reactions such as C 10 H 16 N 3 O n (n=12-15) •, C 10 H 17 N 2 O n (n=11-574 12) •, C 10 H 16 NO n (n=10-14) •, C 10 H 15 NO n (n=9-12) , C 10 H 17 NO n (n=9-15) were also observed. These dimers had low abundance. 575 We note that due to their low signals in the mass spectra, their assignment and thus range of n may be subject to 576 uncertainties. Since C 10 H 16 NO n (n=10-16) •, C 10 H 16 N 3 O n (n=12-15) •, and C 10 H 17 N 2 O n • contain unpaired electrons, they 577 cannot be formed via the direct accretion reaction of two RO 2 . Instead, C 10 H 16 N 3 O n (n=12-15) • (dimer R1) and 578 C 10 H 17 N 2 O n • (dimer R2) were likely RO 2 formed by the reaction of HOM dimers containing a double bond (dimer 579 1) with NO 3 and with OH, respectively, followed by the reaction with O 2 . 580 C 10 H 16 N 2 O n +NO 3 +O 2  C 10 H 16 N 3 O n • R 10 581 C 10 H 16 N 2 O n +OH+O 2  C 10 H 17 N 2 O n • R 11 582 The corresponding termination products of C 10 H 16 N 3 O n • RO 2 series such as C 10 H 15 N 3 O n (ketone), C 10 H 17 N 3 O n 583 (hydroperoxide/alcohol) were also observed, although these compounds can also be formed via reactions between 584 two RO 2 radicals (R9 and R11). Among the termination products, C 10 H 15 N 3 O n had low intensity. Reaction R13 and 585 the termination reaction of C 10 H 17 N 2 O n • with HO 2 provided an additional pathway to C 10 H 17 N 3 O n besides the R9 586 pathway discussed above. Similarly, other dimers may also be formed by the termination reactions of dimer RO 2 587 with RO 2 or HO 2 . E.g., Only C 10 H 16 NO n • with n≥10 were detected, while according to the mechanism of self-reaction between C 5 H 8 NO n •, 593 the n range of C 10 H 16 NO n • is expected to be 7-14. The absence of C 10 H 16 NO n(n<10) • is likely attributed to their low 594 abundance, which might result from low precursor concentrations, low reaction rates with isoprene, and/or faster 595 reactive losses with other radicals. Such a reaction of RO 2 with isoprene has been proposed by Ng et al. (2008) and 596 Kwan et al. (2012). The corresponding termination products of C 10 H 16 NO n • are C 10 H 15 NO n (ketone) and C 10 H 17 NO n 597 species (hydroperoxide/alcohol). C 10 H 17 NO n species showed a time profile of typical first-generation products (Fig.  598 S11), i.e. increasing immediately with isoprene addition and then decaying with time. This behaviour further supports 599 the possibility of reaction R13. Yet, the reaction rate of alkene with RO 2 is likely low due to the high activation 600 energy (Stark, 1997(Stark, , 2000. It is worth noting that to our knowledge no experimental kinetic data on the addition of 601 RO 2 to alkenes in the gas phase in atmospheric relevant conditions are available, though fast, low-barrier ring closure 602 reactions in unsaturated RO 2 radicals have been reported Peeters, 2004, 2012;Kaminski et al., 2017;603 Richters et al., 2017;Chen et al., 2021). We would like to note that there is unlikely interference to C 10 -HOM from 604 monoterpenes, which has been reported previously (Bernhammer et al., 2018), as the concentration of monoterpenes 605 in the chamber during this study was below the limit of detection, which was ~50 ppt (3σ). 606 Some of the dimers discussed above have been observed in previous studies. Ng et al. (2008) found 607 C 10 H 16 N 2 O 8 and C 10 H 16 N 2 O 9 in the gas phase and C 10 H 17 N 3 O 12 , C 10 H 17 N 3 O 13 , C 10 H 18 N 4 O 16 , and C 10 H 17 N 5 O 18 in the 608 particle phase. C 10 H 16 N 2 O 8 and C 10 H 16 N 2 O 9 were also observed in our study, but their intensity in the MS was too 609 low to assign molecular formulas with high confidence. The low intensity may be due to the low sensitivity of 610 C 10 H 16 N 2 O 8, 9 in NO 3 --CIMS. According to modelling results of the products formed in cyclohexene ozonolysis by 611 Hyttinen et al. (2015), at least two hydrogen bond donor functional groups are needed for a compound to be detected 612 in a nitrate CIMS. As C 10 H 16 N 2 O 8 and C 10 H 16 N 2 O 9 have no and only one H-bond donor function groups, respectively, 613 they are expected to have low sensitivity in NO 3 --CIMS. Moreover, the low intensity can be partly attributed to the 614 much lower isoprene concentrations used in this study compared to previous studies, leading to the low concentration 615 of C 10 H 16 N 2 O 8 and C 10 H 16 N 2 O 9 (Ng et al., 2008 The formation pathways of dimer RO 2 C 10 H 16 N 3 O n (n=12-15) and C 10 H 17 N 2 O n are shown above (reaction R10 and 630 R11). 631 The other trimers were likely formed via similar pathways (Table 2 and Supplement S2). Since NO 3 --CIMS 632 cannot provide the structural information of these HOM trimers, we cannot elucidate the major pathways. However, 633 in all these pathways, dimer-RO 2 is necessary to form a trimer, and most of the dimer-RO 2 formation pathways 634 require at least one double bond in the dimer molecule except for the reaction of RO 2 with isoprene. Since one 635 double bond has already reacted in the monomer-RO 2 formation, we anticipate that in the reaction with NO 3 it is 636 more favourable for precursors (VOC) containing more than one double bonds to form trimer molecules than 637 precursors containing only one double bond, as it is easier to generate new RO 2 radicals from these dimers by 638 attack on the remaining double bond(s). 639 The time profile of C 15 H 24 N 4 O n showed the mixed behavior of first-and second-generation products (Fig.  640 S13), consistent with the mechanism discussed above since C 5 H 8 NO n • and C 10 H 16 N 3 O n • were of first-or second-641 generation and second-generation, respectively. The contributions of the second-generation products became 642 larger as the number of oxygen atoms increased. In contrast, C 15 H 25 N 3 O n showed instantaneous increase with 643 isoprene addition (Fig. S14), which was typical for time profiles of first-generation products. Both proposed 644 formation pathways of C 15 H 25 N 3 O n (RS6 and RS7) contained a second-generation RO 2 , which was not in line with 645 the time profile observed. The observation cannot be well explained, unless we assume molecular adducts of a dimer 646 with one monomer. It is also possible that some C 10 H 17 N 2 O n • were formed very fast or that there were other 647 formation pathways of C 15 H 25 N 3 O n not accounted for here. 648

Contributions of monomers, dimer, and trimers to HOM 649
The concentration (represented by peak intensity) of monomers was higher than that of dimers, but overall 650 their concentrations remained of the same order of magnitude (Fig 1a, inset). The concentration of trimers was much 651 lower than that of monomers and dimers. The relative contributions of monomers, dimers, and trimers evolved in 652 time due to the changing concentration of each HOM species. Comparing the contributions of various classes of 653 HOM in period 1 with those in periods 1-6 reveals that the relative contribution of monomers increased with time, 654 especially that of 2N-monomers, while the contribution of dimers decreased. This trend is attributed to the larger wall 655 loss of dimers compared to monomers because of their lower volatility and also to the continuous formation of 656 second-generation monomers, mostly 2N-momomers. Overall, the relative contribution of total HOM monomers 657 decreased immediately after isoprene addition while the contribution of HOM dimers increased rapidly (Fig. S15), 658 which was attributed to the faster increase of dimers intensity due to their rapid formation. Afterwards, the 659 contribution of monomers to total HOM gradually increased and that of dimers decreased, which was partly due to 660 the faster wall loss rate of dimers and to the continuous formation of second-generation monomers. 661

Yield of HOM 662
The HOM yield in the oxidation of isoprene by NO 3 was estimated using the sensitivity of H 2 SO 4 . It was 663 derived for the first isoprene addition period to minimize the contribution of multi-generation products and to better 664 compare with the data in literature, thus denoted as primary HOM yield (Pullinen et al., 2020) and was estimated to 665 be 1.2% +1.3% -0.7% . The uncertainty was estimated as shown in the Supplement S1. Despite the uncertainty, the primary 666 HOM yield here was much higher than the HOM yield from the ozonolysis and photooxidation of isoprene (Jokinen 667 et al., 2015). The difference may be attributed to the more efficient oxygenation in the addition of NO 3 to carbon 668 double bonds. Compared with the reaction with O 3 or OH, the initial peroxy radicals contains 5 oxygen atoms when 669 isoprene reacts with NO 3 , while the initial peroxy radicals contains only 3 oxygen atoms when reacting with OH, and 670 the ozonide contains 3 oxygen atoms in the case of O 3. 671

4
Conclusion and implications 672 HOM formation in the reaction of isoprene with NO 3 was investigated in the SAPHIR chamber. A number 673 of HOM monomers, dimers, and trimers containing one to five nitrogen atoms were detected, and their time-674 dependent concentration profiles were tracked throughout the experiment. Some formation mechanisms for various 675 HOM were proposed according to the molecular formula identified, and the available literature. HOM showed a 676 variety of time profiles with multiple isoprene additions during the reaction. First-generation HOM increased 677 instantaneously after isoprene addition and then decreased while second-generation HOM increased gradually and 678 then decreased with time, reaching a maximum concentration at the later stage of each period. The time profiles 679 provide additional constraints on their formation mechanism beside the molecular formula, suggesting whether they 680 were first-generation products or second-generation products or a combination of both. 1N-monomers (mostly C 5 ) 681 were likely formed by NO 3 addition to a double bond of isoprene, forming monomer RO 2 , followed by autoxidation 682 and termination via the reaction with HO 2 , RO 2 , and NO 3 . Time series suggest that some 1N-monomer could also be 683 formed by the reaction of first-generation products with NO 3 , and thus be of second-generation. 2N-monomers were 684 likely formed via the reaction of first-generation products such as C5-hydroxynitrate with NO 3 and thus second-685 generation products. 3N-monomers likely comprised peroxy/peroxyacyl nitrates formed by the reaction of 2N-686 monomer RO 2 with NO 2 , and possibly nitronitrates formed via the direct addition of N 2 O 5 to the first-generation 687 products. HOM dimers were mostly formed by the accretion reactions between various HOM monomer RO 2 , either 688 first-generation or second-generation or with the contributions of both, and thus showed time profiles typical of either 689 first-generation products, or second-generation products, or a combination of both. Additionally, some dimers peroxy 690 radicals (dimer RO 2 ) were formed by the reaction of NO 3 with dimers containing a C=C double bond. HOM trimers 691 were proposed to be formed by accretion reactions between the monomer RO 2 and dimer RO 2 . 692 Overall, both HOM monomers and dimers contribute significantly to total HOM while trimers only 693 contributed a minor fraction. Within both the monomer and dimer compounds, a limited set of compounds dominated 694 the abundance, such as C 5 H 8 N 2 O n , C 5 H 10 N 2 O n , C 10 H 17 N 3 O n , and C 10 H 16 N 2 O n series. 2N-monomers, which were 695 second-generation products, dominated in monomers and accounted for ~34% of all HOM, indicating the important 696 role of second-generation oxidation in HOM formation in the isoprene+NO 3 reaction. Both RO 2 autoxidation and 697 "alkoxy-peroxy" pathways were found to be important for 1N-and 2N-HOM formation. In total, the yield of HOM 698 monomers, dimers, and trimers accounted for 1.3% +1.3% -0.7% of the isoprene reacted, which was much higher than the HOM 699 yield in the oxidation of isoprene by OH and O 3 reported in the literature (Jokinen et al., 2015). This means that the 700 reaction of isoprene with NO 3 is a competitive pathway of HOM formation from isoprene. 701 The HOM in the reaction of isoprene with NO 3 may account for a significant fraction of SOA. If all the 702 HOM condense on particles, using the molecular weight of the HOM with the least molecular weight observed in 703 this study (C 5 H 9 NO 6 ), the HOM yield corresponds to a SOA yield of 3.6%. Although SOA concentrations were not 704 measured in this study, Ng et al. (2008) reported a SOA yield of the isoprene+NO 3 reaction of 4.3%-23.8%. Rollins 705 et al. (2009) reported a SOA yield of 2% at low organic aerosol loading (~0.52 μg m -3 ) and 14% if the further 706 oxidation of the first-generation products are considered in the isoprene+NO 3 reaction. Comparing the potential 707 SOA yield produced by HOM with SOA yields in the literature suggests that HOM may play an important role in the 708 SOA formation in the isoprene+NO 3 reaction. 709 T he R O 2 lifetime is approximately 20-50 s in our experiments, which is generally comparable or shorter than 710 the lifetime of RO 2 in the ambient atmosphere at night, varying from several 10 s to several 100 s (Fry et al., 2018), 711 depending on the NO 3 , HO 2 , and RO 2 concentrations. Assuming a HO 2 , RO 2 , and NO 3 concentration of 5 ppt, 5 ppt 712 (Tan et al., 2019), and 300 ppt (Brown and Stutz, 2012) respectively, the RO 2 lifetime in our study is comparable to 713 the nighttime RO 2 lifetime (50 s) found in urban locations and areas influenced by urban plume. In areas with longer 714 RO 2 lifetime such as remote areas, the autoxidation is expected to be more important relative to bimolecular reactions. 715 This may enhance HOM yield and thus enhance SOA yield. However, on the other hand, at lower RO 2 concentration 716 and thus longer RO 2 lifetime, reduced rates of RO 2 +RO 2 reactions producing low-volatility dimers can reduce the 717 SOA yield via reducing dimer yield Pullinen et al., 2020). The RO 2 fate in our experiments 718 is dominated the reaction RO 2 +NO 3 with significant contribution of RO 2 +RO 2 , which can also represent the RO 2 fate 719 in the urban areas and areas influenced by urban plume. Our experiment condition cannot represent the chemistry in 720 HO 2 -dominated regions such as clean forest environment (Schwantes et al., 2015). 721 We observed the second-generation products formed by the reaction of first-generation products. The 722 lifetime of first-generation nitrates in the ambient atmosphere, according their rate constants with OH and NO 3 723 (Wennberg et al., 2018), are ~5 h and ~1.3-4 h, respectively, with respect to the reaction with OH and NO 3 assuming 724 a typical OH concentration of 2×10 6 molecules cm -3 Tan et al., 2019) and NO 3 concentration of 100-725 300 ppt in urban areas (Brown and Stutz, 2012). Therefore, they have the chance to react further with OH and NO 3 726 at dawn. In our experiments, the lifetimes of these first-generation nitrates with respect to OH and NO 3 are 727 comparable to the aforementioned lifetime due to comparable OH and NO 3 concentrations with these ambient 728 conditions. Therefore, our findings on the second-generation products are relevant to the ambient urban atmosphere 729 and areas influenced by urban plumes. Some of these products such as C 5 H 810 N 2 O 8 and multi-generation 730 nitrooxyorganosulfates have been observed in recent field studies in polluted megacities in east China (Hamilton et 731 al., 2021;Xu et al., 2021). 732

Data availability 733
All the data in the figures of this study are available upon request to the corresponding author (t.mentel@fz-juelich. 734 de or dfzhao@fudan.edu.cn). 735