The experiments (temperature: 298 ± 2 K; pressure: 1 atm; dry conditions: relative humidity <1%) were carried out in a newly constructed free-jet flow-tube system (Fig. 1), located in the Physicum building at the University of Helsinki. Similar to the design by Berndt et al. (2015b), our flow-tube system consists of a quartz tube (length: 2 m, inner diameter: 15 cm) and a movable stainless-steel injector (length: 1.8 m, inner diameter: 8 mm) with a nozzle (inner diameter: 3 mm). A total flow of 100 L min⁻¹ is supplied by a 250 L min⁻¹ zero-air generator (ZA-737-250, Tisch Environmental) and regulated by various mass flow controllers (MKS, Inc.). Oxidants such as O₃ or NO₃ are carried by 5 L min⁻¹ of zero air to the central injector and then mixed into the 95 L min⁻¹ main gas flow, which contains reactants such as various VOCs. The narrow nozzle at the end of the injector enables a high flow velocity, causing turbulent mixing at the beginning of the reaction. As the flow slows down, it gradually becomes laminar, as also observed visually using smoke (see Sect. S1 in the Supplement for details). The open outlet design and the exhaust port placed downstream (Fig. 1) help maintain laminar flow while sampling takes place at the center of the outlet. The experimental design allows investigations under nearly wall-free conditions (Berndt et al., 2015b). To enable the use of a box model for simulating reactions inside the free-jet flow-tube system, effective reaction times were experimentally determined via ozonolysis of 2,3-dimethyl-2-butene (TME, ≥ 99 %, Sigma-Aldrich) at varying reaction distances (Fig. S1 and Sect. S1) (Berndt et al., 2015b): 2.5 s (50 cm), 4.6 s (70 cm), 6.4 s (90 cm), and 8.3 s (110 cm).

Using the free-jet flow-tube system at an effective reaction time of 8.3 s, we investigated the formation of RO₂ radicals and closed-shell products in the NO₃ oxidation of five MTs, i.e., α-pinene (AP, 99 %, Sigma-Aldrich), Δ-3-carene (99 %, Sigma-Aldrich), limonene (96 %, Sigma-Aldrich), β-pinene (BP, 99 %, Sigma-Aldrich), and β-myrcene (90 %, Sigma-Aldrich). These precursors were injected into the main gas flow using a 1.5 L min⁻¹ zero-air flow and a syringe pump system (Fusion F100T2, Chemyx, Inc.).

O₃ and NO₂, generated from an ozone generator (Dasibi 1008-PC) and a NO₂ cylinder (0.1 % NO₂ in N₂, Linde Gas) respectively, were mixed in an external 0.7 L cylindrical glass reactor (Meder et al., 2025) to produce NO₃ and N₂O₅. The total flow through the pre-reactor was fixed at 1 L min⁻¹, resulting in a reaction time of 42 s and concentrations of O₃ and NO₂ ([O₃]0,pre-reactor=1200–1800 ppb and [NO₂]0,pre-reactor=1450–8600 ppb) approximately 100 times higher than those in the free-jet flow-tube after dilution. An additional 4 L min⁻¹ of zero air was added to the pre-reactor outflow before it entered the injector. The NO₃ concentration in the reaction region of the flow-tube was sustained at a few ppt (Fig. S2), which is comparable to atmospheric levels (Ayres et al., 2015; Bates et al., 2022). NO levels were negligible due to the lack of NO₂ photolysis, consistent with the very low signals from our NO_x analyzer and the lack of detectable products from NO termination.

The experiments were designed to first ramp up MT concentrations in four stages, followed by a ramp-up of NO₂, with background stages included throughout (Fig. 2). This approach allowed us to distinguish products formed via NO₃ oxidation from those formed by O₃/OH oxidation (see Sect. 3.1). The initial concentrations of each stage shown at the top of each subplot in Fig. 2 refer to the values present in the total flow of 100 L min⁻¹, without any chemical conversion. Since NO₂ and O₃ were reacted in the pre-reactor before entering the flow-tube, their actual concentrations at the start of the oxidation process were slightly lower than the initial values. No particles were present in the input gas, and particle formation did not occur due to low reactant conversion and the short reaction time (Sect. S1).

Gas-phase RO₂ radicals and closed-shell products containing two or more oxygen atoms were measured using a chemical ionization mass spectrometer (CIMS, Tofwerk AG/Aerodyne Research, Inc.), coupled with an Eisele-type inlet (Eisele and Tanner, 1993) and operated with either diethylamine (DEA, C₄H₁₁N, ≥ 99.5 %, Sigma-Aldrich) or isotopically labeled nitric acid (H¹⁵NO₃, ∼10 N in H₂O, 98 atom % ¹⁵N, Sigma-Aldrich) as the reagent ion source (referred to as DEA- or nitrate-CIMS). The DEA mode allows detection of compounds with two or more oxygen atoms, while the nitrate mode is highly selective for HOMs (Cai et al., 2024; Ehn et al., 2014; Riva et al., 2019). The ¹⁵N-labeled nitric acid was used in this study to unambiguously identify the organic nitrate products by distinguishing the N originating from unlabeled oxidant NO₃ (formed via NO₂ + O₃) from the labeled reagent ions. The sampling flow rate was 10 L min⁻¹, and additional operational details are provided in Sect. S2. The CIMS was equipped with a long time-of-flight mass spectrometer (LTOF), achieving a mass resolution of ∼7000 at mass-to-charge ratio (m/z) of 149 Th in DEA mode, and ∼8500 at m/z 125 Th in nitrate mode. Sampling was conducted through a 90° bent 3/4-inch stainless-steel inlet tube (total length: 40 cm; 25 cm from the Eisele inlet to the bend, and 15 cm from the bend to the flow-tube outlet), positioned to sample from the center of the open outlet of the flow-tube. The 90° bend allows side sampling without disturbing the laminar outflow. The reaction time within the inlet is calculated to be 0.46 s, resulting in a total effective reaction time of roughly 8.8 s (at the reaction distance of 110 cm) for measurements taken by the CIMS. The same inlet tube was used in sulfuric acid calibration experiments for the CIMS (Kürten et al., 2012). Based on a two-dimensional (2-D) flow reactor calibration model (He et al., 2023), a calibration factor of 7.3×109 cm⁻³ (at least ± 50 %) was determined, and applied for both DEA and nitrate mode for product quantification (see Sect. S2).

A Vocus proton-transfer-reaction time-of-flight mass spectrometer (Vocus PTR-TOF, Tofwerk AG) was used to validate the syringe pump system (see Sect. S2 for details). Initial concentrations of O₃ and NO₂ were measured using gas monitors: a photometric O₃ analyzer (model 400, Teledyne API) and an NO-NO₂ analyzer (model T200UP, Teledyne API), respectively (see Sect. S2 for details). The O₃ analyzer was also used to quantify O₃ consumption during the reaction time characterization experiments involving the reaction TME + O₃. Data from both the Vocus PTR-TOF and DEA-/nitrate-CIMS were analyzed using the Igor-based Tofware software (Tofware_3_3_0).

We constructed a simple 0-D box model to describe the chemical reactions occurring in the flow-tube system with a defined effective reaction time. Rather than simulating specific RO₂ or closed-shell products, the model was primarily used to estimate the concentrations of reacted MTs (or equivalently, the total amount of products) resulting from NO₃, O₃, and OH oxidation, based on the dominant reaction pathways (Table S1 in the Supplement). Specifically, in the case of the flow-tube system, the model was used in batch mode, meaning no continuous input was applied and only the initial concentrations of precursors were set. The simulation spans the entire experimental setup, from the pre-reactor through the injector to the free-jet flow-tube, as illustrated in Fig. S2. The NO₃ oxidation product molar yields (or fractions) were calculated via dividing the measured product concentrations by the modeled MT concentration ([MT]) reacted by the NO₃ radical (Shen et al., 2021).

A total of ten sets of NO₃ oxidation experiments were conducted, two for each of the five MTs using both DEA- and nitrate-CIMS, with time series presented in Figs. 2 and S3–S6. The experimental procedure varied the initial concentrations of MT (i.e., [MT]0), NO₂, and O₃ across distinct stages (concentrations for each stage shown directly at the top of the plots in Figs. 2 and S3–S6). The sequence of these stages included: two initial background stages (with and without MTs); four MT-ramping stages (varying [MT]₀ from 10 to 120 ppb); three background stages (ramping [MT]₀ down to 20 ppb); three NO₂-ramping stages (varying [NO₂]₀ from 32.5 to 86 ppb); a single O₃ perturbation stage (with decreased [NO₂]₀ and a 50 % increase in [O₃]0); and finally, three different background stages. The experimental stages, excluding background stages, are numbered from 1 to 8 (Fig. 2).

During the MT-ramping stages (Stages 1–4 in Fig. 2), products from O₃ or OH (produced from MT + O3) oxidation are expected to increase substantially, as the chemical conversion ratio of both MT and O₃ is small (Sect. S1). In contrast, NO₃ oxidation products would show a much slower increase, limited by the NO₃ radical concentration. This differential behavior is clearly illustrated in Fig. S7, where the ratio of reacted [MT] by NO₃ to total reacted [MT] by all oxidants is shown to decrease significantly as [MT]₀ is ramped from 10 to 120 ppb. Conversely, during the NO₂-ramping stages (Stages 5–7), NO₃ oxidation products would increase notably due to the rising NO₃ radical concentration, while O₃/OH oxidation products would decrease slightly due to enhanced O₃ consumption by NO₂. In the O₃ perturbation stage (Stage 8), where [O₃]₀ was increased by 50 %, O₃/OH oxidation products are expected to increase accordingly, while NO₃ oxidation products are expected to stay almost unchanged or even decrease due to the lower [NO₂]₀. This systematic design allowed us to attribute product origins. For example, in the AP experiments (Fig. 2), compounds such as C₁₀H₁₅O_4,8,10 and C₁₀H₁₄O₇ were identified as ozonolysis products, while C₁₀H₁₆NO_5,7,9 and C₁₀H₁₆O₂ were identified as NO₃ oxidation products. It should be noted that for the DEA mode (Figs. 2A, and S3A–S6A), the injection of MT without added oxidants increased the signal for certain products (e.g., C₁₀H₁₆O2), possibly due to MT impurity or surface reactions. Consequently, the background stages with MT injection were used for background subtractions.

The volatility of multifunctional organic molecules is a function of their carbon number and the type and quantity of functional groups they contain. While a high oxygen-to-carbon ratio (O : C) typically indicates low volatility, it has been suggested that the nitrate group (–ONO₂) contributes to volatility reduction by an amount comparable to a single hydroxyl group (–OH) (Chuang and Donahue, 2016). Therefore, products with a nitrate group (e.g., those initiated by NO₃ radicals) necessitate a higher total oxygen atom count than the common threshold (≥6 oxygen atoms) established for non-nitrate HOMs from O₃/OH oxidation (Bianchi et al., 2019) to reach an equivalent Low Volatility Organic Compound (LVOC) or Extremely LVOC (ELVOC) regime.

O₃, OH or NO₃ can initiate oxidation by directly adding to a double bond, leading to a C-centered radical followed by fast O₂ addition, which yields a primary RO₂ (Atkinson and Arey, 2003) that can then undergo autoxidation (Ehn et al., 2014). The primary peroxy radicals will contain 2–5 O atoms, depending on oxidant and whether the cleavage of the double bond results in fragmentation or not. It is worth noting that a minor oxidation pathway of H-abstraction by OH radical was previously reported (Shen et al., 2022; Vereecken and Peeters, 2000), producing a sequence of radicals such as C₁₀H₁₅O_2,3,4. However, we did not see any noticeable amount of radical C₁₀H₁₅O_x that could be attributed to NO₃ oxidation, meaning that its possible H-abstraction pathways were negligible in our flow-tube experiments.

The recommended definition for HOMs is that they have undergone autoxidation and contain 6 or more O-atoms. We take a slightly more restrictive approach here, since NO₃ oxidation adds more O-atoms to the RO₂ than the more often studied O₃ and OH oxidation. When using the term “HOM”, we use the following criteria: RO₂ radicals with 8 or more oxygen atoms (C₁₀H₁₆NO_x, x≥8), closed-shell products with 7 or more oxygen atoms (C₁₀H_15,17NO_x, x≥7), and peroxynitrates with 10 or more oxygen atoms (C₁₀H₁₆N₂O_x, x≥10); HOM dimers are defined as species with 9 or more oxygen atoms (starting from C₂₀H₃₂N₂O₉, formed by C₁₀H₁₆NO₅ + C₁₀H₁₆NO6). We also include “cross dimers” from NO₃-initiated RO₂ reacting with O₃- or OH-initiated RO₂, i.e. C₂₀H₃₁NO_x/C₂₀H₃₃NO_x with x≥8 or x≥7, respectively, as the initial RO₂ from O₃/OH oxidation has four or three oxygen atoms.

A comparison of concentrations for major monomer compounds (O ≥7), dimers (O ≥11), and peroxynitrates (O ≥10) between nitrate and DEA modes is presented in Fig. S8. For all MTs except carene, the first-autoxidation RO₂ (C₁₀H₁₆NO₇) was detected much more efficiently by the DEA mode. Conversely, the nitrate mode exhibited greater selectivity for products resulting from two or more autoxidation steps (i.e., RO₂ with O ≥9, or O ≥8 if one RO₂ to RO conversion occurred) for all MTs except myrcene. Closed-shell monomers corresponding to these two-autoxidation-step RO₂ species (with O ≥8 or 7) showed comparable concentrations between the two modes, with differences being less than one order of magnitude only for BP and myrcene. Therefore, the monomer results are consistent with the fact that nitrate-CIMS is usually utilized for investigating HOMs due to its high selectivity (Bianchi et al., 2019; Riva et al., 2019). It is notable that some defined HOM dimers exhibited higher signals in the DEA mode (Fig. S8). Furthermore, the HOM dimers C₂₀H₃₂N₂O_9,10 were absent from nitrate spectra (Fig. 4), despite their non-negligible signals in the DEA spectrum of MTs such as BP (Fig. 3D).

As the DEA and nitrate modes collectively cover a wide range of oxidation products (O ≥2), their representative spectra (Figs. 3 and 4) provide insightful molecular information on the NO₃ oxidation products of the five MTs. Normalized signals are displayed for the experimental stage 6 ([MT]0=20 ppb, [O₃]0=12 ppb, and [NO₂]0=50 ppb), where the NO₃ radical dominates the oxidation (Fig. S7), making these spectra highly representative of the NO₃-initiated chemistry. It is worth noting that products in the DEA mode were charged by clustering with C₄H₁₂N⁺, while products in the nitrate mode were charged by clustering with either a primary ion monomer (NO3- or ¹⁵NO3-) or a dimer (H¹⁵NO3⋅ ¹⁵NO3- or HNO3⋅ ¹⁵NO3- or HNO3⋅ NO3-) (see Fig. S9 for detailed charging scheme). For further investigation of the molar yields and trends of individual products as a function of reacted [MT] by NO₃ radicals, Figs. 5 and S10 utilize data from five experimental stages (2 and 5–8) with [MT]0=20 ppb and the NO₃ oxidation was the dominant oxidation process (Fig. S7).

The DEA-CIMS spectra (Fig. 3) show that the closed-shell species C₁₀H₁₆O₂ was the dominant product for limonene, AP, and carene, with yields exceeding 50 % for the former two (Fig. 5A and C). This finding is consistent with earlier chamber studies which identified pinonaldehyde and endolim as the major NO₃ oxidation products of AP (reported yields of 39 %–71 %) and limonene (reported yields of 25 %–72 %), respectively (Hallquist et al., 1999; Spittler et al., 2006; Wängberg et al., 1997). Although the yield of caronaldehyde from carene + NO₃ was previously estimated to be minor (2 %–3 %; Hallquist et al., 1999), our results suggest that C₁₀H₁₆O₂ represents the largest single molar yield for carene at approximately 10 % (Fig. 5B). The formation of C₁₀H₁₆O₂ can be attributed to bimolecular reactions of the peroxy radical C₁₀H₁₆NO₅ forming the nitrooxy alkoxy radical (RO) C₁₀H₁₆NO₄. This RO radical then undergoes nitrooxy-side β-scission (i.e., breaking the C–C bond in ⋅ O–C–C–ONO₂), a process followed by NO₂ loss, resulting in the C₁₀H₁₆O₂ product (Fig. S11) (Bates et al., 2022; Draper et al., 2019; Kurtén et al., 2017; Novelli et al., 2021). The comparative low C₁₀H₁₆O₂ yield observed from carene + NO₃ is consistent with its alkoxy radical C₁₀H₁₆NO₄ tending toward alkyl-side β-scission (i.e., breaking of the RC–CO⋅ bond), which favors further autoxidation over C₁₀H₁₆O₂ formation (Fig. S11) (Draper et al., 2019; Kurtén et al., 2017).

This favored alkyl-side β-scission for carene would initiate a sequence of RO₂ radicals (C₁₀H₁₆NO_6,8,10), aligning with the high signals of C₁₀H₁₆NO_8,10 observed (Figs. 3B–5B). The relative low concentration of C₁₀H₁₆NO₆ suggests rapid autoxidation to the more oxygenated C₁₀H₁₆NO₈. Conversely, the absence of C₁₀H₁₆NO₈ and the low signals of C₁₀H₁₆NO₆ for AP and limonene align with their high yields of C₁₀H₁₆O₂ (Figs. 3–5), reinforcing that the alkyl-side β-scission is unfavored for these two MTs. For limonene, NO₃ addition could also occur at the exocyclic double bond forming C₁₀H₁₆NO₅, then leading to the formation of C₁₀H₁₆O₂ via bimolecular reactions or initiation of autoxidation (Mayorga et al., 2022). The dominance of odd-oxygen-number RO₂ (C₁₀H₁₆NO_7,9) for AP and limonene (Figs. 3–5) indicates “direct” autoxidation steps from C₁₀H₁₆NO₅ with minor RO₂ to RO conversion. It is noteworthy that, for limonene, the second NO₃ addition to the double bond of C₁₀H₁₆O₂ could directly produce C₁₀H₁₆NO₇, followed by autoxidation to C₁₀H₁₆NO_9,11 (Guo et al., 2022). But this second NO₃ addition was unfavored due to the short effective reaction time at 8.8 s. Overall, the comparatively low signals and yields of each HOM for AP and limonene (panels A and C in Figs. 4, 5, and S10), suggest that they do not possess ring-opening processes as effective as carene for fostering subsequent autoxidation, and the second NO₃ addition for limonene is negligible.

In contrast, BP and myrcene, which do not have the same endocyclic double bond as the other three MTs, did not generate C₁₀H₁₆O₂ in NO₃ oxidation (Fig. 3). BP has the highest yields of the radical C₁₀H₁₆NO₆ and closed-shell species C₁₀H_15,17NO₅ (formed from bimolecular reactions of C₁₀H₁₆NO6) among the five MTs (Figs. 3 and 5), supporting the mechanism proposed by Claflin and Ziemann (2018), where the RO radical C₁₀H₁₆NO₄ from bimolecular reactions of C₁₀H₁₆NO₅, experiences a ring-opening process leading to C₁₀H₁₆NO₆. Subsequent bimolecular reactions can convert C₁₀H₁₆NO₆ to the RO radical C₁₀H₁₆NO₅, which can consequently trigger another ring-opening to form C₁₀H₁₆NO₇ after O₂ addition. With less constraints by rigid cyclic structures (Kurtén et al., 2015), C₁₀H₁₆NO₇ is expected to easily undergo autoxidation steps. The presence of considerable C₁₀H₁₆NO_7,9 and the absence of C₁₀H₁₆NO₈ (Figs. 3D and 4D) suggest the second ring-opening process and subsequent autoxidation. Although abundant C₁₀H₁₆NO₈ was observed in an earlier chamber study focusing on BP + NO₃ (Shen et al., 2021), it was not formed fast as C₁₀H₁₆NO₉ at the beginning based on their timeseries, suggesting that C₁₀H₁₆NO₈ likely resulted from C₁₀H₁₆NO₇ undergoing RO-forming bimolecular reactions followed by one autoxidation step. Furthermore, due to the short reaction time of 8.8 s in our flow-tube experiments, we did not detect second-generation peroxy radicals (i.e., those resulting from two NO₃ additions) with two nitrogen atoms, which were reported in Shen et al. (2021).

The acyclic structure, featuring three double bonds, makes the reaction of myrcene with the NO₃ radical mechanistically distinct from the other four cyclic MTs. The dominance of odd-oxygen-number peroxy radicals C₁₀H₁₆NO_5,7,9,11 suggest the fast autoxidation steps of myrcene comparing to RO-forming bimolecular reactions (Figs. 3E–5E). Moreover, the ring closures between RO₂ and double bonds are normally fast, leading to the formation of C–O–O–C peroxide groups (Vereecken et al., 2021). The proposed ring-closure processes are supported by the relative detection efficiency of myrcene + NO₃ products by DEA and nitrate modes (Fig. S8E): only when RO₂ radicals reached C₁₀H₁₆NO_10,11 and dimers reached C₂₀H₃₂N₂O₁₈, were they detected more efficiently by the nitrate mode. Because after two ring-closure steps (which consume the remaining two double bonds following NO₃ addition), those species would just begin to possess –OH/–OOH groups (via H-shift), which enhance the detection efficiency by the nitrate mode as hydrogen bond donors (Hyttinen et al., 2015). Considering bimolecular reactions RO₂ + R'O₂ forming ROH and R'C=O (Bianchi et al., 2019), the substantial amount of closed-shell species C₁₀H_15,17NO_6,8,10 potentially indicates that these RO₂ bimolecular reactions were fast for myrcene (Figs. 3E, 4E, and S10E).

It's notable that for AP, the concentration of the closed-shell monomer C₁₀H₁₇NO₅ is almost 100 times higher than that of the RO₂ radical C₁₀H₁₆NO₆, without the presence of the closed-shell C₁₀H₁₅NO₅ (Figs. 3A, 5A, and S10A). This suggests that the formation of C₁₀H₁₇NO₅ is likely due to the reaction C₁₀H₁₆NO₅ + HO₂, which was reported as an important pathway with a high molar yield (Bates et al., 2022). The potential involvement of HO₂ in other MTs could also be indicated by the relative abundance of some closed-shell monomers. For instance, the C₁₀H₁₇NO₅ was more abundant than C₁₀H₁₅NO₅ for both carene and BP (Fig. 3).

An unexpected observation is the considerable amount of C₁₄H₂₀O₂ across all MTs (Fig. 3). Since this species always increased when both MTs and NO₃ were available and followed trends similar to other NO₃ products (Figs. 2 and S3–S6), it is attributed to NO₃ oxidation. Its presence even for BP and myrcene (Figs. S5 and S6), which did not have C₁₀H₁₆O₂, rules out the initial speculation that it was formed by C₁₀H₁₆O₂ clustering with a C₄H₄ (which is possibly a fragment of the primary ion and had constant high concentration for all MTs; see Fig. S5A for example), and suggests the involvement of some unknown fragmentation processes.

The RO₂ bimolecular reactions also form dimers (ROOR') besides RO radicals and closed-shell monomers (Bianchi et al., 2019). The dimer C₂₀H₃₂N₂O₈ (from two C₁₀H₁₆NO₅) was the dominant dimer for all MTs except myrcene, where the most abundant dimer was C₂₀H₃₂N₂O₁₂, likely formed from two C₁₀H₁₆NO₇ (Fig. 3). It's notable that among all MTs, BP has the highest yield of C₂₀H₃₂N₂O₈, which is approximately an order of magnitude higher than its corresponding peroxy radical C₁₀H₁₆NO₅ (Figs. 3 and 5). Claflin and Ziemann (2018) proposed that in BP + NO₃, C₂₀H₃₂N₂O₈ was formed in the particle phase by two closed-shell monomers, however, our observation suggests that the C₂₀H₃₂N₂O₈ could be formed rapidly in the gas phase. It remains unclear why BP in particular has such a high yield of this dimer. While we cannot rule out that this signal is impacted by some undesired chemical or instrumental effects, it is puzzling why such an effect would be so dramatic only for BP.

The dimer patterns overall match the RO₂ radical distributions. AP, limonene, and myrcene, having major RO₂ radicals with odd oxygen number, produced series of even-oxygen-number dimers C₂₀H₃₂N₂O_x (Figs. 3–4). On the contrary, with considerable even-oxygen-number RO₂ radicals present alongside the odd ones, carene and BP also have noticeable amounts of odd-oxygen-number dimers C₂₀H₃₂N₂O₁₁ (via C₁₀H₁₆NO₅ + C₁₀H₁₆NO8) and C₂₀H₃₂N₂O₉ (via C₁₀H₁₆NO₅ + C₁₀H₁₆NO6), respectively. In the DEA spectrum of myrcene (Fig. 3E), the formation of dimers C₂₀H₃₂NO₇ and C₁₉H₃₀N₂O₁₁ was likely due to the fragmentation occurring during bimolecular reactions of two NO₃-initiated RO₂ (namely NO₃-RO₂), while C₂₀H₃₃NO₁₀ could be from a NO₃-RO₂ (C₁₀H₁₆NO₇) reacting with an OH-RO₂ (C₁₀H₁₇O₅).

From both DEA and nitrate spectra, we observed abundant peroxynitrates (RO₂NO2) from NO₃-RO₂ + NO₂, such as C₁₀H₁₆N₂O₁₀ for carene (Figs. 3B and 4B) and C₁₀H₁₆N₂O_9,11,13 for myrcene (Figs. 3E and 4E), and the yields of these RO₂NO₂ expectedly increased with higher NO₂ concentrations (Fig. S10). Earlier studies using NO₂ + O₃ as NO₃ source also reported noticeable amounts of RO₂NO₂ (Dam et al., 2022; Draper et al., 2019; Guo et al., 2022; Mayorga et al., 2022). These RO₂NO₂ were especially significant among the HOMs in nitrate spectra (Fig. 4) and tended to be charged by clustering with dimer primary ions (e.g., H¹⁵NO3⋅ ¹⁵NO3-) (Fig. S9). Furthermore, we also observed a noticeable amount of C₁₀H₁₅NO_10,12 in NO₃ + limonene (Figs. 4C and S4B), as previously reported by Guo et al. (2022). However, instead of attributing these species directly to NO₃ oxidation products, we regard them as RO₂NO₂ formed from C₁₀H₁₅O_8,10 (O₃-RO₂) + NO₂, since their behavior in the time series mirrored that of C₁₀H₁₅O_8,10 during stages 1–4 (Fig. S4). Generally, more oxygenated RO₂ radicals exhibited higher conversion to RO₂NO₂ (Fig. S12). This is likely due to the formation of more stable RO₂NO₂ structures, such as peroxyacetyl nitrates (PANs), which feature longer atmospheric lifetimes (Atkinson, 2000; Russell et al., 2025).

Generally, the concentrations of most NO₃ products increased monotonically with the rising reacted [MT] by the NO₃ radicals (Figs. 5 and S10). The most notable exception is that for AP, the peroxy radical C₁₀H₁₆NO₅ and its closed-shell monomer C₁₀H₁₇NO₅ significantly decreased with increasing reacted [MT], beyond expectation (Figs. 5A and S10A). As all stages in Figures 5 and S10 have the same [MT]₀, the reacted [MT] by NO₃ is directly proportional to the amount of NO₃ in the system. The faster-than-linear increase of C₁₀H₁₆O₂ (which approximately follows a 1:1.3 line, as shown in Fig. 5A) suggests that with increasing [NO₃], the peroxy radical C₁₀H₁₆NO₅ was converted to C₁₀H₁₆O₂ more efficiently. Also, AP has the highest yield of the radical C₁₀H₁₆NO₅ among all five MTs studied (Fig. 5), proposing that both autoxidation and bimolecular reactions are comparatively slow. The findings appear to be consistent with the previous studies that estimated the SOA yield of AP + NO₃ to be near 0 % using N₂O₅ as NO₃ source (Fry et al., 2014), as high [NO₃] could significantly enhance the role of the RO₂ + NO₃ reaction in the experiments, leading to the formation of the comparatively volatile C₁₀H₁₆O₂ (Bates et al., 2022). We observed that only the dimer C₂₀H₃₂N₂O₈ from BP + NO₃ follows a near-quadratic trend with the reacted [MT] (Fig. 5D). This indicates that the reaction coefficient of the dimer-forming bimolecular reaction is the fastest compared to other competing pathways, which is consistent with C₂₀H₃₂N₂O₈ being the main product (Figs. 3D, 5D, and S10D). It is noteworthy that the data points corresponding to the column with [NO₂]0=32.5 ppb but the higher reacted [MT] (stage 8), often deviated from the general trend (Figs. 5 and S10). This deviation occurred because the increased [O₃]₀ in stage 8 enhanced the production of O₃/OH oxidation products, such as O₃/OH-RO₂ radicals, which subsequently affected the concentrations of NO₃ oxidation products.

Product closure was reasonably reached for AP, limonene, and myrcene, given that the fractions of observed NO₃-initiated products out of the total NO₃-oxidized MT were calculated to be 50 %–70 % (Fig. 6A). Considering the inherent uncertainties stemming mainly from the calibration factor applied to CIMS quantification (Sect. S2) and the estimated coefficients of NO₃ and N₂O₅ wall losses within the box model (Table S1), it is possible that we were able to observe almost all the products. On the contrary, carene and BP exhibited lower fractions, at 20 %–40 % (Fig. 6A). This reduced closure could be attributed to the unaccounted formation of products containing one O-atom, as these cannot be effectively detected by the DEA mode (Riva et al., 2019). An earlier flow-tube study reported that the yield of nopinone (C₉H₁₄O) from BP + NO₃ varied substantially (20 %–80 %) across different experimental pressures and NO concentrations (Berndt et al., 1999). To our knowledge, no previous studies have explicitly identified and quantified any major products containing only one O-atom from carene + NO₃, proposing either a new reaction pathway or a severely underestimated calibration factor for some carene products.

To maintain consistency with previous studies, which exclusively used nitrate-CIMS for HOM investigations (Dam et al., 2022; Day et al., 2022; Draper et al., 2019; Ehn et al., 2014; Guo et al., 2022; Harb et al., 2025; Li et al., 2024; Luo et al., 2022; Shen et al., 2021; Zhang et al., 2024a, b; Zhao et al., 2024), HOM yields were calculated solely using data from the nitrate mode in this study. However, we note that the HOM yields may be underestimated because of the low selectivity of nitrate-CIMS toward some HOM dimers with relatively low oxygen numbers (discussed in Sect. 3.1). One example is that the proposed formation of C–O–O–C groups inhibited the effective detection by the nitrate mode of some HOMs formed from myrcene + NO₃ (such as C₁₀H₁₆NO₉). Despite this underestimation, the acyclic myrcene exhibits the highest average HOM yield (∼6.5%; Fig. 6B), as could be expected, since its open structure imposes fewer constraints on autoxidation compared to the cyclic MTs. Among the four cyclic MTs, NO₃ oxidation of carene produced the highest average HOM yield at approximately 6.1 %, closely approaching that of myrcene. This is consistent with the finding that carene undergoes a ring-opening process (i.e., the alkyl-side β-scission of the nitrooxy alkoxy radical) that facilitates autoxidation (Sect. 3.2; Figs. 3–5, and S11) (Draper et al., 2019; Kurtén et al., 2017). The HOM yield of BP + NO₃ (at ∼1.8%) exceeds that of AP (∼0.8%) and limonene (∼1.1%). Directly compared to our results, Guo et al. (2022) reported a similar HOM yield (1.5 %) for limonene + NO₃, while Shen et al. (2021) estimated a much higher HOM yield (4.8 %) for BP. Due to the difference of experimental setups and conditions (e.g., reaction time and NO₃ source), direct quantitative comparison of HOM yields across various studies is often challenging. Nevertheless, if combining findings from earlier studies that have measured HOM yields from more than one MT using the same sampling system, we can conclude that HOM yields from ozonolysis can be listed in the order (from highest to lowest): limonene > carene > AP > myrcene > BP (Jokinen et al., 2015; Zhao et al., 2024). This order contrasts with the NO₃ oxidation results in this study. The relatively low HOM yield of myrcene + O₃ is likely due to decomposition into smaller fragments following the breaking of the primary ozonide (Atkinson and Arey, 2003). Conversely, Jokinen et al. (2015) reported myrcene having the highest HOM yield in OH oxidation (∼1%), followed by limonene, BP, and AP.

We can compare the HOM yields from NO₃ oxidation (Fig. 6B) to their corresponding SOA formation reported in earlier studies. These studies consistently found that AP has the lowest SOA yield (DeVault et al., 2022; Hallquist et al., 1999), even approaching zero (Fry et al., 2014). This is possibly due to excessive [NO₃] that favors volatile product formation, as discussed in Sect. 3.2. However, the relative SOA yields for cyclic MTs vary across different studies (DeVault et al., 2022; Fry et al., 2014; Hallquist et al., 1999), thereby making comparisons to our HOM yields inconclusive. The discrepancies may relate to different conditions during the experiments and suggest that simultaneous measurements of HOMs might have shed some light on the relevant reaction pathways taking place in the experiments.

Our findings validate the previous observations that small structural differences among MTs strongly influence the product distributions during oxidation, and demonstrate that the HOM yield of an individual MT from NO₃ oxidation can differ significantly from that by O₃/OH oxidation. Still, the overall HOM yields are comparable between oxidants, generally falling in the range 0 %–10 %, although yields from OH oxidation are typically the lowest (Bianchi et al., 2019; Jokinen et al., 2015; Zhao et al., 2024). Since HOMs are a large source of SOA (Ehn et al., 2014), the SOA formation is expected to vary between day and night, depending on the VOC distribution and the dominant oxidant (e.g., OH vs NO₃). For instance, if limonene is the key precursor driving SOA formation during the day, its role would diminish at night because the rapid reaction limonene + NO₃ yields far fewer HOMs and more of the volatile compound C₁₀H₁₆O₂. The correlation between HOM formation and SOA mass is most evident at low OA mass concentrations, where extremely low-volatile HOM species dominate new particle formation and early growth. In more polluted environments with higher pre-existing OA mass, however, low-volatile and semi-volatile (i.e., non-HOM) oxidation products can contribute substantially to SOA mass. Therefore, HOM and SOA yields are not always closely related, and their relationship can vary significantly across different chemical regimes and environments (with differences in VOC composition, oxidant conditions, and background OA loadings). The difference between the relative magnitudes of HOM and SOA yields of each MT (DeVault et al., 2022; Fry et al., 2014; Hallquist et al., 1999) can partly be explained by the potentially underestimated HOM yields and contribution of non-HOM products to SOA formation, but also by differing reaction conditions between studies. In our flow-tube experiments, we have much shorter residence time compared to traditional chamber SOA yield experiments (seconds vs. hours), during which multigenerational products can form and contribute to SOA formation, for instance, NO₃ addition to the first-generation product C₁₀H₁₆O₂ from limonene + NO₃ reactions. Moreover, particle-phase reactions occurring after condensation introduce additional uncertainties when directly comparing our HOM yields with previously reported SOA yield results. Overall, our results revealed that the NO₃ oxidation mechanisms are highly structure-dependent, and their contribution to atmospheric particles varies significantly among different MTs.

A major challenge in studying NO₃ chemistry is replicating atmospherically relevant RO₂ radical fates. Since we used NO₂ + O₃ to supply NO₃, the excessive NO₂ relative to NO₃ (Fig. S2) resulted in the formation of a noticeable amount of RO₂NO₂ (Figs. 3, 4, S9, S10, and S12). This competing pathway (RO₂ + NO2) may obscure the importance of other reactions involving RO₂ radicals. While using the thermal decomposition of N₂O₅ could avoid the RO₂NO₂-forming issue, it often provides too high [NO₃], causing the bimolecular reaction RO₂ + NO₃ to dominate (Bates et al., 2022). For instance, this excessive [NO₃] pushes AP + NO₃ to form more volatile C₁₀H₁₆O₂, underestimating the importance of AP in SOA formation. This highlights the inherent difficulty in studying NO₃ + MTs mechanisms in laboratory settings.

One major limitation of our study is the incomplete product closure observed for carene and BP, possibly due to the DEA mode failing to detect products containing one O-atom. The formation of these unseen products can be investigated by future studies using instruments with better selectivity. Another limitation is the inability to perform dilution experiments without a well-designed dilution unit attached to the CIMS inlet, preventing us from ruling out potential ion-induced reactions taking place in the chemical ionization inlet (Berndt et al., 2016; Peräkylä et al., 2023). However, as the levels of reacted [MT] in this study are comparable to earlier flow-tube studies where ion-induced dimer formation was found not to be significant (Berndt et al., 2018a; Peräkylä et al., 2023), we do not expect such processes to be dominant in our experiments. The design of the dilution unit is crucial, as our unit caused too much turbulence that decreased all signals far beyond the expected dilution factor, warranting future study. It is worth noting that the reagents which are selective to low-oxygenated compounds (O <6), such as the DEA used in this study, can be very sensitive to contaminants. For example, nitric acid (HNO₃) from the NO₂ cylinder initially depleted our primary ion (C₄H₁₂N⁺), affecting quantification, but the addition of a HEPA filter (Whatman plc) after the gas cylinder removed most, though not all, of the HNO₃. Moreover, the lack of more specific standard calibration compounds than sulfuric acid (Sect. S2) limits our CIMS quantification for the larger organic compounds.

It is notable that the box model used for estimating concentrations of reacted MTs does not capture turbulent mixing, and thus an instantaneous dilution of the injector flow into the main flow was assumed. However, the experimentally determined reaction times theoretically account for turbulent mixing. Nevertheless, some uncertainties may arise from different relative concentrations of oxidants and reactants. We did not explore the low levels of MTs where bimolecular reactions are negligible and RO₂ concentrations increase linearly with reacted [MT]. Because this study does not focus on kinetics, and since bimolecular reactions commonly occur in the atmosphere, we believe our experimental conditions provide an atmospherically relevant distribution of radicals and closed-shell products.