A mechanistic understanding of the varying yields of highly oxygenated organic molecules

Domain: earth_science
Published: 2025-12-09
Editorial outcome: minor_revision

Abstract
Highly oxygenated organic molecules (HOM) play a crucial role in the formation and growth of atmospheric particles, thereby influencing air quality and climate. A comprehensive understanding of HOM formation, particularly an accurate quantification of their yields, is essential to constrain the climate and health impacts of aerosols. Previous studies often reported constant HOM yields as averages, overlooking nuanced changes. Here we revisit several experimental datasets and demonstrate that HOM yields from single volatile organic compounds (VOCs) can vary by more than a factor of 3, depending on numerous parameters affecting peroxy radicals (RO2) autoxidation. Additionally, we propose a concept of RO2 oxidation fraction, which provides a unified explanation for variations in the HOM yields. Our findings indicate that applying the laboratory-derived HOM yields to the interpretation of ambient data may lead to substantial biases, especially when VOC and oxidant concentrations in the laboratory were higher than those in the real atmosphere.

Introduction
Atmospheric aerosols degrade air quality1, threaten human health2–4, and influence climate5. Highly oxygenated organic molecules (HOM), first identified as low-volatility products of monoterpene oxidation in a boreal forest6, are now known to form from a wide variety of precursors, including isoprene7–9, sesquiterpenes10,11, aromatics12–14 and anthropogenic alkenes15,16. These compounds play a pivotal role in the formation of aerosol particles. HOM can participate in particle nucleation17–20, dominate particle growth21–23, and drive the formation of secondary organic aerosol (SOA)24–26, a major component of global fine particles27–29. Therefore, a comprehensive understanding of HOM production, especially their yields and volatilities, is crucial for an accurate evaluation of the budget of global fine particles.

The atmospheric discovery of HOM6, together with the further demonstration of their crucial impact on aerosol formation in various environments24,26,30–32, has led to rapidly growing interest in understanding the HOM formation mechanism. In general, HOM formation proceeds through three consecutive steps that are tightly associated with the fate of peroxy radicals (RO2), including:
Step 1, the oxidation of volatile organic compounds (VOCs) that produce first-generation RO2;
Step 2, the autoxidation of RO2 that produces HOM-RO2 with higher numbers of oxygen atoms in the molecules;
Step 3, the termination of HOM-RO2 chain propagation through uni- or bi-molecular reactions that form closed-shell products, i.e., HOM.

While the above description refers to RO2 formed directly from parent VOCs (e.g., monoterpenes) as examples of first RO2, the same processes can also involve RO2 formed from multi-generation oxidation products. Early studies implicitly assumed that the HOM yields were pre-determined at Step 1 by the initial distribution of first-generation RO2. More specifically, it was assumed some first-generation RO2 were structurally favorable for potent autoxidation (i.e., with unity HOM yield), while other (and the majority of) RO2 could not autoxidize due to the lack of loosely bonded H atom or strong steric hindrance (i.e., with zero HOM yield). The overall HOM yields could then be expressed as a linear combination of the two extremes. With such a presumption, constant HOM yields, derived through a linear regression between HOM production rate and VOC oxidation rate in laboratory experiments, have been reported for certain combinations of VOC precursors and oxidants10,13,16,17,26,33,34. It should be noted that such an assumption was only made under a certain temperature, since it has been well recognized that the RO2 autoxidation is strongly temperature-dependent. For instance, it has been measured that the atmospheric concentrations of α-pinene HOM yields decrease with a decreasing temperature from 6.2% at 298 K to 0.7% at 223 K20. More recently, the reaction kinetics of HOM formation have been extensively studied using laboratory experiments and computational methods, which revealed strong structure-activity relations in RO2 autoxidation and HOM formation10,16,33–43. It has been shown that the efficiency of autoxidation is strongly enhanced by the activating function groups (e.g., –OH, –OOH, =O) added to the carbon from which the H is being abstracted44, and suppressed by the steric hindrance of rigid transition state geometry (e.g., C3 and C4 rings)45. More importantly, it has been calculated that the first-order reaction coefficient of effective RO2 autoxidation, for monoterpene, mostly ranges in the order of 0.01–1 s−1 under typical atmospheric temperatures46, equivalent to a bi-molecular reaction rate with 2 ppt–2 ppb of NO or HO2 (assuming k=2×10−11 cm3 s−1)47 or 0.2 ppt – 20 ppb of RO2 (assuming kRO2=1–100×10−12 cm3 s−1)48. This means that RO2 autoxidation and bi-molecular reactions are occurring at comparable rates under atmospheric or atmosphere-relevant laboratory conditions. In light of this, the HOM yields ought to vary even under the same chemical system when concentrations of reacting species and/or oxidants are changing. However, such variations have seldom been recognized and reported in previous studies.

To our best knowledge, only a handful of studies have raised the concerns of the inconsistency in the HOM yields between experiment observations and theoretical expectations. Molteni et al.49 demonstrated that the production of C10-HOM species is non-uniform and non-linear in an ozone + monoterpene system. The addition of isoprene50–52 and sesquiterpene53 in monoterpene system can also change the yield of accretion HOM products (i.e., HOM dimers). In addition, a varying HOM yield has been shown in the monoterpene + NOx system, Shen et al.54 and Pye et al.55 found that HOM yields were significantly lower under high NO conditions compared to low NO. Building on these, Nie et al.56 demonstrated a non-monotonic response, with a maximal HOM yield observed at low but non-zero NO concentrations. Furthermore, increasing HO2 concentrations have been shown to suppress the formation of HOM-accretion products and alter the functionalization of HOM monomers, favoring hydroperoxide over carbonyl groups57. While HOM formation has been observed under different chemical settings, existing models such as Master Chemical Mechanism (MCM), Peroxy Radical Autoxidation Mechanism (PRAM)58 and the recently proposed automated alkoxy/peroxy radical autoxidation mechanism framework (autoAPRAM-fw)59 have also begun to provide detailed descriptions of HOM formation processes. However, there still lacks a unified and intuitive parameter that can capture the main factors controlling HOM yields across diverse conditions. Here, we first revisit experimental data from the CLOUD chamber and complement this analysis with additional data from other chambers and flow reactors. We point out that the variation in the HOM yields can be easily overlooked when using the linear-regression method (see Fig. 1a), where the yield is derived as the slope of the linear fit. Instead, the nuanced changes in the HOM yield can be clearly observed when calculated independently for each steady state condition. We further introduce a parameter, the oxidation fraction of RO2, which characterizes the potential of RO2 autoxidation and provides a unified description of the HOM yields for different chemical systems.

Results
Re-examination of the HOM yield from monoterpene oxidation
First, we revisit HOM datasets of α-pinene oxidation in the absence of NOx conducted in multiple laboratory facilities (see Methods). In these experiments, α-pinene was oxidized by O3 and OH, where OH was produced either by the reaction between α-pinene and O326,33 or additionally by the photolysis of O317,20. Details of the experimental conditions are listed in Supplementary Table 1. In Fig. 1a, we plot the production rate of HOM (PHOM) as a function of the monoterpene oxidation rates (MTreact), with the slope denoting the HOM yield. Besides a clear increasing trend in PHOM alongside the increase of MTreact, the slope decreases toward high MTreact, suggesting a decreasing tendency of the HOM yield. In previous studies, the HOM yields have often been obtained as the slope of a linear fit between PHOM and MTreact determined for multiple steady-state stages which only reflected an average HOM yield of the multiple stages in the experiment but ignored the subtle variation. To better reveal the variation in the HOM yield, we calculate the HOM yield (i.e., PHOM/MTreact) of each steady-state stage and plot it against MTreact. As shown in Fig. 1b, the HOM yields decrease considerably at high MTreact. For instance, the HOM yields decrease approximately from 10% to 6% in the experiment conducted by Ehn et al., where a 7% average HOM yield has been reported26.

In Fig. 1, we also observe notable systematic differences in the HOM yields and their decreasing tendencies between experimental datasets. This could be attributed to a few factors. First, these experiments were conducted at different temperatures, which greatly affect the RO2 autoxidation. Second, the relative abundance of O3 and OH were not the same in these experiments. O3-initiated α-pinene oxidation is known to have a higher HOM yield compared to the OH-initiated oxidation17,26,60. Third, the definition of HOM in these studies is not consistent. Specifically, HOM were either defined as all species measured with a NO3-CIMS in some studies17,20, or by the mass-to-charge ratio between 280 and 620 Th33. It should be clarified that HOM is defined by the number of oxygen atoms (NO)≥7 in this study, despite that NO≥6 has been suggested as a more appropriate criterion from a theoretical aspect26,61. This practical choice aligns with our use of NO3-CIMS, which has good sensitivity for HOM with seven or more oxygen atoms62. Last but not least, measurement uncertainty, which has been reported as ~±50%, also contributes to the systematic differences of the HOM yields17,26.

Mechanistic understanding of the varying yield
Next, we investigate the fundamental mechanism of the varying yield based on a proof-of-concept experiment. This experiment was conducted in the CLOUD chamber at 278 K. The configuration of CLOUD chamber facilities is provided in our previous works and the detailed experimental settings are described in Methods. Briefly, the concentration of α-pinene was changed stepwise from 30 ppt to 1050 ppt, covering the typical monoterpene concentration in the atmosphere (Supplementary Fig. 1). We calculate the HOM yields at these monoterpene concentrations under steady state (see Methods). As shown in Fig. 2a, the HOM yields decrease by >60%, from 2.7% to 1.0%, when the α-pinene concentration increases from 30 ppt to 1050 ppt, corresponding to an α-pinene oxidation rate of 1.20×105 cm−3 s−1 to 3.97×106 cm−3 s−1 (Supplementary Fig. 3a). Meanwhile, we simulate HOM formation in the experiment by employing the Aerosol Dynamics gas- and particle-phase chemistry model for laboratory CHAMber studies (ADCHAM)63. This model integrates the comprehensive Peroxy Radical Autoxidation Mechanism (PRAM) and Master Chemical Mechanism (MCMv3.3.1), and also incorporates HOM deposition on chamber walls and condensation/evaporation on particle surfaces63. Details of the model setups are provided in Methods. The model performance is verified by the reasonable agreement with experimental observations for the concentrations of both hydroxyl radicals (OH) and different HOM species at different α-pinene concentrations (Supplementary Fig. 3 and Supplementary Fig. 4). Although some deviations exist between simulated and observed concentrations, the model captures the overall HOM distribution well, with coefficients of determination (R2) exceeding 0.7 across different conditions.

This level of agreement enables us to quantify the fate of RO2 on a quasi-molecular level and further investigate the fundamental reasons why the HOM yield varies as a function of the α-pinene oxidation rate. To aid the illustration, we classify RO2 into a few categories according to their roles in HOM formation. First, RO2 containing at least 7 oxygen atoms are termed HOM-RO2. They are the direct precursors of HOM through termination reactions, and thus the HOM yields are directly associated with the formation of HOM-RO2. Second, in light of a recent study by Iyer et al.37, only a small fraction of initial RO2 can autoxidize and potentially become HOM-RO2. This type of RO2 is termed potential HOM-RO2 (p-HOM-RO2). In our model, the fractions of first-generation p-HOM-RO2 are set as 1.12% and 9% of the total initial RO2 for OH-initiated and O3-initiated α-pinene oxidation, respectively (Supplementary Table 4). The fraction of p-HOM-RO2 becoming HOM-RO2 is regulated by the competition between autoxidation and termination. Third, the rest of the initial RO2, incapable of autoxidation, is termed non-HOM-RO2. They solely act as a reaction partner of p-HOM-RO2 and HOM-RO2 through RO2 cross-reactions. The schematics describing the relationship and roles of these different RO2 categories are shown in Supplementary Fig. 2. A similar consideration has been incorporated in the R2D-VBS model developed by Schervish and Donahue64–66 and the CRI-HOM model by Weber et al.67.

As illustrated above, the fate of p-HOM-RO2 determines the overall HOM yield. Therefore, we quantify the probability of p-HOM-RO2 undergoing autoxidation versus termination reactions in the experiment using the ADCHAM model by calculating the contribution of various chemical and physical processes of p-HOM-RO2 as a function of α-pinene concentration. As shown in Fig. 2a, along with the increase in α-pinene oxidation rate (achieved by increasing α-pinene concentration while maintaining constant O3 and OH concentrations), the relative contribution of RO2 cross-reactions progressively increases, while that of RO2 autoxidation gradually decreases. This is because the rates of RO2 cross-reactions are proportional to the square of the total RO2 concentration, while the rate of RO2 autoxidation is linearly proportional to the p-HOM-RO2. From another perspective, the substantial enhancement of RO2 cross-reactions reduces the lifetime of p-HOM-RO2, thereby lowering its probability of undergoing autoxidation. This results in a significant reduction in the formation of HOM-RO2 and eventually in the HOM yield.

If all bi-molecular termination reactions of p-HOM-RO2 (with other RO2 and HO2) strictly stop the radical propagation, a reduction in p-HOM-RO2 lifetime by 83% should cause a reduction in the HOM yield by the same fraction. However, we only observe a decline in the HOM yield by 62%. This reduction is attributed to the formation of alkoxy radicals (RO) via bimolecular termination pathways47. RO can also undergo fast intra-molecular H-shift followed by O2 addition, referred to as “RO autoxidation” hereafter. The RO autoxidation mechanism is kinetically possible and needs to be invoked to explain HOM distribution in previous studies39,49,56. The branching ratios of RO formation channels are listed in Supplementary Table 4.

In accordance with the formation mechanism, HOM of different types (i.e., monomers and dimers) show notably different responses to the VOC oxidation rate. HOM monomers, mostly classified as low-volatility organic compounds (LVOC, 10−4.5 μg/m3 ≤ C* ≤ 10−0.5 μg/m3), are responsible for the growth of nanoparticles22. Differently, HOM dimers are mostly ultra-low volatility organic compounds (ULVOC, C* < 10−8.5 μg/m3) and extremely low volatility organic compounds (ELVOC, 10−4.5 μg/m3 < C* ≤ 10−8.5 μg/m3) that can be important for particle nucleation18. Therefore, capturing their responses is crucial for the model prediction of new particle formation. As shown by both the observation and model simulation, HOM monomers (NC ≤ 10 and NO ≥ 7) are direct products of HOM-RO2, and thus, the yields of HOM monomers largely follow the change of HOM-RO2, showing a monotonically decreasing trend (Fig. 2b). Differently, HOM dimers (NC > 10 and NO ≥ 7), as referred to in this work, are accretion products of the cross-reactions of two monoterpene-derived RO2 (RO2 + R’O2 → ROOR’ + O2). Reactions between all types of RO2 may form HOM dimers, as long as the two parent RO2 together contain 9 or more oxygen atoms. Consequently, the yield of HOM dimers increases with α-pinene concentration until the step of 400 ppt α-pinene, due to enhanced RO2 cross reactions that directly form dimers. At higher concentration, the yield gradually declines as the autoxidation of p-HOM-RO2 is increasingly outcompeted by terminating reactions, particularly RO2 cross reactions involving species with fewer oxygens (Fig. 2c).

A framework quantifying the HOM yield
As discussed above, the HOM yield is essentially affected by both the yield of first p-HOM-RO2 (γp-HOM-RO2) and the probability that the formed p-HOM-RO2 undergoes further oxidation to become HOM-RO2. The former is pre-determined by the chemical system (the type of VOC and oxidant), while the latter depends on the competition between the oxidation and loss processes of p-HOM-RO2. To quantitatively describe this competition, we introduce a normalized parameter, the oxidation fraction of p-HOM-RO2 (OFp-HOM-RO2), defined as oxidation/(oxidation + loss) (see Methods). This parameter ranges from 0 to 1, reflecting the probability that p-HOM-RO2 proceed to form HOM-RO2 rather than being removed by loss processes. In this formulation, oxidation includes both RO2 and RO autoxidation pathways, whereas loss encompasses condensation onto chamber and aerosol surfaces, as well as bimolecular reactions with RO2, NO, and HO2. Conceptually, OFp-HOM-RO2 is analogous to the survival probability widely used in new particle formation studies, which describes the fraction of nascent particles that can grow rather than be lost to coagulation22,68.

We examine the relationships of γp-HOM-RO2, OFp-HOM-RO2 with the HOM yields among 5 experimental settings (and 23 steady-state conditions), covering different monoterpene types (α-pinene and Δ−3-carene) and concentrations, and various NOx conditions. The O3 concentration was kept nearly constant at ~40 ppb across these experiments, as detailed in Supplementary Table 2. Supplementary Fig. 5a shows the relationship between γp-HOM-RO2 and the HOM yields. Within each experimental setting, the change in γp-HOM-RO2 is mainly driven by the varying relative contribution of different oxidants, i.e., O3, OH, and NO. For instance, when NO is involved in experiments, an elevated NO level translates into greater contribution by NO-initiated oxidation and larger γp-HOM-RO2 (see Supplementary Table 4). In most NOx-involved experiments, HOM yields increase with γp-HOM-RO2, except in the “pure NO2” experiments, where an opposite dependence is observed. This indicates that γp-HOM-RO2 is not the sole factor determining the HOM yield. For any given γp-HOM-RO2, a higher HOM yield is generally observed at greater OFp-HOM-RO2. This is exemplified by the experiments without NOx, where γp-HOM-RO2 remains relatively constant at ~0.06 (filled circles in Supplementary Fig. 5a), while the HOM yield increases from ~1% to ~2.6% as OFp-HOM-RO2 rises from ~0.2 to ~0.7.

To further illustrate this relationship, Supplementary Fig. 5b shows the HOM yield as a function of OFp-HOM-RO2 across all conditions. While both γp-HOM-RO2 and OFp-HOM-RO2 contribute to the variability in HOM yields, the relatively small variation in γp-HOM-RO2 across the dataset makes its effect less evident, yet it still plays a meaningful role in shaping HOM formation. Therefore, we additionally examine the product of γp-HOM-RO2 and OFp-HOM-RO2, which capture the combined effect of formation efficiency and availability of the precursor, and yields the strong correlation with HOM yield (Fig. 3). To conclude, γp-HOM-RO2 and OFp-HOM-RO2 determine the HOM yields synergistically. The former represents a theoretical upper bound of the HOM yield; the latter regulates the fraction of p-HOM-RO2 that can eventually form HOM.

We have shown in Fig. 1b that the dependence of the HOM yields on α-pinene oxidation rates seems to vary at different temperatures. Although a quantitative understanding of this phenomenon requires future studies on the exact temperature effects on the kinetics of RO2/RO autoxidation, the parameter OFp-HOM-RO2 helps to explain it qualitatively. High temperature enhances RO2 autoxidation20,69 without significantly affecting the bi-molecular termination reactions. Thus, greater OFp-HOM-RO2 can be expected in higher-temperature experiments, leading to higher HOM yields, e.g., those reported by Ehn et al.26. Conversely, when RO2 autoxidation is substantially suppressed at low temperatures, the RO2 termination could always outcompete the autoxidation even at low α-pinene oxidation rates, explaining the stable and low HOM yields reported by Simon et al.20.

Although this framework has been evaluated under monoterpene oxidation conditions, it is theoretically applicable to broader VOC systems. In more complex environments, additional RO2 radicals (e.g., CH3O2) can compete with autoxidation by enhancing the loss of p-HOM-RO2, thereby lowering HOM yields. Since these radicals act in the same way as the non-HOM-RO2 already considered, their influence should be inherently captured by the unified parameter as long as they are represented in the model. Another remaining challenge is that the role of RO2 formed from multi-generation products is not explicitly considered. This omission is minor for monoterpenes, where HOM formation is dominated by the rapid autoxidation of first-generation RO2, but it becomes important in systems such as isoprene and aromatics where multi-generation chemistry contributes substantially. In such cases, the framework could be extended by treating first-generation products, i.e., OVOCs, as separate precursors and reapplying the same formulation, though this extension is required further validation under more complex and representative conditions.

Methods
Data source
The data source for this study are derived from a variety of experiments conducted under different conditions, selected based on specific criteria. To be included in this study, an experiment must involve α-pinene oxidation, employ Nitrate-CIMS for detection and provide information on α-pinene concentration or their reaction rate. The experiments are divided into two categories: flow reactor and chamber experiments.

The Jokinen’s experiment was conducted in a flow tube with α-pinene ranging from 0.09 to 173.95 ppb and O3 concentrations from 23.9 to 25.5 ppb33. Additionally, several chamber experiments were conducted under varying conditions. The experiment conducted by Ehn et al. was carried out at Jülich Plant Atmosphere Chamber facility (JPAC)26 with a temperature of 289 K, relative humidity of 63 %, α-pinene concentrations of 1–30 ppb and O3 concentrations of 12–86 ppb. Kirkby et al.17 conducted experiments in CLOUD chamber (Cosmics Leaving OUtdoor Droplets) at 38% relative humidity, 278 K, with α-pinene concentrations of 70–440 ppt, O3 at 21–35 ppb with UV levels ranging from 0% to 100%. Simon et al.20 also employed the CLOUD chamber at 5 different temperatures, with α-pinene concentrations ranging from 0.1 to 1 ppb and O3 levels varying between 30 and 40 ppb.

The primary data in this study were obtained from additional experiments conducted in the CLOUD chamber. In these experiments, pure α-pinene was gradually increased from 0 to ~1 ppb, with steady state concentrations of 30 ppt, 70 ppt, 180 ppt, 400 ppt, 850 ppt, and 1050 ppt. O3 was directly injected into the chamber, while OH was produced both from the ozonolysis of monoterpene and by the photolysis of ozone. The concentrations of O3 and OH were kept stable during each experiment (Supplementary Fig. 1a). The loss of HOM was mainly due to the chamber wall loss and loss on particle surfaces, whereas the loss by dilution was negligible (Supplementary Fig. 1b).

Additionally, it should be noted that the definition of HOM employed in this study differs from these experiments, where HOM were defined based on specific spectral ranges in NO3-CIMS. However, in this study, we define as HOM containing at least 7 oxygen atoms, which are assumed to be sufficiently sensitive in NO3-CIMS. Monoterpene was measured using a proton transfer reaction time-of-flight mass spectrometer (PTR3)82, while SO2 and O3 were measured using Thermo Scientific gas monitors (model 42i for SO2 and model 49i for O3). The dilution loss rate was within 1-2×10−4 s−117,20, corresponding to a residence time of ~120 min.

Calculation of the HOM yields
HOM is formed through a series of reactions initiated by the oxidation of precursor VOCs. In this study, the oxidants involved are O3 and OH. OH concentration in CLOUD chamber was calculated using the following equation:
[OH] = (k_loss * [SA]) / (k_SO2+OH * [SO2]) (1)
Where k_loss represents the loss rate of sulfuric acid due to condensation onto aerosol particles (condensation sink) and to the chamber wall (wall loss); k_SO2+OH is the reaction rate constant between OH and SO2 at 278 K, which was set at 1.2×10−12 cm3 s−183. Under steady-state conditions, the production rate of HOM is equivalent to its loss rate. Therefore, the HOM yields can be expressed as
HOM yield = PHOM / (k * [MT] * [Oxidant]) = (k_wall,i * HOM_i + k_CondS,i * HOM_i) / (k * [MT] * [Oxidant]) (2)

The wall and condensation all losses for HOM were calculated. For wall losses, the molecules detected by Nitrate-CIMS84,85 usually have a very low saturation vapor pressure, leading to the assumption that they undergo irreversible losses upon contact with the surface. We adopted the method of Simon et al.20 to calculate: the diffusion coefficients Di for each HOM are approximated with the expression:
Di (cm3 s−1) = 0.31 * Mi−1/3 (3)
where Mi (g mol−1) is the mass of the molecule. The wall loss rate inside the CLOUD chamber at each temperature is determined from the following expression:
k_wall(T) = C_wall(T) * Di (4)
where C_wall is an empirical parameter and set to 0.0075 cm−1 s−0.5 at 5 °C in this study.

ADCHAM model
We use the Aerosol Dynamics gas- and particle-phase chemistry model for laboratory CHAMber studies (ADCHAM)63 with a detailed gas-phase kinetic code that combines peroxy radical autoxidation mechanism (PRAM) and MCMv3.3.1 using the Kinetic PreProcessor (KPP)86. As described by Roldin et al.58, like most current model frameworks for modelling HOM formation64,67, by assigning specific molar yields for the formation of the first p-HOM-RO2 that initiates the autoxidation chain, PRAM further explicitly described how autoxidation proceeds through successive intramolecular H shift and O2 addition. Autoxidation can be terminated by a bimolecular reaction in which the formed RO2 reacts with NO, HO2 and other RO2.

In our model, the rate constants for RO2+NO and RO2+HO2 reactions are adopted directly from the MCMv3.3.1, using the structure-independent rate constants. For the RO2+HO2 reaction, the product formed is always a closed-shell molecule with a hydroperoxide functional group (-OOH) replacing the peroxy group (-OO·). For RO2+RO2 reactions, which can lead to either alkoxyl radicals (RO·), closed-shell monomers, or dimers, we follow the structure-dependent treatment described in the PRAM framework. Given the large number of RO2 in the mechanism, assigning individual rate constants for all possible RO2–RO2 combinations is computationally impractical. To address this, we adopt a hybrid approach:
RO2+RO2 reactions leading to RO and closed-shell monomer products are treated using a simplified “RO2 pool” scheme. All RO2 radicals are assumed to react collectively, and the total rate of RO2 cross-reactions for a given species is approximated as a pseudo-unimolecular reaction with a rate coefficient of k * Σ[RO2], where Σ[RO2] is the sum of all RO2 concentrations. This ensures computational efficiency while retaining a representation of overall termination by RO2–RO2 interactions.

RO2+RO2 reactions forming HOM dimers are treated explicitly as bimolecular reactions between selected RO2 types. We differentiate between p-HOM-RO2 (capable of autoxidation) and non-HOM-RO2 (those that do not autoxidize). p-HOM-RO2, due to their high oxygen content, are assigned faster dimerization rates. Non-HOM-RO2, while typically more abundant, are assumed to promote accretion with slower rates. This treatment captures key differences in dimer formation potential between RO2 subtypes while maintaining model simplicity.

The rate constants for RO2+RO2 reactions are further scaled based on the oxygen content of the reacting species. RO2 with lower oxygenation are assigned lower rate constants, while those with higher oxygen content are given higher rates, consistent with their increased reactivity toward dimer formation. Specifically, rate constants for RO2+RO2 reactions leading to closed-shell monomers range from 1×10−12 to 1×10−11 cm3 s−1, while those leading to HOM dimers span 8×10−15 to 8×10−13 cm3 s−1 depending on the oxygen content of the reacting RO2. Detailed assignments of reaction pathways, branching ratios, and rate constants are summarized in Supplementary Table 4.

Calculation of the p-HOM-RO2 yields (γp-HOM-RO2)
The p-HOM-RO2 yields are determined by the type of VOCs and oxidants. In this study, α-pinene was used as the only VOC precursor and the oxidants involved were O3 and OH. However, in the NOx experiments, not only the effect of NO as oxidant was introduced, but also a mixture of 2:1 α-pinene and Δ−3-carene comprised the VOC precursors. We therefore calculated the average yields for these different conditions based on VOC and oxidant concentrations, defined as the ratio of the first p-HOM-RO2 yields to the monoterpene reaction rate:
γp-HOM-RO2 = (γMT,oxidant * k_MT,oxidant * [MT] * [Oxidant]) / (k_MT,oxidant * [MT] * [Oxidant]) (5)
where k is the rate constant for the reaction of the VOC with the oxidant, which is the same as in Master Chemical Mechanism version 3.3.1 (MCMv3.3.1, http://mcm.leeds.ac.uk/MCM/). γMT,oxidant denotes the first p-HOM-RO2 yield for different monoterpenes and oxidants, deriving from a combination of literature-based mechanistic insights and adjustments to more accurately replicate the observed HOM concentrations:
For α-pinene + O3, we adopt a first p-HOM-RO2 yield of 9%, following the theoretical considerations of Iyer et al.37. In their study, α-pinene ozonolysis is assumed to form four Criegee intermediates with roughly equal likelihood (~25%), but only one of them efficiently forms RB1-RO2 capable for autoxidation (with a branching ratio of ~89%), leading to a maximum yield of ~22%. In a lower-limit scenario (~12% branching ratio), this value decreases to ~3%. Given the large uncertainty in these branching ratios (3–22%), we chose 9% as a representative value that falls within the physically reasonable interval and provides good agreement with observed HOM concentrations. For the same consideration, we use a γp-HOM-RO2 of 1.12%, corresponding to the upper limit of reported HOM yields in α-pinene + OH system (~0.44% by Jokinen et al.33, 1.1% by Shen et al.54 and 1.2% by kirkby et al.17).

Calculation of the oxidation fraction of p-HOM-RO2 (OFp-HOM-RO2)
To characterize the competition between oxidation and termination processes of autoxidation-capable RO2 radicals (p-HOM-RO2), we define a metric, the Oxidation Fraction (OFp-HOM-RO2), as
OFp-HOM-RO2 = (Oxidation rate) / (Oxidation rate + Loss rate) (6)
The oxidation rate pertains to the rate at which p-HOM-RO2 (defined as RO2 species are capable of autoxidation and contains fewer than 7 O atoms) becomes HOM-RO2 (≥7 O atoms):
Autoxidation pathway. A H-shift followed by O2 addition adds two O atoms per step. Thus, p-HOM-RO2 with at least 5 O atoms can reach the HOM-RO2 threshold via one autoxidation step.
RO2 pathway. RO2 radicals formed via RO2+RO2 or RO2+NO reaction can undergo rapid isomerization followed by O2 addition, contributing one O atom. Therefore, p-HOM-RO2 with 6 O atoms can become HOM-RO2 through this route.
The contribution from RO2 pathway can be calculated using the following equation:
Oxidation rate of RO2 pathway = k_RO2+RO2 * [RO2] * γRO2+RO2 + k_RO2+NO * [NO] * γNO+RO2 (7)
where γRO2+RO2 and γNO+RO2 denote the branching ratios of RO2 that eventually form new RO2 from RO2-RO2/NO reactions, respectively. These parameters, like the reaction rate constants, are determined by the property of the precursor p-HOM-RO2.

The loss rate of p-HOM-RO2 encompasses influences from surfaces losses to chamber walls and particles and chemical loss through termination reactions with other RO2, NO and HO2. For condensation sinks and wall losses, we apply the same calculation method for p-HOM-RO2 as for closed-shell molecules. Reactions of RO2 with HO2 and NO are all treated as termination. As for the reaction of RO2 with NO/RO2, all of reactions are termination except for the portion (γRO2+RO2 and γNO+RO2) that produces RO2.

In this calculation, the p-HOM-RO2 pool is treated as an integrated whole. The numerator in Eq. 6 represents the total rate at which p-HOM-RO2 are converted into HOM-RO2 (i.e., RO2 with ≥7 O atoms) through autoxidation or RO2 pathways. The denominator includes all processes that remove p-HOM-RO2 from this pool, including both oxidation and termination reactions. Importantly, internal transformations within the p-HOM-RO2 pool (e.g., oxygen addition that does not lead to HOM-RO2 formation) are not considered, as they do not reflect a net transition out of the p-HOM-RO2 category. This approach allows us to assess the net competition between oxidation and loss for the whole p-HOM-RO2 pool.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_2": "Key results\nYang et al. report three novel results: first that previously reported HOM yields can be more precisely interpreted, second that\nthe HOM yield across multi-dimensional space may be quantified by a single parameter, and third that across some of this\nmulti-dimensional space laboratory experiments have rarely overlapped with ambient conditions.\nValidity\nThere is some extrapolation in the interpretation of the presented evidence. The authors are searching for a unifying concept\nto characterise HOM yields and therefore provide a framework to support meaningful HOM and SOA research. The authors\nclaim to have resolved their search and provided a ‘universal’ (abstract wording) explanation for HOM yield variation.\nHowever, the evidence presented through comparison of the presented unifying concept and observations (Figure 3) covers\na limited space in the multi-dimensions of the ambient atmosphere that does not comprehensively cover the HO2, or RO2\nfrom multiple parent VOC (e.g. CH3O2) space. In theory, the unifying concept does work across this space, however the\nobservations presented here do not prove that. Therefore, there should be further clarification on the limits of the presented\nevidence.\nSignificance\nThe results presented here are significant. I think some more acknowledgment of the information on which the unifying\nconcept is based is needed, i.e. the work underlying the MCM, PRAM and autoAPRAM-fw. However, the concept itself is\nrobustly derived and extremely helpful for researching HOM evolution in the atmosphere (lab and field). I do encourage the\nauthors to consider whether the abscissa in Figure 4 could be the same as in Figure 3, so that the multi-dimensional space\ncontained in the unifying parameter is better represented than the current limits of [NO] and parent VOC oxidation rate. If this\ncould be achieved, I think the full potential of the unifying parameter will be better demonstrated.\nData and methodology\nOverall the data and methodology are well presented. There are some minor details that I include in the line-by-line list\nbelow. The major omission is the setup of the ADCHAM model for the presented results, and I suggest this be provided\neither as a table in the supplementary material or through a link to a digital repository.\nThe method is sound, and I am very pleased to see well planned chamber experiments used to validate the unifying\nparameter. I do have a reservation of how well the unifying parameter also accounts for autoxidation from different (not just\nthe first generation) generations of peroxy radical, and it may be that the residence time in the steady-state chamber\nexperiments does not allow for these later generations to be significant. Therefore, I invite the authors to discuss this aspect.\nAnalytical approach\nThe method, or main text, should state explicitly what R in Figure 3 is, rather than needing to look in the caption of\nsupplement figure 5. The pearson correlation coefficient measures linear relationships, however Figure 3 and supplement\nFigure 5 suggest non-linearity between HOM yields and the abscissa. Therefore, I suggest a different/additional statistic be\nused to test for correlation. Otherwise analysis is very good.\nSuggested improvements\nIn terms of experiment and data, my suggestion for improvement is included under the Significance section of the review\n(above).\nClarity and context\nThe paper is generally very clear, though I include some minor issues in the list below. The context could be improved\nthrough better acknowledgement of the preceding work needed to calculate the unifying parameter, i.e. the work that has\nenabled MCM, PRAM and autoAPRAM-fw. It would also be good (as I mention in the list below and sections above) to set\nthe context somewhat wider by better inclusion of HO2 and RO2 from different parent VOCs, along with autoxidation of\nbeyond first generation peroxy radicals, or even alkoxy radicals. Finally, discussion of the atmospheric implication on\nambient SOA mass is needed.\nReferences\nSome additional references are suggested in the list below\nYour expertise\nI think my expertise aligns well with the study.\nComments by line\nLine 33 - Question whether ‘universal’ in ‘universal explanation’ is appropriate, given that temperature, [NOx] and [RO2 from\ntwo VOCs] are the only dimensions varied, whilst [HO2] and RO2 from other VOCs are not considered (at least not in\nfigures), nor are autoxidation products from later generation radicals.\nLine 40 - Given the broad nature of the first paragraph, the sentence mentioning HOM as mainly from monoterpene oxidation\nis misleading. This needs to be broader to point to sources of HOM other than monoterpene, such as aromatics (e.g.\ndoi.org/10.5194/acp-20-515-2020) and isoprene (e.g. doi.org/10.5194/acp-21-9681-2021)\nLine 52 - colon needed\nLine 53 - Step 1 and Step 2 imply that first-generation RO2 are only available for autoxidation, however evidence indicates\nthat later-generation RO2 (generated without autoxidation, e.g. through the MCM pathways) can also autoxidise, e.g.\ndoi.org/10.5194/acp-20-515-2020, so this needs making clearer. Generally, the study appears to focus on the autoxidation of\nfirst-generation (from VOC oxidation) RO2, but it would be good to see a mention of whether the autoxidation of later\ngeneration RO2 is compatible with the presented framework.\nLine 89 - This paragraph should also note the HOM yield dependence on HO2 reported by doi.org/10.5194/acp-24-4789-\nLine 96 - In terms of a compelling framework that provides a unified description of varying HOM yields, is this not provided by\nthe MCM and, for monoterpenes, by the PRAM mechanism (cited later in the paper) and the more broadly applicable\nautoAPRAM-fw (doi.org/10.1039/D4EA00054D). With this comment, I don’t question the importance of the ideas detailed in\nthe reviewed paper, but I do question the acknowledgement of previously published frameworks and the phrasing used at\nline 96.\nLine 98, what exactly is the issue? The authors show through the evaluation of MCM+PRAM against CLOUD observations,\nthat the issue is not a lack of chemical understanding, nor a chemical scheme to express that chemical understanding\n(however as written, this section could be interpreted as a lack of chemical understanding). Rather, it seems the study offers\na unification of the detail contained in the chemical scheme into a single parameter for quantifying HOM yield. The derivation\nof the single parameter is important, as is its ability to quantify the HOM yield. The single parameter is a characterisation (as\nexpressed in line 313), that explicitly and clearly demonstrates the key processes of the chemistry. Therefore, the authors\nneed to explain why the current lack of such a characterisation needs resolving.\nLine 133 and following lines: there is a conflict when saying that your study defines HOM as NO>=7 whilst (I think) plotting\nHOM with different definitions in Fig. 1. If it is the case that the HOMs from different experiments in Figure 1 represent\ndifferent definitions, then the wording in the main text needs to be changed to make it even clearer.\nLine 183 needs to give the source of the values for fractions of the first-generation p-HOM-RO2. I.e. need to know where p-\nHOM-RO2 yields used in PRAM in this study come from - in the Methods section the Nie et al. 2023 paper is referenced but I\ncannot see a derivation for the p-HOM-RO2 yields in that paper (or its supplement). Moreover, the yields are different to the\noriginal 2019 PRAM paper (e.g. 6 % branching ratio from APINOOA decomposition in the original compared to 9 % in this\npaper)\nGenerally, are the authors comfortable with referring to the accretion of two peroxy radicals as dimers, which implies a\nsimilarity between the constituent monomers, rather than accretion products? I ask because, in terms of monomer similarity\nin the ambient atmosphere, the extreme case is methyl peroxy radical accreting with a peroxy radical that has ten (or more)\ncarbons and more than ten oxygens. There is an argument that using ‘dimer’ for this extreme case is misleading since the\nmonomers are dissimilar, and therefore ‘dimer’ should be replaced by ‘accretion product’ throughout the paper.\nLine 237 - I wonder if this final sentence could more clearly (possibly by splitting into more sentences) distinguish between\nthe role of RO2 cross reaction that forms HOM dimers and RO2 cross reaction that increasingly outcompetes autoxidation\nwith increasing VOC oxidation rate. One way would be to replace ‘suppressed’ by ‘out-competed through terminating\nreactions, including RO2 cross reaction with RO2 of few oxygens’, or something along these lines.\nLin 265-277 - please tidy this section so that it is clear Fig 5b is being referred to earlier on and not to duplicate stating the\nfact that there is a stronger correlation between HOM yield and OLR than with yield of p-HOM-RO2.\nLine 280 - sentence does not make sense, does ‘p-HOM-RO2’ need placing between ‘of’ and ‘that’?\nIn Figure 4, given the focus on the unifying parameter in this paper, and given that the authors may want to demonstrate\ncompatibility with the Kenagy et al. 2024 framework, would it be more suitable to have (gamma p-HOM-RO2)(OLR_{p-HOM-\nRO2}) as the abscissa (as in Fig. 3) in Fig 4a and b, whilst the ordinate in Fig 4b is HOM yield (as in Fig 3). Similarly, would\nthe authors consider opening the main text in the ‘Summary and atmospheric implications’ section up to consider more than\njust the NO and VOC oxidation rate dimensions, and rather discuss how several dimensions affect OLR_{p-HOM-RO2}\n(including HO2, RO2 (of different parent VOC), NO and NO2). Either way, please edit the colour bar in Fig 4. so that it aligns\nonly with the sub plot to which it corresponds, and edit the caption so it is clearer where descriptions about sub plot a) end\nand sub plot b) begin.\nLine 343 - although discussion around physico-chemical properties of individual aerosol particles is important, it seems\nstrange that the authors do not discuss implications of their work for secondary particulate matter mass (and possibly particle\nnumber).\nLine 470, the text suggests that only RO2 with 5 oxygens and RO with 6 oxygens are considered for estimating the oxidation\nrate in the OLR calculation, but on line 488 its says that oxidation rate and loss rate are averaged across all p-HOM-RO2,\nwith ‘all’ implying to include p-HOM-RO2 with less oxygens. Please clarify and define what averaging method is used. An\nexample calculation for both the numerator and denominator in eq. 6 would be useful.\nLine 478 ‘ultimately p-HOM-RO2’ does not make sense\nSupplement\nSupplementary Fig. 2 uses the phrase ‘self-termination’, but this phrase is not used in the main text, which appears to use\nthe phrase ‘termination’ instead. To my mind, ‘self-termination’ implies an equivalence to self reaction (as opposed to cross\nreaction), implying that the specific peroxy radical in question reacts with itself to terminate, however this interpretation\nconflicts with the +HO2•/RO2•/NO label. Therefore, consistency between the main text and Supplementary Fig. 2 is needed.\nThe caption of supplementary Fig. 2 should be updated to clarify that only an example of HOM formation pathways is shown\n(starting with C10H16+03), whilst other pathways are present in the PRAM, e.g. C10H16+OH\nThe ADCHAM model setup for the mentioned simulations should either be linked to in a digital repository or tabulated in the\nsupplementary material. Including information such as the residence time in CLOUD.\nSimon P. O’Meara", "reviewer_3": "Please see details in the attached file.", "reviewer_4": "HOM are key to the nucleation and growth of organic aerosol particles. Understanding their formation mechanism and HOM yield is essential to quantify their roles in numerical models. In the literature, HOM yields from different studies vary significantly, which is puzzling. This manuscript mechanistically explains the reasons for the variance in HOM yields across different studies. The authors propose a new metric, the product of the yield of initially formed RO2 that can form HOM-RO2 (p-HOM-RO2) and the ratio of the oxidation rate of p-HOM-RO2 to the loss rate of p-HOM-RO2 (OLR). They found that this product correlates well with HOM yield. The findings of this study are novel, timely, and important for better quantifying the role of HOM in new particle formation and growth in regional and global models. I recommend its publication after considering the following specific comments:\n1.Parameterization in Models: I suggest including more discussion on how to use the new HOM yield parameterization in regional and global models compared with a constant HOM yield. This may help bridge the gap between laboratory and modeling studies.\n2.Dependence on RO2 Loss Pathways: The authors focus on the role of RO2+RO2 in the dependence of HOM yield on monoterpene (MT) oxidation rate. However, the dependence of HOM yield on MT oxidation rate may differ when the dominant RO2 loss pathway changes, e.g., in RO2+RO2/HO2 dominant regimes versus RO2+NO dominant regimes. For example, RO promotes both the oxidation rate of p-HOM-RO2 and their loss rate to a different extent compared to HO2. I suggest adding some discussion on this aspect.\n3.Determination of p-HOM-RO2 Yield: In line 458, I suggest clarifying how the first p-HOM-RO2 yield is determined. Additionally, if p-HOM-RO2 is derived from the oxidation of first-generation products, it would be helpful to explain how this is treated in the model.\n4.Dependence on RO2 Structure: The RO2+RO2 rate is highly dependent on RO2 structure. I recommend providing a more detailed description of this in the model, e.g., in the Supplementary Information (SI).\n5.Ambient Conditions and HOM Yields: In lines 323-325 and Figure 4a, it is not new that earlier secondary organic aerosol (SOA) studies used high VOC or oxidant concentrations. To support the argument that \"applying the HOM yields derived from laboratory experiments to the interpretation of ambient data may lead to substantial biases,\" it might be better to limit the discussion to literature reporting HOM yields, as some studies cited in Figure 4a did not report HOM yield. Additionally, Shen et al. (2022) reported HOM yield from α-pinene+OH. In lines 327-329, the authors state that \"the chemical settings in most previous experiments clearly deviate from atmospheric conditions (Fig. 4b).\" However, the ambient conditions of NO are not discussed here. I suggest including a discussion of atmospheric NO levels in different environments.\n6.Visualization in Figure 4b: In Figure 4b, one could color-code the measured data to show that the model can capture the HOM yield under different MT oxidation rates and NO levels.\n7.Definition of HOM: In lines 139-140, it is still not entirely clear why NO≥7 is used to define HOM here. Additionally, it would be helpful to discuss how much this differs compared to traditional yields in the literature (e.g., in Figure 1b).", "reviewer_1": "Key results\nYang et al. report three novel results: first that previously reported HOM yields can be\nmore precisely interpreted, second that the HOM yield across multi-dimensional space\nmay be quantified by a single parameter, and third that across some of this multi-\ndimensional space laboratory experiments have rarely overlapped with ambient\nconditions.", "reviewer_2_round_2": "The authors have responded to the referee comments fully. The result is a paper that\nis highly significant and novel. It gives credit to past works whilst presenting new\nevidence and concepts that will greatly support future work by the gas-phase\nchemistry community. The work is very well written and presented, it is a pleasure to read. I recommend publication after\nattention to the following minor revisions\nThere are some minor revisions remaining:\nLine 105: 'While these observations under different chemical settings, existing models such' does not make sense.\nLine 293: 'the relatively small variation in γp-HOM-RO2 across the dataset limits its\nexplanatory power when considered. Therefore, ' does not make sense.\nLine 328: remain -> remaining?\nLine 328, should 'first-generation' be 'multi-generation' or 'later-generation'?\nLine 491 (Methods), please state the version of the ADCHAM model used\nSimon P. O'Meara", "reviewer_3_round_2": "The authors have addressed the comments properly. Considering the novelty and scientific significant of this work, I\nrecommend the publication of this paper on Nature Communications.", "reviewer_4_round_2": "The authors have well addressed all my comments. I recommend its publication in current form."}, "author_response": "Response: We appreciate the reviewer’s recognition of our effort in introducing the\nconcept to interpret variations in HOM yields. At the same time, we value the\nreviewer’s critical feedback regarding ambiguities in our methods and analysis. We\nhave carefully considered all the concerns raised and have revised the manuscript\naccordingly to improve clarity and robustness. Detailed responses to each comment are\nprovided below.\nMajor comments:\n1) The method part, which is the foundation of this study. a. The calculation of HOM\nyields here was based on the assumption that wall loss and condensation are the\nonly loss pathways for HOM. Since HOMs are generally low-volatility species,\nhave the authors considered the gas-to-particle partitioning as a potential sink for\nHOMs?\nResponse: We thank the reviewer for raising this important point. We agree that gas-to-\nparticle partitioning includes not only condensation onto existing particles but also the\ndirect involvement of HOMs in new particle formation.\nIn our CLOUD chamber experiments, no seed particles were introduced; therefore, all\naerosol particles contributing to the condensation sink were formed solely through new\nparticle formation. The wall loss rate was constant at ~1.65 × 10-3 s-1, while the\ncondensation sink remained much smaller, with values typically below 8.0 × 10-4 s-1\n(median ~1.85 × 10-5 s-1; Supplementary Fig. 1). This indicates that wall loss was the\ndominant sink throughout the experiments.\nFor nucleation, previous studies (Kirkby et al., 2016; Lehtipalo et al., 2018) have shown\nthat HOM monomers do not directly participate in cluster formation. Even if we assume\nthat each 1.7 nm particle contains up to five HOM dimers in the pure biogenic\nnucleation case (Kirkby et al., 2016), the maximum nucleation rate observed in these\nexperiments (<4 cm-3s-1) would correspond to a HOM dimer loss rate of less than 20\ncm-3s-1. Given the measured average HOM dimer concentrations on the order of 9.0×\n105 cm-3, this corresponds to a loss frequency of <2.3 × 10-5 s-1, which is more than\nthirtyfold lower than both wall loss and condensation.\nTherefore, the omission of nucleation in the HOM yield calculations is well justified,\nas wall loss clearly dominates under our experimental conditions.\nSupplementary Figure 1. Overview of the CLOUD experiment. Timeseries of (a) α-\npinene, O , OH concentrations (b) HOM and their average loss rate, including wall loss\n3\nand condensation sink, in the experiment. A NO - CIMS was employed to measure the\n3\ngas-phase HOMs.\nReference:\nKirkby J., et al. Ion-induced nucleation of pure biogenic particles. Nature 533, 521-526 (2016).\nLehtipalo K., et al. Multicomponent new particle formation from sulfuric acid, ammonia, and biogenic\nvapors. Science Advances 4, (2018).\nb. Lines 137-139: The authors mentioned HOM is defined by No≥7 in this study, does\nit mean the HOM yields reported in this study is somewhat biased low?\nResponse: We thank the reviewer for this question. In definition, HOM used in this\nstudy is lower than those that use No≥6. To assess the potential bias introduced by HOM\ndefinition, we performed a sensitivity analysis that compares HOM yields under\ndifferent definitions, both in the measurements and in the model simulations.\nWe found that for the observational data, HOM yields varied only slightly (within 8%)\nacross different definitions (N ≥ 6), which could be explained by that NO -CIMS is\nO 3\ninherently more sensitive to highly oxygenated species, and has low sensitivity to\nspecies with fewer than 7 oxygen atoms. In contrast, the model showed much larger\nvariability in HOM yield depending on the chosen threshold.\nThis highlights the importance of using a consistent and measurement-representative\nHOM definition when comparing model and observation. Therefore, we consider the\nuse of 𝑁 ≥7 in this study to be appropriate and necessary, and have added clarification\n𝑂\nin the revised manuscript.\nFigure R1. (a–b) HOM yields calculated using different HOM definitions in (a)\nobservations and (b) model simulations. (c–d) The ratios of HOM yields calculated\nusing previously used definition (N ≥ 6) to those based on the N ≥ 7 definition in (c)\nO O\nobservations and (d) simulations.\n2) The model performance.\na. The paragraph of Lines 128-142: From Figure 1a, it could be seen that the HOM\nyields vary by up to one order of magnitude, i.e., from less than 1% to ~10%. For the\nseveral potential reasons raised here, can the authors add more quantitative discussions,\ne.g., the RO autoxidation is temperature-dependent, then considering the temperature\n2\ndifference here ranging from 248 K to 298 K, how much difference would be caused?\nConsidering the relative abundance of O and OH, since the OH and ozone\n3\nconcentration could be measured, then can the authors estimate how much difference\nwould be caused by the different HOM yields in ozone- and OH-initiated alpha-pinene\noxidation?\nResponse: We appreciate the reviewer’s constructive comment. After carefully\nevaluation, however, we cannot reach quantitative conclusions for the inconsistent\nHOM yields among different experiments. Detailed reasons are provided below.\nFirst, regarding the temperature dependence of RO autoxidation, we agree that\n2\ntemperature can significantly influence HOM formation. However, the temperature\ndependence is non-linear, and the reaction kinetics are not yet well understood. So far,\nvery few investigations have focused on the temperature effect, and they are not\nconsistent. Quéléver et al. (2019) reported α-pinene HOM yields of 5.2 % at 293 K,\n0.10 % at 273 K, and 6.3×10-3 % at 258 K, showing a drop by nearly three orders of\nmagnitude with decreasing temperature by 35 K. In another study, Simon et al. (2020)\nobserved a smoother trend: 6.2 % at 298 K, 4.7 % at 278 K, 2.9 % at 263 K, 1.3 % at\nHOM yield at lower temperatures. In both studies, no modeling efforts have been paid\nto explain the effect of temperature. In fact, our collaboration team is performing a\nsystematic analysis on the temperature effect using the data sets from Simon et al.,\n(2020), so that we only qualitatively describe influence of temperature in our study.\nSecond, regarding the impact of different oxidants (O and OH). In general, ozonolysis\n3\nof α-pinene produces RO that favor autoxidation and subsequent HOM formation\n2\n(with p-HOM-RO yield of 9 %), while OH-initiated oxidation has a much lower p-\n2\nconcentration of non-HOM-RO , which enhances RO loss via bimolecular reactions\n2 2\nand subsequently, reducing HOM yield. In our experiments, OH and O can be well\n3\nquantified, so that we are able to quantify their contributions to HOM production.\nHowever, in other experiments, the OH concentration is hard to quantify, given that\nmany key parameters, such as light intensity, chamber impurity (may serve as either\nsource or sink of OH), NO concentrations, etc., are not provided.\nx\nOverall, we’d like to stress that the Figure 1b serves as a demonstration of decreasing\nHOM yields along with increasing monoterpene oxidation rates as a common\nphenomenon. However, a quantitative understanding of the yield difference among\nthese experiments cannot be obtained.\nReference:\nQuéléver L. L. J., et al. Effect of temperature on the formation of highly oxygenated organic\nmolecules (HOMs) from alpha-pinene ozonolysis. Atmos Chem Phys 19, 7609-7625 (2019).\nSimon M., et al. Molecular understanding of new-particle formation from alpha-pinene between -\n50 and +25 °C. Atmospheric Chemistry and Physics 20, 9183-9207 (2020).\nBerndt T., et al. Hydroxyl radical-induced formation of highly oxidized organic compounds. Nat\nCommun 7, (2016).\nb. Line 175: Here it mentioned that the model has a robust performance. However,\nbased on Figure S4, the model showed a clear overestimation on C10H14O9 and\nC10H16O9, by a factor of 2. Can this be considered as “good agreement”?\nResponse: We thank the reviewer for the comment. We acknowledge that the model\noverestimates certain products, such as C H O and C H O , by up to a factor of ~2\n10 14 9 10 16 9\nunder some conditions, as shown in Supplementary Figure 4. While these discrepancies\nexist, the model generally captures the broader features of the HOM distribution, with\ncoefficient of determination (R2) exceeding 0.7 across different conditions. This\nsuggests reasonable agreement in the overall spectrum, though not necessarily for every\nindividual compound. Considering the complexity of the chemistry involved and\ninherent uncertainties in both observations and model mechanisms, we believe the\nmodel demonstrates a solid performance. In light of this, we have revised the wording\nfrom “such robust performance” to “good overall agreement” to better reflect the\nmodel’s strengths while acknowledging its limitations.\nLine 187-190: Although some deviations exist between simulated and observed\nconcentrations, the model captures the overall HOM distribution well, with coefficients\nof determination (R2) exceeding 0.7 across different conditions.\nThis level of agreement enables us to quantify the fate of RO on a quasi-molecular\n2\nlevel….\nSupplementary Figure 4. Comparisons between modeled and observed spectrum in α-\npinene oxidation experiment with (a) 30 ppt, (b) 70 ppt, (c) 180 ppt, (d) 400 ppt, (e)\n850 ppt and (f) 1050 ppt α-pinene. Mass/charge ratio is plotted in units of Thomson (Th)\nand it should be noted that the nitrate reagent ions has been removed from mass. The\ncoefficient of determination (R2) between the modeled and observed spectrum is shown\nin each panel, indicating the degree of overall agreement under each condition.\nc. Lines 184-185: The fractions set here for OH- and O3-initiated p-HOM-RO differ\n2\nby a factor of 8, why are the fractions set as these two values? Is the setting associated\nwith the OH and O levels in the chamber?\nand O -initiated p-HOM-RO yields in our model (1.12% vs. 9%) is not due to\n3 2\ndifferences in OH and O concentrations in the chamber but rather reflects different\n3\nefficiencies of producing p-HOM-RO associated with the two oxidation pathways.\n3 2\nformation of RB1-RO from stabilized Criegee intermediate (sCI) decomposition.\nwith roughly equal probability (~25%). Only one of them efficiently forms\nautoxidation-capable RB1-RO , with a branching ratio of ~89%, giving an estimated\n2\nyield of ~22%. In the lowest-yield scenario (~12% branching ratio), the overall yield\nwould be ~3%. Considering this wide theoretical range (3–22%), we performed\nsensitivity tests and found that adopting a yield of 9% best reproduces the observed\nHOM concentrations while remaining within the plausible interval. For the OH-\ninitiated pathway, we adopt an effective p-HOM-RO yield of 1.12%, corresponding to\n2\nthe upper bound of reported HOM yields from OH + α-pinene, as derived from studies\nby Kirkby et al., (2016) Shen et al., (2022) and Jokinen et al. (2015).\nWe have revised our manuscript to include the information as follows:\nLine 545-555: For α-pinene + O , we adopt a first p-HOM-RO yield of 9%, following\n3 2\nthe theoretical considerations of Iyer et al. In their study, α-pinene ozonolysis is\nassumed to form four Criegee intermediates with roughly equal likelihood (~25%), but\nonly one of them efficiently forms RB1-RO capable for autoxidation (with a branching\n2\nratio of ~89%), leading to a maximum yield of ~22%. In a lower-limit scenario (~12%\nbranching ratio), this value decreases to ~3%. Given the large uncertainty in these\nbranching ratios (3–22%), we chose 9% as a representative value that falls within the\nphysically reasonable interval and provides good agreement with observed HOM\nconcentrations. For the same consideration, we use a γ of 1.12%,\np₋HOM₋RO2\ncorresponding to the upper limit of reported HOM yields in α-pinene + OH system\n(~0.44% by Jokinen et al, 1.1% by Shen et al and 1.2% by kirkby et al).\nReference:\nIyer S., et al. Molecular mechanism for rapid autoxidation in α-pinene ozonolysis. Nat Commun 12,\n6 (2021).\nBerndt T., et al. Hydroxyl radical-induced formation of highly oxidized organic compounds. Nat\nCommun 7, (2016).\nKirkby J., et al. Ion-induced nucleation of pure biogenic particles. Nature 533, 521-526 (2016).\nShen H. R., et al. Unexpected significance of a minor reaction pathway in daytime formation of\nbiogenic highly oxygenated organic compounds. Science Advances 8, (2022).\nJokinen T., et al. Production of extremely low volatile organic compounds from biogenic emissions:\nMeasured yields and atmospheric implications. Proc Natl Acad Sci U S A 112, 7123-7128 (2015).\nd. Lines 238-240: From Fig. 2c, it could be seen that the model captured the trend of\nobserved HOM dimers with increasing MTreact; however, the HOM dimers are largely\noverestimated, especially at low alpha-pinene levels. Is it due to measurement\nuncertainty, or the setting of model parameters?\nResponse: Thanks for pointing this out. Indeed, the model show higher HOM dimer\nconcentrations, particularly at low α-pinene concentrations. There are a few reasons.\nFirst, this is related to the detection limit of the NO -CIMS instrument (on the level of\n3\n103 cm-3) used for measurements. Since HOM dimers are only a minor product channel\nof RO –RO reactions, concentrations of many HOM dimers were not high enough to\n2 2\npass the detection limit. This has a more pronounced influence in low-monoterpene\nexperiment, as more HOM dimers are below the detection limit (Fig. R2). However,\nmodel still simulates the total dimer production, while the observed values may reflect\nonly those dimers that are sufficiently abundant to be detected.\nFigure R2. Observed concentration distribution of HOM dimers across varying α-\npinene concentrations. The region to the left of the dashed line indicates concentrations\nbelow the detection limit, while the region to the right represents concentrations above\nthe detection limit.\nSecond, the formation of accretion products (i.e., dimers) involves a range of complex\ngas-phase pathways that have not yet been fully understood. While peroxide-type\ndimers are known to form via gas-phase RO –RO cross reactions, recent studies\n2 2\nsuggest that these reactions may also lead to the formation of esters and other accretion\nproducts through intermediate RO–RO complexes (Peräkylä et al, 2023). In such\ncomplexes, rapid intramolecular rearrangements or β-scissions can occur prior to\nrecombination, resulting in stable products such as esters, hemiacetals, or ethers. The\ncurrent model incorporates peroxide-type RO –RO chemistry but does not yet resolve\n2 2\nthe full spectrum of possible isomerization and decomposition pathways, which could\nlead to discrepancies in both yield and distribution.\nIn summary, the overestimation of HOM dimers in the model likely stems from a\ncombination of instrument detection limitations and incomplete understanding of\ncomplex dimerization pathways, which can lead to unmeasured or mischaracterized\nspecies.\nReference:\nPeräkylä, O., Berndt, T., Franzon, L., Hasan, G., Meder, M., Valiev, R. R., Daub, C. D., Varelas, J.\nG., Geiger, F. M., Thomson, R. J., Rissanen, M., Kurtén, T., and Ehn, M.: Large Gas-Phase Source\nof Esters and Other Accretion Products in the Atmosphere, J. Am. Chem. Soc., 145, 7780-7790,\n10.1021/jacs.2c10398, 2023.\n2) Lines 274-277: I do not understand the casual relationship of these two sentences.\nEven if γ has a larger variation, does it mean that γ could have\np-HOM-RO2 p-HOM-RO2\npositive relationship with HOM yields, and the results could be used to interpret the\nrelative role of OLR and γ ?\np-HOM-RO2\nResponse: We thank the reviewer for this important comment. We agree that the\nstrength of correlation alone cannot be used to determine the relative importance in\ncontrolling HOM yields. In the revised manuscript, we highlight the combined\ninfluence of the formation efficiency of p-HOM-RO (γ ) and its subsequent\n2 p-HOM-RO2\noxidation toward HOM-RO . The revised formulation varies between 0 and 1 and\n2\nrepresents the fraction of p-HOM-RO₂ that becomes HOM-RO via oxidation, offering\n2\na more intuitive and interpretable measure of how favorable the environment is for\nHOM formation.\nWe believe that these changes enhance the physical interpretability of the framework.\nLine 283-297: In most NO -involved experiments, HOM yields increase with γ\nx p-HOM-\n, except in the “pure NO ” experiments, where an opposite dependence is observed.\nRO2 2\nThis indicates that γ is not the sole factor determining the HOM yield. For any\np-HOM-RO2\ngiven γ , a higher HOM yield is generally observed at greater OF . This\np-HOM-RO2 p-HOM-RO2\nis exemplified by the experiments without NO , where γ remains relatively\nx p-HOM-RO2\nconstant at ~0.06 (filled circles in Supplementary Fig. 5a), while the HOM yield\nincreases from ~1% to ~2.6% as OF rises from ~0.2 to ~0.7. To further\np-HOM-RO2\nillustrate this relationship, Supplementary Fig. 5b shows the HOM yield as a function\nof OF across all conditions. While both γ and OF contribute\np-HOM-RO2 p-HOM-RO2 p-HOM-RO2\nto the variability in HOM yields, the relatively small variation in γ across the\np-HOM-RO2\ndataset limits its explanatory power when considered. Therefore, we additionally\nexamine the product of γ and OF , which captures the combined effect\np-HOM-RO2 p-HOM-RO2\nof formation efficiency and availability of the precursor, and yields the strong\ncorrelation with HOM yield (Fig. 3).\nOther comments:\nLine 31: “a factor 3” -> “a factor of 3”;\nResponse: Thanks. It has been corrected accordingly in the revised manuscript.\nLine 49: “has” should be “have”, since the subject of this sentence is “A and B”; Lines\n48-52: Long sentence.\nResponse: In the revised version, we have restructured the sentence using “together\nwith” to improve clarity and flow. As a result, the subject is now singular, and the use\nof “has” is grammatically correct. In addition, the sentence spanning Lines 50–54 has\nbeen revised and split into shorter, clearer statements to improve readability.\nLine 50-54: “The atmospheric discovery of HOM, together with the further\ndemonstration of their crucial impact on aerosol formation in various environments, has\nled to rapidly growing interest in understanding the HOM formation mechanism. In\ngeneral, HOM formation proceeds through three consecutive steps that are tightly\nassociated with the fate of peroxy radicals (RO ), including…”\nResponse: We thank the reviewer for pointing out the ambiguity in the original sentence.\nTo clarify the meaning, we have revised the sentence as follows:\nLine 92: In light of this, the HOM yields ought to vary even under the same chemical\nsystem when concentrations of reacting species and/or oxidants are changing. However,\nsuch variations have seldom been recognized and reported in previous studies.\nLine 99: The use of “more” is not proper here; Lines 99-100: Two “and”s in one\nsentence. Please re-write.\nResponse: Thanks. In the revised manuscript, we have restructured the sentence to\navoid the redundant use of “and”. The revised sentence now reads:\nLine 111-113: Here, we first revisit experimental data from the CLOUD chamber and\ncomplement this analysis with additional data from other chambers and flow reactors.\nLine 159: The unit of alpha-pinene concentration is ppt, or ppb? In supplementary Table\n1 it showed “30-1050 ppb”. Please keep consistency throughout the paper.\nResponse: Thank you for pointing this out. We apologize for this typo. The unit should\nbe ppt, and we have resolved this inconsistency throughout the manuscript.\nLines 205: “and consequently”, this expression shows redundant conjunction. Please\nre-write this sentence.\nResponse: In the revised manuscript, we have removed the redundant use of “and\nconsequently” and restructured the sentence to improve clarity and logical flow. The\nrevised sentence now reads:\nLine 218-221: From another perspective, the substantial enhancement of RO cross-\n2\nreactions reduces the lifetime of p-HOM-RO , thereby lowering its probability of\n2\nundergoing autoxidation. This results in a significant reduction in the formation of\nHOM-RO and eventually in the HOM yield.\nResponse: Sorry for the unclarity. We have revised the sentence to clarify that it refers\nto the observed reduction in HOM yield. The revised text now reads:\nLine 233-234: However, we only observe a 62% decline in the HOM yield. This\nreduction is primarily attributed to the formation of alkoxy radicals (RO) via\nbimolecular termination pathways.\nLines 225-230: Long sentence. I think the authors could consider split it into two\nseparate sentences.\nResponse: We have split the long sentence into two separate ones to improve clarity\nand readability. The revised text now reads:\nLine 240-245: HOM monomers, mostly classified as low-volatility organic compounds\n(LVOC, 10-4.5 g/m3  C*  10-0.5 g/m3), are responsible for the growth of\nnanoparticles. Differently, HOM dimers are mostly ultra-low volatility organic\ncompounds (ULVOC, C* < 10-8.5 g/m3) and extremely low volatility organic\ncompounds (ELVOC, 10-4.5 g/m3 < C*  10-8.5 g/m3) that can be important for particle\nnucleation.\nLines 254-255: relationship -> relationships; between -> among; and -> with;\nResponse: Thanks. Revised as suggested.\nLines 256-257: This sentence here did not mention the ozone concentration, was it\nconstant? At what level?\nResponse: We thank the reviewer for the comment. The O concentration was indeed\n3\nkept nearly constant at approximately 40 ppb in all five experimental settings, as shown\nin Supplementary Table 2. We have now added a sentence in the main text to clarify\nthis point.\nLine 274-278: We examine the relationships of  ,OF , with the HOM\np-HOM-RO2 p-HOM-RO2\nyields among 5 experimental settings (and 23 steady-state conditions), covering\ndifferent monoterpene types (-pinene and -3-carene) and concentrations, and various\nNO conditions. The O concentration was kept nearly constant at approximately 40\nx 3\nppb across these experiments, as detailed in Supplementary Table 2.\nLines 284: “P-HOM-RO2”, “p” should be lower case.\nResponse: Thank you for pointing this out. We have corrected “P-HOM-RO ” to “p-\nclarify.\nResponse: We have revised the figure caption to explicitly indicate that both the blue\nmarkers and the grey areas refer to Figure 4(b), to improve clarity.\nLine 385-388: In panel (b), the blue markers denote the laboratory experimental data\npoints: blue-bordered ones from the CLOUD and JPAC experiments, and borderless\nones from other studies. The grey areas represent the real atmospheric ranges of NO\nconcentrations and monoterpene oxidation rate."}]

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