Reactive aldehyde chemistry explains the missing source of hydroxyl radicals

Domain: earth_science
Published: 2024-02-22
Editorial outcome: accept

Abstract
Hydroxyl radicals (OH) determine the tropospheric self-cleansing capacity, thus regulating air quality and climate. However, the state-of-the-art mechanisms still underestimate OH at low nitrogen oxide and high volatile organic compound regimes even considering the latest isoprene chemistry. Here we propose that the reactive aldehyde chemistry, especially the auto-oxidation of carbonyl organic peroxy radicals (R(CO)O2) derived from higher aldehydes, is a noteworthy OH regeneration mechanism that overwhelms the contribution of the isoprene autoxidation, the latter has been proved to largely contribute to the missing OH source under high isoprene condition. As diagnosed by the quantum chemical calculations, the R(CO)O2 radicals undergo fast H-migration to produce unsaturated hydroperoxyl-carbonyls that generate OH through rapid photolysis. This chemistry could explain almost all unknown OH sources in areas rich in both natural and anthropogenic emissions in the warm seasons, and may increasingly impact the global self-cleansing capacity in a future low nitrogen oxide society under carbon neutrality scenarios.

Introduction
Hydroxyl radicals (OH) are the most important oxidant in the atmosphere, which largely control the removal of most trace gas compounds from local to global scales, and determine the atmospheric self-cleansing capacity. The OH chemistry initiates the formation of secondary pollution (mainly haze and ozone)1–4, worsens air quality, and threatens human health and the ecological environment. The OH radical also regulates the fate of greenhouse gases like methane, chlorofluorocarbon, ozone, and aerosols to affect the climate5,6. For example, tropospheric OH concentration decreased by 1.6±0.2%, largely contributing to the methane growth rate anomaly in 2020 relative to 20195. Despite its critical role in atmospheric chemistry and climate change, the budget of OH is still not well understood from local to global scales7.

There is a long-standing puzzle that OH concentrations measured in environments with low nitrogen oxide (NO) and high volatile organic compounds (VOCs) are usually significantly underestimated by the state-of-the-art models2,8–18. Prior studies attempted to explain the deviation in the past decades and proposed numerous radical generation mechanisms. Leuven Isoprene Mechanism (LIM)19,20 and self-reactions of peroxy radicals10,21 were proposed mainly for the forested areas, whereas these mechanisms are still insufficient to explain the discrepancy between the OH observations and model results. Additionally, a parameterized mechanism in the form of RO2+X→HO2 and HO2+X→OH was proposed to reproduce OH radicals without HO2 generation11. It is demonstrated that more detailed mechanisms are urgently needed to narrow the gaps of OH radical chemical mechanisms in the troposphere10,11,19–21.

In this study, with a retrospective meta-analysis of the surface-based radical observation dataset spreading over the major city clusters in China (Supplementary Text 1, Supplementary Figs. 1–2, and Supplementary Tables 1–3) in warm seasons during 2006-20192,11,14–17,22,23, we showed the missing OH source is closely related to the oxygenated volatile organic compound (OVOC) chemistry. Based on the combination of quantum chemical calculations and observation-constrained model simulations, we report the detailed reaction processes of the autoxidation mechanism of high aldehydes and further confirm its importance by examination in numerous field studies worldwide.

Results
Characterization of the OH missing source
We revisit the OH budget in seven campaigns conducted in China in warm seasons and find that although the model (Methods, Supplementary Text 1, Supplementary Figs. 1–2, and Supplementary Tables 1–3) reproduces the observed OH at high NO conditions (>1 ppb), it underestimates the observed OH radicals at low NO conditions (<1 ppb), and the OH underestimation becomes systematically more severe with the decreasing NO concentrations (Fig. 1a and Supplementary Fig. 3). Possible measurement interference, derived from the decomposition of the Stable Criegee Intermediates or a new class of molecule (ROOOH), was proved to be negligible15,17,22,24–29. This confirms that OH underestimation by model simulation derives from the incomplete understanding of atmospheric radical chemistry. The experimental budget analysis was applied to cross-check the chemistry, by comparing the classical and well-known OH production rate and the total OH destruction rate (Methods and Supplementary Text 2). The OH production rate is the summed experimentally determined reaction rates of nitrous acid photolysis, ozone photolysis, ozonolysis of alkenes, and hydroxyl peroxy radicals (HO2) plus NO as well as O3. The total OH destruction rate is calculated by the product of the observed OH concentration and total OH reactivity (kOH)2,11,15–17. It revealed a universal fact of unidentified missing OH sources for all seven warm-season campaigns in China, especially around noontime and afternoon with low NO levels (Supplementary Fig. 4).

The correlation between missing OH sources and the inverse of NO reactivity (1/kNO) is positive within low NO regimes NO concentration below 1 ppb, equivalent to 1/kNO above 5 s (Supplementary Fig. 5a), indicative of the missing OH processes closely related to the level of NO. Here we find that adding VOC reactivity into the expression significantly improves the correlation between missing OH sources and 1/kNO (Supplementary Fig. 5b). Among the VOC species, it is notable that missing OH sources show a perfect positive correlation with ratios of OVOC reactivity versus NO reactivity (kOVOCs/kNO), which is much better than the other sets of correlations by anthropogenic or biogenic VOCs (Fig. 1b). Coincidentally, high OVOC concentrations generally occurred during noontime and afternoon30, consistent with the OH underestimation periods. Moreover, OVOCs play a crucial role in the total VOC reactivity, with a large fraction of about half (Supplementary Fig. 2). Thus, it indicated that OVOCs might be tightly related to the missing OH sources, and the missing OH sources from OVOC chemistry show a competitive relationship with NO.

The reactive aldehyde chemistry mechanism
Quantum chemical calculations are used to explore the OH regeneration pathways related to OVOCs. Prior studies examined the H-migration rate constants of carbonyl organic peroxy (R(CO)O2) radicals from C3-C5 aldehydes and found the H-migration rates dramatically increased as the carbon number increased31. For C3 and C4 aldehydes, the H-migration rate for peroxy radicals is predicted to be negligible compared to the reaction rate with NO at typical NO concentrations in the troposphere. For C5 aldehydes, the H-migration rate of RC(O)O2 from iso-pentanal was estimated to be up to 0.58 s-131, which will then overshoot the effect of NO to dominate the fate of peroxy radicals. Wang et al. further affirmed the high autoxidation potential of aldehydes under atmospheric conditions32.

Here, we further determined the H-migration rate of the organic peroxy radicals derived from hexanals through the WMS33//M06-2X34/MG3S35 method (Methods and Supplementary Text 3). The kinetic calculation results showed that the 1,7 H-migration with a rate constant of 0.321 s-1 at 298 K is the most favorable pathway among all possible H-migration reactions based on the multi-structural transition state theory36 with Eckart tunneling37 (Supplementary Fig. 6a and Supplementary Table 4). It is noted that the conformers for reactants, transition states, and intermediate products are the lowest conformers, respectively. The molecules of reactant and transition states for generating conformers are shown in Supplementary Fig. 6b. Combining the estimations of both C5 and C6 aldehydes, we estimated the H-migration rate of organic peroxy radicals from higher aldehydes with the lower one. Thus, it represents a kind of conservative evaluation for this channel.

As shown in Fig. 2a, the R(CO)O2 radicals undergo an H-migration process and are transformed to ·OOR(CO)OOH radicals, which then react with NO to produce ·OR(CO)OOH radicals. Subsequently, the ·OR(CO)OOH radicals mainly undergo two consecutive fast H-migration reactions and then react with O2 to produce HO2 radicals and hydroperoxyl-carbonyls (HPC)31. The photolysis of HPC is rapid, with a photolysis frequency as high as 10-4 s-1 producing OH radicals, which has been proved by ref. 38. Here, for a conservative result, we set the HPC photolysis frequency to 10 times the methacrolein photolysis frequency, which is approximately (0.6–0.9)×10-4 s-1 around the noontime and corresponds to the lower limit of HPC photolysis frequencies38. The detailed reactions and rate constants of the higher aldehydes autoxidation chemistry are shown in Supplementary Table 5.

Performance evaluation of the mechanism
We parameterized the Higher Aldehyde Mechanism (HAM) into the state-of-the-art atmospheric chemical mechanisms (RACM2, Regional Atmospheric Chemical Mechanism updated version 2)39 and evaluated the contribution of HAM to radical chemistry (Methods). It is worth emphasizing that LIM, which involves the H-migration of RO2 from isoprene19,20, has been proven to be an OH regeneration mechanism that mainly works under high isoprene conditions40. Here, we set the box model with RACM2 as the base mechanism and further updated it by incorporating LIM1 (LIM updated version 1)15,19,20 and HAM. We diagnosed the averaged contribution of the unknown OH sources to the total OH production rates within the corresponding period (10:00-15:00) through the OH experimental budget analysis (Fig. 2b). It shows that the known OH radical sources are insufficient to match the total OH destruction rates. The unclassical OH sources accounted for 15-68% of the determined total OH production rates at low NO conditions in China.

Figure 2c shows the HAM explains 10–90% of unclassical OH sources in the seven campaigns. The contribution of HAM is always much larger compared to that of LIM1 for various campaigns, and the ratios of HAM contribution to LIM1 contribution vary between 1.7 and 8.2. At low kOVOCs/kNO conditions represented by the Taizhou, Wangdu, and Shenzhen sites (Fig. 1), almost all unclassical OH sources could be explained within the uncertainties. With respect to the case of Backgarden, Yufa, Heshan, and Chengdu, unclassical OH sources were still missed by 68–86%, although the contribution of HAM is about 1–3 times larger than that of LIM1. The presence of still unexplained OH sources after including HAM in these campaigns may be tightly related to the following factors: (1) aldehydes from primary emissions, especially aldehydes with high carbon numbers (≥C8/C9) from biomass burning41,42 or cooking activities43,44, are not considered in the model, which are likely to be oxidized into RO2 radicals with much higher H-migration rates than those currently used in this study; (2) the total concentrations of HPC groups were underestimated as they could also be produced from many other VOCs than higher aldehydes (e.g., long-chain alkanes45, ethers46, alcohols47, alkenes48); (3) HPC photolysis rate for HPC species with different functional groups was underestimated. Additionally, aromatic autoxidation mechanisms have been proposed recently, demonstrating the significant role of OH-initiated oxidation of aromatics in forming highly oxidized products and thus secondary organic aerosols49,50, while the mechanism was found negligible for OH generation in the seven field campaigns (Supplementary Text 4 and Supplementary Fig. 7). In short, the higher aldehydes play a much more profound role in the OH regeneration chemistry than isoprene, providing an important theoretical explanation for the unrecognized OH regenerations in China11.

Recent studies have suggested that RO2 derived from VOCs besides aldehydes, such as alkanes, aromatics, and other OVOCs (ketones, ethers, etc.), could also undergo autoxidation with possible subsequent generation of radicals32,45,46,50–53. It is reported that HPC-like substances are generated rapidly by two or more H-migration processes of RO2 radicals54. Herein, we made a rule of thumb assumption, in which certain kinds of VOCs (including alkanes, alkenes, and aromatics, the detailed VOCs summed in Supplementary Text 5) could undergo OH oxidation process, successive H-migration processes and subsequently produce HPC-like reactive substances with a molar yield (named as Reactive Aldehyde Mechanism, RAM). RAM is a broad sense of HAM to some extent. We defined a simple index, named as φ, to characterize the generalized molar yield of OH regenerated by the oxidation of VOCs through the HPC chemistry. The index φ is derived from an inverse modeling method, to achieve a good agreement between the modeled and observed OH radicals (Supplementary Text 5). A reasonable φ of 0.4–2.2 is derived for our seven warm-season campaigns (Supplementary Table 6). Additionally, we show the incorporation of RAM into the model would further improve the agreement between the observed and simulated HO2 concentrations to some extent (Supplementary Fig. 8).

The variation of the index φ in different campaigns may be caused by: (1) HPC species and HPC yield produced by different VOC oxidation processes may be highly varied54. (2) The OH yield from the HPC photolysis may be varied for different HPC species. (3) HPC photolysis frequencies which may differ by over four times38.

From a global perspective, the atmospheric impact of RAM is evaluated through the OH recycling probability, which is a metric of the stability of atmospheric hydroxyl chemistry55 (Methods). We focused on the seven warm-season campaigns in China and seven campaigns in other countries with reported radical observations and missing OH sources9,10,12,27,56,57 (Supplementary Text 6 and Supplementary Table 7)—all together, fourteen campaigns across East Asia, Europe, and America (Fig. 3a). For each campaign, the OH recycling probability calculated by the observations and those simulated by the model sensitivity tests (Methods) were shown in Fig. 3b. The OH recycling probability observations were within 0.8–1.0 in most campaigns, without strong correlations with NO concentrations.

The base model underestimated the OH recycling probability observations which denote the stability of the OH chemical system, especially under low NO regime, which is consistent with the missing OH regeneration processes in the base model. When the LIM1 and RAM mechanisms were added into the base model with a fitted φ (0.2–2.93), the discrepancy between the OH recycling probability observations and simulations was well eliminated (Supplementary Table 6).

We subdivide the NO concentration intervals into ultra-low NO regime (NO < 0.1 ppb, mainly forested areas), low NO regime (0.1 ppb < NO < 1 ppb, mainly suburban areas), high NO regime (1 ppb < NO < 10 ppb, mainly urban areas), and ultra-high NO regime (NO > 10 ppb, mainly urban center of megacities). The importance of LIM1 and RAM mechanisms varies greatly at different NO intervals (Fig. 3c). The impacts of LIM1 on the OH recycling probability were significant under the ultra-low NO regime (forested areas). Nevertheless, the RAM mechanism acts over a wide range of NO concentrations, covering both suburban and urban areas (corresponding to low and high NO regimes). The contributions of autoxidation mechanisms involving LIM1 and RAM to OH recycling probability are insignificant in ultra-high NO regimes (megacities) where the underestimation of OH recycling probability is non-severe.

Increasing importance in the future
A conceptual model is proposed to highlight the role of RAM on OH regeneration in different geophysical areas (Fig. 4). Under the forested areas, the fresh plume is characterized by ultra-low NOx concentrations and high BVOC reactivities, and thus the OH productions belong to the LIM1-dominated areas besides the classical mechanism. While with the air masses aging, the primary BVOCs may be gradually oxidized to OVOCs and the LIM1-dominated areas are gradually transformed into RAM-dominated areas. Under the suburban and urban areas with a NO concentration range of about 0.1–10 ppb, the OH generation rates from RAM are proved to be fast to compete with their reactions with NO. Additionally, for the urban plume with high AVOC concentrations, OVOC concentrations continue to increase over the photochemical development due to the AVOC oxidation, thereby the aging air masses are more conducive to RAM. Under ultra-high NO concentrations, although carbonyl RO2 autoxidation remain effective32, the RAM cannot compete with the bimolecular reactions of RO2 with NO anymore, so the effects of LIM1 and RAM on OH production become negligible (Supplementary Text 7 and Supplementary Fig. 9). With the implementation of global pollutant control policies, especially the proposal of a ‘carbon neutral’ strategy goal in China and the global, NO concentrations in megacities will be greatly reduced to the high or low regime, or even ultra-low NO regime. Under this condition, the contribution of the RAM mechanism to OH regeneration and OH recycling would get significant. Thus, we should be alert to the potential effects of these autoxidation mechanisms on tropospheric oxidation capacity.

Methods
Radical observations
The observations of radical concentrations in China during 2006–2019 come from our seven warm-season campaigns, including CareBeijing-2006 (Yufa site) and NCP2014 (Wangdu site) campaigns conducted in North China Plain; PRIDE-PRD2006 (Backgarden site), PRIDE-PRD2014 (Heshan site), and STORM2018 (Shenzhen site) campaigns conducted in Pearl River Delta; EXPLORE-YRD2018 (Taizhou site) campaign conducted in Yangtze River Delta; CHOOSE2019 (Chengdu site) campaign conducted in Szechwan Basin (Supplementary Fig. 1). These sites located in the four major urban agglomerations in China, all suffering from severe secondary pollution such as both high O3 and PM2.5 concentrations. During these campaigns, radical concentrations are measured by the laser-induced fluorescence system (LIF) based on the fluorescence assay by gas expansion technique2,18. Both OH and HO2 concentrations were measured in the seven field campaigns, and RO2 measurements were only carried out at the Wangdu, Heshan, and Chengdu sites. Besides radical concentrations, a comprehensive set of meteorological and chemical parameters was measured, including the temperature, pressure, relative humidity, photolysis frequency, OH reactivity, and the concentrations of related trace gases (NO, NO2, O3, VOCs, etc.), as shown in Supplementary Text 1 and Supplementary Tables 1–3.

Radical experimental budget analysis
The numerical radical closure experiment constrained by the observations is applied to examine the state-of-the-art chemical mechanism by use of the short lifetime of the HOx radicals3,58. In this study, we mainly conducted the OH experimental budget by comparing the OH production and destruction rates. As introduced in detail in Supplementary Text 2, the OH production rate is the sum of primary sources (HONO photolysis, O3 photolysis, ozonolysis of alkenes) and secondary sources (dominated by HO2+NO and HO2+O3). The total OH destruction rate is directly obtained from the product of the observed OH concentration and the observed kOH values. The discrepancy between the OH destruction and production rates denotes the missing OH sources.

Quantum chemical calculations and kinetic methods
The reactants, transition states, and products were optimized using CCSD(T)-F12a/cc-pVDZ-F1259 for the H-migration of carbonyl peroxyl radical (CH3C(O)O2). Benchmark values are calculated using W3X-L60//CCSD(T)-F12a/cc-pVDZ-F12 for CH3C(O)O2. Here, the WMS33//M06-2X34/MG3S35 method was considered to be the most accurate method by comparing the results between different methods and W3X-L//CCSD(T)-F12a/cc-pVDZ-F12 method (Supplementary Text 3, Supplementary Fig. 10, and Supplementary Table 8). Thus, we used WMS//M06-2X/MG3S method to investigate the H-migration process of R(CO)O2 radicals derived from hexanes (Supplementary Fig. 6a and Supplementary Tables 9–12). Intrinsic reaction coordinate (IRC)61–63 were also calculated to show that the transition state connects with the corresponding reactant and intermediate product (Supplementary Figs. 11–15). Reaction rate constants of H-migration were calculated by using the multi-structural transition state theory36 with Eckart tunneling37. Additionally, the daytime temperatures of the seven campaigns were all above 295 K (Supplementary Fig. 16), indicating that temperatures were not so low that it would overestimate tunneling probability. The electronic structure calculations were executed using the Gaussian 1664, Molpro 202165, and MRCC computer codes [www.mrcc.hu.]66,67, and the rate constants were calculated using KiSThelP software package68 and FM fw S d (cid:1)T were calculated using MSTor 2017 program package69,70.

Framework for sensitivity test of HAM and LIM1
The radical simulation was carried out based on a zero-dimensional box model constrained with the observed photolysis frequency, meteorological parameters, and the critical trace gas compounds in five-minute averaged values. The box model is running with a spin-up time of two days and the dry deposition rates were set according to that reported in Wesely et al.71. The uncertainty of the model simulation is a combination of uncertainties in the measurements used as model constraints and reaction rate constants, and it is approximately 40%2,15. Here, we used the RACM2 as the base mechanism and conducted sensitivity experiments by adding the LIM1 (Sensitivity test 1) and HAM (Sensitivity test 2).

Sensitivity test 1. The LIM1 was proposed by ref. 20 and updated by ref. 19. In this study, we incorporated the updated LIM1 in the base model to evaluate the contribution of LIM1 to the OH production rates15.

Sensitivity test 2. Based on our quantum chemical calculations about the H-migration of R(CO)O2 radicals from higher aldehydes, the reported generation of HPC-like substances by H-migration processes54, and the reported photolysis of HPC38, we summarized the chemical reactions and reaction rate constants of the HAM in Supplementary Table 5. The H-migration rate constants of R(CO)O2 radicals from higher (carbon number larger than four) aldehydes are estimated to be fast enough to compete with or even dominate over their bimolecular reactions with NO in the troposphere. The higher aldehydes dominated the ALD (propanal, butanal, and larger R-groups aldehydes) concentrations, with a contribution of 62%–81% (Supplementary Figs. 17–18). Moreover, the H-migration rate constants of R(CO)O2 radicals increase with increasing carbon numbers for R-groups. Here, we used the H-migration rate constant of R(CO)O2 radicals from hexanals to denote that of higher aldehydes.

Calculation of OH recycling probability
The stability of OH chemical system mainly could be affected by emissions of NOx, CO, and CH4. The OH recycling would be inefficient under low NOx levels. When CO and CH4 are very high and growing rapidly, such conditions can become catastrophic as both O3 and HOx are removed. Conversely, when NOx concentrations are high, the OH recycling is efficient and the system could become autocatalytic, causing a runaway of oxidants. Such high-NOx conditions would lead to efficient OH recycling on the one hand, and on the other hand, it would lead to an increase in OH removal due to the reaction of OH and NO2. Herein, to evaluate the effect of HAM on radical chemistry, we utilized the OH recycling probability, calculated from primary OH formation and OH recycling, to reflect the stability of tropospheric hydroxyl chemistry.

OH recycling probability (γ) was once defined by Lelieveld et al. in which both OH primary production rate and secondary production rate are taken into account55. The oxidation power (G) denotes the gross OH formation, which is the sum of primary(P) and total secondary(S) OH formation, as shown in Eq. (1).

G = P + S = P + γ(cid:3)P + γ2(cid:3)P + ... = P / (1 (cid:1) γ) (1)

Thus, the OH recycling probability is calculated by Eq. (2).

γ = 1 (cid:1) P / G (2)

When γ approaches 1, it is indicated that OH radicals are insensitive against primary pathways and are almost entirely from secondary generation pathways. Under such conditions, the OH recycling is very efficient and the OH chemistry system could become autocatalytic. The γ being approximately equal to 0.5 denotes the OH formation is quite efficient but not autocatalytic, demonstrating the OH chemical system may be stable. Under low γ conditions, OH radicals are mainly from primary pathways, and thus, greatly sensitive to O3 photolysis, etc. Overall, for the evaluation of the aldehyde chemistry, OH recycling probability is a comprehensive indicator from the perspective of primary and secondary generation pathways.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This work addresses the issue of the underestimation of OH concentrations by theoretical atmospheric models in the low NO and high VOC regime.\nAlthough my own work lies within the atmospheric chemistry field, I was actually unaware of this very interesting problem. Because of this, I cannot give a full account on how much effort has been put over the years into clarifying this divergence between experimental observation and theoretical modeling. However, the authors did a great job in contextualizing and explaining the scientific problem, revealing that the scientific community still has an incomplete understanding (at least until now, in this reviewer’s perspective) of the chemistry behind OH regeneration.\nThe authors tackle this problem by performing a retrospective meta-analysis of a comprehensive warm-season field observation dataset and also by performing a theoretical study, discovering that the autoxidation of carbonyl RC(O)O2 radicals derived from higher aldehydes could prove to be a novel and noteworthy (again, in this reviewer’s eyes) OH regeneration mechanism that could explain the missing source of OH radicals.\nAs a theoretical and computational chemist I prefer not to make comments about the experimental observations. However, I can provide some comments on the theoretical calculations.\nThe authors start with hexanal, a C6 aldehyde, which suffers oxidation mainly by OH and then reacts with O2 to yield the respective R(CO)O2 radical. The latter radical then undergoes an H-migration reaction, for which its rate constant is calculated with multi-structural transition state theory (MS-TST). The choice of MS-TST is completely adequate for this problem, as also the level of theory used for the respective electronic structure calculations that support this rate constant, based on their careful benchmark calculations. However, the Supplementary Information (SI) does not provide enough information to make a full analysis or reproduction of the calculations. I believe that, at this stage, this manuscript lacks technical information in order for it to be more consistent and for it to better support the conclusions made by the authors. The authors may consider the following suggestions/questions:\n- The total number of calculated conformers (reactants and transition states, TSs) and their relative energies (in a separate Table) should be mentioned somewhere in the “Text S3” part of the SI. Figure S6 only shows one reactant R(CO)O2 conformer, but there should be much more, given the number of rotatable bonds in this molecule.\n- Do the five shown TSs all connect to that one specific reactant conformer as shown in Figure S6?\n- Are there only five TSs or these are only the lowest energy ones?\n- Please provide Cartesian coordinates for all calculated reactant and TS conformers.\n- Please provide the value for all imaginary frequencies of the TSs, along with the respective energetic data of the relevant stationary points that are needed to calculate the Eckart tunneling correction.\n- Do the dashed lines in Figure S6 mean that there were Intrinsic Reaction Coordinate (IRC) calculations performed? If so, please state this in “Text S3”. If not, how do the authors know that those connections in Figure S6 exist?\n- Could the authors specifically state the type of H-migration (1,x) associated to each TS, for clarity purposes?\n- The Eckart tunneling correction is well known to be overestimated at low temperatures (clear and very recent examples are shown here: DOI: 10.1039/d2ea00164k), so it is possible that some of the values shown in Table S5 of the present manuscript are overestimated. Such a possibility should be mentioned in the “Text S3” part of the SI.\n- The previous point leads into this next one: how exactly were the RACM2 simulations performed? If the reader, like me, does not know anything about this simulation procedure, then some more details should be given. For example, at what temperature was the simulation performed? Or was it performed at several temperatures? This is important because of the concerns raised in the previous point, which could undermine some of the conclusions of this paper. I assume, however, that because the manuscript refers to “warm-season” several times, the simulation(s) was performed at 298 K, a temperature at which the overestimation of the Eckart tunneling correction is usually not troublesome. If so, please confirm this.\n- Please cite the original RACM2 paper in the main manuscript,\nhttp://dx.doi.org/10.1016/j.atmosenv.2012.11.038\nThe comments made above are mainly related to the first H-migration reaction of Figure 2A in the main manuscript. The authors then support the remaining reactions of Figure 2A with references.\nSpecifically, in Table S6, they claim that “The rate constants of Nos. 3-5 were from Wang et al.”, which for what I could understand is reference 25 of the SI:\nhttps://pubs.acs.org/doi/10.1021/acs.est.7b02374 However, I could not find the rate constant values for reactions 3-5 of Table S6 in this reference 25 paper. Could the authors provide a clear explanation of how they came up with these numbers? This is very important in order to make a good case for their conclusions.", "reviewer_2": "Hydroxyl Radicals (OH) is the most important oxidant in the atmosphere, it is critical to understand the atmospheric chemistry as well as the climate, since it determines the fate of almost all air pollutants and reactive greenhouse gases. This study aims to solve a very critical and fundamental problem in the field of atmospheric free radical chemistry, that is, the systematic underestimation of OH radical concentration by existing models under low NO and high VOC regimes. They used the most comprehensive field measurement datasets of atmospheric radical and precursors in the world, as far as I know, to identify the missing source of tropospheric OH radicals, they revealed the higher aldehydes, a typical class of oxygen volatile organic compounds that less concerned in the atmospheric chemistry, play an important role in the regeneration of OH. The new regeneration of OH mechanism by reactive aldehydes is clarified by a series of quantum chemical calculations and well assessed by the field datasets. In the end, they also argued that this new chemistry mechanism proposed in the study would be more important in the low NOx conditions in the future.\nThe methods of data acquisition appear sound to me, conclusions are fully supported by data and well-argued based on relevant literature. I’m convinced and impressed by discussion data from different field campaigns across the world to draw the conclusions, which nicely emphasizes the locally wide spread importance of the findings. Overall, this study is well designed and nicely presented. This novel work is potentially important for understanding the atmospheric radical chemistry, and the article will attract widespread attention and have a far-reaching impact in the community of atmospheric and climates sciences, and beyond. Thus, I would like to recommend this interesting article for publication after addressing the minor comments shown below.\n1. The first part of the Main Test seems a little confused. The background is introduced and followed by the meta-analysis of the field OH budget. I suggest the author adding a section header to distinguish the background (or Introduction) from the analysis of OH missing source. And in the end of the introduction section, a brief introduction about the method and purpose of this study should be outlined.\n2. This paper proposed the OH regeneration mechanism by the quantum chemical calculations method, we understand that the fine quantification of these key kinetic parameters of higher aldehydes chemistry is a very long-term and large project, it would be too harsh to ask for achieving it in this study. But a clearer outlook should be provided to direct the laboratory studies in the future. I would like to see the author add some discussions in the last paragraph.\n3. Line203-210, the explanation of high HPC yield seems to be plausible, but related references should be added to support this argument, especially the cooking emission source of high aldehydes. I suggest the author add the temperature information into the Table S7 to clarify the relationship of temperature and the HPC yield.\n4. Line 165-174, why the HAM can largely explain the missing source but still cannot well address this issue in Backgarden, Yufa, Heshan, and Chengdu? Are there air mass conditions differences or something else, more discussions should be added to address this point.", "reviewer_3": "Review on” Reactive Aldehyde Chemistry Explains the Missing Source of Hydroxyl Radicals” by Yang and Wang et al.\nThe authors propose that higher aldehydes represent a significant OH source in the atmosphere, under relatively low nitrogen oxide concentrations. They show that the ratio between the observed and modeled OH concentration exceeds unity at low NO concentrations in seven measurement locations within China that serve as the key observational data set for this study. The authors further suggest that the unexplained OH production rate correlates with the ratio between NO and OVOC concentration. Based on a previous quantum chemical calculation study, they formulate a hypothesis that atmospheric aldehydes, comprising five or more carbon atoms, undergo autoxidation yielding a hydroperoxyl-carbonyl (HPC) and an HO2 radical. They note, based on one another theoretical study, that HPC can undergo rapid photolysis yielding an OH radical. The authors perform estimations on the H-migration speeds for higher aldehydes (definition is unclear) using 1,7 H-migration speeds from quantum chemical calculations performed for R(CO)O2 radicals ./93</. 0975 2/>,6,4 -/:=//6 &%% ,6. '(% * \"A+ ) &% *#$ +2/? 0;9:2/9 8,9,5/:/93@/. :2/ 2312/9 aldehydes autoxidation mechanism (termed HAM) into the RACM2 model and evaluated the contribution of HAM to the observed radical chemistry. The base case set for RACM2 included the well-established OH production rates from HONO and ozone photolysis, alkene ozonolysis, and the HO2+NO and HO2+O3 reactions. In addition, it includes H-migration from isoprene-derived RO2s (LIM).\nThe classical OH production channels could explain 15–68% of the OH production (POH) across the seven sites. The importance of the HAM in explaining the remaining OH production seemed to be highly pronounced for the measurement sites, where the classical OH production channels already explained the majority of the OH. In contrast, the modelled importance of HAM was lowest in in the sites where OH production could not be reproduced with the classical production channels. HAM was reported as more critical than LIM in OH production across the sites.\nNext, the authors suggest (with support from a number of references) that certain VOC species can produce HPC-like reactive aldehydes via autoxidation. As the molar yields for such aldehydes remain unresolved, the authors derive the required HPC yields to bridge the gap between the modeled and measured OH concentrations through sensitivity studies. The molar yields range from 0.1 to 35 for the different sites, and the highest yields correspond to the measurement locations, where HAM showed little relevance in OH production in the previous RACM2 simulations, and the unexplained OH production fraction was the highest. The authors suggest that the need for the very high HPC yield for these measurement sites could arise from temperature effects on HPC formation as the two sites experienced high temperatures albeit based on the shown data in the SI, the temperature differences were not significant.\nThe new mechanism including the specified VOC autoxidation to HPC with the determined HPC yields is then included in RACM2 (RAM simulations). Because of the fixed yields, the model evaluation could not be performed via OH concentration comparisons, as the “fitted” HPC yields would guarantee a perfect agreement. Instead, the authors evaluate the modeled and observed OH recycling probabilities and state that a discrepancy that exists in the RACSM2 base case is now eliminated. The authors finally suggest that the HAM mechanism is important over a wide range of NO concentrations and could be highly important in the future due to emission regulations yet the LIM mechanism dominates in the cleanest environments.\nOverall, I do find the manuscript interesting and also interesting to a broader audience as understanding the OH budget is crucial from both climate and air quality perspectives from multiple angles. The proposed idea is very good and exciting, and the autoxidation of aldehydes has also been discussed previously in experimental contexts. However, I am unfortunately not convinced about the presented proof of the hypothesis, the quality of the analysis, and the descriptions of the utilized methodologies. Therefore, I cannot recommend the publication of this paper in its current state in Nature Communications.\nI have listed a few suggestions below on how to improve this manuscript:\n1. Could you perhaps evaluate how reasonable the utilized HPC molar yields are? The average temperatures do not look that different in Table S3. Yufa has a lower temperature than Wangdu, but the HPC yield for Yufa is almost two orders of magnitude higher. Are the HPC yields used as constants per measurement sites as shown in Table S7?\n2. Could explain the methods behind the observed OH recycling probability? If this is used as some sort of validation metric for your proposed hypothesis, I believe it is crucial to explain it thoroughly.\n3. How does the measured HO2 concentration compare with your RAM simulation outputs? Are there other ways you could evaluate your model results? How can you be sure that what you propose is actually happening?\n4. Regarding the aromatic autoxidation mechanism discussed in L174–L177, you might be interested in the very recent publication by Iyer et al. (2023) and the discussion related to the findings reported by Wang et al. (2017).\n5. The discussion about aldehyde autoxidation is also presented in Wang et al. (2021) could perhaps interest the authors of this manuscript.\n6. I would also be curious to hear your motivation for the discussion in L262–L264 presented in your manuscript on the effects of NO on RAM. In the Wang et al. (2021) study, they measure increases in the molar yields of alkane-derived oxygenated products (incl. RO2) as a function of NO. They suggest that multi-step isomerization of RO and/or RO2 radicals are likely for all types of alkanes even at high NO concentrations (they went up to roughly 10 ppb). How would accounting for such change your results and the OHobs/OHmod under high NO concentrations?\n7. The presentation of field data should be improved as they motivate much of the modeling work.\na. I would suggest presenting Figure 1A for all measurement sites separately in the SI without any NO-dependent binning.\nb. The distributions of the observed NO concentrations and OHobs/OHmod could be useful. These plots could help with justifying such binning shown in Fig. 1A – a description that remains missing.\nc. I strongly encourage you to show the range of variability in OHobs/OHmod per each NO bin e.g., with error bars.\nd. It was also hard to notice at first glance that the x-axis in Fig. 1A is logarithmic. Could you perhaps add more tick marks to the axis to clarify this, or write it in the caption?\ne. You mention in the SI that the Taizhou data points should be interpreted with caution because kOH was not measured. Could it explain why the trend is not so clear for the lowest NO concentration for that given campaign?\nf. Fig. 1B shows one point per measurement site. Are these points campaign means? I suggest you add the error bars to these figures and provide information on where kOVOCs, kAVOCs, kBVOCs, and kNO are obtained from. Are all the data from low NO concentrations or just the OVOC panel?\ng. You state many places throughout the manuscript that they measure radical concentrations, but do not specify which radicals they measure.\nh. The laser-induced fluorescence system (LIF) based on fluorescence assay by gas expansion technique does not have a reference.\n8. I suggest some grammar checks for the manuscript in addition to improving the clarity and precision of the text. At its current state, I do not believe the methodology is reproducible.\nReferences:\nIyer, S., Kumar, A., Savolainen, A., Barua, S., Daub, C., Pichelstorfer, L., Roldin, P., Garmash, O., Seal, P., Kurtén, T., and Rissanen, M.: Molecular rearrangement of bicyclic peroxy radicals is a key route to aerosol from aromatics, Nat Commun, 14, 4984, https://doi.org/10.1038/s41467-023-40675-2, 2023.\nWang, S., Wu, R., Berndt, T., Ehn, M., and Wang, L.: Formation of Highly Oxidized Radicals and Multifunctional Products from the Atmospheric Oxidation of Alkylbenzenes, Environ. Sci. Technol., 51, 8442–8449, https://doi.org/10.1021/acs.est.7b02374, 2017.\nWang, Z., Ehn, M., Rissanen, M. P., Garmash, O., Quéléver, L., Xing, L., Monge-Palacios, M., Rantala, P., Donahue, N. M., Berndt, T., and Sarathy, S. M.: Efficient alkane oxidation under combustion engine and atmospheric conditions, Commun Chem, 4, 1–8, https://doi.org/10.1038/s42004-020-00445-3, 2021."}, "author_response": "Response to Reviewer #1:\nGeneral comments:\nThis work addresses the issue of the underestimation of OH concentrations by theoretical atmospheric models in the low NO and high VOC regime.\nAlthough my own work lies within the atmospheric chemistry field, I was actually unaware of this very interesting problem. Because of this, I cannot give a full account on how much effort has been put over the years into clarifying this divergence between experimental observation and theoretical modeling. However, the authors did a great job in contextualizing and explaining the scientific problem, revealing that the scientific community still has an incomplete understanding (at least until now, in this reviewer’s perspective) of the chemistry behind OH regeneration.\nThe authors tackle this problem by performing a retrospective meta-analysis of a comprehensive warm-season field observation dataset and also by performing a theoretical study, discovering that the autoxidation of carbonyl RC(O)O radicals derived from higher aldehydes could prove to be a novel 2 and noteworthy (again, in this reviewer’s eyes) OH regeneration mechanism that could explain the missing source of OH radicals.\nAs a theoretical and computational chemist I prefer not to make comments about the experimental observations. However, I can provide some comments on the theoretical calculations.\nThe authors start with hexanal, a C6 aldehyde, which suffers oxidation mainly by OH and then reacts with O to yield the respective R(CO)O 2 2 radical. The latter radical then undergoes an H-migration 2 reaction, for which its rate constant is calculated with multi-structural transition state theory (MS-TST). The choice of MS-TST is completely adequate for this problem, as also the level of theory used for the respective electronic structure calculations that support this rate constant, based on their careful benchmark calculations. However, the Supplementary Information (SI) does not provide enough information to make a full analysis or reproduction of the calculations. I believe that, at this stage, this manuscript lacks technical information in order for it to be more consistent and for it to better support the conclusions made by the authors. The authors may consider the following suggestions/questions.\nResponse: Thanks for your constructive comments. We have taken all these suggestions into account and have made corrections in this revised manuscript. Below are our responses to the specific comments and revised our manuscript and Supplementary Information.\nSpecific comments:\nQ1. The total number of calculated conformers (reactants and transition states, TSs) and their relative energies (in a separate Table) should be mentioned somewhere in the “Text S3” part of the SI. Figure S6 only shows one reactant R(CO)O conformer, but there should be much more, given the number of 2 rotatable bonds in this molecule.\nResponse: Thank you for your comment! We have added the calculated details for searching the conformers in “Text S3” part of the SI. The original Supplementary Fig. 6 is Supplementary Fig. 6A in the revised manuscript because we also added Supplementary Fig. 6B.\nThe additions to Supplementary Text 3 are shown below:\nFor the reactant CH CH CH CH CH C(O)O , we considered five rotation bonds that are C1-O6, 3 2 2 2 2 2 C1-C3, C3-C8, C8-C11, and C11-C14, which produce 63 distinguishable conformers. However, for the transition state TS2, there is only one rotation bond C11-C14, producing 3 distinguishable conformers. For the transition state TS4, there are two rotation bonds C8-C11 and C11-C14, producing 8 distinguishable conformers. For the transition state TS5, there are three rotation bonds C3-C8, C8-C11, and C11-C14, producing 21 distinguishable conformers. There are no rotation bonds for TS1 and TS3. The molecules of reactant and transition states for producing conformers are plotted in Supplementary Fig. 6B. The relative energies of the distinguishable conformer of the reactants and transition states are listed in Supplementary Table 8. The conformers shown in Supplementary Fig. 6A are the lowest energy structures for both the reactant and transition states. Extra information on vibrational frequency, absolute energies, and cartesian coordinates are shown in Supplementary Tables 10-12.\nThe revised Supplementary Fig. 6A and 6B are as follows:\nSupplementary Figure 6A. The relative enthalpies at 0 K for the H-migration of R(CO)O radicals derived from hexanals 2 (CH CH CH CH CH C(O)O ). Values (black) are given for all species as calculated by M06-2X/MG3S, and values in 3 2 2 2 2 2 parentheses (red) are calculated by WMS//M06-2X/MG3S. It is noted that the conformers for reactants, transition states, and intermediate products are the lowest conformer, respectively.\nSupplementary Figure 6B. The molecules of reactant and transition states for producing conformers.\nSupplementary Table 8. The relative energies (kcal/mol) of distinguish conformers for reactant and transition states.\n[...Table omitted for brevity...]\nNote: This table marked in bold font is the lowest energy structure, which is set to the energy zero, and the energy of other independent structures is obtained relative to the lowest energy structure. All conformers of the reactant (R) were optimized using M06-2X/MG3S method. Due to the higher barrier of TS2, TS4, and TS5, they hardly effect the kinetics of the reaction. Thus, all conformers of transition states (TS2, TS4 and TS5) were optimized using the more economical B3LYP/6-31G (d, p) method. Then, all lowest energy conformers of reactant and transition states were reoptimized using M06-2X/MG3S method to obtain the zero-point vibrational energy correction.\nQ2. Do the five shown TSs all connect to that one specific reactant conformer as shown in Figure S6?\nResponse:Yes, we had done the IRC calculation to verify the TSs correctly connect to the specific reactant conformer. Moreover, we have provided IRC calculated results as shown in Supplementary Figs. 14-18. However, in Supplementary Fig. 6A of the revised article, we only consider the lowest reactant conformer for the reactant. In the revised article, we have added some comments in original Line 133: It is noted that the conformers for reactants, transition states, and intermediate products are the lowest conformer, respectively. The original Supplementary Fig. 6 is Supplementary Fig. 6A in the revised article and we also added Supplementary Fig. 6B.\nThe revised Supplementary Figs. 14-18 are shown below.\nSupplementary Figure 14. Intrinsic Reaction Coordinate (IRC) for TS1 (1,7-H migration).\nSupplementary Figure 15. Intrinsic Reaction Coordinate (IRC) for TS2 (1,6-H migration).\nSupplementary Figure 16. Intrinsic Reaction Coordinate (IRC) for TS3 (1,8-H migration).\nSupplementary Figure 17. Intrinsic Reaction Coordinate (IRC) for TS4 (1,5-H migration).\nSupplementary Figure 18. Intrinsic Reaction Coordinate (IRC) for TS5 (1,4-H migration).\nQ3. Are there only five TSs or these are only the lowest energy ones?\nResponse: We considered five H-migration sites along the C-C skeletal chain of the reactant CH CH CH CH CH C(O)O , which produces five transition states, as plotted in Supplementary Fig. 3 2 2 2 2 2 6A. All TSs are the lowest energy conformers. The original Supplementary Fig. 6 is Supplementary Fig. 6A in the revised article and we also added Supplementary Fig. 6B.\nQ4. Please provide Cartesian coordinates for all calculated reactant and TS conformers.\nResponse: Thanks for your helpful suggestions. The optimized geometries of all calculated reactants and TS conformers are provided in Supplementary Table 12 of the Supplementary Information.\nThe newly added Supplementary Table 12 is shown below:\n[...Table omitted for brevity...]\nQ5. Please provide the value for all imaginary frequencies of the TSs, along with the respective energetic data of the relevant stationary points that are needed to calculate the Eckart tunneling correction.\nResponse: All imaginary frequencies of the TSs and the energetic data of all calculated reactants and transition states in Supplementary Fig. 6A are provided in Supplementary Table 8 and Supplementary Table 10. The Supplementary Table 8 has been shown in the Response to Q1, and Supplementary Table 10 is shown below.\n[...Table omitted for brevity...]\nQ6. Do the dashed lines in Figure S6 mean that there were Intrinsic Reaction Coordinate (IRC) calculations performed? If so, please state this in “Text S3”. If not, how do the authors know that those connections in Figure S6 exist?\nResponse: We had done IRC calculations for all TSs to verify it connect to the reactant and the products, as shown in Supplementary Figs. 14-18, as shown in the Response of Q2. We have added some comments in Supplementary Text 3: We also did intrinsic reaction coordinate (IRC) 1, 2, 3 calculations to show that the transition state connects with the corresponding reactant and intermediate\nQ9. The previous point leads into this next one: how exactly were the RACM2 simulations performed? If the reader, like me, does not know anything about this simulation procedure, then some more details should be given. For example, at what temperature was the simulation performed? Or was it performed at several temperatures? This is important because of the concerns raised in the previous point, which could undermine some of the conclusions of this paper. I assume, however, that because the manuscript refers to “warm-season” several times, the simulation(s) was performed at 298 K, a temperature at which the overestimation of the Eckart tunneling correction is usually not troublesome. If so, please confirm this.\nResponse: Thank for your helpful suggestions. We have added the description of the model configuration, especially the detailed temperature-related descriptions, as your valuable suggestions in Supplementary Text 2, as shown below: As for the comparison between observed and simulated radical concentrations, a zero-dimensional chemical box model based on RACM2 was utilized in this study. The model was constrained to CO, NO, NO , CH , O , HONO, and VOC concentrations and photolysis 2 4 3 frequencies, water vapor, ambient temperature and pressure as well. For RACM2, the measured detailed VOC species were lumped into several categories, which is introduced in previous studies 6, 7. The H and CH mixing ratio was assumed to be 550 ppb and 1900 ppb, respectively. Other 2 4 parameters were from the observations with 5-min time resolution, which represents the actual atmospheric environmental conditions every day during campaigns. Given the significance of ambient temperature on the results of quantum chemical calculations, herein, it's worth mentioning that the temperature input in the model was the real ambient temperature observed in campaigns rather than a constant value. Additionally, a spin-up time with 2 days at the beginning of simulations was used to reach steady-state conditions for long-lived species. A fixed dilution equivalent of 24-h lifetime was added in the model to represent the dry deposition. Based on the above configuration in the model, simulated radical concentrations would be obtained and then they will be compared to the observed concentrations to investigate whether the chemical mechanisms are correct, which is the most direct indication to identify whether the chemical mechanisms in the troposphere are complete or not.\nBesides, the detailed temperature-related descriptions have been added in Supplementary Text 3, as shown in the Response to Q8.\nQ10. Please cite the original RACM2 paper in the main manuscript, http://dx.doi.org/10.1016/j.atmosenv.2012.11.038\nResponse: Thanks, we have cited it in the manuscript and Supplementary Information.\nQ11. The comments made above are mainly related to the first H-migration reaction of Figure 2A in the main manuscript. The authors then support the remaining reactions of Figure 2A with references.\nSpecifically, in Table S6, they claim that “The rate constants of Nos. 3-5 were from Wang et al.”, which for what I could understand is reference 25 of the SI: https://pubs.acs.org/doi/10.1021/acs.est.7b02374However, I could not find the rate constant values for reactions 3-5 of Table S6 in this reference 25 paper. Could the authors provide a clear explanation of how they came up with these numbers? This is very important in order to make a good case for their conclusions.\nResponse: Thanks for your helpful comments. We really did not make it clear where the reaction rates came from in original Table S6 (Now is Supplementary Table 5). The rate constants of Nos. 3-5 are from Wang et al. (2019) (DOI:10.1063/1674-0068/cjcp1811265), which was shown in reference 28 in the original manuscript titled “Role of Hydrogen Migrations in Carbonyl Peroxy Radicals in the Atmosphere” 8. The rate constants of Nos. 3-4 come from the picture of “Scheme 1 -- New pathways of CH CH CH C(O)O radical after H-migration”. As for No. 5, Wang et al. (2019) did not give the 3 2 2 2 rate constant directly. However, as mentioned by Wang et al. (2019) 8, the RO radicals could react with O at effective rates of (0.5~5) ×104 s-1 with rate 2 coefficients of 10-15~10-14 cm3 molecules-1 s-1 according to the studies from Atkinson et al. (1997) (https://doi.org/10.1002/(SICI)1097- 4601(1997)29:2<99::AID-KIN3>3.0.CO;2-F) 9& :DA L=@E?=F EH 5I& * EM U%DS@LIRS L=@E?=FM (R R COH), and Atkinson (1994) (https://doi.org/10.1016/0960-1686(90)90438-S) 10 once reported 1 2 the reactions of O =H@NDAMEGJFAMN U%DS@LIRSL=@E?=FM \"/1 OH) with the k(CH OH+O ) is 9.0×10-12 2 2 2 2 cm3 molecules-1 s-1 at 298 K, which is larger than the rate constant of RO+O . The rate coefficients of 2 CH OH+O reactions reported in previous studies were summarized on the IUPAC website 2 2 (https://iupac-aeris.ipsl.fr/show_datasheets.php?category=Gas-phase+organics%3A+R_oxygen) and were all larger those that of RO+O reactions. To obtain a conservative result, we chose the rate constant in No. 2 5 as 104 s-1. Herein, we added details about the provenance of these reaction rates in the revised manuscript and Supplementary Table 5 in the new version.\nThe revision of the notes in the new Supplementary Table 5 is:\nNote that:\n(1) ACO and HKET denote acetyl peroxy radicals and hydroxy ketone, respectively. jMACR 3 represents the photolysis rate constant of methacrolein (MACR).\n(2) The rate constant of No. 1 is from our quantum chemical calculations.\n(3) The rate constant of No. 2 is from Table 1 of Tan et al. 11.\n(4) The reactions of Nos. 3-5 are from Wang et al.8 and the rate constants of both No. 3 and No. 4 are from Wang et al. 8.\n(5) As for No. 5, Wang et al. 8 did not give the rate constant directly. However, as mentioned by Wang et al. 8, the RO radicals could react with O at effective rates of (0.5~5) ×104 s-1 with rate 2 coefficients of 10-15~10-14 cm3 molecules-1 s-1 according to the studies from Atkinson 9. The radical EH5I&*EM U%DS@LIRSL=@E?=FM \"8 R COH), and Atkinson 10 once reported the reactions of O and 1 2 2 NDA MEGJFAMN U%DS@LIRS L=@E?=FM \"/1 OH) with the k(CH OH+O ) is 9.0×10-12 cm3 molecules-1 s- 2 2 2 1 at 298 K, which is larger than the rate constant of RO+O . The rate coefficients of CH OH+O 2 2 2 reactions reported in previous studies were summarized in IUPAC website (https://iupac- aeris.ipsl.fr/show_datasheets.php?category=Gas-phase+organics%3A+R_oxygen) and were all larger those that of RO+O reactions. To obtain a conservative result, we chose the rate constant in No. 5 as 2 104 s-1.\n(6) The photolysis rate of No. 6 is a conservative result from Liu et al. 12.\nResponse to Reviewer #2:\nGeneral comments:\nHydroxyl Radicals (OH) is the most important oxidant in the atmosphere, it is critical to understand the atmospheric chemistry as well as the climate, since it determines the fate of almost all air pollutants and reactive greenhouse gases. This study aims to solve a very critical and fundamental problem in the field of atmospheric free radical chemistry, that is, the systematic underestimation of OH radical concentration by existing models under low NO and high VOC regimes. They used the most comprehensive field measurement datasets of atmospheric radical and precursors in the world, as far as I know, to identify the missing source of tropospheric OH radicals, they revealed the higher aldehydes, a typical class of oxygen volatile organic compounds that less concerned in the atmospheric chemistry, play an important role in the regeneration of OH. The new regeneration of OH mechanism by reactive aldehydes is clarified by a series of quantum chemical calculations and well assessed by the field datasets. In the end, they also argued that this new chemistry mechanism proposed in the study would be more important in the low NOx conditions in the future.\nThe methods of data acquisition appear sound to me, conclusions are fully supported by data and well-argued based on relevant literature. I’m convinced and impressed by discussion data from different field campaigns across the world to draw the conclusions, which nicely emphasizes the locally wide spread importance of the findings. Overall, this study is well designed and nicely presented. This novel work is potentially important for understanding the atmospheric radical chemistry, and the article will attract widespread attention and have a far-reaching impact in the community of atmospheric and climates sciences, and beyond. Thus, I would like to recommend this interesting article for publication after addressing the minor comments shown below.\nResponse: Thanks for your constructive comments. We have taken all these suggestions into account and have made corrections in this revised manuscript. Below are our responses to the specific comments and revised our manuscript and Supplementary Information.\nSpecific comments:\nQ1. The first part of the Main Test seems a little confused. The background is introduced and followed by the meta-analysis of the field OH budget. I suggest the author adding a section header to distinguish the background (or Introduction) from the analysis of OH missing source. And in the end of the introduction section, a brief introduction about the method and purpose of this study should be outlined.\nResponse: Thanks. We adjusted the structure of the manuscript based on the formatting requirements of this journal and this suggestion accordingly. We added one section “Introduction” without subheadings according to the requirements, and move the meta-analysis part to the first part of the Result section “Characterization of the OH missing source.”\nIn the last of the “Introduction”, we added a paragraph to introduce the main content of this study:\nBased on the combination of quantum chemical calculations and observation-constrained model simulations, we report the detailed reaction processes of the autoxidation mechanism of high aldehydes and further confirm its importance by examination in numerous field studies worldwide.\nQ2. This paper proposed the OH regeneration mechanism by the quantum chemical calculations method, we understand that the fine quantification of these key kinetic parameters of higher aldehydes chemistry is a very long-term and large project, it would be too harsh to ask for achieving it in this study. But a clearer outlook should be provided to direct the laboratory studies in the future. I would like to see the author add some discussions in the last paragraph.\nResponse: Thanks for your suggestions, we added the further potential directions of RO 2 autoxidation in the last paragraph: For example, the kinetic parameters of RO autoxidation from high 2 aldehydes, involving rate constants and product yields, and the photolysis process of hydroperoxyl- carbonyls are need to be further quantified through both quantum chemical calculations and kinetic experiments.\nQ3. Line203-210, the explanation of high HPC yield seems to be plausible, but related references should be added to support this argument, especially the cooking emission source of high aldehydes. I suggest the author add the temperature information into the Table S7 to clarify the relationship of temperature and the HPC yield.\nResponse: Thanks for your suggestions. We have added several papers related to high aldehydes from cooing emission in original Lines 165-174: The presence of still unexplained OH sources after including HAM in these campaigns may be tightly related to the following factors: 1) aldehydes from primary emissions, especially aldehydes with high carbon numbers from biomass burning 13, 14 or cooking activities 15, 16, are not considered in the model, which are likely to be oxidized into RO 2 radicals with much higher H-migration rate than those currently used in this study.\nThe references related to biomass emission are:\nS. Inomata et al., Laboratory measurements of emission factors of nonmethane volatile organic compounds from burning of Chinese crop residues. Journal of Geophysical Research- Atmospheres 120, 5237-5252 (2015). DOI: 10.1002/2014JD022761.\nY. Zhang et al., Emission inventory of carbonaceous pollutants from biomass burning in the Pearl River Delta Region, China. Atmospheric Environment 76, 189-199 (2013). DOI: 10.1016/j.atmosenv.2012.05.055.\nThe references related to cooking emissions are:\nA. Atamaleki et al., Emission of aldehydes from different cooking processes: a review study. Air Quality Atmosphere and Health 15, 1183-1204 (2022). DOI: 10.1007/s11869-021-01120-9.\nR. Dominguez, M. Gomez, S. Fonseca, J. M. Lorenzo, Effect of different cooking methods on lipid oxidation and formation of volatile compounds in foal meat. Meat Science 97, 223-230 (2014). DOI: 10.1016/j.meatsci.2014.01.023.\nAdditionally, according to the suggestions of the reviewer #3, we optimized the derivation of OH yields from the VOC oxidation through HPC photolysis, as shown in the revised Supplementary Table 6, and the ambient temperatures of our seven campaigns were added into this table as well.\nSupplementary Table 6. :DA V P=FOAM=?DEAPEHCIJNEGETA@=CLAAGAHN>ANQAAHNDAI>MALPA@=H@GI@AFA@61&\n[...Table omitted for brevity...]\nQ4. Line 165-174, why the HAM can largely explain the missing source but still cannot well address this issue in Backgarden, Yufa, Heshan, and Chengdu? Are there air mass conditions differences or something else, more discussions should be added to address this point.\nResponse: Thanks for your suggestions. We added some discussions in original Line 174 as following: The presence of still unexplained OH sources after including HAM in these campaigns may be tightly related to the following factors: 1) aldehydes from primary emissions, especially aldehydes with high carbon numbers from biomass burning 13, 14 or cooking activities 15, 16, are not considered in the model, which are likely to be oxidized into RO 2 radicals with much higher H-migration rate than those currently used in this study; 2) the total concentrations of HPC groups were underestimated as they can also be produced from many other VOCs than higher aldehydes (e.g., long-chain alkanes 17, ethers 18, alcohols 19, alkenes 20); 3) the underestimation of HPC photolysis rate for HPC species with different functional groups.\nResponse to Reviewer #3:\nGeneral comments:\nThe authors propose that higher aldehydes represent a significant OH source in the atmosphere, under relatively low nitrogen oxide concentrations. They show that the ratio between the observed and modeled OH concentration exceeds unity at low NO concentrations in seven measurement locations within China that serve as the key observational data set for this study. The authors further suggest that the unexplained OH production rate correlates with the ratio between NO and OVOC concentration. Based on a previous quantum chemical calculation study, they formulate a hypothesis that atmospheric aldehydes, comprising five or more carbon atoms, undergo autoxidation yielding a hydroperoxyl-carbonyl (HPC) and an HO radical. They note, based on one another theoretical study, that HPC can 2 undergo rapid photolysis yielding an OH radical. The authors perform estimations on the H-migration speeds for higher aldehydes (definition is unclear) using 1,7 H-migration speeds from quantum chemical calculations performed for R(CO)O radicals derived from hexanal between 200 and 340 K 2 \"W:-)'3#&:DASBOLNDALJ=L=GANALETA@NDADECDAL=F@ADS@AM=ONIRE@=NEIHGA?D=HEMG\"NALGA@1.4# into the RACM2 model and evaluated the contribution of HAM to the observed radical chemistry. The base case set for RACM2 included the well-established OH production rates from HONO and ozone photolysis, alkene ozonolysis, and the HO +NO and HO +O reactions. In addition, it includes H- 2 2 3 migration from isoprene-derived RO s (LIM).\nNext, the authors suggest (with support from a number of references) that certain VOC species can produce HPC-like reactive aldehydes via autoxidation. As the molar yields for such aldehydes remain unresolved, the authors derive the required HPC yields to bridge the gap between the modeled and measured OH concentrations through sensitivity studies. The molar yields range from 0.1 to 35 for the different sites, and the highest yields correspond to the measurement locations, where HAM showed little relevance in OH production in the previous RACM2 simulations, and the unexplained OH production fraction was the highest. The authors suggest that the need for the very high HPC yield for these measurement sites could arise from temperature effects on HPC formation as the two sites experienced high temperatures albeit based on the shown data in the SI, the temperature differences were not significant.\nThe new mechanism including the specified VOC autoxidation to HPC with the determined HPC yields is then included in RACM2 (RAM simulations). Because of the fixed yields, the model evaluation could not be performed via OH concentration comparisons, as the “fitted” HPC yields would guarantee a perfect agreement. Instead, the authors evaluate the modeled and observed OH recycling probabilities and state that a discrepancy that exists in the RACSM2 base case is now eliminated. The authors finally suggest that the HAM mechanism is important over a wide range of NO concentrations and could be highly important in the future due to emission regulations yet the LIM mechanism dominates in the cleanest environments.\nOverall, I do find the manuscript interesting and also interesting to a broader audience as understanding the OH budget is crucial from both climate and air quality perspectives from multiple angles. The proposed idea is very good and exciting, and the autoxidation of aldehydes has also been discussed previously in experimental contexts. However, I am unfortunately not convinced about the presented proof of the hypothesis, the quality of the analysis, and the descriptions of the utilized methodologies. Therefore, I cannot recommend the publication of this paper in its current state in Nature Communications.\nI have listed a few suggestions below on how to improve this manuscript:\nResponse: Thanks for your summary and the critical and constructive comments. We have taken all these suggestions into account and well addressed them in this revised manuscript.\nSpecific comments:\nQ1. Could you perhaps evaluate how reasonable the utilized HPC molar yields are? The average temperatures do not look that different in Table S3. Yufa has a lower temperature than Wangdu, but the HPC yield for Yufa is almost two orders of magnitude higher. Are the HPC yields used as constants per measurement sites as shown in Table S7?\nResponse: Previous studies have reported that the HPC species generated from VOC oxidation could vary significantly from each other 21, and the photolysis rate of different HPC species could also exhibit great differences with up to around 4 folds, as shown in Table 2 reported by Liu et al. 12. These all indicates that the HPC molar yields may highly varied in different air masses.\nAccording to your valuable suggestions, we redefined “HPC molar yields” in the original manuscript and renamed it “OH yields from the VOC oxidation through HPC photolysis” which is @AHINA@ >S = MEGJFA EH@AR =M V$ NI ?D=L=?NALETA NDA CAHAL=FETA@ SEAF@ IB 61 LACAHAL=NA@ >S NDA oxidation of VOC through the HPC chemistry based on an inversed model. We further clarified its @ABEHENEIH EH @AN=EFM EH NDA MOJJILNEHC EHBILG=NEIH& 2H >LEAB$ NDA V EH?FO@EHC NDA SEAF@M IB @EBBALAHN HPC species from the oxidation of different VOCspecies, the yields of OH radicals in photolysis of different HPC species, and the ratio of the HPC photolysis rate to ten times of the MACR photolysis frequency.Ten times MACR photolysis frequency order of about 10-4 s-1, which is the base case setup of HPC photolysis rate used in the HAM.\nFurthermore, we have improved the inversed model approach for the calculation ofV$QDE?D=PIE@M the large bias from the using of undue high HPC photolysis rate. In the revised manuscript, we updated NDA V P=FOAMEH9OJJFAGAHN=LS:=>FA+based on the newly revised approach, which makes more sense ?IGJ=LA@NINDIMAEHNDAILECEH=FPALMEIH&4ILA@AN=EFA@EHBILG=NEIHIHNDA?=F?OF=NEIHIB V D=M>AAH added into Supplementary Text 5:\nTo further explore the effects of generalized RO autoxidation on radical chemistry, we made a rule 2 of thumb assumption named RAM scheme,in which RO from some certain VOCs (alkanes, alkenes, 2 aromatics, etc.) could undergo autoxidation process similar to that of RO from aldehydes in HAM 2 scheme. In the RAM scheme, specific VOCs classes were set to generate HPC according to Table 1 of Bianchi et al. 21. Here, the specific VOCs include HC5 (alkanes, esters, and alkynes with OH rate constant (298 K, 1 atm) between 3.4×10-12 and 6.8×10-12 cm3 s-1), HC8 (alkanes, esters, and alkynes with OH rate constant (298 K, 1 atm) greater 6.8×10-12 cm3 s-1), OLT (terminal alkenes), OLI (internal alkenes), DIEN (butadiene and other anthropogenic dienes), BEN (benzene), TOL (toluene), XYM (m-xylene), XYP (p-xylene), XYO (o-xylene), ISO (isoprene) in RACM2.\n2HNDEMM?DAGA$QA@ABEHA@=MEGJFAEH@AR$H=GA@=M V$NI?D=L=?NALETANDACAHAL=FETA@SEAF@IB61 regenerated by the oxidation of VOC through the HPC chemistry, which is derived from an inversed modeling method, to achieve a good agreement between the modeled and observed OH radicals. The @ABEHENEIHIB V EM MDIQH=M BIFFIQM \"9OJJFAGAHN=LS0KO=NEIH\"*##&\n\"- Xn \"Xn A ×HPC)×B)×R Supplementary Equation (5) j=1 i=1 ij j j j\nA denotes the yields of different HPC species from the oxidation of different VOC species.\nij j i\nB denotes the yields of OH radicals in photolysis of different HPC species.\nj j\nR denotes the ratio of the HPC photolysis frequency to ten times MACR photolysis frequency. Ten j j times MACR photolysis frequency order of about 10-4 s-1, which is the base case setup of HPC photolysis rate used in the HAM.\n<DALA V @AJAH@M IH NDA P=FOAM IB. , B andR. The HPC species and the HPC yield are heavily ij j j dependent on VOC species (A , referred to Table 1 of Bianchi et al. 21). Subsequently, in the HPC ij photolysis reaction, different HPC species would have different OH yields (B) as well as the photolysis j frequencies (R). For example, the photolysis frequencies may differ by more than a factor of 4 between j different HPC species (referred to Table 2 of Liu et al. 12). The three coefficients would be highly P=LEA@ EH @EBBALAHN ?=GJ=ECHM$ QDE?D QIOF@ JLI>=>FS BOLNDAL =GJFEBS NDA @EBBALAH?AM EH NDA @ALEPA@ V in different campaigns.\nHerein, based on the reversed model, we calculated the \" value, which is the equivalent mean value for each campaign, in our fourteen campaigns in Supplementary Table 6.\nBesides, the ambient temperature might not be the limited factor to influence the OH yields from the VOC oxidation through HPC photolysis (Supplementary Table 6) in RAM, since the daily maximum temperature were over 296 K in our seven campaigns and showed overall small temperature differences. Compared to the ambient temperature, VOC components may be more decisive for OH yields. Despite of the similar ambient temperature at Yufa and Wangdu sites, their reactive VOC species exhibited great different 7, 22, 23. Thus, we updated the explanation for different contributions of RAM to different campaigns in the original Lines 199-210: We defined a simple index, named as V$ NI ?D=L=?NALETA NDA CAHAL=FETA@ GIF=L SEAF@ IB 61 LACAHAL=NA@ >S NDA IRE@=NEIH IB ;6/M NDLIOCD NDA 17/ ?DAGEMNLS& :DA EH@AR V EM @ALEPA@ BLIG =H EHPALMA@ GI@AFEHC GANDI@$ NI =?DEAPA = CII@ =CLAAGAHN >ANQAAH NDA GI@AFA@ =H@ I>MALPA@ 61 L=@E?=FM \"9OJJFAGAHN=LS :ARN *#&. LA=MIH=>FA V of 0.4-2.2 is derived for our seven warm-season campaigns (Supplementary Table 6). Additionally, we show the incorporation of RAM into the model would further improve the agreement between the observed and simulated HO concentrations to some extent (Supplementary Fig. 8). The variation of 2 NDA EH@AR V EH @EBBALAHN ?=GJ=ECHM G=S >A ?=OMA@ >S, (# 17/ MJA?EAM =H@ 17/ SEAF@ JLI@O?A@ >S different VOC oxidation processes may be highly varied 21. 2) The OH yield from the HPC photolysis may be varied for different HPC species. 3) HPC photolysis frequencies which may differ by over four times 12.\nSupplementary Table 6. :DA V P=FOAM=?DEAPEHCIJNEGETA@=CLAAGAHN>ANQAAHNDAI>MALPA@=H@GI@AFA@61&\n[...Table omitted for brevity...]\nQ2. Could explain the methods behind the observed OH recycling probability? If this is used as some sort of validation metric for your proposed hypothesis, I believe it is crucial to explain it thoroughly.\nResponse: We apologize for the misunderstanding. In fact, the observed OH recycling probability is not a validation metric for our proposed hypothesis but a metric to evaluate the environmental impact of new reaction pathway.\nTo further clarify the OH recycling probability, we added more detailed description in “Method: Calculation of OH recycling probability” in the revised manuscript:\nThe stability of OH chemical system mainly could be affected by emissions of NOx, CO, and CH . 4 The OH recycling would be inefficient under low NOx levels. When CO and CH are very high and 4 growing rapidly, such conditions can become catastrophic as both O and HOx are removed. 3 Conversely, when NOx concentrations are high, the OH recycling is efficient and the system could become autocatalytic, causing a runaway of oxidants. Such high-NOx conditions would lead to the efficient OH recycling on the one hand, and on the other hand it would lead to an increase in OH removal due to the reaction of OH and NO . 2 Herein, to evaluate the effect of the newly proposed HAM on radical chemistry, we utilized the OH recycling probability, calculated from primary OH formation and OH recycling, to reflect the stability of tropospheric hydroxyl chemistry.\nOH recycling probability (#) was once defined by Lelieveld et al., in which both OH primary production rate and secondary production rate are taken into account 24. The oxidation power (G) denote the gross OH formation, which is the sum of primary (P) and total secondary (S) OH formation, as shown in Equation (1).\nG = P + S = P + #*P + #2*P + … = P Equation (1)\n1 - #\nThus, the OH recycling probability is calculated by Eq. S7.\n# = 1 - P Equation (2)\nG\nWhen # approaches 1, it is indicated that OH radicals are insensitive against primary pathways and are almost entirely from secondary generation pathways. Under such condition, the OH recycling is very efficient and the OH chemistry system could become autocatalytic. The # being approximately equal to 0.5 denotes the OH formation is quite efficient but not autocatalytic, demonstrating the OH chemical system may be stable. Under low # conditions, OH radicals are mainly from primary pathways, and thus, greatly sensitive to O photolysis, etc. Overall, for the evaluation of newly 3 proposed mechanism, OH recycling probability is a comprehensive indicator from the perspective of primary and secondary generation pathways.\nQ3. How does the measured HO concentration compare with your RAM simulation outputs? Are 2 there other ways you could evaluate your model results? How can you be sure that what you propose is actually happening?\nResponse:\nWe evaluated the impacts of RAM scheme in HO concentrations accordingly. We found the RAM 2 improve the agreement between the observed and simulated HO concentrations to some extent. 2 Therefore, here we added some discussion into the revised manuscript in original around Lines 200- 210: Additionally, we show the incorporation of RAM into the model would further improve the agreement between the observed and simulated HO concentrations to some extent (Supplementary 2 Fig. 8).\nkey route to aerosol from aromatics, Nat Commun, 14, 4984,https://doi.org/10.1038/s41467-023- 40675-2, 2023.\n[2] Wang, S., Wu, R., Berndt, T., Ehn, M., and Wang, L.: Formation of Highly Oxidized Radicals and Multifunctional Products from the Atmospheric Oxidation of Alkylbenzenes, Environ. Sci. Technol., 51, 8442–8449, https://doi.org/10.1021/acs.est.7b02374, 2017.\nResponse: Thanks for the suggestion. We have carefully studied the above two papers and cited these two papers and updated the description of aromatic autoxidation mechanism, as shown in original Lines 174-177: Additionally, aromatic autoxidation mechanisms have been proposed recently, demonstrating the significant role of OH-initiated oxidation of aromatics in forming highly oxidized products and thus secondary organic aerosols 27, 28, while the mechanism was found negligible for OH generation in the seven field campaigns (Supplementary Text 4 and Supplementary Fig. 7).\nQ5. The discussion about aldehyde autoxidation is also presented in Wang et al. (2021) could perhaps interest the authors of this manuscript.\nReference: Wang, Z., Ehn, M., Rissanen, M. P., Garmash, O., Quéléver, L., Xing, L., Monge-Palacios, M., Rantala, P., Donahue, N. M., Berndt, T., and Sarathy, S. M.: Efficient alkane oxidation under combustion engine and atmospheric conditions, Commun Chem, 4, 1– 8,https://doi.org/10.1038/s42004-020-00445-3, 2021.\nResponse: Thanks for your suggestions. Your recommended paper would further enrich our understanding of aldehyde autoxidation and further support the significance of aldehyde autoxidation process under atmospheric conditions in our study. We have cited this paper in original Line 127 and Lines 190-192 to support the autoxidation of RO radicals derived from alkanes. 2\nLine 127: Wang et al. further affirmed the high autoxidation potential of aldehydes under atmospheric conditions 25.\nLines 190-192: Recent studies have suggested that RO derived from VOCs besides aldehydes, such 2 as alkanes, aromatics, and other OVOCs (ketones, ethers, etc.), could also undergo autoxidation with possible subsequent generation of radicals 17, 18, 25, 28, 29, 30, 31.\nQ6. I would also be curious to hear your motivation for the discussion in L262–L264 presented in your manuscript on the effects of NO on RAM. In the Wang et al. (2021) study, they measure increases in the molar yields of alkane-derived oxygenated products (incl. RO ) as a function of NO. They suggest 2 that multi-step isomerization of RO and/or RO radicals are likely for all types of alkanes even at high 2 NO concentrations (they went up to roughly 10 ppb). How would accounting for such change your results and the OH /OH under high NO concentrations?\nobs mod\nResponse: Thanks for your helpful suggestions and we have studied the research of Wang et al. (2021) which would further enrich our study. This study reported that alkane autoxidation process would also exist even at high NO concentrations. Nevertheless, in theory, although RO autoxidation 2 could occur under high NO conditions, while this process becomes less significant for radical generation under high NO conditions because RO removal is dominated by the reactions with NO 2 under these ambient conditions. Additionally, our study focuses more on radical chemistry under low-chemical species on radical chemistry, we further categorized k into k , k , k , k , and OH NO VOCs AVOCs BVOCs k . k denotes the NO reactivity, and k denotes the difference between k and inorganic OVOCs NO VOCs OH reactivities (CO, NOx, O , and SO ). k represents the sum reactivities of alkanes, alkenes, and 3 2 AVOCs aromatics. k mainly represents the isoprene reactivity. k represents the k minus the sum BVOCs OVOCs VOCs of k , k , and HCHO reactivity. In this case, k denotes all known and unknown OVOCs AVOCs BVOCs OVOCs except HCHO. The removal of HCHO from k is mainly since the simple structure of HCHO OVOCs makes the contribution of HCHO to radical chemistry clear.\n(3) The data in Figure 1A is from the daytime (around 08:00-17:00 local time) and data in Figure 1B is only from low NO periods (10:00-15:00 local time), which is further explained in the above revised Figure 1 and Supplementary Fig. 5.\ng. You state many places throughout the manuscript that they measure radical concentrations, but do not specify which radicals they measure.\nResponse: Thanks, we clarified it in “Methods: Radical observations” in the revised manuscript, as shown below: Both OH and HO concentrations were measured in the seven field campaigns, and RO 2 2 measurements were carried out in the Wangdu and Heshan sites.\nh. The laser-induced fluorescence system (LIF) based on fluorescence assay by gas expansion technique does not have a reference.\nResponse: We added several references related to the LIF system accordingly in “Methods: Radical observations” in the revised manuscript:\nDuring these campaigns, radical concentrations are measured by the laser-induced fluorescence system (LIF) based on the fluorescence assay by gas expansion technique 6, 37.\nD. E. Heard, M. J. Pilling, Measurement of OH and HO in the Troposphere. Chemical Reviews 103, 2 5163-5198 (2003).\nK. D. Lu et al., Observation and modelling of OH and HO2 concentrations in the Pearl River Delta 2006: a missing OH source in a VOC rich atmosphere. Atmospheric Chemistry and Physics 12, 1541-1569 (2012).\nQ8. I suggest some grammar checks for the manuscript in addition to improving the clarity and precision of the text. At its current state, I do not believe the methodology is reproducible.\nResponse: Thanks for your valuable suggestions, we have done a careful and comprehensive grammar check for the manuscript accordingly, which largely enhanced the clarity and precision of the text.\nWith respect to the methodology reproductivity, since the field observation dataset used in this study have been published in peer reviewed journals 6, 7, 11, 23, 33, 35, 38, 39. Furthermore, the main analytical methods and research framework based our radical data have been well established and widely used in previous studies 33, 40, 41. We are aware of this misunderstanding may be caused by the grammar issues or missing details for the description of data, methods, and other supporting information. To further ensure that methodology can be more easily following and reproducible by readers, we upload the related data and calculation to the figshare website proposed by the journal for open access, and added more detailed information for methodology and dataset in the revised manuscript, including:\n(1) More description on radical closure experiments have been added in Supplementary Text 2 (see below).\n(2) More information for OH recycling probability has been added in “Methods: Calculation of OH recycling probability” in the revised manuscript. The newly added information has been shown in the Response to Q2.\n(3) The method of OH yields from the VOC oxidation through HPC photolysis have been refined, as shown in Supplementary Text 5 (Response to Q1).\n(4) More detailed information for HAM scheme have been added in Supplementary Table 5 (see below).\n(5) More detailed information on the dataset for the HAM scheme, as mentioned by reviewer #1, including four tables and six figures, including Supplementary Table 8. Supplementary Tables 10- 12. Supplementary Figure 6B. Supplementary Figures 14-18.\nThe update of radical closure experiment description.\nAs for the comparison between observed and simulated radical concentrations, a zero-dimensional chemical box model based on RACM2 was utilized in this study. The model was constrained to CO, NO, NO , CH , O , HONO, and VOCs concentrations and photolysis frequencies, water vapor, 2 4 3 ambient temperature, and pressure as well. For RACM2, the measured detailed VOC species were lumped into several categories, which is introduced in previous studies 6, 7. The H and CH mixing 2 4 ratio was assumed to be 550 ppb and 1900 ppb, respectively. Other parameters were from the observations with 5-min time resolution, which represents the actual atmospheric environmental conditions in every day during campaigns. Given the significance of ambient temperature on the results of quantum chemical calculations, herein, it's worth mentioning that the temperature input in the model was the real ambient temperature observed in campaigns rather than a constant value. Additionally, a spin-up time with 2 days at the beginning of simulations was used to reach steady-state conditions for long-lived species. A fix dilution equivalent of 24-h lifetime was added in the model to represent the dry deposition. Based on the above configuration in the model, simulated radical concentrations would be obtained and then they will be compared to the observed concentrations to investigate whether the chemical mechanisms are correct, which is the most direct indication to identify whether the chemical mechanisms in the troposphere are complete or not.\nSupplementary Table 5.\n\" ACO and HKET denote acetyl peroxy radicals and hydroxy ketone, respectively. jMACR 3 represents the photolysis rate constant of methacrolein (MACR).\n\" The rate constant of No. 1 is from our quantum chemical calculations.\n\" The rate constant of No. 2 is from Table 1 of Tan et al. 11.\n\" The reactions of Nos. 3-5 are from Wang et al. 8 and the rate constants of both No. 3 and No. 4 are from Wang et al. 8.\n\" As for No. 5, Wang et al. 8 did not give the rate constant directly. However, as mentioned by Wang et al. 8, the RO radicals could react with O at effective rates of (0.5~5) ×104 s-1 with rate 2 coefficients of 10-15~10-14 cm3 molecules-1 s-1 according to the studies from Atkinson 9. The radical EH5I&*EM U%DS@LIRSL=@E?=FM \"8 R COH), and Atkinson 10 once reported the reactions of O and 1 2 2 NDAMEGJFAMN U%DS@LIRS L=@E?=FM \"/1 OH) with the k(CH OH+O ) is 9.0×10-12 cm3 molecules-1 s- 2 2 2 1 at 298 K, which is larger than the rate constant of RO+O . The rate coefficients of CH OH+O 2 2 2 reactions reported in previous studies were summarized in IUPAC website (https://iupac- aeris.ipsl.fr/show_datasheets.php?category=Gas-phase+organics%3A+R_oxygen) and were all higher those that of RO+O reactions. To obtain a conservative result, we chose the rate constant 2 in No. 5 as 104 s-1.\n\" The photolysis rate of No. 6 is a conservative result from Liu et al. 12.\nReferences:\n[...References omitted for brevity...]\nReviewer #1 (Remarks to the Author):\nThere is no doubt that the authors exerted extra effort to respond to all comments and questions made by the reviewers. With respect to my comments/questions, I am satisfied (in general) to the new information provided by the authors.\nI only have minor corrections and suggestions:\n1 - I believe it is more correct to say \"rotatable bonds\" instead of \"rotation bonds\", so I would change this in the Supplementary Information.\n2 - The authors state that they obtain 63 distinguishable conformers for the CH3CH2CH2CH2CH2C(O)O2 reactant. If I take this molecule's Cartesian coordinates from the Supplementary Information and use them on Confab (with default settings), I obtain 1728 conformers:\n**Starting Confab 1.1.0\n**To support, cite Journal of Cheminformatics, 2011, 3, 8.\n..Input format = xyz\n..Output format = sy2\n..RMSD cutoff = 0.05\n..Energy cutoff = 500\n..Conformer cutoff = 1000000\n..Write input conformation? False\n..Verbose? False\n**Molecule 1\n..title = reactant.xyz\n..number of rotatable bonds = 5\n..tot conformations = 1944\n..tot confs tested = 1944\n..below energy threshold = 1728\n..generated 1728 conformers\nAnd this number can rise up to 1857, if one of those 1728 conformers is used again as \"seed\" to a new calculation in Confab. Of course, this is based on force fields and after a better calculation, the number of found conformers will most likely decrease. My question is: how did the authors arrive at the number 63? What calculations did they perform? Did they use some code (like Confab, or similar) to get a first set of conformers, and then they refined this number with a better electronic structure calculation? The authors should clarify this.\n3 - The two-time used expression \"producing conformers\" is strange. Please remove this or change the way those sentences are written.\n4 - In their rebuttal file, the authors reply to one of my initial questions as:\n\"Q2. Do the five shown TSs all connect to that one specific reactant conformer as shown in Figure S6?\nResponse: Yes, we had done the IRC calculation to verify the TSs correctly connect to the specific reactant conformer.\"\nBut the answer should clearly be \"No.\". By looking at the energies and drawings of the reactant conformers in Supplementary Figures 14 to 18, the reactant conformers connected to each of the TSs are different. Please include in those figures what reactant conformer does the first IRC point correspond to. Also, is the IRC path in Supplementary Figure 14 well converged in the reactants direction? It looks like it still has some slope there.\n5 - Please provide Cartesian coordinates for ALL (not just the lowest energy ones) calculated reactant and TS conformers, as the data in Supplementary Table 8 should be reproducible. These can be in the form of .xyz files inside a zip.\n6 - Please provide the value for ALL (not just the lowest energy ones) imaginary frequencies of the TS conformers.\nReviewer #2 (Remarks to the Author):\nThe authors have clarified all the comments and improved the quality of the manuscript. I recommend it to be accepted.\nReviewer #3 (Remarks to the Author):\nThe paper demonstrates that aldehydes can act as a major source of OH radicals in low NO environment. This novel hypothesis provides an explanation why models struggle reproducing OH concentration under low NO concentrations. The work has high significance for both climate and air quality as OH radicals greatly influence e.g. atmospheric methane concentrations and oxidation capacity in general.\nThe authors have nicely addressed all my previous comments during the first review round. The manuscript looks better, and I believe the methodology description has greatly improved towards being reproducible!\nSome comments/suggestions below for further improvement:\n1. Thank you for the HO2 vs NO plots (SI Fig. 8). As the OH yields from aldehydes are currently estimated using the inverse modeling techniques by selecting yields that guarantee a good agreement between modeled and measured OH, I find it interesting to see how other radicals are affected by the reactive aldehyde chemistry, and whether any improvements can be seen e.g., in HO2 concentrations between modeled and measured having the new chemistry is included in the model.\na. In SI Fig. 8, I can see that the green markers represent Base+RAM. Does this mean that LIM1 was not involved (sorry if I missed this)?\nb. Assuming LIM1 is not included, how would including it change the picture?\nc. Can you really say that the HO2 improves (to some extent) when RAM is involves? I find it hard to say from this figure. Can you quantify the improvement with a scatter plot + regression analysis (HO2 obs vs HO2 meas)?\nd Can these plots be made also for RO2?\n2. While the conclusions of the study will not be affected, I believe for that for the sake of credibility of the statistical analyses, Figure 1 should still be further improved.\na. Error bars are currently stated to describe uncertainty in the data. What do you mean by uncertainty? Does this mean measurement uncertainty involving some estimated measurement error or do you mean variability in the data?\nb. My suggestion is to show the data variability. Because the markers are median values, I would draw the error bars between 25th and 75th percentiles within the data. I would say that utilizing standard deviation (which is maybe what you show?) makes sense only if your data is normally distributed, which I assume is not the case.\nc. I would also add error bars in the x direction to show the width of the NO bins.\nd. Maybe the error bars could be same color as the markers?\ne. Could you add confidence intervals to Fig. 1B using the data variability?\nTechnical:\n- L70 “It is demonstrated” \" “this study demonstrates” or “It is demonstrated” + reference.\n- L208 define “high carbon numbers”\n- L411 define “ALD”\nResponse to Reviewer #1:\nGeneral comments:\nThere is no doubt that the authors exerted extra effort to respond to all comments and questions made by the reviewers.\nWith respect to my comments/questions, I am satisfied (in general) to the new information provided by the authors.\nI only have minor corrections and suggestions.\nResponse: We appreciate the reviewer’s positive comments about the revised manuscript. Below are our responses to the specific comments and revisions.\nSpecific comments:\nQ1. I believe it is more correct to say \"rotatable bonds\" instead of \"rotation bonds\", so I would change this in the Supplementary Information.\nResponse: Thanks for your suggestions. We have corrected it.\nQ2. The authors state that they obtain 63 distinguishable conformers for the CH3CH2CH2CH2CH2C(O)O2 reactant. If I take this molecule's Cartesian coordinates from the Supplementary Information and use them on Confab (with default settings), I obtain 1728 conformers:\n[...Table omitted for brevity...]\nAnd this number can rise up to 1857, if one of those 1728 conformers is used again as \"seed\" to a new calculation in Confab. Of course, this is based on force fields and after a better calculation, the number of found conformers will most likely decrease. My question is: how did the authors arrive at the number 63? What calculations did they perform? Did they use some code (like Confab, or similar) to get a first set of conformers, and then they refined this number with a better electronic structure calculation? The authors should clarify this.\nResponse: In our calculations, the initial guess conformers for CH CH CH CH CH C(O)O is 237 generated by 3 2 2 2 2 2 using MSTor 2017 program 1, 2. These initial conformers were firstly optimized by B3LYP3/6-31G(d,p) method. As a result, there are only 70 distinguishable conformers from B3LYP/6-31G(d,p) calculated results. Furthermore, the 70 distinguishable conformers were reoptimized by using M06-2X4/MG3S5 method to lead to the formation of 63 distinguishable conformers. The input of the CH CH CH CH CH C(O)O reactant for obtaining conformer is 3 2 2 2 2 2 provided as follows.\n[...Table omitted for brevity...]\nQ3. The two-time used expression \"producing conformers\" is strange. Please remove this or change the way those sentences are written.\nResponse: Thank you for your suggestion! We have rewritten the corresponding sentences in the revised Supplementary Information.\nQ4. In their rebuttal file, the authors reply to one of my initial questions as:\n\"Q2. Do the five shown TSs all connect to that one specific reactant conformer as shown in Figure S6?\nResponse: Yes, we had done the IRC calculation to verify the TSs correctly connect to the specific reactant conformer.\"\nBut the answer should clearly be \"No.\". By looking at the energies and drawings of the reactant conformers in Supplementary Figures 14 to 18, the reactant conformers connected to each of the TSs are different. Please include in those figures what reactant conformer does the first IRC point correspond to. Also, is the IRC path in Supplementary Figure 14 well converged in the reactants direction? It looks like it still has some slope there.\nResponse: We agree with your comments. We have added some comments in Supplementary Information: We also did intrinsic reaction coordinate (IRC) calculations to show that the transition state connects with the corresponding reactant and intermediate product conformer as listed in Supplementary Figures 14-18. However, in Supplementary Figure 6A, the reactant and intermediate product are both the lowest conformers of the reactants and intermediates. The lowest conformers can facilely convert to the specific conformer along internal rotation, which is connected with the corresponding transition state.\nQ5. Please provide Cartesian coordinates for ALL (not just the lowest energy ones) calculated reactant and TS conformers, as the data in Supplementary Table 8 should be reproducible. These can be in the form of .xyz files inside a zip.\nResponse: We have provided Cartesian coordinates for all calculated reactant and transition state conformers in a separate file with named as xyz.zip.\nQ6. Please provide the value for ALL (not just the lowest energy ones) imaginary frequencies of the TS conformers.\nResponse: The value for all imaginary frequencies of the TS conformers was provided in an Excel file named imaginary frequencies in the xyz.zip file.\nReferences:\n[...References omitted for brevity...]\nResponse to Reviewer #3:\nGeneral comments:\nThe paper demonstrates that aldehydes can act as a major source of OH radicals in low NO environment. This novel hypothesis provides an explanation why models struggle reproducing OH concentration under low NO concentrations. The work has high significance for both climate and air quality as OH radicals greatly influence e.g. atmospheric methane concentrations and oxidation capacity in general.\nThe authors have nicely addressed all my previous comments during the first review round. The manuscript looks better, and I believe the methodology description has greatly improved towards being reproducible!\nSome comments/suggestions below for further improvement.\nResponse: Thank you very much for recognizing our paper and your constructive comments, which are critical to improving our manuscript. Below are our responses to the specific comments and revision.\nSpecific comments:\nQ1. Thank you for the HO vs NO plots (SI Fig. 8). As the OH yields from aldehydes are currently estimated using 2 the inverse modeling techniques by selecting yields that guarantee a good agreement between modeled and measured OH, I find it interesting to see how other radicals are affected by the reactive aldehyde chemistry, and whether any improvements can be seen e.g., in HO concentrations between modeled and measured having the new chemistry is 2 included in the model.\na. In SI Fig. 8, I can see that the green markers represent Base+RAM. Does this mean that LIM1 was not involved (sorry if I missed this)?\n[...Response omitted for brevity...]\nReferences\n[...References omitted for brevity...]\nReviewer #3 (Remarks to the Author):\nI am very happy with the current state of the paper. I have no further comments."}]

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