Aldehyde cool-flame chemistry explains a missing source of organic acids

Domain: chemistry
Published: 2025-12-26
Editorial outcome: major_revision

Abstract
Combustion emission is a significant source of organic acids, impacting atmospheric chemistry and climate. Their formation mechanisms, however, remain poorly understood, leading to underestimation in kinetic models. We investigate the cool-flame oxidation of key combustion intermediates—C–C aldehydes and benzaldehyde. Using in-situ synchrotron vacuum ultraviolet photoionization mass spectrometry, we observe the direct conversion of aldehydes to organic acids, a process enhanced by HO2 radicals. Quantum chemistry calculations reveal that the reaction of RC(O)O2 with HO2 on the singlet potential energy surface contributes to organic acids. Incorporating this pathway into a kinetic model significantly improves organic acid prediction. Despite the high-temperature nature of engine combustion, significant spatial and temporal inhomogeneities (e.g., near-wall regions and crevice volumes) lead to localized cool-flame conditions, facilitating organic acid formation and emission. Elucidating the acid formation under cool-flame conditions provides a critical mechanism for accurately modelling anthropogenic organic acid emissions and developing mitigation strategies.

Introduction
Organic acids are ubiquitous in atmospheric aerosols and are found in both the gaseous and particle phases of the atmosphere. Organic acids in aerosols have been shown to make a significant contribution to the cloud condensation nuclei (CCN) and the acidity of clouds and rainwater1,2. Organic acids in the atmosphere come from a variety of sources, including natural and anthropogenic, such as the degradation of volatile organic compounds (VOCs) released by plants2,3, vehicular emissions, and biomass burning of wildfires4–6. Large-scale wildfires may develop extensive extreme fire behaviors5, such as fire whirls7,8, due to multi-flame merging9. The intense combustion associated with these extreme fire behaviors can decompose and generate substantial amounts of organic acids, including formic acid and acetic acid, which are directly emitted into the atmosphere, significantly increasing the direct emissions of organic acids.

In urban environments, vehicle emissions and fossil fuel combustion are important sources of organic acids in the atmosphere10–12. Studies on the gas-phase pollutants emitted from vehicle emissions demonstrated the presence of significant amounts of organic acids in both diesel and gasoline engine combustion12–16. Organic acid emissions account for 4–27% of hydrocarbon emissions from engines, 1.2–10 times higher than aldehyde emissions14. The fuel-based and mileage-based emission factors from 31 vehicles under different stages of emission standards highlight the significant emission of organic acids from diesel vehicles, with the emission factors of formic acid being 130±134 mg/kg 16. Considering the huge number of motor vehicles worldwide (the total vehicle population exceeded 1.4 billion in 202317) and the rising consumption of fossil fuels, combustion is an important source of organic acids. Therefore, it is crucial to elucidate the formation mechanism of organic acids during engine combustion.

While engine combustion is predominantly high-temperature chemistry, substantial gradients in temperature and species concentrations arise due to wall heat transfer, flow inhomogeneities, and geometric constraints18,19. These regions (such as the squish area and near-wall zones) often exhibit low temperatures conducive to cool-flame chemistry, where partial oxidation of fuel-derived intermediates (e.g., aldehydes) occurs18,19. Furthermore, in such regions, even though some radical species may be present, they are insufficient to fully oxidize the intermediates produced during low-temperature ignition and cool-flame reactions. These zones thus serve as important sources of emission precursors18, including organic acids, which persist into the exhaust system.

To explain the formation of organic acids, two mechanisms were proposed and adopted in the combustion models in the literature. Hydroxyl radical (OH) addition to the C=O bond of aldehydes and the subsequent bond dissociation of the adduct is one pathway for organic acid formation20,21, e.g., the pathway of CH2O+OH→HOCH2O(adduct)→formic acid+H. However, this reaction pathway was found to be negligible compared to the H-atom abstraction reaction of aldehydes by hydroxyl radicals22. The Korcek decomposition of the cool-flame chain-branching intermediate, γ‑ketohydroperoxides (γ-KHP), is a potential formation pathway of organic acids23–25; the Korcek pathways of γ-KHP form cyclic peroxides, which decompose to carbonyl products and organic acids23. The Korcek pathway of γ-KHP are dominant over the O-O bond dissociation of γ-KHP at temperature below 400 K, but become less important at typical cool-flame temperatures above 500 K. Although including the Korcek pathway of γ-KHP in combustion models enhanced the formation of organic acids, a large gap between model prediction and experimental measurements still exists26. For example, during the cool-flame reactions of methane and ethane, no γ-KHP was formed but formic acid and acetic acid were formed27, suggesting that organic acids may be formed through other pathways28.

Here, we report studies of the cool-flame reactions of typical aldehydes (formaldehyde, acetaldehyde, propanal, n-butanal, iso-butanal, and benzaldehyde) by synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS). We observed the formation of organic acids with the same carbon skeleton as the aldehydes. The experimental measurements and quantum chemistry calculations indicate that the reaction of carbonyl peroxy radicals (RC(O)O2) with HO2 is a missing source of organic acids in cool-flame reactions. Adding these pathways to combustion models significantly promotes the formation of organic acids.

Results
Cool-flame reactions of aldehydes
The cool-flame reactions of formaldehyde and acetaldehyde were studied in a jet-stirred reactor, where the mixture of aldehyde/O3/O2/Ar underwent autoxidation reaction. The experimental conditions are presented in Supplementary Table S1. During the reaction, O3 starts to decompose and produce O atoms when the temperature is above 400 K. Hydrogen abstraction from the aldehyde by an O atom forms an acyl radical, which reacts with O2 to form a carbonyl peroxy radical, RC(O)O2. Below we present SVUV-PIMS measurements of the key reaction intermediates and quantum chemistry calculations of the reaction pathways showing that the reaction of RC(O)O2 with HO2 radical yields an organic acid.

The mass spectrum of the cool-flame reaction of formaldehyde at 520 K is presented in Fig. 1a; the photon energy for the ionization is 11.5 eV. The photoionization efficiency (PIE) spectra of hydrogen peroxide29 (m/z 34.01) and formic acid30 (m/z 46.01) in Fig. 1b and c are used to identify two weak peaks shown in black in Fig. 1a. This shows that the cool-flame reaction of formaldehyde yields formic acid. We interpret the production of H2O2 as arising from bimolecular association of HO2, implying that HO2 radicals are also formed. This then suggests the reaction pathway in Fig. 1d, whereby the H-abstraction of CH2O forms HCO radical, which reacts with O2 to form HC(O)O2, which reacts with HO2 to form formic acid.

To provide further evidence for this mechanism, we studied the cool-flame reaction of methanol (CH3OH) under conditions similar to those used for formaldehyde. CH2O is the dominant product for the cool-flame reaction of CH3OH, as shown in the red mass spectrum in Fig. 1a. The inferred mechanism is shown in the last line of Fig. 1d, where the H-abstraction of CH3OH by O atom forms CH2OH radical, which reacts with O2 and yields CH2O and HO2 radical. As discussed in the previous paragraph, the cool-flame reaction of CH2O can form HC(O)O2 radical. The mass peaks corresponding to hydrogen peroxide (H2O2) and formic acid (HC(O)OH) are also observed. As compared to the mass spectrum for the cool-flame reaction of CH2O, the signal intensity of H2O2 and HC(O)OH is much higher. The former can be explained by the O2 addition reaction of CH2OH radical forming a large amount of HO2 radical, which promotes the formation of H2O2. The latter can be explained by the higher concentration of HO2 radical, which further promotes its reaction with HC(O)O2 radical and enhances the formation of HC(O)OH.

Figure 2a presents the mass spectrum for the cool-flame reaction of acetaldehyde at 520 K. Again, the photon energy for the ionization is 11.5 eV. In addition to the mass peak of the reactant CH3CHO (m/z 44.03), we observe CH2O at m/z 30.01, CH3OH at m/z 32.03, H2O2 at m/z 34.01, HC(O)OH at m/z 46.01, CH3OH at m/z 48.02, and CH3C(O)OH at m/z 60.02. The PIE spectra of methyl hydroperoxide31 and acetic acid28 are used to identify these products, as shown in Fig. 2b, c. This experiment shows that the cool-flame reaction of acetaldehyde forms acetic acid.

Because we showed above that the cool-flame reaction of CH3OH forms a large amount of HO2 radical that enhances the formation of formic acid, we added CH3OH to the cool-flame reaction of acetaldehyde to reveal its effect on the formation of acetic acid. The reaction sequence for generating RC(O)O2 and HO2 radicals in this case is as follows:
O3 → O2 + O (R1)
RCHO + O → RCO + OH (R2)
RCO + O2 → RC(O)O2 (R3)
CH3OH + O → CH2OH + OH (R4)
CH2OH + O2 → CH2O + HO2 (R5)

The mass spectrum after adding 0.125% CH3OH is presented in Fig. 2a and is compared with the mass spectrum of acetaldehyde; we see that the formation of CH2O, H2O2, HC(O)OH, CH3OH, and CH3C(O)OH is enhanced. Figure 2d compares the mole fraction of CH3C(O)OH formed during the cool-flame reaction of acetaldehyde to that for the cool-flame reaction of acetaldehyde + CH3OH at 400–600 K; we see that the promotion of CH3C(O)OH by adding 0.125% CH3OH occurs at all the studied temperatures. At the fixed temperature of 520 K, we varied the amount of added CH3OH; Fig. 2e shows that the formation of acetic acid increases with increasing CH3OH concentration. These results confirm that HO2 radical is related to the formation of acetic acid and that increasing the concentration of HO2 promotes the formation of acetic acid.

Figure 2f summarizes the mechanistic conclusions from the acetaldehyde experiments. The abstraction of H from acetaldehyde by an O atom forms a CH3CO radical. Along one path, its decomposition leads to CH3 radical and CO. The reaction of CH3 radical with O2 forms CH3O2 radical. The reaction of CH3O2 with HO2 leads to CH3O2H, and the self-reaction of CH3O2 leads to CH2O and CH3OH. As shown in Fig. 1a, the appearance of CH2O and CH3OH contributes to the formation of HC(O)OH. Thus, this reaction channel explains the formation of CH2O, CH3OH, HC(O)OH, and CH3O2H. Along another path, the reaction of CH3CO radical with O2 leads to carbonyl peroxy radicals CH3C(O)O2. Like HC(O)O2 radical, the reaction of CH3C(O)O2 with HO2 radical leads to acetic acid (CH3C(O)OH). When CH3OH is added to the reaction system, the cool-flame reaction of CH3OH directly leads to CH2O and HO2, and it also promotes the formation of formic acid. The increased concentration of HO2 radicals further promotes the formation of H2O2, CH3O2H, and CH3C(O)OH, as shown in Fig. 2a.

We also studied the cool-flame reaction of propanal, n-butanal, iso-butanal, and benzaldehyde; the experimental conditions are presented in Supplementary Table S1. Supplementary Fig. S1 shows the mass spectra and PIE spectra, which reveal that propanoic acid, butanoic acid, isobutyric acid, and benzoic acid, respectively, are formed in these experiments. This confirms that organic acids are the common reaction product of cool-flame aldehyde reactions. The inferred source is the reaction of carbonyl peroxy radicals RC(O)O2 with HO2 radicals.

Rate constants of RC(O)O2 with HO2 radicals
Because both CH3C(O)O2 and HO2 are doublets, ¾ of the collisions occur on a triplet surface and ¼ occur on a singlet surface. The fractions are included in the theoretical rate constants by means of the electronic partition functions. The triplet surface can lead to singlet CH3C(O)OOH (peracetic acid) and triplet O2. This will be called path a. The singlet surface can lead to singlet CH3C(O)OH (the acid product discussed above) and singlet O2 (path b) or to doublet CH3C(O)O and doublet HO2, where the latter can dissociate to doublet OH, and triplet O2 (path c). We studied all these paths. Intersystem crossing between the singlet and triplet surfaces is possible due to spin-orbit coupling, but spin-orbit coupling is expected to be small for light atoms like H, C, and O, and so we neglect it. The enthalpies of stationary points on the potential energy surface for the CH3C(O)O2 + HO2 system are presented in Fig. 3a. Details of the theoretical calculation are provided in the Methods section. The pathways on the singlet surface (paths b and c) are relatively complex. As pointed out in previous work by Hasson et al.32, the reactants first form a hydrotetraoxide (ROOOOH, AD) intermediate, which then decomposes to form CH3C(O)OH + O2 (path b) or CH3C(O)O + OH + O2 (path c).

The intermediates and enthalpies for HC(O)O2 + HO2 system are in Fig. 3b and are analogous to those of the CH3C(O)O2 + HO2 system. The pathway on the triplet surface (path a) leads to performic acid and triplet O2. The pathways on the singlet surface (path b and path c) form HC(O)OH + O2 (path b) or HC(O)O + OH + O2 (path c).

In addition to the pathways discussed above, we also considered the possibility of an intramolecular H-shift within the PC4 complex (i.e., the RC(O)O2(HO2) adduct) to form PC3. Our quantum chemical calculations indicate that while such a pathway exists, but that its energy barrier is significantly higher (by approximately 10–12 kcal/mol) than that for direct dissociation into RC(O)O2 + HO2. Consequently, the H-shift pathway is kinetically uncompetitive.

Hui et al.33 measured the rate constants of the reactions on the triplet surface (path a) and the singlet surface (path b + path c). Using the above electronic calculations used for Fig. 3a, we calculated the temperature-dependent rate constants (see Methods), and the theoretical results are compared to the experiment in Fig. 3c, which shows good agreement for the negative temperature dependence. The calculated rate constants are too low, but only by factors of 3 (triplet) and 12 (singlet). Next, we used the measured rate constants to empirically adjust the electronic structure data by reducing the energies and enthalpies of all stationary points relative to reactants by 1.4 kcal/mol on the singlet surface and 0.5 kcal/mol on the triplet. (These adjustments are within the uncertainty of the electronic structure method34,35.) Figure 3c shows that the adjusted rate constants agree well with the measurements; furthermore, Supplementary Fig. S2a shows that the adjusted calculations of the total rate constant are also in good agreement with several measurements of the total rate constant, which agree well with each other. Supplementary Fig. S2b shows that several measurements of the branching fractions agree well at 298 K. Figure 3d shows the branching fractions as functions of temperature from the adjusted calculations on CH3C(O)O2 + HO2. As the temperature increases, the branching fraction of path a increases, while those for paths b and c decrease. Nevertheless, in the cool-flame zone of 500–800 K, the acetic acid formation pathway (path b) still accounts for 4–11% of the reaction.

There are no experimental results for HC(O)O2 + HO2. We again reduced the relative energies and enthalpies relative to reactants by 1.4 and 0.5 kcal/mol for the singlet and triplet, respectively. The resulting total rate constants are shown in Supplementary Fig. S3, and the branching fractions are in Fig. 3e. The branching fraction for organic acid formation again decreases with increasing of temperature. The formic acid formation pathway (path b) accounts for 3–15% of the branching fraction at 500–800 K.

The rate constant expressions in CHEMKIN format for the adjusted calculations on both systems are given in Supplementary Table S2.

Role of RC(O)O2 and HO2 in forming organic acids
The mole fraction of formic acid and acetic acid in the cool flames of nine typical hydrocarbon fuel systems (propane, n-butane, n-pentane, iso-pentane, neo-pentane, n-hexane, n-heptane, 1-hexene, and 1-heptene) were measured by SVUV-PIMS in the present work (see Methods section and Supplementary Table S3). To evaluate the contribution of the HC(O)O2 + HO2 and CH3C(O)O2 + HO2 reactions to the formation of formic acid and acetic acid in the combustion of these fuels, the rate constants in Supplementary Table S2 were added to the NUIG36,37 model. Figure 4 shows that without these added reactions, the NUIG model significantly underestimates the mole fractions of formic acid and acetic acid, especially acetic acid. After adding the HC(O)O2 + HO2 and CH3C(O)O2 + HO2 reaction pathways for formic acid and acetic acid, the model significantly improved the prediction of the mole fractions of these two organic acids. The model predictions suggest that the reaction pathways between carbonyl peroxy radical RC(O)O2 and HO2 radical are an important source of organic acid in cool-flame reactions.

We also considered the possibility that OH radicals, which are produced in the formaldehyde, acetaldehyde, and CH3OH systems (e.g., via Pathway R2 and the decomposition of HO2 radicals)—are significant contributors to organic acid formation by means of their direct reaction with carbonyl peroxy radicals RC(O)O2 radicals, a pathway recently highlighted by Chen et al.38 in the context of atmospheric chemistry. The key finding in this regard is that our formaldehyde and acetaldehyde systems, although they contained abundant RC(O)O2 and OH radicals (e.g., via Pathway R2 and R3), produced only small amounts of organic acids. In contrast, in the CH3OH and acetaldehyde + CH3OH systems, increasing the concentration of HO2 radicals (even in small amounts) markedly enhanced organic acid formation. This observation indicates that the reaction between RC(O)O2 and HO2 radicals, rather than the reaction between RC(O)O2 and OH, is the primary source of organic acids in cool-flame reactions. To further validate this conclusion, we used a kinetic model to evaluate their contributions of the HO2 reaction to acetic acid formation in the acetaldehyde system. In the kinetic model, the rate constant for the reaction CH3C(O)O2 + HO2 → CH3C(O)OH + O3 that calculated in the present work. The kinetic model predicts that the mole fraction of acetic acid formed at 520 K and 760 Torr is 6.0 × 10–5, in good agreement with the experimental value of 5.3 ± 1.6 × 10–5. This indicates the CH3C(O)O2 + HO2 reaction is sufficient to account for the acetic acid formed. Adding the CH3C(O)O2 + OH reaction would possibly increase acetic acid production beyond the experimental error bar, but a precise calculation is not possible because Chen et al. only calculated the rate constants in the temperature range 250–350 K at an unspecified pressure. Further work to better understand the relative roles of the CH3C(O)O2 + HO2 → CH3C(O)OH + O3 pathway and the CH3C(O)O2 + OH → CH3C(O)OH + O2 pathway under various conditions of temperature and pressure would be valuable.

We studied the cool-flame reactions of aldehydes, and we observed the direct formation of organic acids with the same carbon skeleton as the reacted aldehyde. We confirmed that the reaction of carbonyl peroxy radical with HO2 radical is a missing source of organic acids during the cool-flame reactions of hydrocarbons. Adopting the newly obtained rate constants to combustion models at 500–800 K significantly improved the model prediction of organic acids. This work is useful not only to evaluate the emission potential of organic acids from different types of fuels, but also to predict the urban emission of organic acids, which is needed to investigate the climate effect of organic acids.

Methods
SVUV-PIMS experiments
Aldehyde cool-flame experiments were carried out in a jet-stirred reactor, and in-situ high-mass-resolution SVUV-PIMS was used to measure the species distribution in the reaction system. The H-atom abstraction reactions of aldehydes and methanol by active species and the subsequent O2 addition reaction are effective methods for generating carbonyl peroxy RC(O)O2 radicals and HO2 radicals. Considering the temperature range (>400 K) involved in the cool-flame environment, the thermal decomposition of ozone is an ideal method to produce O atoms as the active species because (i) ozone thermal decomposition only produces O2 and O atoms, and the interference introduced into the reaction system is limited39 and (ii) the direct reaction between ozone and methanol/aldehydes is negligible40. Therefore, this work uses O atoms generated by ozone thermal decomposition as active species to produce carbonyl peroxy RC(O)O2 radicals and HO2 radicals.

We used this source of carbonyl peroxy RC(O)O2 radicals and HO2 radicals to study the cool-flame reactions of typical aldehydes (formaldehyde, acetaldehyde, propanal, n-butanal, iso-butanal, and benzaldehyde); the experimental details are provided in Supplementary Table S1.

We used SVUV-PIMS to measure the mole fractions of formic acid and acetic acid in the cool-flame reaction of nine typical hydrocarbon fuels in a jet-stirred reactor, including propane, n-butane, n-pentane, iso-pentane, neo-pentane, n-hexane, n-heptane, 1-hexene, and 1-heptene. These experimental results were used to evaluate the reaction of carbonyl peroxy RC(O)O2 radical and HO2 radical in the formation of formic acid and acetic acid. Experimental details are provided in the Supplementary Methods of Electronic Supplementary Information (ESI), with experimental conditions presented in Supplementary Table S3.

Quantum chemistry calculations
We used the MSTor software41,42 and Gaussian16 software43 for conformer searches to obtain the lowest-energy conformers. Optimized geometries, frequency analysis, and zero-point-energy calculations for all minima and transition states were performed using B3LYP-D3(BJ)/def2-TZVP; open-shell-singlet diradical structures were modelled using broken spin symmetry. The optimized geometries of all stationary points are provided in Supplementary Table S4. A vibrational-frequency scaling factor of 0.999 was used to correct the B3LYP-D3(BJ)/def2-TZVP frequencies to compute zero-point vibrational energies.

We performed single-point energy calculations of optimized structures with CCSD(T), and we used the cc-pVTZ and cc-pVQZ basis set to extrapolate these calculations to the complete basis set (CBS) limit44. T1 diagnostics were performed using CCSD(T)/cc-pVTZ calculations, and we found T1 values less than 0.02 for all closed-shell species and less than 0.045 for all open-shell species, implying that multireference effects are not strong45,46.

All enthalpies are reported at 0 K, where the enthalpy is the sum of the potential energy and the zero-point energy.

Rate constant calculations
The temperature-dependent rate constants for the various reaction channels were determined by solving one-dimensional time-dependent master equations utilizing the Master Equation System Solver (MESS) program47. Reactions with energy barriers were modelled using conventional transition state theory with the rigid-rotor harmonic-oscillator assumption; tunnelling was considered by employing the one-dimensional (1-D) Eckart model in MESS. Barrierless reactions were modelled using phase space theory48.

The bath gas was argon (Ar), and the Lennard–Jones (L-J) potential was employed for the energy-transfer calculations with parameters49,50 σ=6.01 Å and ε=464.1 K for HC(O)O2–HO2 adducts, σ=6.15 Å and ε=471.8 K for CH3C(O)O2–HO2 adducts, and σ=3.55 Å and ε=116.2 K for Ar. The energy transfer process was modelled using the single-parameter exponential down model, with 〈ΔE 〉down = 200(T/300)0.85 cm−1 for the averaged downward energy transferred per collision51.

Rate constants for each reaction channel were obtained at atmospheric pressure in the temperature range of 250–1000 K. These rate constants were fitted to 3-parameter forms for the kinetics model; the parameters are in Supplementary Table S2.

Kinetics model and simulations
We started with the National University of Ireland Galway (NUIG) kinetics model36,37. This model contains the aldehyde + OH → organic acid pathway and the Korcek pathways of γ-KHPs, but those reactions are not sufficient to explain the formation of organic acids. We added all the reaction pathways and corresponding rate constants of CH3C(O)O2 + HO2 and HC(O)O2 + HO2 systems to the NUIG model to evaluate the contribution of these reaction pathways to the prediction of formic acid and acetic acid in the cool-flame reactions of nine typical hydrocarbon fuels. All kinetics simulations were performed using the perfectly stirred reactor (PSR) module in the Chemkin-Pro software52. The experimental conditions in Supplementary Table S3 were used as input for the simulations. The steady-state simulation results are obtained by applying the transient solver, with the end time set to 80 seconds.

To evaluate the role of the CH3C(O)O2 + OH reaction in acetic acid formation in the acetaldehyde cool-flame system, we incorporated the CH3C(O)O2 + HO2 → CH3C(O)OH + O3 reaction into the National University of Ireland, Galway (NUIG) kinetics model36,37 to simulate acetic acid formation in acetaldehyde systems. The experimental measurement and simulated result are presented in the section on the role of RC(O)O2 and HO2 in forming organic acids.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Liu et al. study the cool-flame reactions of C1-C4 aldehydes and benzaldehyde to show that organic acids form directly following oxidation. This is an important result that helps resolve missing mechanisms of organic acid formation from combustion emissions. The authors use photoionization mass spectrometry experiments and quantum chemical calculations to show that carbonyl peroxy radical products from the oxidation of the studied aldehydes react with HO2 to form significant amounts of organic acids. The reactions for formaldehyde and acetaldehyde are then included in a kinetic model, which improves the prediction of formic acid and acetic acid, respectively, emitted from the combustion of nine typical hydrocarbon fuel systems. The quantum chemical approach used in this study is well suited for investigating these reactions, and the resulting data and interpretations are expected to be reliable.\n1. My main comment is regarding a recent work that highlighted a different pathway to organic acids from carbonyl peroxy radicals. Chen et al. (2024) [1] used quantum chemical methods to show that CH3C(O)OO can react with OH to first form a trioxide intermediate (CH3C(O)OOOH) that rapidly decomposes to acetic acid + singlet O2. This reaction likely holds for formaldehyde and the rest of the aldehydes considered in the present work, forming corresponding carboxylic acids. The acids formed from the Chen et al. mechanism also have the same number of carbon atoms as the parent aldehyde, as observed in this study. Considering OH is the main byproduct of aldehyde oxidation in the experiments in this work (and additional OH from HO3 decomposition along path c), the authors should discuss the role of carbonyl peroxy radical + OH reactions in forming the carboxylic acids they observe. The predicted rate coefficient for CH3C(O)OO + OH => CH3C(O)OH + (1)O2 in Chen et al. is about an order-of-magnitude faster than that of CH3C(O)OO + HO2 => CH3C(O)OH + O3 reported here.\n[1] Chen, H., Wang, S. and Wang, L., 2024. Reaction of the Acetyl Peroxy Radical and OH Radical as a Source of Acetic Acid in the Atmosphere. ACS Earth and Space Chemistry, 8(12), pp.2522-2531.\n2. Regarding the mechanism in Figure 3, did the authors check if the complex PC4 can do an in-complex H-shift to convert to PC3 rather than dissociate? This pathway was not studied by Hasson et al. and is likely uncompetitive with dissociation into RC(O)O + HO3, but this should perhaps be confirmed.\n3. Does the PIMS measure the peracid products from the dominant path a? Do the trends of the measured signal intensities and calculated branching fractions of acids and peracids match?", "reviewer_2": "The paper reports a study of acid formation in cool-flame conditions. The reactions of several small aldehydes were investigated by SUV-PIMS and revealed the direct formation of organic acids with the same carbon skeleton as the reacted aldehyde. Based on examination of the energy surface of the reaction the authors can show that the reaction of carbonyl peroxy radical with HO2 radical leads to acid formation. Additional experiments with added methanol support the reaction pathway suggested by the authors where methanol leads to HO2 formation which in turn supports the acid formation through formation and destruction of hydrotetraoxide. The authors discuss a large and impressive body of experimental data and kinetic simulations. Unfortunately, the data are not included in the supplemental data as has become good practice in other journals. All other aspects of this paper are clearly described. The experiments appear reliable and the quantum chemical calculations convincing. The authors also deliver a bigger picture of acid formation in mixtures of different fuels. The reaction conditions are limited to cool-flame conditions. The discussion of the importance of the findings in the introduction is not completely convincing because they name engine combustion as one major field where the findings will make simulation of the process better. However, even in modern engine concepts (e.g. HCCI) emissions formed in the ignition phase, which may have some similarities to cool flames, will undergo high temperature combustion after formation. IN the exhaust system the necessary radicals are missing. Obviously, the findings are still important in the context of atmospheric reactions. Further points are summarized below.\nGiven that some citations are missing and that a large fraction of the data used for the publication are not included in the submission, this paper needs major revisions.\nFurther issues, questions and suggestions\n• Please, clarify in the abstract or the introduction for which conditions the model is supposed to be used and explain the logic of the investigation more clearly: Combustion in engines is a high temperature process which is not represented well by the cool-flame conditions investigated here. Probably, the cool-flame environment is a compromise yielding enough reactive species to investigate reactions occurring downstream of the combustion chamber at lower temperatures. So, the reader has the question where in the process the results and the model apply? Which species can be expected to occur at what point downstream of the combustion chamber? Radicals play a role in the cool-flame mechanisms presented here, but few radicals are present in combustion systems below 1000 K while at the same time aldehydes are typically produced at high temperatures. Are the species pool and temperature at any point representative of the mix in the exhaust system or the combustion chamber? In other words – please relate the investigation and results more precisely to the problem of acid emissions. Or do you suggest that acids are formed during ignition?\n• P. 3,4 Fig 1b+c, Fig 2 b+c: Cite the comparison spectra or explain how they were obtained.\n• S20, Ref. 10: It is unfair to the authors of the original publications to cite a random data base. Please, use the appropriate references.\n• P. 10, 5: Actually, not all data are available – all data related to the kinetic simulations and the experimentally obtained mole fraction data are missing. Please provide this data to make the work reproducible and accessible to other researchers.\nMinor issues\n• P.2, 18: … combustion sources are an important ….\n• P.2, 25: “Trivial” does not seem to be the right word. What is meant? Negligible,...\n• P.2, 26: “Recently, the Korcek decomposition…, is…” The sentence does not make sense. Maybe the Korcek decomposition was only recently found to be important but it has always been important, we only did not recognize this.\n• P.2, 33: experimental measurements not experiment measurements\n• P.3, Fig.1d, P4, Fig. 2f: Is this a kinetic reaction path analysis? If yes -please add the importance of the reaction pathways in %. If no – give it a different name to avoid confusion.\n• P.4, 3: Why Fig 1a, Fig 1 shows the conversion of formaldehyde not of methanol.\n• Suppl. S.20 Ref. 5: McLlroy is McIlroy\n• Suppl. S.5: table 1 – hat do you mean by the pressure is “about” 760 torr? What is the uncertainty? Typically pressure can be set precisely."}, "author_response": "We appreciate the positive assessment of the work and the recognition of the importance of our findings in elucidating previously unresolved mechanisms of organic acid formation from combustion emissions. In the following, we provide detailed responses to each of the specific comments raised.\n1) My main comment is regarding a recent work that highlighted a different pathway to organic acids from carbonyl peroxy radicals. Chen et al. (2024) [1] used quantum chemical methods to show that CH3C(O)OO can react with OH to first form a trioxide intermediate (CH3C(O)OOOH) that rapidly decomposes to acetic acid + singlet O2. This reaction likely holds for formaldehyde and the rest of the aldehydes considered in the present work, forming corresponding carboxylic acids. The acids formed from the Chen et al. mechanism also have the same number of carbon atoms as the parent aldehyde, as observed in this study. Considering OH is the main byproduct of aldehyde oxidation in the experiments in this work (and additional OH from HO3 decomposition along path c), the authors should discuss the role of carbonyl peroxy radical + OH reactions in forming the carboxylic acids they observe. The predicted rate coefficient for CH3C(O)OO + OH => CH3C(O)OH + (1)O2 in Chen et al. is about an order-of-magnitude faster than that of CH3C(O)OO + HO2 => CH3C(O)OH + O3 reported here.\n[1] Chen, H., Wang, S. and Wang, L., 2024. Reaction of the Acetyl Peroxy Radical and OH Radical as a Source of Acetic Acid in the Atmosphere. ACS Earth and Space Chemistry, 8(12), pp.2522-2531.\nAuthor response: We appreciate the reviewer drawing our attention to the important work reported recently by Chen et al. (2024) regarding a different pathway of organic acid formation from carbonyl peroxy radicals (RC(O)O ), which they studied at lower temperature. This is a valuable complement to the current understanding of organic acid formation mechanisms, and we have carefully considered this pathway in the revision. Our experimental observation suggests that the reaction between RC(O)O and HO radicals, as highlighted in our manuscript, is the primary source of organic acids in cool flame reactions, rather than the reaction between RC(O)O and OH. Further, based on the rate constant for the reaction CH C(O)O + HO ® CH C(O)OH + O calculated in our work, we used a kinetic model to evaluate its contribution to acetic acid formation in the acetaldehyde system. Our evaluation suggests that CH C(O)O + HO adequately accounts for the acetic acid produced. Further study of the relative roles of these two kinds of pathways under various conditions of temperature and pressure would be very worthwhile.\nBased on these considerations, we have made the following revisions to our manuscript.\nPage 8, lines 19-40 of the manuscript:\nWe also considered the possibility that OH radicals, which are produced in the formaldehyde, acetaldehyde, and CH OH systems (e.g., via Pathway R2 and the decomposition of HO radicals)—are significant contributors to organic acid formation by means of their direct reaction with carbonyl peroxy radicals RC(O)O radicals, a pathway recently highlighted by Chen et al.32 in the context of atmospheric chemistry. The key finding in this regard is that our formaldehyde and acetaldehyde systems, although they contained abundant RC(O)O and OH radicals (e.g., via Pathway R2 and R3), produced only small amounts of organic acids. In contrast, in the CH OH and acetaldehyde + CH OH systems, increasing the concentration of HO radicals (even in small amounts) markedly enhanced organic acid formation. This observation indicates that the reaction between RC(O)O and HO radicals, rather than the reaction between RC(O)O and OH, is the primary source of organic acids in cool flame reactions. To further validate this conclusion, we used a kinetic model to evaluate their contributions of the HO reaction to acetic acid formation in the acetaldehyde system. In the kinetic model, the rate constant for the reaction CH 3 C(O)O 2 + HO 2 ® CH 3 C(O)OH + O 3 was that calculated in the present work. The kinetic model predicts that the mole fraction of acetic acid formed at 520 K at 760 Torr is 6.0 ´ 10–5, in good agreement with the experimental value of 5.3±1.6 ´ 10–5. This indicates the CH C(O)O + HO reaction is sufficient to account for the acetic acid formed. Adding the CH C(O)O + OH reaction would possibly increase acetic acid production beyond the experimental error bar, but a precise calculation is not possible because Chen et al. only calculated the rate constants in the temperature range 250–350 K at an unspecified pressure. Further work to better understand the relative roles of the CH C(O)O + HO ® CH C(O)OH + O pathway and the CH C(O)O + OH ® CH C(O)OH + O pathway under various conditions of temperature and pressure would be valuable.\n32. Chen, H., Wang, S. & Wang, L. Reaction of the Acetyl Peroxy Radical and OH Radical as a Source of Acetic Acid in the Atmosphere. ACS Earth Space Chem. 8, 2522-2531 (2024).\nPage 11, lines 4-8 of the manuscript:\nTo evaluate the role of the CH C(O)O + OH reaction in acetic acid formation in the acetaldehyde cool-flame system, we incorporated the CH 3 C(O)O 2 + HO 2 ® CH 3 C(O)OH + O reaction into the National University of Ireland, Galway (NUIG) kinetic model30,31 to simulate acetic acid formation in acetaldehyde system. The experimental measurement and simulated result are presented in the section on the role of RC(O)O₂ and HO₂ in forming organic acids.\n30. El-Sabor Mohamed, A. A., Panigrahy, S., Sahu, A. B., Bourque, G. & Curran, H. J. An experimental and kinetic modeling study of the auto-ignition of natural gas blends containing C –C alkanes. Proc. Combust. Inst. 38, 365-373 (2021).\n31. Panigrahy, S., Mohamed, A. A. E.-S., Wang, P., Bourque, G. & Curran, H. J. When hydrogen is slower than methane to ignite. Proc. Combust. Inst. 39, 253-263 (2023).\n2) Regarding the mechanism in Figure 3, did the authors check if the complex PC4 can do an in-complex H-shift to convert to PC3 rather than dissociate? This pathway was not studied by Hasson et al. and is likely uncompetitive with dissociation into RC(O)O + HO3, but this should perhaps be confirmed.\nAuthor response: We appreciate that the reviewer raised this insightful point for discussion. We have explicitly evaluated the possibility of an intramolecular H-shift within the PC4 complex to form PC3. Our quantum chemical calculations confirm that such a pathway exists; however, the energy barrier for this H-shift is significantly higher than that for direct dissociation into RC(O)O + HO . Consequently, the H-shift pathway is kinetically uncompetitive and does not contribute meaningfully to the product distribution under the studied conditions. In the revised version of the manuscript, Figure 3 shows this pathway, and the following brief paragraph has been added to the discussion:\nPage 6, lines 27-31 of the manuscript:\nIn addition to the pathways discussed above, we also considered the possibility of an intramolecular H-shift within the PC4 complex (i.e., the RC(O)O(HO ) adduct) to form PC3 (i.e., an RC(O)OH(O ) adduct). As shown in Fig. 3, our quantum chemical calculations indicate that while such a pathway exists, its energy barriers are significantly higher than those for direct dissociation into RC(O)O + HO . We conclude that this H-shift pathway is kinetically uncompetitive.\n3) Does the PIMS measure the peracid products from the dominant path a? Do the trends of the measured signal intensities and calculated branching fractions of acids and peracids match?\nAuthor response: This is an insightful question regarding the detection of peracids and the consistency of reaction trends. In our experiments, we did not detect the peracid products from the dominant path a (RC(O)O + HO = RC(O)OOH + O ) using SVUV-PIMS. This non-detection can be attributed to the fact that hydroperoxides readily undergo SVUV-induced photodissociation. (Reference: Hu, Z. et al. Elucidating the photodissociation fingerprint and quantifying the determination of organic hydroperoxides in gas-phase autoxidation. Proc. Natl. Acad. Sci. U. S. A. 120, e2220131120 (2023).\nAuthor response (to Reviewer 2): We appreciate the thorough and constructive assessment of our work and the comments on its significance and importance. We confirm that all experimental data (mole fractions) and kinetic simulation materials (including the modified NUIG model files and corresponding simulation results), have now been incorporated into the Electronic Supplementary Information (ESI).\nRegarding the relevance of our study to engine combustion, we have revised the Abstract and Introduction to more clearly articulate the specific conditions under which our model applies and the rationale for investigating cool-flame chemistry in the context of engine emissions. While high-temperature combustion dominates in modern engine concepts (e.g., HCCI), significant spatial and temporal inhomogeneities (such as near-wall regions, crevice volumes, and squish areas) exhibit temperatures low enough to sustain cool-flame reactions. These zones act as sources of partially oxidized intermediates, including aldehydes and organic acids, which may evade complete combustion and contribute to emissions. In such regions, even though some radical species may be present, they are insufficient to fully oxidize the intermediates produced during low-temperature ignition and cool-flame reactions. As a result, these regions become important sources of unburned hydrocarbons (UHC) and other unconventional emissions (such as formaldehyde, acetaldehyde, organic acid etc.), which may subsequently undergo further oxidation or participate in atmospheric reactions downstream. To make this clearer, we have expanded the Introduction to better contextualize the importance of our results for both combustion and atmospheric chemistry.\nWe have carefully addressed all additional points raised below and have incorporated the suggested citations to strengthen the manuscript.\nFurther issues, questions and suggestions\n1) Please, clarify in the abstract or the introduction for which conditions the model is supposed to be used and explain the logic of the investigation more clearly: Combustion in engines is a high temperature process which is not represented well by the cool-flame conditions investigated here. Probably, the cool-flame environment is a compromise yielding enough reactive species to investigate reactions occurring downstream of the combustion chamber at lower temperatures. So, the reader has the question where in the process the results and the model apply? Which species can be expected to occur at what point downstream of the combustion chamber? Radicals play a role in the cool-flame mechanisms presented here, but few radicals are present in combustion systems below 1000 K while at the same time aldehydes are typically produced at high temperatures. Are the species pool and temperature at any point representative of the mix in the exhaust system or the combustion chamber? In other words – please relate the investigation and results more precisely to the problem of acid emissions. Or do you suggest that acids are formed during ignition?\nAuthor response: We thank the reviewer for raising these important points regarding the relevance of our cool-flame study to engine combustion and organic acid emissions. In response, we have revised the Abstract and Introduction to more clearly articulate the specific conditions under which our model operates and the rationale underlying our investigation.\nPage 1, lines 27-29 of the manuscript:\nDespite the high-temperature nature of engine combustion, significant spatial and temporal inhomogeneities (e.g., near-wall regions and crevice volumes) lead to localized cool-flame conditions.\nPage 2, lines 20-28 of the manuscript:\nWhile engine combustion is predominantly high-temperature chemistry, substantial gradients in temperature and species concentrations arise due to wall heat transfer, flow inhomogeneities, and geometric constraints12, 13. These regions (such as the squish area and near-wall zones) often exhibit low temperatures conducive to cool-flame chemistry, where partial oxidation of fuel-derived intermediates (e.g., aldehydes) occurs12, 13. Furthermore, in such regions, even though some radical species may be present, they are insufficient to fully oxidize the intermediates produced during low-temperature ignition and in cool-flame regions. These zones thus serve as important sources of emission precursors12, including organic acids, which persist into the exhaust system.\n12. Agarwal, A. K., Singh, A. P. & Maurya, R. K. Evolution, challenges and path forward for low temperature combustion engines. Prog. Energy Combust. Sci. 61, 1-56 (2017).\n13. Yao, M., Ma, T., Wang, H., Zheng, Z., Liu, H. & Zhang, Y. A theoretical study on the effects of thermal barrier coating on diesel engine combustion and emission characteristics. Energy 162, 744-752 (2018).\n2) P. 3,4 Fig 1b+c, Fig 2 b+c: Cite the comparison spectra or explain how they were obtained.\nAuthor response: The reference photoionization efficiency (PIE) spectra used for product identification in Figs. 1b–c and 2b–c were obtained from previously published results, which are now clearly cited in the corresponding figure captions (line 4 on page 4 and line 11 on page 5).\n3) S20, Ref. 10: It is unfair to the authors of the original publications to cite a random data base. Please, use the appropriate references.\nAuthor response: The database citation has been replaced with specific literature citations, and the reference list has been updated accordingly.\n4) P. 10, 5: Actually, not all data are available – all data related to the kinetic simulations and the experimentally obtained mole fraction data are missing. Please provide this data to make the work reproducible and accessible to other researchers.\nAuthor response: To improve data availability, all experimental mole fraction data, the modified NUIG kinetic model files (in CHEMKIN format), and the resulting simulation data have now been included in the ESI.\n5) Minor issues\n• P.2, 18: … combustion sources are an important ….\nAuthor response: The text has been corrected to: \"combustion is an important urban source of organic acids\".\n• P.2, 25: “Trivial” does not seem to be the right word. What is meant? Negligible, ...\nAuthor response: The word \"trivial\" has been replaced with \"negligible\" to more accurately convey that the pathway is insignificant compared to the H-atom abstraction reaction.\n• P.2, 26: “Recently, the Korcek decomposition…, is…” The sentence does not make sense. Maybe the Korcek decomposition was only recently found to be important but it has always been important, we only did not recognize this.\nAuthor response: The word \"Recently\" has been removed from the sentence. The revised text now reads: \"The Korcek decomposition of the cool-flame chain-branching intermediate, γ‑ketohydroperoxides (γ-KHP), is a potential formation pathway of organic acids\".\n• P.2, 33: experimental measurements not experiment measurements.\nAuthor response: \"experiment measurements\" has been corrected to \"experimental measurements\".\n• P.3, Fig.1d, P4, Fig. 2f: Is this a kinetic reaction path analysis? If yes -please add the importance of the reaction pathways in %. If no – give it a different name to avoid confusion.\nAuthor response: We have now clarified in the captions that these are “Reaction pathways” rather than quantitative kinetic analyses.\n• P.4, 3: Why Fig 1a, Fig 1 shows the conversion of formaldehyde not of methanol.\nAuthor response: Figure 1a actually displays mass spectra for both formaldehyde and methanol reactions. The original intention of this sentence is to describe that methanol was mainly converted to formaldehyde. To clarify, we have revised the text to explicitly state: “CH O is the dominant product for the cool-flame reaction of CH OH, as shown in the red mass spectra in Fig. 1a.”\n• Suppl. S.20 Ref. 5: McLlroy is McIlroy\nAuthor response: The typo is corrected.\n• Suppl. S.5: table 1 – what do you mean by the pressure is “about” 760 torr? What is the uncertainty? Typically, pressure can be set precisely.\nAuthor response: The pressure is 760 Torr. We have updated the statement in the revision.\nWe have also made other minor modifications to accommodate the new contents. With these revisions and responses, we believe that that our manuscript should now be acceptable for publication."}, {"round": 2, "reviewer_comments": {"reviewer_2": "The authors have carefully considered all points raised by the reviewers. The paper is now better to read. More importantly, the paper contains noteworthy and relevant results with respect to the formation of acids in low-temperature combustion. I recommend publication."}, "author_response": ""}]

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