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 wildfires4,5,6. 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 atmosphere10,11,12. 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 combustion12,13,14,15,16. 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/kgfuel16. 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 acids23,24,25; the Korcek pathways of γ-KHP form cyclic peroxides, which decompose to carbonyl products and organic acids23. The Korcek pathways 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 pathways 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.

Fig. 1: Cool-flame chemistry of CH2O and CH3OH.
Fig. 1: Cool-flame chemistry of CH2O and CH3OH.
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a Mass spectrum of the cool-flame reactions of CH2O and CH3OH recorded by synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS) at 520 K with a photon energy of 11.5 eV. Black line: the experimental spectra of the cool-flame reactions of CH2O; Red line: the experimental spectra of the cool-flame reactions of CH3OH. b, c H2O2 and HC(O)OH product identification by comparing the photoionization efficiency (PIE) spectra of hydrogen peroxide29 and formic acid30. Red symbols: the experimental PIE spectra measured in this work; Black lines: the reference PIE spectra from the literature (hydrogen peroxide29 and formic acid30). d Reaction pathway of the cool-flame reaction of formaldehyde and methanol. The characteristic products (HC(O)OH, H2O2 and CH2O) formed through the pathway are highlighted in bold.

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, CH3O2H 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.

Fig. 2: Cool-flame chemistry of CH3CHO and CH3OH + CH3CHO.
Fig. 2: Cool-flame chemistry of CH3CHO and CH3OH + CH3CHO.
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a Mass spectra of the cool-flame reactions of CH3CHO and the CH3OH + CH3CHO mixture recorded by synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS) at 520 K with a photon energy of 11.5 eV. Black line: the experimental spectra of the cool-flame reactions of CH3CHO; Red line: the experimental spectra of the cool-flame reactions of CH3OH + CH3CHO. b, c CH3O2H and CH3C(O)OH product identifications by comparing the photoionization efficiency (PIE) spectra of methyl hydroperoxide31 and acetic acid28. Red symbols: the experimental PIE spectra measured in this work; Black lines: the reference PIE spectra from the literature (methyl hydroperoxide31 and acetic acid28). d The mole fraction of acetic acid formed in the cool-flame reaction of CH3CHO in the temperature range of 400–600 K with or without CH3OH addition. Black: experimental results for CH3CHO system; Red: experimental results for CH3OH + CH3CHO system. The data points are also plotted with symbols. Source data are provided as a Source Data file. e The mole fraction of acetic acid formed by adding various amounts of CH3OH to the reaction system of CH3CHO at 520 K. The data points are also plotted with symbols. Source data are provided as a Source Data file. f Reaction pathway of the cool-flame reaction of acetaldehyde. The characteristic products (CH2O, CH3OH, CH3O2H and CH3C(O)OH) formed through the pathway are highlighted in bold.

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:

$${{{{\rm{O}}}}}_{3}\to {{{{\rm{O}}}}}_{2}+{{{\rm{O}}}}$$
(R1)
$${{{\rm{RCHO}}}}+{{{\rm{O}}}}\to {{{\rm{RCO}}}}+{{{\rm{OH}}}}$$
(R2)
$${{{\rm{RCO}}}}+{{{{\rm{O}}}}}_{2}\to {{{\rm{RC}}}}\left({{{\rm{O}}}}\right){{{{\rm{O}}}}}_{2}$$
(R3)
$${{{{\rm{CH}}}}}_{3}{{{\rm{OH}}}}+{{{\rm{O}}}}\to {{{{\rm{CH}}}}}_{2}{{{\rm{OH}}}}+{{{\rm{OH}}}}$$
(R4)
$${{{{\rm{CH}}}}}_{2}{{{\rm{OH}}}}+{{{{\rm{O}}}}}_{2}\to {{{{\rm{CH}}}}}_{2}{{{\rm{O}}}}+{{{\rm{H}}}}{{{{\rm{O}}}}}_{2}$$
(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, CH3O2H, 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 O3 (path b) or to doublet CH3C(O)O and doublet HO3, 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 + O3 (path b) or CH3C(O)O + OH + O2 (path c).

Fig. 3: Energetics, rate constants and branching fractions of carbonyl peroxy radicals + HO2 reaction.
Fig. 3: Energetics, rate constants and branching fractions of carbonyl peroxy radicals + HO2 reaction.
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a, b Enthalpies of reactants, intermediates, transition states, and products of CH3C(O)O2 + HO2 and HC(O)O2 + HO2 reactions calculated by CCSD(T)/CBS//B3LYP-D3(BJ)/def2-TZVP. Enthalpies are in kcal/mol at 0 K, at which temperature the enthalpy equals the sum of the potential energy and the zero point energy. Blue (Path b and Path c): singlet pathways; Red (Path a): triplet pathways. c Rate constants for the CH3C(O)O2 + HO2 reaction: dashed lines represent unadjusted predictions (without energy corrections), solid lines represent adjusted predictions (with energy corrections applied), and symbols denote experimental data for singlet (blue) and triplet (red) pathways of the CH3C(O)O2 + HO2 reaction, which from Hui et al.28. The adjustment refers to 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. Adjusted calculations of the branching fractions of the reaction pathways of CH3C(O)O2 + HO2 (d) and HC(O)O2 + HO2 (e). Blue lines: the result of singlet pathways; Red lines: the result of triplet pathways.

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 + O3 (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)O(HO3) 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)O + HO3. 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 single 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.

Fig. 4: Formic and acetic acid formation during cool-flame oxidation of hydrocarbon fuels.
Fig. 4: Formic and acetic acid formation during cool-flame oxidation of hydrocarbon fuels.
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Measured and calculated mole fractions of (a) formic acid and (b) acetic acid formed during the cool-flame reactions of nine typical hydrocarbon fuels: propane, n-butane, n-pentane, iso-pentane, neo-pentane, n-hexane, n-heptane, 1-hexene, and 1-heptene. Black (Experiment): experimentally measured mole fractions; Blue (NUIG model): the calculation results from the National University of Ireland Galway kinetics model31,32; Red (This work): the calculation results in this work after adding the HC(O)O2 + HO2 and CH3C(O)O2 + HO2 pathways to the National University of Ireland Galway kinetics model31,32. The data points are also plotted with symbols. The error bars of the experimental measured mole fractions ( ± 30%) are also given. Source data are provided as a Source Data file.

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 HO3 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 was 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 Gaussian 16 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 〈ΔEdown〉 = 200(T/300)0.85 cm−1 for the average 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) kinetic 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.