We employ quantum chemical calculations to find the most efficient route to an OH oxidized hexanal product containing seven oxygen atoms. Some of the intermediates and transition states along the reaction pathway possess RR and RS configurational isomers, each with many potential conformers. Since the inter-conversion between different isomers typically involves the breaking and reformation of covalent bonds and is consequently associated with high barriers, we consider the RR and RS isomers separately.

We employ the master equation solver for multi-energy well reactions (MESMER) program to carry out RRKM simulations to estimate the branching ratios of selected products following unimolecular isomerization and O2 addition reactions. The unimolecular isomerization reactions are treated using the SimpleRRKM method with Eckart tunneling. The O2 addition reactions to carbon-centered radicals are treated using the “simple bimolecular sink” method in MESMER. In this case, a bimolecular loss rate coefficient of 2×10-12 cm3molec-1s-1 and an O2 “excess reactant” concentration of 5×1018 molec.cm-3 are used, which is the approximate O2 concentration under standard atmospheric conditions. The intermediates are assigned as “modeled” in the simulations and given Lennard–Jones parameters sigma=6.25 Å and epsilon=343 K . MESMER utilizes the exponential down (ΔEdown) model for simulating the collisional energy transfer. For N2 bath gas, the MESMER-recommended values for ΔEdown are between 175 and 275 cm-1. We used a ΔEdown value of 225 cm-1 in our simulations. In addition, a grain size of 100 and a value of 60 kBT for the energy spanned by the grains were used. The MESMER input file corresponding to one of the studied reactions is provided in Sect. S9 in the Supplement as an example.

The unimolecular H-shift rate coefficients (k) reported in this work are calculated using the multi-conformer transition state theory (MC-TST) including quantum mechanical tunneling , as shown in Eq. (1). 1k=κkBTh∑iall TS conf.exp⁡-ΔEikBTQTS,i∑jallRconf.exp⁡-ΔEjkBTQR,j×exp⁡-ETS-ERkBT The constants kB and h are Boltzmann's constant and Planck's constant, respectively. Absolute temperature, T, is set to 298.15 K. ΔEi is the zero-point-corrected energy of the ith TS conformer relative to the lowest-energy transition state conformer, and QTS,i is the partition function of the ith transition state conformer. Similarly, ΔEj and QR,j are the corresponding values for reactant conformer j. ETS-ER is the zero-point-corrected barrier height corresponding to the lowest-energy TS and reactant conformers. The partition functions are calculated at the ωB97X-D/aug-cc-pVTZ level of theory (MN15/def2-tzvp for the aldehydic H-abstraction case), while the energies include the final coupled-cluster correction. The tunneling coefficient κ is calculated using the one-dimensional Eckart approach as reported in . This method requires the energies of the reactant and product wells that are connected to the lowest-energy TS geometry, which are found by running forward and reverse intrinsic reaction coordinate (IRC) calculations on that TS geometry and optimizing the end geometries at the B3LYP/6-31+G* level of theory. The reactant and product wells are subsequently re-optimized at the ωB97X-D/aug-cc-pVTZ level of theory, followed by single-point RHF-RCCSD(T)-F12a/VDZ-F12 energy corrections.

The rate coefficients of the H-abstraction reactions of hexanal by OH are calculated in three different ways (see Sect. S2 in the Supplement for details). The rate coefficients presented here involve only the lowest-energy conformers of TS and reactants using the bimolecular TST expression shown in Eq. (2): 2k=σκkBThc∘QTSQOHQhexexp⁡-ETS-ERkBT, where σ is the symmetry factor that is related to the reaction path degeneracy. Here, the values of σ are 1, 2, and 3 for the aldehydic H abstraction, abstraction from a secondary carbon (C2–C5), and abstraction from the primary carbon (C6), respectively . c∘=p∘/kBT is the total concentration of molecules in standard condition, 2.46×1019 molec.cm-3. Qhex and QOH are the partition functions of the lowest-energy hexanal and OH conformers, respectively.

The equation that accounts for multiple conformers of TS and hexanal reduces the rate coefficient of the aldehydic H abstraction. We find only three TS conformers for this reaction, while we have 18 conformers of hexanal that are within 2 kcalmol-1 in relative energy. Because the former goes into the numerator and the latter in the denominator of the bimolecular MC-TST equation, this reduces the rate. studied fluorinated aldehydes with three carbon atoms employing an MC-TST equation that likely did not encounter this issue with the TS conformers. studied a similar aldehydic system to ours where they used the lowest-energy conformer TST (LC-TST) equation. We therefore adopt the same approach in this work to calculate the rate coefficients and consequently the branching ratios of OH H abstractions of hexanal.

The experimental hexanal OH oxidation reaction is conducted in a laboratory applying a flow rector setup (see Fig. 2). A nitrate-based time-of-flight chemical ionization mass spectrometer (nitrate-CIMS) is used to detect the products of hexanal OH oxidation. Chemical ionization is achieved by supplying synthetic air (sheath flow) containing nitric acid (HNO3) under exposure to X-rays. This produces nitrate (NO3-) ions that are mixed with the sample flow and that ionize HOMs as NO3- adducts. A sheath flow of 20 Lmin-1 and a sample flow of around 10 Lmin-1 (synthetic air as diluent) are used. The precursors are mixed in a quartz flow tube reactor where the oxidant OH is produced in situ by the ozonolysis reaction of tetramethylethylene (TME) (see Fig. 2). An ozone concentration of 225 ppb, which is generated by flowing synthetic air through an ozone generator fitted with a 184.9 nm (UVP, Analytik Jena) Hg Pen-Ray lamp, is allowed to react with 40 ppb of TME supplied from a gas cylinder to the reactor. A hexanal precursor concentration of 1 ppm is added to the reactor from another gas cylinder. The reaction time is controlled by adjusting the distance between the mass spectrometer orifice and the place where hexanal and OH meet inside the reactor. This is done by providing the hexanal flow through a moveable injector tube within the reactor. Accordingly, separate sets of experiments are conducted with variable reaction times (1.4, 3.1, and 12 s) to track the oxidation chain propagation. In addition, to confirm the structures of the identified products in favor of the proposed mechanisms, we conduct a hydrogen/deuterium (H/D) exchange experiment (12 s) by adding D2O from a bubbler with N2 flow.

We inspect autoxidation propagation with bimolecular interventions under pristine boreal forest to polluted urban conditions using a kinetic simulator Kinetiscope version 1.1.956.x64 . A single-reactor model with constant volume, pressure, and temperature is employed in the simulation. The temperature is set to 298.15 K. In the simulation setting, a total number of particles 1×108 and a random number seed 12 947 are used, while the maximum simulation time is set to 20 s.

Relative zero-point-corrected electronic energies (ZPE) and Gibbs free energies (for T=298.15 K and P=1 atm) of the TSs and overall reactions for the H-atom abstraction reactions of hexanal by OH are reported in Table 1. Ea (ΔZPE±) is the barrier of the reaction, which is calculated as ΔZPE±=ZPETS-ZPEReactants; ΔZPE is the overall reaction energy, ΔZPE=ZPEProducts-ZPEReactants. Analogously, ΔG± is the Gibbs free energy of activation, and ΔG is the reaction Gibbs free energy. The H-abstraction rate coefficients shown in Table 1 were calculated using Eq. (2). The corresponding branching ratios (BRs) are determined as ratios of the individual rate coefficients (ki) against the overall rate coefficient (koverall).

The results of Table 1 show that the zero-point-corrected electronic TS energy of the aldehydic H abstraction in hexanal OH oxidation is slightly below the separated reactants; the γ H abstraction on C4 has almost no barrier (i.e., 0.1 kcalmol-1), while the other H-abstraction channels have discernable barriers. The β and δ H abstractions on C3 and C5, respectively, have near-identical barriers, while the α H-abstraction barrier on C2 is 0.7 kcalmol-1 less than the primary H abstraction on C6. The H-abstraction barriers tend to increase as we move from C4 towards the carbon atoms along either the left or the right direction of the carbon chain (excluding the aldehydic carbon). This trend is consistent with the results of , who showed that from ethanal to pentanal OH oxidation the β H-abstraction barriers are less than that of α H abstractions, while the aldehydic H abstractions have the lowest barriers.

Based on the decreasing trend of Ea with the increasing carbon chain length as shown by for aliphatic aldehydes up to five carbon atoms, it is expected that there will be somewhat lower barriers for similar H abstractions in hexanal. They calculated the barriers at the CCSD(T)/6-311++G**//BHandHLYP/6-311++G** level. However, using our method the barriers we calculated are roughly 0.5–2.5 kcalmol-1 higher in comparison to the values obtained by the aforementioned study for the different H abstractions.

It is apparent that our calculated overall rate coefficient 3.3×10-12 cm3s-1 is about an order of magnitude lower than the experimental rate coefficient 2.9×10-11 cm3s-1 measured for the hexanal + OH reaction and SAR prediction rate coefficient (see Table 1; detailed SAR calculations in Sect. S1 in the Supplement) . Reducing the barrier height by 1 kcalmol-1 (within the error margin of the method used), we obtain an overall rate coefficient of 1.8×10-11 cm3s-1 that is compatible with the reported experimental results.

The potential energy surface (PES) of hexanal for the different H-abstraction channels is shown in Fig. 3. The C1 channel associated with aldehydic H abstraction has a submerged barrier. Among other channels, the γ H abstraction on C4 shows the lowest barrier. The radical (C6H11O) formed via the α H abstraction is more stable than those obtained from β, γ, δ, and primary H abstractions because the unpaired electron in the former can delocalize over the carbonyl double bond. Although the stability of C6H11O radicals with respect to β, γ, and δ H abstractions are similar, the stability of the radical after primary H abstraction on C6 is the lowest.

C1 is the dominant channel, with a yield of 86 % (see Table 1), followed by the C4 channel, with a yield of around 8 %. The energies of the intermediate peroxy radicals A and D (see Fig. 3; C1 and C4 channels), which both have a molecular formula of C6H11O3, are below the separated reactants hexanal + OH by 63.3 and 54.5 kcalmol-1, respectively.

Mechanistic details of the HOM formation through both C1 and C4 channels are shown in Fig. 4. The PES of two lowest-energy barrier H-shift pathways of the peroxy radicals A and D are shown in Fig. 5, and the calculated transition state energies and rate coefficients are shown in Table 2. Although we report both MC-TST and MESMER rate coefficients, we use the MC-TST rate coefficients in the following discussions to compare with relevant literature rate coefficients. We found that the MC-TST rate coefficients are roughly an order of magnitude lower than those derived from MESMER. The MC-TST treatment includes the influence of several lowest-energy conformers, while MESMER only considers the lowest-energy TS and reactant conformers, and therefore the estimates are likely the upper limits. Both sets of rate coefficients are provided in Table 2 to establish a range of possible values. Additionally, hindered rotor calculations are performed to assess the error introduced to the calculated rate coefficients by treating anharmonic low-frequency torsions as harmonic oscillators. The hindered rotor treatment is not applied to those reactions where hindered rotor calculations failed for one or more conformers. Therefore, the resultant rate coefficients are not used here for the calculation of branching ratios as they are not suitable for direct comparison. The hindered rotor treatment changes the rate coefficients by about a factor of 2 in most of the cases (see Sect. S3 in the Supplement).

The initial abstraction of the H atom from C1 by OH creates a radical center on the terminal carbon giving intermediate A′ (Fig. 4a). The intermediate A′ has the possibility of either fragmenting towards pentyl (C5H11) radical and carbon monoxide (CO) or adding an O2 molecule to form an APR intermediate A (C6H11O3). The calculated rate coefficient of the fragmentation pathway is 2.27×103 s-1, which is significantly slower than O2 addition (∼107 s-1 under atmospheric conditions). The formation of intermediate A is therefore the most competitive route available to A′. Subsequent intramolecular H-shift reactions of A are key for rapid autoxidation and the formation of highly functionalized products.

In the current analysis, we exclude RO2+RO2/HO2 and RO2+NOx reactions and focus on unimolecular autoxidation reactions that lead to rapid functionalization and formation of HOMs. The intermediate APR A can follow either the 1,6-H-shift reaction (C1 green channel) or the 1,5-H-shift reaction (C1 purple channel) and subsequently form the peroxy radical intermediates A61 and A51, respectively, both with the composition C6H11O5 and having a terminal peroxy acid group. The calculated barrier heights of A towards 1,6-H-shift (green route) and 1,5-H-shift (purple route) reactions are 19.1 and 20.5 kcalmol-1, respectively, with corresponding rates of 1.69×10-1 and 3.49×10-2 s-1, respectively. We did not find similar acyl peroxy H-shift rate coefficients reported in the literature for comparison.

The initial H abstraction by OH from the C4 carbon and the subsequent rapid O2 addition gives the peroxy radical D (Fig. 4b). This peroxy radical can readily abstract the aldehydic hydrogen via an intramolecular 1,6-H-shift reaction and subsequently form the APR A62 (C4 green channel). The peroxy radical D can also abstract an H atom from carbon C2, which is the next most competitive channel (purple arrows, C4 channel) after the aldehydic H-shift. The calculated barrier heights of the 1,6-H-shift (green route) and 1,5-H-shift (purple route) reactions are 18.7 and 21.1 kcalmol-1, respectively, with corresponding rate coefficients of 8.63×10-1 and 3.91×10-2 s-1, respectively. The literature rate coefficient of a similar aldehydic 1,6-H-shift from CHO to >CHOO reported by is higher (k=7.9 s-1) by about a factor of 9 than the rate reported here (1,6-H-shift in C4 channel mentioned above), while the rate coefficient of peroxy H-shift from -CH2- with 1,5 span is about an order of magnitude lower (k=1.23×10-3 s-1). The higher rate coefficient for the peroxy H-shift reaction we report could be due to the presence of the α-CHO group next to the -CH2- group. The branching of A and D (both C6H11O3) towards green and purple sub-channels are governed by these initial H-shift barriers. The MESMER simulation derived branching ratios of A towards green and purple channels of 91 % and 9 %, respectively, while the same ratios for D are 95 % and 5 %, respectively.

In the C1 green channel, the alkyl peroxy radical intermediate A61 (C6H11O5) with a terminal peroxy acid group needs to overcome a barrier of 21.5 kcalmol-1 to undergo a 1,5-H-shift reaction to form a carbon-centered radical on C2. The rate coefficient for this isomerization is 3.90×10-3 s-1. Subsequently, the alkyl radical A61a′ (see Fig. 5, not shown in Fig. 4) can add an O2 molecule to form the C6H11O7 peroxy radical (A61a). As the peroxy acid group is significantly more stable than the acyl peroxy group, the barrier for the H-scrambling reaction (between γ-OO and peroxy acid groups) of A61 is quite high (Ea=25.28 kcalmol-1, k=3.72×10-6 s-1), making the formation of A62 unlikely (orange double arrow in Fig. 4a).

Along the C1 purple channel, the intermediate A51 needs to overcome the barriers of 22.3 and 24.4 kcalmol-1 to undergo 1,5- and 1,6-H-shift reactions to yield A51a5′ and A51a6′ radicals, respectively (see Fig. 5), and subsequently, by O2 addition, they form the non-terminal peroxy radical A51a5 and the terminal peroxy radical A51a6, respectively (purple and blue arrows, Fig. 4a). The corresponding rate coefficients are 7.81×10-4 and 2.77×10-5 s-1, respectively; too slow to significantly compete with bimolecular RO2+RO2/HO2/NO reactions. Comparing with the literature data, the analogous rate coefficient of peroxy 1,6-H-shift reaction from a terminal CH3 group found by is even lower (k=4.06×10-6 s-1). The difference is likely due to the dissimilarity in the molecular structures in terms of the functional groups on the carbon chain in the studied cases.

In the C4 green channel, the A62 peroxy radical can immediately undergo an H-scrambling reaction between γ-OOH and acyl peroxy groups, and form the peroxy radical A61 with a terminal peroxy acid group (the same intermediate as in C1 channel). The fast H-scrambling reaction with a barrier of 15.8 kcalmol-1 and rate coefficient 6.92×102 s-1 switches the radical center in C6H11O5 intermediate turning A62 to more stable A61. This fast reaction is the reverse of the previous A61 to A62 conversion reaction in C1 channel. This rate coefficient is similar to that reported by for H-scrambling reactions with 1,8 spans (k=4.17×102 to 1.36×103 s-1). The α-OOH H atom of A62 can also migrate to the terminal acyl peroxy radical by 1,6-H-shift reaction leading it towards the radical termination channel (red arrows), giving the closed-shell ketohydroperoxide product C6H10O4 (see Fig. 4b). The rate coefficient of such 1,6-H-migration to a tertiary peroxy radical was estimated by to be 2.45×10-2 s-1. In our acyl peroxy radical case, we found a very fast rate coefficient (2.08 s-1) for A62 to A62a6′ conversion. Based on our calculated rate coefficients, the branching ratios of A62 towards the green and red channel are 99.70 % and 0.30 %, respectively. This channel thus regenerates the same A61 intermediate that follows the identical pathway, as we observed in C1 green channel, leading to the C6H11O7 peroxy radical.

Continuing to the C4 purple channel, we get to the intermediate D51 with an OOH functionality at C4 and with an intact aldehydic functionality. The D51 radical intermediate can then follow a rapid H-scrambling reaction to form the peroxy radical D52. The H-scrambling rate corresponding to the conversion of intermediate D51 to D52 is around 5 times lower than that of in the green channel. The H-scrambling barrier in the latter case is 1.27 kcalmol-1 higher, and the corresponding D52 intermediate is 1.17 kcalmol-1 less stable than D51. However, the faster aldehydic 1,6-H-shift reaction (k=1.38×10-1 s-1) in D52 makes it possible to quickly form C6H11O7 APR through the formation of D52n′ (shown in Fig. 5) acyl radical intermediate followed by O2 addition. The same D52n′ intermediate can also be formed directly from D51 by aldehydic 1,4-H-shift reaction (blue arrow, Fig. 4b), which seems to be very unlikely due to the higher barrier of 23.1 kcalmol-1 and corresponding low rate coefficient of 2.67×10-2 s-1. reported a similar rate coefficient (k=6.64×10-2 s-1) for such aldehydic H-shift reaction with 1,4 span. The APR D52n is likely to follow similar subsequent reactions to the other APR A62. However, the former has an additional OOH functionality on carbon C2, allowing for two competing H-scrambling reactions. Here the MESMER simulation derived a branching ratio of D51 (C6H11O5) towards purple and blue channel of 97 % and 3 %, respectively. We did not calculate the relative energies of the final C6H11O7 intermediates, which we expect to get further energetically lowered by 25–35 kcalmol-1 due to O2 addition at the last step of their formation. Note that the reported unimolecular rate coefficients have an error margin of about a factor of 5 for the method used.

The overall maximum yields of the different oxidation products up to C6H11O7 HOM from initial hexanal OH oxidation are calculated by multiplying the branching ratios of each intermediate along the reaction pathway. When considering the two competing isomerization channels of the APR A shown in Fig. 4a (and excluding possible bimolecular reactions), the overall maximum yield of C6H11O5 intermediate (A61) through the C1 green channel is 78 %, which subsequently leads to an O7 HOM via a 1,5-H-shift reaction. The overall yield of the same A61 intermediate formed by the C4 green channel is 7.7 %, which can follow similar chain propagation steps towards HOM. The O5-intermediate associated with the C1 purple channel has a yield of 7.7 %, but the subsequent H-shift rates are very slow, and it is unlikely to efficiently form an O7 HOM through this channel. On the other hand, the overall C6H11O7 yield by the C4 purple channel is 0.4 %, where the only limiting step is the initial branching of the green and purple pathways.

The evolution of mass spectra at variable reaction time experiments is in agreement with the proposed OH initiated hexanal autoxidation mechanism. In our experiments, we use high precursor concentrations, and the experimental condition does not exclude the bimolecular RO2+RO2/HO2 reactions. The formation of O7 HOM (C6H11O7) is observed at a 3.1 s reaction time, strongly supporting the proposed computational mechanism (see Fig. 6b and c ; blue and purple). In addition, kinetic modeling simulations using atmospherically relevant concentrations and including RO2+RO2 and RO2+NO loss processes show the formation of O5 and O7 products in the expected timescales (details in Sect. 3.4). The C6H11O6 peak in Fig. 6a appears as early as 1.4 s reaction time, and it almost certainly involves RO2 bimolecular reactions, as only odd numbers of O atoms would be expected for purely RO2-mediated aldehyde autoxidation. A possible formation mechanism of C6H11O6 peroxy radical is the conversion of C6H11O5 (A61 in Fig. 4) to an alkoxy radical C6H11O4 via a bimolecular step, followed by a 1,4-H-shift reaction and subsequent O2 addition (see Fig. S2 in the Supplement). The absence of the C6H11O5 peroxy intermediate can be due to the poor detection sensitivity of NO3- for species with less than two hydrogen bonding functional groups . In Fig. 6b, we observe the appearance of O7 HOM (C6H11O7), HOM accretion products (C12H22O9-10), O4 and O5 closed-shell products, and a cross-reaction product C9H16O7 (i.e., a peroxide accretion product formed from hexanal-derived C6H11O6 and TME-produced C3H5O3 peroxy radical; see Fig. S4 in the Supplement) at 3.1 s reaction time. For the closed-shell C6H10O5 product, it could be formed through the classical Russell mechanism producing an alcohol and ketone (see Fig. S3a in the Supplement), or it could alternatively also form through the C6H11O7 (A61a in Fig. 4) involving a bimolecular step to produce an alkoxy radical C6H11O6 followed by a 1,4-H-shift reaction and a subsequent OH loss (see Fig. S3b). As the reaction proceeds up to 12 s (Fig. 6c; purple), we see that the previously observed product peaks grow larger and more peaks appear, including the HOM accretion product C12H22O11. The likely formation processes of C9H16O7 and HOM accretion products (C12H22O9-11) are discussed in Sect. S5 in the Supplement.

The structures that we propose for C6H11O7 (A61a), C6H11O6, and C6H10O5 contain two labile hydrogen atoms (either two -OOH groups or one -OH together with an -OOH group). Accordingly, the D2O experiment associated with the spectrum (red) in Fig. 6d shows mass shifts of two units for these products in support of the assigned structures. Regarding the accretion products, the mass shifts of 3–4 units in the D2O experiment are according to the presence of 3–4 labile hydrogen-containing groups in their structures, and they are in full agreement with the proposed peroxy radical structures forming them according to a general reaction RO2+RO2→ROOR+O2 .

The hexanal peroxy radical autoxidation process producing HOM described in the current work is in competition with bimolecular sink reactions under most atmospheric conditions. In our kinetic modeling simulations, we include RO2+RO2 and RO2+NO reactions as bimolecular sinks to illustrate the relative role of autoxidation in hexanal OH oxidation leading to HOM. We use a range of precursor concentrations to simulate situations from pristine boreal forest conditions to moderately polluted urban conditions (details are provided in Sect. S7 in the Supplement). Considering a cleaner environment with 0.1 ppb of NO (2.46×109 molec.cm-3), a generic 1.0×108 molec.cm-3 of RO2, 1 ppb (2.46×1010 molec.cm-3) of hexanal, and 1.0×107 molec.cm-3 of OH, the simulation leads to an appreciable concentration (3.0×103 molec.cm-3) of O5 intermediate formed as early as after 0.3 s of reaction time while O7 HOM is at 3.8 s. The concentrations grow to a maximum of 1.9×106 and 3.2×104 molec.cm-3 for O5 intermediate and O7 HOM, respectively, after 10 s of reaction time. Under high hexanal concentrations (maximum of 8.8 ppb), the above product concentrations increase by roughly a factor of 3 to 4. At a very low NO condition (0.01 ppb), these product concentrations increase by a factor of up to 1.6. Interestingly, even at 1 ppb of NO with 1.0×108 molec.cm-3 of RO2, the O7 HOM concentration goes as high as 1.3×104 molec.cm-3 after 10 s of reaction time. However, a NO level of 4 ppb practically halts O7 HOM production through C4 channel even at higher hexanal conditions, while 40 ppb of NO significantly prohibits any O5 intermediate formation. Although we use higher precursor and oxidant concentrations in our laboratory experiments (1 ppm hexanal, 225 ppb ozone, 40 ppb TME) to allow for efficient HOM production and detection, the trend in the evolution of mass spectral peaks matches with that of the simulations. The H-shift rate coefficients in autoxidation are highly temperature dependent, and the MESMER simulations carried out over a range of temperatures show that the second H-shift rate coefficients that lead to O7 HOM are increased by a factor of ∼2 to 8 at 310 and 330 K, respectively, relative to the rate coefficients at 298.15 K (see Sect. S8 in the Supplement). It should also be noted that bimolecular reactions involving NO, RO2, and HO2 that produce RO radicals do not necessarily terminate autoxidation but can also propagate it .