Hydroxyl radical-induced formation of highly oxidized organic compounds

Explaining the formation of secondary organic aerosol is an intriguing question in atmospheric sciences because of its importance for Earth's radiation budget and the associated effects on health and ecosystems. A breakthrough was recently achieved in the understanding of secondary organic aerosol formation from ozone reactions of biogenic emissions by the rapid formation of highly oxidized multifunctional organic compounds via autoxidation. However, the important daytime hydroxyl radical reactions have been considered to be less important in this process. Here we report measurements on the reaction of hydroxyl radicals with α- and β-pinene applying improved mass spectrometric methods. Our laboratory results prove that the formation of highly oxidized products from hydroxyl radical reactions proceeds with considerably higher yields than previously reported. Field measurements support these findings. Our results allow for a better description of the diurnal behaviour of the highly oxidized product formation and subsequent secondary organic aerosol formation in the atmosphere.

. Accretion product formation. Product mass spectra in the range of 450 -600 Th for identical reaction condition as shown in Supplementary Fig. 14a, reacted α-pinene of ∼2 × 10 10 molecules cm -3 (black, lower spectrum) and ∼4 × 10 10 molecules cm -3 (red, upper spectrum   (Fig. 4a) can be due to a couple of reasons: First, Melpitz is a rural background station whereas Hyytiälä is located in a remote area and the global radiation, connected to the OH radical concentration, in July in Melpitz was much higher than during the Hyytiälä measurements in March. Secondly, it is expected that the monoterpene emission, and consequently the resulting monoterpene concentrations, in the beginning of spring in Hyytiälä were definitely smaller than those in Melpitz in the summertime. That means that both reactant concentrations needed to form the HOM-RO 2 radicals were most likely higher in Melpitz. A more quantitative explanation including an assessment of the loss processes is impossible due to the lack of measurement data.

Influence of unwanted processes in the ionization region
It was checked, whether unwanted processes in the chemical ionization (CI) region (other than ionization) were responsible for the measured signals or influenced them. First, time-dependent RO 2 radical measurements for constant reactant conditions showed a linear behaviour of RO 2 radical concentrations with time providing a clear indication for negligible RO 2 radical generation in the CI region ( Supplementary Fig. 1).
Secondly, measurements with varying O 2 concentration in the free-jet flow system (including the CI region) showed distinct O 2 -dependent RO 2 radical concentrations obviously caused by competitive processes (unimolecular steps vs. O 2 addition) in the course of RO 2 radical generation 1 (Supplementary Fig. 2). On the other hand, changing O 2 concentrations in the CI region only did not show any effect ( Supplementary Fig. 3). These tests confirm that the highly oxidized RO 2 radicals were exclusively formed in the flow system and not in the CI region. Moreover, the time-dependent experiment reveals that the formation of highly oxidized RO 2 radicals in this system proceeds at a time scale of the lowest reaction time of 3 s or less (Supplementary Fig. 1).

Theory and computational details
The rate coefficients (k) of the possible unimolecular H-shift and endo-cyclization reactions have been calculated with Transition State Theory (TST), either using only the lowest energy conformer (LC-TST) or using multiple conformers within a given energy cutoff (MC-TST). The MC-TST rate coefficient is given by 2 where is the Eckart tunnelling correction factor, is the Boltzmann constant, T is the temperature and h is Planck's constant. The summations are over all included conformers of the transition state and reactant, respectively. Q i is the partition function of either transition state (TS) or reactant (R) for each conformer, while is the energy difference between conformer i and the lowest energy conformer. E TS and E R is the lowest energy conformer of the transition state and reactant, respectively. All energies are zero-point (vibrational) energies. To calculate the rate coefficient for the backward reaction, the reactant in Eq.(S1) is substituted with the product (P). For the reactant or product we introduce an energy cut-off in the selection of conformers to include.
We performed systematic conformer searches in Spartan'14 with either the MMFF or SYBYL force fields [3][4][5] . The searches were run with the keywords (systematic, keepall, keepverbose and geometrycycles = 500). In the MMFF conformer searches of the reactant, product and TS with MMFF were performed with the keyword 'ffhint=Ox~~+0', where x is the number of the peroxy oxygen (or C if the radical center is on carbon), MMFF-charge. This keyword changes the charge of the atom to neutral. The conformer searches of the TS were done by freezing the bond lengths, which changes the most during the reaction. We froze the O-O, O-H and C-O bonds. The length of the frozen bonds were based on a prior optimization with B3LYP/6-31+G(d) of a single TS conformer 6-12 . In the SYBYL searches, the conformer search was followed by a B3LYP/6-31+G(d) single point energy calculation in Gaussian09 and all structures with energy less than 5 kcal/mol was kept for a subsequent B3LYP/6-31+G(d) optimization. The lowest energy structure was then optimized at wB97X-D/aug-cc-pVTZ and frequency calculation performed. Rate coefficients calculated with this approach is called LC-TST/wB97X-D. The Eckart tunneling factor was calculated using the energy of the R, TS and P, and the wB97X-D imaginary frequency.
In the MMFF-charge conformer searches, all conformers found were optimized at the B3LYP/6-31+G(d) level of theory in Gaussian09 and frequencies calculated. The TS conformers were optimized at the same level of theory, with the keywords 'opt=(ts,calcfc,noeigentest)'. MC-TST rate coefficients were then calculated including all these B3LYP/6-31+G(d) conformers, which is called MC-TST/B3LYP. The Eckart tunneling is calculated with the conformers connected from the intrinsic reaction coordinate (IRC) of the lowest energy TS conformer. The electronic structure level is increased to improve the MC-TST/B3LYP rate coefficient. However, to limit the computational time an energy cut-off, at 2 kcal/mol in the B3LYP/6-31+G(d) energies is implemented. The remaining conformers are then optimized at the wB97X-D/aug-cc-pVTZ level and frequencies calculated. The Eckart tunneling is calculated with the R and P conformers connected via the B3LYP/IRC of the lowest energy wB97X-D optimized TS conformer. Energy and frequencies of these conformers are calculated with the wB97X-D/aug-cc-pVTZ method. We call this approach MC-TST/wB97XD. 13 Clearly the MC-TST/wB97XD is the best approach as it included both high level conformational sampling and high level energetics and we used this for the first reaction step (the three oxygen compound 4). This was not feasible for the subsequent reactions but we tested high-level conformational sampling via MC-TST/B3LYP and the high level energetics via LC-TST/wB97X-D and although both might lead to high H-shift rate coefficients, they should provide order of magnitude rate coefficients.

Calculated rate coefficients
Compound 4, Supplementary Fig.6, exist in both a syn and anti conformer. We have not attempted to run calculations on all possible combination in all of the steps, but focus on showing that it is possible to react within the timeframe of the experiment from compound 4 to a seven oxygen containing RO 2 radical with a reasonable lifetime. The first possible steps in the reaction of 4 are shown in Supplementary Fig. 6, and the calculated rate coefficients for two H-shifts and the endo-cyclization are given Supplementary Table 1. We find that the forward reaction of the initial H-shift reactions happens with a rate coefficient of about 1 s -1 , and is about an order of magnitude faster than the cyclization reaction. The 1,6-H-shift (anti only) and endo cyclization (syn and anti) reactions were also considered previously at the B3LYP level. 14 The previously calculated B3LYP rate coefficients (faster than 11.5 s -1 for the 1,6-H-shift and 2.6/0.6 s -1 for the syn/anti endo-cyclization reactions) are in agreement with our B3LYP rate coefficients shown in brackets in Supplementary Table 1.
Following the H-shift reactions, rapid O 2 addition on the timescale of 10 7 s -1 will lead to the five oxygen containing RO 2 radicals 12-15, shown in Supplementary Fig. 6. Compound 15 would likely eliminate HO 2 and is not considered further. In Supplementary Figures 7 -9, we show possible reaction mechanisms RO 2 radicals 12-14. Some syn/anti conformers of compounds 12-14 will be able to undergo OO-HOO H-shift, which were recently shown to be very rapid, partly due to large tunneling factors. 15 Here, we tested one of the OO-HOO Hshifts and found with the LC-TST/wB97X-D method a forward rate coefficient of about 300 s -1 for the OO-HOO, 1,8-H-shift from 14 to 27. The OO-HOO H-shift rate coefficients are possibly a bit faster in 1,7-H-Shift and a bit slower in the 1,9-H.shift. 15 The generated five oxygen containing RO 2 radicals, 17, 23, and 27 have a range of possible H-shifts, one of which is the 1,6-H-shift, shown in Supplementary Figures 7 -9. The rate coefficients of H-shifts in RO 2 radicals are often fastest for 1,5 and 1,6 H-shifts and often enhanced further with OH or OOH group attached to the C from which the H is abstracted. 16 The H-shift examples shown in Supplementary Figures 7 -9 all lead to termination via loss of OH (if abstraction from C with OOH attached, compounds 30/31) or loss of HO 2 after O 2 addition (if abstraction from C with OH attached, compound 21/22 or 25/26). We have not calculated the rate coefficients of these H-shifts possibilities, but expect them to be of the order of 1 s -1 . 15,16 In addition, the RO 2 radicals 17, 23, and 27 have the possibility of endo-cyclization similar to compound 4 as illustrated in Supplementary Figures 7 -9. We have used the MC-TST/B3LYP method to calculate the rate coefficients for endo-cyclization in both the anti and syn for compound 23 and get rate coefficients of 1. Based on these rate coefficients it seems plausible that the seven oxygen containing RO 2 radicals 19, 20 and 29 will be formed in reasonable amounts within the timescale of the experiment (seconds), assuming that these seven oxygen containing RO 2 radicals do not further react rapidly.
To investigate the lifetime of this RO 2 , we have calculated the rate coefficients for the H-shift reactions of the RO 2 radicals 20 and 29. The rate coefficients are calculated with MC-TST/B3LYP (20) and LC-TST/wB97X-D (29) methods, and are given in Supplementary  Tables 2 and 3, respectively. Only forward rates have been calculated for 29. It is clear from the tables that the only reaction that might have an impact is the abstraction of the hydrogen on the OH group via an OO-HO 1,5-H-shift, which has a MC-TST/B3LYP rate coefficient of 0.79 s -1 . However, a significantly higher level calculation (LC-TST/F12/wB97X-D/aug-cc-pVTZ) on a similar OO-HO 1,5-H-shift found a rate coefficient of about 10 -3 s -1 . 15 Thus, the rate coefficient 0.79 s -1 based on MC-TST/B3LYP calculations represents most likely an overestimation. We find it likely that these seven oxygen containing RO 2 radicals 19, 20 and 29 will have lifetimes of at least few 10 seconds in the experiment.

Computational details
Configurational sampling was carried out using an approach similar to that described in Rissanen et al. 17 . All possible conformers of each molecule or ion-molecule cluster were first generated by scanning over torsional angles at 120° intervals using the MMFF force field and the Spartan '14 program 3 . For the ion-molecule clusters, the conformer search was initiated from a structure containing the maximum number of intermolecular hydrogen bonds (1 or 2 depending on the molecule). In the force-field calculations, the charge of the RO 2 radical oxygen was manually set to zero using the FFHINT keyword, as the default atom type assignment led to a negative charge on this group. The MMFF conformer generation was followed by ωB97XD/6-31+G(d) 18 single-point energy evaluations on all conformers, and subsequent ωB97XD/6-31+G(d) optimizations on structures with ωB97X/6-31+G(d) singlepoint energies within 5 kcal/mol of the lowest-energy conformer. The lowest-energy structure for each molecule and cluster was then selected for a subsequent higher-level optimization and frequency calculation at the ωB97XD/aug-cc-pVTZ level using the Gaussian 09 program suite 19 , with the ultrafine integration grid. Default convergence criteria were used, except when these led to spurious low imaginary frequencies; in these cases the tight optimization criteria were applied, leading to negligible changes in energy but the disappearance of the imaginary frequencies. The nitrate ion was constrained to have the experimentally observed D3h symmetry. (Enforcing symmetry has a negligible effect on the energy and enthalpy, but a significant effect on the rotational entropy.) Formation enthalpies and free energies were computed using the standard rigid rotor and harmonic oscillator models.

Calculated cluster stabilities
The greater sensitivity of acetate (CH 3 COO -) chemical ionization mass spectrometry (CIMS) compared to nitrate (NO 3 -) CIMS, and the greater difference between the sensitivities toward OH oxidation products compared to O 3 oxidation products, may be explained by a combination of several factors. First, since nitric acid is a much stronger acid than acetic acid, the nitrate ion is a weaker base than the acetate ion. Thus, acetate ions should in general bind more strongly to acidic organic groups (such as alcohols, peroxides, carboxylic acids or peroxy acids). Second, the nitric acid -nitrate dimer is somewhat more strongly bound than the acetic acid -acetate dimer. Ligand exchange reactions of the type HA⋅A -+ X => X⋅A -+ HA (which form the dominant charging mechanism in these CIMS setups) are thus generally much more favourable for a given molecule X when A -= CH 3 COOthan when A = NO 3 -, since the reactant cluster is weaker and the product cluster stronger. Thus, the greater sensitivity of acetate CIMS in general is easily understandable based on the chemical properties of the reagent ions. However, the large difference in relative sensitivities toward OH and O 3 oxidation products is more challenging to explain. One possibility is that the greater basicity of the acetate ion makes it more sensitive toward the relative acidity, or more generally the relative H-bond donor strength, of organic H-bond donor groups. For example, the relative sensitivity of acetate CIMS toward carboxylic acid groups could thus be expected to be greater than that of nitrate CIMS.
In order to investigate the validity of these explanations, and further understand the observed differences in sensitivity between acetate -and nitrate -based detection schemes, calculations were performed on a series of model peroxy radical (RO 2 ) species with either one or two functional groups in addition to the COO radical group. The chosen functional groups were alcohol (OH), hydroperoxide (OOH), carboxylic acid (C(O)OH) and peroxy acid groups (C(O)OOH), since these are believed to be the main functional groups produced by autoxidation processes. The structures of the model RO 2 compounds investigated are shown in Supplementary Fig. 10.
The structures of the clusters of these five RO 2 model compounds with the two charger ions are shown in Supplementary Fig. 11 (along with the nitric acid -nitrate and acetic acid -acetate clusters). The binding enthalpies and free energies of all clusters are given in Supplementary Table 4.
The results in Supplementary Table 4 support the general hypothesis that acetate is more strongly bound to the different RO 2 species than nitrate is, while simultaneously the binding of CH 3 C(O)OH⋅CH 3 COOis somewhat weaker than that of HNO 3 ⋅NO 3 -. An interesting detail is that while the formation enthalpies of the CH 3 C(O)OH⋅CH 3 COOand HNO 3 ⋅NO 3 clusters are almost identical, the formation free energies differ by almost 4 kcal/mol. This is mostly due to the relative entropies of the free ions: the nitrate ion has a low entropy due to its high rotational symmetry number (six) and high vibrational frequencies, while the acetate ion has no rotational symmetry and one very low-frequency vibration corresponding to the torsional motion of the methyl group, leading to a high entropy. (Treating the methyl torsion of the acetate ion as a hindered rotation using the HinderedRotor package of the Gaussian program 20 does not significantly change the free energy of the acetate ion, and thus the formation free energy of the CH 3 C(O)OH⋅CH 3 COOcluster, as the entropy decrease at 298.15 K is almost exactly matched by a decrease in the vibrational zero-point energy.) For the RO 2 ⋅NO 3 clusters, the computed energetics in Supplementary Table 4 match the patterns predicted for closed-shell ELVOC⋅NO 3 clusters by Hyttinen et al. 21 . Organic molecules or radicals with only one (OH, OOH or even C(O)OH) H-bond donating functional group do not bind to NO 3 strongly enough to compete with HNO 3 , and are therefore not detectable using nitrate CIMS. Even for the model RO 2 radicals with two functional groups investigated here, the HNO 3 ⋅NO 3 -+ RO 2 => RO 2 ⋅NO 3 -+ HNO 3 ligand exchange reactions are only favourable by a few kcal/mol with respect to the free energy. Due to steric constraints in the hydrogen bonding patterns, the RO 2 ⋅NO 3 clusters of some of the larger RO 2 formed in autoxidation might well be a few kcal/mol less strongly bound than those studied here. This would lead to low detection efficiencies with nitrate CIMS despite the presence of multiple Hbonding groups -as predicted for the speculative sterically hindered C 6 H 8 O 8 cyclohexene autoxidation product by Hyttinen et al. 21 . O 3 oxidation has a greater probability than OH oxidation of opening up the carbon backbone of endocyclic alkenes, thus reducing steric hindrances for H-bonding of the products. It could therefore be speculated that OH -initiated autoxidation leads, on average, to RO 2 species with less hydrogen bonding flexibility, and thus lower nitrate CIMS detection efficiencies, than O 3 -initiated autoxidation. This is clearly the case for the bicyclic RO 2 compound proposed in Fig. 2. Furthermore, Supplementary Table 4 shows that RO 2 species containing peroxide groups bind somewhat more strongly to nitrate than equivalent RO 2 radicals with hydroxyl groups. This somewhat surprising observation is likely related to the presence of intramolecular hydrogen bonds already in the isolated RO 2 radicals (Supplementary Fig. 10). The greater H-bonding ability of OH groups compared to OOH groups is thus cancelled out, as both the reactants and the products of the clustering reaction contain COH…O hydrogen bonds. For a given number of oxygen atoms, OH -initiated autoxidation products of alkenes are very likely to contain at least one more OH group than the O 3 -initiated autoxidation products. Based on the results of Supplementary Table 4, this will also lead to a weaker binding to nitrate, and thus a lower detection efficiency with nitrate CIMS.
The RO 2 ⋅CH 3 COOclusters are all more strongly bound than the corresponding RO 2 ⋅NO 3 clusters, both in an absolute sense, and relative to the neutral acid-ion cluster. Even the presence of a single peroxide or carboxylic acid group is enough to make the binding of a RO 2 radical to acetate competitive with that of acetic acid. This explains why acetate CIMS is highly effective at detecting products of both OH-and O 3 -initiated autoxidation. The binding of RO 2 radicals with two H-bond donating functional groups to CH 3 COOis more than 10 kcal/mol stronger than the binding of acetic acid to CH 3 COO -. Thus, acetic acid is not able to compete with the multiply substituted RO 2 at any reasonable concentration ratio, explaining the lack of dependence of the detection efficiency of autoxidation products on the acetic acid concentration, see results in Fig. 3. As expected, the relative sensitivity of acetate CIMS to carboxylic acid groups compared to OH or OOH groups is also much larger than that of nitrate CIMS. If OH -initiated autoxidation has a larger probability of forming carboxylic acid groups than O 3 -initiated autoxidation, this may also help explain the differences in relative sensitivities toward the two groups of products.

Product formation from the reaction of OH radicals with α-pinene in presence of NO
Supplementary Fig. 13 shows the results of the HOM formation from the reaction of OH radicals with α-pinene in presence of NO. NO additions were varied in in the range of (5.6 -280) × 10 8 molecules cm -3 . The red dots show the sum of concentrations of all products arising from the reaction of HO-C 10 H 15 (OO)(OOH)O 2 radicals with NO including the residual HO-C 10 H 15 (OO)(OOH)O 2 concentration. This summation yielded an almost constant value for the whole range of NO additions. Thus, the total product amount seem to be in accordance with the amount of reacted HO-C 10 H 15 (OO)(OOH)O 2 radicals. Furthermore, that indicates that the HO-C 10 H 15 (OO)(OOH)O 2 radical formation was not significantly influenced by the NO additions, even for the highest NO concentration of 2.8 × 10 10 molecules cm -3 . Consequently, the RO 2 isomerization steps leading to HO-C 10 H 15 (OO)(OOH)O 2 must be faster than the corresponding RO 2 reactions with NO.

Possible mechanistic explanation
With increasing NO concentrations, increasing signals with the composition C 10 The detection of the subsequently formed organic nitrate, HO-C 10 H 15 (OO)(OH)ONO 2 (full star in Supplementary Fig. 13

Estimated vapour pressure of HOMs
The vapour pressures of three relevant closed-shell HOMs formed from the reaction of HO-C 10 22 . In the case of C 20 H 34 O 8 , three different combinations for RO 2 + R´O 2 have been considered. SIMPOL.1 states group contributions for all needed functional groups of these molecules except that for the endoperoxide moiety. Therefore, the increment of an aliphatic/cyclic ether was taken as a proxy for the endoperoxide moiety. The use of this proxy overestimates the calculated vapour pressures slightly. The calculated vapour pressures applying SIMPOL.1 22 are all below 10 -10 atm, and thus of the order of magnitude as the vapour pressure of mixed H 2 SO 4 -H 2 O-(NH 4 ) 2 SO 4 solutions 23 , whose value varies depending on the ionic ratio and the relative humidity.
Vapour pressures were also estimated for the same closed-shell HOMs deduced from the RO 2 radical 29 using the COSMO-RS approach 24 , as implemented in the COSMOtherm program 25 . In this approach, charge density surfaces are first computed via quantum chemical methods. The charge density surfaces can then be used to model intermolecular interactions in a computationally affordable manner. Finally, statistical thermodynamics methodology is used to compute chemical potential differences, from which vapour pressures may be determined. While not quantitatively accurate for saturation vapour pressures, this approach has the advantage of needing no system-specific parameterizations, and treating (albeit in an approximate way) the real chemical interactions present in the real chemical systems. Conformers of the three studied structures (with the NO product assumed to have rearranged to the low-energy structure HO-C 10 H 15 (OO)(OOH)ONO 2 rather than HO-C 10 H 15 (OO)(OOH)OONO were first generated using the systematic conformer search in Spartan'14 3 , with subsequent B3LYP/6-31+G(d) calculations to eliminate high-energy conformers as described in Rissanen et al. 17 . The 20 lowest-energy conformers (with different H-bonding patterns and thus potentially different charge density surfaces) from the B3LYP optimizations were then selected for the COSMO-RS and gas-phase calculations on Turbomole 26 , using the standard and default BP/TZVP method to generate the input files for the COSMO vapour pressure calculations.
Both sets of calculations show a reasonable agreement with exception of the organic nitrate (difference by a factor of 10), see Supplementary Table 5. Nevertheless, these closedshell HOMs can be treated as low-volatile and polar substances condensing easily on existing surfaces.