All chemicals were purchased from Sigma-Aldrich with purities of 95 % and above and were used as received: the compound numbers, compound names, and abbreviated names are listed in Table 1. All chemical solutions were prepared using purified water (Milli-Q water) from a Milli-Q Plus system (Millipore; ≥18.2MΩ cm) with an upstream Barnstead activated carbon cartridge. To mimic fog drop acidity (Kaur and Anastasio, 2017), the pH of each reaction solution was adjusted to 5.5(±0.2) using a 1.0 mM phosphate buffer.

Bimolecular rate constants of the alkenes with the triplet state of benzophenone (3BP∗) were measured using a relative rate technique, as described in the literature (Richards-Henderson et al., 2014; Finlayson-Pitts and Pitts Jr., 1999). The technique involves illuminating a solution containing the triplet precursor (BP), a reference compound with a known second-order rate constant with 3BP∗, and one test alkene for which the rate constant is unknown. The reference compound for each alkene was chosen so that the triplet-induced loss rates for the test alkene and reference compound were similar. Buffered, air-saturated solutions containing 50 µM each of the reference and test compounds and 100 µM of BP were prepared, and then 10 mL of this solution was illuminated in a stirred 2 cm, airtight quartz cuvette (Spectrocell) at 25 ∘C. Samples were illuminated with a 1000 W Xenon arc lamp filtered with an AM 1.0 air mass filter (AM1D-3L, Sciencetech) and 295 nm long-pass filter (20CGA-295, Thorlabs) to mimic tropospheric solar light (Fig. S1 in the Supplement). At various intervals, aliquots of illuminated sample were removed and analyzed for the concentration of the reference compound and test alkene using HPLC (Shimadzu LC-10AT pump, Thermo Scientific BetaBasic 18 C18 column (250×33 mm, 5 µM bead), and Shimadzu-10AT UV–Vis detector). For each alkene, illumination experiments were performed in triplicate (Table S1) using total illumination times typically between 60 and 150 min. Parallel dark controls were employed with every experiment using an aluminum-foil-wrapped cuvette containing the same solution and analyzed in the same manner as the illuminated solutions. The dark cuvette was placed in a corner of the sample chamber, out of the path of the light beam. As a direct photodegradation control, each alkene was also illuminated (separately) in solution without benzophenone; there was no loss for any of the compounds.

In every case, loss of test and reference compounds followed first-order kinetics. Plotting the change in concentration of the test alkene against that of the reference compound yields a linear plot that is represented by 1lnReference0Referencet=kReference+3BP∗kALK+3BP∗ln[ALK]0ALKt, where [Reference]0, [Reference]t, [ALK]0, and [ALK]t are the concentrations of the reference and test alkenes at times zero and t, respectively, and kReference+3BP∗ and kALK+3BP∗ are the bimolecular rate constants for the reaction of the reference and test alkenes with 3BP∗, respectively. A plot of Eq. (1) (with the y intercept fixed at the origin) gives a slope equal to the ratio of the bimolecular rate constants; dividing kReference+3BP∗ by the slope gives kALK+3BP∗. The measurement technique is illustrated in Fig. S2. While 3BP∗ makes singlet molecular oxygen (1O2∗), the latter is an insignificant oxidant of alkenes in our solutions: the concentrations of the two oxidants are similar (McNeill and Canonica, 2016), but our measured rate constants of alkenes with 3BP∗ are approximately 2500 times faster than the corresponding rate constants with 1O2∗ (Richards-Henderson et al., 2014).

All calculations were completed using the Gaussian 09 software suite (Frisch et al., 2009). Structures of alkenes were optimized using uB3LYP/6-31+G(d,p) (Becke, 1992, 1993; Lee et al., 1988; Stephens et al., 1994; Tirado-Rives and Jorgensen, 2008) for reaction coordinate calculations and the CBS–QB3 (Montgomery Jr. et al., 1999) method for predicting bond dissociation enthalpies (BDEs), bond dissociation free energies (BDFEs), and oxidation potentials (OPs). This method has a mean absolute deviation of approximately 1 kcal mol-1, which corresponds to 0.04 V in Eox (i.e., OP). Transition-state structures (TSSs) were optimized in the triplet state using uB3LYP/6-31+G(d,p) (Becke, 1992, 1993; Lee et al., 1988; Stephens et al., 1994; Tirado-Rives and Jorgensen, 2008). TSSs were confirmed by the presence of an imaginary frequency, and minima (reactants and products) were confirmed by the absence of imaginary frequencies. Free energy (ΔG) and enthalpy (ΔH) differences were determined by comparing TSS energies relative to their reactant energies. For solvent-phase calculations, the solvent model density (SMD) (Marenich et al., 2009) continuum model was used with water as the solvent. To calculate BDEs, the neutral (AH) and radical species (A⚫) (resulting from H atom abstraction) of each alkene and the H radical (H⚫) were optimized in the gas phase. Using the computed enthalpies (H) and Eq. (2), the predicted BDEs of each alkene were determined. 2BDE=HA⚫+HH⚫-HAH To determine the predicted BDFEs, the neutral (AHg, AHaq) and radical species (Ag⚫, Aaq⚫) of each alkene and the H radical (Hg⚫, H⚫aq) were optimized in the gas and solvent phases and their differences taken to give ΔG∘solv,AH, ΔG∘solv,A⚫, and ΔG∘solv,H⚫, respectively. Based on the thermodynamic cycle shown (Scheme 1), these values were used in Eqs. (3) and (4) to calculate the BDFEs of C–H and O–H bonds.

3ΔΔGsolv=ΔG∘solv,A⚫+ΔG∘solv,H⚫-ΔG∘solv,AH4ΔG∘ox=ΔGg+ΔΔGsolv To predict OPs, the neutral (Ag, Aaq) and radical cation (Ag⚫+, Aaq⚫+) forms of each alkene were optimized in the gas and solvent phase, their difference giving ΔG∘solv,A and ΔG∘solv,A⚫. Based on the thermodynamic cycle shown below (Scheme 2), these values were used in Eqs. (5)–(7) to calculate the OP (i.e., Eox) of each alkene.

5ΔΔGsolv=ΔG∘solv,A⚫+-ΔG∘solv,A6ΔG∘ox=IEgas+ΔΔGsolv7Eox=--ΔG∘oxnF+SHE Here, n is the number of electrons, F is Faraday's constant (96485.3365 C mol-1), and SHE is the potential of the standard hydrogen electrode (4.28 V) (Tripkovic et al., 2011).

Subsequent MP2–CBSB3 (Petersson et al., 1988, 1991; Petersson and Al-Laham, 1991; Mayer et al., 1998) single-point calculations were used to compute the highest occupied molecular orbitals (HOMOs) and singly occupied molecular orbitals (SOMOs). Structural drawings were produced using CYLView (Legault, 2009).

Figure 1 shows the chemical structures for all 17 alkenes and the triplet precursor benzophenone. The alkenes have molecular weights ranging between 58 and 220 g mol-1 and include 13 alcohols, three esters, and one chlorinated compound. The model triplet precursor benzophenone (BP) has been previously employed in surface water studies, and its triplet state rapidly reacts with aromatics such as substituted phenols and phenyl urea herbicides with rate constants faster than 109 M-1 s-1 (Canonica et al., 2000, 2006).

The bimolecular rate constants for the alkenes with the excited triplet state of BP (kALK+3BP∗) vary by a factor of 30, spanning the range of (0.24–7.5) ×109 M-1 s-1. Values are shown in Tables 1 and S1 in the Supplement and in Fig. S3, in which the alkenes are numbered in ascending order of their reactivity towards 3BP∗. Based on their rate constants, the alkenes appear to be broadly split into two groups: the slower alkenes (1–9), whose rate constants lie below 1×109 M-1 s-1 and span a range of only a factor of 2.5, and the faster alkenes (10–17), which vary by a factor of 5. Notably, three of the four BVOCs identified in emissions to the atmosphere – 3MBO (12), cHxO (15), cHxAc (16) and MeJA (17) – react rapidly with 3BP∗, with rate constants greater than 1×109 M-1 s-1.

Three alkene characteristics appear to increase reactivity: internal (rather than terminal) double bonds, methyl substitution on the double bond, and alkene stereochemistry. To more specifically examine the impact of these variables, we compare the rate constants for three sets of alkenes (Fig. 2). The lowest free energy and enthalpy barriers for the abstraction of a hydrogen atom are also shown in Fig. 2 (and in Table 1); while overall these computed barriers are not well-correlated with rate constants (discussed below), lower barriers generally correspond to higher rate constants for the sets of alkenes in Fig. 2. The first two sets of compounds in Fig. 2 indicate that internal alkenes react faster with 3BP∗ than do terminal isomers: cHxAc (16), an internal hexenyl acetate, has a reaction rate constant 11 times faster than its terminal isomer 5HxAc (9). The corresponding alcohols also exhibit the same trend: the internal alkenes cHxO (15) and tHxO (10) react 27 and 5.8 times faster, respectively, than the terminal isomer 5HxO (1). This dependence of reactivity on double bond location has implications for isoprene hydroxyhydroperoxides (ISOPOOHs) and hydroxynitrate (ISONO2), which have both terminal (β-) and nonterminal (δ-) isomers formed from gas-phase oxidation (Marais et al., 2016; Paulot et al., 2009a, b). Based on our results we expect the δ-isomers to react more quickly with organic triplets than the β-isomers.

Alkene stereochemistry also affects the triplet–alkene reaction rate constant. The data in the middle of Fig. 2 show that cis-HxO (15) reacts nearly 5 times more quickly with 3BP∗ than does trans-HxO (10), consistent with the lower predicted energy barrier for hydrogen atom abstraction from the cis-isomer. Finally, the addition of electron-donating substituents (methyl groups) on an unsaturated carbon atom also increases the rate constant. This is evident from comparing 2B1O (8) and its methyl-substituted analog 3MBO (12): kALK+3BP∗ is 3.7 times faster with the methyl group (Fig. 2). Mechanistically, triplet-induced oxidation can proceed via either hydrogen atom transfer or a proton-coupled electron transfer (Canonica et al., 1995; Warren et al., 2010; Erickson et al., 2015), and the presence of an electron-donating substituent on the double bond likely selectively stabilizes the intermediates (e.g., radical or radical cation) formed from these two processes, as well as the transition-state structures for their formation.

Our next goal was to develop a quantitative structure–activity relationship (QSAR) so that we can predict rate constants for alkene–triplet reactions. To use as predictor variables in the QSARs we computed several properties of the alkenes: bond dissociation enthalpy and free energy for various hydrogen atoms (Fig. S4), free energy and enthalpy barriers for hydrogen atom abstraction (Table 1), and one-electron oxidation potentials (Table 1). Apart from the oxidation potential, none of the other properties correlate well with the measured rate constants (Figs. S5 and S6). While there is no correlation between the rate constants and predicted energy barriers, alkenes with lower predicted free energy barriers (ΔG‡) are predicted to be fast-reacting, with rate constants above 5×108 M-1 s-1 (Fig. S6). As shown in Fig. S6, computed barriers predict much larger variation in the rate than observed experimentally, suggesting that the breaking of the C–H or O–H bond does not occur in the rate-determining step for all alkenes.

Of all the properties examined, the one-electron oxidation potential of the alkenes best correlates with the (log of) measured rate constants, with rate constants generally increasing as the alkenes are more easily oxidized, i.e., at lower OP values (R2=0.58) (Fig. 3). Measured rate constants for 13 of the 16 alkenes lie within (or very near) the 95 % confidence interval (blue lines) of the regression fit, but there are three notable outliers: hexen-1,3-diol (3, HDO), cis-3-hexen-1-ol (15, cHxO), and cis-3-hexenylacetate (16, cHxAc). The measured HDO rate constant is 3.3 times lower than that predicted by the regression line, while measured rate constants for cHxO and cHxAc are 3.9 and 4.9 times higher, respectively, than predicted.

To try to assess why these compounds differ from the others, we calculated the highest occupied molecular orbital of the alkene and the singly occupied molecular orbital of the alkene radical cation (i.e., after oxidation) (Fig. 4). Depending on the system, oxidation is predicted to occur by removing an electron either from the π system of the C–C double bond or from a lone pair on the O atom. This is illustrated in Fig. 4, which shows the HOMO and SOMO structures for HDO (3), wherein the electron is removed from the C–C double bond, and 3B1O (5), wherein the electron is removed from the oxygen atom. However, the three outliers in the correlation do not all fall into just one of these categories: for cHxAc (16) the electron is most likely abstracted from the oxygen, while for HDO (3) and cHxO (15) the electron is likely removed from the π system (Tables S2 and S3). This suggests that the location of electron removal does not control the rate constants. We also examined if the rate of loss of cHxO might be enhanced due to oligomerization, whereby an initially formed cHxO radical leads to additional cHxO loss. Since the pseudo-first-order rate constant of oligomerization should increase with initial cHxO concentration, we measured the rate constant for cHxO loss over a range of initial concentrations (2–50 µM). However, as shown in Fig. S8, the rate constant for cHxO loss does not depend on its concentration, suggesting that oligomerization is an unimportant loss process for cHxO in our experiments. Thus, it is not clear why these three compounds do not fall closer to the regression line in Fig. 3. However, except for 16, all of the alkenes fall within a factor of 4 of the correlation line (gray lines). Finally, even though there is a good correlation between rate constant and OP in Fig. 3, it does not indicate whether these reactions proceed via pure electron transfer, proton-coupled electron transfer, or hydrogen transfer. As discussed earlier, since the predicted energy barriers for hydrogen abstraction do not correlate with measured rate constants (Fig. S6) and appear to split into two groups, uncertainty remains about the mechanism of triplet-induced oxidation of the alkenes.

We next use the relationship in Fig. 3, along with calculated oxidation potentials, to predict second-order rate constants for 3BP∗ with a set of unsaturated oxygenated VOCs formed by the oxidation of isoprene and limonene. As shown in Fig. 5, we predict that limonene products generally react faster with 3BP∗ than do isoprene products. For the five isoprene-derived OVOCs that we considered, rate constants vary by a factor of 17 and range (0.080–1.4) ×109 M-1 s-1 (Table 1, Fig. 5). The δ-isomers of ISOPOOH and ISONO2, which contain internal double bonds, have lower computed one-electron oxidation potentials and thus higher predicted rate constants compared to the terminal β-isomers. This is similar to the trend observed with the other alkenes (Fig. 2). In the case of isoprene hydroperoxyaldehydes, we were able to determine the oxidation potential for only HPALD2 (22), and its predicted reaction rate constant (±1 SE) of 4.0(±0.9)×108 M-1 s-1 is among the lowest of the isoprene-derived alkenes (Fig. 5).

We calculated OP values and triplet rate constants for three limonene-derived OVOCs: limonene aldehyde (LMNALD) and two dihydroxy-limonene aldehydes (2,5OH–LMNALD and 4,7OH–LMNALD). Compared to the isoprene-derived alkenes, the rate constants for all three limonene products are high and range (0.89–1.7) ×109 M-1 s-1. All of the limonene aldehydes (as well as the isoprene products) can have several isomers whose calculated oxidation potentials can vary, which affects the predicted rate constant. For example, for 4,7OH–LMNALD (25) the computed oxidation potential for five of its isomers vary between 2.17 and 2.48 V (Table S4), which leads to a relative standard deviation of 40 % in the predicted rate constants for the various isomers. For each OVOC, the predicted rate constants in Table 1 are for the lowest-energy isomers whose structures are shown in Fig. S9.

Next, we use our estimated rate constants, along with previously published estimated values for rates of other loss processes (Table S5), to understand the importance of triplets as sinks for isoprene- and limonene-derived OVOCs in a foggy–cloudy atmosphere. For our simple calculations we use a liquid water content of 1×10-6 L aq / L g, a temperature of 25 ∘C, and calculated Henry's law constants from EPISuite (US EPA, Estimation Programs Interface Suite^™ for Microsoft^® Windows v4.1, 2016) (Table S6). From these inputs, we estimate that between 10 % and 97 % of the OVOCs will be partitioned into the aqueous phase under our conditions (Table S6). The OVOC sinks we consider are photolysis and reactions with the hydroxyl radical (⚫OH) and ozone (O3) in the gas phase as well as hydrolysis and reactions with ⚫OH, O3, and triplets in the aqueous phase (Table S5). Based on typical oxidant concentrations in both phases and available rate constants with sinks, the overall pseudo-first-order rate constants for initial OVOC losses are estimated to be in the range of (0.27–3.0) ×10-4 s-1, corresponding to overall lifetimes of 0.93 to 10 h (Table S7). The only exception is δ-ISONO2, which is expected to undergo rapid hydrolysis to form its corresponding diol (Jacobs et al., 2014) with a lifetime of just 0.078 h (280 s).

Figure 6 shows the overall loss rate constants and the contribution from each pathway for four of these OVOCs: δ4-ISOPOOH (19), β-ISONO2 (20), HPALD2 (22), and 4,7-OH–LMNALD (25). Overall, aqueous-phase processes dominate the fate of these OVOCs, accounting for the bulk of their loss, but the contribution of aqueous triplets to OVOC loss depends strongly on the triplet reactivity. Panel (a) of Fig. 6 shows OVOC loss when we assume that the aqueous triplets are highly reactive, i.e., using rate constants estimated for 3BP∗ (Fig. 5). Since our recent measurements (Kaur et al., 2018; Kaur and Anastasio, 2018) indicate that, on average, ambient triplets are not this reactive, this scenario likely represents an upper bound for the triplet contribution. In this case highly reactive triplets are the dominant sinks for δ4-ISOPOOH and 4,7-OH–LMNALD, accounting for 74 % and 47 % of their total losses, respectively (Fig. 6a). For β-ISONO2 and HPALD2, triplets are not dominant but still significant, accounting for 19 % and 24 % of loss, respectively, while other sinks dominate. For the OVOCs for which we calculated rate constants with 3BP∗ (Fig. 5) but that are not shown in Fig. 6, the triplet contribution varies widely, from less than 1 % for δ-ISONO2 (21), for which hydrolysis dominates, to 59 % for 2,5-OH–LMNALD (24) (Table S7).

While 3BP∗ likely represents an upper bound of triplet reactivity in atmospheric waters, our recent measurements indicate that the triplets in fog waters and particles have an average reactivity that is typically similar to 3'-methoxyacetophenone (3MAP) and 3,4-dimethoxybenzaldehyde (DMB) (Kaur et al., 2018; Kaur and Anastasio, 2018). A comparison of our 3BP∗ rate constants (Table 1) with the average values for the 3MAP and DMB triplets for a subset of the alkenes (Richards-Henderson et al., 2014) indicates that the average 3MAP–DMB triplet rate constants are 1 %–18 % of the corresponding 3BP∗ values. Thus, to scale alkene–triplet rate constants from 3BP∗ to the 3MAP and DMB triplets we take the median value of 4 %, which is derived from the MeJA rate constants (Table S8). Figure 6b shows the calculated fates of the OVOCs in the case in which we consider “typical-reactivity” triplets; i.e., we multiply the 3BP∗ + OVOC rate constants (Fig. 5) by a factor of 0.04. Under these conditions, triplets are minor oxidants (Fig. 6b), accounting for 9 % and 3 % of the loss of δ4-ISOPOOH and 4,7-LMNALD, respectively, and approximately 1 % for the other two OVOCs. This suggests that aqueous triplets are generally minor sinks for OVOCs derived from isoprene and limonene, in contrast to the case for phenols, for which triplets appear to be the major sink (Smith et al., 2014; Yu et al., 2014; Kaur and Anastasio, 2018). However, there are several important uncertainties in our determination that triplets are likely minor sinks for oxygenated alkenes. First, the factor we used to adjust from 3BP∗ rate constants to triplet 3MAP–DMB rate constants (i.e., a factor of 0.04) is quite uncertain: values for the three BVOCs examined range from 0.01 to 0.18 (Table S8). Additionally, there are very few measurements of triplets in atmospheric drops or particles (Kaur et al., 2018; Kaur and Anastasio, 2018) and only from two sites, so it is possible that we are underestimating the average reactivity and/or concentrations of triplets in atmospheric drops and particles.