3.1.1 Relative method

Methyl methacrylate, MMA, was used as the reference compound in this work because the rate coefficient at 298 K for its reaction with the NO₃ radical has been measured in the same chamber using the same method as used here (Zhou et al., 2017) to be k_MMA= ($\mathrm{2.98}\pm \mathrm{0.35})\times {\mathrm{10}}^{-\mathrm{15}}$ cm³ molec.⁻¹ s⁻¹. We acknowledge that there are other recommendations that are slightly higher than the value we used. One can always renormalize the rate coefficient for any specific value. The experimental conditions and associated parameters are shown in Table S2.

Figure 1 shows plots of $\mathit{\{}\ln \left(\frac{{\left[\mathrm{aro}\right]}_{\mathrm{0}}}{{\left[\mathrm{aro}\right]}_t}\right)-k_d\times t\mathit{\}}$ against $\mathit{\{}\ln \left(\frac{{\left[\mathrm{ref}\right]}_{\mathrm{0}}}{{\left[\mathrm{ref}\right]}_t}\right)-k_d\times t\mathit{\}}$ for the seven aromatic aldehydes. Each plot is linear with an intercept of zero within the uncertainties. The k_d×t term is relatively small (3.6 %–7.6 %) compared to the ratio $\mathit{\left\{}\frac{k_d\times t}{\ln \left(\frac{{\left[\mathrm{aro}\right]}_{\mathrm{0}}}{{\left[\mathrm{aro}\right]}_t}\right)\mathrm{or}\ln \left(\frac{{\left[\mathrm{ref}\right]}_{\mathrm{0}}}{{\left[\mathrm{ref}\right]}_t}\right)}\mathit{\right\}}$, and slight variations in its value do not affect the accuracy of the measured rate coefficients. Figure 1 also shows that the measured values of the rate coefficient ratios are reproducible. The ratios of rate coefficients, $\frac{k_{\mathrm{1},\mathrm{7}}}{k_{\mathrm{ref}}}$, were calculated from these plots using the algorithm of Brauers and Finlayson-Pitts (1997), which takes into account errors in both the abscissa and ordinate. These errors were estimated from the uncertainty of the concentration calculated from the calibration plots generated before the kinetics runs. The noted errors for $\frac{k_{\mathrm{1},\mathrm{7}}}{k_{\mathrm{ref}}}$ are twice the standard deviation in the least-squares fits multiplied by a factor to account for the limited number of measurements using the Student's t distribution.

Figure 1Plots of relative kinetic data obtained from the reaction of aromatic aldehydes (aro) with the NO₃ radical using methyl methacrylate (MMA) as the reference. M-TA, P-TA, 3,5-DMBA, O-TA, 2,5-DMBA and 2,4-DMBA were shifted 0.25, 0.5, 0.75, 1.0, 1.25 and 1.5, respectively, for clarity.

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The relative rate coefficients of the studied aromatic aldehydes, termed k_RR, are shown in Table S2. The estimated uncertainties for k_RR were the sum of the precision of our measurements (noted above) and the quoted uncertainties in the rate coefficient for the reference reaction according to the expression

3.1.2 Absolute method

The method used to analyze the temporal profiles of NO₃ and N₂O₅ to obtain k₁–k₇ has been described by Zhou et al. (2017, 2019). Figure 2 shows an example of the temporal profiles of NO₃ and N₂O₅ for Reaction (R1) from which the rate coefficient k₁ was derived. Similar analyses yielded k₂–k₇ (Figs. S2–S7).

Figure 2a shows the temporal profile of NO₃ and N₂O₅ concentrations plotted on a logarithmic scale. The concentrations decrease exponentially (the lines are linear in the log space), and the decay rates are lower in the absence of the reactant aldehyde than in its presence. The rate coefficients for the loss of NO₃ and N₂O₅ to the walls and dilution, k₁₀ and k₁₁, were determined to be in the ranges (3.7–7.1) × 10⁻³ s⁻¹ and (3.2–12.0) × 10⁻⁴ s⁻¹, respectively. As Zhou et al. (2017), we cannot merely take the slopes of decay of NO₃ with time to calculate the rate coefficients k₁–k₇ since NO₃ and N₂O₅ are coupled through their equilibrium. The equilibration is maintained throughout the course of Reactions (R1)–(R7). To account for this situation, we fit the profiles of both NO₃ and N₂O₅ to a reaction scheme, as described previously.

Figure 2 panels (b) and (c) show the NO₃ and N₂O₅ temporal profiles on a linear scale in the absence and the presence of the reactant aldehyde. The two panels also show the fits of the data to the mechanism that included only Reactions (R1)–(R11). The fits are acceptable but with larger variations at longer reaction times. We have to consider the contributions to NO₃ and N₂O₅ losses due to the reactions of NO₃ with the products of Reactions (R1)–(R7). Values of the rate coefficients derived from such fits included all the potential reactions that can contribute to the removal of NO₃, and they are shown in the Supplement (Table S4). When the secondary reactions with the products were included, the fits were better at the longer reaction times, and they are shown in panel (d) of Fig. 2. The residuals of the fits are shown at the bottoms of panels (c) and (d); they clearly show the improvement in the fits and the lack of a trend with reaction time. Larger deviations are to be expected in panel (c) at longer reaction times as the reaction products build up. The rate coefficients k₁–k₇ calculated using the reaction scheme shown in Table S4 are taken to be those measured by the direct method. As expected, the rate coefficients calculated by including the contributions of the secondary reactions were slightly less than those without the secondary reaction contributions (see Fig. S8). The differences were, on average, about 5 %.

Figure 2Observed (points) and simulated (lines) profiles of N₂O₅ (left axis) and NO₃ (right axis) as a function of time. Mixing ratios of o-tolualdehyde are shown in each panel. Panel (a): the temporal profiles on a log scale. Panel (b): temporal profiles on a linear scale and the fits to the data as discussed in the text to determine the wall loss of N₂O₅ and NO₃ during the experiment. Panel (c): fits of simulations not including the subsequent secondary reactions of NO₃ with the products of the initial reaction. The dashed lines at the bottom show the ratio of simulated lines to measured data points (Fit./Exp.) for NO₃ (blue) and N₂O₅ (red). Panel (d): fits of simulations including the subsequent secondary reactions of NO₃ with the initial reaction products (shown in Table S4). The dashed lines at the bottom show the ratio of simulated lines to measured data points (Fit./Exp.) for NO₃ (blue) and N₂O₅ (red). The improvements in the fits are clear in panel (d).

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The results of our measured values for k_1–7 are summarized in Table S3. The quoted errors of the rate coefficient from each experiment are at the 95 % confidence level based on the precision of the fits; they were typically less than 7 %. The weighted averages of results from multiple experiments were calculated, and then the influence of the small number of measurements was accounted for by using a Student's t-distribution table. We added the estimated systematic uncertainties to the precision in quadrature, assuming that they are uncorrelated. Contributions to estimated systematic errors included the following: (1) the systematic errors of $-\mathrm{8}/+\mathrm{11}$ % and $-\mathrm{9}/+\mathrm{12}$ %, respectively, in the measurements of NO₃ and N₂O₅ (Zhou et al., 2019); (2) the uncertainty of around 10 % in the rate coefficients used in the reaction schemes shown in Table S4; and (3) the estimated uncertainty of 7 % in the concentration of aromatic aldehydes. This includes the uncertainties in the calibration and spectral analysis. All the noted uncertainties are at the 95 % confidence level, assuming a Gaussian error distribution.

It is important to note that we need the absolute concentrations of NO₃ and N₂O₅ even though the reaction was first order in NO₃ due to the strong coupling between the concentrations of NO₃ and N₂O₅ via an equilibrium. The presence of the aldehydes would influence the temporal profiles of both N₂O₅ and NO₃. Here we are attributing the entire change to the reaction of NO₃ with the aldehydes. The validity of this assumption is shown by the measured rate coefficients being independent of the ratio of [NO₃] $/$ [N₂O₅]. This ratio was changed simply by changing [NO₂], which shifts the equilibrium concentrations of NO₃ and N₂O₅.

3.1.3 Comparison of rate coefficients obtained from absolute and relative methods

The rate coefficients for the reactions of NO₃ with seven different aromatic aldehydes, k₁–k₇, measured using the absolute and relative methods are summarized in Table 1. The rate coefficient values from the two methods are in good agreement with each other. The differences are less than 10 %, except for k₁, which differs by 18 %.

As shown in Table 2, the final rate coefficients of seven aromatic aldehydes reacting with the NO₃ radical were derived from the weighted average of the absolute and the relative rate methods using the equation discussed above (Eqs. S2 and S3).

Table 1Rate coefficients k₁–k₇ measured in the study using two different methods.

^* Weighted average of these relative and absolute measurements as well as their error calculated using Eqs. (S2) and (S3).

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Table 2Experimental results of this study compared with those from the literature for the reactions of the NO₃ radical with benzaldehyde (BA), o-tolualdehyde (O-TA), m-tolualdehyde (M-TA), p-tolualdehyde (P-TA), 2,4-dimethylbenzaldehyde (2,4-DMBA), 2,5-dimethylbenzaldehyde (2,5-DMBA) and 3,5-dimethylbenzaldehyde (3,5-DMBA).

^a Weighted average of Atkinson (1991), Bossmeyer et al. (2006) and this work including results of the relative and absolute method. ^b Values shown in Table 1.

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3.1.4 Comparison with the literature for NO₃ radical kinetics with aromatic aldehydes

Table 2 summarizes the rate coefficients measured in this work with data from the literature for reactions of the NO₃ radical with aromatic aldehyde, BA, O-TA, M-TA, P-TA, 2,4-DMBA, 2,5-DMBA and 3,5-DMBA. As shown in Table 2, the rate coefficient for BA has been reported by five studies. Three of them (Atkinson et al., 1984; Carter et al., 1981; Clifford et al., 2005) used the relative method with different reference compounds. Atkinson et al. (1991) corrected the values from their earlier report, and they are used for the comparison. Bossmeyer et al. (2006) measured both NO₃ and BA using differential optical absorption spectroscopy (DOAS) in their chamber. They measured the loss of BA in a known (measured continuously) NO₃ concentration and fitted BA's measured temporal profile to obtain k₁. Calvert et al. (2011) recommended k₇ to be $\mathrm{4.0}\times {\mathrm{10}}^{-\mathrm{15}}$ cm³ molec.⁻¹ s⁻¹ with a 30 % uncertainty based on these studies. However, our value from absolute and relative methods using methyl methacrylate as a reference reaction (its rate coefficient was determined using the absolute method in our previous study; Zhou et al., 2017) is in good agreement with Atkinson (1991) and Bossmeyer et al. (2006). Hence, we suggest that the weighted average based on these three studies, $\mathrm{2.6}\pm \mathrm{0.3}\times {\mathrm{10}}^{-\mathrm{15}}$ cm³ molec.⁻¹ s⁻¹ at 298±2 K, is a reliable value. The rate coefficients for ortho-, meta- and para-tolualdehyde have only been studied by Clifford et al. (2005), who reported them to be (9.8±0.4), (9.5±0.4) and (9.5±0.7) $\times {\mathrm{10}}^{-\mathrm{15}}$ cm³ molec.⁻¹ s⁻¹, respectively. In this work, k₁–k₇ were determined relative to MMA as the reference as well as using an absolute method to be (8.5±1.0 and 9.1±1.2), (5.1±0.6 and 4.7±0.6) and (5.0±0.6 and 4.8±0.6) × 10⁻¹⁵ cm³ molec.⁻¹ s⁻¹, respectively. This work agrees best with the value of Clifford et al. (2005) for ortho-tolualdehyde, but those of k₃ and k₄ are smaller than those of Clifford et al. (2005). The reasons for these discrepancies are unclear, but the excellent agreement (< 7 % difference) between the two techniques presented here gives us confidence in our determinations. This work provides the first experimental determinations of the rate coefficients for NO₃ reactions with 2,4-DMBA, 2,5-DMBA and 3,5-DMBA; the two complementary methods agree well. The recommended rate coefficients of the weighted average of the relative method and absolute method are shown in Table 2.

3.2.1 Product investigation from the reaction of benzaldehyde with NO₃

The stable products formed in Reaction (R1) were investigated at 298±2 K and 760 Torr in the same 7300 L simulation chamber. Benzaldehyde at 0.9–1.4×10¹³ molec. cm⁻³ (as shown in Table S5) was introduced into the chamber, and its removal was measured for 2 h to obtain the wall loss rate coefficient. Then, roughly 1.1×10¹²–1.5×10¹⁴ molec. cm⁻³ of N₂O₅ was introduced. Stable products formed in the chamber were identified and quantified (when possible) using the PTR-ToF-MS and FTIR.

Two stable products, C₆H₅C(O)O₂NO₂ (benzaldehyde-PAN; BAPAN) and C₆H₅ONO₂, were detected and measured. The former was detected using both PTR-ToF-MS ($m/z$ 184.024 and its fragment $m/z$ 105.034) and FTIR (965–1005 cm⁻¹ centered at 989 cm⁻¹) and the latter using only PTR-ToF-MS. Since we do not have a sample of BAPAN, we could not quantify the yield of this product using PTR-ToF-MS. However, Caralp et al. (1999) reported the IR band strengths for BAPAN. Using their reported band strength, we could quantify BAPAN to be 80±10 % of the benzaldehyde that was removed via reaction; the quoted uncertainty is the precision in the fit at the 2σ level. When we account for the uncertainties in the absorption cross sections of BAPAN reported by Caralp et al. (1999) (∼20 %), account for the uncertainties in the concentration of the initial benzaldehyde concentration (∼10 %) and add the precision of the measurements, we conclude that the yield of BAPAN is 80±22 %. We assume that the uncertainties are uncorrelated and hence added them in quadrature. The obtained BAPAN amounts are shown in Fig. 3 as a function of benzaldehyde consumption; the details are shown in Table S5 in the Supplement. We could not quantify C₆H₅ONO₂ because of the lack of a standard. Assuming that the ion–molecule reaction rate coefficients for proton transfer to BAPAN and C₆H₅ONO₂ are similar, we estimate that the yield of C₆H₅ONO₂ is smaller than that of BAPAN. These two products are expected if the reaction proceeds via H-atom abstraction and most of the peroxy radical reacts with NO₂ (Platz et al., 1998), as denoted by Reaction (A).

A fraction of the peroxy radicals reacts with itself (or other peroxy radicals) to make phenoxy radicals, which ultimately leads to a nitrate, according to Reaction (B).

Unfortunately, we could not reduce the concentration of NO₂ sufficiently to suppress Reaction (B) completely. A small fraction of the C₆H₅C(O)O₂ would also react with NO₃ but would still yield the C₆H₅C(O)O radicals. Also, any reactions of the phenyl radical with NO₂ can be neglected because of the large abundance of O₂ that will quickly convert it to the C₆H₅O₂ radical. Numerical modeling of the reaction sequence shown in the Supplement (Table S4) suggests that the yield of BAPAN is more than 95 % under our experimental conditions. Based on these results, we suggest the yield of BAPAN in our reaction system to be essentially 1 and that we detect the nitrate because of the high sensitivity for its detection in our PTR-ToF-MS.

Figure 3A plot of benzaldehyde PAN (C₆H₅C(O)O₂NO₂; BAPAN) concentrations measured by FTIR as a function of depletion of benzaldehyde. The slope of the plot gives a yield of the BAPAN in the NO_x-rich environment of roughly 80±22 %. Note: the different colors and markers represent repeated experiments with different initial NO₂ concentrations. Red filled circles: [NO₂]₀= 1.4–2.9 ×10¹² molec. cm⁻³ molec. cm⁻³, blue triangle: [NO₂]₀] = $\sim \mathrm{2.8}\times {\mathrm{10}}^{\mathrm{13}}$ molec. cm⁻³, green square: [NO₂]₀= $\sim \mathrm{1.4}\times {\mathrm{10}}^{\mathrm{14}}$ molec. cm⁻³, red open diamond: [NO₂]₀= $\sim \mathrm{3.3}\times {\mathrm{10}}^{\mathrm{14}}$ molec. cm⁻³.

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3.2.2 Kinetic isotope effect in the reaction

To further examine the mechanism of NO₃ reactions with the aromatic aldehydes, we measured the rate coefficient for the reaction of the NO₃ radical with benzaldehyde-α-d1 (C₆H₅CDO).

As shown in Fig. 4, k₁₃ is half that of k₁ – i.e., $k_{\mathrm{1}}/k_{\mathrm{13}}$ is 1.92. A factor of 2 decrease in the rate coefficient going from benzaldehyde to benzaldehyde-α-d1 is consistent with a primary kinetic isotope effect (KIE), suggesting that abstraction of the aldehydic H atom occurs in the rate-limiting step of this reaction pathway (see calculated KIE below).

Figure 4The plot of the logarithm (base e) of the ratio of the initial benzaldehyde-d1 concentration to those at other reaction times against the logarithm (base e) of the ratio of the initial benzaldehyde concentration relative to those at different times. Both benzaldehyde and benzaldehyde-d1 were competing for the same pool of NO₃ radicals. The slope of the plot is 0.53±0.01. The red and blue circles represent two experiments with different concentrations of NO₃ radicals.

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3.2.3 Reaction pathway

Linear free-energy relationships comparing the reactivities of OH and NO₃ with a series of organic compounds are shown in the Supplement (Fig. S9). Such correlations have been demonstrated in the past by Clifford et al. (2005). We have added our measured values of k₁–k₇ to the plot. This plot suggests that the linear free-energy relationship is consistent with NO₃ radicals adding to the seven aromatic aldehydes studied here. Even the reaction of OH radicals with aliphatic aldehydes is known to proceed by forming a pre-reaction complex.

Figure 5 shows the rate coefficients for the reaction of the NO₃ radical with the seven aldehydes studied here (also presented in Table 2), along with those with benzene and toluene ($\mathit{<}\mathrm{3}\times {\mathrm{10}}^{-\mathrm{17}}$ and $\mathit{<}\mathrm{6.6}\times {\mathrm{10}}^{-\mathrm{17}}$ cm³ molec.⁻¹ s⁻¹) (Calvert et al., 2002). Benzene and toluene do not react with NO₃ to measurable extents; such reactions may be expected if they proceeded via electrophilic addition. Since it is not sufficiently reactive to abstract an H atom from either the ring or the methyl group, the rate coefficient is very slow, if not zero. Therefore, the observed reaction rate coefficients suggest that the reaction proceeds via an H-atom abstraction from the −CHO group (Clifford et al., 2005; Wayne et al., 1991). The rate coefficient for the reaction of NO₃ with benzaldehyde, ($\mathrm{2.6}\pm \mathrm{0.3})\times {\mathrm{10}}^{-\mathrm{15}}$ cm³ molec.⁻¹ s⁻¹, is similar to that with acetaldehyde of ($\mathrm{2.7}\pm \mathrm{0.5})\times {\mathrm{10}}^{-\mathrm{15}}$ cm³ molec.⁻¹ s⁻¹, as shown in Fig. 5. The mechanism for the reaction of NO₃ with acetaldehyde is believed to be H-atom abstraction from the −CHO group after the formation of a pre-reaction complex.

Figure 5The measured rate coefficients for reactions of the NO₃ radical with the seven aldehydes studied here. The results of previously reported rate coefficients are also shown (values are presented in Table 2). The rate coefficient for acetaldehyde of $k_{\left({\mathrm{CH}}_{\mathrm{3}}\mathrm{CHO}\right)}=$ $(\mathrm{2.7}\pm \mathrm{0.5})\times {\mathrm{10}}^{-\mathrm{15}}$ cm³ molec.⁻¹ s⁻¹ is from IUPAC recommendations. The rate coefficients for benzene of $k_{\left(\mathrm{benzene}\right)}\mathit{<}\mathrm{3}\times {\mathrm{10}}^{-\mathrm{17}}$ cm³ molec.⁻¹ s⁻¹ and for toluene of $k_{\left(\mathrm{toluene}\right)}\le \mathrm{6.6}\times {\mathrm{10}}^{-\mathrm{17}}$ cm³ molec.⁻¹ s⁻¹ are from Calvert et al. (2002).

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As shown in Fig. 5 (also presented in Table 2), this work finds a higher rate coefficient for the reactions of NO₃ with ortho-, meta- and para-tolualdehydes than that with benzaldehyde. This enhanced reactivity with ring substitution by electron-donating groups suggests an electrophilic role for NO₃ in the reaction. Clifford et al. (2005) noted that the direct influence of the electron donation to the ring by the CH₃ group is effectively canceled out by the electron-withdrawing effect of the −CHO group as an explanation for their measured rate coefficients being the same for all the tolualdehydes. The trends we observe for substituting methyl groups in the tolualdehydes and the demethylated aldehydes could suggest electrophilic addition. Of course, the initial addition has to lead to the abstraction of the aldehydic H atom, as shown by the products and the kinetic isotope effect. Alternatively, the reactivity trend could simply be due to the C–H bond energy changes in the aldehydic group upon methyl substitution.

The C–H bond dissociation enthalpies (BDEs) of benzaldehyde and the three tolualdehydes have been obtained from Active Thermochemical Tables (ATcT). As opposed to traditional sequential thermochemistry, ATcT obtains enthalpies of formation by constructing, statistically analyzing and solving a global thermochemical network (TN), which is formed by including experimental and theoretical determinations pertinent to the chemical species that are included in the network, as explained in more detail elsewhere (Ruscic et al., 2004, 2005).

The results presented here are based on the most current ATcT TN (ver. 1.122x), obtained by further expanding prior (Bross et al., 2019; Zaleski et al., 2021) versions (1.122r and 1.122v) by including species of interest in the present study, as well as other ongoing investigations. The current TN incorporates ∼ 2350 species, interconnected by ∼29 000 experimental and theoretical determinations.

Typically, the insertion of a new chemical species in the TN begins by linking the new species to the already existing species via a provisional skeleton of theoretical isodesmic reactions computed using a standard set of mid-level composite calculations carried out in-house and currently consisting of W1 (Martin and de Oliveira, 1999; Parthiban and Martin, 2001), CBS-APNO (Ochterski et al., 1996), G4 (Curtiss et al., 2007), G3X (Curtiss et al., 2000) and CBS-QB3 (Montgomery et al., 1999, 2000). This is subsequently complemented by experimental and theoretical determinations from the literature and, when possible, additional state-of-the-art high-level composite calculations that can deliver sub-kJ mol⁻¹ accuracies. As the number and accuracy of additional determinations grow, the dependence of the final result on the determinations spanning the initial skeleton diminishes and ultimately vanishes.

However, while the enthalpies of formation of gas-phase benzaldehyde and the three tolualdehydes are linked in the TN to their condensed phases, for which there are some thermochemically relevant experimental data in the literature, the reported BDEs rely heavily on the results of mid-level composite methods given the paucity of literature on experimental or theoretical data involving the benzoyl and toluyl radicals and the prohibitively high cost of state-of-the-art high-level composite calculations for this size of species. Analogously, our attempts to expand the TN with dimethyl benzaldehydes and their related radicals were frustrated by a virtual absence of experimental and worthwhile theoretical data in the literature, combined with the high cost of theoretical calculations even using mid-level composite methods.

The ATcT BDEs of the aldehydic C–H in benzaldehyde and the three tolualdehydes are given at 298.15 and 0 K in Table S6, together with the corresponding enthalpies of formation of the parents and the related radicals. While only the 298.15 K BDEs are discussed below, the corresponding 0 K BDEs (a.k.a. D₀ values) are also given in the same table and are, as expected, approximately 6.3 kJ mol⁻¹ (or ∼2.5 RT) lower. The ATcT uncertainties provided in Table S6 correspond to 95 % confidence intervals, following the standard in thermochemistry (Ruscic, 2014; Ruscic and Bross, 2019), and were obtained by using the full ATcT covariance matrix. Consequently, when the enthalpy of formation of the radical is highly correlated with that of the parent, as happens to be true in benzaldehyde and tolualdehydes, the uncertainty of the resulting BDE is perceptibly lower than the uncertainty that would be obtained by manually propagating the uncertainties of the individual enthalpies of formation in quadrature, since the latter summation assumes zero covariances.

The ATcT BDE of the aldehydic C–H in benzaldehyde is BDE₂₉₈(C₆H₅C(O)-H) = 380.10 ± 0.84 kJ mol⁻¹. This is noticeably higher (by 6.77 ± 0.84 kJ mol⁻¹) than the corresponding BDE of the prototypical aldehyde – acetaldehyde – for which the current version of the ATcT TN produces BDE₂₉₈(CH₃C(O)-H) = 373.37 ± 0.29 kJ mol⁻¹ (essentially unchanged from the web-accessible value in the earlier ATcT TN ver. 1.122p; Rusic and Bross, 2020).

Of particular relevance here is the fact that the aldehydic C–H BDEs in meta- and para-tolualdehyde, which are BDE₂₉₈(m-CH₃C₆H₄C(O)-H) = 379.93 ± 1.13 kJ mol⁻¹ and BDE₂₉₈(p-CH₃C₆H₄C(O)-H) = 379.85 ± 1.13 kJ mol⁻¹, are indistinguishable (within the uncertainty) from each other and when compared to the BDE in benzaldehyde. However, in ortho-tolualdehyde, the corresponding BDE is consistently lower essentially by 4.2 kJ mol⁻¹ (BDE₂₉₈(o-CH₃C₆H₄C(O)-H) = 376.09±1.13 kJ mol⁻¹), lower by 3.85 ± 1.00 kJ mol⁻¹ than that of meta-tolualdehyde, 3.76 ± 1.00 kJ mol⁻¹ than that in para-tolualdehyde and 4.01 ± 0.92 kJ mol⁻¹ than that in benzaldehyde. Therefore, the likely origin of the reactivity differences is simply due to the bond enthalpies in the abstraction of aldehydic H atoms.

Based on the discussion above, it appears that the preponderance of evidence is consistent with the abstraction of the aldehydic H atom. However, could such an abstraction reaction start via the addition of NO₃ to the ring followed by abstraction? To examine this possibility, we carried out quantum mechanical calculations of the reaction pathways in Reaction (R1). Stationary points on the potential energy surface (PES) were optimized with the BH&HLYP density functional and 6-311G(d,p) basis set in Gaussian 16 (Becke, 1993; Frisch et al., 2016), except for the NO₃ radical, for which the MP2-D3h geometry was used. This level of theory and empirical treatment of NO₃ follows Boyd's computational studies with smaller aldehydes, XCHO (X = H, F, Cl, Me) (Mora-Diez and Boyd, 2002). Single-point energies were evaluated at the DLPNO-CCSD(T)/cc-pVTZ level of theory with tight SCF convergence and TightPNO cutoffs in Orca (Neese, 2012; Riplinger and Neese, 2013; Riplinger et al., 2013). Relative energetics with this basis set are essentially converged, since the effect of using cc-pVQZ on the activation barrier is less than 1 kJ mol⁻¹. The calculated PES is shown in Fig. 6. Computed enthalpic and Gibbs energy changes include unscaled vibrational zero-point energies and translational, rotational and vibrational contributions at 298.15 K (Luchini et al., 2020).

Figure 6Pathways for the reaction between BA and NO₃ calculated using DLPNO-CCSD(T)/cc-pVTZ//BH&HLYP/6-311G(d,p). Enthalpic and Gibbs energy values are in kilojoules per mole (kJ mol⁻¹). Key distances are in Ångströms (Å).

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The computed reaction pathways show that the NO₃ radical can form a dearomatized σ adduct (Fig. 6, LHS). The most stable of these adducts (by more than 10 kJ mol⁻¹) occurs at the para-position. While this complexation is exothermic, it is endergonic by 17.0 kJ mol⁻¹ due to unfavorable entropic effects, implying this is a readily reversible process. H-atom transfer first forms a pre-reaction complex with the aldehydic group. This complex can undergo H-atom abstraction to yield the stable products observed in our experiments. Application of the Bigeleisen–Mayer equation to this H-atom transfer transition structure (TS) results in a computationally predicted primary KIE of 2.16 (2.17 with Bell's 1D-tunneling correction) (Bigeleisen and Mayer, 1947; Paton, 2016; Rzepa, 2015). This value is almost identical to the measure KIE of 1.92.

Table 3Summary of rate coefficients and estimated atmospheric lifetimes of benzaldehyde (BA), o-tolualdehyde (O-TA), m-tolualdehyde (M-TA), p-tolualdehyde (P-TA), 2,4-dimethylbenzaldehyde (2,4-DMBA), 2,5-dimethylbenzaldehyde (2,5-DMBA) and 3,5-dimethylbenzaldehyde (3,5-DMBA) with respect to their reactions with OH, NO₃ and Cl at 298 ± 2 K and atmospheric pressure. ^a For comparison, the rough photolysis lifetimes are also noted for roughly 40^∘ N during summer.

^a We show a range of lifetimes by assuming [OH] = 1–10 × 10⁶ molec. cm⁻³, [NO₃] = 5 × 10⁸ molec. cm⁻³ (Atkinson et al., 1991) and [Cl] = 1 × 10⁴ (Wingenter et al., 1996). ^b The rate coefficients for the OH and Cl atom reactions are from Calvert et al. (2011). ^c Recommended values in Table 2.

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Based on this evidence, we suggest that the reactions of NO₃ with aromatic aldehydes lead to the abstraction of the aldehydic H atom. The cleavage of the aldehydic C–H bond in this step is consistent with the observation that a weaker BDE value is correlated with a larger reaction rate of Reaction (R1). CBS-QB3 calculations (see the Supplement) imply that 2,4-DMBA and 2,5-DMBA, like O-TA, have weaker aldehydic C–H bonds than the other aromatic aldehydes that lack an ortho-substituent. Since the geometry of the formyl radical is more linear than the aldehyde (the C–C–O angle increases by around 4^∘ upon H-atom abstraction), steric strain relief is likely a contributing factor to the C–H bond weakening by an ortho-methyl substituent. Additionally, charge transfer of 0.22e from BA to NO₃ occurs in the computed H-atom transfer TS, consistent with the observation that additional electron-donating substituents, such as methyl groups, promote Reaction (R1). To sum up, the combination of the changes in the C–H bond energies and the changes in the variations in the initial addition to form a pre-reaction complex contributed to the observed reactivity trend.

There are potential future experiments that could shed light on the proposed reaction pathway. They include the following: (1) measurement of the temperature dependence of the reaction rate coefficient; (2) investigating the influence of various isotopic substitutions (e.g., OD reaction studies); (3) studying further substitution of the aromatic ring, for example, with fluorine; and (4) directly detecting the radical formed in the reaction. Further quantum calculations may also be useful.