# Theoretical and experimental study of peroxy and alkoxy radicals in the NO 3 -initiated oxidation of isoprene

L. Vereecken, P. T M Carlsson, A. Novelli, F. Bernard, S. S Brown, C. Cho, J.

N Crowley, H. Fuchs, Wahid Mellouki, D. Reimer, et al.

► To cite this version:

L. Vereecken, P. T M Carlsson, A. Novelli, F. Bernard, S. S Brown, et al.. Theoretical and experimental study of peroxy and alkoxy radicals in the NO 3 -initiated oxidation of isoprene. Physical Chemistry Chemical Physics, 2021, 23 (9), pp.5496-5515. 10.1039/d0cp06267g. insu-03352185

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Cite this: Phys. Chem. Chem. Phys.,
2021, **23**, 5496

# Theoretical and experimental study of peroxy and alkoxy radicals in the NO₃-initiated oxidation of isoprene†

L. Vereecken, ID* a P. T. M. Carlsson, ID a A. Novelli, ID a F. Bernard,‡ b

S. S. Brown, ID cd C. Cho, ID a J. N. Crowley, ID e H. Fuchs, ID a W. Mellouki, ID b

D. Reimer, ID a J. Shenolikar, e R. Tillmann, ID a L. Zhou,§ b

A. Kiendler-Scharr ID a and A. Wahner ID a

The initial stages of the nitrate radical (NO₂) initiated oxidation of isoprene, in particular the fate of the peroxy (RO₂) and alkoxy (RO) radicals, are examined by an extensive set of quantum chemical and theoretical kinetic calculations. It is shown that the oxidation mechanism is highly complex, and bears similarities to its OH-initiated oxidation mechanism as studied intensively over the last decade. The nascent nitrated RO₂ radicals can interconvert by successive O₂ addition/elimination reactions, and potentially have access to a wide range of unimolecular reactions with rate coefficients as high as 35 s⁻¹; the contribution of this chemistry could not be ascertained experimentally. The chemistry of the alkoxy radicals derived from these peroxy radicals is affected by the nitrate moiety, and can lead to the formation of nitrated epoxy peroxy radicals in competition with isomerisation and decomposition channels that terminate the organic radical chain by NO₂ elimination. The theoretical predictions are implemented in the FZJ-NO₃-isoprene mechanism for NO₃-initiated atmospheric oxidation of isoprene. The model predictions are compared against peroxy radical (RO₂) and methyl vinyl ketone (MVK) measurements in a set of experiments on the isoprene + NO₃ reaction system performed in the SAPHIR environmental chamber (IsopNO₃ campaign). It is shown that the formation of NO₂ from the peroxy radicals can prevent a large fraction of the peroxy radicals from being measured by the laser-induced fluorescence (ROxLIF) technique that relies on a quantitative conversion of peroxy radicals to hydroxyl radicals. Accounting for the relative conversion efficiency of RO₂ species in the experiments, the agreement between observations and the theory-based FZJ-NO₃-isoprene model predictions improves significantly. In addition, MVK formation in the NO₃-initiated oxidation was found to be suppressed by the epoxidation of the unsaturated RO radical intermediates, allowing the model-predicted MVK concentrations to be in good agreement with the measurements. The FZJ-NO₃-isoprene mechanism is compared against the MCM v3.3.1 and Wennberg et al. (2018) mechanisms.

Received 3rd December 2020,
Accepted 8th February 2021

DOI: 10.1039/d0cp06267g

rsc.li/pccp

## 1 Introduction

Of the volatile organic compounds (VOCs) emitted to the atmosphere, isoprene is among the most important, contributing

half of the mass of non-methane VOCs released.¹ Its tropospheric oxidation is predominantly initiated by hydroxyl (OH) radicals during the daytime, but at nighttime the lack of photolytic sources of OH shifts the main initiation channels to the nitrate radical,

<figure><img src="image_3.png" /></figure>

<footnote>a Institute for Energy and Climate Research, Forschungszentrum Jülich GmbH, 52428 Jülich, Germany. E-mail: l.vereecken@fz-juelich.de</footnote>

<footnote>b Institut de Combustion, Aérothermique, Réactivité et Environnement (ICARE), CNRS (UPR 3021)/OSUC, 1C Avenue de la Recherche Scientifique, 45071 Orléans CEDEX 2, France</footnote>

<footnote>c NOAA Chemical Sciences Laboratory, 325 Broadway, Boulder, CO 80305, USA</footnote>

<footnote>d Department of Chemistry, University of Colorado Boulder, Boulder, CO 80209, USA</footnote>

<footnote>e Atmospheric Chemistry Department, Max-Planck-Institut für Chemie, 55128 Mainz, Germany</footnote>

<footnote>† Electronic supplementary information (ESI) available: Additional oxidation schemes, rate coefficients, experimental data, modeling results, RO₂ speciation and conversion efficiencies, discussion of converter- and fluorescence cell specific chemistry, the full FZJ-NO₃-isoprene model, and calculated geometries, frequencies and energies for all intermediates and transition states. See DOI: 10.1039/d0cp06267g</footnote>

<footnote>‡ Present address: Laboratoire de Physique et Chimie de l'Environnement et de l'Espace (LPC2E), Centre National de la Recherche Scientifique (CNRS), Université d'Orléans, Observatoire des Sciences de l'Univers en Région Centre - Val de Loire (OSUC), Orléans, France.</footnote>

<footnote>§ Present address: College of Architecture and Environment, Sichuan University, Chengdu, China.</footnote>
$NO_3$, and $O_3$.²⁻⁶ Although isoprene emissions are predominantly biogenic and light-driven, residual isoprene is left during the night, allowing a sizable fraction of the emitted isoprene to be oxidized by $NO_3$ in the nocturnal boundary layer.⁷⁻⁹ Furthermore, under some conditions $NO_3$ oxidation can still contribute for a sizable fraction to daytime atmospheric VOC oxidation.¹⁰,¹¹

The OH-initiated reaction of isoprene has been well-studied, where the last decade has seen many studies examining the complex oxidation pathways, the formation of oxygenated products, and the regeneration of OH radicals.⁴,¹²⁻²² The oxidation was shown to comprise a rapidly branching mechanism where correct treatment of the site-specificity of the initial OH addition and subsequent (reversible) $O_2$ addition is critical:

$$ \begin{array}{l} \text{isoprene} + \text{OH} \rightarrow \text{HO-isoprene radicals (4 isomers)} \quad (\text{R1}) \\ \text{HO-isoprene} + \text{O}_2 \leftrightarrow \begin{array}{l} \text{HO-isoprene-OO}^\bullet \text{ peroxy radicals} \\ \text{(8 isomers)} \end{array} \quad (\text{R2}) \end{array} $$

The product speciation is sensitive to the rate of unimolecular reactions of the peroxy radicals ($RO_2$) formed, i.e. redissociation by $O_2$ loss or isomerisation by H-migration, in competition with more traditional bimolecular reaction of these $RO_2$ with $NO$, $NO_3$, $HO_2$ and $R'O_2$ co-reactants. Due to the critical role of unimolecular $RO_2$ reactions in OH/$HO_x$ regeneration, the formation of highly oxidized organic molecules (HOMs), and of low-volatility compounds partitioning to the aerosol phase, these reactions have received significant attention in recent years, both for isoprene and for other VOCs.²³⁻³³

Although the reaction of the $NO_3$ radical with isoprene can be expected to show the same complexity and to proceed through similar pathways, currently available mechanisms such as the Master Chemical Mechanism³⁴⁻³⁶ or the recent model by Wennberg et al.⁴ tend to include only a simplified version with a selected set of intermediates. Similar to the OH-initiated oxidation though, analyses based on the full branched reaction mechanism are necessary to elucidate the chemistry, and to decide which reactions can be omitted in specific reaction conditions. As indicated in a recent perspective on mechanism development,³⁷ the formulation of such (near-)explicit models is an important tool in tackling modern challenges facing atmospheric sciences. Literature data³⁸ suggests that nitrate substitution leads to slower radical chemistry compared to OH-substitution, and the relative importance of the individual channels can be expected to be different between OH- and $NO_3$-initiated isoprene chemistry. A recent review by Wennberg et al.⁴ gives a good overview of the status quaestionis of isoprene oxidation by OH and $NO_3$, based on the available literature on the $NO_3$-initiated oxidation of isoprene up to now.³⁹⁻⁴⁸

In this work, we investigate several aspects of the first stages of the $NO_3$-initiated oxidation of isoprene, and of measurements of nitrated $RO_2$ radicals, as summarized in Fig. 1. First, we present a combined theoretical and experimental study on the initial steps in the isoprene + $NO_3$ + $O_2$ reaction mechanism, i.e. the formation and destruction of the initial set of 8 nitrated alkylperoxy radical isomers (called nitrate-$RO_2$ hereafter). The subsequent chemistry of the isoprene-$NO_3$ alkylperoxy and alkoxy radicals is likewise examined in detail. Their fate as governed by the competition between unimolecular and bimolecular reactions is important not only for the atmospheric chemistry of isoprene, but also plays a critical role in the experimental detection of the nitrate-$RO_2$ radicals by a ROxLIF instrument. For the latter, we extend the

<figure><img src="image_4.png" /><figcaption>Fig. 1 Summarizing scheme showing the investigated steps, which includes the $NO_3$ and (reversible) $O_2$ addition (site- and stereospecificity omitted), unimolecular chemistry of the nitrate peroxy and alkoxy radicals, and interpretation of the experimental $RO_2$ and MVK/MACR measurements. All chemistry is implemented in the FZJ-$NO_3$-isoprene model.</figcaption></figure>

<figure><img src="image_5.png" /></figure>
recent work by Novelli *et al.*⁴⁹ on nitrate-substituted alkoxy radicals (called nitrate-RO hereafter) to the nitrate-RO derived from isoprene. The chemistry of these unsaturated alkoxy radicals can proceed by reversible epoxidation and subsequent O₂ capture, which affects both the detection of RO₂ in the ROxLIF instrument, and the yield of MVK and MACR in the SAPHIR chamber and the atmosphere. The chemistry characterized is implemented in the FZJ-NO₃-isoprene model.

# 2 Methodologies

## 2.1 Theoretical methodology

The nitrate-RO₂ and nitrate-RO radicals derived from isoprene + NO₃ were first optimized using the M06-2X/cc-pVDZ level of quantum chemical theory,⁵⁰,⁵¹ characterizing all conformers of reactants and transition states for the reactions studied. The resulting geometries were re-optimized at the M06-2X/aug-cc-pVTZ level of theory,⁵⁰ and combined with single point energy calculations on the lowest conformers at the CCSD(T)/aug-cc-pVTZ level of theory.⁵² ZPE corrections are done at the M06-2X/aug-cc-pVTZ level of theory, with vibrational wavenumbers scaled by 0.971.⁵³,⁵⁴ All quantum chemical calculations were performed using the Gaussian-16 software suites.⁵⁵

The rate coefficients of the reactions are obtained using multi-conformer transition state theory, MC-TST,⁵⁶,⁵⁷ incorporating the characteristics of all conformers in a rigid rotor harmonic oscillator approximation, as obtained at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ level of theory. Tunneling is included using an asymmetric Eckart barrier correction.⁵⁸,⁵⁹ At the chosen level of theory used here, the rate coefficients are expected to have an accuracy of a factor of 2 to 4. We also compare the rate coefficient predictions against available structure-activity relationships (SARs) for alkoxy decomposition³⁸,⁴⁹ and H-migration,⁶⁰ and RO₂ radical H-migration.³³ The analysis of nitrate-RO₂ thermal equilibrium population was likewise based on the ratios of the multi-conformer RO₂ partition functions. The method for calculating bulk rate coefficients across rapidly equilibrating groups of reactants is already described for conformer and isomer equilibration by internal rotation⁶¹ or H-migration;²⁷,³³ it is also applicable¹²,¹³ to RO₂ populations equilibrated by O₂ addition/elimination as in the nitrate-RO₂ radicals discussed in this work. Note that the rate of O₂ addition forming the RO₂ intermediates, and their reverse O₂ elimination reactions, cannot be predicted *a priori* with the necessary accuracy for the task at hand, owing to the difficulties in characterizing the (near-)barrierless transition state on the flat potential energy surface for recombination of a doublet radical with a triplet biradical. We will thus base our analysis for the R to RO₂ interconversion on the more reliable equilibrium constants, as discussed below.

The (de-)epoxidation reactions characterized in this work are fast, nearing the collision limit, and deviations from the Boltzmann distribution might occur. Any chemical activation effects depend on temperature, pressure, and the bath gas, and would be different for each source reaction of the epoxidizing

alkoxy radical as formed from the parent RO₂ radical reacting with NO, NO₃, HO₂ and each of the individual R'O₂. Nguyen and Peeters²¹ examined the reaction rate of a similar epoxidation reaction based on energy-specific *versus* Boltzmann population based paradigms, but found only small differences. A second important criterion for thermalization is the rate of effective loss of conformers out of the epoxidation systems. In this work, these are unimolecular reactions and recombination with O₂ removing the interconverting alkoxy and epoxy-alkyl radicals. The effective loss rates are typically slower than the (de-)epoxidation reactions, allowing for substantially more collisions than would be expected solely from the (de-)epoxidation rates, and hence provide better adherence to the thermal Boltzmann distribution across all conformers. To estimate the impact of chemical activation, we examined the fraction of prompt decomposition of 1-NO₃-isoprene-2-O• radicals, the main alkoxy radical in our system, to MVK + NO₂ (see ESI†).⁶² At 1 bar as in the SAPHIR chamber, we find that prompt decomposition is negligible, and all of the 1-NO₃-isoprene-2-O• radicals form epoxy-peroxy radicals. At 25 mbar, we find some prompt decomposition only at internal energies above 17 kcal mol⁻¹, and reaching a contribution of 10% only at 21 kcal mol⁻¹, while the internal energy is estimated to be on average less than that. As such, we estimate that chemical activation effects are not overly critical, and the product distributions predicted in this work are sufficiently accurate even if the absolute rate coefficient may carry a somewhat larger uncertainty, and the predicted detectability of the nitrate-RO₂ are likely somewhat overestimated. Quantifying the chemical activation effects, even in the low-pressure converter, are thus considered outside the scope of this work.

## 2.2 Experimental methodology

The experiments described here were part of a larger campaign on the NO₃-initiated oxidation of isoprene (IsopNO₂ campaign) conducted in the atmospheric simulation chamber SAPHIR. More details about the campaign can be found in Dewald *et al.*⁴⁶ The SAPHIR chamber is made of a double-wall Teflon (FEP) film that is inert, and is kept under slightly higher than ambient pressure (by ~30 Pa) to avoid external air penetrating the chamber. Due to small leakages and air consumption by instruments, a steady replenishment flow keeps the over-pressure constant, causing trace gases to be diluted at a rate of ~6% h⁻¹. More details regarding the chamber can be found elsewhere.⁶³⁻⁶⁵

For all three experiments described within this study, the chamber was cleaned before each experiment by flushing with more than 6 times its volume with ultra-pure synthetic air provided by mixing nitrogen and oxygen (Linde, >99.99990%). Isoprene, O₃ and NO₂ were injected several times over the course of one experiment. Between 1.8 and 6 ppbv of isoprene were injected directly from the liquid (99% purity, Sigma Aldrich), while O₃ was produced by a silent discharge ozonizer (O₃onia) and added to reach concentrations between 40 and 110 ppbv. NO₂ was added *via* calibrated flow controllers as a dilution of 519 ppm in N₂ for concentrations between 3 and 25 ppbv. Two fans in the chamber ensure complete mixing of trace gases
within 2 min. The NO₃ oxidant is formed rapidly in the reaction of O₃ with NO₂:

$$NO_2 + O_3 \rightarrow NO_3 + O_2 \quad (R3)$$

Concentrations of HO₂ and RO₂ radicals were measured with the laser-induced fluorescence (LIF) instrument permanently in use at the SAPHIR chamber and described previously.⁶⁶,⁶⁷ Briefly: the instrument measures HO₂ by conversion to OH radicals in the fluorescence cell (~4 hPa) by reaction with NO. Several studies⁶⁷,⁶⁸ have highlighted how RO₂ radicals can interfere with the HO₂ detection because the alkoxy radicals formed in the reaction of RO₂ radicals with NO, may decompose and/or react with O₂ sufficiently fast such that a detectable amount of HO₂ radical is produced despite the short residence time (<4 ms) in the fluorescence cell. In order to reduce the impact of this interference, the concentration of NO in the HO₂ detection cell was reduced to ~2.5 × 10¹³ molecule cm⁻³ in the experiments in this work. However, as discussed in detail in the ESI,† the modelled HO₂ still differs substantially by up to a factor 10 from the measured HO₂ radical concentrations, and at this time we are unable to ascertain whether this is due to missing chemistry in the model, remaining interference in the measurement, or a combination thereof. The analysis in this work will thus consider two limiting cases, one with the modelled HO₂ concentration constrained to the measurement, and the other with the modelled HO₂ unconstrained.

For the measurement of RO₂ radicals using the ROxLIF system, these RO₂ are first converted into alkoxy radicals in a converter (~25 hPa) by reactions with NO. Subsequent chemistry of these RO radicals leads to formation of HO₂ radicals, which are sampled in the fluorescence cell (~4 hPa) downstream of the converter and are detected by OH fluorescence described above. The conversion efficiency through the ROxLIF system is calibrated using a reference RO₂ (CH₃OO). The final signal also includes the contribution from HO₂ radicals present in the air sampled from the chamber, and the RO₂ concentration is derived by subtracting this contribution from the ROxLIF measurement based on the HO₂ LIF measurement described higher. A recent paper by Novelli et al.⁴⁹ highlights how the LIF technique is likely to be blind to specific nitrated RO₂ radicals due to the necessity of an OH or an HO₂ radical to be formed for an RO₂ radical to be detected. Specifically, it was found that the LIF technique cannot measure nitrated RO₂ radicals formed from cis-2-butene and 2,3-dimethyl-2-butene, as the corresponding alkoxy radicals decompose to NO₂ instead of forming HOₓ radicals. Similarly, the theoretical rate predictions for isoprene alkoxy radical reactions by the SAR described in that paper indicate that many of the nitrate-RO₂ radicals from isoprene would not form HO₂, and thus would not be detectable by the ROxLIF system. In this work, we estimate the conversion efficiencies of the dominant RO₂ to detectable OH by explicit modelling of the converter and fluorescence cell chemistry (see ESI†).

Measurements of isoprene (Fig. S11, ESI†), as well as the sum of methyl vinyl ketone (MVK) and methacrolein (MACR)

were performed by VOCUS PTR-MS (Tofwerk AG and Aerodyne Research Inc.). The VOCUS isoprene concentration profiles were calibrated against the change in kOH and kNO₃ (total OH and NO₃ reactivity measurements as shown for these experiments in Dewald et al.⁴⁶) at the time of injection, to correct for any dependence of the VOCUS signal on relative humidity. Our kinetic model (see below) finds MVK and MACR to be present in similar concentrations. Therefore, we convert the signal strength measured by the VOCUS to the summed concentration of MVK + MACR by applying the mean of their respective instrumental sensitivities. NO₃ concentrations (Fig. S11, ESI†) were measured by a custom-built cavity ring down spectroscopy instrument as described in Dewald et al.⁴⁶

## 3 Theoretical results on the initial NO₃ and O₂ addition on isoprene

The site- and stereo-specific NO₃ and O₂ addition chemical scheme for isoprene is reminiscent of the LIM¹²,¹³ mechanism for isoprene + OH, i.e. both OH and NO₃ addition leads to allyl-resonance stabilized alkyl radicals, which can reversibly add O₂ on several radical sites forming distinct RO₂ radicals. Such schemes for isoprene + OH are already implemented in the Master Chemical Mechanism, MCMv3.3.1,³⁶ and in the recent isoprene mechanism described by Wennberg et al.⁴ Fig. 2 depicts the scheme for the dominant NO₃ radical addition channel on carbon C1 in isoprene, which constitutes⁴ 87% of the reaction flux. The ESI† has the corresponding schemes for addition on carbon C4, with a contribution⁴ of 13%, and on the inner carbons C2 and C3, which have only a minor contribution and are neglected here. The addition reaction is exothermic by ~32 kcal mol⁻¹ for the formation of resonance-stabilized alkyl radicals. The redissociation of NO₃-isoprene adducts to the reactants is negligible in our reaction conditions. Stereo-isomerisation of the cis- and trans-alkyl radicals at thermal energies is slow compared to O₂ addition and has no significant influence. Theoretical work by Peeters et al.¹²,¹³ and Dibble⁶⁹ showed however that the internal rotation is fast at the internal energies available through the addition of the radical oxidant. As discussed in more detail in the ESI,† we adopt an initial distribution of 1:1 for cis:trans 1-NO₃-isoprenyl, and 7:3 for cis:trans 4-NO₃-isoprenyl, based on these studies.

Similar to OH-adducts of isoprene, the O₂ addition is not overly exothermic, ≤20 kcal mol⁻¹, and the O₂ addition is reversible, allowing re-equilibration of the RO₂ isomers by repetitive O₂ elimination/addition events. This re-equilibration occurs in competition with unimolecular and bimolecular loss processes of the RO₂ radicals, as discussed in a later section. An a priori characterization of the O₂ addition and elimination reaction rates at sufficient accuracy for a kinetic model is computationally very expensive due to the (nearly) barrierless addition process,¹² and the complexity in the quantum chemical description of the spin states of the many unpaired electrons. At this time, we therefore choose not to predict rate coefficients for these reactions directly. Instead, we adopt O₂

<figure><img src="image_6.png" /></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 2 Reaction scheme for the site-specific addition of NO₂ on C1 of isoprene, and the subsequent stereo-specific addition of O₂. The ESI† includes schemes for NO₃-addition on carbons C2, C3 and C4. Co-reactant concentrations are taken as in Peeters et al.¹²</figcaption></figure>

addition rate coefficients as for the OH-isoprenyl + O₂ reaction in the MCM v3.3.1 as based on the available literature data¹²,¹³,¹⁸,³⁶ and evaluated by Novelli et al.¹⁴ The detailed analysis of Novelli et al.¹⁴ showed that a suitable ratio of formation to destruction rates is critical for a correct product distribution. The rate coefficients for O₂ elimination from NO₃-isoprene-O₂ radicals are then obtained from the forward O₂-addition reaction rates and theory-derived equilibrium constants, similar to the approach by Peeters et al.¹³ More details, the temperature-dependent rate coefficients, and the equilibrium constants are provided in the ESI.†

# 4 Theoretical results on nitrate-RO₂

## 4.1 Elementary reactions

Table 1 summarizes the rate coefficients obtained for the unimolecular reactions of RO₂ radicals formed in the isoprene + NO₃ + O₂ reaction. The theoretical results are compared against SAR predictions in the ESI.†

1,6-H-Migration of the α-nitrooxy H-atom (–CH₂ONO₂) is the most favorable transition state, followed by migration of the methyl H-atoms. 1,4-H-Migrations are never competitive, nor are H-migrations between trans-substituents of the double bond. HO₂ elimination with either the α-nitrooxy or the methyl H-atom was only examined for a single compound (1-ONO₂-isoprene-2-OO•) but as expected this reaction has sizable barriers exceeding 26 kcal mol⁻¹, in agreement with earlier work,⁷⁰⁻⁷³ and can be neglected. Ring closure reactions should be divided into three categories: formation of 5-membered peroxide rings with an endo-cyclic alkyl radical site, formation of 5-membered rings with an exo-cyclic radical site, and formation of 6-membered rings (here always with an endo-cyclic radical site). Most nitrate-RO₂ discussed here only have access to the first category, which typically has higher barriers ≥25 kcal mol⁻¹, making them non-competitive. The barriers

are a direct result of the ring strain in the TS, where the double bond is still intact and reaching the outer alkenic carbon with a 5-membered ring structure induces significant ring strain. If, on the other hand, the ring closure occurs on the inner carbon of the double bond, as e.g. in 2-ONO₂-isoprene-1-OO• or 3-ONO₂-isoprene-4-OO• formed in the minor isoprene + NO₃ addition channels, the ring strain in the TS is significantly less and ring closure TS energies of ~13–15 kcal mol⁻¹ are found even for 5-membered rings. For 6-membered ring closure, here possible only in the latter two nitrate-RO₂, the ring strain is significantly reduced despite the endo-cyclic double bond in the TS, and attack on the outer alkenic carbon also has low barriers, 14–16 kcal mol⁻¹.

Compared to the OH-substituted RO₂ radicals formed in isoprene + OH, the unimolecular rate coefficients for nitrate-RO₂ are generally slower. For example, the NO₂-forming 1,6-H-migration in Z-1-ONO₂-isoprene-4-OO• forming HPALD has a calculated rate coefficient k(298 K) = 1.9 × 10⁻² s⁻¹, whereas the analogous OH-regenerating H-shift in Z-1-OH-isoprene-4-OO• has a predicted rate of ~0.5 s⁻¹,¹²⁻¹⁴,⁷⁴ a factor of 25 faster. The few RO₂ for which faster reactions are accessible, such as ring closure in 2- and 3-ONO₂-isoprene-RO₂, are formed only in minor to negligible NO₃ addition channels on isoprene. Unimolecular reactions of nitrate-RO₂ will thus be less important than for OH-RO₂ under atmospheric conditions, and become negligible even for only moderately elevated NOₓ, HO₂, and RO₂ concentrations. In the current experiments, the OH reaction still contributes for ~10% of the isoprene loss, and given the expected small yields through unimolecular channels in the NO₃-isoprene system, and the possibility of formation of isobaric products in other channels, products measurements such as for HPALD can likely not be used to verify a product yield prediction.

## 4.2 Equilibrium populations and bulk rate coefficients

As already discussed in detail in the literature on OH-initiated oxidation of isoprene and aromatic compounds,¹²,¹³,¹⁷ a key

<figure><img src="image_8.png" /></figure>
<table><caption>**Table 1** Theoretical rate predictions for nitrated alkylperoxy radicals derived from isoprene + NO₃ + O₂, at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ with MC-TST level of theory. Indicated are the ZPE-corrected barrier height (E<sub>b</sub>, kcal mol⁻¹), the 298 K rate coefficient (k(298 K), s⁻¹), and the parameters for a Kooij expression k(T) = A × (T/K)ⁿ × exp(-E<sub>a</sub>/T) (A in s⁻¹, E<sub>a</sub> in K). The rate coefficients are the rate of product formation across all equivalent H-atoms</caption><thead><tr><th>Reactant</th><th>Mechanism and products</th><th>E<sub>b</sub></th><th>k(298 K)</th><th>A</th><th>n</th><th>E<sub>a</sub></th></tr></thead><tbody><tr><td rowspan="3">ONO<sub>2</sub><br>·O··</td><td>1,6-Migration of CH<sub>2</sub>ONO<sub>2</sub> H-atom forming OCHC(CH<sub>3</sub>)=CHCH<sub>2</sub>OOH (HPALD I) + NO<sub>2</sub></td><td>23.4</td><td>1.9 × 10<sup>-2</sup></td><td>7.72 × 10<sup>-78</sup></td><td>28.02</td><td>-4158</td></tr><tr><td>Ringclosure to 5-membered ring</td><td>27.5</td><td>2.1 × 10<sup>-9</sup></td><td>2.07 × 10<sup>9</sup></td><td>0.42</td><td>13 062</td></tr><tr><td>1,6-Migration of CH<sub>3</sub> H-atom forming O<sub>2</sub>NOCH<sub>2</sub>C(C*H<sub>2</sub>)=CHCH<sub>2</sub>OOH</td><td>50.4<sup>a</sup></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="3">ONO<sub>2</sub><br>·O··</td><td>1,6-Migration of CH<sub>3</sub> H-atom forming O<sub>2</sub>NOCH<sub>2</sub>C(C*H<sub>2</sub>)=CHCH<sub>2</sub>OOH</td><td>23.3</td><td>1.5 × 10<sup>-3</sup></td><td>2.58 × 10<sup>-84</sup></td><td>30.21</td><td>-4128</td></tr><tr><td>Ringclosure to 5-membered ring</td><td>28.6</td><td>7.2 × 10<sup>-11</sup></td><td>3.43 × 10<sup>4</sup></td><td>1.90</td><td>13 292</td></tr><tr><td>1,6-Migration of CH<sub>2</sub>ONO<sub>2</sub> H-atom forming OCHC(CH<sub>3</sub>)=CHCH<sub>2</sub>OOH (HPALD I) + NO<sub>2</sub></td><td>46.9<sup>a</sup></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">O<sub>2</sub>NO<br>·O··</td><td>Ringclosure to 5-membered ring</td><td>26.6</td><td>2.2 × 10<sup>-8</sup></td><td>3.87 × 10<sup>4</sup></td><td>2.13</td><td>12028</td></tr><tr><td>1,4-Migration of CH<sub>2</sub>ONO<sub>2</sub> H-atom forming NO<sub>2</sub> + OCHC(CH<sub>3</sub>)(OOH)CH=CH<sub>2</sub></td><td>33.1</td><td>1.8 × 10<sup>-8</sup></td><td>8.78 × 10<sup>-73</sup></td><td>26.48</td><td>827</td></tr><tr><td>1,4-Migration of CH<sub>3</sub> H-atom forming O<sub>2</sub>NOCH<sub>2</sub>C(C*H<sub>2</sub>)(OOH)CH=CH<sub>2</sub></td><td>35.9</td><td>1.6 × 10<sup>-10</sup></td><td>4.82 × 10<sup>-75</sup></td><td>27.35</td><td>2170</td></tr><tr><td>HO<sub>2</sub> elimination CH<sub>2</sub>ONO<sub>2</sub> H-atom forming O<sub>2</sub>NOCH=C(CH<sub>3</sub>)CH=CH<sub>2</sub></td><td>26.3</td><td>3.5 × 10<sup>-7</sup></td><td>4.09 × 10<sup>-38</sup></td><td>16.41</td><td>6650</td></tr><tr><td rowspan="3">O<sub>2</sub>NO<sub>2</sub><br>·O··</td><td>HO<sub>2</sub> elimination CH<sub>3</sub> H-atom forming O<sub>2</sub>NOCH<sub>2</sub>C(=CH<sub>2</sub>)CH=CH<sub>2</sub></td><td>28.8</td><td>6.1 × 10<sup>-9</sup></td><td>1.65 × 10<sup>-32</sup></td><td>14.48</td><td>8418</td></tr><tr><td>1,6-Migration of CH<sub>2</sub>ONO<sub>2</sub> H-atom forming HOOCH<sub>2</sub>C(CH<sub>3</sub>)=CHCHO (HPALD II) + NO<sub>2</sub></td><td>22.3</td><td>5.4 × 10<sup>-2</sup></td><td>2.52 × 10<sup>-75</sup></td><td>27.06</td><td>-4374</td></tr><tr><td>1,5-Migration of CH<sub>3</sub> H-atom forming HOOCH<sub>2</sub>C(C*H<sub>2</sub>)=CHCH<sub>2</sub>ONO<sub>2</sub></td><td>25.2</td><td>3.3 × 10<sup>-4</sup></td><td>1.07 × 10<sup>-96</sup></td><td>34.33</td><td>-5178</td></tr><tr><td rowspan="3">O<sub>2</sub>NO<sub>2</sub><br>·O··</td><td>Ringclosure to 5-membered ring</td><td>27.4</td><td>3.1 × 10<sup>-9</sup></td><td>9.51 × 10<sup>8</sup></td><td>0.50</td><td>12 845</td></tr><tr><td>1,5-Migration of CH<sub>3</sub> H-atom forming HOOCH<sub>2</sub>C(C*H<sub>2</sub>)=CHCH<sub>2</sub>ONO<sub>2</sub></td><td>24.4</td><td>4.8 × 10<sup>-4</sup></td><td>2.94 × 10<sup>-97</sup></td><td>34.68</td><td>-5088</td></tr><tr><td>Ringclosure to 5-membered ring</td><td>26.7</td><td>2.0 × 10<sup>-9</sup></td><td>5.01 × 10<sup>7</sup></td><td>0.74</td><td>12 514</td></tr><tr><td rowspan="3">O<sub>2</sub>NO<sub>2</sub><br>·O··</td><td>1,6-Migration of CH<sub>2</sub>ONO<sub>2</sub> H-atom forming HOOCH<sub>2</sub>C(CH<sub>3</sub>)=CHCHO (HPALD II) + NO<sub>2</sub></td><td>47.1<sup>a</sup></td><td></td><td></td><td></td><td></td></tr><tr><td>1,5-Migration of CH<sub>3</sub> H-atom forming CH<sub>2</sub>=C(C*H<sub>2</sub>)CH(OOH)CH<sub>2</sub>ONO<sub>2</sub></td><td>24.0</td><td>8.5 × 10<sup>-4</sup></td><td>5.58 × 10<sup>-89</sup></td><td>32.05</td><td>-4050</td></tr><tr><td>Ringclosure to 5-membered ring</td><td>27.7</td><td>5.1 × 10<sup>-9</sup></td><td>1.03 × 10<sup>7</sup></td><td>1.31</td><td>12 722</td></tr><tr><td rowspan="5">ONO<sub>2</sub><br>·O··</td><td>Ringclosure to 5-membered ring</td><td>14.4</td><td>7.7 × 10<sup>0</sup></td><td>1.04 × 10<sup>7</sup></td><td>1.19</td><td>6218</td></tr><tr><td>(R,S/S,R)-Product (syn)</td><td>14.5</td><td>3.5 × 10<sup>0</sup></td><td>1.63 × 10<sup>7</sup></td><td>1.04</td><td>6348</td></tr><tr><td>(R,R/S,S)-Product (anti)</td><td>14.4</td><td>4.2 × 10<sup>0</sup></td><td>6.94 × 10<sup>6</sup></td><td>1.12</td><td>6176</td></tr><tr><td>Ringclosure to 6-membered ring</td><td>14.7</td><td>2.1 × 10<sup>0</sup></td><td>2.69 × 10<sup>7</sup></td><td>0.91</td><td>6420</td></tr><tr><td>1,5-Migration of CH<sub>3</sub> H-atom forming HOOCH<sub>2</sub>C(C*H<sub>2</sub>)(ONO<sub>2</sub>)CH=CH<sub>2</sub></td><td>25.3</td><td>8.9 × 10<sup>-6</sup></td><td>6.45 × 10<sup>-40</sup></td><td>16.30</td><td>4235</td></tr><tr><td rowspan="4">ONO<sub>2</sub><br>·O··</td><td>Ringclosure to 5-membered ring</td><td>13.4</td><td>4.1 × 10<sup>1</sup></td><td>9.60 × 10<sup>9</sup></td><td>0.12</td><td>5951</td></tr><tr><td>(R,S/S,R)-Product (anti)</td><td>13.4</td><td>3.5 × 10<sup>1</sup></td><td>6.28 × 10<sup>11</sup></td><td>-0.57</td><td>6060</td></tr><tr><td>(R,R/S,S)-Product (syn)<sup>b</sup></td><td>14.7</td><td>5.5 × 10<sup>0</sup></td><td>4.44 × 10<sup>11</sup></td><td>-0.43</td><td>6748</td></tr><tr><td>Ringclosure to 6-membered ring</td><td>15.7</td><td>1.5 × 10<sup>0</sup></td><td>2.47 × 10<sup>13</sup></td><td>-1.00</td><td>7384</td></tr><tr><td rowspan="2">ONO<sub>2</sub><br>·O··</td><td>1,6-Migration of CH<sub>3</sub> H-atom forming CH<sub>2</sub>=C(C*H<sub>2</sub>)CH(ONO<sub>2</sub>)CH<sub>2</sub>OOH</td><td>22.8</td><td>1.7 × 10<sup>-2</sup></td><td>8.97 × 10<sup>-67</sup></td><td>24.55</td><td>-2426</td></tr><tr><td>Ringclosure to 5-membered ring</td><td>13.4</td><td>4.1 × 10<sup>1</sup></td><td>9.60 × 10<sup>9</sup></td><td>0.12</td><td>5951</td></tr></tbody></table>

feature of the atmospheric chemistry of allylic radicals is the reversibility of the O₂ addition. For isoprene in particular this means that the RO₂ radicals can interconvert by redissociation and O₂ addition, in competition with unimolecular and bimolecular RO₂ loss processes. In this context, three RO₂ populations are of interest. The first is the nascent RO₂ distribution formed directly from the isoprene + NO₃ + O₂ reaction sequence. This distribution governs the product distribution at high rates of RO₂ loss, e.g. in experiments with very high co-reactant concentrations. The second is the equilibrium RO₂ population, established when the loss processes are negligible compared to re-equilibration by O₂ elimination/addition. Finally, there is the instantaneous RO₂ distribution, intermediate between the above two limiting

distributions and determined by the competition between RO₂ formation, reactive loss, and re-equilibration as governed by the specific reaction conditions; this distribution can be time-dependent if the environment (e.g. co-reactant concentrations) changes at a time scale comparable to the rate of population change.

These distributions are derived and discussed in more detail the ESI.† Briefly: the nascent RO₂ distribution can in principle be derived from measured product ratios at high co-reactant concentrations (e.g. NO), where the re-equilibration is overwhelmed, but no sufficiently detailed data are available. In this work, we estimate the nascent distribution by assuming a cis:trans ratio for NO₃-isoprenyl radicals as calculated by Peeters et al.¹²,¹³ for the HO-isoprenyl radicals. Reaction rates of the subsequent O₂

<figure><img src="image_9.png" /></figure>

<footnote><sup>a</sup> Energies at the M06-2X/aug-cc-pVTZ level of theory. Given the barrier height, CCSD(T) and rate calculations were not done. <sup>b</sup> Less favorable as the adjacent syn-positioned –CH<sub>3</sub> and –ONO<sub>2</sub> groups induce more geometric hindrance.</footnote>
<figure><img src="image_10.png" /></figure>

addition are adopted from the MCM v3.3.1 for OH-isoprenyl + O₂,³⁶ which are calibrated against the experimental data on RO₂ decomposition from Teng *et al.*¹⁸ and evaluated in Novelli *et al.*¹⁴ Combined, this yields the nascent RO₂ population (see ESI†). The equilibrium RO₂ populations can be predicted directly from the theoretical data. Strictly speaking, this distribution cannot be reached experimentally even in dilute conditions due to (slight) perturbations of the population due to unimolecular and bimolecular reactions. For the OH-initiated oxidation, it was found that in atmospheric conditions the instantaneous isoprene-RO₂ concentration is intermediate between the nascent and equilibrium populations, and that kinetic models need to include all chemical pathways.¹²⁻¹⁴ For nitrated RO₂, unimolecular loss is slower and the instantaneous population is expected to be close to equilibrium distributions under atmospheric conditions, and under the conditions in our experiments.

To aid in the characterization of the nitrate-RO₂, we provide the theoretically derived temperature-dependent equilibrium contributions to the population in Table 2, and shown in Fig. 3 (see ESI† for more populations). At temperatures below 450 K, the population is dominated by 1-ONO₂-isoprene-2-OO• isomers, the most stable of the RO₂ isomers formed after the dominant NO₃ addition on isoprene. The 4-ONO₂-isoprene RO₂ are not dominated by a single RO₂ isomer. The distribution of the RO₂ has its impact on the phenomenological rate coefficient, i.e. the bulk rate coefficient for product formation from the total pool of RO₂ isomers. For unimolecular reactions, these differ from the elementary reaction rates as the re-equilibration allows access to all reaction channels independent of the starting RO₂ isomer, and because the effective

<table><caption>**Table 2** Theoretical predictions for the equilibrium population for nitrated alkylperoxy radicals derived from isoprene + NO₃ + O₂, at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ with MC-TST level of theory. Indicated are the relative energies (kcal mol⁻¹) of the lowest conformer, the 298 K population fraction *f* (298 K), and the parameters for a Kooij expression *f*(*T*) = *F* × (T/K)ⁿ × exp(-*E*<sub>a</sub>/T) (*E*<sub>a</sub> in K). This Boltzmann distribution is attained only in the absence of loss processes, but is closely adhered to under the conditions of our experiments (see ESI)</caption><thead><tr><th>Reactant</th><th><i>E</i><sub>rel</sub></th><th><i>f</i>(298 K)</th><th><i>F</i></th><th><i>n</i></th><th><i>E</i><sub>a</sub></th></tr></thead><tbody><tr><td>ONO<sub>2</sub><sup>•</sup></td><td>1.3</td><td>0.08</td><td>2.59 × 10<sup>2</sup></td><td>-0.96</td><td>788</td></tr><tr><td>ONO<sub>2</sub><sup>•</sup></td><td>2.3</td><td>0.18</td><td>6.55 × 10<sup>9</sup></td><td>-3.18</td><td>1851</td></tr><tr><td>O<sub>2</sub>NO<sup>•</sup></td><td>0.0</td><td>0.74</td><td>4.02 × 10<sup>5</sup></td><td>-2.10</td><td>365</td></tr><tr><td>ONO<sub>2</sub><sup>•</sup></td><td>0.3</td><td>0.20</td><td>1.03 × 10<sup>-3</sup></td><td>0.90</td><td>-34</td></tr><tr><td>ONO<sub>2</sub><sup>•</sup></td><td>0.8</td><td>0.40</td><td>2.72 × 10<sup>2</sup></td><td>-0.92</td><td>373</td></tr><tr><td>ONO<sub>2</sub><sup>•</sup></td><td>0.0</td><td>0.40</td><td>5.44 × 10<sup>1</sup></td><td>-0.50</td><td>-67</td></tr></tbody></table>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 3** Temperature-dependent equilibrium population contribution for the individual RO₂ isomers formed after NO₃ addition to C1 (top) or C4 (bottom) of isoprene.</figcaption></figure>

reactant concentration for any particular channel is only a fraction of the total RO₂ concentration. In Table 3, we provide the bulk rate coefficients for the nitrated RO₂ in an equilibrium population; the experimental bulk rate coefficient can differ as the RO₂ distribution and re-equilibration will be different.

## 5 Theoretical results on nitrate-RO

Table 4 lists the predicted rate coefficients for the most important reaction pathways of the alkoxy radicals formed from the primary nitrate-RO₂ from isoprene + NO₃. The theoretical results are compared against SAR predictions in the ESI.† Decomposition reactions eliminating the nitrate-bearing moiety, and H-migration of the γ-ONO₂ hydrogen atoms are among the most important channels. These reactions lead to fragmentation of the nitrate moiety in the product γ-ONO₂ alkyl radicals, forming NO₂ and aborting the organic radical oxidation chain. In two cases, migration of a methyl H-atom is among the faster reactions, though these H-shifts are typically slower than migration of the γ-ONO₂
<table><caption>**Table 3** Theoretical predictions for bulk rate coefficients of the main unimolecular loss channels for nitrated alkylperoxy radicals derived from isoprene + NO₃ + O₂, in their equilibrium concentrations, at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ with MC-TST level of theory. Indicated are the ZPE-corrected barrier height (kcal mol⁻¹), the 298 K rate coefficient (k(298 K), s⁻¹), and the parameters for a Kooij expression k(T) = A × (T/K)ⁿ × exp(-Eₐ/ T) (A in s⁻¹, Eₐ in K). The rate coefficients are the rate of product formation across all equivalent H-atoms</caption><thead><tr><th>Reactant</th><th>Mechanism and products</th><th>E<sub>b</sub></th><th>k(298 K)</th><th>A</th><th>n</th><th>E<sub>a</sub></th></tr></thead><tbody><tr><td rowspan="3">[Image of a structure with an O<sub>2</sub> molecule, an O<sub>2</sub>NO<sub>2</sub> molecule, and an O<sub>2</sub>NO<sub>2</sub>O<sub>2</sub> molecule]</td><td>Migration of CH<sub>2</sub>-ONO<sub>2</sub> H-atoms forming NO<sub>2</sub> + O=CHC(CH<sub>3</sub>)=CHCH<sub>2</sub>OOH (HPALD I)</td><td>24.7</td><td>1.5 × 10<sup>-3</sup></td><td>2.00 × 10<sup>-75</sup></td><td>27.06</td><td>-3369</td></tr><tr><td>Migration of CH<sub>3</sub> H-atoms forming O<sub>2</sub>NOCH<sub>2</sub>C(C*H<sub>2</sub>)=CHCH<sub>2</sub>OOH</td><td>25.6</td><td>2.6 × 10<sup>-4</sup></td><td>1.69 × 10<sup>-74</sup></td><td>27.03</td><td>-2275</td></tr><tr><td>Total</td><td></td><td>1.7 × 10<sup>-3</sup></td><td>1.25 × 10<sup>-79</sup></td><td>28.62</td><td>-3663</td></tr><tr><td rowspan="3">[Image of a structure with an O<sub>2</sub>NO<sub>2</sub> molecule, an O<sub>2</sub>NO<sub>2</sub> molecule, and an O<sub>2</sub>NO<sub>2</sub>O<sub>2</sub> molecule]</td><td>Migration of CH<sub>2</sub>ONO<sub>2</sub> H-atoms forming NO<sub>2</sub> + HOOCH<sub>2</sub>C(CH<sub>3</sub>)=CHCHO (HPALD II)</td><td>22.7</td><td>1.1 × 10<sup>-2</sup></td><td>2.60 × 10<sup>-78</sup></td><td>27.97</td><td>-4410</td></tr><tr><td>Migration of CH<sub>3</sub> H-atoms forming HOOCH<sub>2</sub>C(C*H<sub>2</sub>)=CHCH<sub>2</sub>ONO<sub>2</sub></td><td>25.2</td><td>2.0 × 10<sup>-4</sup></td><td>8.02 × 10<sup>-95</sup></td><td>33.76</td><td>-4718</td></tr><tr><td>Migration of CH<sub>3</sub> H-atoms forming CH<sub>2</sub>=C(C*H<sub>2</sub>)CH(OOH)CH<sub>2</sub>ONO<sub>2</sub></td><td>23.9</td><td>3.4 × 10<sup>-4</sup></td><td>3.04 × 10<sup>-88</sup></td><td>31.55</td><td>-4116</td></tr><tr><td></td><td>Total</td><td></td><td>1.1 × 10<sup>-2</sup></td><td>3.24 × 10<sup>-82</sup></td><td>29.36</td><td>-4732</td></tr></tbody></table>

hydrogen atoms. All the above nitrate-RO reactions are typically faster than the reaction of the nitrate-RO with O₂, forming a carbonyl and HO₂, thus often forgoing chain termination forming HO₂ by formation of NO₂ instead. It is important to note that reactions of the nitrate-RO are typically slower than the analogous reactions of hydroxylated alkoxy radicals formed in the OH-initiated oxidation of isoprene, enabling alternative reactions to become competitive. In particular, the adjacent double bond allows for epoxidation reactions (see Table 4), leading to the formation of nitrated epoxy alkyl radicals, which are isoenergetic with the parent nitrate-RO radicals within a few kcal mol⁻¹. Epoxidation reactions in unsaturated compounds has been studied before, mainly in the atmospheric oxidation of aromatic compounds,⁷⁵,⁷⁶ and are found to be fast and reversible (see below). The competitive epoxidation has important ramifications for the predicted product distribution. For example, the main fate of 1-NO₃-isoprene-2-O• is now predicted to be formation of the epoxide, hampering formation of methyl vinyl ketone (MVK), a well-known product of atmospheric isoprene oxidation. This epoxidation channel would also preclude MVK formation as proposed by Wennberg *et al.*⁴ in the reaction of 1-NO₃-isoprene-2-O• with HO₂. As the epoxidation is reversible, the final product formation from the nitrate-RO can only be assessed through an explicit chemical mechanism. Contrary to the ring closure reaction in nitrate-RO₂, ring closure in the isoprene-derived nitrate-RO radicals across longer spans than epoxidation is not competitive.

# 6 Theoretical results for epoxy radicals

Chemical schemes for epoxidation and subsequent chemistry are shown in Fig. 4. Due to the highly branching nature of the chemistry, not all pathways were theoretically characterized,

but rely on SAR predictions instead. The theoretical predictions available are discussed below.

## 6.1 Epoxy-alkyl radicals: ring breaking versus O₂ addition

The epoxy-alkyl radicals formed from the nitrate-RO have two reaction pathways available: ring opening back to the nitrate-RO, or addition of an O₂ molecule, forming an epoxy-nitrate-RO₂. The epoxy-alkyl radicals have an interesting impact on the stereo-specificity of the reaction, where the Z- and E-1-NO₃-isoprene-4-O• radicals form the same alkyl-epoxy radical (Table 5 and ESI†). As the internal rotation of the epoxy-moiety is comparable in rate or faster than the epoxy ring opening,²¹ this enables Z/E-stereo-isomerisation by reversible epoxidation; similar stereo-isomerisation has been reported earlier by Nguyen and Peeters²¹ for other unsaturated alkoxy radicals. A different type of stereo-chemistry is found for the 1-NO₃-isoprene-2-O• radical, which leads to two stereo-specific alkyl-epoxy radicals with distinct chemistry (Table 5 and Fig. 4). Similar stereo-specific considerations apply to the intermediates formed after NO₃ addition on C4 of isoprene (see ESI†). As the epoxidation is essentially energy-neutral and the barriers for ring opening/closing are low, the ring opening is as fast as the epoxidation reaction, k(298 K) ~ 10⁸ s⁻¹, enabling fast interconversion between the nitrate-RO and the epoxy-alkyl radical (Tables 4 and 5). The ultimate fate of the nitrate-RO is then determined by the competition between O₂ addition on the epoxy-alkyl radical, versus the dissociation or H-migration in the nitrate-RO. Recombination reactions of larger alkyl radicals with O₂ are comparatively fast, k(298 K) ~ 5.6 × 10⁻¹³ to 1.7 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹.⁷⁷⁻⁸⁰ Contrary to the nitrate-RO₂ discussed above, the product epoxy-RO₂ are not expected to redissociate as the parent epoxy-alkyl radicals are not resonance stabilized. Adopting a value for O₂ addition of

<figure><img src="image_13.png" /></figure>
<table><caption>**Table 4** Theoretical rate predictions for nitrate-RO radicals derived from isoprene + NO₃, at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ with MC-TST level of theory. Indicated are the ZPE-corrected barrier height (E<sub>b</sub>, kcal mol<sup>-1</sup>), the 298 K rate coefficient (k(298 K), s<sup>-1</sup>), and the parameters for a Kooij expression k(T) = A × (T/K)<sup>η</sup> × exp(-E<sub>a</sub>/T) (A in s<sup>-1</sup>, E<sub>a</sub> in K). Reaction channels anticipated by SARs to be negligible are omitted</caption><thead><tr><th>Reactant</th><th>Mechanism and products</th><th>E<sub>b</sub></th><th>k(298 K)</th><th>A</th><th>n</th><th>E<sub>a</sub></th></tr></thead><tbody><tr><td rowspan="2">1,5-Shift of O<sub>2</sub>NOCH<sub>2</sub> H-atom forming NO<sub>2</sub> + O=CHC(CH<sub>3</sub>)=CHOH</td><td>Epoxidation forming 1-NO<sub>3</sub>-3,4-epoxy-isoprene-2-yl</td><td>7.9<br>5.6</td><td>5.1 × 10<sup>7</sup><br>2.3 × 10<sup>8</sup></td><td>8.93 × 10<sup>-30</sup><br>1.62 × 10<sup>12</sup></td><td>13.31<br>-0.01</td><td>-2629<br>2622</td></tr><tr><td>1,5-Shift of CH<sub>3</sub> H-atom forming O<sub>2</sub>NOCH<sub>2</sub>C(C*H<sub>2</sub>)=CH<sub>2</sub>OH</td><td>Epoxidation forming 1-NO<sub>3</sub>-3,4-epoxy-isoprene-2-yl</td><td>9.7<br>5.9</td><td>2.2 × 10<sup>6</sup><br>1.2 × 10<sup>8</sup></td><td>2.08 × 10<sup>-37</sup><br>1.24 × 10<sup>10</sup></td><td>15.82<br>0.77</td><td>-2675<br>2682</td></tr><tr><td rowspan="4">Decomposition forming NO<sub>2</sub> + CH<sub>2</sub>O + MVK</td><td>Epoxidation forming syn-1-NO<sub>3</sub>-2,3-epoxy-isoprene-4-yl</td><td>9.5<br>13.6</td><td>2.7 × 10<sup>5</sup><br>8.0 × 10<sup>2</sup></td><td>2.69 × 10<sup>6</sup><br>1.00 × 10<sup>6</sup></td><td>2.24<br>2.47</td><td>4491<br>6325</td></tr><tr><td>Epoxidation forming anti-1-NO<sub>3</sub>-2,3-epoxy-isoprene-4-yl</td><td>5.0<br>4.7</td><td>4.7 × 10<sup>8</sup><br>9.8 × 10<sup>8</sup></td><td>8.96 × 10<sup>9</sup><br>4.24 × 10<sup>9</sup></td><td>0.78<br>0.92</td><td>2207<br>1996</td></tr><tr><td>1,5-Shift of CH<sub>2</sub>ONO<sub>2</sub> H-atom forming HOCH<sub>2</sub>C(CH<sub>3</sub>)=CHCH<sub>2</sub>O + NO<sub>2</sub></td><td>Epoxidation forming 4-NO<sub>3</sub>-1,2-epoxy-isoprene-3-yl</td><td>7.9<br>6.3</td><td>2.7 × 10<sup>7</sup><br>3.9 × 10<sup>7</sup></td><td>1.35 × 10<sup>-27</sup><br>1.15 × 10<sup>9</sup></td><td>12.67<br>1.12</td><td>-1997<br>2906</td></tr><tr><td>Epoxidation forming 4-NO<sub>3</sub>-1,2-epoxy-isoprene-3-yl</td><td></td><td>7.3</td><td>8.6 × 10<sup>6</sup></td><td>8.91 × 10<sup>8</sup></td><td>1.09</td><td>3233</td></tr><tr><td rowspan="3">Decomposition forming MACR + CH<sub>2</sub>O + NO<sub>2</sub></td><td>Epoxidation syn-4-NO<sub>3</sub>-2,3-epoxy-isoprene-1-yl forming</td><td>9.0<br>6.2</td><td>3.3 × 10<sup>5</sup><br>1.4 × 10<sup>8</sup></td><td>8.06 × 10<sup>5</sup><br>1.19 × 10<sup>12</sup></td><td>2.19<br>0.06</td><td>3981<br>2795</td></tr><tr><td>Epoxidation anti-4-NO<sub>3</sub>-2,3-epoxy-isoprene-1-yl forming</td><td>6.3</td><td>5.2 × 10<sup>7</sup></td><td>2.31 × 10<sup>10</sup></td><td>0.54</td><td>2736</td></tr><tr><td>Decomposition forming CH<sub>2</sub>O + MVK + NO<sub>2</sub></td><td></td><td>10.4<br>14.9</td><td>1.6 × 10<sup>5</sup><br>8.8 × 10<sup>0</sup></td><td>1.98 × 10<sup>8</sup><br>6.92 × 10<sup>8</sup></td><td>1.64<br>0.87</td><td>4901<br>6905</td></tr><tr><td rowspan="3">1,5-Ring closure forming</td><td>Decomposition forming MACR + NO<sub>2</sub> + CH<sub>2</sub>O</td><td></td><td>10.4</td><td>8.6 × 10<sup>4</sup></td><td>1.16 × 10<sup>9</sup></td><td>1.24</td><td>4931</td></tr><tr><td>1,5-shift of CH<sub>3</sub> H-atom forming CH<sub>2</sub>=C(C*H<sub>2</sub>)CH(ONO<sub>2</sub>)CH<sub>2</sub>OH</td><td></td><td>10.2<br>14.9</td><td>3.4 × 10<sup>5</sup><br>1.6 × 10<sup>1</sup></td><td>5.53 × 10<sup>-33</sup><br>7.31 × 10<sup>11</sup></td><td>14.16<br>-0.08</td><td>-1882<br>7187</td></tr><tr><td>1,5-Ring closure forming</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="3">Epoxidation forming anti-5-NO<sub>3</sub>-isoprene-2,3-epoxide-4-OH-1-yl</td><td>Epoxidation forming syn-5-NO<sub>3</sub>-isoprene-2,3-epoxide-4-OH-1-yl</td><td>7.4<br>8.5</td><td>3.4 × 10<sup>7</sup><br>4.9 × 10<sup>6</sup></td><td>5.74 × 10<sup>13</sup><br>2.09 × 10<sup>16</sup></td><td>-0.49<br>-1.40</td><td>3440<br>4227</td></tr><tr><td>Decomposition forming nitrooxy-methyl-acrolein + C*H<sub>2</sub>OH</td><td>4.0</td><td>2.8 × 10<sup>9</sup></td><td>1.39 × 10<sup>6</sup></td><td>2.11</td><td>1314</td></tr></tbody></table>

$k(298 K) = 7.5 \times 10^{-12} \text{ cm}^3 \text{ molecule}^{-1} \text{ s}^{-1}$ leads, under atmospheric conditions (0.2 atm O<sub>2</sub>), to a pseudo-first order rate coefficient of $k(298 K) \approx 5 \times 10^7 \text{ s}^{-1}$. For many of the nitrate-RO radicals formed from isoprene, the main fate is then formation of an epoxy-nitrate-RO<sub>2</sub> radical.

The rate of opening of the epoxy-ring is of the same order of magnitude as the O<sub>2</sub> addition in most cases, such that bulk rate coefficients across the alkoxy/epoxy system are not valid. Still, for atmospheric modeling purposes, some model simplification remains possible. Between 250–350 K and 0.2 to 1 atm air, 1-NO<sub>3</sub>-isoprene-2-O• radicals convert to $68 \pm 2\% anti-1-NO<sub>3</sub>-2,3-epoxy-isoprene-4-OO•$, with the remainder forming syn-1-NO<sub>3</sub>-2,3-epoxy-isoprene-4-OO•, while direct alkoxy radical reaction with O<sub>2</sub> or alkoxy dissociation to NO<sub>2</sub> constitute less than 0.1%. For 4-NO<sub>3</sub>-isoprene-3-O• radicals we find $26 \pm 3\% anti-4-NO<sub>3</sub>-2,3-epoxy-isoprene-1-OO•$, with the remainder forming syn-4-NO<sub>3</sub>-2,3-epoxy-isoprene-1-OO•, while direct reactions with O<sub>2</sub> and dissociation to NO<sub>2</sub> constitute less than 0.4%. For the 1-NO<sub>3</sub>-2,3-epoxy-4-OH-isoprene-5-yl and 5-NO<sub>3</sub>-4-OH-isoprene-3-O• radicals (Fig. 4) the near-exclusive fate is formation of

nitrated MACR + HCHO + HO<sub>2</sub>, owing to the fast decomposition in the alkoxy radical. For the other nitrate-RO<sub>2</sub>, the unimolecular reactions are more competitive against O<sub>2</sub> addition in the epoxy-alkyl radical, and the final product distribution shows stronger temperature- and pressure dependencies that are not readily reduced to a single value.

It is interesting to note that unsaturated, hydroxylated RO radicals are less likely to form epoxy-RO<sub>2</sub> radicals than unsaturated nitrate-RO radicals. Compared to a nitrate group, an -OH substituent tends to lead to faster isomerisation and decomposition reactions,<sup>38,49,60</sup> which often dominate over the O<sub>2</sub> addition in the epoxy-alkyl intermediate. Examples include the fast elimination of C*H<sub>2</sub>OH radicals from the β-OH-alkoxy radical in Fig. 4, or the fast H-migration in the δ-OH-alkoxy radical studied by Nguyen and Peeters.<sup>21</sup> This suggests that formation of epoxides could be more prevalent in nighttime NO<sub>3</sub>-initiated oxidation of terpenoids, compared to the OH-initiated oxidation dominant during daytime, which may have repercussions for aerosol formation and growth by reactive uptake. In judging the impact of epoxidation, one should also consider that

<figure><img src="image_14.png" /></figure>
<figure><img src="image_15.png" /><figcaption>Fig. 4 Oxidation scheme showing the dominant pathways for 1-NO₃-isoprene-2-O• radicals formed in the NO₃-initiated oxidation of isoprene. The dotted arrows indicates alkoxy radical formation in the reaction of RO₂ with NO, NO₃, HO₂, or R'O₂; these reactions are not depicted. In the high-NO low-pressure conditions of the converter, anti-stereoisomers will be detectable by partially forming HO₂, while syn-isomers will eliminate NO₂ and can not be detected by ROxLIF.</figcaption></figure>

subsequent chemistry of the epoxy radicals formed could form β-epoxy-alkyl radicals that de-epoxidize, and thus reduce the yield of epoxidized products. Fig. 4 shows an example for 1-NO₃-isoprene-2-O• radicals: about two thirds of this nitrate-RO radical forms anti-substituted epoxy-RO₂, but subsequent H-migration in the product alkoxy radical allows for rapid de-epoxidation and fragmentation forming nitrated MACR + HCHO + HO₂ as the main product under oxidative conditions.

## 6.2 H-Migration reactions in epoxidized nitrate-RO₂ radicals

Table 6 lists a set of calculations on epoxy-nitrate-RO₂ radicals derived from isoprene. H-Migration of an aliphatic or an α-ONO₂-H-atom across the epoxide functionality is an order of magnitude faster than the predictions by the SAR by Vereecken and Nozière for corresponding H-migrations in non-cyclic RO₂ radicals. This contrasts with the results for epoxidized alkoxy radicals by Novelli *et al.*,⁴⁹ who found little

<table><caption>**Table 5** Theoretical rate predictions for ring opening in nitrate-epoxy-alkyl radicals derived from isoprene + NO₃, at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ with MC-TST level of theory. Indicated are the ZPE-corrected barrier height ($E_b$, kcal mol⁻¹), the 298 K rate coefficient ($k(298 K)$, s⁻¹), and the parameters for a Kooij expression $k(T) = A \times (T/K)^n \times \exp(-E_a/T)$ (A in s⁻¹, $E_a$ in K). The rate of recombination with O₂ molecules under atmospheric conditions is estimated at $k(298 K) \approx 5 \times 10^7$ s⁻¹ (see text)</caption><thead><tr><th>Reactant</th><th>Products</th><th>E<sub>b</sub></th><th>k(298 K)</th><th>A</th><th>n</th><th>E<sub>a</sub></th></tr></thead><tbody><tr><td rowspan="2">1-NO<sub>3</sub>-3,4-epoxy-isoprene-2-yl</td><td>Z-1-NO<sub>3</sub>-isoprene-4-O•</td><td>6.0</td><td>7.3 × 10<sup>7</sup></td><td>7.51 × 10<sup>8</sup></td><td>1.10</td><td>2556</td></tr><tr><td>E-1-NO<sub>3</sub>-isoprene-4-O•</td><td>6.3</td><td>1.5 × 10<sup>8</sup></td><td>3.86 × 10<sup>10</sup></td><td>0.72</td><td>2877</td></tr><tr><td>syn-1-NO<sub>3</sub>-2,3-epoxy-isoprene-4-yl</td><td>1-NO<sub>3</sub>-isoprene-2-O•</td><td>5.6</td><td>3.4 × 10<sup>8</sup></td><td>7.42 × 10<sup>9</sup></td><td>0.95</td><td>2535</td></tr><tr><td>anti-1-NO<sub>3</sub>-2,3-epoxy-isoprene-4-yl</td><td>1-NO<sub>3</sub>-isoprene-2-O•</td><td>5.6</td><td>3.5 × 10<sup>8</sup></td><td>1.57 × 10<sup>10</sup></td><td>0.80</td><td>2489</td></tr><tr><td rowspan="2">4-NO<sub>3</sub>-1,2-epoxy-isoprene-3-yl</td><td>Z-4-NO<sub>3</sub>-isoprene-1-O•</td><td>6.9</td><td>4.9 × 10<sup>7</sup></td><td>3.46 × 10<sup>10</sup></td><td>0.77</td><td>3270</td></tr><tr><td>E-4-NO<sub>3</sub>-isoprene-1-O•</td><td>7.6</td><td>2.8 × 10<sup>7</sup></td><td>9.63 × 10<sup>11</sup></td><td>0.37</td><td>3745</td></tr><tr><td>syn-4-NO<sub>3</sub>-2,3-epoxy-isoprene-1-yl</td><td>4-NO<sub>3</sub>-isoprene-3-O•</td><td>5.4</td><td>8.1 × 10<sup>8</sup></td><td>8.15 × 10<sup>10</sup></td><td>0.65</td><td>2475</td></tr><tr><td>anti-1-NO<sub>3</sub>-2,3-epoxy-isoprene-1-yl</td><td>4-NO<sub>3</sub>-isoprene-3-O•</td><td>5.0</td><td>8.5 × 10<sup>8</sup></td><td>5.53 × 10<sup>9</sup></td><td>0.93</td><td>2142</td></tr><tr><td>anti-5-NO<sub>3</sub>-isoprene-2,3-epoxide-4-OH-1-yl</td><td>5-NO<sub>3</sub>-isoprene-4-OH-3-O•</td><td>4.7</td><td>1.2 × 10<sup>9</sup></td><td>1.66 × 10<sup>8</sup></td><td>1.33</td><td>1652</td></tr><tr><td>syn-5-NO<sub>3</sub>-isoprene-2,3-epoxide-4-OH-1-yl</td><td>5-NO<sub>3</sub>-isoprene-4-OH-3-O•</td><td>5.4</td><td>5.4 × 10<sup>8</sup></td><td>4.04 × 10<sup>11</sup></td><td>0.24</td><td>2377</td></tr></tbody></table>
<table><caption>**Table 6** Theoretical predictions for a series of epoxy-peroxy and epoxy-nitrate-peroxy radicals, at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ with MC-TST level of theory. Indicated are the ZPE-corrected barrier height ($E_b$, kcal mol⁻¹), the 298 K rate coefficient ($k(298 K)$, s⁻¹), and the parameters for a Kooij expression $k(T) = A \times (T/K)^n \times \exp(-E_a/T)$ (A in s⁻¹, $E_a$ in K)</caption><thead><tr><th>Reactant</th><th>Mechanism and products</th><th>Stereo<sup>a</sup></th><th>E<sub>b</sub></th><th>k(298 K)</th><th>A</th><th>n</th><th>E<sub>a</sub></th></tr></thead><tbody><tr><td>O<sub>2</sub>NO·<sub>2</sub>OO·</td><td>1,6-H-shift of O<sub>2</sub>NOCH<sub>2</sub>H-atom<br>NO<sub>2</sub> + O<sub>2</sub> → O<sub>2</sub>OOH</td><td></td><td>24.0</td><td>3.7 × 10<sup>-3</sup></td><td>1.77 × 10<sup>-83</sup></td><td>30.09</td><td>-4035</td></tr><tr><td>O<sub>2</sub>NO·<sub>2</sub>OO·</td><td>1,6-H-shift of CH<sub>3</sub>H-atom<br>O<sub>2</sub>NO·<sub>2</sub>OOH</td><td></td><td>24.8</td><td>1.2 × 10<sup>-4</sup></td><td>1.71 × 10<sup>-96</sup></td><td>34.52</td><td>-4434</td></tr><tr><td>O<sub>2</sub>NO·<sub>2</sub>OO·</td><td>1,5-H-shift of α-epoxy H-atom<br>O<sub>2</sub>NO·<sub>2</sub>OOH</td><td>(R<sub>2</sub>S)/(S<sub>2</sub>R)<br>(R<sub>2</sub>R)/(S<sub>2</sub>S)<br>Geom. ave.</td><td>24.5<br>25.2</td><td>3.6 × 10<sup>-4</sup><br>9.7 × 10<sup>-5</sup><br>1.9 × 10<sup>-4</sup></td><td>1.35 × 10<sup>-93</sup><br>7.30 × 10<sup>-98</sup><br>9.92 × 10<sup>-96</sup></td><td>33.70<br>35.03<br>34.36</td><td>-4165<br>-4442<br>-4304</td></tr></tbody></table>

<sup>a</sup> Stereo-designator and stereo-specific rate coefficient for molecules with 2 chiral centers. Also indicated is the geometric average over the stereoisomers, as used in the kinetic model.

influence of the ring structure for H-migration across an epoxide ring. Similar to the findings of Novelli *et al.*, we find that migration of an α-epoxy H-atom is not very favorable, despite the presence of an oxygen atom, and is only as fast as migration of an aliphatic H-atom. All the calculated H-migrations are slow, $k(298 K) \le 10^{-3} s^{-1}$, and do not contribute significantly in our experimental conditions.

## 6.3 Isomerisation and decomposition of epoxidized nitrate-RO radicals

The rate coefficients for decomposition and isomerisation of a set of β-epoxidized alkoxy radicals are listed in Table 7. Decomposition forming an α-epoxy-alkyl radical is slow, due to high barriers owing to the increase in ring strain in these products. This is in agreement with our earlier work that found that a β-epoxy-moiety is less effective in lowering the barrier height for decomposition than alkyl or oxygenated substituents.⁴⁹ Likewise, the barrier heights for the unfavorable elimination of a bare methyl radical product are comparatively high, making this reaction slow. Elimination of a *CH<sub>2</sub>ONO<sub>2</sub> radical, where possible, is the most favorable decomposition; this radical readily decomposes further to HCHO + NO<sub>2</sub>. The decomposition barriers for all these processes are reproduced within 1 kcal mol⁻¹ by the SARs by Vereecken and Peeters³⁸ and Novelli *et al*.³⁸,⁴⁹ The fastest reactions for the set of alkoxy radicals listed in Table 7 are syn-1,5-H-migrations across the epoxy moiety, either of a methyl H-atom, or more favorably of a –CH<sub>2</sub>ONO<sub>2</sub> hydrogen leading to NO<sub>2</sub> elimination. As already anticipated by Novelli *et al.*,⁴⁹ the rate coefficients for H-migration across the epoxy moiety are within a factor of 2 of the rate of isomerisation in aliphatic alkoxy radicals (see SAR by Vereecken and Peeters⁵⁷,⁶⁰), where the α-ONO<sub>2</sub> substituent has a similar impact on the rate as an alkyl group.

## 7 Chemical mechanism implementation

The reactions and their theory-derived rate coefficients described in the earlier sections embedded in extended oxidation mechanisms

for the relevant RO<sub>2</sub> and RO radicals, are implemented in a zero-dimensional box model, called FZJ-NO<sub>3</sub>-isoprene henceforth, which can be used for modeling the trace gas concentration time series in the experiments.

As discussed higher, the rates of the re-equilibration reactions of the primary nitrate-RO<sub>2</sub> radicals by O<sub>2</sub>-elimination/re-addiction are optimized to reproduce the theoretically derived RO<sub>2</sub> equilibrium distribution in the absence of other loss processes. Since the system of variables is under-determined, we choose to approximate the oxygen addition rates to have the same rates as for the alkyl radicals in the OH + isoprene system.¹²⁻¹⁴ The ESI† lists $k(T)$ values for all isoprene-derived RO<sub>2</sub> radicals, while the resulting rates at 298 K are illustrated in Fig. 2 for the main addition channel. Note that this approach only yields correct rate ratios between O<sub>2</sub> addition and elimination, where the absolute magnitude of the values is inherited from the isoprene + OH + O<sub>2</sub> system. The site- and stereo-specificity of the initial NO<sub>3</sub> addition is obtained from literature data (see above).

Unimolecular reaction rates for nitrate-RO<sub>2</sub>, nitrate-RO, and epoxy-RO radicals from isoprene were taken from theoretical calculations in this work. Where necessary to derive extended oxidation schemes (see Fig. 4 and ESI†), these were supplemented by application of the pertinent SARs.³³,³⁸,⁴⁹,⁶⁰ The RO<sub>2</sub> bimolecular rate coefficients and product distributions were derived using the structure-activity relationship (SAR) by Jenkin *et al.*,⁸¹ which does not explicitly incorporate the effect of the nitrate substituent. However, for the reaction rates for nitrate-RO<sub>2</sub> + NO<sub>3</sub>, we used the data by Dewald *et al*.⁴⁶ In addition, an OH-product channel is added to the reaction of β-ONO<sub>2</sub>-RO<sub>2</sub> + HO<sub>2</sub>, as introduced in earlier work.⁴,⁴¹⁻⁴³,⁴⁹,⁸²

<figure><img src="image_16.png" /></figure>

As discussed in Novelli *et al.*,⁴⁹ the mechanism for this reaction likely requires strong H-bonding between the nitrate group and the HO<sub>x</sub> moiety, or at least an inductive effect by a neighbouring nitrate group, which is possible for β-nitrate-RO<sub>2</sub> + HO<sub>2</sub> but is unlikely to be effective for longer separations between the nitrate

<figure><img src="image_17.png" /></figure>
<table><caption>**Table 7** Theoretical predictions for a series of epoxy-alkoxy and epoxy-nitrate-alkoxy radicals, at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ with MC-TST level of theory. Indicated are the ZPE-corrected barrier height ($E_b$, kcal mol⁻¹), the 298 K rate coefficient ($k(298 K)$, s⁻¹), and the parameters for a Kooij expression $k(T) = A \times (T/K)^n \times \exp(-E_a/T)$ (A in s⁻¹, $E_a$ in K)</caption><thead><tr><th>Reactant</th><th>Mechanism and products</th><th>Stereo<sup>a</sup></th><th>E<sub>b</sub></th><th>k(298 K)</th><th>A</th><th>n</th><th>E<sub>a</sub></th></tr></thead><tbody><tr><td rowspan="2">O<sub>2</sub>NO<sub>2</sub><sup>•</sup></td><td>1,5-H-Shift of O<sub>2</sub>NOCH<sub>2</sub>H-atom<br>NO<sub>2</sub> + O<sub>2</sub>NO<sub>2</sub><sup>•</sup> + O<sub>2</sub>OH</td><td>8.8</td><td>6.0 × 10<sup>6</sup></td><td>4.14 × 10<sup>-16</sup></td><td>8.68</td><td>-477</td></tr><tr><td>Decomposition<br>HCHO + O<sub>2</sub>NO<sub>2</sub><sup>•</sup></td><td>17.9</td><td>1.5 × 10<sup>0</sup></td><td>3.65 × 10<sup>10</sup></td><td>1.02</td><td>8861</td></tr><tr><td rowspan="2">O<sub>2</sub>NO<sub>2</sub><sup>•</sup></td><td>1,5-H-Shift of CH<sub>3</sub>H-atom<br>O<sub>2</sub>NO<sub>2</sub><sup>•</sup> + O<sub>2</sub>OH</td><td>10.6</td><td>1.9 × 10<sup>5</sup></td><td>3.23 × 10<sup>-23</sup></td><td>10.99</td><td>-400</td></tr><tr><td>Decomposition<br>HCHO + O<sub>2</sub>NO<sub>2</sub><sup>•</sup></td><td>18.3</td><td>4.3 × 10<sup>-1</sup></td><td>9.28 × 10<sup>8</sup></td><td>1.61</td><td>9134</td></tr><tr><td rowspan="4">O<sub>2</sub>NO<sub>2</sub><sup>•</sup></td><td>Decomposition<br>NO<sub>2</sub> + HCHO + 1,2-epoxy-3-butanone</td><td>(R,S)/(S,R)<br>(R,R)/(S,S)</td><td>9.9<br>11.4</td><td>4.0 × 10<sup>4</sup><br>1.1 × 10<sup>4</sup></td><td>2.44 × 10<sup>5</sup><br>2.33 × 10<sup>7</sup></td><td>2.28<br>1.83</td><td>4416<br>5376</td></tr><tr><td>Decomposition<br>CH<sub>3</sub> + 1-ONO<sub>2</sub>-3,4-epoxy-2-butanone</td><td>Geom. ave.<br>(R,S)/(S,R)<br>(R,R)/(S,S)</td><td>14.5<br>13.9</td><td>2.1 × 10<sup>4</sup><br>1.7 × 10<sup>2</sup><br>2.4 × 10<sup>2</sup></td><td>2.38 × 10<sup>6</sup><br>5.12 × 10<sup>6</sup><br>5.22 × 10<sup>2</sup></td><td>2.06<br>2.22<br>3.52</td><td>4896<br>6852<br>6209</td></tr><tr><td>Decomposition<br>1,2-Epoxy-ethyl + 1-ONO<sub>2</sub>-2-propanone</td><td>Geom. ave.<br>(R,S)/(S,R)<br>(R,R)/(S,S)</td><td>13.0<br>12.5</td><td>2.0 × 10<sup>2</sup><br>3.1 × 10<sup>3</sup><br>5.5 × 10<sup>3</sup></td><td>5.17 × 10<sup>4</sup><br>1.33 × 10<sup>9</sup><br>3.84 × 10<sup>8</sup></td><td>2.87<br>1.48<br>1.56</td><td>6530<br>6372<br>5978</td></tr><tr><td>Decomposition<br>1,2-Epoxy-ethyl + 1-ONO<sub>2</sub>-2-propanone</td><td>Geom. ave.</td><td></td><td>4.1 × 10<sup>3</sup></td><td>7.14 × 10<sup>8</sup></td><td>1.52</td><td>6175</td></tr></tbody></table>

and peroxy groups. Contrary to the mechanism by Wennberg et al.⁴ (called CalTech from here onward), we therefore do not include this channel for the γ- and δ-nitrate-RO₂ radicals. At this time, we adopt a nitrate-RO + OH yield of ~50%, compatible with the available literature,⁴,⁴¹⁻⁴³,⁴⁹ while retaining the total rate coefficient for an aliphatic RO₂ + HO₂ reaction. This potentially underestimates the reaction rate somewhat, as similarly to the acylperoxy + HO₂ reaction, the RO + OH product channel (occurring on the singlet electronic surface) does not compete against the ROOH channel (proceeding on the triplet surface) but is rather an additional reaction pathway that enhances the total reaction rate.⁷⁹,⁸³,⁸⁴

As we focus mainly on the formation and consumption of the initial RO₂, the subsequent chemistry of the products following RO₂ uni- or bimolecular reactions is included following the CalTech mechanism or, if none is provided there, we adopt the chemistry as described by the Master Chemical Mechanism v3.3.1³⁴⁻³⁶ (available at http://mcm.leeds.ac.uk). The isoprene ozonolysis mechanism is updated based on the literature data and is described in detail in the ESI.† The chemistry following the NO₃-addition on the central carbons of isoprene is not fully expanded in our current model. The yields for these channels are expected to be low, and we currently do not have product information that would allow determining these yields. These channels are rendered inoperable in the current model with a zero yield. The resulting FZJ-NO₃-isoprene model is provided in the ESI.†

For modeling the current set of experiments, the model also incorporates chamber-specific processes. A dilution coefficient

was added for all trace gases in the model. This is necessary due to the replenishment flow required to keep the over-pressure in the chamber (see Experimental methodology). Isoprene, O₃ and NO₂ injections in the experiment were incorporated into the model as a short-period source reaction optimized to yield concentrations in agreement with their respective measurements, leaving these species concentrations otherwise unconstrained; Fig. S11 (ESI†) shows a comparison of the measured against modelled isoprene concentrations. The concentration of NO₃ was constrained to the measurement in order to reduce the impact of uncertainty in NO₃ and/or N₂O₅ loss on the chamber wall, which can be significant⁴⁶ and variable in time. Temperature, pressure and water content were also constrained to the measurements. As discussed in detail in the ESI,† there is an unresolved discrepancy between the modelled HO₂ concentration in the simulations, and the HO₂ measurement from the LIF system, with the latter higher by up to a factor of 10. Two limiting cases are considered: (i) the discrepancy is assumed to be solely due to missing sources of HO₂ radicals in the models, and therefore the modelled HO₂ concentration is constrained to the measured HO₂ radicals, and (ii) the discrepancy is assumed to be fully due to RO₂ radicals interfering in the LIF HO₂ measurement,⁶⁷ and the HO₂ and RO₂ measurement are corrected for accordingly. These two limiting cases allows bracketing the impact of the uncertainty on the HO₂ radical concentrations in the experiments described. It is important to underline that the chemical conditions within the experiments described in this study, specifically the lack of NO, result in much larger RO₂ radical concentrations as compared to the HO₂ radicals (a factor of 10 more). Therefore,

<figure><img src="image_18.png" /></figure>

<footnote><sup>a</sup> Stereo-designator and stereo-specific rate coefficient for molecules with 2 chiral centers. Also indicated is the geometric average over the stereoisomers, as used in the kinetic model.</footnote>
even a small interference (less than 10%) from the RO₂ radicals would drastically affect the measured HO₂ radicals (Fig. S9, ESI†).

The main differences between the MCM v3.3.1, CalTech, and FZJ-NO₃-isoprene models can be summarized as follows. The CalTech mechanism by Wennberg et al. ignores the stereo-specificity of the δ-NO₃-isoprene-OO isomers, lumping the Z- and E-isomers into a single species despite their distinct chemistry both at the RO₂ and the subsequent RO stage. After NO₃ addition on isoprene, the CalTech model favors O₂ addition on the δ-position over the β-position, whereas the FZJ-NO₃-isoprene model predicts a much higher contribution of the β-ONO₂-RO₂ radicals based on the theoretical Boltzmann distribution (Fig. 3). The CalTech mechanism also does not include the reversible epoxidation reactions for β-unsaturated nitrate-RO. Finally, the CalTech mechanism applies an OH-forming channel in the nitrate-RO₂ + HO₂ reaction irrespective of the distance between the –ONO₂ and –OO• substituents, whereas FZJ-NO₃-isoprene considers this path viable only for β-nitrate-RO₂. The MCM v3.3.1 model incorporates only a single nitrate-RO₂ isomer with limited subsequent chemistry. As such, it does not yet include nuances in chemistry such as the RO₂ re-equilibration (which is implemented for isoprene + OH), RO₂ unimolecular reactions, epoxidation in nitrate-RO, or the OH-channel in nitrate-RO₂ + HO₂.

## 8 Prediction of the ROxLIF detectable RO₂ fraction

The RO₂ radicals are sampled from the SAPHIR chamber in the ROxLIF converter at a lower pressure (25 hPa), and NO is added; due to the low pressure, bimolecular reactions other than with NO and O₂ are negligible. During the residence time in the ROxLIF converter, ~0.6 s, the RO₂ radicals react with NO forming RO radicals, which in turn are expected to convert to HO₂, as described below. Finally, the ROxLIF system measures the HO₂ concentration by sampling in a fluorescence cell, where HO₂ gets converted to OH in reaction with NO, and detected by LIF. The ROxLIF system thus measures the sum of HO₂ formed from RO₂ in the converter, and the HO₂ radicals already present in the sampled SAPHIR chamber air; subtracting the SAPHIR HO₂ and OH concentrations as measured directly by two additional and separate fluorescence cells (OH and HOₓ cells) then yields the HO₂ signal attributable to conversion of RO₂. Calibration of this signal relative to a known CH₃O₂ standard allows determination of absolute total RO₂ concentrations, thus accounting for residence time, wall losses, and other characteristics of the converter.

The observation of RO₂ radicals in the ROxLIF instrument thus hinges on the formation of OH or HO₂ radicals from the alkoxy radicals derived from these RO₂ radicals under the high-NO conditions of the converter. Aliphatic and hydroxylated alkoxy radicals react with O₂ (R5) and (R6), possibly after one or more decomposition steps, to form HO₂ and are thus typically detectable. However, as already studied in detail by Novelli et al.,⁴⁹ nitrate-substituted RO₂ radicals can undergo chain termination

by decomposition of the nitrate group (R7), forming NO₂, and are thus undetectable in the ROxLIF measurement.

$$ \chemfig{CH-O^{\bullet}-O^{\cdot-}} \xrightarrow{+O_2} \chemfig{C=O+HO_2} \quad (R5) $$

$$ \chemfig{C=O+OH^{\bullet}-OH^{\cdot-}} \xrightarrow{+O_2} \chemfig{HO_2+O=C^{\bullet-}} \quad (R6) $$

$$ \chemfig{C=O+ONO_2^{\bullet}-ONO_2^{\cdot-}} \xrightarrow{+ONO_2^{\bullet}} \chemfig{NO_2+O=C^{\bullet-}} \quad (R7) $$

Also, if the alkoxy radical isomerises, e.g. by H-migration or epoxidation, followed by O₂ addition, the resulting new RO₂ radical must again react with NO to allow HO₂ formation. Thus, dependent on the residence time and NO concentration in the converter, some RO₂ may not yield HO₂. Such additional steps can thus lead to reduced conversion of the parent RO₂ to HO₂.

To aid the interpretation of the RO₂ measurements in the NO₃-initiated oxidation experiments on isoprene, we modelled the fate of the RO₂ radicals under the reaction conditions in the converter (25 hPa, 0.55 ppmv of NO, 0.17% CO, residence time ~0.6 s),⁸⁵ using the relevant subsets of the FZJ-NO₃-isoprene model for the target RO₂ radicals. From these model calculations, we find that the isoprene-derived nitrate-RO₂ radicals, and the RO₂ radicals formed in their subsequent reactions in the SAPHIR chamber, are not converted fully to OH or HO₂ radicals but rather generate NO₂ under the conditions in the converter, and will thus remain partially invisible in the LIF measurement of RO₂. For example, at 298 K the main nitrate-RO₂ species 1-NO₃-isoprene-2-OO• and 1-NO₃-isoprene-4-OO• are estimated to produce only 25% and 11–15% HOₓ, respectively, in the fluorescence cell relative to the calibrating CH₃O₂ radical, with the remainder forming undetectable NO₂ or remaining as one of the intermediate RO₂. For the nitrate-RO₂ formed in the minor addition channel, 4-NO₃-isoprene-3-OO• and 4-NO₃-isoprene-1-OO•, less than 3% are predicted to be detectable. The temperature-dependent detectability for all relevant nitrate-RO₂ and nitrate-epoxy-RO₂ is listed in Table S2 in the ESI.† The ROxLIF instrument in use at the SAPHIR chamber is thus not expected to return the sum of all RO₂ concentrations (called “total RO₂” hereafter) as predicted in the model, but measurements instead correspond to the summation of all RO₂ concentrations weighted by their speciated HOₓ yields to obtain the so-called “detectable RO₂” sum. For non-nitrated RO₂, we adopt unity HO₂ formation efficiency relative to the calibrating CH₃O₂ radical.⁸⁵ As the relative nitrate-RO₂ radical detectability depends on the conditions in the converter and fluorescence cell, e.g. NO concentration, pressure, etc., the detectability can't be generalized to other ROxLIF instruments, and each system needs to be experimentally characterized. The *a priori* predictions of the detectability in the current work do not benefit from any such experimental calibration, and are thus affected by the combined uncertainties on temperature, pressure, converter and fluorescence cell residence time, wall losses, rate coefficients, chemical activation, and possible unknown reactions in a complex reaction mechanism. Several of these aspects are discussed in more detail in the ESI.† Overall, we

<figure><img src="image_19.png" /></figure>
estimate an uncertainty of about a factor of 2 to 3 on the estimated relative conversion efficiency governing the detectability of RO₂, mostly due to the uncertainties on the various rate coefficients in the kinetic model used to derive these conversion efficiencies. It must be stressed that the reduced O₂ concentrations in the converter affects the chemistry rather significantly. Under atmospheric conditions, formation of epoxy-RO₂ is expected to be more prevalent, whereas in the converter, direct alkoxy decomposition and isomerisation reactions are more competitive.

# 9 Comparison to experimental observations

## 9.1 Peroxy radical concentration

Modelling the experiments using the FZJ-NO₃-isoprene mechanism indicates that oxidation of isoprene by NO₃ was the dominant degradation pathway, with 10–15% of isoprene oxidized each by ozone and hydroxyl radicals. Isoprene ozonolysis forms mainly stable products and has only a small contribution to the RO₂ pool; these ozone-RO₂ are not discussed further in this work. RO₂ radicals from the oxidation of isoprene by OH radicals contribute about 20% to the total RO₂ according to our model, and all these RO₂ are detectable in the ROxLIF instrument.³⁸,⁴⁹,⁶⁰ The bulk of the RO₂ radicals in the reaction mixture of the experiments, however, is nitrate-RO₂ radicals which, as discussed above, are only partially detectable (see Fig. S14 in the ESI†). As shown in Fig. 5 and additional figures in the ESI,† we predict for all three experiment days large discrepancies between the total RO₂ and the RO₂ detected by the ROxLIF instrument. The modelled detectable RO₂, however, differs from the measured RO₂ concentration only by about a factor of 2, if the FZJ-NO₃-isoprene chemical mechanism is applied. The fate of the nitrate-RO₂ is strongly affected by the O₂-driven RO₂ re-equilibration as implemented in the FZJ-NO₃-isoprene model. This re-equilibration is rapid compared to the rate of RO₂ loss processes, such that the instantaneous RO₂ population is always close to the equilibrium fractions, with 1-NO₃-isoprene-2-peroxy radicals being the dominant RO₂ species (Fig. 3), with 70 to 75% contribution in the 1-NO₃-isoprene peroxy radical pool, depending on the temperature. This tertiary peroxy radical acts as a reservoir species, owing to its comparatively slow bimolecular loss processes ($k \sim 1.6 \times 10^{-2} s^{-1}$ for HO₂/RO₂/NO₃ combined, see below),⁸¹ and combined with the slow unimolecular reactions ($k \sim 1.8 \times 10^{-3} s^{-1}$, Table 3) this leads to lifetimes of about 2 min for 1-NO₃-RO₂ radicals. In contrast, bimolecular and unimolecular reactions of 4-nitrooxy RO₂ radicals have overall higher (pseudo-first order) rate coefficients (respectively $2.1 \times 10^{-2}$ and $1.1 \times 10^2 s^{-1}$, Table 3), have lifetimes of around 1 min, and contribute significantly less to the RO₂ concentration. Table 8 lists the contributions of the respective loss processes for each nitrate-RO₂. Overall, the majority of the nitrate-RO₂ are lost by reaction with HO₂ and NO₃. RO₂ + RO₂ reactions are never dominant, even for the experiment with the highest modelled peak RO₂ concentrations in excess of $8 \times 10^9$ molecule cm⁻³. Some nitrate-RO₂ have a fast unimolecular loss channel, which can

<figure><img src="image_20.png" /><figcaption>Fig. 5 Measured and modelled RO₂ concentration time profiles for the experiment on 13 Aug 2018, as described in Dewald et al.,⁴⁶ with reaction conditions shown in ESI† Section K. Dashed lines represent the total RO₂ predicted by the models; upper panel: model results with HO₂ constrained to measurements, bottom panel: unconstrained HO₂. For the more detailed CalTech and FZJ-NO₃-isoprene models, additional traces (solid lines) show the estimated detectable RO₂, which can be compared to the measurements. The shaded area shows a factor of 2 uncertainty on the estimated conversion efficiency factors of the detectable RO₂ predicted by the FZJ-NO₃-isoprene model.</figcaption></figure>

become the dominant loss path for these specific isomers but has only a small overall contribution.

If the MCM v3.3.1 mechanism instead of FZJ-NO₃-isoprene is used in the model, the nitrate-RO₂ population is represented by a single RO₂ isomer (E-1-NO₃-isoprene-4-OO•) and at room temperature only 15% of this RO₂ isomer would be detectable in the ROxLIF. However, due to the reduction in the MCM to only one RO₂ isomer, measured and modelled RO₂ concentrations can hardly be compared.

If the CalTech mechanism is applied, the predicted detectable RO₂ also reproduces the experimental measurements well (Fig. 5), indicating that the more refined description of the nitrate-RO₂ radicals similar to the FZJ-NO₃-isoprene model is beneficial. The lower ratio of 1-NO₃-isoprene-2-OO• to 1-NO₃-isoprene-4-OO• radicals in the CalTech mechanism compared to the FZJ-NO₃-isoprene mechanism leads to a shorter chemical
<table><caption>**Table 8** Modelled fates of the nitrate-RO₂, averaged across the three experiment days. HO₂ concentrations were in the range of 0.1–8 × 10⁸ molecule cm⁻³, NO₃ concentrations were in the range of 1–50 × 10⁸ molecule cm⁻³, and sustained RO₂ concentrations were at 1–3 × 10⁹ molecule cm⁻³. The range or value before the slash shows the fates when constraining HO₂ concentrations to the measurement, and uses an HO₂ concentration of 5 × 10⁸ molecule cm⁻³ to estimate the lifetime. The values after the slash correspond to the unconstrained model, using 1 × 10⁸ molecule cm⁻³ of HO₂ for the lifetime estimate</caption><thead><tr><th>Reactant</th><th>Unimolecular</th><th>HO<sub>2</sub></th><th>NO<sub>3</sub></th><th>RO<sub>2</sub></th></tr></thead><tbody><tr><td>ONOO<sub>2</sub></td><td>46-79%/49-82%</td><td>9-21%/2-4%</td><td>5-12%/5-12%</td><td>6-21%/10-35%</td></tr><tr><td>ONOO<sub>2</sub></td><td>—</td><td>36-44%/8-13%</td><td>20-25%/22-28%</td><td>31-44%/59-70%</td></tr><tr><td>O<sub>2</sub>NOO<sub>2</sub></td><td>—</td><td>63-64%/26-32%</td><td>35-38%/67-72%</td><td>0-1%/1-2%</td></tr><tr><td>All 1-NO<sub>3</sub>-isoprene-RO<sub>2</sub> average lifetime: ~113/164 s</td><td>4-6%/4-7%</td><td>54-57%/20-27%</td><td>30-34%/53-59%</td><td>6-10%/12-17%</td></tr><tr><td>ONOO<sub>2</sub></td><td>72-92%/76-93%</td><td>3-11%/1-2%</td><td>2-6%/2-7%</td><td>2-10%/3-16%</td></tr><tr><td>ONOO<sub>2</sub></td><td>—</td><td>41-44%/9-14%</td><td>23-28%/27-32%</td><td>28-36%/51-65%</td></tr><tr><td>ONOO<sub>2</sub></td><td>—</td><td>53-55%/17-22%</td><td>31-35%/49-53%</td><td>11-15%/24-35%</td></tr><tr><td>All 4-NO<sub>3</sub>-isoprene-RO<sub>2</sub> average lifetime: ~65/73 s</td><td>14-18%/15-19%</td><td>38-42%/10-15%</td><td>22-26%/30-36%</td><td>16-22%/30-43%</td></tr><tr><td>All isoprene-RO<sub>2</sub> average lifetime: ~107/153 s</td><td>5-8%/5-8%</td><td>52-55%/19-25%</td><td>29-33%/51-56%</td><td>7-12%/14-20%</td></tr></tbody></table>

lifetime of the nitrate-RO₂ and hence lower RO₂ concentrations. Given the uncertainty of the estimated detectability, however, we cannot confirm that these lower predicted detectable RO₂ concentrations are in better agreement with the experiment. The RO₂ concentrations predicted with the CalTech mechanism are more constant over time, while the FZJ-NO₃-isoprene mechanism follows a more gradual decrease in RO₂ concentration (Fig. 5). This suggests that the modeling of the RO₂ population may be further improved by explicitly incorporating the distinct stereo-specific chemistry of Z- and E-nitrate-RO₂ radicals, and basing the nitrate-RO₂ populations on the theory-derived equilibria, as done in FZJ-NO₃-isoprene. Without accurate calibration of the detectability of the nitrate-RO₂, it is hard to further characterize the relative performance of the CalTech and FZJ-NO₃-isoprene mechanisms on the RO₂ concentration. This is especially true for later times in the experiment where secondary chemistry becomes increasingly important, and the uncertainty in the modelled value increases as the chemical mechanism for these species has not yet been updated to the latest chemical insights.

## 9.2 Methyl vinyl ketone and methacrolein yields

Prominent stable products from isoprene oxidation are methyl vinyl ketone (MVK) and methacrolein (MACR), produced from and destroyed by various reaction channels such as ozonolyis, NO₃ and OH reactions.⁴ Therefore, differences between measured and modelled MVK and MACR concentrations can be caused by incorrect production or loss from either one of the pathways. For the conditions of the experiments in this work,

80% of isoprene is lost in the reaction with NO₃. In the FZJ-NO₃-isoprene model, however, less than 1% of the modelled MVK and MACR concentrations originate from the NO₃ + isoprene oxidation. The remaining part is formed through the isoprene + OH chemistry (80%) and through ozonolysis (19%) although these two channels represent only ~10-15% each of the isoprene loss. The FZJ-NO₃-isoprene mechanism reproduces the measured MVK + MACR concentrations within 25% (Fig. 6 and additional figures in the ESI†). This difference is close to the uncertainty of the MVK and MACR yields in the mechanism and the measurement uncertainty (±14%). The latter is partially due to the difference in sensitivities for MVK and MACR in the VOCUS PTR-MS, such that the comparison depends on the knowledge of the MACR to MVK ratio.

Applying the MCM v3.3.1 mechanism, MVK + MACR concentrations are reproduced within 15%, even though no formation of these compounds from NO₃ chemistry is included. This is compensated by a higher MVK yield from isoprene ozonolysis, compared to the FZJ-NO₃-isoprene scheme (see ESI†). In contrast to the FZJ-NO₃-isoprene and MCM v3.3.1 mechanisms, the CalTech mechanism overestimates MVK + MACR concentrations by between 250 to 400%, mainly due to the complete conversion of 1-NO₃-isoprene-2-O• radicals, formed in the 1-NO₃-isoprene-2-OO• + HO₂/RO₂/NO₃ reactions, to MVK. In the FZJ-NO₃-isoprene model these nitrate-RO radicals are also formed, but their decomposition to MVK is overwhelmed by the epoxidation reactions described above. Without the competing epoxidation channel, the MVK + MACR concentration predicted by FZJ-NO₃-isoprene would even exceed that predicted by CalTech model, owing to the larger

<figure><img src="image_21.png" /></figure>
<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /><figcaption>**Fig. 6** Measured and modelled methyl vinyl ketone + methacrolein (MVK + MACR) concentration time profiles for the experiment on 13 Aug 2018 as described in Dewald et al.,⁴⁶ with reaction conditions shown in ESI† Section K. Upper panel: Model results with HO₂ constrained to measurements; bottom panel: unconstrained HO₂. The measurement assumes equal amounts of MVK and MACR are present to account for the differing sensitivities. For the conditions present in these experiments, this assumption is validated by the modelling.</figcaption></figure>

fraction of 1-NO₃-isoprene-2-OO• radicals in the nitrate-RO₂ population. A prominent source of 1-NO₃-isoprene-2-O• radicals is the reaction of nitrate-RO₂ + HO₂ forming nitrate-RO + OH (reaction (R4)). The need for OH formation in this channel as put to evidence by other experimental studies,⁴¹⁻⁴³ combined with the low measured MVK + MACR concentrations in our experiments indirectly validates the proposed epoxidation with O₂ addition chemistry in the FZJ-NO₃-isoprene model. Due to the competing, faster bimolecular reactions and its lower yield, the decomposition of the 4-NO₃-isoprene-3-OO• to MACR only plays a minor role.

## 10 Conclusions

The NO₃-initiated chemistry of isoprene appears to be as complex as the OH-initiated oxidation of isoprene. The available theoretical and experimental data indicates that, similar to the

LIM-mechanism for OH-initiated oxidation,¹²,¹³ the initial steps of the isoprene + NO₃ mechanism must take the site- and stereo-specificity of the NO₃ and O₂ addition into account, as well as the re-equilibration of the RO₂ isomers by O₂ elimination/re-addition. The nitrate-RO₂ radicals show several reaction channels that may be competitive in pristine environments. For the main NO₃-addition channels on the outer carbons of isoprene, the dominant unimolecular reactions of the RO₂ formed, with k(298 K) up to 5 × 10⁻² s⁻¹, are the migration of the CH₂ONO₂ H-atoms, forming HPALD + NO₂, thus linking the mechanism to the OH-initiated oxidation of isoprene where HPALD is thought to be a key intermediate in OH regeneration.¹⁴,¹⁹,⁸⁶ The rate predictions for RO₂ H-migration are found to be in good agreement with a recent SAR by Vereecken and Nozière³³ for H-migration in RO₂ radicals. The rate coefficients for H-migration in nitrate-RO₂ are generally slower than in hydroxylated RO₂, such that the impact of unimolecular RO₂ chemistry in the atmosphere will be significantly less for isoprene + NO₃ than for isoprene + OH; at this time we have no experimental evidence for significant HPALD formation in the NO₃-initiated oxidation. Only for the RO₂ formed in the minor addition channels, i.e. with NO₃ adding on the central carbons, are fast ring closure reactions with k(298 K) exceeding 1 s⁻¹ possible that might prove competitive against bimolecular reactions, and might lead to highly oxygenated molecules, albeit in small yields. We observed no products we could assign uniquely to these channels.

The chemistry of the nitrated alkoxy radicals shows several fast decomposition and isomerisation reactions leading to the fragmentation of the nitrate group, forming a carbonyl compound and NO₂. Decomposition and isomerisation reactions of nitrate-RO radicals are typically slower than in the analogous OH-substituted alkoxy radicals,³⁸,⁴⁹,⁶⁰ allowing epoxidation reactions in unsaturated nitrate-RO to become competitive. The role of these epoxidized compounds is not fully elucidated yet, but has important impact on the predicted product formation. For example, the theoretical predictions indicate a very small yield of methyl-vinyl-ketone (MVK) from 1-NO₃-isoprene-2-O• radicals, contrary to expectations by Wennberg et al.⁴ The predicted MVK + MACR yields are in good agreement with the experimental observations, provided epoxidation is taken into account. The formation of epoxides could indicate a higher propensity for aerosol formation at nighttime due to reactive uptake on particles. Still, a strong contribution of epoxidation also does not necessarily imply a high yield of epoxidized products, as the epoxide may undergo ring opening in subsequent reaction steps. For example, the dominant epoxidation channel in the important 1-NO₃-isoprene-2-O• radical still leads mainly to non-epoxidized nitrated MACR, due to ring reopening after a hydrogen shift (Fig. 4).

As predicted in a recent study by Novelli et al.,⁴⁹ the observation of nitrated RO₂ radicals formed from isoprene using a LIF instrument by their conversion to alkoxy radicals and ultimately HO₂ with an excess NO is not straightforward, owing to the potential NO₂ elimination. When considering this chemistry in the comparison between model and experiment, we find that less than a third of the nitrate-RO₂ are detectable, and
agreement within a factor ~2 is obtained, subject to considerable uncertainties on the exact relative conversion efficiency.

Though the current work has characterized a large number of reactions important in the initial stages of the NO₃-initiated oxidation of isoprene, further work is needed to elucidate the later stages of the chemistry. The theoretically characterized pathways may also be of importance in the NO₃-driven atmospheric chemistry of other unsaturated organic compounds. Finally, though the results in this work are only weakly dependent on the HO₂ concentration, further investigation of the cause of the difference between modelled and measured HO₂ would be useful.

## Author contributions

All authors contributed to the conceptualization, execution and discussion of the campaign on NO₃-initiated isoprene oxidation. LV performed the quantum chemical and theoretical kinetic calculations, and derived the oxidation schemes. PC, LV and AN implemented the mechanisms and performed the modeling studies. HF and SSB planned the experiments and organized them. RT and DR provided isoprene and MVK + MACR data. FB, JC, SSB, WM, JS, and LZ provided NO₃ data. AN and CC provided the RO₂ and HO₂ data. LV, AN, PC, and HF wrote the paper.

## Conflicts of interest

There are no conflicts to declare.

## Acknowledgements

This research has received support by Horizon 2020 Projects EUROCHAMP-2020 (grant no. 730997) and SARLEP (grant no. 681529).

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