Atmospheric Fate of Methacrolein. 2. Formation of Lactone and

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Atmospheric Fate of Methacrolein. 2. Formation of Lactone and Implications for Organic Aerosol Production Henrik G. Kjaergaard,*,† Hasse C. Knap,† Kristian B. Ørnsø,† Solvejg Jørgensen,† John D. Crounse,§ Fabien Paulot,‡,∥ and Paul O. Wennberg*,‡,§ †

Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, United States § Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, United States ‡

S Supporting Information *

ABSTRACT: We investigate the oxidation of methacryloylperoxy nitrate (MPAN) and methacrylicperoxy acid (MPAA) by the hydroxyl radical (OH) theoretically, using both density functional theory [B3LYP] and explicitly correlated coupled cluster theory [CCSD(T)-F12]. These two compounds are produced following the abstraction of a hydrogen atom from methacrolein (MACR) by the OH radical. We use a RRKM master equation analysis to estimate that the oxidation of MPAN leads to formation of hydroxymethyl−methyl-α-lactone (HMML) in high yield. HMML production follows a low potential energy path from both MPAN and MPAA following addition of OH (via elimination of the NO3 and OH from MPAN and MPAA, respectively). We suggest that the subsequent heterogeneous phase chemistry of HMML may be the route to formation of 2-methylglyceric acid, a common component of organic aerosol produced in the oxidation of methacrolein. Oxidation of acrolein, a photo-oxidation product from 1,3-butadiene, is found to follow a similar route generating hydroxymethyl-α-lactone (HML).

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INTRODUCTION Isoprene (2-methyl-1,3-butadiene) is emitted by plants in enormous quantities (440−660 Tg yr−1).1 The oxidation of isoprene by the hydroxyl radical is suggested to produce a large fraction of the secondary organic aerosol (SOA) present in the atmosphere.2−4 Evidence in support of this hypothesis is derived from the strong consistency between the molecular composition of ambient aerosol and aerosol produced in the oxidation of isoprene in environmental chambers.5 In particular, five-carbon tetrols (and derivatives such as oligoesters and sulfates), and the four-carbon 2-methylglyceric acid, 2-MG, and derivatives appear to be excellent chemical tracers of isoprenegenerated SOA.6 The formation of the tetrols (and their derivatives) has been traced to ring-opening heterogeneous phase reactions of dihydroxyepoxides7−11 that are produced in the gas phase oxidation of isoprene under low-NOx conditions (Figure 1).12 In contrast, the immediate gas phase precursor of 2-MG is not known. It has, however, been traced to the photooxidation of methacryloylperoxy nitrate (MPAN)10,11 produced in highNOx oxidation path from isoprene through methacrolein (Figure 1).5,13,14 Ravishankara and colleagues demonstrated that the atmospheric fate of methacrolein (MACR) was dominated by its reaction with the hydroxyl radical, OH.13 This chemistry proceeds via two reaction channels: abstraction of the aldehydic hydrogen atom (followed by O2 addition leading to formation © 2012 American Chemical Society

of peroxy acyl radical) or addition to the double bond, primarily at the external carbon atom. The branching ratios of the two reaction channels have been found to be 45% H-abstraction and 55% addition.15,16 Here, we focus on the fate of the peroxy acyl radical that is formed in the abstraction channel. In a companion study, we investigate the fate of the hydroxy peroxy radicals formed following addition of OH to MACR.17 Within the atmosphere the primary fate for peroxy acyl radicals is reaction with NO2 to form peroxy acyl nitrates (PANs) or reaction with HO2 radical to form peracids. Reaction of peroxy acyl radicals with HO2 has also been reported to have a significant yield for a radical propogating channel (generating OH + O2 + CO2 + alkyl radical) and a channel forming an acid and ozone. These additional reaction channels have only been studied in detail for the peroxy acetyl + HO2 reaction (e.g., Hansson et al.).18 For the purpose of this study, we assume that the peroxy acyl radical formed from MACR, reacts with NO2 to form methacryloylperoxy nitrate (MPAN) and with HO2 to form methacrylicperoxy acid (MPAA). In this study, we use high level quantum chemical calculations in combination with kinetics analysis, to show that the oxidation of MPAN by OH may produce an α-lactone in Special Issue: A. R. Ravishankara Festschrift Received: November 11, 2011 Revised: March 27, 2012 Published: March 27, 2012 5763

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Figure 1. Mechanism for the isoprene oxidation under low NOx condition to form dihydroxy-epoxides (IEPOX) and under high NOx condition to form methacrolein (MACR). MACR further oxidizes to form hydroxymethyl−methyl-α-lactone (HMML) under both high and low NOx conditions. Additional abbreviations used are methacryloylperoxy nitrate (MPAN), methacrylicperoxy acid (MPAA), isoprene hydroxyhydroperoxide (ISOPOOH), and hydroxyacetone (HAC). X is a base (e.g., OH, NO3) in HX (aq).

the gas phase at high yield. This α-lactone is a plausible precursor to formation of 2-MG as such compounds are known to undergo facile polymerization reactions.19 Here, we demonstrate the existence of a low potential energy path from MPAN following addition of OH to form hydroxymethyl−methyl-α-lactone (HMML) via elimination of the nitrate (NO3) radical (Figure 1). In an analogous fashion although with lower yield, we find that addition of OH to methacrylicperoxy acid (MPAA) (produced from the same peroxy radical as MPAN by reaction with HO2) can lead to a loss of OH and form hydroxymethyl−methyl-α-lactone (HMML). The reactions we describe for isoprene are also possible for other 1,3-dienes. As a parallel to MACR, we have also investigated the OH abstraction reactions from acrolein (ACR), a compound produced in the oxidation of butadiene and emitted from gas and diesel engines.20 For ACR we demonstrate that similar low potential energy paths exist to formation of hydroxymethyl-α-lactone (HML) with low yield.

for the open-shell species. For the latter no significant spin contamination is observed, with ⟨S2⟩ less than 0.82 before spin annihilation and approximately 0.75 after spin annihilation. The natural bond order was calculated at the B3LYP/aVTZ level using Gaussian09 with standard convergence criteria. We report the Wiberg bond indexes.28 All DFT calculations are calculated using the Gaussian09 program suite with the default convergence criteria.29 We improve the energies, by calculating single point energies with the explicitly correlated CCSD(T)-F12a/VDZ-F12 method (F12) at the B3LYP/aug-cc-pVTZ optimized structures.30,31 The F12 energies are zero point vibrational energy corrected with the B3LYP/aVTZ harmonic frequencies. The CCSD(T)-F12/VDZ-F12 method has been shown to be similar to the accurate and well recognized CCSD(T)/aug-ccpVQZ level of theory. 32 For the explicitly correlated calculations the CCSD(T)-F12a method has been chosen, because it has been recommended for use with double-ζ basis sets, and it has been shown that the choice between the F12a and F12b variants are negligible for relative energies.32,33 The calculations on open-shell species are unrestricted coupled cluster [UCCSD(T)-F12a] calculations based on a restricted-open Hartree−Fock (ROHF) determinant. The T1 diagnostic is less than 0.03 in all F12 calculations, which indicates that multiconfiguration effects are limited. All the coupled cluster calculations are calculated using the MOLPRO2010 program suite with the default convergence criteria.34 We have estimated the yield for the different reaction channels using the Rice−Ramsperger−Kassel−Marcus (RRKM) master equation model within the MultiWell 2011 program suite.35−37 We have used collisional activation and deactivation with the generalized exponential energy distribution.38 We have assumed irreversible reactions and used the B3LYP/aVTZ zero point vibrational energy corrected F12 energies, and the B3LYP/aVTZ vibrational frequencies and rotational constants. Further details are given in the Supporting Information.

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THEORETICAL METHODS All structures are initially optimized using the B3LYP21,22 hybrid density functional with the standard 6-31+G(d,p) double-ζ basis set.23,24 The optimized structures are then further refined using B3LYP with the aug-cc-pVTZ triple-ζ basis set (B3LYP/aVTZ).25 Harmonic vibrational frequencies are calculated for both B3LYP methods to confirm that each structure is either a minimum or a transition state (one imaginary frequency). The transition state (TS) structures are shown to connect the reactant and product on either side via intrinsic reaction coordinate (IRC) calculations with the B3LYP/6-31+G(d,p) method.26,27 The IRCs for the MPAN reaction are shown in the Supporting Information (Figure S1). The B3LYP energies are zero point vibrational energy corrected with the harmonic frequencies at the given method. For all the closed shell species, the restricted Kohn−Sham formalism is used, whereas the unrestricted Kohn−Sham formalism is used 5764

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RESULTS AND DISCUSSION In Figure 1 we sketch an overview of the mechanism for reaction of isoprene with OH to form epoxy compounds. Previously, the energetics of the low NOx reaction leading to formation of IEPOX have been calculated.12 Here, we have calculated the route to formation of hydroxymethyl−methyl-αlactone (HMML) from methacryloylperoxy nitrate (MPAN) or methacrylicperoxy acid (MPAA). MPAN and MPAA are formed from the peroxy acyl radical that arise from the hydrogen atom abstraction channel of MACR.13 The structure and relative energy of the stationary points found in the reaction from MPAN and MPAA to HMML are given in Figures 2 and 3, respectively. We compare the relative energies calculated with the three different methods in Tables 1 and 2, respectively. As a parallel reaction, we have also investigated the

reaction of the three-carbon equivalent, acrolein, leading to formation of peroxyacryloyl nitrate (APAN) and peroxyacrylic acid (APAA), which subsequently form hydroxymethyl-αlactone (HML) in a reaction similar to the one presented for MACR. (See the Supporting Information, Figures S2−S4 and Tables S1 and S2.) The energy calculated at the B3LYP/6-31+G(d,p) and B3LYP/aVTZ levels differ by less than 2 kcal/mol for all four reactions. Comparison with a B3LYP/aVTZ//B3LYP/6-31+G(d,p) calculation for the MPAN + OH reaction indicates that most of this difference is due to changes in basis set rather than changes between B3LYP/6-31+G(d,p) and B3LYP/aVTZ optimized geometries. The F12 single point energies at the B3LYP/aVTZ geometries are close to the B3LYP/aVTZ energies. The differences are less than 4 kcal/mol for all stationary points, similar in magnitude to difference found between these two approaches for sulfur related reactions.39,40 In the following we discuss only the F12 energies. The bond orders and bond lengths of selected bonds in the B3LYP/aVTZ optimized structure of HMML are shown in Figure 4.28 The structure is similar to structure of IEPOX, which is shown in the Supporting Information, Figure S5. In HMML, the carbonyl group strains the epoxide such that the C−O on the carbonyl side is significantly shorter than the C−O on the other side (1.32 versus 1.57 Å). A similar strain is observed in HML (see Figure S6 in Supporting Information). This asymmetry is visible in the bond orders, which are 1.09 versus 0.78 for the near and far side C−O bond, respectively. In comparison, the C−O bond lengths in IEPOX are almost equivalent with a length of 1.45 Å (1.44 Å) and a bond order 0.90 (0.87). Calculation of Reactions. The MPAN−OH and MPAA− OH compounds are both about 33 kcal/mol lower in energy than the corresponding reactants, MPAN + OH and MPAA + OH. The transition state to formation of HMML, M-TS, is about 18 and 12 kcal/mol lower in energy than the reactants, for the MPAN and MPAA reactions, respectively. Formation of HMML is exothermic from both intermediates, with a reaction energy of −45.8 kcal/mol for the elimination of NO3 from MPAN and −32.5 kcal/mol for the elimination of OH from MPAA. The reaction coordinate of the elimination reaction is the movement of the O atom from the NO3/OH fragment to the carbon atom. The distance between the breaking oxygen− oxygen bond is 1.66 and 1.79 Å in the elimination of NO3 and OH, respectively, whereas the forming oxygen−carbon bond is 2.15 and 2.08 Å in the elimination of NO3 and OH, respectively. The transition state describing the elimination of NO3 is more reactant-like than the transition state describing the elimination of OH; therefore the height of the energy barrier is lower for the elimination of NO3 from MPAN−OH than elimination of OH from MPAA−OH. The frequency of the reaction coordinate for elimination of NO3 is slightly lower than the one for the elimination of OH. We have found that HMML can further decompose to form hydroxyacetone (HAC) and CO through a transition state, ETS, with a relatively high barrier of about 25 kcal/mol. The reaction energy of this decomposition reaction is about −21 kcal/mol (exothermic). The reaction coordinate of E-TS describes the motion of the asymmetric epoxide structure, where the carbon−carbon bond on the carbonyl side and the short oxygen−carbon bond are breaking whereas the second oxygen−carbon bond is shortening and becoming a double bond.

Figure 2. Relative energies for the reaction of MPAN with OH with a loss of NO3 to form hydroxymethyl−methyl-α-lactone (HMML). The F12//B3LYP/aVTZ energies are corrected for zero point vibrational energy with the B3LYP/aVTZ harmonic frequencies. The B3LYP/ aVTZ geometries for each of the stationary points are shown.

Figure 3. Relative energies for the reaction of MPAA with OH with a loss of OH to form hydroxymethyl−methyl-α-lactone (HMML). The F12//B3LYP/aVTZ energies are corrected for zero point vibrational energy with the B3LYP/aVTZ harmonic frequencies. The B3LYP/ aVTZ geometries for each of the stationary points are shown. 5765

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Table 1. Energetics of the MPAN + OH Reaction (kcal/mol) compound

B3LYP/6-31+G(d,p)a

B3LYP/aVTZ//B3LYP/6-31+G(d,p)b

B3LYP/aVTZb

F12b

ΔHc

ΔGc

MPAN + OH MPAN−OH M-TS HMML + NO3 E-TS + NO3 HAC + CO + NO3 M-TS ν̃IMAG (cm−1) E-TS ν̃IMAG (cm−1)

0.0 −33.5 −22.7 −48.0 −22.7 −66.8 544i 411i

0.0 −32.4 −20.9 −47.5 −22.8 −67.5

0.0 −32.3 −20.8 −47.4 −22.7 −67.4 570i 397i

0.0 −32.9 −17.7 −45.8 −21.5 −66.8

0.0 −33.3 −17.9 −45.8 −21.7 −65.7

0.0 −25.3 −10.8 −49.7 −25.4 −81.3

a

Including B3LYP/6-31+G(d,p) ZPVE. bIncluding B3LYP/aug-cc-pVTZ ZPVE. cIncluding F12 energies and B3LYP/aug-cc-pVTZ thermal corrections at 298.15 K.

for energies above their respective decomposition barriers, the fraction of MPAN−OH reacting with O2 is small assuming kR+O2 = 2.3 × 10−12 cm3 molecules−1 s−1, which gives k′R+O2 = 1.2 × 107 s−1 at 1 atm pressure and 298 K.41 We have tested the sensitivity of the yields in the MPAN− OH decomposition to the energy of the NO3 leaving fragment (Table S4, Supporting Information). The HMML yield increases from 61% to 74% as the NO3 excess energy is increased from 3 to 6 kcal/mol. In comparison, the average excess thermal energy of the MPAN−OH is 6 kcal/mol. A decrease in temperature from 298 to 248 K will increases the HMML yield from 61% to 72% (Table S5, Supporting Information). Atmospheric Implications. The importance of the chemistry described in this study for atmospheric processes lies primarily in the potential for formation of atmospheric aerosol. In most atmospheric chemistry models, the formation of SOA is treated as a simple gas phase−heterogeneous phase equilibrium problem.2−4,42 If the route to SOA from isoprene leads through formation of gas phase epoxides, however, the aerosol production will depend critically on the chemical composition of the existing aerosol seeds. In particular, the production of low vapor pressure compounds will be determined by the rate and products of the ring-opening heterogeneous phase chemistry.7−9 The critical importance of heterogeneous phase chemistry is highlighted by the relative gas phase yields of IEPOX and HMML calculated using the GEOS-Chem photochemical transport model. We use the GEOS-Chem global 3-D chemical transport model v8.2.1.43 The model is driven by the GEOS-5 assimilated meteorology from the NASA Goddard Earth Observing System. Here the resolution of the model is 4° × 5° and 47 vertical layers. We have implemented the HMML formation pathway described here into the isoprene oxidation mechanism recently described by Paulot et al.44 Here, we assume that the addition of OH to the double bond of MPAN (MPAA) produces HMML with 61% (17%) yield. We find that ∼4 Tg of HMML are produced each year, with about 90% originating from MPAN. In contrast, we estimate approximately 250 Tg of IEPOX is produced each year.12,44 Shown in Figure 5 is a map of the amount of HMML produced in the boundary layer each day during northernhemisphere summer (August). Production of HMML is focused in regions with high isoprene emission and has a larger yield in areas with higher NOx concentrations (e.g., Southeast US). We express the production rate of HMML in μg m−3 day−1 to provide some context for the potential of this chemistry to impact organic aerosol. Boundary layer measurements of organic matter in aerosol are typically in the range 1−

Table 2. Energetics of the MPAA + OH Reaction (kcal/mol) compound MPAA + OH MPAA−OH M-TS HMML + OH E-TS + OH HAC + CO + OH M-TS ν̃IMAG (cm−1) E-TS ν̃IMAG (cm−1)

B3LYP/631+G(d,p)a

B3LYP/ aVTZb

F12b

ΔHc

ΔGc

0.0 −33.2 −16.5 −30.4 −5.1 −49.2

0.0 −32.0 −15.1 −30.1 −5.4 −50.1

0.0 −32.7 −11.5 −32.5 −8.2 −53.4

0.0 −33.6 −12.1 −32.4 −8.2 −52.3

0.0 −24.0 −3.3 −32.0 −7.6 −63.5

527i

548i

411i

397i

a

Including B3LYP/6-31+G(d,p) ZPVE. bIncluding B3LYP/aug-ccpVTZ ZPVE. cIncluding F12 energies and B3LYP/aug-cc-pVTZ thermal corrections at 298.15 K.

Figure 4. Hydroxymethyl−methyl-α-lactone (HMML) with bond orders (top) and bond lengths (bottom) indicated for selected bonds.

Kinetics. We have estimated the fraction of MPAN−OH and MPAA−OH that decompose to form HMML using a RRKM master equation model.35 In all calculations we have used a pressure of 1 atm and temperature of 298 K, unless otherwise stated. The RRKM-rate constant for decomposition of nascent MPAN−OH into HMML and NO3 is kMPAN−OH = 8.6 × 108 s−1 whereas the decomposition rate for nascent MPAA−OH into HMML and OH is much slower at 1.7 × 107 s−1, assuming no excess energy of MPAN−OH/MPAA−OH, and kMPAN−OH = 4.4 × 109 s−1 and kMPAA−OH = 1.3 × 108 s−1 assuming thermally averaged excess energy. At 1 atm pressure, the collision rate between MPAN−OH and the surrounding bath gases is ∼1.7 × 1010 s−1. We assume that the NO3 (OH) fragment leaves with 3 kcal/mol of excess energy. For the MPAN−OH (MPAA−OH) decomposition, we predict that 98% (17%) should decompose and that 2% (83%) will be collisionally stabilized below the decomposition barrier and ultimately react with O2. Of the 98% MPAN−OH that decomposes, 61% will be stabilized as HMML and 36% will undergo an additional decomposition yielding HAC. For MPAA the HMML yield is 17% with less than 1% HAC being formed (Table S3, Supporting Information). Note that 5766

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Danish Council for Independent Research - Natural Sciences, the Danish Center for Scientific Computing (DCSC), NASA (NNX08AD29G), and NSF (ATM-0934408) for funding. F.P. is supported by a Ziff environmental fellowship through the Harvard University Center for the Environment.

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Figure 5. The formation rate of hydroxymethyl−methyl-α-lactone (HMML) in the planetary boundary layer (here defined as pressure >800 mbar) in August calculated using the GEOS-Chem photochemical transport model with the isoprene mechanism updated to include the chemistry described here.12,47 Units are μg m−3 day−1.

5 μg m−3, and their lifetime is estimated to be no more than a few days.45,46 Thus, only if the yield of aerosol from HMML is high will this chemistry contribute significantly to the total organic aerosol burden.

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CONCLUSIONS We have identified a thermodynamically accessible route to αlactone production following OH addition to MPAN and MPAA. Both density functional theory and explicitly correlated coupled cluster theory suggest that, following OH addition, NO3 or OH can be eliminated from MPAN and MPAA, respectively, forming HMML. Our RRKM master equation analysis suggests that the HMML yield from MPAN is about 60% with a smaller HMML yield of about 20% from MPAA. Unfortunately, we have no direct experimental evidence for this chemistry. Because the α-lactone is likely very unstable on surfaces, their formation may need to be evaluated by heterogeneous phase trapping experiments or perhaps a search for the NO3 produced from MPAN plus OH reaction.

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ASSOCIATED CONTENT

* Supporting Information S

IRC for the MPAN reaction; acrolein hydrogen abstraction reaction mechanism; relative energies and structures of APAN + OH and APAA + OH reactions; bond order and bond lengths in IEPOX and HML; tables with calculated relative energies. Details of RRKM master equation analysis and tables of yields. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: H.G.K., [email protected]. Phone: 45-35320334. Fax: 45-35320322; P.O.W., [email protected]. Phone: 626395-2447. Present Address

∥ Now with the School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to the reviewers for suggesting the RRKM master equation analysis and to John Barker for helpful discussions regarding the MultiWell program. We thank The 5767

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dx.doi.org/10.1021/jp210853h | J. Phys. Chem. A 2012, 116, 5763−5768