The Importance of Peroxy Radical Hydrogen Shift Reactions in

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The Importance of Peroxy Radical Hydrogen Shift Reactions in Atmospheric Isoprene Oxidation Kristian H. Møller, Kelvin H Bates, and Henrik Grum Kjaergaard J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b10432 • Publication Date (Web): 07 Jan 2019 Downloaded from http://pubs.acs.org on January 10, 2019

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The Journal of Physical Chemistry

The Importance of Peroxy Radical Hydrogen Shift Reactions in Atmospheric Isoprene Oxidation Kristian H. Møller,

†

Kelvin H. Bates,

‡

and Henrik G. Kjaergaard

∗,†

†Department

of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark ‡Harvard University, Center for the Environment, 29 Oxford St., Cambridge, MA, USA 02138 E-mail: [email protected]

Phone: +45-35320334. Fax: +45-35320322

Abstract With an annual emission of about 500 Tg, isoprene is an important molecule in the atmosphere. While much of its chemistry is well constrained by either experiment or theory, the rates of many of the unimolecular peroxy radical hydrogen shift (H-shift) reactions remain speculative. Using a high-level multi-conformer transition state theory (MC-TST) approach, we determine recommended temperature dependent reaction rate coecients for a number of the H-shift reactions in the isoprene oxidation mechanism. We nd that most of the (1,4; 1,5 and 1,6) aldehydic and (1,5 and 1,6) α-hydroxy H-shifts have rate constants at 298.15 K in the range 10-2 s-1 - 1 s-1 , which make them competitive with bimolecular reactions in the atmosphere under typical atmospheric conditions. In addition, we nd that the rate coecients of dierent diastereomers can dier by up to three orders of magnitude, illustrating the importance of chirality. 1

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Implementation of our calculated reaction rate coecients into the most recent GEOSChem model for isoprene oxidation shows that at least 30 % of all isoprene molecules emitted to the atmosphere undergo a minimum of one peroxy radical hydrogen shift reaction during their complete oxidation to CO2 and deposited species. This highlights the importance of peroxy radical H-shifts reactions in atmospheric oxidation.

Introduction With an estimated annual emission of about 500 Tg, isoprene (2-methyl-1,3-butadiene, C5 H8 ) is the most highly emitted non-methane hydrocarbon in the atmosphere. 14 Not surprisingly, its oxidation chemistry plays a crucial role in the chemistry of the atmosphere and has motivated substantial eorts towards unravelling its oxidation mechanism. Recently, the gas-phase chemistry of isoprene and its major oxidation products was reviewed. 5 While parts of its chemistry are well constrained, much still remains to be determined. 5 Although the key unimolecular peroxy radical hydrogen shift (H-shift) reactions in the atmospheric oxidation of isoprene were proposed in 2009, the rates of most of the possible H-shifts in the isoprene oxidation remain poorly constrained, as only very few H-shift reactions have experimentally determined rate coecients. 610 The rate coecients determined for these reactions show that the unimolecular peroxy radical H-shifts may be competitive with the ever-present bimolecular reactions (e.g. with HO2 , NO or RO2 radicals) at typical atmospheric concentrations of the bimolecular reaction partners. 11,12 However, both theory and experiments have shown that the rates of H-shifts are highly sensitive to the chemical structure of the peroxy radical and the type of H-shift. 69,1316 To assess the competition between uni- and bimolecular reactions, it is thus important to know the rate coecients of the Hshift reactions accurately.

Due to the scarcity of available experimental rate coecients, the rate coecients for the majority of the peroxy radical hydrogen shift reactions in the reviewed isoprene oxidation 2


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mechanism are described by generic temperature-dependent rate coecients estimated from known, primarily calculated, rate coecients. 59,14,17 For example, rate constants (at 298 K) of 0.5, 20, and 5 s-1 were employed for 1,4; 1,5 and 1,6 aldehydic H-shifts, respectively. 5 For both 1,5 and 1,6 α-hydroxy H-shifts that form allylic, secondary, and primary carboncentered radicals, respectively, rate constants of 5, 0.1, and 0.05 s−1 were employed. 5 The dierent types of H-shifts are illustrated in Figure 1. All H-shift rate coecients employed in Wennberg et al. 5 are summarized in Table S1.

Figure 1: Schematic overview of the types of hydrogen shift reactions studied here exemplied as the simplest 1,6 H-shifts. The red hydrogen atom corresponds to the one being abstracted by the peroxy radical during reaction. In an eort to constrain the reaction rates for some of the unimolecular H-shifts in the isoprene oxidation, we use the high-level quantum chemical kinetics multi-conformer transition state theory (MC-TST) approach by Møller et al. to calculate their rate coecients. 18 This approach has repeatedly shown excellent results with calculated reaction rate coecients within a factor of ve of the corresponding experimental values. 9,10,18,19 In Table 1 we compare our calculated rate coecients with the available experimental values. Compared to a high-level theoretical MC-TST benchmark, the approach developed in Møller et al. was found to dier less than about a factor of two for the system studied. 18

Here, we focus on selected peroxy radicals formed in signicant yields according to the current isoprene oxidation mechanism and whose H-shift rates are largely undetermined. The peroxy radicals studied are (1) three dierent peroxy radicals formed in the oxidation of two C4 carbonyls from the the OH oxidation of IEPOX: 2-hydroxy-3-oxobutanal (HOBA) and 2,3-dihydroxy-2-methylpropanal (DHMP); (2) the two CO, OH and OOH-substituted 3



peroxy radicals (isoprene-CO-OH-OOH-OO) produced by isoprene hydroxy peroxy radicals (ISOPOO) + NO; (3) the peroxy radicals formed following the 1,6 α-hydroxy H-shifts in the two Z-δ -ISOPOO isomers; and (4) those formed in the OH-induced oxidation of isoprene hydroxy hydroperoxide (ISOPOOH). 6,2023 The reactants of the studied reactions are shown in Figure 2. Schemes for their formation are shown in Section S14 and include 1,6 α-OH peroxy H-shifts, fast enolic peroxy H-shifts and alkoxy H-shifts. 6,21,22

The reactions studied here primarily encompass those H-shift reaction classes expected to be competitive with bimolecular chemistry in the environment. 59,1315 The calculated reaction rate coecients provide guidelines for the ranges of rate coecients one can expect for a given reaction type and expand recent systematic studies by including a more diverse set of reactions within the same reaction class. 15,16,2426 Such guidelines are useful for future modeling of H-shifts for systems where experimental or theoretical values are not available.

4


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Figure 2: Reactants of the peroxy H-shift reactions studied along with the scheme in which they are studied. For the origin of these in the isoprene oxidation, see text and Section S14. Due to the rapid hydroperoxy H-shifts, the other peroxy radicals formed from these are also studied. 14

5



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Table 1: Reaction rate coecients (s-1 ) determined experimentally (kexpt. ) and calculated with the approach by Møller et al. 18 which uses F12 for the barrier height (kF12 ) and using the same approach without the F12 single-point energy correction (kωB97X-D ) along with the temperature (T in K) at which they are determined. The hydrogen highlighted in red in the reactant is the one being transferred in the reaction. Reactant

a b

c

Ref.

Reaction

T

kF12

kωB97X-D

kexpt.

7,18

1,4 aldehydic H-shift

296 (expt.) 298.15 (calc.)

0.48

0.20

0.5 ± 0.3

13,18

1,5 alkyl H-shift

296 (expt.) 298.15 (calc.)

9.2 × 10−3

2.7 × 10−3

≤ 2 × 10−3

13,18

1,5 α-OOH H-shift

296 (expt.) 298.15 (calc.)

(R,S ) 0.25 (S,S ) 0.54

(R,S ) 0.30 (S,S ) 0.89

> 0.1a

9

1,5 α-OH H-shift

296

(R,S ) 0.13 (S,S ) 0.11

0.048a +0.036/-0.024

9

1,6 α-OH H-shift

296

(R,S ) 0.30 (S,S ) 0.055

(R,S ) 0.087 (S,S ) 0.11

10

1,5 α-OOH H-shift

296

10

1,5 α-OH H-shift

19

19

(R,S ) 0.48 (S,S ) 0.16

0.14a +0.071/-0.053

0.045

0.031

0.050 +0.065/-0.023

296

0.28

0.11

0.22 +0.14/-0.04

Sum of unimolecular reactionsb

296 (expt.) 298.15 (calc.)

anti 1.8 syn 2.5

anti 1.7 syn 1.4

4a ± 2

Sum of unimolecular reactionsc

296 (expt.) 298.15 (calc.)

5.7

1.1

16 ± 5

Average of diastereomers. The reactions calculated to dominate are: anti : 1,5 allylic H-shift; 1,6 allylic α-OH H-shift and 6-membered endoperoxide formation. syn : 6-membered endoperoxide formation and 1,5 allylic H-shift. The reactions calculated to dominate are: 6-membered endoperoxide formation; 1,5 allylic H-shift and 1,6-allylic H-shift.

We incorporate our calculated temperature-dependent reaction rate coecients into the isoprene oxidation model compiled as part of the recent review on isoprene. 5 We implement 6


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this mechanism in GEOS-Chem, to assess the atmospheric importance of the dierent peroxy radical hydrogen shift reactions for the overall isoprene oxidation. 27

Theory and Methods Calculation of Reaction rate coecients Reaction rate coecients are calculated using the approach by Møller et al., but with a single-point energy cut-o of conformers at the B3LYP/6-31+G(d) (abbreviated B3LYP) level rather than optimizing all conformers at this level. 18 Initially, a structure of an arbitrary conformer of reactant and transition state (TS) is optimized in Gaussian 09 using B3LYP/631+G(d). 2833 For these optimized structures, a conformational sampling is done in Spartan '14 or '16 using MMFF with a neutral charge enforced on the radical atom center. 18,34,35 Due to the high number of conformers for most of the exible systems studied here (up to ∼6000 for a single TS), the conformational sampling is followed by single-point energy calculations at the B3LYP/6-31+G(d) level in Gaussian 09. 18 Following the single-point calculations, a high energy cut-o of 100 kcal/mol relative to the lowest-energy structure was used to eliminate very high-energy structures, while keeping all potentially important conformers. For a test set of 11 reactions for which all conformers were B3LYP optimized, the 100 kcal/mol cut-o following single-point calculations was found to yield results identical to the values obtained without the cut-o (see Section S4). However, even with a cut-o of 100 kcal/mol following the B3LYP single-point calculations, the risk of missing important conformers is slightly increased and so is the uncertainty in our calculated rate coecients. Following the single point energy calculations, all structures with electronic energies below the 100 kcal/mol cut-o are optimized at the B3LYP/6-31+G(d) level in Gaussian 09. Duplicate conformers are removed based on their energies and dipole moments the bash-wrapped Python script "confcheck". 18,36 All unique conformers with electronic energies (Ee ) within 2 kcal/mol of the lowest-energy conformer are further optimized using ω B97X-D/aug-cc-pVTZ, as in the 7



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approach by Møller et al. 18,3739 A 2 kcal/mol cut-o based on electronic energy was found to make only a small dierence to the rate coecient calculated using all conformers. 18 A likely explanation is that the decrease in electronic energy of even a weak hydrogen bond of 2 kcal/mol is only very partially oset in Gibbs energy by loss of entropy. Furthermore, any eect will likely be comparable for reactant and TS and thus to some extent cancel. For the lowest energy conformer at the ω B97X-D/aug-cc-pVTZ level (electronic energy including the zero-point vibrational energy (ZPVE) correction) of each reactant and transition state, an ROCCSD(T)-F12a/VDZ-F12//ω B97X-D/aug-cc-pVTZ (abbreviated F12) singlepoint calculation is done in Molpro 2012 to obtain more accurate electronic energies. 4045 The restricted open-shell (RO) formalism was used to minimize potential issues with spincontamination. Output les for all ω B97X-D/aug-cc-pVTZ and F12 calculations are available online (https://sid.erda.dk/public/archives/741e77b865aca935fa574fcfc152b3d9/publishedarchive.html). These include all the ω B97X-D/aug-cc-pVTZ optimized xyz-geometries used.

Reaction rate coecients are calculated using multi-conformer transition state theory (MCTST). 18,4648 The inclusion of multiple conformers is important as it can have a large eect on the calculated rate coecient as shown e.g. in Møller et al. and in a very recent study employing multi-structural variational transition state theory (MS-VTST). 18,49 The expression for the reaction rate coecient, k, in MC-TST is: 18,4648 All TP S conf.

kB T k=κ h

i All R Pconf. j

exp

−∆Ei kB T

exp

−∆Ej kB T

QT Si QRj

E T S − ER exp − kB T

where κ is the tunneling coecient, kB is Boltzmann's constant,

T

(1)

is the temperature, h is

Planck's constant, E is the energy (Ee + ZPVE) and Q is the partition function (harmonic oscillator and rigid rotor). The sums over all transition state and reactant conformers sum their partition functions (evaluated at the lowest vibrational energy level) weighted by their Boltzmann factor calculated relative to the corresponding lowest-energy conformer. For8


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mally, all conformers should be included, but here only conformers within 2 kcal/mol of the lowest-energy conformer at the B3LYP/6-31+G(d) level are included in the sum, which has previously been shown to add only little error. 18 The nal exponential term depends on the reaction barrier: the ZPVE-corrected energy dierence between the lowest-energy conformer of transition state and reactant. In Section S5 we derive Equation 1 from the TST equation and the expression for the total Gibbs energy in a system of multiple conformers, as an alternative to the earlier derivation. 18,46,47,50 The MC-TST rate coecients are high-pressure limit values. Several studies have suggested that this is a good assumption for peroxy radical H-shifts at 298.15 K and 1 atm. 22,51,52 Tests done here for selected representative reactions (see Section S2) show that even for the fastest reactions, the eect is less than 6%. Thus using a high-pressure approach (MC-TST) appears to be valid for these reactions. No corrections have been applied for hindered rotation, as it has been suggested to be only a small eect when used in combination with MC-TST. 18 A very recent theoretical study found agreement to within a factor of two of rate coecients calculated using the MC-TST approach by Møller et al. and conventional TST using the lowest-energy conformers and including a hindered rotor correction. 15

In accordance with the approach by Møller et al., the tunneling coecient is calculated using the one-dimensional Eckart approach based on the conformers connected by an IRC to the lowest-energy TS conformer. 18,53 Barriers are calculated at the F12 level of theory, while the imaginary frequency of the TS is calculated using ω B97X-D/aug-cc-pVTZ. For the α-hydroperoxy H-shifts, the product end-point is unstable with regard to OH-loss. 54,55 To obtain reverse tunneling barriers for these, constrained optimizations of the products are used, with the O-O bond length constrained to the value for which the IRC has the smallest gradient before the OH group starts dissociating. See Section S3 for a full description of the calculation of the reaction rate coecients.

9



For most of the reactions studied, the reaction barrier is calculated using the F12 electronic energy with ω B97X-D/aug-cc-pVTZ ZPVE and ω B97X-D/aug-cc-pVTZ is used for the relative energies between conformers and partition functions. However, for the hydroxy and hydroperoxy H-shifts, the electronic energies (for both the reaction barrier and the tunneling coecient) are also calculated using ω B97X-D/aug-cc-pVTZ. For the transition states of these reactions, we nd that the HF calculation providing the reference wave function for the F12 calculation can yield multiple solutions depending on how it is initiated, resulting in large dierences in the F12 energies (see Section S6). Therefore, the F12 energies are not used for these two reaction classes. Similar issues are not observed at the ω B97X-D/aug-cc-pVTZ level. The use of ω B97X-D/aug-cc-pVTZ for the barrier height increases the uncertainty of the H-shift rate coecients. We estimate the uncertainty for the ω B97X-D/aug-cc-pVTZ H-shift rate coecients to be about a factor of 100 due to the increased uncertainty in the barrier height (see below). However, the results in Table 1 suggest that the ω B97X-D/augcc-pVTZ rate coecients are generally better than this.

Abstraction from hydroperoxy groups has previously been found to be very rapid and thus likely to outcompete all other reactions. 14,17,56 As these are also reversible, the subsequent chemistry is governed more by the relative rate of the forwards and backwards reactions than the absolute rate coecients. The ratio of the forward and reverse reactions depends only on the reactant and products, and can thus be obtained at the F12 level, as the abovementioned issue is observed only for the transition states. In the GEOS-Chem modeling, the distribution between peroxy radicals is included at the F12 level. However, the ratio calculated with ω B97X-D/aug-cc-pVTZ and F12 diers by at most a factor of three (see Table S4).

Tests for three H-shift reactions leading to a carbon centered radical conrm, as previously observed, that the reverse H-shifts are not competitive with the competing O2 -addition (see Table S5) and the reaction rate coecients for the reverse reactions are thus not calculated 10


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for the remaining H-shifts forming carbon-centered radicals. 15,26,57

Most of the peroxy radicals studied here have two chiral centers and thus exist as two sets of diastereomers, each consisting of a pair of enantiomers. Recent calculations on the Hshifts in two hexanol-derived peroxy radicals and in a series of hydroperoxy peroxy radicals have suggested that dierent diastereomers may have rate coecients that dier by up to

R,R and R,S isomers The S,S (S,R ) isomer and R,R (R,S ) isomer are

an order of magnitude. 9,16 We therefore calculate the rate of both the for all reactions with two stereocenters.

enantiomers and have identical reaction rate coecients.

The reaction rate coecients for the

R,R isomers of the peroxy radicals in Schemes 8 and 9

were calculated previously using a slightly dierent approach, but are included here following slight modications (see Section S9). 57 Following the modications, the two approaches yield identical results for a test reaction.

Previous studies have shown a strong temperature dependence of the H-shift rate coecients and therefore, we determine also the temperature dependence of the rate coecients. 9,21,22,58 The temperature dependence of the rate coecients, k, is tted as: 5,9,22

k = Ae−B/T eC/T The parameters

A, B

and

3

(2)

C, are determined from independent ts of the rate coecients

(without tunneling) and tunneling coecients calculated in the temperature range from 290 K - 320 K in steps of 5 K.

B

is obtained from the t of the rate coecients and

the t of the tunneling coecients, while

C

from

A is the product of the prefactors from the two

independent ts. These ts reproduce the calculated rate coecients for all reactions and temperatures to within 3 %. The temperature dependence t parameters for all reactions are given in Section S12. 11



Throughout this work, we evaluate our temperature-dependent rate coecients at 298.15 K for discussion in the text and incorporation into gures, and refer to these values as rate constants (rather than coecients). The temperature dependences of the coecients, along with their barrier heights, partition functions, and tunneling coecients, can be found in Tables S7-S12.

Uncertainty in the MC-TST calculation arises from errors in 1) the barrier height, 2) tunneling and 3) the sums of partition functions. For the barrier heights at the ROCCSD(T)F12a/VDZ-F12//ω B97X-D/aug-cc-pVTZ level, we assign an uncertainty of 0.7 kcal/mol, which is the mean average deviation observed in a large study of 104 reaction energies comparing CCSD(T)-F12a/VDZ-F12 (albeit with scaled triples) to CCSD(T)/CBS. 59 For two recently studied peroxy radical H-shift reactions, the ROCCSD(T)-F12a/VDZ-F12//ω B97XD/aug-cc-pVTZ barrier heights is found to be within 0.6 kcal/mol of barrier with geometries at the ROCCSD(T)-F12a/VDZ-F12 level and single-point energies at higher levels, see Otkjaer et al. and Section S16. 15,18 A 0.7 kcal/mol dierence in barrier height corresponds to about a factor of three dierence in the rate coecient. Compared to higher level tunneling approaches, the Eckart approach has been reported to deviate between factors of 0.7 and 2.3, so we assign a factor of two uncertainty to the tunneling coecient. 60,61 For the uncertainty of the 2 kcal/mol cut-o of conformers and the use of the harmonic oscillator partition functions, we assign a total of a factor of two uncertainty based on the analysis in Møller et al. and comparisons of the harmonic oscillator to hindered rotor calculations for other systems. 15,18,60,62 A recent study found agreement to within a factor of two for the MC-TST approach employed here and several studies using conventional TST with hindered rotor corrections. 15 As some of these uncertainties are expected to partly cancel, we thus assign a total uncertainty of a factor of 10 to the rate coecients calculated using barriers at the ROCCSD(T)-F12a/VDZ-F12//ω B97X-D/aug-cc-pVTZ (abbreviated F12) level. 9,15 Due to 12


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the larger uncertainty of the barrier heights calculated at the ω B97X-D/aug-cc-pVTZ level, we assign a factor of 100 total uncertainty to the hydroxy and hydroperoxy rate coecients with barrier heights at that level.

GEOS-Chem Modeling Global simulations of the isoprene chemistry described here are conducted using GEOS-Chem v11-02c. 27 GEOS-Chem integrates assimilated observations of meteorological data from the NASA Goddard Earth Observing System (GEOS) to run a three-dimensional model of atmospheric chemistry using an editable chemical mechanism. Here, we perform ve separate simulations with diering isoprene oxidation mechanisms on a global grid of 4◦ latitude by 5◦ longitude with 72 vertical levels. We spin each model up with a preliminary 12-month simulation, after which results from the following 12 months are recorded and used. The results reported in Table 3 and Section S15 are annual global averages over the period 1 July 2014 - 1 July 2015.

Our ve unique iterations of the isoprene chemistry used in the model include: (1) one with the basic v11-02c chemistry ("v11"); (2) one using the revised isoprene mechanism from the recent review ("Review"); 5 (3) one with the new rate coecients calculated herein averaged

R,R and R,S isomers ("NewMean"); (4) one with the new rate coecients calculated herein and treating R,R and R,S isomers separately ("New"); and (5) one with the same

across

mechanism as (2) but with all H-shift rate coecients set to zero ("NoShifts").

GEOS-Chem v11-02c includes a simplied isoprene oxidation framework 63 which has been updated extensively to incorporate novel results from chamber and eld observations. 6468 The "Review" mechanism simply replaces this isoprene chemistry with the "reduced-plus" model presented in the review by Wennberg et al. 5 The "reduced-plus" model uses available measured H-shift rate coecients and the generic estimates described in the introduction 13



and shown in Table S1 where no measurements exist. 5 The "NewMean" simulation uses the "Review" mechanism but replaces the generic rate coecients of H-shifts with our calculated temperature-dependent rate coecients, using an average of the calculated rate coecients of R,R and R,S stereoisomers where applicable. In the "New" mechanism, the R,R and R,S stereoisomers are assumed to form as a 50:50 racemic mixture and react by their individual H-shift rate coecients.

The hydroperoxy peroxy radicals in Schemes 4-10 are all able to undergo rapid hydroperoxy H-shifts (as dened in Figure 1). 14 For the global modeling, we assume that these are fast enough that the corresponding peroxy radicals are in constant equilibrium. Therefore, they are not treated individually in the model, but rather as a single species. The rate coecients of each of the subsequent H-shifts are multiplied by the relative abundance of the corresponding peroxy radical, as determined from the equilibrium constants.

Results and Discussion The dominant reactions competing with unimolecular H-shifts of peroxy radicals are the bimolecular reactions with NO, HO2 and RO2 radicals. 11,12 The GEOS-Chem modeling conducted as part of this study suggests that under typical conditions of isoprene emission, unimolecular reaction rate constants need to be about 10−2 s-1 at 298.15 K to start being competitive with the bimolecular chemistry. On the other hand, unimolecular reactions with rate constants above 1 s-1 are typically fast enough to dominate over most of the competing bimolecular reactions.

Calculated Reaction Rate Coecients Three dierent peroxy radicals are formed in the OH-initiated oxidation of HOBA and DHMP. 20 The possible 1,5 and 1,6 peroxy radical H-shifts of these species along with their 14


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calculated reaction rate constants are shown in Schemes 1-3. The calculated rate coecients are summarized in Table S7.

Scheme 1: Peroxy radical hydrogen shift reactions studied for the peroxy radical formed in the OH oxidation of HOBA (boxed).

Scheme 2: Peroxy radical hydrogen shift reactions studied for the rst of the peroxy radicals formed in the OH oxidation of DHMP, DHMP-OOA (boxed).

Scheme 3: Peroxy radical hydrogen shift reactions studied for the second of the peroxy radicals formed in the OH oxidation of DHMP, DHMP-OOB (boxed). The two largest rate constants are found for the 1,5 aldehydic (3C in DHMP-OOB, k = 0.26 s-1 ) and 1,5 α-hydroxy (2C in DHMP-OOA, k = 0.030 s-1 ) H-shifts corresponding to the classes of H-shifts that have previously been observed to be fast. 7,9 With rate constants of 0.26 s-1 and 0.030 s-1 , respectively, these reactions are fast enough that they need to be 15



considered in the atmospheric oxidation of DHMP. As previously observed, abstraction from a methyl group is found to be slow (< 6×10−3 s-1 ) in all cases, due to the formation of a primary radical. 15,24,25 However, the methyl hydrogen shifts calculated here are signicantly faster than those calculated at the same level of theory in comparable systems without oxygen-containing substituents (∼10−6 s-1 ) suggesting signicant substituent eects. 15

The remaining peroxy radical hydrogen shifts from the isoprene oxidation mechanism studied here are shown in Schemes 4-10. For simplicity, we have included only the reaction rate constants of the

R,R

isomers. The barrier heights for the hydroperoxy H-shifts are

calculated using ω B97X-D/aug-cc-pVTZ, while the barrier heights for all other H-shifts are calculated using F12. All calculated reaction rate coecients along with their temperature dependencies are summarized in Tables S8-S12.

Scheme 4: Unimolecular reactions of the isoprene-CO-OH-OOH-OO isomer produced by δ 1,4-ISOPOO + NO (boxed). Solid arrows correspond to the reactions studied here, while the dashed arrow corresponds to a reaction not studied here, but assumed to be fast and with a yield of unity in the model. Rate coecients given in the gure are for the R,R isomer, with the R,S rate coecients given in Table S8. Based on Figure 7 in Wennberg et al. 5 .

16


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Scheme 5: H-shift reactions of the isoprene-CO-OH-OOH-OO isomer produced by δ -4,1ISOPOO + NO (boxed). Solid arrows correspond to the reactions studied here, while the dashed arrow corresponds to a reaction not studied here, but assumed to be fast and with a yield of unity in the model. Rate constants given in the gure are for the R,R isomer, with the R,S rate constants given in Table S8. Based on Figure 7 in Wennberg et al. 5

Scheme 6: H-shift reactions of the peroxy radical formed following the 1,6 H-shift of the Z-(1-OH,4-OO)-ISOPOO radical (boxed). Solid arrows correspond to the reactions studied here, while the dashed arrow corresponds to a reaction not studied here, but assumed to be fast and with a yield of unity in the model. Rate constants given in the gure are for the R,R isomer, with the R,S rate constants given in Table S8. Based on Figure 9 in Wennberg et al. 5

17



Scheme 7: H-shift reactions of the peroxy radical formed following the 1,6 H-shift of the Z-(4-OH,1-OO)-ISOPOO radical (boxed). Solid arrows correspond to the reactions studied here, while the dashed arrow corresponds to a reaction not studied here, but assumed to be fast and with a yield of unity in the model. Rate constants given in the gure are for the R,R isomer, with the R,S rate constants given in Table S8. Based on Figure 10 in Wennberg et al. 5

Scheme 8: H-shift reactions of the peroxy radicals formed from external addition of OH to β -(1,2)-ISOPOOH (boxed top) and β -(4,3)-ISOPOOH (boxed bottom). Solid arrows correspond to the reactions studied here, while the dashed arrows correspond to reactions not studied here, but assumed to be fast and with a yield of unity in the model. Rate constants given in the gure are for the R,R isomer, with the R,S rate constants given in Table S9. Based on Figures 19 and 20 in Wennberg et al. 5

18


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Scheme 9: H-shift reactions of the peroxy radicals formed from internal addition of OH to β -(1,2)-ISOPOOH (boxed). Solid arrows correspond to the reactions studied here, while the dashed arrows correspond to reactions not studied here, but assumed to be fast and with a yield of unity in the model. Rate constants given in the gure are for the R,R isomer, with the R,S rate constants given in Table S9. Based on Figure 19 in Wennberg et al. 5

Scheme 10: H-shift reactions of the peroxy radicals formed from internal addition of OH to β -(4,3)-ISOPOOH (boxed). Solid arrows correspond to the reactions studied here, while the dashed arrows correspond to reactions not studied here, but assumed to be fast and with a yield of unity in the model. Rate constants given in the gure are for the R,R isomer, with the R,S rate constants given in Table S9. Based on Figure 20 in Wennberg et al. 5 With calculated rate constants in the range 2.9 × 101 s-1 to 6.5 × 105 s-1 , the hydroperoxy H-shifts are faster than the competing uni- and bimolecular reaction. This leads to rapid scrambling back and forth between the dierent hydroperoxy peroxy radicals, in agreement with previous studies. 14,56 Thus, the abundance of the individual peroxy radicals connected by such reactions are governed by the relative rate constants for these rapid hydroperoxy H-shifts. In some of the systems studied here (e.g. the oxidation of ISOPOOH, see Schemes 9 and 10), the rapid hydroperoxy peroxy scrambling will not only aect the overall rate of peroxy radical conversion, but may lead to dierent products with vastly dierent functionality and reactivity (e.g. epoxides vs. aldehydes). 14 The unity yield of epoxides from 19



the dihydroperoxy dihydroxy alkyl radicals in Schemes 8-10 are based on the calculations in D'Ambro et al. for the external addition products (Scheme 8). 57 Due to the similar structure of the radicals from internal addition, they are assumed to react comparably fast. Unlike the reaction forming IEPOX from OH-addition to ISOPOOH, the epoxide formation in D'Ambro et al. does not rely on excess energy, but has a thermalized rate which is able to outcompete O2 -addition. 57,69

Most of the other reactions studied here have rate constants in the range 10−3 s-1 - 1 s-1 which is comparable to the rates of the competing bimolecular reactions under typical atmospheric conditions. While this means that the importance of these pathways will depend on the atmospheric conditions, the range of these rate constants also suggests that these types of H-shift reactions need to be considered when compiling atmospheric oxidation models.

A very recent paper on the OH-initiated oxidation of isoprene includes a calculated rate constant for reaction 7D studied here. 70 They calculate a multi-conformer TST rate constant at the ROCBS-QB3//M06-2X/6-311++G(2df,2p) level of 0.86 s-1 at 298 K, which is about a factor of 4-5 larger than the rate constants of 0.20 s-1 (R,R ) and 0.15 s-1 (R,S ) calculated here. Their somewhat larger rate constant is likely due to a dierent level of theory for the barrier height and consideration of fewer conformers. For the reactant, they identify a total of 9 conformers (considering rotation around two of the bonds), whereas we identify more than 600 conformers and include the 8 lowest-energy of these at the ω B97X-D level (2 kcal/mol cut-o) in addition to three IRC end-point conformers. As part of this previous study, ow tube experiments were performed using a CI-APi-ToF mass spectrometer with nitrate (NO3 - ) and Iodide (I- ) as the reagent ions. These identify masses corresponding to the peroxy radicals in Schemes 4-7 as well as the products of their aldehydic H-shifts, in agreement with the review by Wennberg et al. 5 and this work. As the authors argue, the H-shifts in Schemes 4-7 provide a route from isoprene to highly oxidized molecules (HOM) 20


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without invoking a second reaction with OH. Eorts to minimize multigenerational chemistry in the experiments also explains why they do not observe the reactants and products of the remaining schemes in this work. An earlier study estimated reactions 6D and 7D to have rate constants on the order of 0.1 s-1 based on barriers for similar reactions. 22 Based on barrier heights of about 20 kcal/mol at the CBS-QB3 level, the rate constants for the 1,4-aldehydic H-shifts 4B and 5B were previously estimated to be in the range 0.01-0.1 s-1 . 21 The range we nd here for the two reactions (including the variation from stereoisomers) is 0.04 s-1 to 0.67 s-1 .

Trends in the Calculated Reaction Rate Coecients For atmospheric modeling and determination of new reaction mechanisms, it is useful to be able to estimate rate coecients of potential hydrogen shift reactions. Clearly, the exact rate depends on the specic system studied, but rules of thumb can signicantly limit the reactions that need to be considered. Figure 3 summarizes all the reaction rate constants calculated here. The rate constants are sorted according to the ring size of the TS (1,4; 1,5; 1,6 or 1,7) and the type of H-shift (as dened in Figure 1).

21



Figure 3: All calculated reaction rate constants, k, (black) sorted by the ring size in the TS and the type of H-shift (as dened in Figure 1). The reaction barriers for the hydroxy and hydroperoxy H-shifts are calculated using ω B97X-D/aug-cc-pVTZ, whereas F12 is used for the other reactions. Shown in red are experimentally determined rate constants for reactions of the same reaction classes, but not identical to the reactions studied here (see text). Experimental results are taken from references. 710 The hydroperoxy H-shifts are very fast (in the range 101 - 106 s-1 ). The aldehydic, α-hydroxy and most of the α-hydroperoxy H-shifts have rate constants in the range ∼10−2 s-1 - ∼10 s-1 . Therefore, these are reaction types that need to be considered in the context of atmospheric oxidation. Compared to these, methyl and hydroxy H-shifts appear to be slower and are thus generally less likely to be of atmospheric importance.

While the rate coecients presented here can be useful for rough estimates of H-shift rate coecients without the need for specic calculations or measurements, the spread within each dierent reaction class also clearly highlights the diculty of estimating exact rate co22


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ecients. This is likely primarily an issue in systems that are able to form intramolecular H-bonds in either reactants or transition states, which will be more and more prevalent as oxygen is added during oxidation. The exponential dependence of the rate coecient on the reaction barrier (see Equation 1) means that even relatively small changes in the energy of a hydrogen bond can have signicant impacts on the rate coecient. 9 In most cases, the spread within a reaction class is about 2-3 orders of magnitude. Assuming the entropy term is comparable, this corresponds to dierences in barrier heights of about 2.5 to 4 kcal/mol, which is comparable to the energy of a hydrogen bond in bimolecular complexes. 71,72 In Mohamed et al., the hydrogen bond stabilization was dened as the dierence in enthalpy between the lowest-energy hydrogen bonded conformer and the lowest-energy non-hydrogen bonded conformer and was found to be as large as 3.5 kcal/mol for a single hydrogen bond. 73

The median rate constants for the dierent reaction types studied here could represent estimates for generic values to be used for a specic reaction type. These are summarized in Table 2. It should be noted that all the α-hydroxy and most of the α-hydroperoxy H-shifts studied here abstract from a primary carbon atom and rate coecients greater than the values calculated here could therefore be expected for abstractions from more highly substituted carbon atoms in other systems. 15,24,25,7476 In line with earlier observations, we nd that the 1,5 and 1,6 H-shifts tend to have comparable rate coecients. 9,15,16,24

The reaction rate coecient ranges calculated here are in good agreement with the few available experimental results for comparable H-shifts as illustrated in Figure 3. 79 Similarly, the generic rate coecients employed in the recent isoprene oxidation review are in reasonable agreement with the rate coecient ranges calculated here, see Table S1 and Section S16. 5

23



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Table 2: Median reaction rate constants (s-1 , 298.15 K) for the reactions studied here proposed as generic values for those reaction classes. The H-shift types are dened in Figure 1. Reaction type Aldehydic α-hydroxya α-hydroperoxyb Methyl Hydroxy Hydroperoxy a b

1,4 H-shift

1,5 H-shift

1,6 H-shift

1,7 H-shift

0.4 -

0.3 0.3 8 × 10−3 4 × 10−4 9 × 10−3 -

3 0.3 6 × 10−3 5 × 10−4 6 × 102

1 × 105

Forming primary radicals. Primarily forming primary radicals.

Stereospecicity of the Calculated Rate Coecients The previously observed dierences in hydrogen shift rate coecients for dierent diastereomers 9,13,16 has been linked to subtle dierences in the available hydrogen bond patterns. 9 These earlier studies have included reactants with only a single non-alkyl functional group apart from the peroxy radical moiety. The reactants studied here include up to three nonalkyl functional groups apart from the peroxy group and thus allow for more complex patterns of hydrogen bonding. As shown in Figure 4, this yields dierences between the R,R and R,S diastereomers by up to almost three orders of magnitude.

Figure 4: Ratio of rate coecients for R,R and R,S diastereomers for all reactions calculated here with two chiral centers. The values are sorted by the magnitude of the dierence.

24


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The two largest dierences between the rate coecients of the diastereomers (factors of about 900 and 200 for reactions 6E and 7F, respectively) are seen for two of the peroxy radicals formed from the Z-ISOPOO radicals. Apart from the peroxy radical moiety, these compounds are characterized by having two hydroperoxy groups and an aldehyde group. Hydroperoxides have been found to be very good and exible hydrogen bond donors and similarly, carbonyl groups are known to be good hydrogen bond acceptors. 71,7780 It may thus not be too surprising that these systems can exhibit large dierences between the diastereomers, as the change in chirality may limit the available hydrogen bond patterns, which can change the favorability of reaction. For the case with the largest dierence (reaction 6E), the dierence in the barrier height is about 3.5 kcal/mol, showing that even relatively subtle dierences can have a large eect. Previously, rate constant dierences of up to an order of magnitude, corresponding to a barrier height dierence of about 1.5 kcal/mol, was found between diastereomers in systems able to form a single hydrogen bond. 16 However, the systems studied here are complex enough that no general trends can be extracted and whether or

R,R

R,S reacts fastest depends on the system, as shown in Figure 4. This highlights the need

for studying both of the stereoismers, especially for systems with a large number of functional groups capable of forming hydrogen bonds. For accurate modeling of the atmospheric chemistry it is important to account for these potentially signicant dierences between the reaction rate coecients of dierent diastereomers.

Most atmospheric peroxy radicals are formed by addition of molecular oxygen to a carboncentered radical, suggesting that the dierent diastereomers are usually formed in comparable amounts. H-shift reactions for which competition with bimolecular reactions is signicantly dierent for the two diastereomers may thus result in chiral enhancement of either reactants or products (if these retain their chirality) in the atmosphere. This may in turn aect the overall reactivity of the atmosphere or the interaction between the atmosphere and e.g. the biosphere. 25



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Atmospheric Implications To assess the overall importance of peroxy radical hydrogen shift reactions in isoprene oxidation, the rate coecients calculated here are implemented into the most recent mechanism of isoprene oxidation and simulated globally using GEOS-Chem. 5 For the hydrogen shift reactions not calculated here, we use the values already present in the "Review" model. Unless otherwise noted, the values presented in this section are from the "New" model, explicitly modeling the stereoisomery. The results of the GEOS-Chem modeling are summarized in Table 3, with additional details of the modeling results given in Section S15.

Table 3: Summary of model yieldsa for the four dierent models. Model v11 Review NewMean New

Total H-shift

Uniqueb H-shift

OH

HO2

RO2

0.24 0.42 0.50 0.49

0.18 0.30 0.31 0.30

0.11 0.48 0.48 0.47

0.00 0.15 0.13 0.13

0.05 0.01 0.12 0.12

a

Yields are reported per isoprene molecule emitted, and include only H-shifts of isoprene-derived products. b Excluding all H-shifts of peroxy radicals that may have previously undergone another H-shift. The yield of H-shift products from peroxy radicals studied here, as opposed to the products of bimolecular reactions, ranges from 10−5 (9C (R,S )) to 1 (7F (R,S )). For about half of the reactions, the H-shift yield is at least 0.1, showing that H-shifts are an important class of reactions. However, the overall importance of a given H-shift for the oxidation depends on both the competitiveness of the H-shift and the amount of reactant formed. By this measure, reaction 7F is the most important of the ones calculated here with about 7.4 % (summing both

R,R and R,S ) of all isoprene oxidized in the atmosphere undergoing this unimolecular

hydrogen shift. In total 8 of the reactions studied here have a ux greater than 0.5 % (2.5 Tg/y) of total isoprene emitted reacting via that pathway. It is worth noting that some of the branching ratios to form these peroxy radicals are still speculative in the recently compiled 26


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isoprene mechanism, and thus their importance may be over- or understated. 5

Our modeling (Table 3) shows that in total, approximately 30 % of all isoprene molecules emitted to the atmosphere undergo at least one hydrogen shift reaction, highlighting the importance of these reactions in the atmosphere. This value represents a lower limit, because hydrogen shifts of reactants that can be formed by both uni- and bimolecular reactions are not counted, to avoid potential double counting of unique H-shifts. Secondly, the rapid hydroperoxy H-shifts are not included in this count. Thirdly, only H-shifts treated explicitly in the "reduced-plus" model in the recent review are included in this count, but this misses some that are lumped together or assumed to fully isomerize. 5 For the most part, these are minor pathways and channels that have already undergone at least one H-shift, so they are not expected to aect the total much. Finally, some H-shifts other than those considered here may also have appreciable rate coecients. 70

Over multiple generations of oxidative chemistry, peroxy radicals derived from a single isoprene molecule can undergo multiple H-shifts; we estimate the total H-shift yield per isoprene molecule oxidized to be about 50 %. The most important H-shifts in the isoprene oxidation are the 1,6 H-shifts in the rst generation hydroxy peroxy radicals formed by addition of OH and subsequently O2 to isoprene, as studied experimentally by Teng et al. 8 Our modeling suggests that more than 15 % of emitted isoprene undergoes this reaction. This value is about half of that modeled with the purely theory-based upgraded LIM1 mechanism. 22

An important consequence of the H-shift reactions is recycling of OH. In the "New" model, the total OH yield from hydrogen shift reactions per isoprene molecule emitted (i.e. the OH recycling) is 47%. This degree of OH recycling is consistent with experimental atmospheric simulation chamber studies and eld measurements. 81,82 The H-shifts thus signicantly lower the net loss of atmospheric oxidants in the isoprene oxidation, particularly in 27



the more oxidant-consuming low-NO oxidative chemistry in which H-shifts prevail. To investigate these eects in greater detail, the boundary level mixing ratios of OH were compared between the "New" and "NoShifts" mechanisms. As shown in Figure 5, removing all H-shifts from the isoprene mechanism leads to local reductions of OH mixing ratios of up to 70 %. Unsurprisingly, the most signicant dierences are observed in the regions with the largest isoprene emissions. The total globally averaged HOx (OH + HO2 + RO2 ) radical recycling from isoprene H-shifts is 72 %.

Figure 5: Percentage dierence in annual average OH concentrations between the "New" and the "NoShifts" models, the latter excluding all H-shift reactions. Compared to the model run with the estimates from Wennberg et al. 5 ("Review"), the minimum fraction of isoprene molecules undergoing hydrogen shift reactions is virtually unchanged (see Table 3). To a large extent this is because the dominant rst-generation 1,6 H-shift has an experimentally determined rate coecient and thus does not change between the two models. Additionally, the "Review" mechanism assumed that some of the fast subsequent H-shift, e.g. the aldehydic H-shifts in Schemes 6-7, progressed to completion, and therefore skipped the intermediate radicals; treating these peroxy radicals and H-shifts ex28


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plicitly in the "NewMean" and "New" mechanisms accounts for the majority of the increase in the fractional yields of both H-shifts from isoprene (from 42 % to 49 %) and RO2 from Hshifts (from 1% to 12 %). Thus, the relatively small actual dierences between the outcomes of the "Review", "NewMean", and "New" simulations suggest that combining diastereomers and employing reasonable estimates for the H-shift rate coecients of minor pathways is a cost-eective approach for global modeling.

Despite the small changes in overall H-shift prevalence and HOx recycling between mechanisms with and without explicit separate treatment of stereoisomers, it is important to determine the rate coecients for each stereoisomer individually, as the potentially large dierence between the two can signicantly alter the importance of the given reaction. One benet of explicitly distinguishing the diastereomers is that it prevents both isomers from rapidly undergoing a particularly fast H-shift that is actually only available to one isomer. Furthermore, it allows modeling of potentially diasteremeric excess of certain reactants or products. For example, in the "New" model, the bimolecular products (e.g. dihydroxy dihydroperoxides and dihydroxy hydroperoxy nitrates) of the peroxy radicals formed following internal addition of OH to β -(1,2)-ISOPOOH (Scheme 9) are made in a 12:1 (R,R +S,S ):(R,S +S,R ) ratio, because the

R,S

and

S,R isomers have faster H-shifts, leading them to preferentially

isomerize instead of reacting bimolecularly. The subsequent deposition of these bimolecular products could thus provide a source of diastereomeric excess to the biosphere. Finally, in cases where the two rates are signicantly dierent, the average will be far from both values. However, for most model applications explicit modeling of the diastereomers is likely not necessary and using an average rate coecient ("NewMean") seems a good alternative.

29



Conclusion Using a high-level theoretical multi-conformer transition state theory (MC-TST) approach, we have calculated recommended temperature-dependent reaction rate coecients for a number of unimolecular peroxy radical hydrogen shift reactions in the oxidation of isoprene. We nd that most of the aldehydic and α-hydroxy H-shifts have rate coecients comparable with the competing bimolecular reactions (10−2 - 1 s-1 ) and thus need to be considered when compiling atmospheric oxidation mechanisms. However, the rate coecients can vary by more than two orders of magnitude for reactions of the same class, to a large extent likely due to dierences in the possible hydrogen bond patterns. Furthermore, we nd that the rate coecients of diastereomers can vary by as much as three orders of magnitude, an eect that is important to consider in atmospheric modeling. The current GEOS-Chem model of isoprene oxidation is updated to include the newly calculated H-shift rate coecients and shows that at least 30 % of all isoprene molecules emitted to the atmosphere undergo a minimum of one hydrogen shift reaction, highlighting the crucial importance of this reaction class in the context of atmospheric oxidation.

Acknowledgement We are grateful to Prof. Paul O. Wennberg, Prof. Stephan P. A. Sauer, Prof. Kurt V. Mikkelsen, Rasmus V. Otkjær and Helene H. Jacobsen for helpful discussions. We acknowledge the nancial support of the Center for Exploitation of Solar Energy, University of Copenhagen and Danish Center for Scientic Computing. K. H. M. acknowledges the nancial support of the Danish Ministry for Higher Education and Science's Elite Research travel grant. K. H. B. acknowledges the support of the National Ocean Atmospheric Administration's Climate & Global Change Fellowship and the Harvard University Center for the Environment.

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Associated Content H-shift rate coecients currently employed in the isoprene review, pressure eect of selected rate coecients, description of the eect the single-point cut-o, new derivation of MC-TST, a description of the issue of multiple HF solutions for the hydroxy and hydroperoxy H-shifts, ratios of the forward and reverse hydroperoxy H-shift rate coecients, rate coecients for the reverse H-shift reactions, comparison of the two dierent computational approaches, all calculated reaction rate coecients, data used for calculating the reaction rate coecients, temperature dependence of rate coecients, barrier heights at dierent levels of theory, formation pathways of the peroxy radicals studied, detailed GEOS-Chem modeling results, and comparison to the rate coecient estimates in the isoprene review.

The updated isoprene oxidation mechanism used in the GEOS-Chem modeling is available free of charge at the Caltech repository: DOI: 10.22002/D1.247. ω B97X-D/aug-cc-pVTZ and F12 log les of all structures including their geometries can be found at: https://sid.erda.dk/public/archives/741e77b865aca935fa574fcfc152b3d9/published-archive.html

Author Information Corresponding Author *Henrik G. Kjaergaard [email protected] Phone: +45-35320334 Fax: +45-35320322

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Orcid Kristian H. Møller: 0000-0001-8070-8516 Kelvin H. Bates: 0000-0001-7544-9580 Henrik G. Kjaergaard: 0000-0002-7275-8297

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Table of Content Figure

43


The Importance of Peroxy Radical Hydrogen Shift Reactions in

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