unusually fast 1,6-h shifts of enolic hydrogens in peroxy radicals: formation of the...

Unusually Fast 1,6-H Shifts of Enolic Hydrogens in Peroxy Radicals:Formation of the First-Generation C2 and C3 Carbonyls in theOxidation of IsopreneJozef Peeters* and Thanh Lam Nguyen†

Department of Chemistry, University of Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium

*S Supporting Information

ABSTRACT: In a theoretical investigation using the CBS-QB3//UB3LYP/6-31+G** method supported by higher-level computations such as CBS-QB3//UQCISD/6-31+G**, the 1,6-H shifts of the enolic hydrogen inperoxy radicals of the type Z-HOCHCHCH2OO• were found toface exceptionally low energy barriers of only about 11 kcal mol−1i.e., 6−9kcal mol−1 lower than the barriers for similar shifts of alkane hydrogenssuch that they can proceed at unequaled rates of order 105 to 106 s−1 atambient temperatures. The unusually low barriers for enolic 1,6-H shifts inperoxy radicals, characterized here for the first time to our knowledge, arerationalized. As cases in point, the secondary peroxy radicals Z-HOCHC(CH3)-CH(OO

•)CH2OH (case A) and Z-HOCHCHC(CH3)(OO

•)CH2OH (case B) derived from the primary Z-δ-hydroxy-peroxy radicals in the oxidation ofisoprene, are predicted to undergo 1,6-H shifts of their enolic hydrogens at TST-calculated rates in the range 270−320 K ofk(T)A = 5.4 × 10−4 × T5.04 × exp(−1990/T) s−1 and k(T)B = 109 × T3.13 × exp(−3420/T) s−1, respectively, i.e., 2.0 × 106 and6.2 × 104 s−1, respectively, at 298 K, far outrunning in all relevant atmospheric and laboratory conditions their reactions with NOproposed earlier as their dominant pathways (Dibble J. Phys. Chem. A 2004, 108, 2199). These fast enolic-H shifts are shown toprovide the explanation for the first-generation formation of methylglyoxal + glycolaldehyde, and glyoxal + hydroxyacetone in theoxidation of isoprene under high-NO conditions, recently determined by several groups. However, under moderate- and low-NOatmospheric conditions, the fast interconversion and equilibration of the various thermally labile, initial peroxy conformers/isomers from isoprene and the isomerization of the initial Z-δ-hydroxy-peroxy radicals, both recently proposed by us (Peeters etal. Phys. Chem. Chem. Phys. 2009, 11, 5935), are expected to substantially reduce the yields of the small carbonyls at issue.

■ INTRODUCTIONIsoprene, emitted from vegetation into the atmosphere inquantities of ca. 500 Tg year−1,1 shows a high reactivity towardthe hydroxyl radical and so has important impacts on theoxidative capacity of the atmosphere.2 Among the variousknown products of the atmospheric oxidation of isoprene, theC2 and C3 dicarbonyls and hydroxycarbonyls: glyoxal (GLY),hydroxyacetone (HYAC), methylglyoxal (MGLY), and glyco-laldehyde (GLYALD) are of interest within the context ofsecondary organic aerosol (SOA) formation and cloudprocessing, as recently briefly reviewed by Fu et al.,3 Thalmanand Volkamer,4 and by Galloway et al.5 Though these smallbifunctional compounds are in majority second-generationproducts from isoprene, via methyl vinyl ketone (MVK) and/ormethacrolein (MACR), as well as via the C5 hydroxycarbonylsat high NO, they have been proposed by several authors to be,in part, minor first-generation products too. Volkamer et al.6

derived a first-generation GLY yield from isoprene of 0.3−3%,whereas Paulot et al.7 observed first-generation GLYALD (4.2%yield) and HYAC (3.8% yield) at 500 ppbv NO and assumedthese to be formed together with coproducts MGLY and GLY,respectively, from the initial Z-δ-hydroxy-isoprenylperoxyradicals as had been theoretically predicted by Dibble8 forhigh-NO conditions. In their field study in Amazonia, Karl et

al.2 considered partial first-generation HYAC formation fromisoprene, attributing this likewise to the mechanism proposedby Dibble. In a recent, detailed laboratory study at NO levelsaround 300 ppbv, Galloway et al.5 presented conclusiveevidence for first-generation GLY from isoprene, with a yieldof 2.1 (±0.6)%, and further evaluated first-generation yields ofHYAC at 2.9 (±0.05)% and of GLYALD at 2.69 (±0.82)%.The mechanism proposed by Dibble8 for the first-generation

carbonyls above concerns the subsequent chemistry at high NOof the primary Z-δ-hydroxy-peroxy radicals that result from theinitial addition of OH to either one of the terminal carbons ofisoprene. For a schematic of the initial steps in the OH-initiatedoxidation of isoprene, i.e., the branching to the major OHadduct isomers/conformers and to the subsequent hydroxy-peroxy isomers/conformers, we refer to Figures S1 and S2 inthe Supporting Information, adopted from our recent work,9 inwhich we theoretically quantified the initial branching fractionsfor the four major OH-adduct isomers/conformers, in good

Special Issue: A. R. Ravishankara Festschrift

Received: November 28, 2011Revised: January 13, 2012Published: January 17, 2012

Article

pubs.acs.org/JPCA

© 2012 American Chemical Society 6134 dx.doi.org/10.1021/jp211447q | J. Phys. Chem. A 2012, 116, 6134−6141

pubs.acs.org/JPCA

agreement with the predictions by Dibble,10 and derived initialformation rates of the various hydroxy-peroxy isomers/conformers based on the large body of available product dataat high NO (see, e.g., Park et al.,11 and references therein) andusing an estimated overall O2-addition rate.11

We consider now the case (case A) of the primary Z-δ-OH-peroxy radical Z-HOCH2-C(CH3)CHCH2OO

•, where“primary”, or “secondary” etc., purposefully in italics, are meanthere in the mechanistic sense. In the Dibble mechanism,8 thisprimary radical reacts with NO forming the oxy radical Z-HOCH2C(CH3)CHCH2O

•, which in turn undergoes a fast1,5-H shift of the α-hydroxy-H to the oxy function, forming theallylic radical Z-HOC•HC(CH3)CHCH2OH (de-noted as Z-VII by Dibble). The reaction of the allylic productradical with O2 was proposed to form for a minor fraction thesecondary peroxy radical Z-HOCHC(CH3)CH-(OO•)CH2OH (Z-VIIOO).8 The overall yields of thissecondary peroxy from case A and its counterpart from case B(where the CH3 group is on the other central C) wereestimated at only a few percent each but, given the highisoprene emissions, could still result in large global impacts asargued by Dibble. The critical phase of the mechanism is thefate of the secondary Z-VIIOO radical. As a possibleisomerization process of this peroxy, Dibble considered onlythe double hydrogen shift depicted here

and, computing a barrier of ca. 23 kcal mol−1 (and even higherfor the analogous radical from case B), discarded isomerizationas a viable pathway and adopted the reaction with NO aspredominant fate of Z-VIIOO.8 In the next steps, the resultingoxy radical (Z-VIIO) was proposed to undergo a double H shiftthat was found to face a low barrier, followed by O2 addition tothe product radical (Z-VII′OH) and reaction of the subsequenttertiary peroxy with NO to form an oxy radical of which thedecomposition finally yields MGLY and GLYALD for case A,whereas case B results finally in GLY + HYAC via a similarroute.8

In the present work, we intend to examine the possibilityleft unexplored by Dibblethat the crucial secondary peroxyradical (Z-VIIOO) above, after H-bonding rearrangement, canrapidly isomerize by a single H shift of the enolic hydrogendirectly to the peroxy function, resulting in a differentsubsequent chemistry than proposed by Dibble, but likelyleading to the same products. Below, we will discuss the a priorireasons why such enolic-H shifts may face a sufficiently lowbarrier and hence be fast enough for the peroxy radical inquestion to outrun reaction with NO. The prime objective ofthis study was therefore to theoretically characterize andkinetically quantify the direct 1,6-H shift of the enolic hydrogenin the secondary peroxy radicals from isoprene above, aiming toestablish whether this particular peroxy isomerization can befaster than its reaction with NO, in particular under the high-NO experimental conditions (300−500 ppbv) at which the C2

and C3 carbonyls at issue were recently determined andquantified as first-generation oxidation products from iso-prene.5,7

■ THEORETICAL METHODOLOGIES

Quantum Chemical Calculations. Optimized geometriesof all stationary points were first obtained using the UB3LYP/6-31+G(d,p) level of theory.12,13 The UB3LYP method is agood compromise between high performance and low cost forthe secondary dihydroxy-peroxy radicalshaving nine heavyatomsconsidered in this paper. Analytical harmonic vibra-tional analyses were then done to obtain harmonic vibrationalfrequencies and rotational constants as well as to characterizeall stationary points located, e.g., all real, positive frequenciesfor a minimum and only one imaginary frequency for atransition structure. For some cases, intrinsic reactioncoordinate (IRC) calculations were done with the same levelof theory to verify a natural connection from a reactant via a TSto a product.For the smaller hydroxy-peroxy radical Z-HOCHCH

CH2OO• (see next section), in addition to the UB3LYP

method, higher levels of theory including UM05-2X/6-311G(d,p),14 UQCISD/6-31+G(d,p)15 and UCCSD(T)/6-311G(d,p)15 are also used for geometry optimizations. Notethat UCCSD(T) optimization with the eigenvalue-followingalgorithm in Gaussian was carried out by using a numericalgradient and an initial guess of the UB3LYP-Hessian matrix.We found (see next section) that calculated barrier heightsfrom single-point energies, calculated at higher levels of theory,for various optimized geometries are in good agreement witheach other, within 0.5 kcal/mol. Therefore, UB3LYP/6-31+G(d,p) geometries appear to be adequate for the currentpurposes.For some key critical stationary points (e.g., transition

structures of the 1,6-H shift), whose electrons are highlydelocalized, the CASSCF(5,5)/6-31+G(d) level of theory wasused to check for a multireference character in their wavefunctions. However, the results from CI vectors show that allthese TSs have a single dominant HF-reference.Energies were then refined using the CBS-QB3 composite

method,16 which recovers the most important part of electroncorrelations using the CCSD(T) method with a medium-sizedbasis set and the remaining part by extrapolation to a competebasis set limit with the MP2 method.16 It is well documentedthat the CBS-QB3 method gives an error bar of ca. 1−2 kcal/mol for thermochemistry data (e.g., heats of formation, protonaffinity, ...)16 and for relative energies (i.e., reaction enthalpies),but about twice as much for barrier heights. The effects ofUB3LYP geometries and the CBS-QB3 method on thecalculated barrier heights were further checked using IRCMax-(CBS-QB3//UB3LYP) computations.17 However, the IRCMaxapproach left all barrier heights computed in this workunchanged. To our experience, barrier heights computed withthe IRCMax(CBS-QB3//UB3LYP) approach for similarsystems have an error bar of ca. 1−2 kcal/mol provided thatthe wave function is a dominant HF-reference, as is the case forthe structures in this work.In this work, CASSCF calculations were carried out using

Molpro18 whereas Gaussian19 was used for the others.Chemical Kinetics Calculations. Thermal rate constants

for the unimolecular title reactions, under high-pressure limitconditions, were computed using transition state theory:

= κ × ×

× −

k T T k T h Q Q

E k T

( ) ( ) ( / ) ( / )

exp( / )

B TS React

o B

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp211447q | J. Phys. Chem. A 2012, 116, 6134−61416135

where kB is Boltzmann’s constant, h is Planck’s constant, Eo isthe adiabatic barrier height, QTS and QReact are the totalpartition functions for transition state and reactant, respectively,and κ(T) is the tunneling factor. The latter was computed usingthe zero-curvature-tunneling model by assuming an asymmetricEckart potential.20,21 For 1,5-H shifts in alkylperoxy radicals,around room temperature, this approach was recently found togive a satisfactory agreement with higher-level multidimen-sional treatments.22

■ RESULTS AND DISCUSSIONFast 1,6-H Shift of the Enolic Hydrogen in Z-HO

CHCHCH2OO•. The reactions of interest in this paperare 1,6-H shifts of an enolic hydrogen in secondary peroxyradicals derived from isoprene. However, for the purpose ofgenerally characterizing such reactions, we first address the 1,6-shift of an enolic H in the smallest peroxy where it can occur,i.e., Z-HOCHCHCH2OO•:

‐

→ ‐

•

•

Z HO CH CH CH OO

Z O CH CH CH OOH2

2

The most stable resonance structure of the product features aCO π-bond, which is about 20 kcal mol−1 stronger than theCC π-bond of the reactant; moreover, the product is furtherstabilized by a vinoxy-type resonance. Thus, even though aregular alcohol O−H bond is much stronger than an alkane C−H bond, an enolic-hydrogen shift is exothermal for about 2−7kcal mol−1 and more favorable than a similar shift of a regularalkane-H, which is endothermal for some 6−12 kcal mol−1. Inaddition, the already strong hydrogen bond of some 5 kcalmol−1 between the positively charged enolic H and the peroxyfunction in the reactant, is preserved during the H-migrationwhile converting gradually to an H-bond of similar strengthbetween the hydroperoxide-H and the carbonyl-O (Figure 1).Furthermore, the enolic H might leave even more of itselectron density to its oxygen ex-partner upon migration, thusfacilitating the formation of the stronger CO π-bond in theproduct. Together, these effects are expected to result in asubstantially lower energy barrier for an enolic-H shiftcompared to an alkane-H shift. This is borne out by thecomputational results presented below.The energy barrier for this simplest case of enolic 1,6-H shift,

above, was computed, at various levels of theory, ranging fromUB3LYP/6-31+G(d,p) to CBS-QB3//UQCISD/6-31+G(d,p).The results are displayed in Table 1. Except for the value at theUB3LYP/6-31+G(d,p) level, generally known to underestimateH-transfer barriers, all computed values are in the range from11 to 12.7 kcal mol−1.The highest value is found with UM05-2X/6-311G(d,p), a

DFT functional that was found to yield high barrier values alsofor other H-migrations.23 The most reliable methods forgeometry optimization of an open-shell TS24,25 used here areUQCISD/6-31+G(d,p) and UCCSD(T)/6-311G(d,p), and thetwo geometries for TS as well as reactant at these levels werequasi identical, albeit that the convergence criterion for the(lengthy) geometry optimization of the reactant at the latterlevel was relaxed to 10−6 hartree. The QCISD geometries ofreactant, TS, and product are depicted in Figure 1. The bestbarrier values are therefore expected to be these from thesingle-point energies using the complete-basis-set CBS-Qextrapolation methods on the QCISD or CCSD(T) geometriesabove, with a preference here for the former, which results in a

barrier height of 11.63 kcal mol−1. Most interestingly, thishighest-level value is nearly exactly reproduced by thecomputationally less expensive CBS-QB3//UB3LYP/6-31+G-(d,p) result of 11.69 kcal mol−1; moreover, the more reliableIRCMax(CBS-QB3//UB3LYP/6-31+G(d,p)) method yieldsan identical result of 11.69 kcal mol−1. The reaction energiescomputed at the CBS-QB3//UQCISD/6-31+G(d,p) and CBS-QB3//UB3LYP/6-31+G(d,p) levels are −1.94 and −1.76 kcalmol−1, respectively.Returning to the geometries and other features of the

transition state, at the QCISD level (Figure 1), it should benoted that (i) in the TS, the π-bond in the >CO moiety(carbon 4 and oxygen 8) is already far developed (rC−O = 1.28A), whereas the spin density on carbon 3 is already 1.0, and (ii)the Mulliken charge on the migrating H of +0.56 in the TS ishigher than the +0.40 in the reactant. These values may becompared to the spin density of 0.50 on the carbon that losesthe H, and the charge of +0.2 on the migrating H in the TS of

Figure 1. Structures, geometries, and energies, at the CBS-QB3//UQCISD/6-31+G(d,p) level of theory (with ZPE from UM05-2X/6-311G**), of reactant, transition state and product for the isomer-ization of the Z-HOCHCHCH2OO• radical to Z-OCHCH•CH2OOH by 1,6-H shift of the enolic hydrogen;interatomic distances in angstroms.

Table 1. Computed Adiabatic Barrier Height (InclusiveZPE), at Various Levels of Theory, for the 1,6-H Shift in theZ-HO−CHCH−CH2−OO• Peroxy Radical

methodbarrier height(kcal mol−1) notes

UM05-2X/6-311G** 12.69

CBS-QB3//UQCISD/6-31+G**

11.63 ZPE from M05-2X

CBS-QB3//UCCSD(T)/6-311G**

11.07 ZPE from M05-2X; geometryoptimization criterion for reactantrelaxed: see text

UB3LYP/6-31+G** 6.45

CBS-QB3//UB3LYP/6-31+G**

11.69 IRCMax gives an identical value of 11.69

UCCSD(T)/aVDZ//UM05-2X/6-311G**

12.64 ZPE from M05-2X



the 1,6-H shift of the alkane H in the primary Z-δ-hydroxy-peroxy of isoprene.9 It thus appears that the migrating enolichydrogen leaves indeed much of its electron density behind,facilitating early formation of the strong CO π-bond and sodepressing the TS energy.Thus, a first finding of major interest is the strikingly low

barrier heights for enolic 1,6-H shifts in peroxys, i.e., 6−9 kcalmol−1 lower than the energy barriers for similar shifts of alkanehydrogens.23,26,27 As a result, thermal enolic-H shifts in peroxyradicals will be some 5 orders of magnitude faster than theiralkane-H counterparts. Given that the energy barrier is muchlower than the nearly 20 kcal mol−1 internal energy that such aperoxy will have acquired upon the O2 addition to its allyl-typeprecursor radical, enolic 1,6-H shifts might in some cases evenoccur promptly, i.e., while the nascent peroxy is still chemicallyactivated.It should be mentioned that the special case of an enolic 1,5-

H shift in the HOCHCHOO• radical has alreadyattracted the attention of several workers earlier. Theoreticalstudies of Maranzana et al.28 and of Glowacki and Pilling29 haveshown that the reaction of 2-hydroxyvinyl with O2 yields ahighly activated adduct (for ca. 45 kcal mol−1) that is unstableand undergoes a quasi-barrierless 1,5-H shift in near-concertation with decomposition to glyoxal + OH. Likely, itis the pseudopericyclic character of this overall reaction and itshigh overall exothermicity of 75 kcal mol−1 that leads to thisunique behavior.Enolic 1,6-H Shifts in the Secondary Z-1,4-Dihydrox-

yisoprenyl-3-peroxy radicals: Z-HOCHC(CH3)CH-

(OO•)CH2OH (Case A; Dibble’s Z-VIIOO) and Z-HOCHCHC(CH3)(OO

•)CH2OH (Case B; Dibble’s Z-IXOO). Of the two cases to be considered, denoted here ascase A and case B, the first, which stems from the moreabundant primary Z-δ-hydroxyisoprenyl-peroxy Z-HOCH2C(CH3)CHCH2OO

•,8−10 will be discussed herein detail. The mechanism, energetics, and kinetics features forcase B are similar and only the crucial data will be given for it.As shown in Figure 2, the migration of the enolic H to the

peroxy function of the Z-HOCHC(CH3)CH(OO•)CH2OH reactant, denoted further as Re, does not occurdirectly in its most stable conformer, ReC1, but requires apreceding conformational change that involves an H-bondrearrangement, either in two steps or in one step. Theseprereaction conformation changes also face energy barriers,which in principle could be high enough to become ratecontrolling and therefore have to be quantified too. Theenergies of these prereaction transition states and theintermediate conformers involved, as well as the transitionstates for the 1,6-H shifts proper and the product conformershave all been computed at the CBS-QB3//UB3LYP/6-31+G(d,p) level and were found to remain unchanged within<0.03 kcal mol−1 in IRCMax searches at that level.The potential energy surfaces of the two lowest-energy

pathways characterized for case A are depicted in Figure 2.Pathway 1 (Scheme 1) involves the intermediate conformersReC2 and ReC3, connected by TSs with energies 4.77 and 6.08kcal mol−1 relative to ReC1, and leads finally, over the H shifttransition state TS1−16Hs at 10.18 kcal mol−1, to product

Figure 2. Structures, geometries, and energies, at the CBS-QB3//UB3LYP/6-31+G(d,p) level of theory, of the lowest reactant conformer;intermediate conformers and connecting transition states; the transition states for the H migration; and the products for the isomerization of the Z-HOCHC(CH3)CH(OO•)CH2OH radical by 1,6-H shift of the enolic hydrogen (case A).



conformer Pr1 at −5.42 kcal mol−1. Pathway 2 proceeds via asingle intermediate conformer ReC4, connected to ReC1 by aTS at 4.4 kcal mol−1, and leads, over the H shift TS2−16Hs at12.37 kcal mol−1, to product conformer Pr2 at −6.48 kcalmol−1.All energies listed in Table 2 are relative to the lowest

reactant conformer ReC1. That TS1−16Hs and TS2−16Hs

are indeed transition states for the 1,6-H shift proper wasverified by IRC analyses. Three additional reactant conformers,ReC5 to ReC7 (not shown in Figure 2) have beencharacterized, lying 4−5 kcal above ReC1; also, a third productconformer was characterized with stability close to that of Pr2.The energy differences of the various Re conformers mainlyreflect the relative strengths of the various H-bondingarrangements. For both reaction paths, (1) and (2), thetransition state for the 1,6-H shift proper is by far the highest-lying TS, such that the thermal reaction rates from reactant toproduct are determined solely by these TSs, whereas theintermediate structures ReC2, ReC3 and ReC4 as well as ReC5to ReC7 are to be considered merely as higher-energyconformers in thermal equilibrium with ReC1, all with almostnegligible thermal populations compared to ReC1, only ReC3contributing marginally, by about 7%, to the total reactantpopulation at 300 K. Similarly, TS2−16Hs has a thermalpopulation of only 2.5% of TS1−16Hs, such that path 2 canalso be neglected.The thermal rate coefficient k(T)A of the overall reaction can

therefore be estimated using conventional TST theory, i.e.,considering only the lowest conformers for the reactant and TSpartition functions, however, duly accounting for tunneling. Weadopted the approximate ZCT tunneling treatment based on anasymmetric Eckart potential,20,21 which according to Zhang andDibble gives a fair approximation of the more involvedmultidimensional SCT treatment for 1,5-H migrations in n-

propylperoxy radicals.22 This treatment must be applied herefor the barrier from ReC3 over TS1−16Hs to Pr1 (Figure 2).Using the CBS-QB3//UB3LYP/6-31+G** energies andUB3LYP/6-31+G** imaginary frequency, it yields tunnelingfactors of about 15 at 298 K. It may be noted that the TSTfrequency factor (kBT/h) × (QTS/QReact) without tunneling isby itself fairly high, 3.8 × 1012 s−1 at 298 K, because, due to thestrong H-bonding in the reactant, there is no loss of internalrotors on going to the TS. Table 3 lists the resulting TST rate

coefficient for case A without and with tunneling for the range270−320 K. The modified Arrhenius fit over this T-rangedisplayed in Figure 3, can be expressed as k(T)A = 5.4 × 10−4 ×

T5.04 exp(−1990/T) s−1. Note that when the imaginaryfrequency ν≠ of ≈2210i cm−1 at the UM05-2X/6-311G**level is used instead of the ν≠(UB3LYP/6-31+G**) value of1543i cm−1 adopted here, the calculated Eckart tunnelingfactors and hence the rate coefficients become even a factor15−25 higher, which might suggest that the k(T) above and inTable 3 and Figure 3 are lower limits. However, the precisevalue of the tunneling factor is of little importance, becauseeven when the Wigner tunneling factor is used, which is foundgenerally to be a lower limit22 and amounts to only ≈5 here,

Scheme 1

Table 2. Computed Relative Energies (kcal mol−1)(Including ZPE), of the Various Structures (Figure 2) for theEnolic 1,6-H Shift in Peroxy Radical Z-HOCHC(CH3)CH(OO•)CH2OH (Case A)

species UB3LYP/6-31+G** CBS-QB3//UB3LYP/6-31+G**

ReC1 0.00 0.00ReC2 5.47 3.95ReC3 2.81 2.10ReC4 4.84 4.40Pr1 −3.62 −5.42Pr2 −4.99 −6.48TSa-1 4.88 4.29TSa-2 6.01 4.77TSb-1 7.64 6.08TS1−16Hs 5.13 10.18 (10.18)a

TS2−16Hs 6.76 12.37 (12.37)a

aThe values in parentheses are obtained using IRCMax(CBS-QB3//UB3LYP/6-31+G**).

Table 3. Calculated k(T) (s−1) for the Enolic 1,6-H Shifts inZ-HOCHC(CH3)CH(OO•)CH2OH (Case A) andZ-HOCHCHC(CH3)(OO

•)CH2OH (Case B)

T (K)

k(T)Awithouttunneling

k(T)A withtunneling (see

text)

k(T)Bwithouttunneling

k(T)B withtunneling (see

text)

270 2.01 × 104 6.23 × 105 3.26 × 102 1.46 × 104

280 4.07 × 104 9.55 × 105 7.53 × 102 2.49 × 104

290 7.84 × 104 1.44 × 106 1.65 × 103 4.17 × 104

298.15 1.30 × 105 2.00 × 106 3.00 × 103 6.23 × 104

300 1.45 × 105 2.14 × 106 3.42 × 103 6.81 × 104

310 2.58 × 105 3.13 × 106 6.78 × 103 1.09 × 105

320 4.42 × 105 4.52 × 106 1.29 × 104 1.71 × 105

Figure 3. Arrhenius plot of the predicted rate coefficients of the enolic1,6-H shifts Z-HOCHC(CH3)CH(OO•)CH2OH → Z-OCHC•(CH3)CH(OOH)CH2OH (case A), k(T)A, and Z-HOCHCHC(CH3)(OO

•)CH2OH → Z-OCHC•HC(CH3)(OOH)CH2OH (case B), k(T)B.



the calculated rate of this reaction remains high enough to faroutrun all its competitors in all conditions relevant for thisissue, as shown below.For case B, the enolic 1,6-H shift proceeds via identical paths

as case A, the sole difference being the position of the methylgroup, which leads to about 2 kcal mol−1 higher relativeenergies than in case A for the rate-controlling 1,6-H shift TSs,due to the absence of the stabilizing CH3 group on the radicalsite in the forming Z-HOCHC•H−C(CH3)(OOH)CH2OH product; note that the spin density on the productradical center is already 1.0 in the TS (see above). Table 4 lists

only the relative energies of the rate-limiting transition states;the notations, discerned by a prime, are as for the analogues ofcase A with the CH3 group on the other central carbon. TheTST-calculated rate coefficients k(T)B for 270−320 K are listedin Table 3; the ν≠(UB3LYP/6-31+G**)-based tunnelingfactors were slightly higher than for case A, e.g., 21 at 298 K.The modified Arrhenius fit for case B displayed also in Figure 3can be expressed as k(T)B = 109 × T3.13 exp(−3420/T) s−1.The predicted rate coefficients for the enolic 1,6-H shifts at

issue, with kA around 106 s−1 and kB around 5 × 104 s−1 atboundary layer temperatures (Table 3), are exceptionally highfor peroxy radical isomerizations. The values can be comparedfor example with the theoretically derived rate for the 1,6-Hshift of an α-OH alkane-hydrogen in the primary Z-δ-hydroxy-peroxys of isoprene9 of order 1 s−1, which is already consideredfast for a peroxy isomerization.It is worth noting that the rates predicted in this work for the

direct 1,6-H shifts of the enolic H to the peroxy function are atleast 7 and possibly even 12 orders of magnitude higher thanthese calculated for the double H shift that Dibble consideredfor these peroxy radicals.8 Still, the major conclusion of thiswork is that the isomerization of the Z-1,4-dihydroxyisoprenyl-3-peroxys by direct enolic-H shifts will even outrun theirreaction with NO by many orders of magnitude in allatmospheric conditions. Even at extreme NO levels of ≈5ppmv in laboratory experiments, the NO reaction at rate ≈1000s−1 will still be orders of magnitude slower than the enolic-Hshift. Even allowing for an error of 2 kcal mol−1 on the energyof the rate determining TSs or for an overestimation of thetunneling correction by a factor of 5−10, there can be littledoubt that the enolic 1,6-H shifts characterized in this work arethe sole fate of any importance of the secondary peroxy radicalsof interest here, in all relevant conditions.As anticipated above, the possibility of a prompt 1,6-H shift

in the nascent, still chemically activated reactant radical Re†

should be examined. The computed addition energy of O2 tothe allylic precursor radical is 18 kcal mol−1; adding ≈3 kcalmol−1 thermal reactant energy puts the average energy contentof nascent ReC1† at about 21 kcal mol−1. Different from theevaluation of the thermal TST rate, an RRKM estimate30 of theprompt rate has to take into account all other reactant

conformers (ReC2 to ReC7), because, at the high internalenergy involved, the higher-energy but (much) looser con-formers contribute in a major way to the total density ofinternal states of Re†. Also, besides TS1-16Hs, the higher-lyingTS2-16Hs contributes significantly to the total sum ofaccessible states of the transition structures. This results in anRRKM-estimated prompt 1,6-H shift rate of Re† of only about 2× 108 s−1 (case A), which, remarkably, is only 2 orders ofmagnitude faster than the thermal rate at 298 K. The 5 ns longisomerization lifetime of the nascent Re† means that, atatmospheric pressure, the nascent Re† will have suffered onaverage some 50 collisions prior to reacting, such that the largemajority will instead become effectively collisionally stabilized.The fraction of nascent, activated Re† reacting promptly willtherefore be minor, of order of 10% at most, the precise valuedepending on the (uncertain) average energy lost per collision.Note, however, that this conclusion would not necessarily bevalid for enolic 1,6-H shifts in smaller activated peroxys withless internal modes.

Subsequent Chemistry of the 1,6-H Shifted ProductRadicals Z-OCHC•(CH3)CH(OOH)CH2OH (Pr)and Z-OCHC•HC(CH3)(OOH)CH2OH (Pr′). Thelarge majority of the product radicals Pr (or Pr′) arise initiallyin the thermal 1,6-H shift of ReC1 via TS1−16Hs (or Re′C1via TS′1−16Hs) and contain internal energies of some 20 kcalmol−1. The only conceivable unimolecular reactions of Prwould be (i) HO2 elimination facing a CBS-QB3 barrier of ca.20 kcal mol−1 and (ii) concerted ring closure to an epoxide withOH elimination, over a computed barrier of ca. 18 kcal mol−1;these rather high barriers, which are due to the strong doubleH-bonding involving the HOO moiety in Pr (Figure 2),preclude any prompt unimolecular reaction of the nascent Pr†

competing with their fast collisional thermalization. Even forthe small fraction of the Pr formed from the still chemicallyactivated Re (see above) and hence containing a nascent energyof some 28 kcal mol−1, the mentioned unimolecular reactionsoccur at initial rates well below 108 s−1 and will therefore be faroutrun by collisional energy loss and O2 addition inatmospheric conditions. Thus, in such conditions and inlaboratory simulations, the dominant if not sole fate of theproduct radicals Pr of the 1,6-H shift at issue is addition of anO2 molecule, resulting in tertiary peroxy radicals PrOO. Again,multiple H-bonding schemes and hence many conformers ofPrOO are possible.Scheme 2 summarizes the dominant reaction sequence under

high-NO conditions for case A as proposed and characterizedin this work, starting from the very fast enolic 1,6-H shift of Re(i.e., Z-VIIOO8) to form Pr and hence PrOO, and followed bythe chemistry detailed here. At the high NO levels of theexperiments of Paulot et al.7 and Galloway et al.,5 thepredominant fate of the PrOO peroxys is reaction with NOto yield NO2 plus the oxy radical PrO. The product oxy PrOshould decompose very fast into CH3C(O)CHO +HOCH2C•HOOH at a rate of order 1010 s−1 accordingto our generalized SAR, which predicts a barrier below 5 kcalmol−1 for this structure.31,32 We showed in previous work thatall α-hydroperoxyalkyl radicals are unstable, in the sense thatthey are not even local minima on the potential energysurface,33 such that the coproduct radical above should fall

Table 4. Computed Relative Energies (kcal mol−1),Including ZPE, of the Rate-Controlling Transition Statesand Products of the Enolic 1,6-H Shift in Peroxy Radical Z-HOCHCHC(CH3)(OO•)CH2OH (Case B)

species UB3LYP/6-31+G(d,p) CBS-QB3//UB3LYP/6-31+G(d,p)

Re′C1 0.00 0.00TS′1−16Hs 8.25 12.23TS′2−16Hs 10.15 14.17



apart spontaneously into OH and HOCH2CHO. Therefore,PrOO should yield

+ → +

→ + + +

PrOO PrONO NO

NO MGLY GLYALD OH2

2

It is easily seen that the Pr′OO radical counterpart from case B,with the methyl group on the other central carbon, reacts in asimilar way, to yield

′ + → ′ +

→ + + +

Pr OO Pr ONO NO

NO GLY HYAC OH2

2

Thus, it appears that the presently proposed mechanisms,based on the pivotal, unusually fast enolic 1,6-H shift in thesecondary Z-1,4-dihydroxyisoprenyl-3-peroxy radicals, provide asolid explanation for the observed first-generation MGLY +GLYALD and GLY + HYAC carbonyls in the oxidation ofisoprene at high NO.However, at this stage it should be recognized that at low

NO two possibly competing reactions of PrOO and Pr′OOneed to be considered. The first involves a 1,6-H shift of thehydroperoxide-H to the peroxy function, forming an isomericperoxy radical, but facing a high barrier of 22.0 kcal mol−1 (forPrOO, computed at CBS-QB3 level) and expected anyway toresult in identical final products as PrOO by reaction with NO.More important is the possible 1,4-H shift in PrOO and Pr′OOof the formyl hydrogen to the peroxy function, with CBS-QB3-computed barrier for PrOO of 20.2 kcal mol−1 and henceexpected rate in the range 0.01−0.1 s−1 at 300 K, such that itmight become competitive at sub-ppbv NO levels. An accurateevaluation of the critical barrier and the rate of the 1,4 formyl-Hshift, as well as a detailed examination of the subsequentchemistry is far beyond the scope of the present work, whichfocuses on isoprene oxidation mechanisms and first-generationcarbonyl production at high NO levels, but nevertheless it mustbe stressed that this competing process could becomeimportant at the low or moderate NO levels of the PBL inless polluted regions.

■ CONCLUSIONS AND ATMOSPHERICIMPLICATIONS

In this work, we have proposed and theoretically quantified, forthe first time to our knowledge, the unusually fast 1,6-H shift ofenolic hydrogens in peroxy radicals of the type Z-HOCH

CHCH2OO•, finding barriers that are only about 11 kcal

mol−1, i.e., some 6−9 kcal mol−1 lower than for similar shifts ofalkane hydrogens in peroxys.9,23,26,27

Second, we have established that the secondary 1,4-dihydroxyisoprenyl-3-peroxy radicals Z-HOCHC-(CH3)CH(OO•)CH2OH (Dibble’s Z-VIIOO8) and Z-HOCHCHC(CH3)(OO•)CH2OH (Dibble’s Z-IXOO8) from isoprene undergo a very fast 1,6-H shift of theenolic hydrogen at rates of order 105 to 106 s−1, far outrunningin all relevant atmospheric and laboratory conditions thereaction with NOadopted by Dibble as their dominantroute8and resulting finally in the formation of first-generation methylglyoxal + glycolaldehyde and glyoxal +hydroxyacetone at high NO, as observed by Volkamer et al.,6

Paulot et al.,7 and Galloway et al.5

However, it must be noted that at sub-ppbv NO levels, apossibly competing 1,4-H isomerization reaction of asubsequent intermediate peroxy could divert a fraction of thereaction fluxes of the radicals above to other products. Thekinetics of this potentially interfering reaction and the follow-upchemistry need be addressed in future work.More important, the fast interconversion and near-equilibra-

tion at low NO levels of the various peroxy radical isomers/conformers from both major initial OH-isoprenyl adducts, andthe competing isomerizations of the primary Z-δ-hydroxyiso-prenyl-peroxys to form hydroperoxy-enones, both recentlyproposed and theoretically quantified by us9 and supported byexperimental evidence,34,35 might substantially reduce thefraction of the primary Z-δ-hydroxy-peroxys available forreaction with NO (or RO2) and subsequent formation of thesecondary peroxy radicals that result in the C2 and C3 carbonyls.The absence of evidence in low- or moderate-NO atmosphericconditions for the C5 hydroxy-carbonyls found in yields of 20−31% under high-NO laboratory conditions11 and shown to beformed from the primary Z-δ-hydroxyisoprenyl-peroxys,10,11 isconsistent with these views. The above implies that the trueatmospheric yields of the C2 and C3 carbonyls from isoprenecould be considerably smaller than these observed at high NOlevels. These considerations underscore once more thepotential importance of the new LIM isoprene oxidationchemistry9,34,36 for real atmospheric conditions and the need toaccurately quantify both the equilibria between the varioushydroxyisoprenyl-peroxy isomer/conformers and the rates ofthe Z-δ-hydroxyisoprenyl-peroxy isomerizations proper.

■ ASSOCIATED CONTENT*S Supporting InformationSchematic of the initial steps in the OH-initiated oxidation ofisoprene giving the branching to the major OH adductisomers/conformers and to the subsequent hydroxy-peroxyisomers/conformers. Geometries, energies, ZPEs, rotationalconstants, and vibration frequency data of the discussedstructures. This information is available free of charge fromthe authors or via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected].

Present Address†Department of Chemistry and Biochemistry, The University ofTexas at Austin, 1 University Station A5300, Austin, TX 78712-0165.

Scheme 2



http://pubs.acs.org

mailto:[email protected]

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This research was carried out in the frame of the “BIOSOA”project within the Science for Sustainable Developmentprogramme of the Belgian Science Policy Office. J.P. thanksDr. Jean-Francois Muller of the Belgian Institute for SpaceAeronomy, Brussels, for many stimulating discussions andmuch valued comments on the manuscript. Useful suggestionsof an anonymous reviewer helped improve this paper.

■ REFERENCES(1) Guenther, A.; Hewitt, C.; Erickson, D.; Fall, R.; Geron, C.;Graedel, T.; Harley, P.; Klinger, L.; Lerdau, M.; Mckay, W.; et al. J.Geophys. Res.-Atmos. 1995, 100, 8873−8392.(2) Karl, T.; Guenther, A.; Turnipseed, A.; Tyndall, G.; Artaxo, P.;Martin, S. Atmos. Chem. Phys. 2009, 9, 7753−7767.(3) Fu, T.-M.; Jacob, D. J.; Wittrock, F.; Burrows, J.; Vrekoussis, M.;Henze, D J. Geophys. Res. 2008, 113, D15303.(4) Thalman, R.; Volkamer, R. Atmos. Meas. Tech. 2010, 3, 1797−1814.(5) Galloway, M. M.; Huisman, A. J.; Yee, L. D.; Chan, A. W. H.;Loza, C. L.; Seinfeld, J. H.; Keutsch, F. N. Atmos. Chem. Phys. 2011, 11,10779−10790.(6) Volkamer, R., Barnes, I., Platt, U., Molina, L. T., Molina, M. J.Remote sensing of glyoxal by differential optical absorption spectros-copy (DOAS): Advancements in simulation chamber and fieldexperiments. In Environmental Simulation Chambers: Application toAtmospheric Chemical Processes; Barnes, I., Rudinski, J., Eds.; Springer:Dordrecht, Netherlands, 2006; Vol. 62, pp 129−137.(7) Paulot, F.; Crounse, J. D.; Kjaergaard, H. G.; Kroll, J. H.; Seinfeld,J. H.; Wennberg, P. O. Atmos. Chem. Phys. 2009, 9, 1479−1501.(8) (a) Dibble, T. S. J. Phys. Chem. A 2004, 108, 2199−2207.(b) Dibble, T. S. J. Phys. Chem. A 2004, 108, 2208−2215.(9) Peeters, J.; Nguyen, T. L.; Vereecken, L. Phys. Chem. Chem. Phys.2009, 11, 5935−5939.(10) Dibble, T. S. J. Phys. Chem. A 2002, 106, 6643−6650.(11) Park, J.; Jongsma, C. G.; Zhang, R.; North, S. W. J. Phys. Chem.A 2004, 108, 10688−10697.(12) Becker, A. D. J. Chem. Phys. 1993, 98, 1372−1377.(13) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J.Phys. Chem. 1994, 98, 11623−11627.(14) Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J. Chem. Theory Comput.2006, 2, 364−382.(15) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys.1987, 87, 5968−5975.(16) Montgomery, J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G.A. J. Chem. Phys. 1999, 110, 2822−2827.(17) Petersson, G. A.; Malick, D. K.; Wilson, W. G.; Ochterski, J. W.Jr.; M., J. A.; Frisch, M. J. J. Chem. Phys. 1998, 109, 10570−10579.(18) Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schutz,M.; Celani, P.; Korona, T.; Rauhut, G.; Amos, R. D.; Bernhardsson,A.;et al. Molpro, version 2006.1; see http://www.molpro.net, 2006.(19) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, T.; Kudin,K. N.; Burant, J. C.;et al. Gaussian, Revision C.02; Gaussian, Inc.:Wallingford, CT, 2004.(20) Eckart, C. Phys. Rev. 1930, 35, 1303−1309.(21) Johnston, H. S.; Heicklen, J. J. Phys. Chem. 1962, 66, 532−533.(22) Zhang, F.; Dibble, T. S. Phys. Chem. Chem. Phys. 2011, 13,17969−17977.(23) Vereecken, L.; Peeters, J. Structure-Activity Relationship forperoxy radical isomerisations by hydrogen migrations. Manuscript inpreparation.(24) Chuang, Y.-Y.; Coitino, E. L.; Truhlar, D. G. J. Phys. Chem. A2000, 104, 446−450.

(25) Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2002, 106, 842−846.(26) Zhang, F.; Dibble, T. S. J. Phys. Chem. A 2011, 115, 655−663.(27) Miyoshi, A. J. Phys. Chem. A 2011, 115, 3301−3325.(28) Maranzana, A.; Barker, J. R.; Tonachini, G. J. Phys. Chem. A2008, 112, 3666−3675.(29) Glowacki, D. R.; Pilling, M. J. Chem. Phys. Chem. 2010, 11,3836−3843.(30) Holbrook, K. A.; Pilling, M. J.; Robertson, S. A. UnimolecularReactions, 2nd ed.; Wiley: Chichester, U.K., 1996.(31) Peeters, J.; Fantechi, G.; Vereecken, L. J. Atmos. Chem. 2004, 48,59−80.(32) Vereecken, L.; Peeters, J. Phys. Chem. Chem. Phys. 2009, 11,9062−9074.(33) Vereecken, L.; Nguyen, T. L.; Hermans, I.; Peeters, J. Chem.Phys. Lett. 2004, 393, 432−436.(34) Peeters, J.; Muller, J.-F. Phys. Chem. Chem. Phys. 2010, 12,14227−14235.(35) Crounse, J. D.; Paulot, F.; Kjaergaard, H. G.; Wennberg, P. O.Phys. Chem. Chem. Phys. 2011, 13, 13607−13613.(36) Stavrakou, T.; Peeters, J.; Muller, J.-F. Atmos. Chem. Phys. 2010,10, 9863−9878.



http://www.molpro.net

unusually fast 1,6-h shifts of enolic hydrogens in peroxy radicals: formation of the...

Documents