Fast (E)â(Z) Isomerization Mechanisms of Substituted Allyloxy

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Fast (E) - (Z) Isomerization Mechanisms of Substituted Allyloxy Radicals in Isoprene Oxidation Vinh Son Nguyen, and Jozef Peeters J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp512057t • Publication Date (Web): 06 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015

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The Journal of Physical Chemistry

Fast (E) - (Z) Isomerization Mechanisms of Substituted Allyloxy Radicals in Isoprene Oxidation

Vinh Son Nguyen and Jozef Peeters* Department of Chemistry, University of Leuven, B-3001 Heverlee, Belgium

ABSTRACT Unusually rapid (E)

(Z) isomerization mechanisms are proposed and theoretically

quantified for substituted allyloxy radicals, R'RC=CH-CH2O●, with R and R' alkyl or oxygenated substituents, termed below β,γ-enoxy radicals. These conversions are shown to occur by a sequence of (i) ring closure to nearly isoergic oxiranyl-C●RR' radicals, (ii) internal rotation of the oxiranyl-moiety over 180°, and (iii) oxiranyl-ring reopening to yield the (E)

(Z)-isomerized oxy radicals. The barriers for all three steps were

computed at the CCSD(T)/aug-cc-pVTZ//QCISD/6-311(d,p) level to be only ≈ 5±2 kcal mol-1 and the rate constants at 298 K for the overall reactions were evaluated using transition state theory to be in the range 108 to 109 s-1. Specifically, and of relevance to the isoprene oxidation mechanism, it is predicted that the (E)-δ-hydroxy-isoprenyloxy radicals resulting from isoprene oxidation at high NO should isomerize to their (Z)analogues at a rate of about 1.5 × 109 s-1, much faster than the competing 1,5-H shift that was proposed earlier as major fate of these (E)-oxy radicals (Dibble; J. Phys. Chem. A 2002, 106, 6643). It is concluded that under high-NO conditions the (E)- and (Z)-δ-

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hydroxy-isoprenylperoxy

precursors

should

yield

identical

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and

therefore

indistinguishable C5-hydroxycarbonyls as main products.

INTRODUCTION In a recent paper on hydroxyl radical regeneration in the atmospheric oxidation of isoprene at low NO levels,1 we also described a newly identified facile route (see Figure 1) for the interconversion of the Zusammen (Z) and Entgegen (E) isomers of the β,γunsaturated O=CH-C(CH3)=CH-CH2O● and O=CH-CH=C(CH3)-CH2O● oxy radicals, produced together with OH in the fast photolysis of the (Z)-4-hydroperoxy-2/3methylbut-2-enals (HPALDs) that result from the fast 1,6-H shift of the initial (Z)-δhydroxy-isoprenylperoxys radicals in the oxidation of isoprene.1,2,3,4,5 While a (Z) - (E) isomerization generally necessitates a rupture of the carbon-carbon π-bond and hence faces a high activation barrier of at least 50 kcal mol-1, the proposed rapid interconversion of the substituted enoxy or -allyloxy radicals above occurs via a sequence of low-barrier reactions: ring closure to an oxiranyl-alkyl type radical that after internal rotation over 180° reopens the 3-member ring to yield the oxy radical isomer (Figure 1). For the case above, the highest transition state involved in the sequence was reported to have an energy less than 8 kcal mol-1 above the (more stable) (E) isomer. The importance of the facile conversion above is the very different fates expected for the two types of isomers.1 Another issue in the oxidation of isoprene, detailed below, may also hinge on the fast conversion of an (E) isomer of an "initial" enoxy radical from isoprene into its (Z) counterpart that may react in a very different way. In a previous paper on isoprene


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oxidation,2 we confirmed earlier predictions by Dibble,6 that in atmospheric conditions the initial OH-adduct I (see Figure 1) should arise for equal parts as trans- (E) and cis(Z) isomer, while for initial OH-adduct II, i.e. the HOCH2CHC(CH3)CH2 radical, the expected distribution is about 30% (E) and 70% (Z). Because of the allylic character of the initial OH-adducts I and II, they may subsequently add O2 either in the β or the δ position. While the O2-addition in β position allows for near-free internal rotations and so merges the contributions from the cis- and the trans-OH-isoprene radicals, the addition to the δ carbon leads for both initial adducts to distinct (E) or (Z) substituted alkene frames, as depicted in Figure 1 for the OH-adducts I; the scheme for OH-adduct II (not shown in Figure 1) is similar though with different branchings. At issue here is the nature of the reaction products of the (E)-δ-hydroxy-isoprenylperoxys at high NO, with a view mainly to the possible use thereof to determine the initial branching ratio to formation of the (E)and (Z)-δ-hydroxy-isoprenylperoxys. The fate of oxy radicals, formed as the sole products from peroxys at NO levels >10 ppbv (together with minor yields of organic nitrates),1 is generally well known, such that laboratory measurement of the isoprene oxidation product distribution under such conditions may be used for the determination of the initial branchings to the various peroxys. In this way, the (Z)-δ-hydroxyisoprenyloxys (Z)-δ-HOCH2-C(CH3)=CH-CH2O● and (Z)-δ-HOCH2-CH=C(CH3)-CH2O● from both initial OH-adducts I and II are considered to yield C5-hydroxycarbonyls and HO2 radicals by fast 1,5-H shift followed by reaction with O2.6,7,8,9 For example, for the (Z)-oxy from OH-adduct I:


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The consensus yields of the two C5-hydroxycarbonyls as measured by several groups,7 (see also Park et al.8 and references therein), thus allowed to estimate the initial production fraction of the two (Z)-δ-OH-peroxys together at about 25 % overall. On the other hand, the oxy radicals from the (E)-δ-hydroxy-isoprenylperoxys cannot undergo a facile 1,5-H shift of an α-H from the CH2OH- group as in the scheme above, as pointed out in the theoretical study by Dibble,6 who proposed and quantified alternative routes for the (E)-enoxys:

The proposed C4-hydroxycarbonyls expected from the (E)-enoxys are indeed observed products from isoprene at high NO, but with yields of only a few %, compared to the ≈ 25 % C5-hydroxycarbonyls, which was interpreted to mean that the initial branching to the (E)-δ-OH-peroxys from isoprene is almost an order of magnitude below that to the (Z)-δ-OH-peroxys.2,3,8 A low (E)/(Z) formation ratio for the initial peroxys could be rationalized by the theoretical finding that O2 addition to the OH-isoprenyl adducts to form E-δ-OH-peroxys must overcome a small barrier of about 1 kcal mol-1,2 as


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for O2 + allyl,10 while there is no effective barrier for O2 addition to form β-OH-peroxys and Z-δ-OH-peroxys, which feature an H-bond between the -OO and -OH substituents.1,2 However, facile interconversion as for the (E)- and (Z)- isomers of the enoxy radical photoproducts from the HPALDs, reported earlier,1 can be expected also for the oxys from the initial E-δ-OH-peroxys, which are likewise substituted allyloxy (or β,γ-enoxy) radicals. Such (E) → (Z) conversion might possibly outrun the alternative 1,5-H shift proposed by Dibble, such that the products of the initial (E)- and (Z)-δ-OH-peroxys from isoprene at high NO would be identical. Actually, in the Supporting Information of our recent feature article on isoprene, we already anticipated on this and adopted C 5hydroxycarbonyls as the products of both these radicals at high NO.1 The aim of this theoretical study is to verify the above and quantify the rate of the hypothesized fast (E) → (Z) enoxy isomerization. To that end, the barriers and rates of the basic steps of the newly proposed (E) → (Z) conversion mechanism will be evaluated first for two smaller template enoxy radicals, after which the mechanism of the (E)-OHisoprenyloxy radicals at issue will be investigated.

THEORETICAL METHODOLOGIES Quantum chemical computations. Optimized geometries of all stationary points were first obtained using the UM06-2X/6-311G++(3df,2p) level of DFT theory,11 abbreviated below as M06-2X. This advanced DFT functional, combined with a large basis set, is a good compromise between high performance and low cost for the largest structures  having seven heavy atoms  considered in this paper. Analytical harmonic vibrational analyses were performed using the same method to obtain harmonic


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vibrational frequencies and vibrational zero-point energies (ZPVE) and rotational constants, as well as to characterize all stationary points located, i.e. all real frequencies for a minimum and only one imaginary frequency for a transition structure. For some cases, Intrinsic Reaction Coordinate (IRC) calculations were done at the same level of theory to verify a natural connection from a reactant via a TS to a product. Furthermore, M06-2X data is used to obtain the harmonic-oscillator vibration and rotation partition functions for transition state theory (TST) rate coefficient calculations, with the M06-2X vibration frequencies and also the ZPVE scaled by 0.947.12 For all structures of importance: reactants, transition states, intermediates and products, geometries of the lowest-energy conformers were re-optimised using the proven Quadratic Configuration Interaction method, UQCISD/6-311G(d,p),13 and refined single-point energies were computed using the high-performance Coupled Cluster method with large basis set, UCCSD(T)/aug-cc-pVTZ.14,15,16 The T1 diagnostics at the latter level for all the (doublet) structures involved were found to lie in the range from 0.012 to 0.027, i.e. well below the 0.044 limit for reliable energies of radicals at this level according to Rienstra-Kiracofe et al.17 The above combination of coupled cluster singlepoint energies on quadratic configuration geometries is abbreviated below as CC//QC. Note that UQCISD optimization with the eigenvalue-following algorithm in Gaussian was carried out by using a numerical gradient and an initial guess of the UM06-2XHessian matrix. All calculations were carried out with the Gaussian 09 program suite18 and Molpro 2012.1 program.19 Generally, the M06-2X and CC//QC relative energies agreed within 1.5 - 2 kcal mol-1, but for the the 3-member ring oxiranyl-alkyl


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intermediates the M06-2X values are systematically around 3 kcal mol-1 lower than the CC//QC ab initio values. Chemical kinetics calculations. Thermal rate constants for the unimolecular reactions of interest, under high-pressure limit conditions, were computed using conventional transition state theory:20 k(T) = κ(T)  (kBT/h)  (QTS/QReact)  exp(-E0/kBT) where kB is Boltzmann’s constant; h is Planck’s constant; E0 is the adiabatic barrier height; QTS and QReact are the total partition functions for transition state and reactant, respectively; and (T) is the tunneling factor. The latter, which only applies for (competing or subsequent) H-shift side-reactions, was estimated using the zero-curvaturetunneling model by assuming an asymmetric Eckart potential.21,22 For H-shifts in peroxy radicals, around room temperature, this approach was recently found to give a satisfactory agreement with higher-level multi-dimensional treatments.23 The tunneling factors were calculated using the code of Coote et al.24 For the barrier heights E0, the higher-level CC//QC ab initio data were used, with ZPVE obtained from the M06-2X vibration frequencies, while the partition functions were based on the M06-2X vibration frequencies and rotation constants. The overall reaction rate of the full sequences of elementary reactions from initial reactant to final product considered here, including the three-step (Z) to (E) isomerizations, were calculated from the set of TST rate coefficients for all individual forward steps and for all reverse steps but the last, assuming quasi-steady states for all intermediates between the reactant and product.


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RESULTS AND DISCUSSION Ring closure in unsubstituted allyloxy radical CH2=CH-CH2O●. The first enoxy radical addressed in this study is unsubstituted allyloxy, CH2=CH-CH2O●, with no (Z) versus (E) isomer distinction, but the most simple unsaturated oxy radical that can undergo facile ring closure to an 3-member ring, which could be the first step to (Z) (E) conversion for γ-substituted homologues. In a recent theoretical study of the unimolecular rearrangement/decomposition mechanism of the allyloxy radical, at the QCISD(T)/CBS // B3LYP/MG3S level of theory, Goldsmith et al. already identified ringclosure to oxiranyl-methyl as the most facile initial step, facing a barrier of only 7.5 and endoergic for 2 kcal mol-1 (at 0 K).25 These energies are confirmed by the UCCSD(T)/aug-cc-pVTZ // UQCISD/6-311G(d,p) results of this work: a barrier of 7.2 and endoergicity of 2.2 kcal mol-1 (see Figure 2 and Table 1). Importantly, it is found that the epicyclic ●CH2- moiety can rotate 180° about the single C-C bond over a low barrier of only 3.7 kcal mol-1, such that if a substituent is present on the γ-carbon, (Z) to (E) conversion may be expected. CH3-CH=CH-CH2O●: fast (Z)

(E) isomerization. A first substituted allyloxy

for which the (Z) to (E) isomerization via the mechanism above was explored here is (Z)2-buten-1-oxy (or γ-methyl-allyloxy), cis-CH3-CH=CH-CH2O●, labeled below as OX2Z. The PES and the relevant structures are displayed in Figure 3, while relative energies are listed in Table 1. Henceforth only the CC//QC energies will be discussed here. Compared to the allyloxy case above, the ring closure in OX2Z to a 3-member oxiranyl- ring in OR2Z faces an even lower barrier (TS2.1) of only 4.6 kcal mol-1 and is nearly isoergic, owing to the secondary character of the oxiranyl-ethyl product radical OR2Z. The


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counter-rotation of the CH3C●H- and oxiranyl- moieties about the single C-C bond over 180° requires 4.1 kcal mol-1 of activation (TS2.2) to form the slightly higher-lying conformer OR2E, which in turn can re-open the 3-member ring over TS2.3 lying 4.2 kcal mol-1 above the original (Z) reactant to finally yield the (E) isomer OX2E, which is more stable by 2.6 kcal mol-1 than (Z). The highest barrier for the above sequence of steps is only 4.6 kcal mol-1, allowing a surprisingly fast, thermally accessible interconversion of the (Z) and (E) isomers of the 2-buten-1-oxy radical. The TST rate coefficients for the three successive forward steps (ka, kb, kc) and the first two reverse steps (k-a, k-b) of the sequence are calculated using the CC//QC energy data, with M062X-computed ZPVE energies, and the M06-2X-based vibration-rotation partition functions. Assuming canonical quasi-steady states for the two oxiranyl-ethyl intermediates OR2Z and OR2E, the overall rate coefficient for the (Z) → (E) isomerization of CH3-CH=CH-CH2O● can be estimated as: kZ→E = ka kb kc/( k-a k-b + k-a kc + kb kc)

(eq.1)

which yields kZ→E = 5.8 × 108 s-1 at 298 K. However, the steady-state assumption at the canonical level, above, which presumes in effect that both OR2Z and OR2E have a thermal distribution of states, cannot be fully valid at a pressure of 1 atm, as the lifetimes of the nascent, activated OR2Z and OR2E are only tens of picoseconds and hence too short for collisional thermalization. For such a case, following Greenwald et al.,26 one can resort to the steady-state assumption at the microcanonical level, and approximate the overall rate by that for a one-step thermal reaction with an effective sum of accessible internal states of the transition structure Neff = [1/Na + 1/Nb + 1/Nc]-1, in which Na, Nb and Nc are the sums of accessible states for the transition states TS2.1, TS2.2 and TS2.3,


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respectively, at the relevant total energies E. Accordingly, the last equation was rewritten as Neff = Na × [1 + Na/Nb + Na/Nc]-1 and the ratios Na/Nb and Na/Nc were estimated using the Whitten-Rabinovitch approximation,27 but disregarding the high-frequency C-H (and O-H) stretch modes that are inactive at the low vibration energies (≤ 7 kcal/mol) of these TS for reactants at about 298 K. The Neff(E) estimated in this way are mainly in the range (0.45 to 0.75) × Na for the relevant E such that the overall rate coefficient in the microcanonical steady-state approach can be approximated as kZ→E (298 K) ≈ (0.6 ± 0.15) × ka ≈ (5.4 ± 1.5) × 108 s-1, which differs only marginally from the canonical TST estimate above. The important result is that, according to both rate estimates, the (Z) → (E) isomerization of CH3-CH=CH-CH2O● is more than two orders of magnitude faster than the nearest competing reaction: a 1,5-H shift in the (Z) reactant oxy (see Figure 3) that faces a higher energy barrier of 10.6 kcal mol-1 and occurs at a TST calculated rate k(1,5-H) = 1.22 × 106 s-1 at 298 K, which includes a tunneling factor of 38.4 (the imaginary frequency being i 1559 cm-1). The other competitors, β C-C scission of the oxiranyl-ethyl intermediates to form CH3CH=CH-O-CH2●, must overcome barriers found to be 6 - 7 kcal mol-1 higher than for the ring-(re)opening to the 2-buten-1-oxys and are therefore much too slow to interfere with the (Z) → (E) sequence. The reverse overall (E) → (Z) isomerization is 50 times slower at 298 K, but does not have to compete directly with a fast H shift, only with negligibly slow decomposition over a barrier of ca. 23 kcal/mol into methyl-vinyl + formaldehyde.25,28,29 Products of (E)-δ-HOCH2-C(CH3)=CH-CH2O● and (E)-δ-HOCH2-CH=C(CH3)CH2O● radicals from isoprene. Figure 4 shows the structures and CC//QC energies (with ZPVE at M06-2X level included) of the species that are involved in the relevant


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reaction sequences characterized for the (E)-δ-HOCH2-C(CH3)=CH-CH2O● radicals from isoprene at issue. Below, these will be denoted as (E)-δ-OH-enoxy radicals. The less important counterparts from the OH-adducts II

1,2,8

will not be discussed here in detail,

but their chemistry is shown to be very similar. Compared to the preceding case, the ring closure of the (E)-δ-OH-enoxy OX3E and the (Z)-δ-OH-enoxy OX3Z to the respective oxiranyl-hydroxy-alkyl intermediates OR3E and OR3Z face even lower barriers (TS3.1 and TS3.3), of only 3.4 kcal mol-1, owing to the tertiary character of the resulting radicals. The intermediates OR3E and OR3Z have energies very close to the initial oxy reactant OX3E, and are separated by an internal rotation barrier of 3 kcal mol-1 (TS3.2). The (Z)-δ-OH-enoxy radical OX3Z, resulting from the 3-step isomerization of its (E) counterpart, lies 1.6 kcal mol-1 below the initial reactant, owing to a hydrogen bond between the enoxy-O and the hydroxyl-H. Of key importance to the issue is that the (Z)enoxy product radical undergoes in turn a fast 1,5-H shift of an α-hydrogen from the CH2OH group, over a barrier of 4.9 kcal mol-1 (TS3.4), to form the allylic product radical AL3Z, lying ≈26 kcal mol-1 below the (E)-δ-OH-enoxy reactant, such that this H-shift should be the predominant if not sole reaction of OX3Z. The latter is in accord with Dibble's predictions on the (Z)-δ-OH-oxy radical as formed directly from its peroxy precursor. Similar to the case in the preceding subsection, the β C-C scission of the oxiranyl-hydroxy-alkyl intermediates OR3E and OR3Z to form HOCH2C(CH3)=CH-OCH2● face barriers that are 6 - 7 kcal mol-1 higher than those for the ring-(re)opening to the (E)- or (Z)-δ-OH-enoxys and therefore cannot significantly interfere with the rapid, low-barrier (E) → (Z) isomerization sequence. The TST rate coefficients for the four forward reactions of the entire sequence from OX3E via OR3E, OR3Z, OX3Z to AL3Z,


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denoted in that order as ka, kb, kc, kd , and those for the first three reverse reactions denoted as k-a, k-b, k-c (with meaning and values different from the preceding case), are calculated using the CC//QC energy data including the M06-2X-computed ZPVE energies, and the M06-2X-based vibration-rotation partition functions. Assuming canonical quasi-steady states for the two oxiranyl-hydroxy-alkyl intermediates, OR3E and OR3Z, the overall rate coefficient for the (E) → (Z) isomerisation sequence involving the first three steps is calculated using an equation similar to (eq.1), obtaining for this case kE→Z = 1.9 × 109 s-1 at 298 K and values in the 280 - 320 K range that are fitted within 2% by: kE→Z(T) = 1.05 × 1012 exp (-1879/T) s-1

(eq.2)

However, also for this case the lifetimes of the nascent, activated OR3E and OR3Z are only tens of picoseconds, warranting a microcanonical steady-state treatment. Following similar approximations as in the preceding subsection, this yields an overall kE→Z (298 K) estimate of (1.6 ± 0.4) × 109 s-1, which again does not differ significantly from the canonical steady-state result. The last reaction in Figure 4, OX3Z → AL3Z with rate coefficient kd, involves first a breaking of the H-bond in the (Z)-δ-OH-enoxy by internal rotation of the -CH2OH group (not shown in Figure 4), followed by the 1,5-H shift proper that faces only a small barrier of 2.6 kcal mol-1; therefore the latter was taken as an effective forward barrier in calculating the thermal tunneling factor for the H-shift, with a value 4.2 at 298 K (the imaginary frequency being i 1099 cm-1). The TST rate coefficient kd(OX3Z) was thus evaluated at 3.9 × 109 s-1 at 298 K, and can be expressed for the 280 320 range, within 1%, by: kd(OX3Z)(T) = 8.7 × 1011 exp (-1608/T) s-1


(eq.3)

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Finally, assuming canonical quasi-steady states for all three intermediates OR3E, OR3Z and OX3Z, the overall rate coefficient for the entire sequence from the initial (E)-δ-OHenoxy reactant OX3E to the allylic product radical AL3Z, kE→AL = ka kb kc kd/( k-a k-b k-c + k-a k-b kd + k-a kc kd + kb kc kd)

(eq.4)

was evaluated at kE→AL = 1.7 × 109 s-1 at 298 K, while the values for the range 280 - 320 K can be represented within 2% by the Arrhenius expression kE→AL(T) = 6.25 × 1011 exp(-1755/T) s-1

(eq.5)

On the other hand, a similar approximate microcanonical steady-state treatment as above yields kE→AL (298 K) ≈ (1.4 ± 0.5) × 109 s-1, which here too is close to the canonical result. For this case, a potentially competing reaction of the initial oxy reactant OX3E is its direct 1,5-H shift to another allylic product radical AL3E (see Figure 4), which was considered by Dibble6 the dominant (if not only) reaction of the initial (E) enoxy radical. The CC//QC barrier computed in this work for this H shift, of 8.3 kcal mol-1 (TS3.5), is lower than for the similar H-shift of a methyl-H in the (Z)-CH3-CH=CH-CH2O● oxy of the preceding subsection, and is quasi-identical to the B3LYP/6-311G(2df,2p) result reported by Dibble6 but several kcal mol-1 lower than his MPW1K values. Using our CC//QC barrier and taking into account an asymmetric Eckart-barrier tunneling factor of 24.8 at 298 K (imaginary frequency = i 1523 cm-1), the TST rate coefficient k1,5-H(OX3E) at 298 K is calculated to be 4.4 × 107 s-1 at 298 K, which is 25 to 40 times lower than the overall rate coefficient kE→AL above for the 4-step sequence from the initial (E) enoxy to AL3Z. For the 280 - 320 K range, the TST rate coefficient for the competing H shift can be expressed as


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k1,5-H(OX3E)(T) = 1.04 × 1010 exp(-1624/T) s-1

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(eq.6)

Therefore, according to these theoretical predictions, the dominant product from the (E)δ-HOCH2-C(CH3)=CH-CH2O● radical is expected to be the (Z)-δ-HOC●H-C(CH3)=CHCH2OH radical. As generally accepted, this α-hydroxy-peroxy radical should react with O2 to yield HO2 radical and a carbonyl compound,30 in this case the hydroxy-enal or C5hydroxycarbonyl, (Z)-δ-O=CH-C(CH3)=CH-CH2OH, i.e. the same product as known to be formed6,7,8 more directly from the initial (Z)-δ-HOCH2-C(CH3)=CH-CH2O● radical. For the somewhat less important (E)-δ-HOCH2-CH=C(CH3)-CH2O● radicals1,8 that result from isoprene at high NO, a similar conversion to the (Z) isomer should dominate too, the more so since a competing 1,5-H shift as for the case above is not possible while only a 1,4-H shift can occur that faces a much higher barrier of about 20 kcal mol-1.6 Yet, different from Dibble's view that this enoxy should only react with O2, at a rate of order 104 s-1, the fate proposed in this work is the much faster (E) → (Z) isomerization, at rate > 108 s-1 , followed by a 1,5-H shift of an α-H from the alcohol-functionality, and reaction with O2 to yield HO2 and a C5-hydroxycarbonyl:


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Therefore, in isoprene oxidation under conditions of high NO, the major products from the initial (E)-δ-HOCH2-C(CH3)=CH-CH2OO● as well as (E)-δ-HOCH2CH=C(CH3)-CH2OO● radicals are expected to be the same C5-hydroxycarbonyls as those from their (Z)-δ-HOCH2-C(CH3)=CH-CH2OO● and (Z)-δ-HOCH2-CH=C(CH3)-CH2OO● counterparts, respectively.

CONCLUSIONS AND IMPLICATIONS FOR ISOPRENE OXIDATION In this work, a specific mechanism is proposed and theoretically quantified for unusually fast (Z)

(E) isomerizations of substituted allyloxy radicals via three steps: ring

closure to oxiranyl-alkyl radicals, internal rotation of the oxiranyl-moiety over 180°, and ring reopening, all over low barriers of around 5 ± 2 kcal mol-1 and proceeding at high overall rates of order 108 - 109 s-1, readily outrunning all competing and interfering reactions such as H-shifts and other ring-reopenings. Prime examples, both in isoprene oxidation, are the (Z)

(E) conversion of the β,γ-unsaturated enoxy photoproduct

radical from HPALD photolyis,1 and the facile (E) → (Z) isomerization of the (E)-δHOCH2-C(CH3)=CH-CH2O● and (E)-δ-HOCH2-CH=C(CH3)-CH2O● radicals formed at high NO from the two kinds of (E)-δ-hydroxy-isoprenylperoxy radicals. The latter processes are predicted to be much faster than the competing H-shifts proposed earlier such that, different from the earlier views, it is concluded in this work that, at high NO levels, the (E)-δ-hydroxy-isoprenylperoxy precursor radicals should finally yield the same products as their (Z)-counterparts. The important consequence is that, according to the findings in this work, the initial branching ratios to these two different initial δ-


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Page 16 of 29

hydroxy-isoprenylperoxys cannot be determined from isoprene oxidation product measurements at high NO.

AUTHOR INFORMATION Corresponding author *Jozef Peeters: e-mail, [email protected]

ACKNOWLEDGMENTS This research was sponsored by the Belgian Science Policy Office (BELSPO) under contract SD/CS/05A (project BIOSOA) in the frame of the Science for Sustainable Development program.


16

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Table 1. Relative energies including ZPVE, in kcal mol-1, and T1 diagnostic for A) ring closure and internal rotation in allyloxy radical, CH2=CH-CH2O● (see Figure 2); and B) the fast (Z)

(E) isomerization sequence and the competing 1,5-H shift in CH3-

CH=CH-CH2O● (see Figure 3) Structures

Relative energy

T1 diagnostic

UM06-2x/

UCCSD(T)/

6-311++G(3df,2p)

aug-cc-pVTZ a

CCSD(T)

A) CH2=CH-CH2O● OX1

0.00

0.00

0.019

TS1.1

9.36

7.19

0.016

OR1

0.02

2.23

0.014

TS1.2

3.27

5.91

0.012

B) CH3-CH=CH-CH2O● OX2Z

0.00

0.00

0.018

TS2.1

6.06

4.60

0.027

OR2Z

–3.29

–0.66

0.014

TS2.2

0.58

3.48

0.012

OR2E

–2.46

–0.06

0.014


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TS2.3

5.54

4.15

0.027

OX2E

–2.04

–2.59

0.017

TS2.4

8.84

10.62

0.020

a

Page 18 of 29

Geometrical parameters obtained at UQCISD/6-311G(d,p) level of theory.


18

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Table 2. Relative energies including ZPVE, in kcal mol-1, and T1 diagnostic for the fast (E)

(Z) isomerization sequence and subsequent 1,5-H shift, as well as the competing

1,5-H shift of the (E)-δ-HOCH2-C(CH3)=CH-CH2O● radical from isoprene (see Figure 4) Structures

Relative energy

T1 diagnostic CCSD(T)

UM06-2x/

UCCSD(T)/

6-311++G(3df,2p)

aug-cc-pVTZ a

OX3E

0.00

0.00

0.016

TS3.1

4.64

3.44

0.023

OR3E

–3.54

0.08

0.014

TS3.2

–0.33

3.01

0.013

OR3Z

–3.62

–0.13

0.014

TS3.3

5.46

4.16

0.023

OX3Z

–2.07

–1.56

0.017

TS3.4

4.61

3.36

0.027

AL3Z

–25.95

TS3.5

9.51

8.34

0.018

AL3E

–16.15

–16.31

0.017

a

Geometrical parameters obtained at UQCISD/6-311G(d,p) level of theory


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Page 20 of 29

FIGURE CAPTIONS

Figure 1. Initial steps of isoprene + OH and O2-addition; 1,6-H shift to HPALDs and photolysis of HPALDs; (Z) to (E) interconversion of enoxy radical photoproducts from HPALDs. Note that the redissociation of the thermally labile hydroxyperoxys is not relevant under conditions of very high NO

Figure 2. Potential energy surface for ring-closure followed by internal rotation and ring reopening in the unsubstituted allyloxy radical CH2=CH-CH2O●, constructed with UCCSD(T)/aug-cc-pVTZ energies

Figure 3. Potential energy surface for the fast (Z)

(E) isomerization of the CH3-

CH=CH-CH2O● template, constructed with UCCSD(T)/aug-cc-pVTZ energies

Figure 4. Potential energy surface for the fast (E) to (Z) isomerization and subsequent 1,5-H shift, as well as the competing 1,5-H shift, of the (E)-δ-HOCH2-C(CH3)=CHCH2O● radical from isoprene, constructed with UCCSD(T)/aug-cc-pVTZ energies, except AL3Z which is at UM06-2x/6-311++G(3df,2p) level of theory.


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Figure 1.


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Page 22 of 29

Figure 2.


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Figure 3.


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Page 24 of 29

Figure 4.


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Fast (E)â(Z) Isomerization Mechanisms of Substituted Allyloxy

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