Calculated Hydrogen Shift Rate Constants in Substituted Alkyl Peroxy

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Calculated Hydrogen Shift Rate Constants in Substituted Alkyl Peroxy Radicals Rasmus V. Otkjær, Helene H Jakobsen, Camilla Mia Tram, and Henrik Grum Kjaergaard J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b06223 • Publication Date (Web): 29 Sep 2018 Downloaded from http://pubs.acs.org on September 30, 2018

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The Journal of Physical Chemistry

Calculated Hydrogen Shift Rate Constants in Substituted Alkyl Peroxy Radicals Rasmus V. Otkjær, Helene H. Jakobsen, Camilla M. Tram and Henrik G. Kjaergaard* Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark

Abstract

Peroxy radical hydrogen shift (H-shift) reactions are key to the formation of highly oxidized molecules and particle growth in the atmosphere. In an H-shift reaction, a hydrogen atom is transferred to the peroxy radical from within the same molecule to form a hydroperoxy alkyl radical, which can undergo O2 uptake and further H-shift reactions. Here we use an experimentally verified theoretical approach based on Multi-Conformer Transition State Theory to calculate rate constants for a systematic set of H-shifts. Our results show that substitution at the carbon, from which the hydrogen is abstracted, with OH, OOH and OCH3 substituents lead to increases in the rate constant by factors of 50 or more. Reactions with C=O and C=C substituents lead to resonance stabilized carbon radicals and have rate constants that increase by more than a factor of 400. In addition, our results show that reactions leading to secondary carbon radicals (alkyl substituent) are 100 times faster than those leading to primary carbon radicals, and those leading to tertiary carbon radicals a factor of 30 faster than those leading to secondary carbon

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radicals. When the carbon from which the H is abstracted is secondary and has an OH, OOH, OCH3, C=O or C=C substituent, H-shift rate constants are larger than 0.01 s-1 and need to be considered in most atmospheric conditions. H-shift reaction rate constants are largest and can reach 1 s-1 when the ring size in the transition state is 6, 7 or 8 atoms (1,5; 1,6 or 1,7 H-shift). Thus, H-shift reactions are likely much more prevalent in the atmosphere than previously considered.


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Introduction Oxidation of organic compounds in the atmosphere is initiated by reaction with an oxidant, such as a hydroxyl radical, ozone or a chlorine radical. This oxidation forms a carbon-centered radical, which will rapidly react with O2 to form a peroxy radical (RO2). The lifetime of the peroxy radicals are determined by the bimolecular reactions with NO, HO2 or other RO2.1 The rates of reaction for these bimolecular reactions are proportional to the concentration of the reaction partner. Concentrations of NO have been measured to be as high as 200 ppb in New York City during morning rush hour and as low as 20 ppt over the Amazon rain forest,2-3 corresponding to lifetimes with respect to NO in the range of 0.02 s and 200 s, respectively.4 The same studies measured typical daily maximum HO2 concentrations of 2 ppt in New York City and a mean daytime concentration around 40 ppt above the Amazon rain forest, corresponding to lifetimes with respect to HO2 between 1200 s and 60 s (See Section S1 of the SI).4 Recently, RO2 self-reaction rate constants have been measured to be as large as 10-10 cm3 molecule-1 s-1 for larger RO2.5 However, concentrations of these RO2 are likely sufficiently low that it does not affect the RO2 lifetime.6-7 Peroxy radicals have also been proposed to undergo a concerted elimination reaction, where a hydrogen is transferred to the peroxy group, simultaneously with the formation of a C=C double bond and loss of HO2 through scission of the C-OO bond.8-10 However, Hyttinen et al. showed that this reaction is unlikely under atmospheric conditions.11 If the lifetime of the RO2 is long enough, unimolecular hydrogen shift reactions (H-shift) become possible.12 In pristine environments, where NO and HO2 concentrations are low, the lifetime of RO2 are in the range 1-100 seconds.2-4 Especially in those environments, H-shift reactions can make up a significant fraction of the total RO2 reactivity.13 H-shift reactions are isomerization reactions, where a hydrogen atom is transferred to the peroxy moiety from within the same


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molecule. This leads to the formation of a hydroperoxide group, and a new carbon-centered radical, which again can add O2 to form a new peroxy radical. This chain reaction is often referred to as autoxidation,14-16 which is believed to be important in the formation of highly oxidized molecules and key in aerosol growth.12, 17-20 Previously, hydrogen shift reactions have been found to be important in alkoxy (RO) radicals. These alkoxy H-shift reactions have been studied extensively both theoretically21-23 and experimentally.24-26 Multiple structure-activity relationships have been developed for alkoxy hydrogen shift reactions.27-30 Much less is known for peroxy radical H-shifts, shown to be important even at ambient temperatures of the atmosphere, despite them usually being significantly slower than their alkoxy counterparts.31 RO2 H-shift reactions are known in low temperature combustion chemistry32-33. In atmospheric chemistry, they have only recently been considered, by both theoretical34-37 and experimental studies.15-16, 38-41 These initial studies have shown that H-shift reactions can be fast, but that the H-shift rate constants are extremely sensitive to the system.42-43 Even seemingly minor changes in a peroxy radical, such as changing a hydrogen to an OOH group, can result in a large change to the H-shift rate constant.15 There are only few experimentally determined RO2 H-shift rate constants.16,

40-41

In other experiments,

limits are placed on the H-shift rate constants, in order to explain the products observed.15, 17, 38, 44 In addition, a number of theoretical studies have calculated RO2 H-shifts in the oxidation of isolated compounds.12, 34, 45-49 A few studies have investigated some systematic effects, but the scope of these studies was limited by the lack of a cost-effective method for the calculation of accurate rate constants and comparison with experiments.15, 43, 50 Crounse et al. and Jørgensen et al. both did systematic sampling of substituents and found negligible effects from substituents placed on carbons neighbor to the abstraction site.15, 43 In contrast, both studies found increases


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in the rate constant of up to factors of 3,000 (Crounse et al.15) and 106 (Jørgensen et al.43), respectively, with addition of OH, OOH and OCH3 groups at the abstraction site. Mohamed et al. performed a systematic study of H-shift reactions abstracting hydrogen at a carbon with an OOH group, testing different ring sizes in the TS and the effect of CH3 substituents.50 They found both increases and decreases in the rate constant upon addition of methyl groups at the peroxy radical carbon.50 On the other hand, multiple studies have reported that the addition of methyl groups at the abstraction site leads to an increase in the rate constant.10, 50-55 The aforementioned studies used different kinetic theory and ab initio methods, which makes it difficult to combine their results to predict the rate constants of unstudied H-shifts. In this study we attempt to include many of the effects studied previously, but all at the same level of theory and with an accurate and cost-effective approach. Recently, Møller et al. developed a cost-effective approach for obtaining conformers and calculating rate constants using Multi-Conformer Transition State Theory (MC-TST).56 They showed that including the effect of multiple conformers can decrease the calculated rate constant by factors of up to 103 and can thus be important to consider. This approach has been shown to agree to within a factor of five for the five measured H-shift rate constants.15-16, 40, 56 Earlier studies have investigated the effect of using a hindered rotor (HR) approximation instead of a harmonic oscillator for the partition functions. Using single conformer TST, Zhang and Dibble42 reported a factor of five decrease in the rate constant at 298.15 K, while Zheng and Truhlar57 reported a factor of three decrease with the use of the HR approximation. Lin et al. showed that on a per rotor-basis the HO partition functions are only off by 28% on average.58 However, by using HR, these studies include states from multiple minima on the potential energy surface. This inclusion is responsible for at least some of the decrease in the rate constant with


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using HR relative to HO. As such, the effect of using HR instead of HO is likely much smaller if multiple conformers is already included in the TST approach. Møller et al. also assessed the effect of including hindered rotors in combination with MC-TST, using multiple different approaches. They found that using hindered rotor affected the rate constant by less than 30%.56 In this paper, we use the theoretical approach by Møller et al. to perform a systematic study of H-shift rate constants to illustrate the factors that affect the H-shift reactions. In total, 68 different H-shifts are included in this study. As our base backbone, we used straight chain hydrocarbons similar to compounds arising from gasoline emissions, one of which was recently studied.16 We tested the effect of substituents at the carbon, from which hydrogen is abstracted (referred to as abstraction site), with a range of atmospherically relevant functional groups: C=C, CH3, C=O, F, H, OCH3, OH, ONO2 and OOH. In addition, we have investigated the effect of methyl groups (as a proxy for alkyl substituents) at both the peroxy radical carbon and the abstraction site. Finally, we investigated the effect of the transition state (TS) ring size. We will refer to the H-shifts by the number of non-hydrogen atoms between the initial and final position of the transferred hydrogen atom (e.g. in a 1,4 H-shift a five-membered ring is formed in the TS, counting the hydrogen). The reactants of all the reactions we have calculated rate constants for, are shown in Figure 1. They are named according to the length of their carbon backbone, and the position of the substituent. Most of the studied systems have the peroxy radical on a primary carbon. In the two exceptions, we have added an S or T to indicate secondary or tertiary peroxy radical, respectively. We have studied 1,4 H-shifts (C2, C4-2R, C6 and C9), 1,5 H-shifts (C3, C4-3R, C5S-R, C5T-R, C6 and C9), 1,6 H-shifts (C4-4R, C5-4R, C6 and C9), 1,7 H-shifts (C6, C6-5R and C9) and in C9 also 1,8; 1,9 and 1,10 H-shifts. C5S-R has two chiral centers when R is not H or CH3, one at the carbon with the peroxy radical and one attached to the


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substituent. It is therefore present as four stereoisomers, which are pairwise mirror images with identical reactivity. We have calculated the reaction rate constants for both the R,R and R,S isomer.

Figure 1. Reactants of the reactions studied and the notation used to refer to them. The hydrogen atoms abstracted in the H-shift reaction are shown explicitly in red. R represents C=C, CH3, C=O, F, H, OCH3, OH, ONO2 and OOH groups, except in the case of C5T-R, where R only represents H and OH.


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Computational Methods Multi-Conformer Transition State Theory (MC-TST) was used to calculate the rate constants in this work.56, 59-61 The MC-TST rate constants are high-pressure limit rate constants. Multiple studies have shown that H-shift reactions are in the high-pressure limit at 298.15 K and 1 atm.34, 62-63

The MC-TST expression for rate constants, kMC-TST, is:

. exp − , ∑ ,$ − #,$

= exp − ", ! ℎ

∑ # . exp − " ! #,!

(Eq. 1)

where is the tunneling correction, kB is Boltzmann’s constant, T is the temperature, h is Planck’s constant, QTS,i is the partition function of the i’th transition state (TS) conformer and ∆Ei is the energy difference between the i’th TS conformer and the lowest energy TS conformer. ETS,0 is the energy of the lowest-energy TS conformer. The symbols are equally defined for the reactant conformers, with index j instead of i. All energies in (Eq. 1) are corrected for zero-point vibrational energy (ZPVE). The approach used here follows that of Møller et al.

56

and only the main points will be

described here. A guess of the TS structure was drawn and optimized with B3LYP/6-31+G(d) 6468

(from here on denoted B3LYP) using the Gaussian 09 program.69 The optimized structure was

used as input for a systematic molecular mechanics conformer search with the MMFF force field 70-75

in the Spartan’14 program.76 The input for the reactant conformer search was a non-

optimized structure drawn in Spartan’14. As default, the force field places a negative charge on the radical oxygen atom, but using the keyword FFHINT=X~~+0, where X is the atom number of the radical atom, the force field was forced to place no charge on the radical atom. For the TS conformer search, the O-O, O···H and C-H bond distances were constrained. A constrained optimiziation with the same constraints as the conformer search, was performed for the TS


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conformers. All conformers were subsequently optimized with B3LYP (either for a minimum or a first-order saddle point). Duplicate conformers were removed, by comparing their electronic energy and dipole moment.56,

77

Unique conformers within 2 kcal/mol of the lowest energy

conformer in electronic energy were reoptimized with ωB97X-D/aug-cc-pVTZ78-79 (referred to as ωB97X-D) and their frequencies were calculated. We used the energies and frequencies at this level of theory for the relative energy between conformers and the partition functions of each conformer. The partition functions were calculated using the harmonic oscillator approximation. For the lowest energy conformers of both reactant and TS, we calculated a single-point energy with ROHF-ROCCSD(T)-F12a/VDZ-F1280-84 (referred to as F12) on the ωB97X-D geometry (referred to as F12//ωB97X-D), using the MOLPRO 2012 program.85 The ωB97X-D and F12 output

files

needed

to

calculate

the

rate

constants

are

available

online

(https://sid.erda.dk/public/archives/c7756cf94ebfa01a28e1a7b23ce2d2e6/publishedarchive.html). These output files include xyz coordinates of all conformers. We applied the one-dimensional Eckart tunneling correction factor,86 which uses the forward and reverse barrier and the imaginary frequency of the TS as input. An intrinsic reaction coordinate (IRC) was calculated starting from the B3LYP geometry corresponding to the TS conformer lowest in ZPVE corrected energy at the ωB97X-D level of theory. The endpoints of the IRC were optimized at the B3LYP level of theory, and reoptimized with ωB97X-D. The frequencies of the reoptimized endpoints were also calculated with ωB97X-D. Finally, an F12//ωB97X-D single point energy calculation was performed on the ωB97X-D optimized endpoints. The energies used in the Eckart correction were comprised of the F12//ωB97X-D electronic energies and the ωB97X-D ZPVE correction. The imaginary frequency of the TS was calculated with ωB97X-D.


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In some cases (OOH and ONO2 substituents), the IRC led to decomposition of the product by dissociation of the O-O or O-N bond next to the radical formed. In those cases, using the endpoint of the IRC would lead to an overestimation of the reverse barrier height used for tunneling. Instead, we used the geometry of the point on the IRC with the lowest RMS gradient before dissociation as a starting geometry for a constrained optimization. See Section S2 of the SI for an illustration of the point selected. Initially, the O-O or O-N bond distance was locked, and the rest of the molecule optimized with B3LYP. Then, an unconstrained B3LYP optimization was performed and in some cases a minimum was present without dissociation of the O-O or O-N bond. Subsequently, the same procedure was done with ωB97X-D. Finally, the F12//ωB97X-D single-point energy of the lowest energy ωB97X-D structure, which had not dissociated, was calculated. All the rate constants presented in the main manuscript of this work were calculated at 298.15 K. In addition, the temperature dependency of the rate constants was found by calculating the rate constant and the tunneling correction at 5 K intervals for 290-320 K and fitting it to a three parameter expression (see Section S3-S11 in the SI). Extension of the temperature range much beyond this increases the uncertainty of the approach by Møller et al. and decreases the accuracy of the three-parameter expression. For example, for C3 we calculate the 1,5 H-shift MC-TST rate constant at 500 K to be 5.4 s-1, while the three-parameter expression predicts 7.0 s-1.


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Results and Discussion Ring Size

For the faster alkoxy (RO) H-shifts the effect of transition state ring size have

previously been investigated.27 The 1,5 H-shift have been found to dominate, with the 1,6 H-shift slightly slower and the 1,4; 1,7 and 1,8 H-shifts not competitive. For the peroxy H-shifts we have investigated 1,4 to 1,10 H-shifts on a range of straight chain peroxy radicals of increasing size. For the 1,4 to 1,7 H-shifts, we also included all the different functional groups.

Figure 2. Rate constants of H-shift reactions with different ring sizes in the TS and different substituents. The rate constants at 298.15 K of the H-shift reactions of C4-2R (1,4 H-shift), C43R (1,5 H-shift), C5-4R (1,6 H-shift) and C6-5R (1,7 H-shift) are shown. In Figure 2, we show the absolute values of the rate constants of the H-shift reactions of C42R (1,4 H-shift), C4-3R (1,5 H-shift), C5-4R (1,6 H-shift) and C6-5R (1,7 H-shift), i.e. 1,4 to 1,7 H-shifts with all the substituents studied. In all the reactions shown, the peroxy group is on a primary carbon and they lead to the formation of a secondary (tertiary if R=CH3) carbon radical. It is clear, that the 1,5; 1,6 and 1,7 H-shift reactions all have rate constants in the same range for a given substituent, with the 1,6 H-shift reaction usually being slightly faster. The largest


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difference between a 1,5 H-shift and a 1,6 H-shift, with the same substituent is a factor of six (R=OOH). The 1,6 H-shifts in C5-4R with R being C=C, C=O, CH3, OCH3, OH and OOH all have rate constants in the range from 10-2 s-1 to 1 s-1 and should be considered in a low-NO atmospheric or laboratory context. The reactions of the unsubstituted (R=H) peroxy radical and with R being F or ONO2 all have rate constants below 5×10-4 s-1 for all the H-shifts studied here and are unlikely to be of atmospheric importance. As expected from multiple earlier studies, the 1,4 H-shifts are very slow.

15-16, 42-43

The fastest 1,4 H-shift we find here is with the C=O

substituent, which has a rate constant of 3.2×10-4 s-1. Thus 1,4 H-shifts are at most only a minor fraction of the unimolecular reactions of peroxy radicals. They are also likely slower than bimolecular reactions under most atmospheric conditions, with the possible exception of aldehydic H-shifts.40

Figure 3. Rate constants of H-shift reactions with different ring sizes in the TS. Rate constants at 298.15 K of the 1,4-1,7 H-shift reactions in C6 and 1,4-1,10 H-shift reactions in C9 are shown. The results in Figure 2 were based on peroxy radicals of different lengths of the carbon backbone. To test whether the size of the carbon backbone affected the rate constants of the H-


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shift reactions, we calculated the rate constants of the 1,4 and larger H-shift reactions in the peroxy radicals, C6 and C9, and show the results in Figure 3. Similarly to the trends seen in Figure 2, for each RO2 the 1,5; 1,6 and 1,7 H-shift rates are similar (within factor of 2), while the 1,4 H-shift is much slower. In C9, the 1,8 H-shift is around ~100 times slower than the 1,7 Hshift, with the 1,9 and 1,10 H-shifts even slower than the 1,8 H-shift. Previously, Davis and Francisco calculated rate constants at 600 K for 1,3-1,8 H-shifts of a series of 1-alkylperoxy radicals (from methyl to hexyl peroxy), using single conformer TST with the G2 composite method. They found an effect of ring size in agreement with the present results.54 These results clearly illustrate that 1,5; 1,6 and 1,7 H-shifts routinely need to be considered when assessing the reaction mechanism of peroxy radicals. The largest rate constant for the reverse reactions of the H-shifts studied in this work was found for C6-5R where R=OCH3, which has a rate constant of 3.5×106 s-1. The rate constants of the other reverse reactions in this work are smaller by a factor of at least five and often much more. The reverse H-shift reactions are in competition with addition of O2, which has been measured to have a pseudo first order rate constant of about 107 s-1.87 We therefore do not discuss the reverse reactions further, since the majority of H-shifts products likely undergo O2 addition instead. The rate constants of all the reverse H-shift reactions can be found in Section S3-S11 of the SI.


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Figure 4. Rate constants of H-shift reactions upon substitution of an H atom at the hydrogen abstraction carbon. Shown in the figure are the the rate constants at 298.15 K of the H-shift reactions of C4-3R (1,5 H-shift), C5-4R (1,6 H-shift) and C6-5R (1,7 H-shift). All H-shifts lead to a secondary radical (tertiary when R=CH3). Substituent Effects

In Figure 4, we clearly show the potentially large effect on the H-shift

rate constant of substitution at the carbon atom, from which hydrogen is abstracted. Results for C4-2R, C4-4R and C5S-R are available in Section S12 in the SI. For all the investigated reactions of the peroxy radicals in Figure 1, six of the eight substituents considered lead to an increase in the H-shift rate constant, relative to R=H. The substituents C=C, C=O, OH, OCH3, OOH and CH3 all lead to increases in the rate constants by at least a factor ~20 and most significantly more. The unsubstituted 1,5 to 1,7 H-shifts (C4-3R, C5-4R and C6-5R) all have rate constants of around ~10-4 s-1. Since the unsubstituted peroxy radicals all have H-shift reactions too slow to compete in an atmospheric context, this clearly illustrates that substituents in peroxy radicals are essential for the H-shift reactions to be of atmospheric importance. The largest increases arise with C=C and C=O substituents, which lead to increases by factors


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between 400-80,000. H-shift reactions with C=O or C=C at the abstraction site are favorable, as the carbon-centered radical formed in these is stabilized by delocalization of the double bond. The OH, OCH3 and OOH substituents all lead to increases in the rate constants by factors in the range 50-12,000. Peroxy radicals with R=CH3, react slower than those with the OH, OCH3 and OOH substituents, but still have rate constants of up to two orders of magnitude faster than with R=H. The substituents ONO2 and F have limited effects on the rate constants. For some H-shift these (ONO2 and F) cause a small increase in the rate constant and for others a small decrease, but these substituents alone will rarely be sufficient to cause the H-shifts to be of atmospheric relevance. Based on our results it is possible to establish the following rule of thumb, shown in Scheme 1, to serve as a simple guideline for the approximate increase in H-shift rate constants upon substitution at the carbon, from which hydrogen is abstracted.

Scheme 1. Changes in the H-shift rate constants (at 298.15 K) with substitution, relative to R=H. As an illustration, the 1,6 H-shift reaction in C5-4R is shown.

Previously, the effects of substituents (e.g. R = OH, OOH and OCH3) in the alkyl backbone on peroxy H-shifts have been investigated.15, 43 However, neither of these studies included multiple conformers in the TST calculation. Crounse et al. showed experimentally that an OOH substituent in 3-pentanone increases the rate of the 1,5 H-shift by more than a factor of 50.15


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Theoretically, they used single conformer TST and found that OH and OOH substituents at the abstraction site increased H-shift rate constants by 2-3 orders of magnitude. Crounse et al. reported rate constants for the 1,5 H-shift of the compound referred to here as C5S-R with R=H and OOH. Their calculated rate constants are within a factor of two of ours. Much closer than expected for a single conformer TST calculation. However, both these cases are due to cancellation of errors. The barrier height reported by Crounse et al. is 0.2 kcal/mol lower than ours and since they did not use MC-TST their ratio of partition functions is likely too high. These two effects are then countered by differences in the tunneling correction. Our imaginary frequency is 150 cm-1 higher than theirs, which lead to a factor of 2 larger Eckart tunneling correction. Similar differences are responsible for the very good agreement for the R,S isomer of C5S-R with R=OOH. We would expect this error cancellation to vary widely from reaction to reaction. In the theoretical study by Jørgensen et al. on 1,4-1,6 H-shift in CH2OH-CH(OO●)CH2-CH2-CH3, they found that OH, OOH and OCH3 substituents at the abstraction site lead to similar increases in the rate constants, consistent with the present work.43 Substituents at other sites were found to have minor effects on the H-shift rate constant.43 Jørgensen et al. studied compounds very similar to the 1,5 H-shift of C5S-R with R=H,OH,OOH and OCH3, but all with an extra OH group on the primary carbon next to the peroxy radical carbon. They performed conformer searches only for the OOH-substituted peroxy radicals. For the other peroxy radicals the lowest energy OOH-substituted conformer was chosen and the functional group exchanged with either H, OH or OCH3. Their rate constant for the for the 1,5 H-shift of the OOH-substituted peroxy radical is two and 12 times slower than our rate constants for the two diastereoisomers of C5S-R, respectively. The rate constants of the OH-substituted peroxy radicals are faster than the ones reported here by roughly 2000 times. The stability of the conformers of the OH-substituted


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peroxy radical is likely heavily influenced by hydrogen bonds (H-bonds), and the conformer lowest in energy for an OOH substituent is likely not the lowest in energy with a OH substituent. The rate constants for the 1,5 H-shift of the peroxy radicals with H or OCH3 at the abstraction site are larger than the present results by factors between two and 20, as expected from a single conformer TST approach.56 Previously, for the much more reactive alkoxy radicals, an OH group at the abstraction site was found to lead to increases of up to factors of 400 in the alkoxy H-shift rate constant.27 Previously, Praske et al. showed that H-bonds can have a significant effect on the rate constant, by being present in either the reactant or in the TS.16 However, the H-bonded conformers were not always found to be the lowest energy conformers.16 These H-bonds are also prevalent in the systems we have studied here. As an example, the lowest energy product conformer of C5-4R with R=OH has a H-bond between the OH group and the newly formed hydroperoxide. However, the lowest energy reactant conformer of C5-4R with R=OH does not contain a H-bond. Effect of Multiple Substituents In Figure 5, we show the effect on the H-shift rate constant of forming a primary, secondary or tertiary carbon-centered alkyl radical. We find that the rate constants increase as the carbon atom becomes more and more substituted. The reactions forming secondary radicals are about two orders of magnitude faster than those forming primary radicals and reactions leading to tertiary radicals are around 30 times faster than those leading to secondary radicals. We found close to no effect (less than a factor of two increase) of exchanging a methyl group for an ethyl, propyl or butyl group, see Section S13 of the SI. We also studied the effect of the number of methyl groups at the carbon to which the peroxy radical is attached. We found that this only had minor effects on the H-shift rate constant, with one methyl group


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relative to none increasing the rate constant by a factor of two and two methyl groups leading to either increased or decreased rate constants relative to one methyl group, but in none of our examples by more than a factor of three and much less than the variation of up to a factor of 150 found previously.50-51 See Section S14 in the SI for further discussion. Previously, a few theoretical studies have investigated the effect of multiple methyl groups.50-52 Miyoshi studied 1,4 to 1,7 H-shifts in a range of alkyl peroxy and hydroperoxy alkyl peroxy radicals with methyl groups placed at either or both the peroxy carbon and the hydrogen abstraction carbon.51 These rate constants were calculated using TST with the CBS-QB3 composite method and including both Eckart tunneling and hindered rotor corrections. Miyoshi found that adding a methyl group at the abstraction site led to an increase in the H-shift rate constants by factors between 20 and 3500, and addition of a second methyl group led to increases between 35 and 150.51 While these trends are in agreement with those found in the present work differences up to a factor of 15 in the absolute rate constants are found. For example, Miyoshi calculated the rate at 298.15 K for the 1,5 H-shift in C4-3R with R=H to be 1.1×10-1 s-1 compared to our value of 7.7×10-3 s-1. Mohamed et al. studied 1,4 to 1,7 H-shifts in hydroperoxy alkyl peroxy radicals also with methyl groups at either the peroxy carbon and/or the carbon, from which hydrogen is abstracted and at which the hydroperoxyl group is attached.50 They used single conformer TST with an average of composite methods for the barrier height and included the Eckart tunneling correction. They found that adding a methyl group at the abstraction site led to increases in the rate constant of up to a factor of 200. Addition of methyl groups at the peroxy radical carbon were found to lead to both increases in the rate constant of up to a factor of seven and decreases of up to a factor of 4. The rate constants by Mohamed et al. are within a factor of 20 of our


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values. For example, good agreement is found for the 1,5 H-shift of C4-3R, R=OOH, where they report 3.3×10-2 s-1 while we obtain 1.4×10-2 s-1. Finally, as part of a study of oxidation in toluene, ethylbenzene and tert-butylbenzene, Wang et al studied a 1,5 H-shift in the peroxy radical found on the cyclohexene ring which abstract a hydrogen on a methyl (ethyl or tert-butyl) group attached to the ring. They used RiceRamsperger-Kassel-Marcus (RRKM) theory with the CBS-QB3 composite method and the Eckart tunneling correction and found that the H-shift was accelerated by factors of around 2000 upon addition of the first CH3 group, and by about 30 upon addition of the second CH3 group, to the original methyl group.52 Our results are in general agreement with the trends seen in these previous studies.50-52

Figure 5. Rate constants of H-shift reactions (298.15 K) as a function of the degree of substitution at the abstraction site. The rate constants shown correspond (from left to right) to the reactions in C2 and C4-2R, where R = H and CH3 (1,4 H-shift), C3 and C4-3R, where R = H and CH3 (1,5 H-shift), C4-4R, where R = H and CH3 and C5-4R, where R = CH3 (1,6 H-shift), respectively. Accuracy of Calculations The approach by Møller et al.56 has been shown to agree to within a factor of five for the five measured H-shift rate constants.15-16, 40 With the approach by Møller


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et al.56 we calculate the rate constant 1,5 H-shift in C3 to be 2.9×10-6 s-1, in good agreement with earlier theoretical studies, which have reported rate constants between between 2×10-6 s-1 and 5×10-6 s-1.42, 51, 53 As a further investigation of the accuracy in the approach by Møller et al., we have performed a few benchmark calculations assessing both the barrier height and partition functions.56 In Table 1, we show the barrier heights for both the forward and reverse reaction of the 1,5 H-shift in C3 at five levels of theory. F12 is the highest level of theory that is currently feasible for optimizations with our computers for a compound of even this limited size. The forward barrier height (ZPVE corrected) calculated with a F12 optimization and frequency calculation is only 0.1 kcal/mol lower than using the F12//ωB97X-D single point energy combined with a frequency calculation using ωB97X-D. This indicates that using a ωB97X-D geometry is good approximation of the exact geometry. In addition to the F12 single point energy calculation used in the approach by Møller et al., we also calculated CCSD(T)/CBS single point energies. The complete basis set limit energies were found by extrapolation from CCSD(T)/aug-cc-pVDZ and CCSD(T)/aug-cc-pVTZ single point energies, using the extrapolation scheme by Helgaker et al.88 The CCSD(T)/CBS barrier heights based on the ωB97X-D and F12 geometries are within 0.1 kcal/mol, suggesting both geometries are good. The CCSD(T)/CBS//F12 barrier height is 0.5 kcal/mol lower than the F12//ωB97X-D value. In the approach by Møller et al., the error on the F12//ωB97X-D barrier height was estimated to be less than 1 kcal/mol,56 and while the CCSD(T)/CBS//F12 value is not exact, this could indicate that the error in the barrier height is certainly less than 1 kcal/mol. A 0.5 kcal/mol difference would correspond to a factor of 2.3 difference in the rate constant at 298.15 K. The ωB97X-D forward barrier height is 1.24 kcal/mol higher than the CCSD(T)/CBS//F12 value, which corresponds to a factor of eight lower rate constant at 298.15 K. This shows the necessity of performing the F12


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single point energy calculations to obtain accurate rate constants. However, the less than 0.1 kcal/mol difference between F12 and F12//ωB97X-D indicates that the costly F12 optimizations does not improve the accuracy significantly. On the other hand, if one is mainly interested in the reaction mechanisms and thus less concerned with the absolute accuracy of the rate constants, then the MC-TST approach with ωB97X-D calculations may be sufficient.

Table 1. Reaction barrier heights and ratios of vibrational partition functions for the 1,5 H-shift in C3 at increasing levels of theory. The energies are corrected for ZPVE. Ef (kcal/mol)

Er (kcal/mol)

QTS/QR

QTS/QP

ωB97X-Da

26.17

7.26

0.205

0.121

F12//ωB97X-Da

25.48

9.94

-

-

F12b

25.39

10.35

0.243

0.086

CCSD(T)/CBS//ωB97X-Da,c

25.00

9.60

-

-

CCSD(T)/CBS//F12b,c

24.93

10.02

-

-

a

ZPVE calculated at the ωB97X-D level of theory.

b

ZPVE calculated at the F12 level of theory.

c

The CCSD(T) complete basis set limit was calculated by extrapolation from CCSD(T)/aug-ccpVDZ and CCSD(T)/aug-cc-pVTZ single-point energy calculations.88

The reverse barrier heights in Table 1 show larger differences than the forward barrier heights. However, the reverse rate constants are in competition with the O2-addition reaction, which has been measured to have a pseudo first-order rate constant on of the order of 107 s-1, and thus the reverse H-shifts are generally highly uncompetitive.87 The errors in the reverse rate constant are therefore less likely to impact reaction mechanisms. The F12//ωB97X-D single point calculations are 0.41 kcal/mol lower than the F12 optimized value, however, only 0.1 kcal/mol


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lower than the CCSD(T)/CBS//F12 value, while the ωB97X-D value is lower by 3.1 kcal/mol and 2.8 kcal/mol, respectively. We also performed optimizations of the reactant and product using CCSD(T)-F12a/VTZ-F12, but we were unable to optimize the TS due to the large computational cost of the hessian needed to start the optimization. The electronic energy of the product relative to the reactant is overestimated by 0.4 kcal/mol with F12//ωB97X-D and 0.3 kcal/mol with F12 relative to CCSD(T)-F12a/VTZ-F12, see Section S15 in the SI for details. The MC-TST rate constant (Eq. 1) is proportional to the ratio between the Boltzmann weighted sum of partition functions of the TS and of the reactant (or product for reverse reactions). In Table 1, we compare the ratios of vibrational partition functions calculated from harmonic frequency calculations at the ωB97X-D and F12 levels of theory. The ratios in Table 1 are calculated using only the conformer lowest in zero-point corrected energy at the ωB97X-D level of theory. The F12 and ωB97X-D QTS/QR ratios only differ by ~20%, with ωB97X-D overestimating the ratio relative to F12. The difference is larger for the ratio used in the reverse rate constant, where ωB97X-D overestimates the QTS/QP ratio by ~40%. For the forward reaction, this overestimation will counteract the error on the barrier height, while it will worsen the error on the reverse rate constant. Based on the limited data in Table 1, it does not seem necessary to perform F12 optimizations and frequency calculations in order to obtain rate constants of chemical accuracy. The errors on the rate constant in using the F12//ωB97X-D approach is less than a factor of two compared to that obtained using full F12. Previously, comparison with experimental rate constants for five different H-shift reactions have all yielded agreement to within a factor of five.16,

56

Praske et al. estimated the uncertainty in using the

Eckart tunneling correction to be a factor of two. They also estimated the uncertainty due to the combination of using the harmonic oscillator approximation and excluding conformers 2


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kcal/mol or more above the lowest energy conformer to be a factor of two. Based on these estimates and the present results, we estimate the total uncertainty of the F12//ωB97X-D approach by Møller et al.56 to be a factor of 10.


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Conclusions We have calculated the rate constants of hydrogen shift (H-shift) reactions in a set of peroxy radical reactants, to study systematic effects of substituents and TS ring size. We use an approach to calculate rate constants that have been found to agree with the few experimental measurements to within a factor of 5. We have proposed guidelines for when peroxy H-shift reactions need to be considered in atmospheric oxidation. We have found that the substituent at the abstraction site is very important. Substituents C=C and C=O lead to larger than 400-fold increases of the rate constant, while OH, OOH and OCH3 cause increases of a factor of 5012,000 of the rate constants of hydrogen shift reactions and methyl groups by a factor of 20-130. The increases in the H-shift rate constants are close to additive with multiple methyl substituents. ONO2 and F substituents had only minor effects on the rate constants. H-shift reactions with TS ring sizes of 1,5; 1,6 and 1,7 H-shifts were found to have similar rate constants to each other for a given substituent and need to be considered. For 1,5; 1,6 and 1,7 H-shifts, C=C, C=O, OH, OOH and OCH3 substituents all led to rate constants faster than 5×10-3 s-1. With an additional alkyl substituent at the carbon radical site, the rate constant increases to above 0.01 s-1, and it is thus essential to consider these H-shift reactions at most atmospheric conditions. As such, Hshift reactions are likely more ubiquitous in the atmosphere than previously thought.

ASSOCIATED CONTENT Supporting Information All the rate constants and the data used in producing them are available in the SI. The Gaussian and MOLPRO log files and the code used for removal of duplicate conformers are available at https://sid.erda.dk/public/archives/c7756cf94ebfa01a28e1a7b23ce2d2e6/published-archive.html AUTHOR INFORMATION


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Corresponding Author *E-mail: [email protected]. Phone: +45-35320334. Fax: +45-35320322 ORCID Rasmus V. Otkjær: 0000-0002-6094-1828 Helene H. Jakobsen: 0000-0001-9146-9901 Camilla M. Tram: 0000-0003-4503-9155 Henrik G. Kjaergaard: 0000-0002-7275-8297 Notes The Authors declare no competing financial interest. ACKNOWLEDGMENTS (Include Funding Sources) We thank Paul O. Wennberg, Theo Kurtén and Kristian H. Møller for helpful discussions. We acknowledge computer support from the Danish Center for Scientific Computing and the Department of Chemistry at the University of Copenhagen.


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Calculated Hydrogen Shift Rate Constants in Substituted Alkyl Peroxy

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