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Quantum Chemical and Statistical Rate Theory Studies of the Vinyl Hydroperoxides Formed in Trans-2Butene and 2,3-Dimethyl-2-Butene Ozonolysis Keith T. Kuwata, Lina Luu, Alexander B. Weberg, Ke Huang, Austin J. Parsons, Liam A. Peebles, Nathan B. Rackstraw, and Min Ji Kim J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b00287 • Publication Date (Web): 12 Feb 2018 Downloaded from http://pubs.acs.org on February 13, 2018

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The Journal of Physical Chemistry

Quantum Chemical and Statistical Rate Theory Studies of the Vinyl Hydroperoxides Formed in Trans-2-Butene and 2,3-Dimethyl-2-Butene Ozonolysis Keith T. Kuwata,* Lina Luu, Alexander B. Weberg,a Ke Huang,b Austin J. Parsons,c Liam A. Peebles, Nathan B. Rackstraw, and Min Ji Kim Department of Chemistry, Macalester College, Saint Paul, Minnesota 55105-1899

*

Corresponding author. Voice: (651) 696-6768; Fax: (651) 696-6432; e-mail: [email protected]

a

Current address: Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323

b

Current address: Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, TX 78712-1224

c

Current address: Department of Chemistry and Biochemistry, University of California, San Diego, San Diego, CA 92093

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ABSTRACT

The vinyl hydroperoxide (VHP), the major isomerization product of the syn-alkyl Criegee intermediate (CI) formed in alkene ozonolysis, is a direct precursor of hydroxyl radical (OH), the most important oxidant in the troposphere. While simulations of CI reactivity have usually assumed the VHP to be a prompt and quantitative source of OH, recent quantum chemical studies have revealed subtleties in VHP reactivity such as a barrier to peroxy bond homolysis and a possible rearrangement to a hydroxycarbonyl. In this work, we use M06-L, Weizmann-1 Brueckner Doubles, and equation-of-motion spin-flip coupled-cluster theories to calculate a comprehensive reaction mechanism for the syn and anti conformers of the parent VHP formed in trans-2-butene ozonolysis and the 1-methyl VHP formed in 2,3-dimethyl-2-butene ozonolysis. We predict that for the parent VHP, the anti homolysis transition structure (TS) is 3 kcal mol-1 lower in energy than the syn TS, but for the 1-methyl system, the syn TS is 2 kcal mol-1 lower in energy. Statistical rate theory simulations based on the quantum chemical data predict that the parent VHP preferentially decomposes to vinoxy and OH radicals under all tropospheric conditions, while the 1-methyl VHP preferentially decomposes to 1-methylvinoxy and OH radicals only close to 298 K; at 200 K, the 1-methyl VHP preferentially rearranges to hydroxyacetone. Lower temperatures and higher pressures favor the temporary accumulation of both the parent and the 1-methyl VHP.


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INTRODUCTION The carbonyl oxide or Criegee intermediate (CI) formed in alkene ozonolysis1 is one of the most important non-photochemical sources of hydroxyl radical (OH) in the atmosphere.2-6 Two decades ago, Cremer and co-workers7-9 explained OH formation in alkene ozonolysis by proposing that a CI with an alkyl group syn to its peroxy bond can isomerize to a vinyl hydroperoxide (VHP) that then dissociates to OH and vinoxy radicals. Scheme 1 illustrates this mechanism, an extension of Criegee’s original ozonolysis mechanism,1 for the two alkenes considered in this paper, trans-2-butene (R = H) and 2,3-dimethyl-2-butene (R = CH3). (We have omitted the cycloreversion pathway leading to anti CI since the anti conformer will contribute little, if any, to the total OH yield.5, 10)


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Scheme 1. Mechanism of OH Formation in the Ozonolysis of Trans-2-Butene (R = H) and 2,3-Dimethyl-2-Butene (R = CH3)


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In the past decade, experimental and theoretical studies have jointly provided an increasingly complete and quantitative description of both the unimolecular reactions of the CI and its bimolecular reactions with multiple atmospheric species.11 Much of the remaining uncertainty concerns the reactivity of the VHP.

In this paper, we consider the ramifications of four

mechanistic insights into VHP behavior: (1) Kurtén and Donahue’s discovery12 of a tight transition state for peroxy bond homolysis, (2) experimental evidence13-15 from Donahue and coworkers for significant collisional stabilization of VHP prior to OH formation, (3) Bowman, Lester, and co-workers’ characterization16 of both syn and anti pathways for VHP homolysis, and

(4)

Taatjes,

Thompson,

Lester,

and

co-workers’

hydroxycarbonyl formation from the dimethyl CI.

experimental

detection17

of

The final observation, a definitive

corroboration of decades of mechanistic speculation,18-20 may also help account for the less than unity yield of OH from 2,3-dimethyl-2-butene ozonolysis.21-25 Scheme 2 presents the mechanism for the formation, isomerization, and decomposition of the two VHP species we consider in this paper, the parent VHP from the syn-methyl CI (R = H in Scheme 2) and the 1-methyl VHP from the dimethyl CI (R = CH3 in Scheme 2). (Throughout this paper, species labels with an “M” denote structures derived from the syn-methyl CI and labels with a “DM” denote structures derived from the dimethyl CI.) We use a combination of density functional theory and ab initio methods to characterize all of the structures in Scheme 2 and then use our quantum chemical data as inputs for master equation simulations of reactivity, predicting species concentration as a function of temperature and pressure on both prompt and thermal time scales.


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Scheme 2. Reaction Mechanism for the Parent VHP (R = H; X = M in Species Labels) and the 1-Methyl VHP (R = CH3; X = DM in Species Labels)


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The current study goes beyond previous quantum chemical studies of the VHP12, 16-17 in fully characterizing syn and anti pathways (labeled as a and b, respectively, in Scheme 2 and throughout the rest of the paper). This conformational distinction is critical because only the syn VHP (3a-X) can rearrange to the hydroxycarbonyl 11a-X. We treat dynamic correlation in all species with coupled-cluster theory, including an iterative treatment of single and double excitations and a perturbative treatment of triple excitations; we applied CCSD(dT)26-27 theory to open-shell singlets and CCSD(T)28-29 theory to doublets and closed-shell singlets. In this paper, we present evidence that less complete treatments of dynamic correlation fail to predict accurate relative energies for the syn and the anti pathways. The current study goes beyond other recent master equation simulations of CI reactivity30-31 in two substantial ways. First, we include in our simulations both the covalently-bonded VHP (3aX and 3b-X in Scheme 2) and the hydrogen-bonded radical pairs (6a-X and 6b-X), allowing us to predict their populations over time.

Second, we run simulations across the range of

temperatures found in the troposphere. In this paper, we present evidence that the temporary accumulation of VHP significantly delays the formation of both free radicals (8-X + 9) and hydroxycarbonyls (11a-X), but only at temperatures significantly below 298 K.

COMPUTATIONAL METHODS Electronic Structure Calculations.

We obtained optimized geometries and harmonic

vibrational frequencies of all structures considered in this paper with density functional theory (DFT) methods in Gaussian 09.32 We established that a given optimized structure was a minimum if it possessed all real frequencies and that it was a transition structure if it possessed one imaginary frequency.

Animation of the imaginary frequency and intrinsic reaction


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coordinate calculations enabled us to determine the structures of the minima immediately surrounding each transition structure on the potential energy surface.

Based on extensive

benchmarking against Kurtén and Donahue’s multi-reference configuration interaction (MRCI) predictions12 (reported in Table S1 of the Supporting Information), we determined the M06-L functional33 with the def2-TZVP basis set34 to be the most accurate DFT model chemistry for our system. The reliability of M06-L theory, especially for the open-shell singlet species in our reaction mechanisms, is consistent with the lack of Hartree-Fock exchange in M06-L, as noted by Truhlar and co-workers.35 We calculated the M06-L/def2-TZVP optimized geometries and frequencies of open-shellsinglet species using broken-spin-symmetry wave functions.36 Glowacki, Marsden, and Pilling have provided evidence37 that broken-spin-symmetry DFT methods can predict potential energy surfaces for organic singlet diradicals comparable in accuracy to CASPT2 theory. The location of some of the M06-L/def2-TZVP stationary points in our mechanism required extremely high numerical precision. We used the Gaussian 09 ultrafine (75,302) integration grid to optimize all stationary points in the syn-methyl CI system and the Gaussian 09 superfine (150,974) integration grid to optimize all stationary points in the dimethyl CI system. To aid in the interpretation of some of our quantum chemical results, we used the natural bond orbital (NBO) analysis methods of Weinhold and co-workers38 as implemented in the NBO 3.1 routines39 in Gaussian 0932 and the absolutely localized molecular orbital (ALMO) energy decomposition analysis (EDA) method implemented by Head-Gordon and co-workers40 in Q-Chem 4.2.41 We took two different theoretical approaches to obtain accurate relative energies for the species in our mechanisms. We applied the W1BD composite method42 in Gaussian 09 to all closed-shell singlet and doublet species, using the default B3LYP/cc-pVTZ+d optimized


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geometries to provide the atomic coordinates for the suite of single-point energy calculations. W1BD is part of the Weizmann-1 family of methods, all of which extrapolate the CCSD(T) energy to the complete basis set (CBS) limit; W1BD theory predicts the thermochemical properties in the G2/97 test set to an accuracy of ~0.5 kcal/mol. Moreover, the use of Brueckner orbitals as the reference for coupled-cluster calculations in W1BD theory makes its results less prone to spin contamination, making W1BD more reliable for open-shell species.43 Application of Karton’s total atomization energy-based diagnostic %TAE[(T)]44 to the doublets and closedshell singlets in Scheme 2 (X = M; see Table S2 in the Supporting Information) predicts that the TAE of none of these species would change by more than 0.5 kcal mol-1 with post-CCSD(T) levels of theory. Thus, CCSD(T) theory with a sufficiently large basis set should make highly accurate predictions of the energies of all of the closed-shell singlet and doublet species. To obtain the relative energies of open-shell singlet species, we performed single-point calculations in Q-Chem 4.241 with equation-of-motion spin-flip coupled-cluster theory with all single and double excitations26 and a perturbative correction for triple excitations27 (EOM-SFCCSD(dT) or “SF” for short). SF theory enables the construction of a singlet state with multireference character via a complete set of spin-flipping excitations from a high-spin triplet reference state that is itself well described by a single-reference electronic structure method.45-46 Compared to MRCI theory, SF theory provides a computationally more efficient way to treat both the static and dynamic electron correlation present in the oxygenated singlet diradicals in our mechanisms. The SF calculations employed a restricted open-shell B3LYP reference and M06-L/def2-TZVP optimized geometries. We did not find a published scaling factor for M06L/def2-TZVP zero-point vibrational energies and so, using the ZPVE15/10 database of Truhlar and co-workers,47 we obtained a new scaling factor of 0.978 for the zero-point energy (ZPE)


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corrections to our electronic energies. Finally, in order to obtain a self-consistent set of relative energies for a given mechanism, we performed both W1BD and SF calculations on the more stable syn conformer of the VHP (3a-X in Scheme 2). Our choice of basis set for the SF calculations depended on the size of the system. For the parent VHP system, we calculated the EOM-SF-CCSD energies with both the cc-pVTZ and the cc-pVQZ basis sets.48 We used this pair of energies in turn to estimate the EOM-SF-CCSD/CBS energy using the extrapolation formula proposed by Wilson and co-workers.49

Due to

computational limitations, we calculated the (dT) correction to the EOM-SF-CCSD/CBS energy only with the cc-pVTZ basis set. We likewise performed all SF calculations on the 1-methyl VHP system with only the cc-pVTZ basis set. Manohar and Krylov have found that even with the relatively small cc-pTVZ basis set, EOM-SF-CCSD(dT) theory can predict singlet-triplet gaps to within 1 kcal mol-1 of experimental values.27 Moreover, the EOM-SF-CCSD/cc-pVTZ wave function for each open-shell singlet structure in Scheme 2 has a total norm of singly excited amplitudes of well above 0.9 (Table S3 in the Supporting Information). As Krylov and co-workers have noted,50 this provides evidence that for these structures, doubly excited states do not make a significant contribution to the electronic structure and the CCSD(dT) level of theory should provide accurate energetic predictions. Statistical Rate Theory Calculations. We used MultiWell-2014.151-53 to solve the onedimensional master equation for the reaction mechanisms of the chemically activated syn-methyl CI (R = H in Scheme 2 above) and the chemically activated dimethyl CI (R = CH3 in Scheme 2 above). The relative ZPE-corrected electronic energies of all species in the simulations came from the quantum chemical calculations described in the previous section. We determined microcanonical rate constants, k(E), for reactions with tight transition states using Rice-


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Ramsperger-Kassel-Marcus (RRKM) theory54 with the required sums and densities of states computed with the M06-L/def2-TZVP optimized geometries and unscaled harmonic frequencies; we applied the harmonic approximation to low-frequency hindered rotor modes as well. When we calculated sums and densities of states based on M06-L/def2-TZVP frequencies scaled by 0.978, the predicted fractional populations varied by no more than 0.02 from the populations based on unscaled frequencies. Given this small effect and the fact that the scaling factor was not optimized to reproduce overtone frequencies, we decided to report populations based on unscaled frequencies. We included the asymmetric Eckart tunneling model55 and a centrifugal correction described by Barker51 in our treatment of every transition state. Multiple recent papers30-31,

56-57

emphasize the need to include tunneling for accurate modeling of CI reaction

kinetics. Determination of k(E) values for the barrierless dissociation of radical pairs (6a-X and 6b-X in Scheme 2 above) to vinoxy and hydroxyl free radicals (8-X + 9) involved a process we have used previously.58 First, we assumed that the rate of the reverse process, the association of 8-X and 9 to form a radical pair, depends entirely on long-range dipole-dipole interactions. Using Georgievskii and Klippenstein’s59 variational transition state theory expression for the capture rate coefficient, kcap, and CCSD/MG3 dipole moments60 for vinoxy, 1-methylvinoxy, and OH, we found that at 298 K, kcap = 6.43 x 10-10 cm3 molecule-1 s-1 for CH2CHO + OH and kcap = 6.36 x 10-10 cm3 molecule-1 s-1 for CH2C(CH3)O + OH. These values are similar to those obtained in other recent studies58,

61-62

of barrierless dipole-dipole associations. We then used the Thermo

module of Barker’s MultiWell 2014.1 program suite51 to determine the equilibrium constants, Keq, for the dissociation of the syn and anti conformers of the radical pairs. The high-pressurelimit rate constant, kdissoc, for the dissociation of a given radical pair into free radicals is, by


11


detailed balance, kdissoc  K eq kcap .

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Finally, an inverse Laplace transform63 of kdissoc let us

determine k(E) values for the master equation simulations. In all of our MultiWell master equation simulations, we based the initial energy distribution for the CI on Forst’s statistical partitioning63-64 of the difference in the ZPE-corrected electronic energy of the cycloaddition and the cycloreversion transition structures (Scheme 1 above). In our simulations of the syn-methyl CI, we re-used the energy distribution employed in our 2010 study of the Criegee intermediates formed in trans-2-butene ozonolysis.10 In that work, we obtained optimized geometries and harmonic frequencies with the QCISD/6-31G(d) model chemistry and predicted relative energies with Truhlar’s multicoefficient Gaussian 3 (MCG3) composite method.65 For the sake of self-consistency, we also used MCG3//QCISD/6-31G(d) calculations to generate the initial energy distribution for the dimethyl CI formed in 2,3dimethyl-2-butene ozonolysis. We described the collisional stabilization process with the exponential-down model, using an energy grain size of 10 cm-1 and assuming that the average energy lost per collision is 300 cm-1, a typical value in master equation simulations.66 We used as our bath gas N2 at 200 K, 250 K, or 298 K with Lennard-Jones parameters of  = 3.74 Å and kB = 82 K.67-68 Using the same methodology69-72 described in our earlier study of isoprene ozonolysis,73 we estimated LennardJones parameters of  = 5.50 Å and kB = 325 K for the syn-methyl CI and all of its isomers, and parameters of  = 6.17 Å and kB = 345 K for the dimethyl CI and all of its isomers. Each simulation ran for 103 collisions, and the convergence of populations in far fewer than the maximum number of collisions ensured that a given simulation had reached the pseudo steady state.74 We ran trials at pressures from 0.001 Torr to 760 Torr.

Each reported pseudo-steady


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state yield is the average result from 106 Monte Carlo simulations, giving an uncertainty of no greater than ±0.0004. We therefore tabulate all fractional yields to four significant figures. We predicted the temporal evolution in relative species populations resulting from the reaction of the thermalized syn-methyl and dimethyl Criegee intermediates using the MESMER 5.0 code of Glowacki et al.75 For these simulations, we used the same approaches for determining microcanonical rate coefficients and for modeling the collisional stabilization process as we did for the MultiWell simulations, except that we used a grain size of 50 cm-1; this converged species populations to at least four decimal places. Calculating sums and densities of states with vibrational frequencies scaled by 0.978 altered species populations in syn-methyl CI simulations by no more than 0.002. For the same reasons we enumerated above, we chose to report simulation results based on unscaled frequencies.

RESULTS AND DISCUSSION Quantum Chemical Results Parent Vinyl Hydroperoxide. Scheme 3 presents the unimolecular reaction pathways for the syn-methyl CI 1-M and our best estimate of the relative energy of each structure based upon W1BD or SF calculations. (The M denotes that the CI has one methyl group.) First, 1-M can undergo either a 1,4-hydrogen shift via transition structure TS-2-M to form VHP 3a-M or cyclization via transition structure TS-12-M to form methyl dioxirane 13-M. W1BD theory predicts an 8 kcal mol-1 lower barrier for VHP formation than for dioxirane formation. In contrast, our earlier MCG3 calculations10 predicted only a 6 kcal mol-1 lower barrier for VHP formation. Species 1-M is also capable of isomerizing to the anti conformer of the CI (not


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shown), but our previous master equation simulations10 found this isomerization to be negligible under atmospheric conditions.


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Scheme 3. Unimolecular Reactivity of the Syn-Methyl Criegee Intermediatea

aRelative

energies at 0 K in kcal mol-1 from W1BD (in blue) and EOM-SF-CCSD(dT) (in

green) calculations.


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As Kurtén and Donahue12 and Bowman, Lester and co-workers16 have previously reported, we likewise predict that the VHP initiates decomposition via a homolysis transition structure (e.g., TS-5a-M) to a hydrogen-bonded radical pair (e.g., 6a-M), which can in turn dissociate to free vinoxy (8-M) and hydroxyl (9) radicals. Moreover, the VHP, homolysis TS, and radical pair can each adopt both syn and anti conformations. The synperiplanar form of the VHP (3a-M, Figure 1) has essentially eclipsing C=C and O-O bonds; the dihedral angle about the C-O bond is 1.9º. The synperiplanar VHP is 1.18 kcal mol-1 lower in energy than the antiperiplanar form (3b-M, Figure 1), which possesses a dihedral angle about the C-O bond of 156.3º. The eclipsing interaction in the syn form and the slightly lower stability of the anti form are consistent with the conformational preferences adjacent to double bonds elucidated by Wiberg and Martin.76 Minima 3a-M and 3b-M interconvert via the synclinal rotation transition structure TS-4-M (Figure 1), which lies 4-5 kcal mol-1 above the two minima (Scheme 3). The C=C-O-O dihedral angle of the transition structure, 75.5º, is slightly closer to that of the lower energy conformer, contrary to the Hammond postulate.77


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Figure 1. M06-L/def2-TZVP-optimized geometries for the syn and anti conformers of the parent VHP (3a-M and 3b-M, respectively) and their interconversion transition structure (TS-4-M). The magnitude of the C=C-O-O dihedral angle of each structure is in degrees.


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Peroxy bond homolysis alters the VHP’s conformational preference. In the syn homolysis transition structure (TS-5a-M, Figure 2), the magnitude of the C=C-O-O dihedral angle increases to 47.8º, while in the anti homolysis TS (TS-5b-M, Figure 2), this angle decreases to 130.3º. NBO analysis38 reveals that the adoption of synclinal and anticlinal conformations by the transition structures, as opposed to the synperiplanar and antiperiplanar conformations of the VHP minima, enables the delocalization of electron density from the breaking O-O bond into both * and * antibonding orbitals on the vinoxy moiety. Deletion of the interaction of the (O-O) orbital with the (C-H), (C-C), and (C-C) orbitals increases the M06-L/def2TZVP energy of TS-5b-M by 16.29 kcal mol-1, while the same set of deletions increases the energy of TS-5a-M by only 12.03 kcal mol-1. These hyperconjugative interactions help account for our SF prediction that the anti homolysis TS is 2.97 kcal mol-1 lower in energy than the syn TS (Scheme 3).


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Figure 2. M06-L/def2-TZVP-optimized geometries for the syn and anti conformers of the parent VHP homolysis transition structure (TS-5a-M and TS-5b-M, respectively). The magnitude of each C=C-O---O dihedral angle is in degrees and each O---O distance is in Å.


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The conformational preferences among the radical pair structures (6a-M, 6b-M, and TS-7-M, Figure 3) are quite small, as the energies in Scheme 3 indicate. The anti radical pair (6b-M) is only 0.2 kcal mol-1 lower in energy than then syn radical pair (6a-M), and their interconversion transition structure (TS-7-M), which involves an in-plane rocking of the vinoxy and hydroxyl moieties, is only 0.2-0.4 kcal mol-1 above the two radical pair minima. The flatness of the potential energy surface here is unsurprising given that, apart from the hydrogen bond, the closest atom-atom distance between the moieties, which is the distance between H and O is 2.346 Å. As mentioned in the Computational Methods section above, we chose the M06-L/def2-TZVP model chemistry as our source of optimized geometries based on the relatively close agreement with the MRCI geometrical and energetics predictions of Kurtén and Donahue.12 For TS-5b-M, M06-L/def2-TZVP predicts the O---O distance to be 2.041 Å (Figure 2), which is ~0.02 Å shorter than the MRCISD(4,4)/cc-pVTZ-optimized distance of 2.060 Å.

For 6b-M, M06-

L/def2-TZVP predicts the O---H distance to be 1.888 Å (Figure 3), which is ~0.06 Å shorter than the MRCISD(4,4)/cc-pVTZ-optimized distance of 1.945 Å.

While a few other density

functionals predict more accurate atom-atom distances (see Table S1 in the Supporting Information), these methods either predict less accurate relative energies than M06-L or fail to predict the existence of TS-5a-M (Figure 2).


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Figure 3. M06-L/def2-TZVP-optimized geometries for the syn and anti conformers of the vinoxy-hydroxyl radical pair (6a-M and 6b-M, respectively) and their interconversion transition structure TS-7-M. Selected atom-atom distances are in Å.


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Dissociation of the syn and anti radical pairs to free vinoxy (8-M) and hydroxyl (9) radicals requires ~7 kcal mol-1. In addition, the syn conformer can rearrange by migration of OH via TS10a-M to hydroxyacetaldehyde 11a-M.

As shown in Figure 4, the structure retains an

intramolecular hydrogen bond throughout this transformation; the distance between the carbonyl O and the hydroxyl H starts at 1.919 Å in 6a-M and has increased by only 0.149 Å in 11a-M. The barrier against the hydroxyl shift is 1.44 kcal mol-1 and the resulting hydroxyacetaldehyde is 80.12 kcal mol-1 lower in energy than the syn radical pair (Scheme 3). The transition structure is early, as expected based on the Hammond postulate:77 in TS-10a-M the distance between the bonding C and O is only 0.244 Å shorter than in the reactant, and the O=C-C-Ha dihedral angle deviates only 5.5º from planarity. In the product 11a-M, the C-Odistance is now 1.761 Å shorter than in the reactant and the magnitude of the O=C-C-Ha dihedral angle is now 123.3º. The

rearrangement

of

the

vinoxy

and

hydroxyl

radicals

to

the

closed-shell

hydroxyacetaldehyde as an alternative to simple peroxy bond homolysis is reminiscent of the roaming radical mechanism involved in the photodissociation of small organic molecules78-79 and the rearrangement of the chemically activated parent and anti-methyl CI.80 In particular, the steering of the OH moiety to the alpha carbon due to hydrogen bonding is consistent with the definition of a roaming reaction proposed by Klippenstein, Georgievskii, and Harding.78


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Figure 4. M06-L/def2-TZVP-optimized geometries for the syn radical pair minimum (6a-M), the hydroxyl shift transition structure (TS-10a-M) and hydroxyacetaldehyde (11a-M). Selected atom-atom distances are in Å and the magnitude of each O=C-C-H dihedral angle is in degrees.


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Our laboratory’s 2003 study of the syn-methyl CI81 identified a closed-shell, 1,3-sigmatropic shift transition structure (TS-14a-M) directly connecting the syn conformer of the VHP to the hydroxycarbonyl (Reaction 1):

However, in our current study, we found the restricted B3LYP wave function for TS-14a-M to be unstable with respect to spin-symmetry breaking. Moreover, all attempts to locate this transition structure with an unrestricted method instead converged to structures TS-5a-M or TS10a-M (Scheme 3).

Our inability to locate TS-14a-M extended to DFT methods lacking

Hartree-Fock exchange like M06-L and BLYP, which suggests that it is not simply that the putative sigmatropic shift transition structure has a significant amount of multi-reference character, but rather that this feature truly does not exist on the potential energy surface for this system.58, 82-83 We have three additional points of comparison with previous work (Table 1). First, for the 1,4hydrogen shift converting the syn-methyl CI to the VHP, Klippenstein, McCoy, Lester, and coworkers (KML)56 predicted a 0 K barrier of 17.05 kcal mol-1 and a 0 K reaction energy of -18.10 kcal mol-1. Our W1BD barrier is 0.93 kcal mol-1 lower and our W1BD reaction energy is 1.65 kcal mol-1 more exothermic.

KML also reported RRKM theory rate constants for the CI

isomerization based on their barrier and the asymmetric Eckart tunneling model; these rate constants were in excellent agreement with their experimental rate constants for OH appearance. This agreement provides strong support for the accuracy of the KML barrier. The biggest contributor to the discrepancies in the quantum chemical predictions is that the KML calculations include not only a CBS extrapolation of the CCSD(T) energy, as does W1BD


24

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theory, but also a complete treatment of triple excitations and a perturbative estimate of quadruple excitations with CCSDT(Q)/cc-pVDZ calculations. The CCSDT(Q) corrections raise the H-shift barrier by 0.48 kcal mol-1 and makes the reaction energy less exothermic by 0.91 kcal mol-1. Truhlar and co-workers30 came to the same conclusion about the need to go beyond the CCSD(T) level of theory when treating the syn-methyl CI. This partly contradicts the prediction of the %TAE[(T)] diagnostic (Table S2). The non-negligible effect of post-CCSD(T) levels of theory is a consequence of the multi-reference character of the electronic structure of the CI, as noted in Anglada et al.'s re-examination84 of CI electronic structure based on geometry and NBO deletion analysis. In our statistical rate theory simulations presented below, we will consider the impact of using the more accurate KML energetics. Second, Kurtén and Donahue’s seminal MRCI calculations on VHP dissociation12 revealed the existence of the anti conformer of the homolysis transition structure (TS-5b-M) and the hydrogen-bonded radical pair (6b-M). Their best estimates of 0 K relative energies, based on MRCISD(4,4)/aug-cc-pVQZ + D electronic energies (the “+ D” denotes the Davidson correction for higher-order excitations) and MRCISD(4,4)/cc-pVTZ geometries and frequencies, are 17.47 kcal mol-1 for TS-5b-M and 14.31 kcal mol-1 for 6b-M. Given the ability of MRCISD theory with the Davidson correction to treat both static and dynamic electron correlation, we take the Kurtén and Donahue results as benchmark values. Benchmarking work by Green, Truhlar, and co-workers85 demonstrates that MRCISD + D predictions of relative energies can be within 1 kcal mol-1 of full configuration interaction predictions, but this achievement of chemical accuracy is contingent on the overestimate of quadruple excitations with the Davidson correction86-87 canceling out the neglect of higher-order excitations.85 Our SF predictions are 0.2 kcal mol-1 lower for the TS and 1.4 kcal mol-1 lower for the radical pair. Again, in our statistical


25


Page 26 of 68

rate theory simulations presented below, we will consider the impact of using more accurate energetics.


26

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TABLE 1: Relative Energies (kcal mol-1) for Selected Structures in Scheme 3a

species 1-M TS-2-M 3a-M TS-5a-M TS-5b-M 6a-M 6b-M

this work CBS

CCSDT(Q)b

MRCISDc

CCSD(T)-F12b and

19.95e 19.75e

19.3,f 19.3g 18.10

38.34e 35.87e

37.9,f 38.0g 35.15

0.00e,h 0.00e,h

CASPT2d

0.00 0.00

0.0,f 0.0g

0.00

23.44h

29.0,f 29.3g

20.23h 20.71h

21.07

17.26h

17.47

16.88h

22.6,f 23.0g 18.0,f 19.1g

13.13h 16.11h

17.83

12.96h

14.31

22.5,f 22.2g

a

Values based on differences in electronic energy in normal type; values based on differences in zero-point-corrected electronic energy in italics. bFrom Klippenstein, McCoy, Lester, and coworkers.56 cFrom Kurtén and Donahue.12 dFrom Bowman, Lester, and co-workers.16 eFrom W1BD calculations. fBased on potential energy surface calculations. gBased on stationary point calculations. hFrom EOM-SF-CCSD(dT) calculations.


27


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Third, Bowman, Lester, and co-workers16 used a combination of CCSD(T)-F12b/HaDZ and CASPT2(12,10)/cc-pVDZ calculations to map out much of the conformational complexity of VHP chemistry that we have presented in Scheme 3 above. Relative to the electronic energy of the VHP (3a-M), the CASPT2 electronic energies of the anti homolysis transition structure (TS5b-M) and anti radical pair minimum (6b-M) are 2 to 5 kcal mol-1 higher than the benchmark MRCISD electronic energies.

These discrepancies are greater than those for EOM-SF-

CCSD(dT) theory. In addition, the CASPT2/cc-pVDZ model chemistry predicts TS-5a-M to be a second-order saddle point and does not locate a true minimum-energy geometry for 6b-M. As seen before in the case of primary ozonide formation, treatment of dynamic electron correlation only to second order and use of only a double-zeta basis set may be inadequate for describing the reactivity of oxygenated species with significant multi-reference character.88-89 The relatively good agreement of the EOM-SF-CCSD(dT) predictions with the MRCI results gives us confidence in the EOM-SF-CCSD(dT) values for the syn conformers of the transition structure (TS-5a-M) and the radical pair minimum (6a-M).


28

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TABLE 2: Energies (at 0 K, kcal mol-1) Relative to 3a-M for Singlet Diradical Structures in Scheme 3 cc-pVTZa

cc-pVQZb

CBSc

TS-5a-M

20.95

20.46

20.23

TS-5b-M

17.98

17.49

17.26

6a-M

12.40

12.74

13.13

6b-M

12.55

12.70

12.96

TS-7-M

13.59

13.38

13.39

TS-10a-M

14.30

14.37

14.57

species

MRCISDd

17.47

14.31

aThe

EOM-SF-CCSD(dT) energy evaluated with the cc-pVTZ basis set. bThe EOM-SF-CCSD energy evaluated with the cc-pVQZ basis set and the (dT) correction evaluated with the cc-pVTZ basis set. cThe EOM-SF-CCSD energy extrapolated to the complete basis set (CBS) limit using the formula of Wilson and co-workers49 and the (dT) correction evaluated with the cc-pVTZ basis set. dFrom Kurtén and Donahue.12


29


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Finally, Table 2 indicates the variation in the EOM-SF-CCSD(dT) energies of the singlet diradical species in Scheme 3 with changes in basis set. Overall, the variations are rather modest. The relative energy of each homolysis transition structure (TS-5a-M and TS-5b-M) decreases by 0.7 kcal mol-1 when we substitute the cc-pVTZ basis set with a CBS extrapolation. The relative energies of the radical pairs (6a-M and 6b-M) increase by 0.4 to 0.6 kcal mol-1 under the same substitution, and the relative energies of TS-7-M and TS-10a-M change by even smaller amounts. If we again take the Kurtén and Donahue MRCISD results12 as authoritative, the cc-pVQZ value is the most accurate for TS-5b-M while the CBS value is the most accurate for 6b-M. For our simulations below, we chose to use the CBS values for all singlet diradical species. 1-Methyl Vinyl Hydroperoxide.

Scheme 4 presents the unimolecular reactions of the

dimethyl CI 1-DM and our best estimate of the relative energy of each structure based upon W1BD or SF calculations. (The DM denotes that the CI has two methyl groups.) Overall, we find the same reaction pathways and roughly similar energies for the dimethyl system as we found for the syn-methyl system (Scheme 3).


30

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Scheme 4. Unimolecular Reactivity of the Dimethyl Criegee Intermediatea

aRelative

energies at 0 K in kcal mol-1 from W1BD (in blue) and EOM-SF-CCSD(dT) (in

green) calculations.


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W1BD theory predicts a 6 kcal mol-1 kinetic preference for the dimethyl CI to undergo a 1,4hydrogen shift via TS-2-DM than to cyclize to the dioxirane via TS-12-DM. A very recent study of the dimethyl CI by Taatjes, Thompson, Lester and co-workers (TTL)17 likewise predicts a lower barrier for the hydrogen shift than for the cyclization. The CCSD(T)/aug-cc-pVTZ model chemistry employed by TTL predicts a kinetic preference of only 4 kcal mol-1. The CBS extrapolation of the CCSD(T) energy in W1BD theory should make the barrier predictions reported here more accurate than those obtained with a triple-zeta basis set.90-91 Moreover, just as we saw for the syn-methyl system, the CCSDT(Q) calculations of KML56 indicate that CCSD(T) does not provide a fully accurate description of CI isomerization. W1BD predicts the hydrogen-shift barrier to be 15.51 kcal mol-1 and the 1-methyl VHP (3a-DM) to lie 17.28 kcal mol-1 below the CI 1-DM. In contrast, KML predict the barrier to be 16.16 kcal mol-1 and 3aDM to lie 15.90 kcal mol-1 below 1-DM. The simulations we discuss below make use of both sets of energetics predictions. Figure 5 shows the synperiplanar and anticlinal conformers, 3a-DM and 3b-DM, of the 1methyl VHP along with their interconversion transition structure, TS-4-DM.

The

conformational preferences for the 1-methyl VHP are similar to those for the parent system (Scheme 3 and Figure 1 above): the syn conformer has virtually eclipsing C=C and O-O bonds (the C=C-O-O dihedral angle is 2.3º), and the syn form is more stable (by 2.41 kcal mol-1, Scheme 4) than the conformer with anticlinal C=C and O-O bonds.


32

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Figure 5. M06-L/def2-TZVP-optimized geometries for the syn and anti conformers of the 1methyl VHP (3a-DM and 3b-DM, respectively) and their interconversion transition structure (TS-4-DM). The magnitude of the C=C-O-O dihedral angle of each structure is in degrees.


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The syn homolysis transition structure (TS-5a-DM) is ~2 kcal mol-1 lower in energy than the anti transition structure (TS-5b-DM). This conformational preference is the opposite of what we observed for the syn-methyl CI system (see Scheme 3 above). There is also a qualitative change in structure. For the parent VHP, both TS-5a-M and TS-5b-M are gauche with respect to the CO bond (see Figure 2 above). For the 1-methyl VHP, while the anti transition structure TS-5bDM is gauche (Figure 6), the syn transition structure TS-5a-DM is truly synperiplanar; the M06L/def2-TZVP C-C-O---O dihedral angle is 0.0°. Moreover, while TS-5a-M, TS-5b-M, and TS5b-DM all have breaking O---O bond lengths of 1.9-2.0 Å, this distance in TS-5a-DM has opened to 2.571 Å. We tried to account for the switch in conformational preference with NBO analysis.38 Deletion of the interactions of the (O-O) orbital and O lone pairs with all of the (C-C) and (C-C) orbitals increases the M06-L/def2-TZVP energy of TS-5a-DM by 44.04 kcal mol-1 and the energy of TS-5b-M by 71.58 kcal mol-1. Hyperconjugation by itself clearly favors the anti conformer. We obtained a more complete understanding of the homolysis transition structures’ conformational preference with the absolutely localized molecular orbital (ALMO) energy decomposition analysis (EDA) method.40 Table 3 shows that the overall M06-L/def2-TZVP “binding energy,” that is, the electronic energy of each transition structure relative to the combined electronic energies of the separated methylvinoxy and hydroxyl radicals, is -6.89 kcal mol-1 for the syn TS-5a-DM and -5.91 kcal mol-1 for the anti TS-5b-DM. Thus, M06-L/def2TZVP qualitatively replicates the syn conformational preference predicted with the higher-level EOM-SF-CCSD(dT) calculations. The ALMO EDA calculations indicate that charge transfer between the methylvinoxy and hydroxyl moieties preferentially stabilize the anti conformer by


34

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~30 kcal mol-1, roughly consistent with the NBO calculations. What stabilizes the syn transition structure is the presence of largely separated methylvinoxy and hydroxyl moieties. This gives the syn transition structure greater charge separation, particularly in the C=O bond of the methylvinoxy moiety (see Table S4 in the Supporting Information) and far less geometric distortion of the constituent fragments than in the anti transition structure. The combined effect of attractive electrostatic interactions (quantified by the frozen density term in Table 3) and a relatively small energetic penalty due to geometric distortion give the syn conformer of the homolysis transition structure greater overall stability. The favorability of the syn pathway has a significant impact on reaction outcome, as we shall see in the next section.


35


Page 36 of 68

Figure 6. M06-L/def2-TZVP-optimized geometries for the syn and anti conformers of the dimethyl VHP homolysis transition structure (TS-5a-DM and TS-5b-DM, respectively). The magnitude of each C-C-O---O dihedral angle is in degrees and each O---O distance is in Å.


36

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TABLE 3: ALMO Energy Decomposition Analysis of the Dimethyl Homolysis Transition Structuresa energetic component

TS-5a-DM

TS-5b-DM

frozen density

-0.67

17.45

polarization

-1.48

-4.61

charge transfer

-9.30

-39.23

geometric distortion

4.55

20.48

total binding energy

-6.89

-5.91

a

Energetics in kcal mol-1 from M06-L/def2-TZVP calculations in Q-Chem 4.2.


37


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Figure 7 presents the M06-L/def2-TZVP-optimized geometries for additional selected structures in the 1-methyl VHP reaction mechanism. As indicated in Scheme 4 above, the radical pair structures 6a-DM, 6b-DM, and TS-7-DM all lie 12-13 kcal mol-1 above the more stable conformer of the 1-methyl VHP, 3a-DM. As we already saw for the parent VHP system (Figure 3 and Scheme 3 above), there is very little conformation preference among the radical pair structures in Figure 7, and the hydrogen bonds between the methylvinoxy and hydroxyl moieties in 6a-DM, 6b-DM, and TS-7-DM all have lengths that are within 0.06 Å of those predicted for the analogous structures in the parent system (Figure 3). Dissociation of the syn and anti radical pairs to free 1-methylvinoxy (8-DM) and hydroxyl (9) radicals requires 7-8 kcal mol-1 (Scheme 4), and the syn radical pair requires 0.78 kcal mol-1 to overcome the barrier against the 1,3-hydroxyl shift to form hydroxyacetone (11a-DM). These 1-methyl VHP energetics are all within 1 kcal mol-1 of those predicted for the formation of free radicals and hydroxyacetaldehyde in the parent VHP system (Scheme 3). Geometrically, the transformation from 6a-DM through TS-10a-DM to 11a-DM is also quite similar to the transformation from 6a-M through TS-10a-M to 11a-M. Specifically, the radical pair 6a-DM has a hydrogen bond of 1.857 Å that increases by only 0.150 Å in 11a-DM, and the O=C-C-Ha dihedral angle in the hydroxyl shift transition structure TS-10a-DM deviates only 6.1 degrees from planarity.


38

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Figure 7. M06-L/def2-TZVP-optimized geometries for selected structures in the 1-methyl VHP reaction mechanism. Selected atom-atom distances are in Å and the magnitude of selected O=CC-H dihedral angles are in degrees.


39


Page 40 of 68

Finally, we note that TTL17 have also reported a singlet diradical 1,3-hydroxyl shift transition structure directly connecting the completely covalently bonded VHP (3a-DM) and hydroxyacetone

11a-DM.

Their

UCCSD(T)/aug-cc-pVTZ//UM06-2X/aug-cc-pVTZ

calculations predict this transition structure to lie 36.1 kcal mol-1 above 3a-DM. We did not include this TS in our calculations, but since it is more than 20 kcal mol-1 higher in energy that TS-10a-DM, we judged it safe to neglect in the statistical rate theory modeling described below. Statistical Rate Theory Results for the Syn-Methyl Criegee Intermediate System Table 4 presents the pseudo-steady-state yields predicted by the MultiWell RRKM/master equation simulations of the mechanism in Scheme 3 above as a function of pressure at 298 K. At all pressures, the dominant fate for the chemically activated Criegee is dissociation to vinoxy and OH radicals. However, there is a significant decrease in radical yield as pressure increases; the total yield of 8-M + 9 is 0.997 at 0.001 Torr and 0.641 at 760 Torr. There is a concomitant increase in the yield of stabilized CI (SCI) 1-M from essentially zero at 0.001 Torr to 0.356 at 760 Torr. At all pressures studied, ~75% of the total vinoxy + OH production comes via decomposition of the anti radical pair 6b-M. This is a consequence of the fact that the anti homolysis transition structure, TS-5b-M, is 3 kcal mol-1 lower in energy than the syn homolysis transition structure, TS-5a-M (Scheme 3 above). The ability to access the more reactive anti pathway depends almost entirely on the interconversion of the syn and anti conformers of the VHP; removing TS-4-M from the simulations shifts ~99% of vinoxy + OH production to decomposition of the syn radical pair (Table S5 in the Supporting Information).

This

demonstrates that the ability of the syn and anti radical pairs to interconvert via TS-7-M has a virtually negligible impact on reactivity.


40

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TABLE 4: RRKM/Master Equation Yields at 298 K for the Chemically Activated SynMethyl Criegee Intermediate Formed in Trans-2-Butene Ozonolysisa pressure (Torr)

1-M

8-M + 9 via 6a-M

8-M + 9 via 6b-M

total 8-M +9

11a-M

13-M

0.001

0.0000

0.2326

0.7644

0.9970

0.0009

0.0021

0.01

0.0010

0.2326

0.7634

0.9960

0.0008

0.0021

0.1

0.0089

0.2323

0.7559

0.9882

0.0009

0.0021

1

0.0322

0.2278

0.7370

0.9648

0.0009

0.0022

10

0.0799

0.2200

0.6972

0.9172

0.0008

0.0021

50

0.1410

0.2095

0.6468

0.8563

0.0007

0.0021

100

0.1791

0.2018

0.6164

0.8182

0.0007

0.0021

200

0.2255

0.1929

0.5788

0.7717

0.0006

0.0022

300

0.2605

0.1851

0.5517

0.7368

0.0006

0.0020

400

0.2868

0.1793

0.5313

0.7106

0.0005

0.0021

500

0.3097

0.1751

0.5126

0.6877

0.0005

0.0021

600

0.3279

0.1705

0.4990

0.6695

0.0005

0.0021

700

0.3460

0.1659

0.4855

0.6514

0.0005

0.0021

760

0.3563

0.1643

0.4769

0.6412

0.0005

0.0020

aSimulations

are of the mechanism in Scheme 3.


41


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We predict small but statistically significant yields of the other exit channels in Scheme 3. The yield of hydroxyacetaldehyde 11a-M decreases from ~0.0009 at the low-pressure limit to ~0.0005 at 1 atm. At all pressures studied, the yield of methyl dioxirane 13-M is ~0.002. In our earlier RRKM/master equation simulations10 of the chemically activated 1-M formed in trans-2butene ozonolysis, we predicted a prompt 13-M yield a factor of 10 higher under atmospheric conditions. The suppression of dioxirane formation in the current work is a consequence of the ~2 kcal mol-1 increase in the predicted dioxirane formation barrier, as we discussed above. Finally, the yields of collisionally stabilized VHP (3a-M and 3b-M) and the radical pairs (6a-M and 6b-M) are all zero at all pressures. Table S6 in the Supporting Information contain the results of simulations at 298 K using the more accurate KML56 energetics: we increase the 1,4-hydrogen shift barrier to 17.05 kcal mol-1 and we increase the energies of the VHP structures 3a-M, TS-4-M, and 3b-M all by 1.65 kcal mol-1 to match the KML energy for 3a-M. Compared to the results (Table 4) based on the W1BD energetics, the total yield of vinoxy + OH radicals is virtually the same at 0.001 Torr. However, at 760 Torr, the KML energies gives rise to a significantly lower total vinoxy + OH yield of 0.535 and a significantly higher SCI yield of 0.462. It is physically reasonable that the higher isomerization barrier causes greater stabilization and less decomposition at pressures close to 1 atm, at which the collision rate of ~1010 s-1 becomes comparable to k(E) for the isomerization reaction at energies close to the peak of the CI’s nascent energy distribution (~7500 cm-1 above the ground state of the CI). Table S7 in the Supporting Information contains the results of simulations at 298 K using the Kurtén and Donahue MRCI relative energies for the anti homolysis transition structure TS-5b-M and anti radical pair 6b-M. Qualitatively, we would expect the slightly higher MRCI energies


42

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for these two structures to make radical production via the anti pathway to be slightly less favorable. Our simulations bear this out; at all pressures, the syn/anti branching ratio has shifted to the syn pathway by a few percent. There is, however, virtually no change to the total vinoxy + OH radical yield. Figure 8 shows the yields of SCI and total vinoxy + OH from the syn-methyl CI as a function of pressure at 200 K, 250 K, and 298 K, all based upon the W1BD and SF energetics reported in this paper. The simulations predict a modest temperature dependence: at 1 atm pressure, the yield of SCI decreases from 0.434 at 200 K to 0.356 at 298 K, and the total yield of vinoxy + OH concomitantly increases from 0.564 at 200 K to 0.641 at 298 K. This is because at higher temperatures the nascent CI is slightly more activated and therefore slightly less prone to collisional stabilization. Figure S1 in the Supporting Information shows the analogous RRKM/master equation predictions as those shown in Figure 8 based on the more accurate KML56 1,4-hydrogen shift and VHP energies, and Figure S2 shows the analogous RRKM/master equation predictions based on the more accurate Kurtén and Donahue12 energies for the anti homolysis transition structure and radical pair. All three sets of simulations predict a modest temperature dependence and a significant pressure dependence in SCI and vinoxy + OH formation across the range of pressures relevant to the troposphere and laboratory experiments. With the higher KML 1,4-hydrogen shift barrier, we predict that over 50% of the chemically activated CI is collisionally stabilized at 1 atm and 200 K.


43


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Figure 8. RRKM/master equation predictions of the yields of stabilized syn-methyl Criegee intermediate (SCI) and total vinoxy + OH based on W1BD and EOM-SF-CCSD(dT) relative energies.


44

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In our previous work,10 we argued that the collisionally stabilized syn-methyl CI would, under atmospheric conditions, decompose quantitatively to vinoxy and OH radicals because the most important competing CI reaction, the bimolecular reaction with water to form hydroxymethyl hydroperoxide, was orders of magnitude slower than the 1,4-hydrogen shift to form VHP. Thus, the branching ratio between collisional stabilization and unimolecular reaction for the chemically activated syn-methyl CI affected the temporal profile, but not the total yield, of OH. Recent high-level electronic structure and kinetics calculations by Truhlar and co-workers30 provide compelling evidence that the putative bimolecular reactions of the syn-methyl CI with H2O, (H2O)2, and SO2 are negligibly slow compared to the isomerization of the thermalized CI. The SCI’s unimolecular reactivity should therefore dominate under atmospheric conditions. We turn then to our statistical rate theory predictions of this reactivity. Figure 9 shows the time evolution of the relative populations of the thermalized syn-methyl CI (1-M in Scheme 3 above) and of all of the species with non-negligible populations to which the CI can isomerize and decompose. We show simulation results for a range of tropospheric temperatures (200 K, 250 K, and 298 K) and pressure (100 Torr and 760 Torr).92


45


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Figure 9. Master equation predictions of the temporal evolution of species populations for the syn-methyl CI system based on the W1BD and EOM-SF-CCSD(dT) energetics reported in Scheme 3. (a) Simulations at 200 K and 100 Torr of N2 bath gas. (b) Simulations at 200 K and 760 Torr of N2 bath gas. (c) Simulations at 250 K and 100 Torr of N2 bath gas. (d) Simulations at 250 K and 760 Torr of N2 bath gas. (e) Simulations at 298 K and 100 Torr of N2 bath gas. (f) Simulations at 298 K and 760 Torr of N2 bath gas.


46

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At 200 K, the collisionally stabilized syn-methyl CI decays on the ~50 ms timescale. The 200K decay rate is identical at 100 Torr (Figure 9(a)) and 760 Torr (Figure 9(b)). This is consistent with the recent work by Truhlar and co-workers,30 who predict that the unimolecular hydrogen shift reaction rate constant reaches its high-pressure limit at ~10 Torr. The long time scale (i.e. after ~104 s) branching between the two statistically significant product channels is likewise virtually pressure independent from 100 to 760 Torr: vinoxy + OH from the anti VHP conformer (3b-M in Scheme 3 above) has a yield of 0.97 and vinoxy + OH from the syn VHP conformer (3a-M) has a yield of 0.03. The dominance of the anti channel is consistent with the ~3 kcal mol-1 lower barrier for dissociation of the anti VHP (Scheme 3 above).

The yields of

hydroxyacetaldehyde (11a-M) and dioxirane (13-M; not shown in Figure 9) from the thermalized syn-methyl CI are virtually zero. The thermalized syn-methyl CI at 200 K exhibits a significant pressure-dependent reactivity on intermediate time scales (from 0.01 to 1000 s) due to differences in the temporary accumulation of the VHP. The population of the syn VHP is typically one order of magnitude higher than that of the anti VHP, which reflects the W1BD prediction that the syn conformer is ~1 kcal mol-1 more stable than the anti conformer (Scheme 3 above). At 100 Torr, the VHP reaches a maximum relative population of 0.06 at 0.2 s, while at 760 Torr, this intermediate reaches a much larger maximum relative population of 0.36 at 0.2 s.

At both pressures, the VHP

population decays to a negligible value by 1000 s. Our interpretation of this difference is that increasing pressure increases the fraction of VHP that gets collisionally stabilized.

At both

pressures, virtually all of the VHP decomposes to vinoxy + OH via the anti pathway, in spite of


47


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the fact that ~90% of the VHP is in the thermodynamically more stable syn form. This behavior is a manifestation of the Curtin-Hammett principle.93 Finally, we note that at 200 K and 760 Torr, we predict three time regimes for OH formation from trans-2-butene ozonolysis: (1) from the chemically activated syn-methyl CI on the submicrosecond time scale (Figure 8 above), (2) from the thermalized syn-methyl CI on the ~50 ms time scale, and (3) from the thermalized VHP on the ~500 s time scale. As noted by Boering, Lin and co-workers,57 this time delay in OH production due to the VHP intermediate complicates the determination of thermalized CI decay kinetics. Raising the temperature of the SCI to 250 K (Figures 9(c) and 9(d)) and then 298 K (Figure 9(e) and 9(f)) changes its reactivity in two significant ways. First, increasing temperature shortens SCI lifetime, and second, increasing temperature increases the activation of the VHP, making it less prone to collisional stabilization. For example, at 298 K, the CI decays on the ~1 ms time scale, ~50 times faster than at 200 K, and the maximum population of VHP is 0.002 at 100 Torr and 0.03 at 760 Torr. Consequently, the relative populations of the CI reactant and the OH + vinoxy products are almost perfectly anti-correlated; the VHP intermediate should have very little impact on OH formation kinetics at 298 K. Figure S3 in the Supporting Information shows MESMER simulation results based on the higher 1,4-hydrogen shift barrier (TS-2-M in Scheme 3 above) and the higher energies of VHP species (3a-M, TS-4-M, and 3b-M) predicted by KML.56 The higher barrier should slow the decay rate of the CI and increase the chemical activation of the resulting VHP, leading to less VHP accumulation on shorter time scales. The lower stability of the VHP species should further decrease the transient VHP population. A comparison of Figures S3 and 9 confirms these


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expectations. For example, at 200 K and 760 Torr, the maximum VHP relative population based on the KML energetics is 0.20 (Figure S3(b)), some 45% lower than that predicted based on the W1BD energetics (Figure 9(b) above). However, even with the KML energetics, we still predict that at 200 K and 760 Torr, one should observe three time scales for OH formation and a significant transient population of VHP. These simulations also predict that the high-pressurelimit syn-methyl CI decay rate is ~4 s-1 at 200 K, ~40 s-1 at 250 K, and ~300 s-1 at 298 K. These rates are in good agreement with the recent rigorous theoretical predictions of Truhlar and coworkers.30 However, the 298-K rate constant disagrees significantly with the experimental measurement of Novelli, Vereecken, Lelieveld, and Harder,94 who estimated a rate constant of 20 ± 10 s-1 based on OH formation. As Figures 9(f) and S3(f) show, the population vs. time profiles of CI and OH + vinoxy are almost perfectly anticorrelated at 298 K; there is no time lag in OH production due to VHP collisional stabilization. We currently have no way to account for this discrepancy. MESMER simulations based on Kurtén and Donahue’s higher MRCI energies12 for the anti VHP singlet diradical structures predict population vs. time profiles (see Figure S4 in the Supporting Information) almost identical to those in Figure 9 obtained with our EOM-SFCCSD(dT) energies. We noted earlier that the most substantial difference between the MRCI and the SF predictions concerned the stability of the anti radical pair 6a-M (Table 1 above). The close similarity of Figures 9 and S4 indicate that the statistical rate theory predictions are not very sensitive to ~1 kcal mol-1 variations in the energy of 6a-M.


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Statistical Rate Theory Results for the Dimethyl Criegee Intermediate System Next, we consider the prompt and thermal reactivity of the dimethyl Criegee intermediate formed in 2,3-dimethyl-2-butene ozonolysis. Table 5 presents the pseudo-steady-state yields predicted by the MultiWell RRKM/master equation simulations of the mechanism in Scheme 4 above as a function of pressure at 298 K. Across the range of pressures considered in our simulations, a majority of the chemically activated Criegee (1-DM) dissociates to 1methylvinoxy and OH radicals (8-DM + 9). The total yield of 8-DM + 9 from both syn and anti channels is 0.984 at 0.001 Torr and decreases to 0.546 by 760 Torr, while the yield of SCI 1-DM increases from essentially zero at 0.001 Torr to 0.446 at 760 Torr. The chemically activated dimethyl CI is less reactive on the sub-microsecond time scale than the chemically activated synmethyl CI (1-M) at all pressures (compare Table 4 above) since in 1-DM roughly the same amount of chemical activation energy is distributed among more internal degrees of freedom, reducing 1-DM’s specific rate coefficients.


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TABLE 5:

RRKM/Master Equation Yields at 298 K for the Chemically Activated

Dimethyl Criegee Intermediate Formed in 2,3-Dimethyl-2-Butene Ozonolysisa pressure (Torr)

1-DM

8-DM + 9 via 6a-DM

8-DM + 9 via 6b-DM

total 8-DM +9

11a-DM

13-DM

0.001

0.0000

0.9141

0.0704

0.9845

0.0097

0.0058

0.01

0.0001

0.9140

0.0707

0.9847

0.0096

0.0057

0.1

0.0055

0.9098

0.0698

0.9796

0.0093

0.0056

1

0.0300

0.8913

0.0646

0.9559

0.0084

0.0057

10

0.0863

0.8422

0.0588

0.9010

0.0071

0.0056

50

0.1644

0.7730

0.0510

0.8240

0.0060

0.0056

100

0.2129

0.7294

0.0467

0.7761

0.0055

0.0055

200

0.2781

0.6694

0.0421

0.7115

0.0048

0.0056

300

0.3235

0.6275

0.0391

0.6666

0.0046

0.0053

400

0.3572

0.5963

0.0371

0.6334

0.0041

0.0053

500

0.3862

0.5699

0.0348

0.6047

0.0040

0.0051

600

0.4116

0.5466

0.0330

0.5796

0.0037

0.0050

700

0.4338

0.5258

0.0319

0.5577

0.0036

0.0049

760

0.4456

0.5151

0.0311

0.5462

0.0034

0.0049

aSimulations

are of the mechanism in Scheme 4.


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At all pressures studied, over 90% of the total vinoxy + OH production comes via decomposition of the syn radical pair 6a-DM. This conformational preference arises from the syn homolysis transition structure, TS-5a-DM, being ~2 kcal mol-1 lower in energy than the anti homolysis transition structure, TS-5b-DM (Scheme 4 above), a preference we considered in some detail above. The greater proclivity for decomposition of the syn VHP also enhances the yield of hydroxyacetone, 11a-DM: across the pressure range studied, the yield of 11a-DM is roughly one order of magnitude higher than the yield of the analogous hydroxyacetaldehyde, 11a-M, formed from the chemically activated syn-methyl CI (Table 4 above). The yield of dimethyl dioxirane, 13-DM, is a factor of 2-3 larger than the yield of methyl dioxirane, 13-M, from the chemically activated syn-methyl CI. We attribute this to the ~3 kcal mol-1 lower cyclization barrier for the dimethyl system (compare TS-12-M in Scheme 3 and TS-12-DM in Scheme 4). Finally, the yields of collisionally stabilized VHP (3a-DM and 3b-DM) and the radical pairs (6a-DM and 6b-DM) are all zero at all pressures, just as we predicted for the parent system. We repeated the same simulations with the higher KML56 barrier for the 1,4-hydrogen shift and with the energies of 1-methyl VHP structures 3a-DM, 3b-DM, and TS-4-DM all shifted up by 1.38 kcal mol-1 to match the KML energy for 3a-DM. The pseudo-steady-state yields (in Table S8 in the Supporting Information) are all within ±0.001 of those in Table 5. We can thus conclude that the RRKM/master equation predictions are not especially sensitive to ≤1 kcal mol-1 variations in minimum or transition structure energies for the dimethyl CI system.


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Figure 10. RRKM/master equation predictions of the yields of stabilized dimethyl Criegee intermediate (SCI) and total 1-methylvinoxy + OH based on W1BD and EOM-SF-CCSD(dT) relative energies.


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Figure 10 shows the yields of collisionally stabilized dimethyl CI (SCI) and total 1methylvinoxy + OH as a function of pressure at 200 K, 250 K, and 298 K, all based upon the W1BD and SF energetics reported in this paper. Qualitatively, the temperature dependence of the product yields matches that predicted for the syn-methyl system (Figure 8 above) in that lower temperatures make the CI more prone to collisional stabilization and less prone to fragmentation to free radicals. At all temperatures, the yield of SCI approaches zero and the yield of 1-methylvinoxy + OH approaches unity as the pressure approaches zero. Simulations at these three temperatures using the 1,4-hydrogen shift barrier and VHP energies from KML56 (Figure S5 in the Supporting Information) result in almost identical product yields. The shape of our 298-K SCI yield curve agrees qualitatively with the recent experimental measurements of Hakala and Donahue,95 but at higher pressures we overestimate the SCI yield. We attribute this to inaccuracies in the initial energy distribution we assign to the dimethyl CI. The very recent master equation predictions by Drozd, Kurtén, Donahue, and Lester,31 which quantitatively reproduces the Hakala and Donahue measurements, assign to the dimethyl CI an average initial energy of 8500 cm-1, while our average initial energy is ~8050 cm-1. The lesser degree of chemical activation makes the CI in our simulations more prone to collisional stabilization. Our master equation predictions are nevertheless qualitatively sound. Figure 11 shows the time evolution of the relative populations of the thermalized dimethyl CI (1-DM in Scheme 4 above) and of all of the species with non-negligible populations to which the CI can isomerize and decompose. As with the syn-methyl case (Figure 9 above), we show simulation results across the range of tropospheric temperature (200 K, 250K, and 298 K) and pressure (100 Torr and 760 Torr).92


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Figure 11. Master equation predictions of the temporal evolution of species populations for the dimethyl CI system based on the W1BD and EOM-SF-CCSD(dT) energetics reported in Scheme 4. (a) Simulations at 200 K and 100 Torr of N2 bath gas. (b) Simulations at 200 K and 760 Torr of N2 bath gas. (c) Simulations at 250 K and 100 Torr of N2 bath gas. (d) Simulations at 250 K and 760 Torr of N2 bath gas. (e) Simulations at 298 K and 100 Torr of N2 bath gas. (f) Simulations at 298 K and 760 Torr of N2 bath gas.


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At 200 K and 100 Torr (Figure 11(a)), the SCI decays on the ~10 ms timescale. The SCI exclusively undergoes the 1,4-hydrogen shift via TS-2-DM (Scheme 4 above) to form the 1methyl VHP; there is no formation of dimethyl dioxirane 13-DM. Some 80% of the 1-methyl VHP reacts promptly to form, in order of decreasing yield, hydroxyacetone (11a-DM), 1methylvinoxy + OH (8-DM + 9) via the syn pathway, and 1-methylvinoxy + OH via the anti pathway.

A majority of the reactive flux goes through the syn pathway because the syn

homolysis transition structure (TS-5a-DM) is 2 kcal mol-1 lower in energy than the anti transition structure (TS-5b-DM). Moreover, the syn radical pair, 6a-DM, prefers to rearrange to 11a-DM instead of dissociating to 8-DM + 9, whereas the syn-methyl CI analog, 6a-M (Scheme 3 above), prefers to dissociate to 8-M + 9 almost exclusively (Figure 9(a) above). Two factors contribute to this switch in reactivity. First, the barrier against the 1,3-hydroxyl shift is ~0.7 kcal mol-1 lower for 6a-DM than for 6a-M. Second, the additional methyl group in 6a-DM lowers the specific rate coefficients for dissociation. The branching ratio between isomerization to 11a-DM versus dissociation to 8-DM + 9 is also sensitive to the quasi-intermolecular frequencies controlling the relative motion of the 1methylvinoxy and OH moieties along the reaction coordinate. For 6a-DM, these frequencies include the stretching of the hydrogen bond at 196.5 cm-1 and the CH2C(CH3)O---OH rock at 110.1 cm-1. Preliminary simulations that account for the anharmonicities in these vibrations predict a ~50% increase in the final yield of 11a-DM at 298 K and 760 Torr. Future studies should account fully for such breakdowns in the rigid rotor-harmonic oscillator (RRHO) approximation. The relative population of collisionally stabilized 1-methyl VHP (3a-DM and 3b-DM in Scheme 4 above) at 200 K and 100 Torr reaches a maximum of 0.20 at 50 ms, compared to 0.06


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for the parent VHP (Figure 9(a) above). The additional methyl group in 3a-DM and 3b-DM makes them more prone to collisional stabilization. The thermalized 1-methyl VHP reacts almost exclusively via the lowest barrier pathway to form hydroxyacetone. At 200 K and 760 Torr (Figure 11(b)), 1-DM still decays on the ~10 ms timescale, indicating that the 1,4-hydrogen shift rate reaches its high-pressure limit at or below 100 Torr. The predicted pressure dependence is consistent with the recent experimental measurements of Boering, Lin and co-workers.57 The increase in pressure substantially increases the collisional stabilization of the 1-methyl VHP; the combined population of 3a-DM and 3b-DM reaches 0.54 by 50 ms and persists until ~100 s, at which point it reacts to form, in order of decreasing yield, hydroxyacetone (11a-DM), 1-methylvinoxy + OH (8-DM + 9) via the syn pathway, and 1methylvinoxy + OH via the anti pathway. We can also discern a pressure dependence to the VHP reaction kinetics, with decay occurring on the ~300 s time scale at 100 Torr and the ~100-s time scale at 760 Torr. Increasing the temperature of the SCI to 250 K (Figures 11(c) and 11(d)) and 298 K (Figures 11(e) and 11(f)) progressively shortens the CI lifetime and reduces collisional stabilization of the 1-methyl VHP intermediate. At 298 K and 760 Torr, the combined population of 3a-DM and 3b-DM reaches a maximum of only 0.02, and the maximum combined population at 100 Torr is only 0.003. These predictions contradict the VHP behavior implied by the experimental results of Donahue and co-workers.13-15 The large discrepancy between OH yields measured by laserinduced fluorescence versus OH yields (with concomitant SCI removal) measured by reaction with NO2 led Donahue and co-workers to conclude that that maximum population of stabilized 1-methyl VHP is, for example, ~0.6 at 100 Torr. In our model, more efficient collisional stabilization and smaller specific rate coefficients for 3a-DM and 3b-DM would improve our


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agreement with the previous work. Finally, at 298 K, around 88% of the highly chemically activated 1-methyl VHP follows the entropically favored dissociation pathways to form 8-DM + 9, with the other 12% isomerizing to form 11-DM. Figure S6 in the Supporting Information presents simulation results using the higher 1,4hydrogen shift barrier and the higher VHP energies from KML.56 There are two noteworthy differences in the predicted reactivity. First, at all three temperatures, the dimethyl CI decays via the 1,4-hydrogen shift on time scales ~3 times longer than with the W1BD barrier (see Figure 11). Even so, with the more accurate KML barrier at 298 K, we predict a unimolecular thermal decay rate of 794 s-1, which is a factor of 2-3 higher than recent experimental measurements by Boering, Lin, and co-workers57 and by Orr-Ewing, Taatjes, and co-workers.96 The discrepancy may be due in part to our exclusive use of the harmonic approximation in calculating the vibrational contribution to sums and densities of states, unlike other recent theoretical studies.30, 56, 97

Moreover, the recent accurate prediction of the dimethyl CI thermal decay rate by Fang et

al.97 included a semiempirical adjustment of the asymmetric Eckart potential, an adjustment that we did not include in our calculations. Second, there is noticeably less collisional stabilization of the 1-methyl VHP at 200 K and 250 K. At 760 Torr and 200 K, for example, the maximum relative population of 3a-DM and 3b-DM is 0.38 at 0.2 s (Figure S6(b)), 30% lower than the maximum population predicted with all W1BD energetics (Figure 11(b)). Despite these specific differences, the overall picture of thermalized dimethyl CI reactivity is the same with either set of energies. At 200 K, we predict that hydroxyacetone formation is the most favored product channel. At 200 K and 760 Torr, the significant temporary accumulation of 1-methyl VHP delays the formation of a majority of the hydroxyacetone to the minute time scale. At 250 K and 298 K, we predict that a majority of the SCI now dissociates to 1-


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methylvinoxy + OH and that most of the final products form on the ~10 ms time scale. The time scale of hydroxyacetone production we predict here is consistent with the recent experimental measurements of TTL.17 This consistency provides some validation for the unimolecular rearrangement pathway to hydroxyacetone we propose here. Finally, we consider OH yield from 2,3-dimethyl-2-butene ozonolysis. Based on our W1BD and EOM-SF-CCSD(dT) energetics, our MultiWell simulations predict at 298 K and 760 Torr a prompt OH yield of 0.546 and an SCI yield of 0.446 (Table 5 above).

Our MESMER

simulations predict from the SCI a thermal OH yield of 0.881 (Figure 11(f) above). The total OH yield is therefore 0.546 + (0.446)(0.881) = 0.939. Our estimate is higher than the broad experimental consensus21-25 that the OH yield ranges between 0.8 and 0.9. One way to account for this discrepancy is the existence of other pathways besides hydroxyacetone formation that divert the dimethyl CI from OH formation. In addition, the preliminary simulations discussed above suggest that going beyond the RRHO approximation for the low-frequency modes in the dimethyl system would lower the predicted yield of OH. CONCLUSIONS AND FUTURE WORK Our computational modeling of the vinyl hydroperoxides formed in trans-2-butene and 2,3dimethyl-2-butene ozonolysis provides both a more detailed reaction mechanism than previous studies and a number of new and testable predictions. Our electronic structure calculations reveal the existence of syn and anti conformers for the parent and 1-methyl VHP, the peroxy bond homolysis transition structures, and the vinoxy-hydroxyl radical pairs. Moreover, we predict that there is no more than a 3 kcal mol-1 difference in the syn and anti conformers of any of these VHP structures. This means that both syn and anti pathways play non-negligible roles in the reactivity of both the chemically activated and stabilized Criegee intermediates studied


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here. Our statistical rate theory simulations predict that for both the syn-methyl and the dimethyl CI, there should be a significant temporary collisional stabilization of the VHP and a concomitant delay in final product formation at lower temperatures, especially at 200 K. We encourage experimentalists to conduct sub-ambient-temperature experiments to re-measure the kinetics of OH and hydroxyacetone formation and to use recently established methodology98 to look for VHPs from CIs. Our mechanism for hydroxyacetone formation from the thermalized dimethyl CI can partially account for the detection of this molecule in the recent work of TTL.17 TTL also present experimental and quantum chemical evidence that the bimolecular self-reaction of the dimethyl CI also forms hydroxyacetone. The UM06-2X/aug-cc-pVDZ model chemistry used to study the reaction mechanism provides a qualitatively reasonable energy landscape, but ab initio methods like spin-flip theory used in this paper, along with statistical rate theory calculations, will be necessary to quantify the competition between the formation of hydroxyacetone and the formation of acetone. We are currently applying the methodology employed in this paper to characterize the vinyl hydroperoxides formed in the ozonolysis of isoprene, the most abundant hydrocarbon besides methane in the troposphere.99


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ACKNOWLEDGMENTS The authors acknowledge support by the National Science Foundation (CHE-1412622) and the Violet Olson Beltmann and the Collaborative Summer Research funds of Macalester College. The authors used the computational facilities of the Midwest Undergraduate Computational Chemistry Consortium at Hope College (established by past NSF grants CHE-0520704 and CHE-1039925) and the XSEDE facility at the University of California, San Diego (CHE150037). SUPPORTING INFORMATION Additional tables and figures, along with optimized coordinates, electronic energies, and zeropoint vibrational energies of all of the stationary points considered in this manuscript. This material is available free of charge via the Internet at http://pubs.acs.org.


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