A Computational Re-examination of the Criegee IntermediateâSulfur

Article pubs.acs.org/JPCA

A Computational Re-examination of the Criegee Intermediate−Sulfur Dioxide Reaction Keith T. Kuwata,* Emily J. Guinn,† Matthew R. Hermes,‡ Jenna A. Fernandez,§ Jon M. Mathison, and Ke Huang Department of Chemistry, Macalester College, Saint Paul, Minnesota 55105-1899, United States S Supporting Information *

ABSTRACT: The atmospheric oxidation of sulfur dioxide by the parent and dimethyl Criegee intermediates (CIs) may be an important source of sulfuric acid aerosol, which has a large impact on radiative forcing and therefore upon climate. A number of computational studies have considered how the CH2OOS(O)O heteroozonide (HOZ) adduct formed in the CI + SO2 reaction converts SO2 to SO3. In this work we use the CBS-QB3 quantum chemical method along with equation-of-motion spin-flip CCSD(dT) and MCG3 theories to reveal new details regarding the formation and decomposition of the endo and exo conformers of the HOZ. Although ∼75% of the parent CI + SO2 reaction is initiated by formation of the exo HOZ, hyperconjugation preferentially stabilizes many of the endo intermediates and transition structures by 1−5 kcal mol−1. Our quantum chemical calculations, in conjunction with statistical rate theory models, predict a rate coefficient for the parent CI + SO2 reaction of 3.68 × 10−11 cm3 molecule−1 s−1, in good agreement with recent experimental measurements. RRKM/master equation simulations based on our quantum chemical data predict a prompt carbonyl + SO3 yield of >95% for the reaction of both the parent and dimethyl CI with SO2. The existence of concerted cycloreversion transition structures 10−15 kcal mol−1 higher in energy than the HOZ accounts for most of the predicted SO3 formation.

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INTRODUCTION The carbonyl oxide or Criegee intermediate (CI) formed in alkene ozonolysis plays multiple critical roles in the chemistry of the lower atmosphere.1 The fraction of CI formed in atmospheric ozonolysis that is chemically activated can, depending on its substituents and conformation, isomerize on the submicrosecond time scale to species such as the vinyl hydroperoxide (VHP) and the dioxirane. In turn, the VHP is a major nonphotochemical source of hydroxyl radical (•OH) in the atmosphere,2−4 whereas the dioxirane may be a significance atmospheric source of carboxylic acid.5−7 The stabilized CI (SCI) from alkene ozonolysis can undergo both the previously mentioned isomerization reactions, albeit on much longer time scales, as well as bimolecular reactions with atmospheric species such as H2O, NO2, and SO2. The major channel of the SCI-SO2 reaction is believed to involve oxidation of SO2 to SO3 (e.g., reaction 1):8 CH 2OO + SO2 → CH 2O + SO3

provides strong evidence that the stabilized dimethyl CI (or acetone oxide, (CH3)2COO) can be a significant atmospheric oxidant of SO2 regardless of relative humidity, particularly at lower temperatures. The net cooling of the atmosphere expected from the radiative forcing of sulfate aerosols (recently estimated by Myhre et al.17 to be −0.32 ± 0.11 W m−2) underscores the relevance of this reaction to global climate change. Until the ground-breaking kinetics measurements of Welz et al. in 2012,18 much of the mechanistic insight into the reaction of the parent CI, CH2OO, with SO2 came from quantum chemical calculations. Aplincourt and Ruiz-López19 used CCSD(T)//B3LYP calculations to provide evidence for the isomerization of the CI to formic acid via a heteroozonide (HOZ, 5) intermediate (reaction 3) that had been postulated in early work by Schulten and Schurath,20 Martinez and Herron,21 and Hatakeyama et al.11 (The species labels in the following reactions come from Schemes 1−4 below.)

(1)

Under certain atmospheric conditions the SCI may be responsible for more oxidation of SO2 than the oxidation of SO2 by •OH (reaction 2):9 •

OH + SO2 → HOS(O)O•

(2)

The rearrangement and decomposition of 5 triggered by a 1,2-hydrogen shift to a peroxy oxygen (in transition structure

There is some evidence that reaction 1 makes significant contributions to atmospheric H2SO4 aerosol and thus to atmospheric new particle formation,8−13 although the extent to which SCI functions as an atmospheric oxidant of SO2 will depend strongly on the relative humidity.14,15 The recent work of Berndt et al.15,16 © 2015 American Chemical Society

Received: July 8, 2015 Revised: September 22, 2015 Published: September 23, 2015 10316

DOI: 10.1021/acs.jpca.5b06565 J. Phys. Chem. A 2015, 119, 10316−10335

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The Journal of Physical Chemistry A TS-10) provide a mechanism by which isotopically doublelabeled CH218O18O can, by reaction with unlabeled SO2, be transformed to the singly labeled formic acid isotopomer HC(O)18OH observed in Hatakeyama et al.’s early experimental work.11 Subsequent CCSD(T)/6-311G(d,p)//B3LYP/6-31G(d,p) calculations by Jiang et al.22 revealed another HOZ pathway: cycloreversion (via transition structure TS-7) to acetaldehyde and SO3 (reaction 4):

predicted in previous studies22,23 is actually a spurious result based on an unrecognized instability in the wave function of TS-7. RRKM/ME simulations26 predict that under atmospheric conditions 68% of the CH2OO + SO2 reaction proceeds via the pathway shown in (6). Vereecken et al.26 predicted two other pathways arising from the diradical intermediate 13. One is a β-scission that forms SO2 and the 1,3-bis(oxy) diradical 17 (reaction 7):

Jiang et al. predicted that this SO2 oxidation channel has an activation barrier 7 kcal mol−1 lower in energy than the barrier for the HC(O)OH + SO2 channel; oxidation should therefore be the dominant outcome of this reaction. The dominance of SO3, and hence H2SO4, product formation is consistent with the results of many experimental studies of the CH2OO + SO2 reaction.8−14,16 Kurtén et al.23 revisited the isomerization (reaction 3) and oxidation (reaction 4) channels using more accurate quantum chemistry methodology for both the optimized geometries (B3LYP/aug-cc-pV(T+d)Z) and the single-point energies (CCSD(T)-F12a/VDZ-F12). With the improved methodology, Kurtén et al. predicted the activation barrier for reaction 4 to be 18 kcal mol−1 lower in energy than reaction 3. Though numerically quite different from the earlier predictions of Jiang et al.,22 the calculations of Kurtén et al.23 yielded the same qualitative picture: dominance of the oxidation pathway. Using hard-sphere collision theory and CCSD(T)-F12a/VDZ-F12 energetics, Kurtén et al. estimated the transition state theory (TST) rate constant of the SCI + SO2 reaction to be 4 × 10−10 cm3 molecule−1 s−1, 5 orders of magnitude higher than the indirect experimental estimate of Johnson, Marston, and coworkers.24,25 Vereecken et al.26 greatly expanded our understanding of the CH2OO + SO2 reaction both by providing a more detailed mechanism and by performing Rice−Ramsperger−Kassel− Marcus (RRKM)/master equation (ME) simulations to predict product yields. Using mostly CCSD(T)/aug-cc-pVTZ// M06-2X/aug-cc-pVTZ calculations, they reported a number of previously uncharacterized pathways involving the 1,5-(bis)oxy diradical (13) formed by homolytic rupture of the peroxy bond in the HOZ (reaction 5):

Species 17 is the open form of the dioxirane commonly formed in alkene ozonolysis, and on the basis of the quantum chemical work of Cremer et al.,7 a 1,2-hydrogen shift in 17 to form formic acid (reaction 8) has an activation barrier of only ∼3 kcal mol−1:

Vereecken et al. predicted that the formation of HC(O)OH via intermediates 13 and 17 has significantly lower reaction barriers than the direct formation of HC(O)OH from the HOZ (reaction 3 above). Accordingly, the RRKM/ME simulations predicted virtually no reactive flux through reaction 3, but a 17% yield of species 17, which is tantamount to a 17% yield of HC(O)OH. Finally, Vereecken et al.26 also predicted that diradical 13 can undergo an intramolecular 1,4-hydrogen shift (TS-18) to formyl sulfurous anhydride 19 (reaction 9):

Species 19, whose existence had been predicted by Keller et al.27 only a few years before the Vereecken study, is formally derived from a cycloaddition of formic acid to SO2. RRKM/ME simulations indicated a substantial 15% yield of 19. Given the thermodynamic stability of 19, Vereecken et al. assumed it to be a final product of the SCI-SO2 reaction under atmospheric conditions. In the present work we seek to advance the mechanistic understanding of the SCI-SO2 reaction in three ways. First, we employ electronic structure methods that provide a more reliable treatment of the numerous intermediates and transition structures which contain multireference character. Second, we provide a more complete description of the reaction’s potential energy surface. For example, we characterize two distinct stereochemical pathways throughout the entire mechanism arising from the existence of diastereomeric endo and exo conformers of the HOZ. Finally, we apply high-level electronic structure methods and statistical rate theory to predict quantities directly comparable with experimental values. In particular, our detailed treatment of the initial steps of the CH2OO + SO2 reaction leads to a predicted rate coefficient in good agreement with recent experimental measurements. Our simplified simulation of the (CH3)2COO + SO2 reaction

According to Vereecken et al.,26 the β-scission of 13 (reaction 6), and not the cycloreversion of 5 (reaction 4 above), accounts for the formation of the atmospherically consequential SO3:

These authors emphasized that the direct cycloreversion of the HOZ 5 to HCHO + SO3 via TS-7 (reaction 4 above) 10317


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The Journal of Physical Chemistry A predicts a nearly 100% yield of acetone and SO3 on the submicrosecond time scale, predictions that are in excellent agreement with the recent measurements of Berndt et al.16

The second region of the potential energy surface that proved problematic for our CBS-QB3//B3LYP methodology involves the initial cycloaddition of the CI to SO2 (Scheme 1 below). Because B3LYP lacks an explicit treatment of dispersion forces,48 it may fail to provide even qualitatively reasonable geometries for weakly bound complexes and transition structures for low-barrier cycloaddition reactions.49 We therefore took the same approach that we used for reactions 9 and 10: we employed CCSD theory to optimize the geometry and obtain the harmonic frequencies of CH2OO, SO2, the dipole−dipole complexes 3a and 3b, and the cycloaddition transition structures TS-4a and TS-4b using the 6-31+G(d,p) and MG3 basis sets for geometries and the 6-31+G(d,p) basis set for frequencies. Another problem with applying CBS-QB3 to the cycloaddition part of the reaction coordinate, as shown by Wheeler, Ess, and Houk for the cycloaddition of ozone to ethene and ethyne,36 is that the complete basis set extrapolation performed by CBS-QB3 at the MP2 level can be several kcal mol−1 too negative. We likewise found the CBS-QB3 method to predict cycloaddition barriers as much as 2 kcal mol−1 lower in energy than the prereactive complexes (see Table 1 below). We

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COMPUTATIONAL METHODS Electronic Structure Calculations. We optimized the geometries and then calculated the harmonic vibrational frequencies of most of the structures in this paper using density functional theory (DFT), specifically, the B3LYP functional28,29 with the 6-311G(2d,d,p) basis set.30,31 Each minimum we report possesses all real frequencies and each transition structure we report possesses one imaginary frequency. We established the identities of the minima surrounding each transition structure by performing intrinsic reaction coordinate (IRC) calculations. We then used the B3LYP/6-311G(2d,d,p) geometries and frequencies (scaled by 0.99) to perform CBS-QB3 calculations32 of the energies at 0 K. The composite CBS-QB3 method, which approximates a complete-basis-set CCSD(T) calculation, has a track record of predicting accurate reaction energies and, to a lesser extent, accurate reaction barriers, for the closed-shell and open-shell organic species involved in both atmospheric chemistry and combustion.33,34 Three potential limitations of the CBS-QB3 model chemistry are its reliance on B3LYP geometries,35 the extrapolation to the complete basis set limit at the MP2 level,36 and its exclusive use of single-reference methods. These shortcomings manifest themselves in three particular regions of the CI + SO2 potential energy surface. One region involves the formation (reaction 9, considered above) and the interconversion of the two conformers (reaction 10) of the formyl sulfurous anhydride 19.

Table 1. Relative Energies (at 0 K, kcal mol−1) for the Structures in Scheme 1a species

CBS-QB3// B3LYP/ 6-311G(2d,d,p)

CBS-QB3// CCSD/MG3

MCG3// CCSD/ MG3

1+2 3a TS-4a 5a

0.00 −9.76 −10.31 −35.21

0.00 −10.72 −13.16

0.00 −9.15 −8.68

3b TS-4b 5b

−11.10 −11.78 −34.32

−12.31 −12.38

CCSD(T)// M06-2X 0.00

−37.90,b −36.73c −10.56 −10.49

a

Values in bold are the most accurate estimates of the relative energies. bCCSD(T) energy and M06-2X optimized geometry and frequencies evaluated with the aug-cc-pVTZ basis set; from Vereecken et al.26 cCCSD(T) energy and M06-2X optimized geometry and frequencies evaluated with the aug-cc-pV(T+d)Z basis set; from Vereecken et al.26

The B3LYP DFT method was unable to locate transition structure TS-18 between minima 13 and 19, in contrast to the successful transition structure calculation of Vereecken et al.26 using the M06-2X density functional of Zhao and Truhlar.37,38 The failure of B3LYP to locate an open-shell hydrogen shift transition structure in the present study is consistent with the foundational work of Lynch and Truhlar,35 who found that B3LYP was prone to predicting quite inaccurate saddle point geometries for hydrogen transfer reactions of open-shell species. (Lynch and Truhlar also found that B3LYP optimizations with the triple-ζ MG3 basis set were more accurate than with the double-ζ 6-31+G(d,p) basis set.) B3LYP also failed to locate TS-22 in reaction 10, a failure for which we have no straightforward theoretical explanation. To compensate for the failures of B3LYP, we obtained optimized geometries of TS-22 and both conformers of TS-18 using CCSD theory39,40 with both the 6-31+G(d,p)41−44 and the MG3 (that is, 6-311+ +G(3d2f,2df,2p))45,46 basis sets. Calculation of CCSD/ 6-31+G(d,p) harmonic frequencies confirmed that we had located the desired transition structures. We also reoptimized the geometries of both conformers of minima 13 and 19 with CCSD/6-31+G(d,p) and CCSD/MG3 and computed CCSD/ 6-31+G(d,p) frequencies. The 0 K energies of TS-18 and TS22 are relative to the energies of 13 and 19 and all based upon CCSD/MG3 geometries and CCSD/6-31+G(d,p) zero-point energy (ZPE) corrections scaled by 0.9686.47

therefore applied another composite method, multi-coefficient Gaussian-3 (MCG3) with version 3m parameters50 to determine the relative energies of 3a, 3b, TS-4a, and TS-4b. Truhlar and co-workers have shown50,51 that MCG3 does an excellent job in predicting both barrier heights and the binding energies of noncovalent complexes. The requisite single-point energy calculations in the MCG3 method were performed on the CCSD/MG3 geometries, and ZPE corrections were based on the CCSD/6-31+G(d,p) frequencies, again scaled by 0.9686. A final problem with the CBS-QB3 model chemistry pertains specifically to the HOZ cycloreversion transition structure (TS-7 in reaction 4 above). Although TS-7 is indeed a firstorder saddle point on the restricted B3LYP (RB3LYP) surface, TS-7 proved unstable with respect to spin-symmetry breaking. Moreover, we could not locate TS-7 on the unrestricted B3LYP (UB3LYP) singlet surface. Vereecken et al.26 found the same results using RM06-2X and UM06-2X theory. However, as noted by Gräfenstein et al.52 and by Chan et al.,53 the instability of a restricted description of a concerted transition structure at 10318


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The Journal of Physical Chemistry A

values.60 We tested the aptness of applying a single-reference method such as CBS-QB3 to the open-shell singlet and triplet states of selected diradicals by computation of the T1 diagnostic of Jayatilaka and Lee65 for the UCCSD/6-31G† 66 wave functions employed in the CBS-QB3 method. We used Q-Chem 4.267 for the EOM-SF-CCSD(dT) calculations, and Gaussian 03 and Gaussian 0968,69 for all of the other electronic structure calculations. 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-workers70 as implemented in the NBO 3.1 routines built into Gaussian 09. Statistical Rate Theory Calculations. To predict the rate constant of the CH2OO + SO2 reaction and the yields of final reaction products, we first assumed that the rate of CH2OO− SO2 complex formation is governed by long-range dipole− dipole interactions. Georgievskii and Klippenstein71 derived the variational TST expression for the high-pressure-limit capture rate coefficient, kcap, for such a system:

a certain level of theory does not preclude the existence of a concerted pathway in a given pericyclic reaction. It simply means that the electronic structure of the concerted TS contains an appreciable amount of multireference character and is therefore poorly described by methods like B3LYP and M06-2X that contain a significant amount of Hartree−Fock (HF) exchange.28,29,37,38 To treat the concerted decomposition pathway, we therefore chose a density functional method, BLYP,29,54 with no HF exchange. Schultz, Zhao, and Truhlar have provided evidence that this design feature enables BLYP to provide more accurate predictions for multireference systems,55 and we in fact located two conformers of TS-7 with the BLYP/6-311G(2d,d,p) model chemistry. The RBLYP wave functions for TS-7 proved stable with respect to spinsymmetry breaking. Finally, our treatment of the many open-shell singlet species in the mechanism requires some explanation. One theoretically rigorous way to treat the electronic structure of open-shell singlets is to employ complete-active-space self-consistent-field (CASSCF) theory to account for static correlation coupled with a higher level of theory to account for dynamic correlation. As discussed in a recent review,33 the second-order perturbative correction to the CASSCF energy provided by CASPT2 theory is not a sufficiently high level of theory to make accurate energetic predictions for the ethene ozonolysis reaction, a system containing three chalcogen atoms.56 Presumably, CASPT2 theory would likewise prove insufficient for the species in this study, which contain five chalcogen atoms. However, the cost of still higher levels of theory based on CASSCF reference wave functions would be prohibitive for a system of our size. Consequently, we took a different quantum chemical approach. First, we obtained optimized geometries and vibrational frequencies for these species with broken-spinsymmetry U3BLYP/6-311G(2d,d,p) wave functions, following the approach of Noodleman.57 A recent high-level computational study by Glowacki, Marsden, and Pilling58 provides evidence that broken-spin-symmetry DFT methods can predict potential energy surfaces for organic singlet diradicals comparable in accuracy to those predicted by the CASPT2 method. To obtain reliable energies for these inherently multireference species with single-reference methods, we took the following approach: First, we performed the suite of CBSQB3 single point energy calculations on the triplet state of each diradical and combined the electronic energy terms with the scaled broken-spin-symmetry ZPE correction to determine 3 E(CBS-QB3). Then, we used Levchenko and Krylov’s equation-of-motion spin-flip coupled-cluster theory59 with a perturbative correction for triple excitations60 (EOM-SFCCSD(dT) or simply SF for brevity) with the cc-pVTZ basis set61,62 to calculate the singlet−triplet gap, ΔEST(SF) = 1 E(SF) − 3E(SF), for each diradical. We used restricted openshell B3LYP wave functions as the reference for the SF calculations. The ZPE-corrected electronic energy of each open-shell singlet was then taken to be 3E(CBS-QB3) + ΔEST(SF). The spin-flip methodology allows a singlet with multiconfigurational character to be constructed by a complete set of spin-flipping excitations from a high-spin triplet state that is well described by a single-reference electronic structure method.63,64 In particular, EOM-SF-CCSD(dT) theory with the cc-pVTZ basis set allows for the efficient prediction of singlet−triplet gaps within 1 kcal mol−1 of experimental

kcap =

C(d1d 2)2/3 μ1/2 T1/6

(11)

In eq 11, d1 and d2 are the dipole moments of the CH2OO and SO2, μ is the reduced mass of the CH2OO−SO2 collision, T is the absolute temperature, and C is a constant of proportionality whose value depends on the type of interaction being modeled, the dimensionality of the system being treated, and the theoretical method being employed. For the onedimensional energy-resolved master equation simulations we performed on the dipole−dipole interaction between two nonlinear molecules the appropriate value of C, according to Georgievskii and Klippenstein, is 5.87 when all other quantities are expressed in atomic units. We obtained the dipole moments for CH2OO and SO2 on the basis of the coupled-cluster effective density matrix72 for the CCSD/MG3-optimized geometries. At 295 K, we find that kcap = 6.08 × 10−10 cm3 molecule−1 s−1, a value similar to those obtained in other recent studies73,74 of barrierless dipole−dipole associations. Next, we used the Thermo module of Barker’s MultiWell 2014.1 program suite75−77 to determine the equilibrium constants, K3a and K3b, for the formation of the two conformers of the dipole−dipole complex 3a and 3b (see Scheme 1 below). This allowed us to determine the high-pressure limit rate constants, k−1,3a and k−1,3b, for the dissociation of the complex back to the CH2OO and SO2 reactants. Finally, we used MultiWell-2014.175−77 to solve the onedimensional master equation for the entire CH2OO−SO2 reaction mechanism described in Schemes 1−4 below. 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 the passage of intermediates through tight transition states using Rice−Ramsperger− Kassel−Marcus (RRKM) theory78 with the required sums and densities of states obtained from the optimized geometries and harmonic frequencies. We determined the k(E) values for the dissociation of the dipole−dipole complexes back to reactants by employing the inverse Laplace transform (ILT) method of Forst79 based on the k−1,3a and k−1,3b values discussed above. Our modeling of the (CH3)2COO + SO2 reaction did not include finding the optimized geometries of any dipole−dipole 10319


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above, the CBS-QB3 composite method is characteristically unreliable for structures 3 and TS-4, both of which contain weakly interacting moieties. One issue is that B3LYP/ 6-311G(2d,d,p), which is the default geometry optimization method in CBS-QB3, does not locate either minima 3a or 3b nor saddle points TS-4a or TS-4b. Replacement of the default B3LYP/6-311G(2d,d,p) geometries with high-level CCSD/ MG3 geometries leads to CBS-QB3 transition structure energies that are lower than the CBS-QB3 energies of the corresponding preceding minima by 2.85 kcal mol−1 (endo) and by 0.30 kcal mol−1 (exo). Removal of zero-point energy corrections changes the cycloaddition barriers by only 0.2− 0.4 kcal mol−1. In contrast, use of the MCG3 composite method with either the CCSD/6-31+G(d,p) or the CCSD/ MG3 geometries leads to cycloaddition barriers that are indeed positive, albeit very small in magnitude. (Figure S1 in the Supporting Information presents the results of IRC calculations on the CCSD/6-31+G(d,p) optimized geometry for TS-4a; these data provide evidence that the putative stationary point is indeed a first-order saddle point on the CCSD surface and is not merely a shoulder on the energy profile. IRC calculations on TS-4b lead to the same conclusion.) We take the MCG3// CCSD/MG3 values as our best estimates for 3 and TS-4. The endo conformer of both the dipole−dipole complex (3a) and the cycloaddition transition structure (TS-4a) are 1−2 kcal mol−1 less stable than the analogous exo structures, 3b and TS-4b. This is presumably due to greater steric repulsions in the endo structures arising from the greater proximity of the oxo substituent and the ring oxygens. However, the endo conformer of the HOZ, 5a, is ∼1 kcal mol−1 more stable than exo conformer 5b. We ascribe the switch in conformational preference to a hyperconjugative interaction in which the lone pair on the sulfur atom delocalizes into the peroxy bond’s σ antibonding orbital to a greater or lesser extent. Figure 1 presents evidence for this effect based on the B3LYP/ 6-311G(2d,d,p) optimized geometries. In 5a, the dihedral angle

complexes or cycloaddition transition structures. Instead, we simply assumed a direct formation of the covalently bound heteroozonide from the CI and SO2. Our master equation simulations of this reaction included the possibility of HOZ dissociation back to the dimethyl CI + SO2. We calculated specific rate coefficients, k(E), for the dissociation reaction using the ILT method based on the equilibrium constants for the formation of the two dimethyl HOZ conformers (which we calculated with Thermo75−77) and the recently reported80 experimental high-pressure limit rate constant of k∞ = 1.3 × 10−10 cm−3 molecule−1 s−1. 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.81 We used as our bath gas N2 at 295 K with Lennard-Jones parameters of σ = 3.74 Å and ε/kB = 82 K.82,83 Using the same methodology84−87 described in our earlier study of isoprene ozonolysis,49 we estimated Lennard-Jones parameters of σ = 5.43 Å and ε/kB = 387 K for the CH2OO−SO2 adduct and all of its isomers, and parameters of σ = 6.57 Å and ε/kB = 397 K for the (CH3)2COO−SO2 adduct and all of its isomers. Each simulation involved 103 collisions; convergence of populations in typically far fewer than 103 collisions ensured that a given simulation had reached the pseudo steady state.88 We ran trials at pressures from 1 Torr to 108 Torr. Each pseudo steady state yield reported is the average result of a minimum of 106 Monte Carlo simulations.

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RESULTS AND DISCUSSION Quantum Chemical Results. Heteroozonide Formation. Scheme 1 depicts the initial steps of the CH2OO + SO2 Scheme 1. Initial Steps of the CH2OO + SO2 Reactiona

a

Best estimates of relative energies in blue (at 0 K in kcal mol−1).

reaction: the formation of a dipole−dipole complex (3a or 3b), the cycloaddition of the CH2OO 1,3-dipole across a SO bond (via transition structure TS-4a or TS-4b), and the formation of the five-membered ring adduct (5a or 5b). The ring contains three oxygen atoms, like the ozonides formed in alkene ozonolysis, and also contains a sulfur heteroatom and is therefore denominated a heteroozonide (HOZ). Like the primary ozonide (the 1,2,3-trioxolane), the most stable conformation of the HOZ has an envelope shape, and the oxo substituent can be either endo (5a) or exo (5b) to the O−O−C flap. These two stereochemical possibilities also exist for complex 3 and transition structure TS-4. Table 1 summarizes our predictions of relative energies (at 0 K) for the structures in Scheme 1 and compares them to the previous26 CCSD(T)//M06-2X predictions. As discussed

Figure 1. B3LYP/6-311G(2d,d,p)-optimized geometries of the endo (5a) and the exo (5b) conformers of the heteroozonide. Below each structure is a Newman projection down the S−Oα bond of the given conformer.

τ(OSOαOβ) is 76.0°. As depicted in a Newman projection for 5a down the SOα bond, the synclinal SO and OαOβ bonds allow for a fair degree of alignment between 10320


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the n(S) → σ*(OαOβ) interaction causes the B3LYP/ 6-311G(2d,d,p) energy of 5a to increase by 3.08 kcal mol−1 whereas the same deletion causes the B3LYP/6-311G(2d,d,p) energy of 5b to increase by only 0.88 kcal mol−1. Although the energetic impact of the hyperconjugation is modest, it is large enough to overcome the steric interactions destabilizing the endo conformer of 5a. Moreover, as we shall see, the endo preference carries through to several of the subsequent structures in the mechanism. The most recent previous study of Vereecken et al.26 did not report energies for 3 or TS-4 and did not consider the exo conformer. The CCSD(T)/aug-cc-pVTZ relative energy of 5a is 2.7 kcal mol−1 lower than the CBS-QB3 energy. Reevaluation of both the energy and the geometry with the augcc-pV(T+d)Z basis set, which assigns a second set of d functions to the sulfur atom, leads to a relative energy of 5a that is 1.2 kcal mol−1 closer to the CBS-QB3 value. Heteroozonide Reaction Pathways. Scheme 2 depicts the isomerization and decomposition pathways that we have identified for HOZ conformers 5a and 5b, Table 2 presents the energetics of the species depicted in Scheme 2, and Table S1 (in the Supporting Information) presents singlet and triplet energies for the diradical species First, we found a pseudorotation transition structure, TS-6, which interconverts the endo and exo forms of the HOZ. The pseudorotation barrier is 3−4 kcal mol−1, which is consistent with the barriers predicted in Cremer’s seminal work89 on primary and secondary ozonides from alkene ozonolysis. Alternatively, interconversion between the endo and exo rings could proceed via inversion at the sulfur atom. However, we predict that the inversion process has a substantial CBS-QB3 barrier of 43− 44 kcal mol−1 (not in Table 2). We may attribute the barrier’s magnitude in part to the energetic cost of promoting the lone pair from a 3s orbital in the minima to a 3p orbital in the inversion transition structure, with the s character of the lone pair being enhanced by sulfur’s being bound to three electronegative O substituents.90,91 The HOZ can undergo concerted cycloreversion to HCHO + SO3 via TS-7, a 1,2-hydrogen shift via TS-10 that triggers

the lone pair on the sulfur and a lobe of the σ*(OαOβ) orbital. In contrast, the anticlinal SO and OαOβ bonds in 5b (τ(OSOαOβ) is −124.0°) put the lone pair on the sulfur and the σ*(OαOβ) orbital almost perpendicular to each other, minimizing their overlap. The fact that the predicted OαOβ bond length in 5a is 0.016 Å longer than in 5b is consistent with the putative hyperconjugation. NBO analysis provides additional support for our explanation of the conformational preference for the endo form. Deletion of Scheme 2. Reaction Pathways of the Heteroozonidea

a


Table 2. Relative Energies (at 0 K, kcal mol−1) for the Structures in Scheme 2a,b species

CBS-QB3//B3LYP/ 6-311G(2d,d,p)

5a 5b TS-6 TS-7a TS-7b 8+9 TS-10a TS-10b 11 + 2 TS-12a TS-12b 13a 13b

−35.21 −34.32 −31.35 −26.53e −20.11e −74.57 −14.29 −9.77 −115.67 −19.72 −14.72 −29.40 −30.32

CBS-QB3//BLYP/ 6-311G(2d,d,p)

EOM-SF-CCSD(dT)/cc-pVTZ//B3LYP/ 6-311G(2d,d,p)

CCSD(T)// M06-2X −37.90,c −36.73d

−26.91 −21.74

−22.12 −13.45 −27.84 −28.45

−68.39c −11.63f −6.34,c −5.65d,g −115.73c −18.41,c −19.32d

−27.22,c −29.45d

a

Values in bold are the most accurate estimates of the relative energies. bEnergies reported here are relative to the combined energies of species 1 and 2 (see Scheme 1 above). cCCSD(T) energy and M06-2X optimized geometry and frequencies evaluated with the aug-cc-pVTZ basis set; from Vereecken et al.26 dCCSD(T) energy and M06-2X optimized geometry and frequencies evaluated with the aug-cc-pV(T+d)Z basis set; from Vereecken et al.26 eThe restricted B3LYP/6-311G(2d,d,p) geometry was not stable with respect to spin-symmetry breaking. fThe CCSD(T)/aug-ccpVTZ energy was not reported in previous studies and was calculated in this work. gThe CCSD(T)/aug-cc-pV(T+d)Z energy was incorrectly reported in previous work26 and was recomputed for this work. 10321


Article


and low-spin triplet states of TS-12a and TS-12b predicted by the SF calculations.) Given that the concerted cycloreversion barriers are 5−8 kcal mol−1 lower in energy, we anticipate that only a relatively small fraction of the total reactive flux will follow the diradical pathways. We located the same hydrogen-shift transition structure (TS-10) found in previous computational studies19,22,23,26 to trigger the decomposition of the HOZ to formic acid and SO2. Extensive searches with the B3LYP, M06-2X, and CCSD levels of theory failed to reveal the existence of an alternative TS in which the hydrogen migrates to the oxygen directly bonded to the sulfur; this contradicts the results of previous MP2 calculations.22 Extensive searches with the B3LYP method also failed to reveal the existence of a TS in which the axial hydrogen (“Hax” in Scheme 2) migrates to the peroxy oxygen. The exclusive transfer of the equatorial hydrogen (“Heq” in Scheme 2) we predict here is consistent with the primary stereoelectronic effect found in the analogous Baeyer−Villiger reaction,98 namely, that the bond between the carbon and the migrating group (R) will be antiperiplanar to the peroxy bond to facilitate the donation of electron density from the σ(CR) orbital to the σ*(OαOβ) orbital. Figure 2 presents key B3LYP/6-311G(2d,d,p) geometrical parameters for the two conformers, TS-10a and TS-10b, of the hydrogen-shift transition structure. Both structures have the requisite antiperiplanar alignment of the Oα---Oβ and the C---Heq bonds. However, the magnitude of τ(Oα---OβC---Heq) in TS-10 is 8° closer to 180° than in TS-10b, facilitating greater donation of electron density into the σ*(Oα-Oβ) orbital. Moreover, the

decomposition to HC(O)OH + SO2, and peroxy bond homolysis via TS-12. We located diastereomeric pairs of transition structures, labeled as a and b, for each of the three processes. In each case, the endo transition structure conformer (TS-7a, TS-10a, and TS-12a) is lower in energy than the corresponding exo transition structure conformer (TS-7b, TS-10b, and TS-12b). As discussed above, the CBS-QB3//B3LYP results for the cycloreversion transition structures, TS-7a and TS-7b, are arguably bogus due to the instability of the default B3LYP/ 6-311G(2d,d,p) geometries with respect to spin-symmetry breaking. However, the BLYP/6-311G(2d,d,p) geometries are stable with respect to spin-symmetry breaking, and the CBSQB3 cycloreversion barriers based on the BLYP geometries are 8−13 kcal mol−1. (Figures S2 and S3 in the Supporting Information present BLYP/6-311G(2d,d,p) and CBS-QB3 IRC data that substantiate the validity of the saddle points and the accuracy of the predicted barriers.) These barriers are several kcal mol−1 lower than the barrier of 18.7 kcal mol−1 predicted by Anglada et al.92 for the cycloreversion of the primary ozonide formed in ethene ozonolysis. The CBS-QB3 results for the peroxy bond homolysis transition structures, TS-12a and TS-12b, are not bogus; we calculated the optimized geometries and all of the requisite single-point energies using unrestricted broken-spin-symmetry wave functions. Moreover, CBS-QB3 has a correction term that attempts to compensate for the spin contamination introduced by unrestricted calculations. However, there are some doubts93,94 as to the accuracy of this correction term and more general misgivings about applying single-reference methodology to multireference species. Indeed, we found that when we treated TS-12a and TS-12 with broken-spin-symmetry calculations, the T1 diagnostics for the UCCSD/6-31G† wave functions were 0.051 and 0.049, respectively. Schaefer and co-workers95 recommend the use of a multireference electronic structure method for any open-shell species with a T1 diagnostic of greater than 0.044. As noted above in the Computational Methods section, we obtained more reliable energies for open-shell singlets by using SF theory to correct the CBS-QB3 triplet energy of each diradical species. When we treated TS-12a and TS-12b as triplets, the T1 diagnostics for the UCCSD/6-31G† wave functions were 0.044 and 0.038, respectively. The lower T1 diagnostic values lead us to expect the CBS-QB3 method to be more reliable for the triplet states than the open-shell singlet states of TS-12a and TS-12b. Nevertheless, the triplet T1 diagnostics are still quite high. An alternative metric for multireference character is the fractional difference in total atomization energy, %TAE[(T)], based on CCSD(T) and CCSD calculations, as originally proposed by Martin and co-workers.96 The %TAE[(T)] values are 4.1−4.2% for the singlet states of TS-12a and TS-12b and 3.7−3.8% for the triplet states. According to both Martin and co-workers96 and Sprague and Irikura,97 these diagnostic values indicate that each of these electronic states has, at most, a “mild” degree of multireference character. The %TAE[(T)] thus provide additional justification for our single-reference approach. The homolysis barriers we predict on the basis of SF theory, 13.09 kcal mol−1 for 5a and 20.87 kcal mol−1 for 5b, are 1−2 kcal mol−1 different from the CBS-QB3 broken-spinsymmetry barriers. (Figures S4 and S5 in the Supporting Information present the leading configurations for the singlet

Figure 2. B3LYP/6-311G(2d,d,p)-optimized structures of the endo (TS-10a) and the exo (TS-10b) conformers of the hydrogen-shift transition structure.

magnitude of the dihedral angle τ(OSOα---Oβ) in TS-10a is 9° closer to 60° than in TS-10b. As we discussed above for the HOZ, the synclinal alignment of the SO and OαOβ bonds also enhances electron delocalization into σ*(OαOβ). These hyperconjugative interactions cause the endo conformer to have a greater OαOβ bond length (0.037 Å longer than in TS-10b) and to be lower in energy (by 4.52 kcal mol−1 according to Table 2). The previous CCSD(T)//M06-2X calculations of Vereecken et al.26 predict hydrogen-shift (TS-10b) and homolysis (TS-12a) transition structure energies that are 3−4 kcal mol−1 higher in energy than the CBS-QB3 and SF results (Table 2). Moreover, the previous study included only the less stable conformer for the hydrogen shift TS and the more stable conformer for the homolysis TS. We optimized the geometry of TS-10a with the M06-2X/aug-cc-pVTZ model chemistry and computed the structure’s CCSD(T)/aug-cc-pVTZ single-point energy. Both CBS-QB3 and CCSD(T)//M06-2X predict 10322


Article

The Journal of Physical Chemistry A Scheme 3. Reaction Pathways of the Diradicals Formed upon Peroxy Bond Homolysisa

a


a ∼5 kcal mol−1 difference in the energies of TS-10a and TS-10b. Diradical Reaction Pathways. Scheme 3 depicts the isomerization and decomposition pathways available to the 1,5-(bis)oxy diradicals 13a and 13b, Table 3 presents the energetics of the species depicted in Scheme 3, and Table S2 (in the Supporting Information) presents singlet and triplet energies for the diradical species. As is common for alkoxy radicals in the atmosphere,99 two of the possible fates for 13a and 13b are either β-scission of the internal C−O bond (via TS-15a and TS-15b) to make formaldehyde (8) and SO3 (9) or β-scission of the internal S−O bond (via TS-16a and TS-16b) to make SO2 (2) and the 1,3-(bis)oxy diradical (17). The activation barriers and reaction energies for the two β-scission pathways follow the Bell−Evans−Polanyi principle100 in that C−O scission has a barrier 6−11 kcal mol−1 lower in energy than S−O scission, and the C−O scission reaction is significantly more exothermic than the S−O scission reaction. The third reaction pathway available to both diradicals 13a and 13b is an intramolecular 1,4-hydrogen shift (via TS-18a and TS-18b) to form two conformers, 19a and 19b, of the formyl sulfurous anhydride. Our calculations predict hydrogenshift barriers intermediate between those for C−O β-scission and S−O β-scission. Although the SF barriers for C−O β-scission and the 1,4-hydrogen shift are 3−5 kcal mol−1 lower for diradical conformer 13a, derived from the endo HOZ 5a, than for diradical conformer 13b, there is no predicted conformational preference in S−O β-scission. In addition, a very low (0.3−0.9 kcal mol−1) SF barrier (TS-14) exists for the interconversion of the two diradical conformers. Finally, unlike in the previous study,26 we were able to locate a transition structure, TS-20b, connecting the 1,5-(bis)oxy diradical 13b to 1,3,2-dioxathietane, 2,2-dioxide (21). We predict that

the cyclization pathway encounters a small barrier (1.7 kcal mol−1 according to the SF calculations) and is possible only for conformer 13b. The previous M06-2X study of this reaction located minimum 21 but did not locate any transition structure between 21 and 13. This was attributed to a lack of spin density at the sulfur atom of the diradical. We probed the diradical’s electronic structure by computing the UCCSD/6-31G† spin density of 13a and 13b (Figure 3). Contrary to the previous study,26 Figure 3 provides qualitative evidence of significant spin density at the sulfur atom in both 13a and 13b. In 13a, the sulfur spin density is concentrated away from Oβ, whereas in 13b the spin densities on S and Oβ are in close proximity, facilitating S−Oβ bond formation. In terms of quantum chemical methodology (Table 3), we see that the EOM-SF-CCSD(dT) method, which provides a theoretically rigorous treatment of the open-shell singlet species in Scheme 3, predicts relative energies that range from ∼2 kcal mol−1 higher to ∼4 kcal mol−1 lower than the broken-spinsymmetry CBS-QB3 energies. That is, although the errors in the CBS-QB3 approach are not egregiously large, neither are they systematic. There is likewise no consistent pattern in the deviations of the broken-spin-symmetry CCSD(T)//M06-2X energies from the SF values, nor does expansion of the basis set from aug-cc-pVTZ to aug-cc-pV(T+d)Z invariably improve the agreement of the CCSD(T) and the SF predictions. Ultimate Products of the Diradical Pathways. As we noted in the Introduction, Cremer et al.’s7 seminal quantum chemical study of dioxiranes predicts that 17 has only a 3 kcal mol−1 barrier against isomerization to formic acid (reaction 8 above). We characterized the possible chemical fates of the other two molecules formed in Scheme 3, the sulfurous anhydride, 19, and the dioxathietane, 21. Scheme 4 shows the reactions we characterized and Table 4 summarizes the predicted energetics. 10323


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The Journal of Physical Chemistry A Table 3. Relative Energies (at 0 K, kcal mol−1) for the Structures in Scheme 3a,b CBS-QB3// B3LYP/ 6-311G(2d,d,p)

EOM-SF-CCSD(dT)/ cc-pVTZ//B3LYP/ 6-311G(2d,d,p)

13a 13b

−29.40 −30.32

−27.84 −28.45

TS-14 TS-15a

−28.72 −23.59

−27.54 −23.64

TS-15b 8+9 TS-16a TS-16b

−20.01 −74.57 −12.47 −13.08

−18.22 −12.54 −12.36

2 + 17 TS-18a TS-18b

−16.24 −17.85e −14.61e

−20.38 −21.07e −17.52e

19a 19b TS-20b 21

−105.36 −106.32 −25.91 −84.72

species

Scheme 4. Reaction Pathways for Species Formed from Diradicals 13a and 13ba

CCSD(T)// M06-2X −27.22,c −29.45d −24.37,c −20.03d

−11.92,c −12.25d −14.24c −14.06,c −16.36d −108.01c

−26.76 −78.78c

a

Values in bold are the most accurate estimates of the relative energies. bEnergies reported here are relative to the combined energies of species 1 and 2 (see Scheme 1 above). cCCSD(T) energy and M06-2X optimized geometry and frequencies evaluated with the augcc-pVTZ basis set; from Vereecken et al.26 dCCSD(T) energy and M06-2X optimized geometry and frequencies evaluated with the augcc-pV(T+d)Z basis set; from Vereecken et al.26 eBased on CCSD/ MG3 geometries and CCSD/6-31+G(d,p) vibrational frequencies.

a


the alternative interconversion pathway would require inversion at the sulfur atom, which would typically involve a barrier dozens of kcal mol−1 higher than the 2−3 kcal mol−1 barrier predicted for pseudorotation. Although the anhydride is thermodynamically over 100 kcal mol−1 more stable than the original CH2OO and SO2 reactants, it is still energetically ∼10 kcal mol−1 less stable than HC(O)OH and SO2 (11 + 2) and ∼20 kcal mol−1 higher in free energy (results not in Table 4). We therefore would expect 19a and 19b to decompose readily if there were a low-barrier pathway to HC(O)OH and SO2. Our B3LYP calculations revealed such a pathway: a concerted rearrangement involving transition structures (TS-23a and TS-23b) only 1−6 kcal mol−1 higher in energy than the anhydride. The decomposition is formally a retro-ene reaction: the HC(O)OH product (the ene) contains an allylic hydrogen and the SO2 product (the enophile) contains a SO double bond rendered more electrophilic by the oxo substituent.101 The retro-ene decomposition of the formyl sulfurous anhydride is analogous to the decomposition of hydroxymethyl formate (HMF) previously considered by Green and co-workers102 (reaction 12):

The barrier for HMF decomposition via reaction 12 is predicted to be considerably higher than the barrier for decomposition of 19; Green and co-workers predict a CCSD(T)// B3LYP 0 K barrier of 24.6 kcal mol−1. Nevertheless, their master equation simulations of the CH2OO + HCHO system indicate that reaction 12 is the dominant source of formic acid under atmospheric conditions.

Figure 3. UCCSD/6-31G† spin density for diradical conformers 13a and 13b.

First, interconversion of the two conformers of the formyl sulfurous anhydride, 19a and 19b, happens most readily via pseudorotation (TS-22). As we discussed above for the HOZ, 10324


Article

The Journal of Physical Chemistry A Dioxathietane 21 decomposes via two pathways: cycloreversion (via TS-24) and a 1,2-hydrogen shift coupled to S−O

bond homolysis (via TS-25). These pathways are analogous to those observed for HOZ 5a and 5b (Scheme 2): cycloreversion (via TS-7a and TS-7b) and the hydrogen shift (TS-10a and TS-10b). However, the C2v symmetry of 21 precludes the existence of diastereomeric pairs of transition structures that characterize the HOZ. Moreover, we found that the restricted B3LYP/6-311G(2d,d,p) optimized geometries for both TS-24 and TS-25 are stable with respect to spin-symmetry breaking. The barriers against both decomposition pathways are substantial: cycloreversion requires 25.7 kcal mol−1 and the hydrogen shift requires 73.7 kcal mol−1. However, relative to the combined energy of the original CH2OO and SO2 reactants, TS-25 is quite close in energy to the analogous transition structures, TS-10a and TS-10b, involved in HOZ decomposition (Table 2). The extremely high barrier for the dioxathietane arrangement is therefore a consequence of the far greater stability of the four-membered SOCO ring compared to that of the five-membered HOZ ring. We can account for this based simply on bond dissociation energies (BDEs): isomerization of 5 to 21 involves the loss of an alkylperoxy bond, with an average BDE of 35−40 kcal mol−1, and the gain of a sulfur−oxygen double bond, with an average BDE of 100−110 kcal mol−1.103 Finally, we discern no pattern in the discrepancies between the CBS-QB3 and CCSD(T)//M06-2X relative energies.

Table 4. Relative Energies (at 0 K, kcal mol−1) for the Structures in Scheme 4a,b species

CBS-QB3//B3LYP/6-311G(2d,d,p)

19a 19b TS-22 TS-23a TS-23b 21 TS-24 TS-25 8+9 11 + 2

−105.36 −106.32 −103.17d −103.96 −100.72 −84.72 −59.01 −10.98 −74.57 −115.67

CCSD(T)//M06-2Xc −108.01

−78.78 −52.23 −6.72e −68.39 −115.73

a

Values in bold are the most accurate estimates of the relative energies. bEnergies reported here are relative to the combined energies of species 1 and 2 (see Scheme 1 above). cCCSD(T) energy and M06-2X optimized geometry and frequencies evaluated with the augcc-pVTZ basis set; from Vereecken et al.26 dBased on CCSD/MG3 geometries and CCSD/6-31+G(d,p) vibrational frequencies. eThe CCSD(T)/aug-cc-pVTZ energy was incorrectly reported in previous work26 and was recomputed for this work.

Scheme 5. Reaction of the Heteroozonides formed in the Dimethyl CI + SO2 Reactiona

a

Best estimates of relative energies in blue (at 0 K in kcal mol−1). 10325


Article

The Journal of Physical Chemistry A Highlights of the Dimethyl CI + SO2 Reaction. The dimethyl Criegee intermediate (acetone oxide), like the parent Criegee intermediate, undergoes a 1,3-dipolar cycloaddition across one of the double bonds in sulfur dioxide to form either endo or exo heteroozonides. Scheme 5 presents the reaction pathways of the dimethyl HOZ conformers. Table 5 presents

the relative energies of the 1,2-methyl shift transition structures, TS-10a-DM and TS-10b-DM, compared to the energies of the parent 1,2-hydrogen shift transition structures, TS-10a and TS-10b, in spite of the fact that 11-DM + 2 is 10 kcal mol−1 less stable than 11 + 2. The Bell−Evans−Polanyi principle does not apply to the group transfer reaction presumably because the moieties within the transition structures bear little structural resemblance to the final formic acid (11) or methyl acetate (11-DM). Finally, the previous study by Vereecken et al.26 limited consideration of dimethyl HOZ decomposition to peroxy bond homolysis (via TS-12a-DM) to form diradical 13a-DM. The relative energy of the M06-2X/aug-cc-pVTZ TS, −12.34 kcal mol−1, is ∼8 kcal mol−1 higher than the energy of the CBS-QB3 TS. The same 8 kcal mol−1 discrepancy exists with the CCSD(T)/aug-cc-pVTZ model chemistry. We tested our prediction for TS-12a-DM at a higher level of theory by computing the triplet CBS-QB3 energy and the EOM-SFCCSD(dT) singlet−triplet gap, ΔEST(SF), with the 6-31+G(d,p) basis set. This approach lowers the predicted relative energy of TS-12a-DM by ∼4 kcal mol−1. It is the case that for the smaller parent CI + SO2 system, we computed ΔEST(SF) with the larger cc-pVTZ basis set. However, we find that for TS-12a and TS-12b (Table 2), values of ΔEST(SF) computed with the 6-31+G(d,p) basis set are within 0.5 kcal mol−1 of values computed with the cc-pVTZ basis set (results not shown). RRKM/ME simulations based on the M06-2X energies would predict the HOZ to be less reactive under atmospheric conditions than simulations based on the CBSQB3 energetics. Scheme 6 presents selected reactions of the two conformers of the 1,5-bis(oxy) diradical 13a-DM and 13b-DM, and Table 6 presents the CBS-QB3 relative energies of the structures in Scheme 6. As in Table 5, we compare these energies to the CBS-QB3 energies predicted for the analogous parent structures (in Schemes 3 and 4 and Tables 3 and 4) and to the earlier M06-2X/aug-cc-pVTZ predictions of Vereecken et al.26 We have included the lowest-barrier process for each conformer: β-scission of the C−O bond (via TS-15a-DM) for 13a-DM and dioxathietane ring formation (via TS-20b-DM) for 13b-DM. We have also included TS-14-DM, which interconverts the two conformers. According to our CBS-QB3 calculations, adding two methyl groups to the interconversion, ring formation, and β-scission transition structures has qualitatively different effects. The dimethyl diradical interconversion TS-14-DM is 3 kcal mol−1 higher in energy than the parent TS. We attribute this to the greater repulsion between the methyl groups and the lone pairs on the oxygen atoms of TS-14-DM. The TS for the closure of the diradical to the dioxathietane ring, TS-20b-DM, is within 1 kcal mol−1 of the parent TS. Dimethyl diradical 13b-DM has significant spin density at both the S and the terminal O that is in close proximity to one another, as we found to be the case for the parent diradical (see Figure 3 above), and so a low barrier (∼4 kcal mol−1) to cyclization in both systems seems reasonable. The most interesting comparison involves the C−O β−scission transition structure. Relative to the original CI and SO2 reactants, the dimethyl TS-15a-DM is 3 kcal mol−1 lower in energy than the parent TS-15a, making the barrier for C−O β−scission in 13a-DM 4 kcal mol−1 lower than the C−O β−scission barrier in 13a. This is in spite of the fact that formation of acetone and SO3 (8-DM + 9) is 4 kcal mol−1 less

Table 5. Relative Energies (at 0 K, kcal mol−1) for the Structures in Scheme 5a,b,c for (CH3)2COO + SO2 species

CBS-QB3

5a-DM 5b-DM TS-6-DM TS-7a-DM TS-7b-DM 8-DM + 9 TS-10a-DM TS-10b-DM 11-DM + 2 TS-12a-DM TS-12b-DM 13a-DM 13b-DM

−32.31 −30.85 −28.32 −20.68e −14.55e −70.88 −14.10 −10.15 −95.62 −20.61 [−24.66f] −15.08 −28.12 −30.61

M06-2X/ aug-cc-pVTZd −37.86

−12.34 [−12.54g ] −24.20

for CH2OO + SO2 CBS-QB3 −35.21 −34.32 −31.35 −26.91e −21.74e −74.57 −14.29 −9.77 −115.67 −19.72 −14.72 −29.40 −30.32

a

Values in bold are the energies used in the RRKM/ME simulations. Energies reported here are relative to the combined energies of the CI and SO2. cCBS-QB3 energies based on B3LYP/6-311G(2d,d,p) geometries and frequencies unless otherwise noted. dFrom Vereecken et al.26 eBased on BLYP/6-311G(2d,d,p) geometries and vibrational frequencies. fBased on the CBS-QB3 triplet energy and the EOM-SFCCSD(dT)/6-31+G(d,p) singlet−triplet gap. gBased on CCSD(T)/ aug-cc-pVTZ single-point calculations. b

the CBS-QB3 relative energies of the structures in Scheme 5 and compares these energies to the CBS-QB3 energies predicted for the analogous parent structures (in Scheme 2 and Table 2) and to the earlier M06-2X/aug-cc-pVTZ predictions of Vereecken et al.26 Though we have seen that the broken-spin-symmetry CBS-QB3 energies can vary significantly from the energies determined with SF theory (e.g., in Table 3), our ultimate goal is to make qualitative RRKM/ME predictions about the dimethyl CI + SO2 reaction; the CBS-QB3 energies will be sufficiently accurate for this purpose. First, we note that the dimethyl HOZ conformers, 5a-DM and 5b-DM, and their interconversion transition structure, TS-6-DM, are 3−4 kcal mol−1 less stable (relative to the separated CI and SO2 molecules) than the parent structures, 5a, 5b, and TS-6. This energetic change is presumably a consequence of the greater steric interactions between the methyl groups and the oxygen lone pairs in the dimethylated structures. In contrast, the diradical formation transition structures, TS-12a-DM and TS-12b-DM, and the diradicals themselves, 13a-DM and 13b-DM, all have relative energies within ∼1 kcal mol−1 of the analogous parent structures. The changes in the cycloreversion barriers upon dimethylation follow the Bell−Evans−Polanyi principle: TS-7a-DM and TS-7b-DM are 6−7 kcal mol−1 higher in energy than the corresponding TS-7a and TS-7b, and the products of dimethyl HOZ cycloreversion, 8-DM + 9, are 4 kcal mol−1 higher in energy than 8 + 9. In contrast, there is virtually no change in 10326


Article

The Journal of Physical Chemistry A Scheme 6. Selected Reactions of the Diradicals formed in the Dimethyl CI + SO2 Reactiona

a


Table 6. Relative Energies (at 0 K, kcal mol−1) for the Structures in Scheme 6a,b,c for (CH3)2COO + SO2

for CH2OO + SO2

species

CBS-QB3

M06-2X/aug-cc-pVTZd

CBS-QB3

13a-DM 13b-DM TS-14-DM TS-15a-DM 8-DM + 9 TS-20b-DM 21-DM TS-24-DM TS-25-DM 11-DM + 2

−28.12 −30.61 −25.72 −26.33 −70.88 −26.61 −90.43 −70.15 −11.22 −95.62

−24.20

−29.40 −30.32 −28.72 −23.59 −74.57 −25.91 −84.72 −59.01 −10.98 −115.67

−18.12

a

Figure 4. B3LYP/6-311G(2d,d,p)-optimized structure of the dimethyl endo diradical C−O β-scission transition structure (TS-15a-DM). Bond lengths are in Å.

Values in bold are the energies used in the RRKM/ME simulations. Energies reported here are relative to the combined energies of the CI and SO2. cCBS-QB3 energies based on B3LYP/6-311G(2d,d,p) geometries and frequencies. dFrom Vereecken et al.26 b

longer than the other C−H bonds in the TS. More direct evidence comes from NBO analysis. Deletion of the interactions of the antiperiplanar C−H bonds with σ*(C1−O10) raises the B3LYP/6-311G(2d,d,p) energy by 8.42 kcal mol−1. Although we should not put too much trust in the precise magnitude of the deletion energy, it is reasonable to assert that the hyperconjugation in TS-15a-DM is more than enough to reverse the trend in the β-scission reaction barrier expected on the basis of the Bell−Evans−Polanyi principle. Finally, we note that the M06-2X relative energies for the singlet diradical species are all several kcal mol−1 higher in energy than the CBS-QB3 values, a systematic difference also seen in Table 5. Again, we expect that RRKM/ME simulations based on the M06-2X energetics will predict lowered reactivity under atmospheric conditions. Statistical Rate Theory Results for the CH2OO + SO2 Reaction. Table 7 summarizes experimental and theoretical determinations of the room-temperature rate coefficient for the reaction of CH2OO and SO2. Our theoretical approach follows

exothermic than the formation of formaldehyde and SO3 (8 + 9). This apparent contradiction of the Bell−Evans− Polanyi principle is surprising given the close resemblance of the TS moieties to the final separated products. We can account for the apparent contradiction by recognizing the presence of hyperconjugative interactions available only to TS-15a-DM. Figure 4 shows that in this TS, two carbon−hydrogen bonds, C2−H5 and C6−H7, are almost perfectly antiperiplanar to the breaking C1−O10 bond and are therefore capable of donating electron density into the σ*(C1−O10) orbital, facilitating bond homolysis. As discussed above, this effect is reminiscent of the primary stereoelectronic effect found in the Baeyer−Villiger reaction.98 Because the parent transition structure (TS-15a, depicted in Scheme 3) lacks C−H bonds α to the breaking C−O bond, TS-15a cannot be stabilized in this way. A subtle piece of evidence for these interactions is that the lengths of the C2−H5 and C6−H7 bonds are 0.02−0.04 Å 10327


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significant variation in k between 1 Torr and 1 atm is consistent with the recent analysis of experimental values by Chhantyal-Pun et al.109 Simulations at higher pressures suggest that the rate coefficient remains at a constant low-pressure value up to 104 Torr, increases from 104 to 1010 Torr, and reaches its high-pressure limit value of kcap at 1010 Torr. The sigmoidal shape of the semilogarithmic plot of k vs log p (see Figure S7 in the Supporting Information) resembles that observed110 and predicted104 for the HO + CO reaction, another chemical activation system with prereactive complexes, multiple intermediates, and a variety of reaction pathways. A number of significant simplifying assumptions underlie our prediction, including the lack of angular momentum resolution in our master equation simulations, the treatment of lowfrequency motions as harmonic oscillators instead of as hindered rotors, and the absence of variational optimization of the cycloaddition transition states TS-4a and TS-4b. Moreover, although the variational TST expression used to predict kcap is certainly highly rigorous in itself, it is not obvious that considering only the dipole−dipole interaction when modeling the kinetics of the CH2OO + SO2 reaction is fully legitimate.105 Nevertheless, the decent agreement between the present result and experiment provides some tentative support for the validity of our statistical rate theory approach. Finally, we note that our predicted rate coefficient is an order of magnitude lower than the previous theoretical estimate of Kurtén et al.23 There are two main reasons for this discrepancy. First, Kurtén et al. used hard-sphere collision theory to estimate that the rate coefficient for association of the CI and SO2 reactants is kcoll = 4 × 10−10 cm3 molecule−1 s−1. Our treatment predicts a higher association rate (kcap = 6.08 × 10−10 cm3 molecule−1 s−1) because of our inclusion of the mutually attractive permanent dipoles on the parent CI and the SO2. Second, Kurtén et al. assumed that the only way for the reaction to revert to the original reactants was for the HOZ to undergo cycloreversion to the CI + SO2. This cycloreversion pathway was predicted to be negligibly slow, which leads to an overall reaction rate coefficient essentially equal to kcoll. In contrast, we identified an additional dynamical bottleneck, namely the cycloaddition barrier TS-4a or TS-4b (see Scheme 1 above), which we predict turns back some 91−97% of the reactive flux from HOZ formation, as we discussed above. Tables 8 and 9 summarize the product yields predicted on the basis of 109 simulations at 295 K with either 3a or 3b as the

Table 7. Room-Temperature Rate Coefficient (k) for the CH2OO + SO2 Reaction

a

k (10−11 cm3 molecule−1 s−1)

source

3.9 ± 0.7a,b 4.1 ± 0.3c,d 3.5 ± 0.3b,c 3.42 ± 0.42c,d 3.80 ± 0.04d,e 3.68 ± 0.02c,d ∼40c

Welz et al.18 (experiment) Sheps106 (experiment) Liu et al.107 (experiment) Stone et al.108 (experiment) Chhantyal-Pun et al.109 (experiment) this work (theory) Kurtén et al.23 (theory)

At 298 K. bStated uncertainty is a 95% confidence interval. cAt 295 K. Stated uncertainty is one standard deviation. eAt 293 K.

d

that taken by Barker and co-workers104 in their recent study of the HO + CO reaction. First, as described in the Computational Methods section above, we estimate that the rate coefficient for the formation of the CH2OO−SO2 dipole− dipole complex is kcap = 6.08 × 10−10 cm3 molecule−1 s−1 at 295 K. We then performed RRKM/ME simulations on a quantum chemical mechanism that included all of the reactions in Schemes 1−4 and the energies in boldface in Tables 1−4. We ran 106 simulations with 3a as the entrance channel, describing this species with a chemically activated initial distribution satisfying detailed balance.77 These simulations predict that the fraction of 3a that reverts to separated CH2OO and SO2 reactants is 0.9714 ± 0.0002 (one-standard-deviation uncertainty); that is, 0.0286 ± 0.0002 of 3a goes on to form 5a, which then undergoes the subsequent chemistry discussed above. Therefore, the rate coefficient for the reaction of CH2OO and SO2 via the endo pathway a is kendo = (0.0286 ± 0.0002)(6.08 × 10−10 cm3 molecule−1 s−1) = (1.74 ± 0.01) × 10−11 cm3 molecule−1 s−1. Following the same procedure, we predict that the fraction of 3b that reverts to separated CH2OO and SO2 reactants is 0.9076 ± 0.0002, leading to a rate coefficient for the exo pathway b of kexo = (5.62 ± 0.01) × 10−11 cm3 molecule−1 s−1. Following Greenwald et al.’s105 treatment of the four prereactive complexes in the isoprene + •OH reaction, we assumed an equal probability of forming complex 3a and complex 3b. That is, we assume that the dipole−dipole forces responsible for complex formation operate at large enough CH2OO−SO2 distances to make the relative orientations of the two moieties energetically irrelevant. Our assumption implies that exactly half of the reactive flux will enter each of the two channels, leading to an overall rate coefficient of k = (kendo + kexo)/2 = (3.68 ± 0.02) × 10−11 cm3 molecule−1 s−1 at 295 K. The predicted rate coefficients did not vary in a statistically significant way with pressure from 1 to 760 Torr. In addition, in all of our simulations of pathways a and b, once the HOZ was formed, there was no statistically significant reversion back to reactants. This finding is consistent with Figure S6 in the Supporting Information, which shows that at the average energy of the HOZ, ∼12 000 cm−1, the cycloreversion of HOZ back to the dipole−dipole complex has RRKM rate coefficients some 4 orders of magnitude lower than the cycloreversion of HOZ to final products HCHO + SO3. The rate coefficient predicted here falls within the experimental confidence intervals of Welz et al.,18 Liu et al.,107 and Stone et al.108 but is slightly lower than the experimental confidence intervals of Sheps106 and ChhantyalPun et al.109 Still, the accuracy of the present prediction is noteworthy. Moreover, our prediction of no statistically

Table 8. RRKM/Master Equation Relative Yields for the CH2OO + SO2 Reaction at 295 K Initiated by Formation of the Endo Dipole−Dipole Complex (3a)

overall closedshell open-shell stayed endo switched to exo

OCH2O• (17) + SO2 (2)

total

0.025 0.011

0.005 0.000

1.000 0.915

0.014 0.021 0.004

0.005 0.003 0.002

0.085 0.837 0.163

HCHO (8) + SO3 (9)

HC(O)OH (11) + SO2 (2)

0.970 0.904 0.066 0.813 0.157

•

entrance channel. Note that all yields in Tables 8 and 9 have been normalized to quantify the fate of only those CI + SO2 reactive events that lead to HOZ (5a or 5b) formation; the yields are thus relative, not absolute. The first observation to make is that the yields of all intermediates in the mechanism 10328


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The Journal of Physical Chemistry A Table 9. RRKM/Master Equation Relative Yields for the CH2OO + SO2 Reaction at 295 K Initiated by Formation of the Exo Dipole-dipole Complex (3b)

overall closed-shell open-shell stayed exo switched to endo

HCHO (8) + SO3 (9)

HC(O)OH (11) + SO2 (2)

0.973 0.914 0.059 0.705 0.268

0.022 0.010 0.012 0.019 0.003

Table 10. Overall RRKM/Master Equation Yields for the CH2OO + SO2 Reaction at 295 Ka category

•

OCH2O• (17) + SO2 (2)

total

0.005 0.000 0.005 0.003 0.002

1.000 0.924 0.076 0.727 0.273

all closed-shell pathways all open-shell pathways closed-shell HCHO + SO3 open-shell HCHO + SO3 total HOS(O)OCHO HC(O)OH from HOS(O) OCHO total HCHO + SO3 total HC(O)OH + SO2 total •OCH2O• + SO2

[the dipole−dipole complex (3a and 3b, Scheme 1), the HOZ (5a and 5b, Schemes 1 and 2), the 1,5-bis(oxy) diradicals (13a and 13b, Schemes 2 and 3), the formyl sulfurous anhydride (19a and 19b, Schemes 3 and 4), and the dioxathietane (21, Schemes 3 and 4)] are zero. This reflects the high degree of chemical activation in this reaction. As shown in Figure S6 in the Supporting Information, at a HOZ energy of ∼12 000 cm−1, the specific rate coefficient for cycloreversion to HCHO + SO3 is ∼2 × 1012 s−1, 2 orders of magnitude higher than the collision frequency at 760 Torr, which is ∼1 × 1010 s−1. Only at pressures of 106 Torr and higher does collisional stabilization of the HOZ and other intermediates become a significant outcome. The second observation is that there is no statistically significant variation in the yields of any final products with pressure from 1 Torr up to 760 Torr. Our simulations predict that of the ∼5% of CH2OO + SO2 complexes that go on to subsequent reaction, 97% of them form HCHO and SO3, and the remaining 3% of them regenerate SO2 and form HC(O)OH either via direct means or via the •OCH2O• intermediate (17). The very high predicted yield of SO3 is consistent with experimental studies of this reaction.8−14,16 More than 90% of the reactive flux moves irreversibly through the closed-shell transition structures, TS-7a, TS-7b, TS-10a, and TS-10b, shown in Scheme 2 above. The fact that 90−91% of the reaction passes through TS-7a and TS-7b to form HCHO + SO3 is unsurprising given the energetics in Table 2 above; each conformer of the HOZ cycloreversion TS constitutes the lowest-barrier decomposition pathway for the HOZ. A final issue we can address on the basis of the data in Tables 8 and 9 is the extent of endo/exo conformational interconversion. Table 8 indicates that 84% of the CH2OO and SO2 that initiate reaction by formation of the endo dipole− dipole complex 3a retains the endo stereochemistry until decomposition via one of the three exit channels. Compared to the HCHO + SO3 and the HC(O)OH + SO2 exit channels, a significantly higher proportion of the •OCH2O• + SO2 product channel is formed from the exo 1,5-bis(oxy) diradical 13b (Scheme 3). We attribute this to the miniscule barrier of 0.30 kcal mol−1 required for the endo diradical 13a to rotate to the exo form (Table 3). We see similar trends in Table 9. Table 10 summarizes our aggregate predictions for the product yields of the CH2OO + SO2 reaction at 295 K under different sets of assumptions and compares the current results with the previous results of Vereecken et al.26 We aggregate the endo and exo simulation results by weighting the product yields by the branching ratios, Y, given by the predicted rate coefficients discussed above: Yendo = kendo/(kendo + kexo) = 0.236 and Yexo = kexo/(kendo + kexo) = 0.764. Note that even though almost all of the endo structures are lower in energy

case 1b

case 2c

case 3d

past work26

0.923 0.077 0.912 0.061 0.000 0.012

0.922 0.078 0.921 0.061 0.000 0.013

0.967 0.033 0.956 0.028 0.000 0.003

0 1.00 0 0.68 0.15 0

0.973 0.023 0.005

0.982 0.013 0.005

0.984 0.014 0.002

0.68 0 0.17

a Yields of final products in boldface. bSame assumptions as those used to generate the results in Tables 8 and 9. cChange the relative energies of TS-10a and TS-10b to the CCSD(T)/aug-cc-pVTZ//M06-2X/ aug-cc-pVTZ values. dUsing CBS-Q3 open-shell singlet energies for all diradical species in the mechanism.

than the corresponding exo structures due to the hyperconjugative interactions discussed above, the avoidance of steric repulsions by the exo conformer of the cycloaddition transition structure TS-4b (Scheme 1 and Table 1) confers upon the exo entrance channel a kinetic preference of roughly 3:1. We base the predictions in Case 1 upon all of the reactions and energies shown in Schemes 1−4. The most obvious discrepancy between the Case 1 predictions and the previous work of Vereecken et al.26 is that we predict that over 90% of the reactive flux goes through closed-shell pathways, whereas Vereecken et al. predict that all of the HOZ formed at the start of the reaction undergoes homolysis (via TS-12a, Scheme 2) to initiate diradical chemistry. The ∼12 kcal mol−1 energy difference (predicted with the CCSD(T)/aug-cc-pVTZ model chemistry; Table 2) in the open-shell O−O homolysis TS-12a and the closed-shell 1,2-H shift TS TS-10b (Vereecken et al. did not include TS-10a in their calculations) makes the latter pathway negligible. Nevertheless, we agree with Vereecken et al. that the overall yield of HCHO + SO3 is at least ∼70%. Though we attribute most of the SO3 formation to closed-shell cycloreversion (via TS-7a and TS-7b, Scheme 2), Vereecken et al. attribute all of the SO3 formation to β-scission of the 1,5-(bis)oxy diradical (via TS-15a, Scheme 3 and Table 3). There are also significant differences in the predictions for the open-shell pathways. First, we estimate that only ∼1% of the HOZ forms HOS(O)OCHO (19) and that all of this species decomposes to HC(O)OH and SO2. The previous study of Vereecken et al.26 predicts a HOS(O)OCHO of 15% and that all of it will be collisionally stabilized under atmospheric conditions. Second, although the previous study predicts roughly equal yields of HOS(O)OCHO and •OCH2O• (17), we predict that the yield of the HOS(O)OCHO channel is more than twice as large. This is due to the far lower barriers (TS-18a and TS-18b) against formation of the two conformers of HOS(O)OCHO (19a and 19b) compared to the barriers (TS-16a and TS-16b) against S−O bond scission (Scheme 3). Although we predict the yield of the 1,3-(bis)oxy diradical 17 to be only ∼0.5%, its statistically significant nonzero value provides an important point of agreement with the early experimental work of Hatakeyama et al.,11 who observed that the reaction of doubly isotopically labeled CI (that is, CH218O18O) with unlabeled SO2 resulted in the formation of formic acid with either the carbonyl oxygen or the protonated 10329


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The Journal of Physical Chemistry A Scheme 7. Pathways from Doubly Isotopically-Labeled CI to Singly Isotopically Labeled Formic Acid

oxygen isotopically labeled. Scheme 7 shows how the formation and isomerization of 17 can account for the observed isotopic properties of HC(O)OH. The key is that 17 can undergo a 1,2-hydrogen shift to either the 16O or the 18O atom to form formic acid. There is some evidence in the literature111 that CBS-QB3 underestimates hydrogen-shift barriers and we indeed find in Table 2 that the CCSD(T)/aug-cc-pVTZ energies for TS-10a and TS-10b are ∼3 kcal mol−1 higher than the corresponding CBS-QB3 energies. The Case 2 simulations explore the impact of using the CCSD(T) energies for TS-10a and TS-10b; all other quantum chemical parameters are the same as in Case 1. Increasing the energies of the TSs leading directly to HC(O)OH + SO2 decreases the HC(O)OH yield by 1% and increases the production of HCHO + SO3 via the closed-shell cycloreversion pathways (TS-7a and TS-7b) by 1%. The predicted decrease in HC(O)OH yield is due to the complete shutdown of the closed-shell pathway to HC(O)OH + SO2 formation. The Case 2 simulations therefore confirm the earlier prediction of Vereecken et al.26 that, on the basis of the CCSD(T)/aug-cc-pVTZ barriers, direct rearrangement of the HOZ to HC(O)OH + SO2 is negligible. In Case 3, we explore the impact of using purely CBS-QB3 energies for all of the structures in the mechanism: for openshell singlet species, we used the CBS-QB3 composite energies based on broken-spin-symmetry single-point calculations instead of correcting CBS-QB3 triplet energies with the singlet−triplet gaps determined from the EOM-CCSD(dT) spin-flip calculations. In spite of some significant changes in the relative energies of open-shell singlet species (Table 3), the results of the Case 3 simulations vary by at most 4% from the Case 1 simulations. This gives us some confidence in using CBS-QB3 as the exclusive source of relative energies for our dimethyl CI + SO2 reaction simulations below. Cases 1 and 2 constitute the most accurate predictions of the branching ratios for the CH2OO + SO2 reaction in that both cases reflect the complete reaction mechanism presented in Schemes 1−4 and the more rigorous SF-derived energies for open-shell singlet species. On the most important issue, the large extent of CI oxidation by SO2, the current simulation results are consistent with the previous results of Vereecken et al.26 However, we differ significantly from the previous study in both the mechanism by which we account for the high HCHO + SO3 yield and in the predicted yields of other exit channels. Statistical Rate Theory Results for the (CH3)2COO + SO2 Reaction. Table 11 presents our RRKM/ME predictions for the (CH3)2COO + SO2 reaction and compares them to the previous 4 Torr and 1 atm predictions of Vereecken et al.26 Our simulations include all of the reactions depicted in Schemes 5 and 6 and the CBS-QB3 energetics in Tables 5 and 6. For the dimethyl CI, we did not characterize the structures analogous

Table 11. Overall RRKM/Master Equation Yields for the (CH3)2COO + SO2 Reaction at 295 Ka category all closed-shell pathways all open-shell pathways closed-shell CH3C(O)CH3 + SO3 open-shell CH3C(O)CH3 + SO3 total CH3C(O)CH3 + SO3 total CH3CO(O)CH3 + SO2 reactants total HOZ

this workb

past work26 4 Torr

past work26 760 Torr

0.721 0.279 0.683

0.17 0.83 0

0.97 0.03 0

0.279

0.83

0.03

0.962 0.025 0.013 0.000

0.83 0 0 0.17

0.03 0 0 0.97

a Yields of final products in boldface. bNo statistically significant variation in yields from 1 Torr to 1 atm.

to those in Scheme 1. Thus, we have no way of estimating the branching ratio between the endo and exo pathways. However, the endo and exo product yields differed by less than 1% in all cases. Consequently, we simply report the average of the results for simulations initiated by the endo (5a-DM) and the exo (5b-DM) conformers of the heteroozonides. The overall product yields for the dimethyl CI + SO2 system (Table 11) are similar to the results for the parent CI system (Tables 8−10). Oxidation, in which SO2 is converted to SO3 and the CI is converted to a carbonyl, proceeds in 96% yield. Isomerization of the CI to the methyl ester with concomitant regeneration of the SO2, and reversion of the SOZ to the CI + SO2 reactants, account for the remaining 4% of the reaction. Open-shell pathways account for almost 30% of the total reactive flux for the dimethyl system (Table 11) but only 8% of the total reactive flux in the parent system (Table 10). We attribute this to the difference in energetics: in the dimethyl system, peroxy bond homolysis (via TS-12a-DM and TS-12bDM) has barriers virtually identical to those of closed-shell cycloreversion (via TS-7a-DM and TS-7b-DM) (Scheme 5). The higher specific rate coefficients for cycloreversion (see Figure S8 in the Supporting Information) are due to the greater looseness of the cycloreversion transition structures. Finally, our simulations predict no collisional stabilization of any reactive intermediate and no variation in exit channel yield for pressures ranging from 1 Torr to 1 atm. At the average energy of the nascent HOZ 7a-DM, ∼11 000 cm−1, the specific rate coefficient for cycloreversion is ∼5 × 1010 s−1 (Figure S8), only a factor of 5 higher than the 760 Torr collision frequency of ∼1 × 1010 s−1. The nascent parent HOZ is significantly more chemically activated, as discussed above. Significant collisional stabilization of the dimethyl HOZ is predicted for pressures of 104 Torr and higher, whereas the parent HOZ is predicted to undergo significant collisional stabilization for pressures of 106 Torr and higher. 10330


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The Journal of Physical Chemistry A In contrast, the earlier simulations of Vereecken et al.26 predicted a pressure dependence at much lower pressures (Table 11). At 4 Torr, the previous study predicted a high yield (83%) of CH3C(O)CH3 + SO3, which is consistent with the current result. However, the earlier study attributed all SO3 formation to the decomposition of the 1,5-(bis)oxy diradical 13a-DM (Scheme 6), whereas we identify the direct decomposition of the HOZ as the major SO3 formation pathway. At 760 Torr, Vereecken et al. predicted that almost 100% of the HOZ undergoes collisional stabilization, whereas we predict no stabilization of the HOZ until background pressure has reached 104 Torr. The qualitative difference in simulation results is a consequence of fundamental differences in the quantum chemical predictions: the previous study26 identified only one reaction pathway for the HOZ, peroxy bond homolysis (TS-12a-DM), with a TS energy 12 kcal mol−1 below the combined energies of the original dimethyl CI + SO2 reactants (Table 5). In contrast, we identify multiple reaction pathway for the HOZ with TS energies as much as 21 kcal mol−1 below the combined energies of the original dimethyl CI + SO2 reactants (Scheme 5). The quantitative decomposition of the dimethyl HOZ on the nanosecond time scale predicted by the current RRKM/ME simulations are consistent with the recent experimental results of Berndt et al.16 Substantial production of collisionally stabilized HOZ is consistent with Berndt et al.’s study only if a bimolecular reaction, most likely hydrolysis, converts the HOZ to SO3 on the second (or faster) time scale. This is possible, but there is no experimental or theoretical estimate of the rate coefficient for such a reaction.

Scheme 8. Heteroozonides Formed in the Methyl CI + SO2 Reactiona

■

CONCLUSIONS AND FUTURE WORK The calculations reported in this paper successfully account for four experimental observations regarding the CI + SO2 reaction: the room-temperature rate coefficient for CH2OO + SO2 of (3−4) × 10−11 cm3 molecule−1 s−1,18,106−109 oxygenatom exchange between the CI and the SO2 as evidenced by changes in isotopic composition,11 the near-unity yield of SO3 from the reaction of both the parent15 and the dimethyl16 CI, and the reaction of the dimethyl CI’s being dominated by prompt decomposition of the HOZ adduct.16 However, a variety of mechanistic challenges remain. For the parent CI + SO2 reaction, Chhantyal-Pun et al.109 observed a substantial increase in the effective rate coefficient (from ∼4 to ∼7 × 10−11 cm3 molecule−1 s−1) at low SO2 concentrations. These workers were able to fit their pseudofirst-order rate coefficient data by invoking a reversible isomerization of the CH2OO that may involve intersystem crossing (ISC) by one or more of the diradical intermediates in Scheme 3 above. For example, Vereecken et al.26 found that the 1,5-bis(oxy) diradical 13a has a singlet−triplet splitting of only ∼0.1 kcal mol−1. We likewise found in our spin-flip calculations that diradical 13b has a singlet−triplet splitting of ∼0.2 kcal mol−1 (see Table S2 in the Supporting Information). Quantum chemical calculations of ISC rates and stationary points on the triplet energy surface are necessary to account for ChhantyalPun et al.’s kinetic data. The requisite mathematics for the treatment of spin-hopping kinetics has been implemented in the MESMER software package112 and applied to systems such as the ionospheric reaction of singlet molecular oxygen with metal atoms.113,114 Unlike both the parent and the dimethyl CI, the methyl CI, or acetaldehyde oxide, has syn and anti forms with distinct

Relative energies (0 K, kcal mol−1) from B3LYP/6-31+G(d,p) calculations in blue. a

reactivities and atmospheric impacts.115 However, as Scheme 8 shows, reaction of the methyl CI with SO2 effaces the syn/anti stereochemical distinction. Specifically, our preliminary B3LYP/6-31+G(d,p) calculations predict pseudorotation transition structures, TS-6ab-M and TS-6 cd-M, that are only 3−6 kcal mol−1 higher in energy that the heteroozonide conformers formed in the methyl CI + SO2 reaction. Therefore, there should be facile interconversion between the anti-derived 5a-M and 5c-M and the syn-derived 5b-M and 5d-M. However, because pseudorotation involves changing the axial/equatorial disposition of both the oxo and the methyl substituents, it is impossible to convert between 5a-M and 5c-M or between 5b-M and 5d-M except via the much higher-barrier process of inversion at either the sulfur or carbon atom of the HOZ ring. Calculations in progress are characterizing the closed-shell and open-shell singlet reactivity pathways for all of the HOZ conformers in Scheme 8. Although we predict that 100% of the HOZ formed from the dimethyl CI + SO2 reaction will react while still chemically activated at pressures up to 104 Torr, it is doubtlessly true that a significant fraction of the HOZ formed in the reaction of SO2 with larger CIs (e.g., those formed in terpene ozonolysis) will 10331


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Baeyer−Villager reaction and Professor Anna I. Krylov (University of Southern California) for technical assistance with the treatment of singlet diradicals.

be collisionally stabilized under atmospheric conditions. Like the SCI, the stabilized HOZ will be prone to bimolecular reactions with atmospheric species like H2O and SO2. Moreover, the experimental and computational study by Glowacki et al.116 of the acetylene + •OH reaction suggests that even chemically activated HOZ may be intercepted by bimolecular reaction partners before being completely thermalized. Characterizing both the mechanism and rate constants for bimolecular HOZ reactions should therefore be a high priority. Given that the HOZ is an adduct of the acid anhydride SO2 and a carbonyl oxide which, in its anti conformation, readily hydrates to the α-hydroxy hydroperoxide,117 we anticipate that the water reaction will be especially important. We intend to initiate calculations on water reaction pathways in the near future. Finally, the very recent experimental work by Huang et al.80 indicates a strong pressure dependence for the rate coefficient of the dimethyl CI + SO2 reaction from 10 to 770 Torr. Neither the present work nor the earlier simulations of Vereecken et al.26 can account for the observed falloff behavior. A successful theoretical account of these new observations will likely require characterizing the formation and cycloaddition of dipole−dipole complexes of the dimethyl CI and the SO2.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b06565. Additional figures (IRC calculations, configurations, RRKM specific rate coefficients, semilog plot of the rate coefficient vs bath gas pressure) and tables of relative energies, optimized coordinates, electronic energies, and zero-point vibrational energies of all of the stationary points considered in this manuscript (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*Voice: (651) 696-6768. Fax: (651) 696-6432. E-mail: [email protected]. Present Addresses †

QB3 Institute, University of California, Berkeley, CA 947203220. ‡ Department of Chemistry, University of Illinois at Urbana Champaign, Urbana, IL 61801-3364. § Department of Medicinal Chemistry, University of Minnesota, Minneapolis, MN 55414. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge current support by the National Science Foundation (CHE-1412622) and past support from the Camille and Henry Dreyfus Foundation, the donors of the American Chemical Society’s Petroleum Research Fund (44764-B6), and the Violet Olson Beltmann Fund 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). K.T.K. thanks Professor Ronald G. Brisbois (Macalester College) for mechanistic insights into the 10332


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