MRCISD Studies of the Dissociation of Vinylhydroperoxide

May 28, 2012 - In contrast to some previous studies, which claim the reaction has no saddle .... However, later studies by Bozzelli and Sheng(13) and ...
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MRCISD Studies of the Dissociation of Vinylhydroperoxide, CH2CHOOH: There Is a Saddle Point Theo Kurtén*,† and Neil M. Donahue‡ †

Laboratory of Physical Chemistry, University of Helsinki, P.O. BOX 55, Helsinki FI-00014, Finland Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890, United States

‡

S Supporting Information *

ABSTRACT: Multireference ab initio methods are used to investigate the dissociation of vinylhydroperoxide CH2CHOOH into vinyl oxide and hydroxide radicals. In contrast to some previous studies, which claim the reaction has no saddle point, our calculations confirm that the dissociation is associated with a kinetic barrier (transition state). We further propose the existence of a hitherto undiscovered radical−radical complex on the reaction path. The computed reaction energetics are used to estimate VHP dissociation rates, and the results are discussed in the context of atmospheric ozonolysis pathways. Qualitative aspects of the dissociation of larger, substituted vinylhydroperoxides are also discussed.

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INTRODUCTION The oxidation of unsaturated hydrocarbons by ozone is one of the most important, yet least understood, aspects of the atmospheric component of the carbon cycle. Oxidation of terpenes (by ozone and hydroxyl) is likely one of the largest sources of secondary organic aerosols (SOA), with major implications for present and future climate.1 The ozonolysis reaction is strongly exothermic, and proceeds via several intermediate steps, leading to a complex and variable product distribution even for relatively simple reactant alkenes. The short lifetime and high initial energy of the key intermediate species makes experimental characterization and separation of the individual reaction steps difficult, while the complicated electronic structure of ozone and, especially, several of the reaction intermediates decrease the reliability of standard single-reference computational chemistry methods. Alkene ozonolysis is currently thought to proceed as follows.2 First, the addition of ozone to a double bond leads to the formation of a five-ringed primary ozonide (POZ). The POZ very rapidly decomposes into a carbonyl species and a carbonyl oxide, also known as the Criegee Intermediate (CI). The CI has mixed biradical and zwitterionic characteristics, and its existence was postulated already in 1944.3 However, it took over 60 years from this to the first claimed direct experimental observation of the CI,4 illustrating the challenges involved in ozonolysis studies. The CI is known to be challenging for electronic structure methods, and high levels of theory are needed to treat its structure and energetics correctly.5,6 Most of the CIs produced in the POZ decomposition are vibrationally excited.2 Depending on the parent alkene and the reaction conditions (mainly CI carbon number and pressure), these excited CIs may either decompose or be collisionally stabilized to form stabilized CI (sCI). The sCI in turn may react further either via unimolecular or bimolecular routes, with the ratio depending on reactant concentrations as well as the (highly uncertain) sCI thermal lifetime. © 2012 American Chemical Society

One central and much-studied aspect of alkene ozonolysis reactions is OH formation. This link between two of the three major atmospheric oxidants (the third being NO3) is important, as it is one of the main routes by which OH can be formed at night, when direct photochemical sources are absent. The formation of OH radicals has been observed in the ozonolysis of a large variety of alkenes, with the precise yield (number of OH radicals produced per consumed O3 molecule) varying widely.2 OH yields depend on both the carbon number and location of the double bond of alkene as well as the conditions, such as pressure. The mechanism of OH formation from ozonolysis is only partially understood; suggested sources include unimolecular decomposition of both vibrationally excited and thermalized sCIs, as well as more complicated mechanisms involving additional intermediates, such as e.g., hot acid routes7 (where the OH is formed via the dissociation of a vibrationally excited carboxylic acid). A key feature of CI chemisty is the presence of two distinct isomers. There appears to be sufficient zwitterionic content in the CI ground-state wave function to give the C−O bond partial π-bonding character and thus prevent rotation of the terminal oxygen of the carbonyl oxide. If this terminal oxygen faces an H atom, the CI conformer is known as anti, while if the oxygen faces an R group, the conformer is known as syn. The subsequent unimolecular behaviors of the CI conformers are quite different, with the anti-CI favoring ring closure to a dioxirane but the syn-CI favoring H-atom abstraction from the adjacent R group (if this is possible) and thus formation of a vinyl hydroperoxide (VHP, with a general structure R1R2C C(R3)−OOH where R1‑3 are hydrogens or alkyl groups).8 Homolysis of the O−OH bond in the VHP is thought to be the major direct source of OH in ozonolysis.9 Received: March 15, 2012 Revised: May 14, 2012 Published: May 28, 2012 6823

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The Journal of Physical Chemistry A VHP homolysis is generally assumed to be barrierless (except for the O−O dissociation energy), with no distinct enthalpic transition state. Because the energy of the dissociation products is well below the energy of the transition state separating the syn-CI from the VHP, all previous treatments of the reaction dynamics for these systems have assumed that the O−O dissociation is far too rapid for collisional stabilization of the VHP to be important.6,7,10 They have thus equated syn-CI isomerization with OH formation. Recently, Drozd et al.11 studied the pressure dependence of sCI formation from 2,3-dimethyl-2-butene ozonolysis by monitoring the concentration of a CI scavenger, hexafluoroacetone, and its reaction product with the sCI. Comparing sCI formation and OH yields at different pressures (10−1000 Torr) and time scales (from milliseconds to hundreds of milliseconds), they concluded that OH formation from syn-CI proceeds via at least two stabilizable intermediates, one of which is the sCI. The experimental evidence suggests that prompt OH production from ozonolysis is quenched much more easily than sCI is formed and thus that an intermediate following the sCI in the reaction sequence is involved in the collisional stabilization. The only candidate for this stabilization is the VHP. The kinetics of VHP decomposition are currently not well understood. One central, and as yet open, question is whether or not the decomposition reaction is associated with a transition state. Even a shallow (low-barrier) transition state would affect the decomposition rate constant significantly, and make a crucial difference to the interpretation of experimental results: unimolecular A-factors for loose bond scissions are very high, whereas A-factors for tighter transition states with a welldefined saddle point can be much lower. The resulting slower unimolecular rate constants would increase the intermediate lifetimes, potentially enabling collisional stabilization. For example, the suggested mechanism of Drozd et al. can not easily be reconciled with a barrierless VHP dissociation, as suggested, e.g., by Kuwata et al.7 Richardson12 studied the decomposition of the simplest vinyl hydroperoxide CH2CH−OOH at the MP2/6-31G(d) level, with MP4/6-31G(d) energy corrections. They found a transition state located 26 kcal/mol above the reactants in enthalpy. However, later studies by Bozzelli and Sheng13 and Kuwata et al. 7 have found (or assumed) the VHP decomposition to be barrierless, i.e., lacking a transition state. It is unclear from their description to which degree Kuwata et al., who used quite high-level single-reference methods CBSQB3 and CBS-APNO, actually searched for a transition state before stating their prediction that the “dissociation proceeds without an enthalpic barrier along the reaction coordinate.” Vinyl hydroperoxide dissociation is a complicated problem to treat using computational chemistry methods. In the reaction, the singlet hydroperoxide is converted into two doublet radicals, causing significant problems with spin contamination. Also, the product vinoxy radical is stabilized by a resonance state between the CH2 CH−O* and C*H2−CHO configurations (where the asterisk * indicates the radical center), the latter being dominant. Single-reference methods are therefore not well suited for accurate investigations of this system. In this study, we have used the multireference methods CASSCF and MRCISD to study vinylhydroperoxide dissociation and to conclusively prove whether or not the reaction has a well-defined transition-state saddle point.

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COMPUTATIONAL DETAILS

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RESULTS AND DISCUSSION

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B3LYP,14,15 MP2,16 CCSD,17 CBS-QB3,18 W1BD,19 and CASSCF(4,4)20 IRC (Intrinsic Reaction Coordinate)21 calculations (together the associated initial RHF and CISD calculations to obtain input orbitals) were performed with the Gaussian09 program, revision B.01.22 All other CASSCF and MRCI23−26 calculations (including the initial RHF, UHF, and CISD calculations to obtain input orbitals) were performed using Molpro,27 versions 2009.1 and 2010.1 (taking care to always compare absolute values computed with the same program version). Default energy and geometry convergence criteria were used unless otherwise specified. Enthalpies and free energies were computed using the standard harmonic oscillator−rigid rotor approximations. Geometries, vibrations, and orbitals were viewed and drawn using Molden.28

Initial Single-Reference Calculations. We began by recomputing the VHP reactant and transitionn-state structures presented by Richardson.12 We next verified that their MP2/631G(d)29 transition states were not artifacts of either the small basis set or the limited degree of dynamic correlation by reoptimizing the structures at the MP2/aug-cc-pVTZ30 and CCSD/6-31G(d) levels. Reasonably similar transition-state structures were found at both these levels, with the effects of the basis-set increase and improved description of dynamic correlation acting in opposite directions on the O−O distance and vibrational frequency. The optimized transition-state O−O distances were 2.06 Å, 2.04 Å, and 2.13 Å, and the imaginary vibrational frequencies 350i cm−1, 306i cm−1, and 485i cm−1, at the MP2/6-31G(d), MP2/aug-cc-pVTZ, and CCSD/6-31G(d) levels, respectively. It is important to note that the transition-state structure presented by Richardson in reality corresponds to spinrestricted MP2 (RMP2) rather than spin-unrestricted MP2 (UMP2). Unfortunately, simply specifying, e.g., UMP2 in the Gaussian program is not always enough to obtain a spinunrestricted wave function for a singlet system; sometimes (such as in this case), the spin symmetry must explicitly be broken (e.g., using the Guess=Mix keyword) before the true spin-unrestricted wave function is obtained. (Note that neither the reactant VHP, the transition state, nor the product complex discussed below has any spatial symmetry. All belong to point group C1, and any discussion of symmetry breaking in this study thus refers solely to spin symmetry.) This spin symmetry breaking had no effect on the geometry or energy of the reactant vinyl hydroperoxide (the optimized reactant had zero spin contamination regardless of the type of input orbital guess) but resulted in a very different structure for the transition state. At the MP2/6-31G(d) level, allowing the wave function to become spin-unrestricted by forcing the initial guess to break spin symmetry (and reoptimizing) decreased the transition state O−O bond length by 0.3 Å to 1.76 Å, while the imaginary vibrational frequency increased from 350i cm−1 to 798i cm−1. The ⟨S2⟩ value of this structure is 1.0173, indicating that it is significantly spin contaminated, presumably due to a nearby triplet state. Curiously, while the spin-unrestricted transition state is much lower in energy (by over 76 kcal/mol) than the spin-restricted one at the HF/6-31G(d) level, the MP2/6-31G(d) energy of the spin-unrestricted transition state is actually, and counterintuitively, about 10 kcal/mol higher than that of the spin-restricted transition state. This pattern 6824

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unrestricted B3LYP calculations. The latter were found to lead to a significantly lower energy and were therefore used in subsequent steps. The UB3LYP/aug-cc-pVTZ transition state resembled the RMP2/6-31G(d) structure presented by Richardson12 fairly closely, lying 18 kcal/mol above the VHP reactant in energy, with a O−O distance of 1.99 Å and an imaginary frequency of 278i cm−1. The spin contamination of this structure was smaller than for the spin-unrestricted variants of the wave function-based methods, though still quite significant at ⟨S2⟩ = 0.7421. Next, we performed an IRC calculation on the UB3LYP transition state. On the reactant side, the IRC connected to the VHP minimum-energy geometry, as expected. On the product side, the IRC path did not dissociate to the free products (as assumed, e.g., by Richardson) but instead led via a rotation of the OH moiety to a hydrogen-bonded CH2CHO···HO radical−radical complex. See Figure 1 for schematic structures of the stationary points.

persisted after increasing the basis-set size to aug-cc-pVTZ, and after reoptimizing the RMP2 − UMP2 difference was actually larger with the larger basis set. (See Table 1 for relative energies computed at various single-reference levels.) Table 1. Electronic Energies (in kcal/mol, Not Including Zero-Point or Thermal Corrections) Given by Various Single-Reference Methods for the Vinylhydroperoxide Dissociation Reactiona

RMP2/6-31G(d) UMP2/6-31G(d) RMP2/aug-cc-pVTZ UMP2/aug-cc-pVTZ RCCSD/6-31G(d) RCCSD/6-31G(d)//RMP 2/6-31G(d) UCCSD/6-31G(d)// UMP2/6-31G(d) RB3LYP/aug-cc-pVTZ UB3LYP/aug-cc-pVTZ UW1BD

CH2CHOOH ⇒ [CH2CHOOH]‡

CH2CHOOH ⇒ CH2CHO + OH

44.20 33.89 48.15 31.65 40.63 40.61

31.53 31.53 35.79 35.79 17.09 17.37

18.82

17.37

37.24 18.12 26.06

20.63 20.63 26.10

a

CH 2 CHOOH denotes the minimum-energy reactant, while [CH2CHOOH]‡ denotes the transition state. The R and U indexes in front of the methods denote whether or not the spin symmetry of the transition-state wavefunction was broken in the initial guess. Breaking the spin symmetry had no effect on the minimum-energy structure of the reactant and was done by default for the free radical products since they have unpaired electrons. For this reason, the U and R values in the second column are identical.

Figure 1. Structures of the vinyl hydroperoxide reactant (left), transition state (center), and product complex (right). The most important bond lengths (in Ångströ m) are indicated in gray (UB3LYP/aug-cc-pVTZ) and blue (MRCISD(4,4)/cc-pVTZ) text. Color coding of atoms: brown, carbon; red, oxygen; and white, hydrogen.

We also tried to find a UCCSD/6-31G(d) transition state using initial force constants from the spin-unrestricted MP2 transition state, but this led to a system with no less than 14 imaginary frequencies, despite being significantly lower in energy than the spin-restricted optimized RCCSD/6-31G(d) transition state. Because of the expense of computing CCSD frequencies, we did not pursue this particular case further. As can be seen from Table 1, the different single-reference methods predict very different transition-state energies (barrier heights), and the computed energies also depend strongly on whether the spin symmetry of the transition state wave function is broken or not. The T1 diagnostics computed at the CCSD level are large, around 0.0279 for the spin-restricted and 0.0534 for the spinunrestricted MP2 transition-state geometries, respectively, indicating that all the above-mentioned single-reference energies are inherently unreliable since the system has significant multireference character. The T1 diagnostic for the reactant VHP (at the MP2/6-31G(d) geometry) is only 0.0137, indicating that single-reference calculations on this system are likely fairly reliable. Thus, previously computed9 high-level single-reference reaction energies for the overall reaction CH2CHOOH → CH2CHO + OH are likely to be reasonably trustworthy, despite the severe problems associated with the transition states. In order to obtain slightly better input structures for our final multireference studies, we also recalculated the transition-state structures at the B3LYP/aug-cc-pVTZ level, as DFT methods are sometimes found to be less susceptible to errors related to static correlation than single-reference wave function-based methods. We performed both spin-restricted and spin-

At the UB3LYP/aug-cc-pVTZ level, the binding energy of this complex was 5.9 kcal/mol with respect to the free products, but it should be noted that spin contamination is very large, (⟨S2⟩ = 1.0171), probably due to the degeneracy or neardegeneracy of the singlet and triplet states caused by the large separation of the two radical centers. In order to obtain quantitatively reliable reference energies for the reactant and the product radicals, we further performed W1BD calculations on these, as well as on the transition state and product complex. W1BD is a highly accurate and computationally demanding multistep thermochemical procedure, which should19 give an accuracy of about ±0.6 kcal/mol for the reactant and the free products. Energies for the transition state and product complex are also given for comparison, though we caution that, for these, the accuracy of W1BD is likely much worse due to their strong multireference character. The spin-unrestricted transition state was found to be around 9 kcal/mol lower than the spinrestricted one at the W1BD level, and the presented values thus correspond to the unrestricted system. The reaction energetics given by the various single-reference methods are shown in Table 1. Selection of the Active Space. A number of test calculations on the reactant, transition state, and product complex geometries obtained from previous studies and from our UB3LYP calculations were used to determine the active space required for subsequent multireference calculations. These test calculations included both UHF natural orbitals and CISD natural orbitals with various basis sets (from STO6825

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3G to cc-pVTZ), which were ordered by occupation number and visualized using Molden. All these tests yielded the same result: precisely four orbitals for all the three stationary points in the system have UHF or CI natural occupation numbers that differ significantly (by more than about 0.03) from 2.00 or 0.00. At the reactant geometry, two of these orbitals are occupied (occupation number close to 2.00) and two are virtual (occupation number close to 0.00). The two occupied orbitals with fractional population numbers correspond to the bonding σ orbital of the O−O peroxide bond and the bonding π-orbital of the CC bond, while the virtual orbitals correspond to their antibonding pairs. As the O−O bond is stretched toward the transition-state geometry, the fractionally occupied bonding πorbital is first delocalized over the C···C···O system and then increasingly localized on the CO bond, as expected from previous results and chemical intuition. Simultaneously, the occupation numbers of the original bonding and antibonding σorbitals approach each other, as they begin to correspond to the two separated radical centers at the OH oxygen and the distal carbon atom. At the product complex geometry, one orbital is doubly occupied, two orbitals are singly occupied (occupation number close to 1.00) and one is virtual. (The population numbers indicate, and subsequent test multistate CASSCF and MRCI calculations prove, that the singlet and triplet states have become degenerate at the product complex geometry. This degeneracy helps explain why single-reference methods have failed to treat the VHP dissociation reaction accurately, and why huge spin contamination values are observed in unrestricted single-reference calculations on the system.) Electron density maps (at the 0.1 atomic unit isosurface) of the four active space orbitals for all three stationary points are displayed in Figure 2. Different initial geometries and different methods result in numerically slightly different orbitals, but the overall shape and character (e.g., σ/π, bonding/antibonding) was the same for all approaches tested in this study. On the basis of these test calculations, as well as literature recommendations, the following doctrine was used to generate input orbitals for all subsequent calculations in this study. First, an RHF/STO-3G calculation was performed, followed by a CISD/STO-3G calculation yielding CISD natural orbitals. These were then used as input for a CASSCF(4,4)/STO-3G calculation, where the four orbitals in the active space corresponded to the CISD natural orbitals with occupation numbers differing the most from 2.00 or 0.00. The CASSCF(4,4)/STO-3G orbitals were then used as input guess for a CASSCF(4,4)/6-31G(d) calculation, which was then further used as an input guess for the CASSCF(4,4)/cc-pVTZ calculation. Test calculations show that the difference between the orbitals generated by this procedure and those obtained directly from CASSCF(4,4)/cc-pVTZ using CISD/cc-pVTZ natural orbitals are quite small, but on the basis of literature recommendations,31 we adopted the former procedure as more rigorously reliable. CASSCF and MRCISD Calculations. The stationary points obtained at the B3LYP/aug-cc-pVTZ level were next reoptimized at the MRCISD(4,4)/cc-pVTZ level, with the orbitals generated as described above. The optimized structures are shown in Figure 1. The final MRCISD orbitals look essentially identical to the CISD natural orbitals shown in Figure 2; the main difference is that the population numbers of the MRCISD orbitals are further from 2.00 or 0.00 and also closer to each other (as they are not as constrained by the single-reference requirement of normal CISD). Most notably,

Figure 2. Electron density isosurfaces (0.1 atomic units) of the four orbitals used in the active spaces of the CASSCF(4,4) and MRCISD(4,4) calculations, together with their occupation numbers. Top row: reactant vinylhydroperoxide. Middle row: transition state. Bottom row: product complex. The displayed orbitals and occupation numbers correspond to CISD/STO-3G natural orbitals at the optimized MRCISD(4,4)/cc-pVTZ geometries (shown in Figure 1). Color coding of atoms: brown, carbon; red, oxygen; and white, hydrogen.

the populations of the near-degenerate orbitals in the product complex became almost identical (at around 1.00), as could be expected. Numerical frequency calculations verified that the reactant and product complexes were indeed minima and the transition state a saddle point, on the MRCISD potential energy surface. The imaginary vibrational frequency at the MRCISD(4,4)/ccpVTZ level was 300.33i cm−1, which is reasonably close to values given by the single-reference methods. Reaction energies, enthalpies, and free energies computed using the rigid rotor and harmonic oscillator approximations are given in Table 2. Values computed using the single-reference methods UB3LYP/aug-ccpVTZ and W1BD are also given for comparison. Single-point calculations were next performed on the MRCISD(4,4)/cc-pVTZ geometries in order to test the effect of increasing either the basis set size or the size of the active space (doing both at the same time would have been computationally prohibitive). The results are reported in Tables 3 and 4. Table 3 shows that the CASSCF(4,4) energies are essentially converged with the cc-pVTZ basis set, and that even the MRCISD(4,4) energies change quite little beyond this. Extending the basis set from cc-pVTZ to aug-cc-pVQZ slightly increases the relative energy of the product complex, while leaving the relative transition-state energy essentially the same. Davidson cluster corrections for higher-order correlation are more significant than basis-set effects for all basis sets above ccpVTZ and tend to increase both the transition-state and product complex energies by about 1.5 and 3 kcal/mol, respectively. The observation that both basis set size and the 6826

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Table 2. Computed Standard (at 298 K and 1 atm Reference Pressure) Enthalpies (ΔH) and Gibbs Free Energies (ΔG) for the Vinylhydroperoxide Decomposition Reaction, in kcal/mola CH2CHOOH ⇒ [CH2CHOOH]‡

CH2CHOOH ⇒ CH2CHO···HO

CH2CHOOH ⇒ CH2CHO + OH

15.15

11.95

16.40

14.20

9.33

5.84

23.06 22.05 16.13

17.14 14.82 11.29

21.91 11.31

14.97

8.85

UB3LYP/aug-ccpVTZ, ΔH UB3LYP/aug-ccpVTZ, ΔG UW1BD, ΔH UW1BD, ΔG MRCISD(4,4)/ cc-pVTZ ΔH MRCISD(4,4)/ cc-pVTZ ΔG

Table 4. Single-Point Electronic Energies (in kcal/mol, Not Including Zero-Point or Thermal Corrections) for the First Two Steps of the Vinyl Hydroperoxide Dissociation Reaction, Computed at the MRCISD(4,4)/cc-pVTZ Geometries, Using Various Different Active Spacesa CH2CHOOH ⇒ [CH2CHOOH]‡ CASSCF(4,4)/631G(d) CASSCF(6,6)/631G(d) CASSCF(8,8)/631G(d) CASSCF(10,10)/631G(d) CASSCF(12,12)/631G(d) CASSCF(14,14)/631G(d) MRCISD(4,4)/631G(d) MRCISD(4,4)/631G(d) + D MRCISD(6,6)/631G(d) MRCSID(6,6)/631G(d) + D MRCISD(8,8)/631G(d) MRCISD(8,8)/631G(d) + D

a

CH 2 CHOOH denotes the minimum-energy reactant, while [CH2CHOOH]‡ denotes the transition state and CH2CHO···HO the hydrogen-bonded product complex. MRCISD values for the overall reaction are not available since a single, comparable active space cannot be consistently defined for the reactants and the isolated products.

Table 3. Single-Point Electronic Energies (in kcal/mol, Not Including Zero-Point or Thermal Corrections) for the First Two Steps of the Vinyl Hydroperoxide Dissociation Reaction, Computed at the MRCISD(4,4)/cc-pVTZ Geometries, Using Various Different Basis Setsa

CASSCF(4,4)/STO-3G CASSCF(4,4)/6-31G(d) CASSCF(4,4)/cc-pVTZ CASSCF(4,4)/aug-ccpVTZ CASSCF(4,4)/cc-pVQZ CASSCF(4,4)/aug-ccpVQZ MRCISD(4,4)/631G(d) MRCISD(4,4)/631G(d) + D MRCISD(4,4)/cc-pVTZ MRCISD(4,4)/cc-pVTZ +D MRCISD(4,4)/aug-ccpVTZ MRCISD(4,4)/aug-ccpVTZ + D MRCISD(4,4)/ccpVQZ MRCISD(4,4)/ccpVQZ + D MRCISD(4,4)/aug-ccpVQZ MRCISD(4,4)/aug-ccpVQZ + D

CH2CHOOH ⇒ [CH2CHOOH]‡

CH2CHOOH ⇒ CH2CHO···HO

37.33 8.40 11.06 10.69

39.62 0.25 2.77 2.64

10.78 10.69

2.56 2.57

15.28

9.96

16.61

12.21

19.34 21.05

14.00 16.82

18.87

14.34

20.35

17.15

19.49

14.58

21.16

17.50

19.47

14.87

21.07

17.82

CH2CHOOH ⇒ CH2CHO···HO

8.40

0.25

4.74

−4.70

3.90

−6.91

−0.36

−15.74

1.10

−10.77

9.26

−7.11

15.28

9.96

16.61

12.21

13.86

8.66

15.58

11.50

13.53

8.17

15.45

11.45

a

CH 2 CHOOH denotes the minimum-energy reactant, while [CH2CHOOH]‡ denotes the transition state and CH2CHO...HO the hydrogen-bonded product complex. +D indicates Davidson corrections for higher-order correlation, computed with a relaxed reference.

We were able to increase the active space up to 8 electrons in 8 orbitals using MRCISD/6-31G(d) and to 14 electrons in 14 orbitals using CASSCF/6-31G(d). The CASSCF and MRCI occupation numbers of the larger active spaces provide a further test for the sufficiency of our original 4-electron, 4-orbital space. In all of the calculations with larger active spaces, the CASSCF natural orbital occupation numbers of orbitals outside the original 4,4 space were always either above 1.974 or below 0.027. This indicates that larger active spaces are not needed for treating the multireference character of the VHP dissociation reaction. As seen from Table 4, the MRCI(n,n) energies change relatively little when n is increased from 4 to 8. The CASSCF(n,n) energies, however, seem to change more or less randomly as n is increased from 4 to 14. This is likely due to the fact that the occupation numbers of the orbitals outside the original 4,4 space are quite close to each other and that their ordering may thus easily change from one stationary point to another. (The orbitals outside the original 4,4 active space are also quite differently shaped at the different stationary points, and visual inspection could not be reliably used to make the active space assignment more consistent.) The absolute energies of the different stationary points may thus behave very differently with respect to n, leading to the oscillating behavior observed. The fact that the energetics computed with the largest 14,14 active space are quite close to the CAS(4,4) energies could be taken as an encouraging sign, though as we could not compute the CASSCF(16,16) energies, this might as well be a coincidence. By including dynamic electron

a

CH 2 CHOOH denotes the minimum-energy reactant, while [CH2CHOOH]‡ denotes the transition state and CH2CHO···HO the hydrogen-bonded product complex. +D indicates Davidson corrections for higher-order correlation, computed with a relaxed reference.

level of dynamic correlation affects the product complex more is reasonable, as this system involves long-range weak interactions, which are known to require high-level methods for quantitative treatment. 6827

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correlation also outside the active space, the MRCISD calculations provide an inherently more robust description of the system, and thus smooth out the differences observed with respect to active space size in the CASSCF calculations. The near-convergence of the MRCISD calculations with respect to active space size thus indicates that the computed MRCISD(4,4) energetics are likely reliable. Because of technical reasons, we were unable to compute a MRCISD-level IRC path using MolPro. Instead, we computed a CASSCF(4,4)/cc-pVTZ IRC path using Gaussian 09. Singlepoint MRCISD(4,4) energies were then computed along this path with the cc-pVTZ and aug-cc-pVTZ basis sets, using MolPro. The energy profiles are shown in Figure 3. The IRC

Figure 4. Structures of the minimum-energy geometries (top row) and transition states with respect to dissociation (bottom row) of the three isomers of C3O2H6 vinylhydroperoxide, optimized at the CBS-QB3 level, with spin symmetry broken in the transition states. Isomer A, CH2C(CH3)OOH; isomer B, cis-CH3CHCHCOOH; isomer C, transCH3CHCHCOOH. Color coding: brown, carbon; red, oxygen; and white, hydrogen.

Table 5 shows that replacement of the hydrogen bonded to the carbon of the hydroperoxide functional group by a methyl group does not significantly affect the VHP dissociation energetics, while replacement of either hydrogen on the distal carbon atom lowers both the transition state and the overall reaction energies, by almost 8 kcal/mol for the cis isomer. Naively, one might have expected the replacement of the hydrogen closer to the actual O−O bond being broken to have a larger effect, and the results may therefore seem counterintuitive. However, the main reason for the anomalously low (compared to other hydroperoxides) dissociation energy of the vinyl hydroperoxides is the stabilizing resonance between the configurations of the product vinoxy radical of which the R1R2C*−C(R3)O configuration is the dominant one. Clearly, substitution of a hydrogen on the radical center carbon by a methyl group helps stabilize the vinoxy radical more than replacement of a hydrogen on the carbonyl carbon and thus lowers the net reaction energy more. This effect should be accounted for in modeling of the atmospheric chemistry of larger vinyl hydroperoxides; peroxides with substituents on the α-carbon can be expected to dissociate faster. Kinetics. The best description of the overall reaction energetics are obtained by combining the MRISD values for the reactant to transition state and transition state to product complex steps with the overall reaction energy computed at the W1BD level. (Because of the near-impossibility of consistently defining a single active space for both the reactant and the isolated free products, MRCISD could not be applied to compute the overall reaction energy, and in any case, W1BD is expected to perform better for this particular task.) This yields the following reaction enthalpies: 17.85 kcal/mol from reactant to transition state, −2.73 kcal/mol from transition to product complex (using the MRCISD/cc-pVTZ enthalpies, plus the energy correction from the Davidson-corrected MRCISD(4,4)/ aug-cc-pVQZ single-point calculation), and 6.79 kcal/mol from PC to free reactants (subtracting the two previous steps from the W1BD overall reaction enthalpy). The overall kinetics of VHP decomposition will include the influence of both the saddle point connecting the VHP to the

Figure 3. IRC path (relative energies, in kcal/mol) for the vinyl hydroperoxide dissociation reaction. The left-hand side corresponds to the reactant, and the right-hand side to the product complex. Blue line: CASSCF(4,4)/cc-pVTZ. Green line: MRCISD(4,4)/cc-pVTZ singlepoint energies computed along the CASSCF path. Red line: MRCISD(4,4)/aug-cc-pVTZ single-point energies computed along the CASSCF path.

calculation verified that the transition state indeed connects to the VHP reactant and to the CH2CHO···HO product complex. As indicated already by Tables 3 and 4, including dynamic correlation makes the potential energy surface much steeper on the reactant side, but much shallower on the product side. Adding diffuse functions to the basis set does not make a larger difference for the computed reaction path energies. Effect of Substituents. To test the qualitative effect of alkyl substituents on the VHP dissociation energetics, we further performed calculations on three-carbon vinyl hydroperoxides, with empirical formula C3O2H6. There are three possible isomers, depending on which of the three C−H hydrogens in H2CCHOOH are substituted by a methyl group. The three isomers are shown in Figure 4. Because of the large expense and prohibitive scaling of the MRCISD method, the calculations on larger VHPs were carried out at the CBSQB3 level and are therefore not quantitatively accurate, especially for the transition states. The results are given in Table 5 (CBS-QB3 values for the 2-carbon VHP are also given for comparison). Product complexes were not explored for the larger VHPs due to the large computational effort involved in obtaining their optimized geometries, and the general failure of single-reference methods to predict their energetics reliably due to the degeneracy of the singlet and triplet states (as indicated by Figure 3 the potential energy surface around the product complex is quite flat, making even CASSCF optimizations very time-consuming). As many of the transition-state energies are below the overall reaction energies, product complexes analogous to that found for H2CCHOOH presumably exist also for the 3-carbon VHPs. 6828

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Table 5. CBS-QB3 Electronic Energies (ΔEelec, Not Including Zero-Point or Thermal Corrections), Standard (at 298 K and 1 atm Reference Pressure) Enthalpies (ΔH) and Gibbs Free Energies (ΔG) for the Decomposition Reactions of Four Different Substituted Vinylhydroperoxides, in kcal/mola reactant reactant reactant reactant reactant reactant

⇒ ⇒ ⇒ ⇒ ⇒ ⇒

transition state, ΔEelec products, ΔEelec transition state, ΔH products, ΔH transition state, ΔG products, ΔG

CH2CHOOH

CH2C(CH3)OOH (isomer A)

cis-CH3CHCHOOH (isomer B)

trans-CH3CHCHOOH (isomer C)

22.74 26.41 19.74 22.19 18.78 11.59

22.16 26.31 19.33 21.58 18.53 11.63

15.75 18.84 12.97 14.75 12.52 4.47

19.42 22.69 16.63 18.60 15.79 7.90

a

See Figure 4 for illustrations of the reactant and transition-state structures. Transition states have had their spin symmetry broken by the keyword Guess=Mix.

torsion of the terminal H about the O−O bond has a barrier of 2575 cm−1, while torsion of the −OH about the C−O bond has a barrier of 2500 cm−1. For a total excitation of 15 000 cm−1 and 18 internal degrees of freedom, these modes will be effectively harmonic. This is likely true even though frozen torsional scans may somewhat overestimate the true torsional barrier. The hindered rotation of the H atom at the transition state has a lower barrier of 1600 cm−1, but at the excess energies (over the critical energy) relevant to reactive trajectories, this will also be effectively harmonic. Consequently, for the RRKM calculations presented here, we assume that all internal modes are harmonic. The critical issue for VHP stabilization is the microcanonical rate constant at the critical energy for nascent VHP formation, above 12 000 cm−1 as indicated by the blue tick on the y axis of Figure 5. With this considerable chemical activation, the rate constant exceeds 1012 Hz. Because 1 atm collisional frequencies are of the order of 1010 Hz, stabilization of more than a few percent is unlikely for the two-carbon VHP considered here; 99% of the freshly formed, vibrationally excited VHP will decompose before even a single collision with the bath gas. While these calculations appear to confirm the common assumption of rapid VHP decomposition for the smallest VHP considered here, the microcanonical rate constants are none the less much lower than they would be for a simple bond scission without a saddle point. The tight transition state does slow down the decomposition. Consequently, it is highly likely that some of the larger VHP (those that retain the stability of the 2carbon base case considered here) formed via ozonolysis of atmospheric alkenes will be collisionally stabilized, in the very least following thermal decomposition of an sCI precursor. In earlier RRKM studies, we have found that, for homologous sequences with similar potential energy surfaces, pressure and carbon number scale, roughly 5 added carbons are equivalent to a factor of 100 in collision frequency.35,36 Therefore, we would expect substantial stabilization for 7-carbon VHPs. Thus, VHPs from monoterpenes, which dominate chemistry in many forest environments, are likely to be collisionally stablilized. Furthermore, the experimental observation that an entity on the reaction coordinate following the CI is easily stabilized remains to be explained. More detailed master-equation simulations of the entire syn-CI potential energy surface, including the VHP and the product complex, are forthcoming.

product complex and the subsequent decomposition of the complex. At relatively low energies above the critical energy for product formation, the rate-limiting step will be complex decomposition, but at higher energies, complex formation from the VHP will limit the overall rate. This is a recipe for a negative temperature dependence in the reverse reaction (products to VHP), as the inner (VHP to complex) transition state becomes limiting at higher energies.32 For the current discussion, however, our main interest is whether the VHP is stabilizabled under atmospheric conditions. For this reason, the critical question is the microcanonical rate constants at roughly the critical energy for VHP formation: the CI to VHP transition state. At the W1BD level, using input geometries from Kuwata et al.,33 this is located some 38 kcal/mol above the VHP minimum energy. To assess the potential for stabilization, we calculated RRKM rate constants, employing the densum program34 to calculate sums and densities of states at 10 cm−1 intervals above the VHP decomposition transition state. The results are shown in Figure 5. RRKM calculations are straightforward for vibrations but less accurate for hindered rotations. One-dimensional energy scans along the torsional modes at the MRCISD(4,4)/cc-pVTZ level of theory (keeping all other bond lengths, angles, and dihedrals frozen) reveal that torsions for the VHP potential well are sufficiently hindered to be effectively harmonic. Specifically,

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CONCLUSIONS

Vinyl hydroperoxide decomposition is complex. The decomposition reaction includes a transition state with a well-defined saddle point lying well below the ultimate products but connected to a strongly hydrogen-bonded complex typical of

Figure 5. RRKM rate constants as a function of energy. The colored ticks on the y axis are cyan, the actual product energy; blue, the CI → VHP transition state energy; and green, the ozone + alkene transition state energy. 6829

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(11) Drozd, G. T.; Kroll, J.; Donahue, N. M. J. Phys. Chem. A 2011, 115, 161. (12) Richardson, W. H. J. Org. Chem. 1995, 60, 490. (13) Bozzelli, J. W.; Sheng, C. J. Phys. Chem. A 2002, 106, 1113. (14) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (15) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (16) Head-Gordon, M.; Pople, J. A.; Frisch, M. J. Chem. Phys. Lett. 1988, 153, 503. (17) Scuseria, G. E.; Janssen, C. L.; Schaefer, H. F., III. J. Chem. Phys. 1988, 89, 7382. (18) Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. J. Chem. Phys. 2000, 112, 6532. (19) Barnes, E. C.; Petersson, G. A.; Montgomery, J. A.; Frisch, M. J.; Martin, J. M. L. J. Chem. Theory Comput. 2009, 5, 2687. (20) Yamamoto, N.; Vreven, T.; Robb, M. A.; Frisch, M. J.; Schlegel, H. B. Chem. Phys. Lett. 1996, 250, 373. (21) Fukui, K. Acc. Chem. Res. 1981, 14, 363. (22) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, revision B.01; Gaussian, Inc.: Wallingford, CT, 2009. (23) Werner, H. J.; Knowles, P. J. J. Chem. Phys. 1985, 82, 5053. (24) Knowles, P. J.; Werner, H. J. Chem. Phys. Lett. 1985, 115, 259. (25) Werner, H. J.; Knowles, P. J. J. J. Chem. Phys. 1988, 89, 5803. (26) Knowles, P. J.; Werner, H. J. Chem. Phys. Lett. 1988, 145, 514. (27) Werner, H.-J.; Knowles, P. J.; Manby, F. R.; Schültz, M.; Celani, P.; Knizia, G.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B.; Amos, R. D.; Bernhardsson, A.; Berning, A.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.; Goll, C.; Hampel, C.; Hesselmann, A.; Hetzer, G.; Hrenar, T.; Jansen, G.; Köppl, C.; Liu, Y.; Lloyd, A. W.; Mata, R. A.; May, A. J.; McNicholas, S. J.; Meyer, W.; Mura, M. E.; Nicklass, A.; Palmieri, P.; Pflüger, K.; Pitzer, R.; Reiher, T.; Shiozaki, H.; Stoll, H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T.; Wang, M.; Wolf, A. MOLPRO, versions 2009.1 and 2010.1; Cardiff University: Cardiff, U.K., 2010; see http://www.molpro.net. (28) Schaftenaar, G.; Noordik, J. H. J. Comput.-Aided Mol. Design 2000, 14, 123. (29) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724. (30) Dunning, T. H., Jr.; Peterson, K. A.; Wilson, A. K. J. Chem. Phys. 2001, 114, 9244. (31) Veryazov, V.; Malmqvist, P. Å.; Roos, B. O. Int. J. Quantum Chem. 2011, 111, 3329. (32) Smith, W. M.; Sage, A. M.; Donahue, N. M.; Herbst, E.; Quan, D. Faraday Discuss. 2006, 133, 137−156. (33) Kuwata, K. T.; Hermes, M. R.; Carlson, M. J.; Zogg, C. K. J. Phys. Chem. A 2010, 114, 9192−9204. (34) Barker, J. R. Multiwell, 1.3.3 ed.; University of Michigan: Ann Arbor, MI, 2003; see http://data.engin.umich.edu/multiwell/multidistrib.htm. (35) Zhang, J.; Dransfield, T.; Donahue, N. M. J. Phys. Chem. A 2004, 108, 9082−9095. (36) Chuong, B.; Zhang, J.; Donahue, N. M. J. Am. Chem. Soc. 2004, 126, 12363−12373.

association reactions of OH radicals and oxygenated organics. Accurate determination of the reaction energetics required high-level multireference computational techniques, which are difficult to extend to larger carbon-number systems. However, there are indications that the specific structure of larger analogues could change the VHP energetics substantially. While it appears that the smallest VHP considered here is unlikely to be collisionally stabilized under atmospheric conditions, it appears likely that larger analogues will be stabilized. The importance of those stabilized VHPs remains to be determined, but they clearly must be taken into consideration when interpreting data from experiments addressing either collisional stabilization or thermal decomposition of stabilized intermediates in ozonolysis.

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ASSOCIATED CONTENT

S Supporting Information *

W1BD and MRCISD/cc-pVTZ optimized geometries of stationary points for the CH2CHOOH dissociation reaction, MRCISD/cc-pVTZ vibrational frequencies and absolute values for single-point energies computed with various methods at the MRCISD geometries, and CBS-QB3 geometries for stationary points of the dissociation reaction of the three isomers of the C3O2H6 vinylhydroperoxide. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: theo.kurten@helsinki.fi. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Professor Dage Sundholm for helpful discussions on multireference methods and orbital selection. We thank the CSC IT Centre for Science in Espoo, Finland, for computer time and the Academy of Finland for funding. N.M.D. was supported by grant 11-ACLR11-10 from NASA.

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REFERENCES

(1) Hallquist, M.; Wenger, J. C.; Baltensperger, U.; Rudich, Y.; Simpson, D.; Claeys, M.; Dommen, J.; Donahue, N. M.; George, C.; Goldstein, A. H.; Hamilton, J. F.; Herrmann, H.; Hoffmann, T.; Iinuma, Y.; Jang, M.; Jenkin, M. E.; Jimenez, J. L.; Kiendler-Scharr, A.; Maenhaut, W.; McFiggans, G.; Mentel, T. F.; Monod, A.; Prévôt, A. S. H.; Seinfeld, J. H.; Surratt, J. D.; Szmigielski, R.; Wildt, J. Atmos. Chem. Phys. 2009, 10, 5155. (2) Wayne, R. P. Chemistry of Atmospheres, 3rd ed.; Oxford University Press: Oxford, U.K., 2000. (3) Criegee, R. Chem. Ber. 1944, 77, 722. (4) Taatjes, C. A.; Meloni, G.; Selby, T. M.; Trevitt, A. J.; Osborn, D. L.; Percival, C. J.; Shallcross, D. E. J. Am. Chem. Soc. 2008, 130 (11883), 839. (5) Bach, R. D.; Andres, J. L.; Owensby, A. L.; Schlegel, H. B.; McDouall, J. J. W. J. Am. Chem. Soc. 1992, 114, 7207−7217. (6) Anglada, J. M.; Bofill, J. M.; Olivella, S.; Solé, A. J. Am. Chem. Soc. 1996, 118, 4636−4647. (7) Herron, J. T.; Huie, R. E. J. Am. Chem. Soc. 1977, 99, 5430. (8) Kroll, J. H.; Sahay, S. R.; Anderson, J. G.; Demerjian, K. L.; Donahue, N. M. J. Phys. Chem. A 2001, 105, 4446−4457. (9) Kuwata, K. T.; Templeton, K. L.; Hasson, A. L. J. Phys. Chem. A 2003, 107, 11525. (10) Olzmann, M.; Kraka, E.; Cremer, D.; Gutbrod, R.; Andersson, S. J. Phys. Chem. A 1997, 101, 9421−9429. 6830

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