Ozonolysis Reactions of Monoterpenes: A Variational Transition State

Mar 3, 2015 - ... single CC bond distance observed at the molozonide (consequently, the π character of ...... Carlo , P. D.; Brune , W. H.; Martinez ...
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Ozonolysis Reactions of Monoterpenes: A Variational Transition State Investigation. R. C. de M. Oliveira and G. F. Bauerfeldt* Departamento de Química, Universidade Federal Rural do Rio de Janeiro, Rodovia BR465, Km 7, Seropédica, RJ 23890-000, Brazil S Supporting Information *

ABSTRACT: The O3-initiated oxidation reactions of αpinene ([1S,5S]-2,6,6-trimethylbicyclo[3.1.1]hept-2-ene), βpinene ([1R,5R]-6,6-dimethyl-2-methylenebicyclo[3.1.1]heptane), camphene ([1R,4S]-2,2-dimethyl-3-methylenebicyclo[2.2.1]heptane) and sabinene ([1R,5R]-4-methylene1-(1-methylethyl)bicycle[3.1.0]hexane), four monoterpenes typically emitted into the atmosphere, were studied at the B3LYP/6-31+G(2d,2p) level of theory. The rate coefficients were calculated on the basis of the variational transition state theory for two kinetic models, in order to investigate the reaction mechanism: first assuming a direct bimolecular reaction and the second, assuming the formation of a prebarrier-complex, which further reacts forming the corresponding molozonide. The barrier heights leading to the formation of exo-conformers of the molozonides of α-pinene and camphene are lower than the barrier heights for the formation of the endo-conformers of these molozonides, whereas the inverse trend is observed for β-pinene and sabinene. The canonical variational rate coefficients are found in reasonable agreement with the experimental data, especially when the prebarrier complexes are considered. Microcanonical variational rate coefficients are also calculated, as a final validation test, being found in an expected agreement with the canonical rate coefficients. The best predictions for the rate coefficients at 298 K, based on the microcanonical variational method, for α-pinene, β-pinene, camphene, and sabine are (in units cm3 molecule−1 s−1): 6.92 × 10−17, 1.06 × 10−17, 4.61 × 10−19, and 4.81 × 10−17, respectively. Our results suggest that the prebarrier complex is an important specie in the ozone addition mechanism and should be taken into account for the proper description of the overall kinetics. molozonide, a five-membered ring specie, which decomposes rapidly. The cycloaddition step is therefore assumed to be rate determining in the complete reaction mechanism. Concerning the reaction kinetic, experimental rate coefficients of the reactions of α-pinene and β-pinene were determined by several groups.11−17 Unfortunately, few experiments have been carried out for camphene and sabinene.18,19 Quantum chemistry calculations are suitable for establishing reaction mechanisms and have been widely employed for the description of the ozone initiated atmospheric reactions of unsaturated compounds including monoterpenes.20−27 Some theoretical works suggest that the electronic energies of the saddle points are slightly higher or even smaller than the sum of the electronic energies found for the isolated reactants. This situation is also found among the theoretical works describing the mechanisms for the OH addition to unsaturated compounds. Moreover, among all the literature concerning the OH addition, the formation of a prebarrier complex (PC) is suggested, and such an intermediate plays an important role in the kinetics and dynamics of such reactions.28,29

1. INTRODUCTION A great variety of volatile nonmethane organic compounds (NMOCs) is constantly emitted into the atmosphere. A total emission of NMOCs from vegetation is estimated as 1150 Tg carbon per year,1−3 54% corresponding to isoprene and 11% to monoterpenes including α-pinene and β-pinene. Within such estimates, biogenic emissions of NMOCs far exceed those from anthropogenic sources on a global scale.4 The atmospheric chemistry involving biogenic NMOCs plays an important role in several aspects related to air quality, human health, and climate.5 Tropospheric reactions of these molecules occur with hydroxyl (OH) radicals during daylight, with nitrate radicals (NO3) during nighttime, and with ozone (O3). The oxygenated degradation products of these reactions contribute to the formation of secondary organic aerosols.6 Furthermore, there exists increasing evidence that the ozonolysis reactions also contribute to the formation of OH radicals.7 To assess the atmospheric behavior of these compounds, it is crucial to understand the reaction mechanisms involving the reactions of the monoterpenes. The Criegee mechanism is commonly suggested for the description of the ozonolysis of unsaturated compounds.8−10 The first step of this mechanism is the highly exothermic cycloaddition of ozone to the double bond forming a © 2015 American Chemical Society

Received: December 27, 2014 Revised: February 22, 2015 Published: March 3, 2015 2802

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all stationary points (reactants, prebarrier complex, saddle point, and molozonides) and calculations of the vibrational frequencies, which were also used to characterize the stationary points. Imaginary frequencies were not found for the local minima, whereas only one imaginary frequency was observed for each transition state, as expected. Cycloadditions were modeled by taking into account the upward and downward electrophilic attacks of O3 to the double bond. The O3 reactions leading to the exo conformers of the prebarrier complexes, saddle points, and molozonides are labeled as 1, while the label 2 is given for the endo-conformer. Therefore, geometries for two prebarrier complexes (PC1 and PC2), two saddle points (SP1 and SP2), and two primary ozonides (PO1 and PO2) were located for each monoterpene. Starting from the optimized geometries of the saddle points, calculations of the minimum energy paths were performed on the basis of the intrinsic reaction coordinate (IRC) method38 to ensure that reactants, prebarrier complex, and products are connected. To connect the prebarrier complexes and the reactants, relaxed scans calculations were adopted to describe the dissociation paths along the interatomic distances between the carbons atoms in the double bond and the terminal oxygen atoms in the ozone molecule. This particular internal coordinate was chosen as the reaction coordinate for PC1 and PC2 dissociations. In our previous work,37 corrections for the basis set superposition error (BSSE)39 were applied in order to achieve more accurate values for energy differences, including the critical energy, defined as the electronic energy of the saddle point relative to the isolated reactants and corrected by zeropoint vibrational energies. Here, BSSE corrections were also performed. The effects over the optimized geometries and calculated vibrational frequencies are observed when the BSSE corrections are included in the gradient and Hessian calculations.40 This is, in this work, referred as the CP1 procedure. The inclusion of the BSSE corrections to the electronic energy of a previously optimized structure (calculated without the BSSE corrections) is referred as the CP2 procedure. Because of its complexity, CP1 calculations show higher computational cost in comparison to the CP2 corrections. The theoretical calculations were carried out using the Gaussian 03 suite of programs.41 From the vibrational frequencies calculations, thermal contributions to enthalpy and Gibbs free energies were determined considering the harmonic oscillator, rigid rotor, and ideal gas assumptions at the standard statistical thermodynamics equations.42 TST has been satisfactorily and worldwide applied for the calculations of rate coefficients, assuming the quasi-equilibrium and high pressure hypothesis. This theory performs better for chemical reactions with high barrier height, in which the saddle point region is well-defined, being expected that the maximum of the vibrationally adiabatic potential curve coincides with the maximum ΔG. However, for barrierless reactions (or even if a saddle point is present, lying in a flat region of the potential energy surface), the adoption of a more robust dynamical model is necessary in order to predict the fundamental kinetic parameters for the chemical reaction. In such cases, the canonical variational transition state theory (CVTST) represents a more reliable model. In this work, the rate coefficients were calculated using the canonical variational transition state theory (CVTST).43−45

Concerning the ozonolysis reactions, prebarrier complexes have also been characterized along the reaction path, by both experimental and the theoretical methods.30−33 But, the theoretical determination of rate coefficients based on a mechanism explicitly considering the prebarrier complex has, to the best of our knowledge, never been done. Instead, for the prediction of the ozonolysis rate coefficients, the standard Eyring equation (or eventually, a canonical variational transition state method) has been applied, considering a direct reaction path in which the transition state is connected to the isolated reactants. Jiang and co-workers have located van der Waals complexes on the potential energy surface for the ozonolysis of limonene and reported rate coefficients calculated, on the basis of the conventional transition state theory, for individual reaction channels on a mechanism considering two possible orientations for the ozone attack to the double bond of the limonene ozonolysis.34 Clearly, there is a considerable shortage of experimental and theoretical data related to the oxidation mechanism, and the atmospheric role of the primary ozonides formed in the processes is yet to be completely understood. In our laboratory, we have been focused on developing and applying variational transition state methods in order to calculate rate coefficients for chemical reactions of atmospheric chemistry, hoping that these calculations may improve the understanding not only of the corresponding experimental data, but also of the dynamics of the atmospheric processes. Here, our study of the kinetics of the ozonolysis reactions of α-pinene ([1S,5S]-2,6,6-trimethylbicyclo[3.1.1]hept-2-ene), β-pinene ([1R,5R]-6,6-dimethyl-2-methylenebicyclo[3.1.1]heptane), camphene ([1R,4S]-2,2-dimethyl-3-methylenebicyclo[2.2.1]heptane), and sabinene ([1R,5R]-4-methylene-1-(1methylethyl)bicycle[3.1.0]hexane) is introduced. The kinetics of formation of the molozonide is explored in detail by considering the upward and downward attack of the ozone to the double bond (where the upward O3 attack leads to the formation of the exo-conformers and the downward O3 attack leads to the formation of the endo-conformers). The role of possible prebarrier complexes in the O3 addition mechanism is also discussed. The calculation of the rate coefficients was performed at the canonical transition state theory level. The temperature dependence of the rate coefficients was calculated for the temperature range from 100 to 500 K, which includes the accepted range of temperatures of the troposphere. The terpenes have been conveniently chosen, since they show remarkable structural differences which may influence the final kinetic results: the presence of an endo- or exocyclic double bond (at α-pinene and β-pinene, respectively) and the proximity of the methyl groups to the double bond (comparing camphene and sabinene). With these structurally different species, a general mechanism investigation could be validated. Only the above-mentioned stereoisomers were calculated and the geometries for the intermediates, saddle points, and molozonides, resulting from the O3 reaction with each terpene, also kept the initial stereochemical patterns.

2. COMPUTATONAL METHODS The theoretical calculations were performed at the B3LYP level35 adopting the 6-31+G(2d,2p) basis set.36 This methodology was proved to give a satisfactory quantitative description of the ozonolysis reaction,37 and details on the B3LYP performance will be discussed in the next sections. The computational procedures include geometry optimizations for 2803

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Figure 1. Monoterpenes studied in this work: 1A, α-pinene; 1B, β-pinene; 1C, camphene; and 1D, sabinene.

Life times of terpenes with respect to the most common oxidant agents in the troposphere are small, and the chemical removal of these compounds from the atmosphere is expected to occur near the emission source. At this region, the high pressure regime for the rate coefficients is also expected. Moreover, experimental rate coefficients have also been determined at atmospheric pressure and in order to compare and improve the understanding of the experimental results, the high pressure limit rate coefficients should be calculated. Therefore, the calculation of high pressure limit rate coefficients represents no restraint to this study. To assess the role of the prebarrier complex in the ozonolysis mechanism, two kinetic models are considered. First, assuming that the monoterpenes ozonolysis proceed via direct bimolecular reactions (kinetic model I):

II

k =

II k −II1,1 + k 2,1

+

II II k1,2 I k 2,2 II k −II1,2 + k 2,2

(2)

This kinetic scheme is supported by previous reports on the reactions of olefins with oxygen atoms and OH radicals.46,47 The rate coefficients have been calculated on the basis of the CVTST, as implemented in the kcvt program.48 Briefly, the CVTST calculations were performed by considering the molecular properties and electronic energies of a maximum of 40 points along the reaction coordinate. Starting from the saddle points the geometries along the reaction path were symmetrically chosen along the forward and reverse directions. In the canonical variational procedure, the potential curve is projected into a curve of Gibbs free energy, ΔG(s,T), and the maximum, ΔGmax(s*,T), is obtained for each temperature T, the reaction coordinate value being s*, the location of the variational transition state. After the maximization, the ΔGmax(s*,T) values are used for the calculation of the CVTST rate coefficients.

monoterpene + O3 → PO1 k1I

monoterpene + O3 → PO2 k 2I

the rate coefficients kIi (i = 1 for the formation of the exoconformer and 2, for the endo-conformer) are calculated and the global rate coefficients (kI) are k I = k1I + k 2I

II II k1,1 k 2,1

3. RESULTS AND DISCUSSION 3.1. Minimum Energy Paths for the Ozonolysis of the Monoterpenes. According to the Criegee mechanism,8,9,11 the monoterpenes ozonolysis occurs by the cycloaddition of ozone to the double bond forming the molozonide, an intermediate also known as 1,2,3-trioxolane. This initial step is highly exothermic and if, by hypothesis, the energy content is accumulated in the molozonide, it will be formed in a large distribution of excited vibrational states and then undergo fast unimolecular decomposition. This first (cycloaddition) reaction is then the rate-determining step. The structures of the monoterpenes α-pinene, β-pinene, camphene, and sabinene are shown in Figure 1. These terpenes have been chosen because they show remarkable structural differences which may influence the final kinetic results: the presence of an endo- or exocyclic double bond (at α-pinene and β-pinene, respectively) and the proximity of the methyl groups to the double bond (comparing camphene and sabinene). Only the above-mentioned stereoisomers were calculated and the geometries for the intermediates, saddle points, and molozonides, resulting from the O3 reaction with each terpene, also kept the initial stereochemical patterns. The existence of prebarrier complexes is suggested in the literature.46 To investigate the role of such intermediates on the mechanism of ozonolysis, minimum energy geometries were

(1)

The kinetic model II, explicitly considering prebarrier complexes, was evaluated for each ozonolysis reaction, according to the set of reactions: II monoterpene + O3 → PC1 k1,1

PC1 → monoterpene + O3 k −II1,1 II PC1 → PO1 k 2,1

and II monoterpene + O3 → PC2 k1,2

PC2 → monoterpene + O3 k −II1,2 II PC2 → PC2 k 2,2

where kIIi,j are the thermal rate coefficients, based on the kinetic model II, for step i on the mechanism, leading to the formation of the conformer j of the molozonide. The steady state assumption leads to the global rate coefficient (kII) expressed as 2804

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Figure 2. Optimized geometries of the stationary points obtained at the B3LYP/6-31+G(2d,2p) level of theory with CP1 corrections and the values of the most important geometrical parameters for the (A) α-pinene, (B) β-pinene, (C) camphene, and (D) sabinene ozonolysis.

located, and molecular properties (including relative energies) were evaluated. From the calculated vibrational frequencies all these geometries are assigned as minima, except for PC2 of βpinene, which showed one imaginary frequency (3i) for the optimized geometry, obtained with BSSE corrections. However, the modulus of the imaginary frequency is very small and this structure can still be considered a local minimum. The saddle points and molozonides, products of the cycloaddition, were also located. Each saddle point showed only one imaginary frequency, referred to the totally symmetric C−O stretching, which defines the reaction coordinate. The vibrational frequencies calculated for all stationary points at the B3LYP/ 6-31+G(2d,2p) level, as well as electronic energies, zero point vibrational energies, absolute enthalpies at 298 K, and absolute Gibbs free energies at 298 K are given as Supporting Information. The inspection of the changes in geometric parameters can be very useful for the analysis of the dynamics of a reaction, in terms of the minimum energy path. For the monoterpenes ozonolysis, interatomic distances related to the coupling of ozone are good parameters for the discussion of structural changes observed along the reaction. Figure 2 panels A−D shows the optimized geometries of the stationary points and the values of the most important geometrical parameters.

From the isolated reactants, the C1−C2 interatomic distances increase from typical double bond values up to the expected single CC bond distance observed at the molozonide (consequently, the π character of the bond decreases along the reaction). The C1−C2 interatomic distances calculated for αpinene, β-pinene, camphene, and sabinene are 1.340, 1.336, 1.333, and 1.336 Å, respectively. The C1−C2 distances calculated for the prebarrier complexes, saddle points and molozonides are increased, with respect to the distances at the corresponding terpenes, nearly 1%, 3%, and 17%, respectively. The C1−O1 and C2−O2 interatomic distances considerably decrease as the C1−C2 interatomic distances increase, indicating that the ozone molecule is coupling into the double bond. As expected, the O3 attack is initiated at the less substituted carbon atom and the C2−O2 distances, as defined at Figure 2 panels A−D, are lower than the C1−O1 distances. In general, molecular properties (except electronic energies) calculated with the CP1 procedure do not significantly differ from those obtained without BSSE correction. Maximum deviations for the interatomic distances of PC1, PC2, SP1, SP2, PO1, and PO2 are 4% (α-pinene), 2% (camphene), and 1% (βpinene and sabinene). The O1O3O2 angle slightly decreases along the reaction path. The O1O3O2 angle calculated for the O3 molecule at the 2805

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Figure 3. Zero-point corrected electronic energies (E0, kcal mol−1, line/dot/line), Gibbs free energies (G0, in kcal mol−1, line) calculated at the B3LYP/6-31+G(2d,2p) level of theory with CP1 corrections for the structures along the minimum energy path evaluated for the α-pinene, β-pinene, camphene, and sabinene ozonolysis: (1) upward O3 attack (exo-conformers). (2) downward O3 attack (endo-conformers); (∗) values obtained with CP2 correction.

The energy diagrams in Figure 3 show that the molozonides are −52.8 to −48.4 kcal mol−1 (E0) and −39.8 to −35.8 kcal mol−1 (ΔG0) more stable than the reactants. The reaction Gibbs free energy differences show no significant distinction (being less than 1 kcal mol−1) for the formation of endo- and exomolozonides from β-pinene, camphene, and sabinene. For α-pinene, the exomolozonide (PO1) is more stable than PO2 by 3.8 kcal mol−1. For the theoretical description of the ozonolysis reaction,37 the enthalpy values obtained for the global reaction range from −57 to −49 kcalmol−1 and thermochemical data for the gas phase attack to double bonds suggest typical enthalpy values ranging from −59 to −48 kcal mol−1.51 Wheeler and coworkers predicted the ΔH0K as −50.93 kcal mol−1 for the C2H4 + O3 reaction.52 This value was later refined by Zhao et al. to −51.65 kcal mol−1.53 On the basis of this comparison, we can assume that the B3LYP description is a good one. Furthermore, the B3LYP results obtained in our previous work can be considered good since (1) molecular properties and vibrational frequencies showed low deviations to those available in the literature, (2) to those species which showed doublet electronic ground states, spin contaminations calculations were performed and the obtained values did not exceed 0.754, which is a good value, and (3) geometrical parameters predicted by the B3LYP method for the ozonolysis saddle point were compared to accurate values predicted for the saddle point for the ethylene ozonolysis, calculated at the CCSD(T)/cc-pVTZ level.52 Besides the agreement of our predicted reaction energetics and structural data with previous reported results obtained at more robust levels of theory, a further attempt to validate the B3LYP/CP1 results is done, as follows.

B3LYP/6-31+G(2d,2p) level is 118.2°. For the several stationary points reported in this work, this angle varies from 116.2° to 117.4° (prebarrier complexes), from 111.9° to 113.7° (saddle points), and from 101.0° to 101.4° (molozonides). The comparison of our calculated geometrical properties with the previously reported geometries for the saddle points and molozonides for α-pinene and β-pinene ozonolysis49 and for the saddle point for the sabinene reaction50 shows low deviations, with maximum value of 6%. The molecular properties of the stationary points relative to camphene ozonolysis in comparison to other reported data have been previously discussed.37 Figure 3 illustrates the zero-point corrected electronic energies (E0) and standard Gibbs free energies (G0) for the stationary points (with respect to the reactants) located on the B3LYP/6-31+G(2d,2p)/CP1 ground state potential energy surface (absolute values for electronic energies and enthalpies are given as Supporting Information). The relative standard reaction Gibbs free energy differences suggest that prebarrier complexes formation reactions are endergonic, ranging from 6.4 to 8.2 kcal mol−1. Considering the zero-point corrected energies, the exo conformers of the prebarrier complexes of α-pinene and camphene are more stabilized with respect to the isolated reactants, than the endo conformers. An inverted trend is observed for β-pinene and sabinene, and the PC2 structures are more stable than the PC1. The barrier heights follow the same observation, and saddle points are located, with respect to the isolated reactants, at the range from 0.1 to 6.2 kcal mol−1 (considering the zero-point corrected electronic energy values, E0) or from 11.6 to 18.2 (considering the standard Gibbs free energy values, ΔG0). 2806

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The Journal of Physical Chemistry A A first important point to discuss is about the performance of the B3LYP functional for the description of the prebarrier complex formation. Cremer and co-workers have performed ab initio (CASSCF and CCSD(T)) calculations for the investigation of the mechanism for the acetylene ozonolysis.32 DFT calculations, adopting the B3LYP functional, have also been performed, probably inspired by previous works which suggested that the B3LYP functional performs as well as the CCSD(T) method for the prediction of ethylene ozonolysis energy differences54 and that the B3LYP and CCSD(T) descriptions of carbonyl oxides are similar.55−57 It was observed, however, that for the ozonolysis of acetylene an important geometric parameter, the O−C distances of the prebarrier (van der Waals) complex was largely underestimated at the B3LYP level and that a better geometry was obtained at the CCSD(T) level. Moreover, after basis set superposition error (BSSE) corrections, the predicted stabilization energy of the prebarrier complex (with respect to isolated reactants) was 1.1 kcal mol−1 at the CCSD(T) level, whereas the same output obtained at the B3LYP level was 0.7 kcal mol−1.32 These results suggest that even though important geometric parameters for the prebarrier complex may be underestimated at the B3LYP level, the energy differences are comparable to those obtained at the CCSD(T) level. In our calculations, BSSE corrections have also been performed, and by comparing the results obtained at the B3LYP level and at the B3LYP level with BSSE corrections, it can be noted that the O−C distances slightly increase after BSSE corrections, whereas the stabilization energy increases. For α-pinene, for example, the final values 2.04 and 1.29 kcal mol−1 are reported for the stabilization energies of PC1 and PC2, respectively, as predicted at the B3LYP level + BSSE corrections (after zero-point energy corrections, the same quantities are 1.48 and 0.79 kcal mol−1, respectively). The stabilization energies found in our work for the prebarrier complexes are in reasonable agreement with those found by Cremer and co-workers at the CCSD(T) level. In a more recent report, Sharkas and co-workers have proposed a multiconfigurational hybrid density functional method and reported results for the ozonolysis of ethylene and acetylene obtained at this level, comparing to other results obtained at the common single-reference DFT method, using several density functionals.58 The multiconfigurational hybrid density functional methods have provided similar results for the stabilization energies of the prebarrier complexes, in comparison to the standard DFT calculations with the corresponding functional, and all these results were underestimated with respect the best prediction of 1.90 kcal mol−1, at the CCSD(T)/CBS level.52 Double-hybrid functionals, however, were able to give stabilization energies in better agreement with the best estimate (1.90 kcal mol−1) value. Once more, we note that our stabilization energies predicted at the B3LYP level with BSSE corrections are in reasonable agreement with the CCSD(T)/CBS stabilization energy. Different from the prebarrier complex stabilization energy, a direct comparison of our calculated saddle point energies with other saddle points located on the potential energy surfaces for the ethylene and acetylene ozonolysis is not possible, since these relative energies are strongly dependent on the changes of geometric parameters of the unsaturated compound resulting from the O3 approximation and saddle-point formation. It is clear, from the works of Cremer and co-workers32 and Sharkas and co-workers58 that the B3LYP saddle point energies (for the

ethylene and acetylene ozonolysis) are underestimated by 3.5− 5.0 kcal mol−1, with respect to the CCSD(T) values. Moreover, Sharkas and co-workers showed that the adoption of the multiconfigurational hybrid density functional methods led to improved values. In our work, in comparison with the B3LYP/ CP1 results, the saddle point energies calculated at the standard B3LYP level are also underestimated, but by 1 kcal mol−1. This difference is not as remarkable as the 5 kcal mol−1 difference observed by comparing the B3LYP and CCSD(T) saddle point energies for the acetylene ozonolysis. Indeed this increase of the energy of the saddle point for the ozonolysis of terpenes may be quite significant. For ozonolysis of α-pinene, for example, the zero-point energy corrected barrier has been reported as 0.3 kcal mol−1 at the CCSD(T) level, with a correction factor (CF) that approximates the effect of expanding the basis set from 6 to 31G(d) to 6-311++G(d,p) at the CCSD(T) level, referred as CCSD(T) + CF level.49 Our lowest barrier energy found for the α-pinene ozonolysis, 0.1 kcal mol−1, is in good agreement with that CCSD(T) + CF estimate. The barrier height for the β-pinene ozonolysis has also been reported as 2.0 kcal mol−1, at the CCSD(T) + CF level, in agreement with the CBS-QB3 estimate, 1.9 kcal mol−1.27 Also for the β-pinene ozonolysis, a reasonable agreement is found between the CCSD(T) + CF (or CBS-QB3) and B3LYP/CP2 barrier heights (2.0 and 0.8 kcal mol−1, respectively). Moreover, our calculated value for the downward O3 attack to β-pinene (4.3 kcal mol−1) is also in agreement with the report from Nguyen and co-workers, who showed that the barrier for the O3 syn-addition is about 3 kcal mol−1 higher than that for the anti-addition. Reasonable agreements, within 1 kcal mol−1, between B3LYP and CCSD(T) results (the former obtained with the 6-311+(3df,2pd) basis set and the latter obtained with the 6-31G(d) basis set plus a correction factor) have also been observed for the limonene ozonolysis.34 The comparison of our results with previous reports available in the literature suggests that the B3LYP functional with BSSE corrections can provide energy values good enough for the understanding of the ozonolysis mechanism and further rate coefficients calculations. Calculations of the intrinsic reaction coordinate show that each transition state connects the prebarrier complexes and the products. This is a theoretical evidence for taking into account not the mechanism based on a single bimolecular reaction but the chemical model with participation of the prebarrier complex. Relaxed scan calculations are performed in order to connect the reactants and the prebarrier complex and describe the barrierless dissociation of the PC (or formation of the PC from the isolated reactants). We finally note that the conformers of the molozonides reported here are the most stable exo-exo- and endo-exoconformers. Other conformations of PC, SP, and PO can be expected but are omitted in this discussion, since a minor contribution to the overall reaction kinetics is expected from the reaction steps considering these conformers. B. Canonical Variational Rate Coefficients (CVT). As stated above, to investigate the reaction mechanism, two kinetic models were assumed: (I) elementary bimolecular O3 + terpene reaction and (II) the O3 addition reaction passing through a prebarrier complex. The individual kIi values (model I rate coefficients, i = 1 for the formation of the exo-conformer and i = 2 for the endo-conformer) and kIIi,j (model II rate coefficients for the step i on the mechanism, leading to the formation of the 2807

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Table 1. Calculated CVTST Rate Coefficients for the α-Pinene, β-Pinene, Camphene, and Sabinene Ozonolysis Reactions, from Kinetic Models I and IIa i 3

−1

−1

Kinetic Model I

kIi

Kinetic Model II

kI (cm3 molecule‑1 s‑1) kII1,i (cm3 molecule−1 s−1)

(cm molecule

s )

II k−1,i (s−1)

kII2,i (s−1) kII (cm3 molecule‑1 s‑1) experimental values (cm3 molecule−1 s−1)

1 2 1 2 1 2 1 2

α-pineneb −16

7.90 × 10 1.20 × 10−20 7.90 × 10‑16 1.56 × 10−16 2.14 × 10−16 3.51 × 10+08 1.05 × 10+09 1.78 × 10+09 9.10 × 10+04 1.30 × 10‑16 8.7 × 10−17,b 8.4 × 10−17,c 1.64 × 10−16,d 3.3 × 10−16,e 1.46 × 10−16,f 8.6 × 10−17,g 8.11 × 10−17,h

β-pinenec −16

3.16 × 10 3.63 × 10−18 3.19 × 10‑16 1.30 × 10−16 2.48 × 10−16 1.48 × 10+09 1.16 × 10+09 1.05 × 10+09 4.88 × 10+06 5.5 × 10‑17 1.5 2.1 6.5 3.6 1.4 2.24

× × × × × ×

10−17,b 10−17,c 10−17,d 10−17,f 10−17,g 10−17,h

camphened −18

1.08 × 10 2.85 × 10−20 1.11 × 10‑18 4.09 × 10−16 2.82 × 10−16 1.91 × 10+09 2.27 × 10+09 4.91 × 10+06 2.29 × 10+05 1.08 × 10‑18

4.5 × 10−19,i 9 × 10−19,j

sabinenee 6.63 × 10−17 4.90 × 10−16 5.56 × 10‑16 1.94 × 10−16 7.85 × 10−17 2.47 × 10+08 1.96 × 10+09 8.40 × 10+07 1.21 × 10+10 1.17 × 10‑16

8.0 × 10−17,j

a Calculated from molecular properties obtained at the CP1/B3LYP/6-31+G(2d,2p) (α-pinene, sabinene and camphene) and CP2/B3LYP/z31+G(2d,2p) (β-pinene) levels. The index i refers to the upward (1) or downward (2) O3 attacks. Experimental values are given for comparison. b Reference 11. cReference 12. dReference 13. eReference 14. fReference 15. gReference 16. hReference 17. iReference 18. jReference 19

conformer j of the molozonide), calculated at 298 K, are shown in Table 1. Considering the direct bimolecular reaction (kinetic model I), the kIi rate coefficients (i = 1 for the formation of the exoconformer and i = 2 for the endo-conformer) show positive temperature dependence, increasing as the temperature increases. The variational transition states were, in all cases, located moving to positive reaction coordinated values (toward the product regions), as the temperature increases, which is consistent with the expected variational displacements for an exothermic reaction. Rate coefficients, k−1 and k2, were calculated for the kinetic model II according to the canonical variational transition state theory, assuming the prebarrier complexes as the reactant. The k1 rate coefficients were evaluated from the microscopic reversibility assumption. This kinetic model presumes two transition states: the first, an outer transition state, located along the prebarrier complex dissociation path toward the isolated reactants and the second, an inner transition state, located along the reaction coordinate that leads prebarrier complex to the molozonide. The variational location of these two transition states is dependent on the temperature and, as a general remark, as the temperature increases the outer transition states move toward the prebarrier complex region, whereas the inner transition states move toward the positive reaction coordinate values, directed to the molozonide region. Calculated rate coefficients at 298 K from kinetic model I (the elementary bimolecular reaction) are higher than the rate coefficients calculated from kinetic model II by the factors: 6.07, 5.80, 1.03, and 4.75, for α-pinene, β-pinene, camphene, and sabinene, respectively. From both models, the formation of the exo-conformer (from the upward O3 attack) prevails in all cases, except for sabinene. The branching ratios for the exo and endo conformers of sabinene molozonides are 12% and 88%, respectively, from the kinetic model I and 42% and 58%, respectively, from the kinetic model II. We note that the model I rate coefficient values found for α-pinene, β-pinene, and

sabinene show significant deviation from the corresponding experimental values.11−17,19 For the O3 + α-pinene, the experimental rate coefficients (ranging from 276 to 363 K) are in the range of 8.1 × 10−17 to 3.3 × 10−16 cm3 molecule−1 s−1.11−17 The model II rate coefficient, at 298 K, is in much better agreement with the experimental values. Moreover, our calculated rate coefficient is restrained within the dispersion of the experimental data, for which 57% of the experimental values lies in the range of (8.1− 8.7) × 10 −17 cm 3 molecule −1 s −1 .11,12,16,17 Moreover, considering the values obtained by Atkinson and co-workers,11,12 our calculated rate coefficient is about 50% higher. The Model II rate coefficient calculated for the O3 + βpinene at 298 K is also in agreement with the experimental values (1.4−6.5 × 10−17 cm3 molecule−1 s−1, determined at the temperature values ranging from 294 K to 363 K).11−13,15−17 Again, the calculated rate coefficient from kinetic model II shows better agreement with the available experimental data than the model I rate coefficient, the ratios between the theoretical and experimental results being between 0.85 and 3.94 (considering all the experimental data). The experimental rate coefficient for the sabinene + O3 measured at 298 K by Atkinson and co-workers is 8.0 × 10−17 cm3 molecule−1 s−1,19 Our model II rate coefficient is 1.46 times than the latter, whereas a comparison of the model I rate coefficient with the same experimental values reveals that the predicted rate coefficient for the elementary reaction is 7 times the experimental value. A reasonable agreement was found between the rate coefficients calculated for the camphene ozonolysis by both Model I and Model II and the experimental values reported by Atkinson and co-workers and by Johnson and co-workers.18,19 A previous theoretical study of the O3 + camphene reaction indicated that the B3LYP/6-31+G(2d,2p) + CP corrections for BSSE provided accurate kinetic data for the description of this monoterpene.37 In this case, the values from both kinetic models coincide, which should be due to the larger barrier height with respect to the other monoterpenes. In this case, the 2808

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The Journal of Physical Chemistry A

Table 2. Calculated Canonical Variational Rate Coefficients from the Kinetic Model II (kII, cm3 molecule−1 s−1) for the Gas Phase Ozonolysis Reactions of α-Pinene, β-Pinene, Camphene and Sabinene as a Function of the Temperature (K) α-pinene T/K = 100 T/K = 200 T/K = 300 T/K = 400 T/K = 500 Arrhenius Parametersa A (cm3 molecule−1 s−1) Ea (kcal mol−1)

9.82 6.42 1.32 2.06 2.90

× × × × ×

10−18 10−17 10−16 10−16 10−16

5.58 × 10−16 0.82

β-pinene 5.56 3.76 1.04 1.84 2.85

× × × × ×

camphene

10−18 10−17 10−16 10−16 10−16

5.06 4.25 1.16 7.55 2.71

4.71 × 10−16 0.92

× × × × ×

sabinene

10−24 10−20 10−18 10−18 10−17

2.34 3.72 1.19 2.40 3.91

7.98 × 10−16 3.79

× × × × ×

10−18 10−17 10−16 10−16 10−16

1.06 × 10−15 1.24

For α-pinene, the experimental parameters (obtained over the temperature range 288−363 K, taken from ref 17) are 4.8 × 10−16 cm3 molecule−1 s and 1.05 kcal mol−1 and for β-pinene they are 1.74 × 10−15 cm3 molecule−1 s−1 and 2.58 kcal mol−1. a

−1

Table 3. Calculated Microcanonical Variational Rate Coefficients from the Kinetic Model II (kII,mCVT, cm3 molecule−1 s−1) for the Gas Phase Ozonolysis Reactions of α-Pinene, β-Pinene, Camphene, and Sabinene as a Function of the Temperature (K) α-pinene T/K = 100 T/K = 200 T/K = 300 T/K = 400 T/K = 500 Arrhenius Parametersa A (cm3 molecule−1 s−1) Ea (kcal mol−1)

9.26 4.07 6.97 9.12 1.08

× × × × ×

10−18 10−17 10−17 10−17 10−16

1.94 × 10−16 0.61

β-pinene 3.15 2.08 1.27 2.83 5.65

× × × × ×

camphene

10−20 10−18 10−17 10−17 10−17

1.08 1.44 5.66 3.16 1.13

2.69 × 10−16 1.82

× × × × ×

sabinene

10−24 10−20 10−19 10−18 10−17

6.04 1.49 4.98 8.87 1.27

4.42 × 10−16 3.97

× × × × ×

10−19 10−17 10−17 10−17 10−16

4.56 × 10−16 1.32

For α-pinene, the experimental parameters (obtained over the temperature range 288−363 K, taken from ref 17) are 4.8 × 10−16 cm3 molecule−1 s−1 and 1.05 kcal mol−1 and for β-pinene they are 1.74 × 10−15 cm3 molecule−1 s−1 and 2.58 kcal mol−1. a

located on the potential energy surfaces that describe the OH addition to unsaturated compounds, leading us to doubt whether the canonical assumption for our prebarrier complexes would be valid. Nevertheless, the total energy and angular momentum conservations should be assumed and a microcanonical ensemble should furnish a better description of the system. The mCVT rate coefficients were calculated as described elsewhere.59 Briefly, the microcanonical variational transition states were located by minimization of the sum of states along each reaction path, in the range from 1 to 50 kcal mol−1 and from J = 0 to 200. The RRKM code60 was used for this procedure. The energy and angular momentum dependent sum of states, Nin(E,J) and Nout(E,J), for the inner and outer transition states were used for the calculation of an effective sum of states, Neff(E,J), according to61

assumption of a prebarrier complex is not the most important physical insight governing the overall kinetics; instead, the rate coefficients are most dependent on the barrier height. Since the global CVT rate coefficients for the mechanism involving the prebarrier complexes are generally better than the simplest direct (elementary reaction) model, it can be inferred that the prebarrier complex plays a distinct role in the α-pinene, β-pinene, sabinene, and camphene ozonolysis reaction mechanism. Table 2 introduces the global rate coefficients calculated on the basis of the CVT, in the range of 100−500 K. The rate coefficients for camphene are the most distinguished among the four monoterpenes, which can be also observed from the Arrhenius parameters. Experimental values for the preexponential factor and activation energies (288−363 K) are available in the literature for α- and β-pinene (given in the footnotes of Table 2). A good agreement of our values with the experimental parameters can be observed. C. Microcanonical Variational Rate Coefficients. As a final test of the validity of our previously discussed canonical rate coefficients, microcanonical variational rate coefficients (mCVT) were also calculated. This procedure is mainly motivated by the previous works on the OH attack to unsaturated compounds, in which a thermal distribution for the prebarrier complex is not expected and the canonical assumption seems not to be valid. The prebarrier complexes and saddle points found for the OH addition reactions lie generally below the reactants, and non-Arrhenius profiles are observed for these reactions (i.e., the rate coefficients decrease as the temperature increase). Even though this temperature behavior was not found for the ozonolysis rate coefficients reported above, our prebarrier complexes are stabilized by only a few kcal mol−1, as the prebarrier complexes are generally

1 1 1 = + Neff (E , J ) Nin(E , J ) Nout(E , J )

(3)

The global, high pressure limit and temperature-dependent rate coefficients, kII,mCVT(T) were finally obtained by integration of the effective sum of states: k II,mCVT(T ) = σr ×

1 hQ terQ O3Q rel ⎛

⎞

∫ gJNeff (E , J) exp⎜⎝− k ET ⎟⎠ dJ dE B

(4)

where σr, gJ, Qter, QO3 and Qrel are the reaction path degeneracy, the degeneracy of the rotational states, and the partition function for the monoterpene for O3, and the relative translational partition function. The Planck and Boltzmann constants are conventionally represented by h and kB. 2809

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The Journal of Physical Chemistry A At 298 K, the mCVT rate coefficients obtained for α-pinene, β-pinene, camphene, and sabine are (in units cm3 molecule−1 s−1): 6.92 × 10−17, 1.06 × 10−17, 4.61 × 10−19, and 4.81 × 10−17, respectively. Reasonable agreement among the CVT and mCVT rate coefficients is observed, the mCVT rate coefficients being lower than the CVT rate coefficient values. This is an expected feature, since the microcanonical variational transition states are located for each energy and angular momentum, being more flexible than the canonical variational transition states, located at each temperature value. Calculated microcanonical variational rate coefficients, as a function of the temperature and according to the kinetic model II, are shown in Table 3. Arrhenius parameters, calculated for the mCVT rate coefficients in the temperature range from 100 to 500 K, are also given in Table 3. A comparison of the mCVT with the CVT Arrhenius parameters (Table 3) shows that the CVT preexponential factors are higher by factors ranging from 1.75 (βpinene) to 2.89 (α-pinene). The CVT activation energies are not significantly different from the mCVT activation energies, except on the case of β-pinene. It can be seen that the α-pinene rate coefficient (endocyclic double bond) is 2.4 times higher than the β-pinene rate coefficient (exocyclic double bond). The ozone attack to the endocyclic double bond is predominant, and this fact should also be observed if the ozonolysis kinetics of the 1methylcyclohexene62 and methylenecyclohexane18 are compared (the rate coefficients, in units of cm3 molecule−1 s−1 are 1.53 × 10−16 and 2.82 × 10−17, respectively). Jiang and coworkers concluded that the branching ratios for the endocyclic pathways on the limonene ozonolysis mechanism correspond to 76% of the overall kinetics.34 The proximity of the alkyl groups on the cyclic chain to the double bond largely affects the kinetic of camphene and sabinene, the rate coefficient of the latter structure being 108 times faster than that of the former structure, due to the repulsion promoted by the methyl groups. Finally, it can be noted that the kinetic model II gives the best theoretical description of the ozonolysis kinetics and that the prebarrier complex is an important specie in the reaction mechanism.

the elementar bimolecular reaction model. The CVT rate coefficients showed reasonable agreement with the mCVT rate coefficients, the latter being smaller than the CVT rate coefficients and representing the best theoretical results for the cases studied here. Our results finally suggest that the role of the prebarrier complex must be taken into account for the description of reaction mechanism of the monoterpenes.

■

ASSOCIATED CONTENT

S Supporting Information *

Geometries, vibrational frequencies and energy values for the stationary points. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank the research and fellowship support given by ́ the Conselho Nacional de Desenvolvimento Cientifico e Tecnológico (CNPq).

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REFERENCES

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4. CONCLUSIONS In this paper we introduced the theoretical study of the gasphase ozonolysis of α-pinene, β-pinene, camphene, and sabinene by using DFT at the B3LYP/6-31+G(2d,2p) level. All the stationary points were calculated either by considering different O3 attacks to the double bond, leading to distinct conformations of the molozonides. The kinetic of the O3 additions was shown to be influenced by the location of the endo- or exocyclic double bond (α-pinene and β-pinene) and the proximity of the methyl groups to the double bond (camphene and sabinene, respectively). The formation of both exo- and endoconformers of the molozonides were considered and, even though the relative Gibbs free energies differences show no significant distinction (the exo- to endo-ΔG0 differences being less than 1 kcal mol−1 for β-pinene, camphene, and sabinene and 3.8 kcal mol−1 for α-pinene), the branching ratios for formation of the exoconformers are greater than 97% for α-pinene, β-pinene, and camphene, whereas for sabinene the formation of exo- and endoconformers seems to compete. The kinetic Model II, explicitly considering the reversible prebarrier complex formation and conversion into the molozonide, provided better results than 2810

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DOI: 10.1021/jp5129222 J. Phys. Chem. A 2015, 119, 2802−2812