Hydration and Secondary Ozonide of the Criegee Intermediate of Sabinene.

A computational study of the formation of secondary ozonide (SOZ) from the Criegee intermediates (CIs) of sabinene, including hydration reactions with H2O and 2H2O, was performed. All of the geometries were optimized at the B3LYP and M06-2X with several basis sets. Further single-point energy calculation at the CCSD(T) was performed. Two major pathways of SOZ formation suggest that it is mainly formed from the sabinene CI and formaldehyde rather than sabina ketone and formaldehyde-oxide. However, in both pathways, the activation energies are within a range of ±5 kJ mol-1. Furthermore, the hydration reactions of the anti-CI with H2O and 2H2O showed that the role of the second water molecule is a mediator (catalyst) in this reaction. The dimer hydration reaction has lower activation energies than the monomer by 60 and 69 kJ mol-1, at the M06-2X/6-31G(d) and CCSD(T)+CF levels of the theory, respectively. A novel water-mediated vinyl hydroperoxide (VHP) channel from both the monomer and dimer has been investigated. The results indicate that the direct nonmediated VHP formation and dissociation is interestingly more possible than the water-mediated VHP. The density functional theory calculations show that the monomer is faster than the dimer by roughly 22 kJ mol-1. Further, the infrared spectrum of sabina ketone was calculated at B3LYP/6-311+G(2d,p); the calculated carbonyl stretching of 1727 cm-1 is in agreement with the experimental range of 1700-1800 cm-1.

Introduction

A great variety of biogenic volatile organic compounds (BVOCs) is continuously emitted into the earth’s atmosphere. They mostly include isoprene, methylbutenol, and monoterpenes that cover α-pinene, β-pinene, limonene, and sabinene. These compounds are emitted from natural plants, for example, they are emitted from lemon, lavender, and thyme and present in fruits, blossoms, leaves, citrus fruits, and vegetables. Emission rates of BVOCs are estimated to be 1014 g/year.[1,2] Globally, within such high emission rates, the biogenic largely exceeds the anthropogenic sources by a factor of 10, which is dominated by isoprene, oxygenated compounds, and monoterpenes.[3,4]

Sabinene is a bicyclic monoterpene composed of an exocyclic double bond. It contains a C=C bond with the familiar stereoisomers of [1R,5R] and [1S,5S]. Our recent study of the ozonolysis of sabinene included only the [1R,5R] stereoisomer[5] because of the fact that monoterpenes with stereoisomers mostly have similar energy profiles for ozonolysis reactions. The sabinene concentration ranges from ppt to ppb in the atmosphere,[6] mainly in the tropospheric level. The emission of this compound is commonly recognized from European beech,[7] silver birch,[8] and evergreen holm oak.[9] Emission of BVOCs along with their chemical fate plays a significant role in the atmosphere quality,[10−13] and this is due to the fact that their removal occurs through oxidation reactions with OH-radicals during the day, NO3-radicals overnight, and O3. These oxygenating reactions account for a significant low vapor pressure compounds that involve forming the so-called secondary organic aerosol (SOA).[13−17] This, in turn, affects climate, air quality, environment, and human health.

The ozonolysis (ozone addition) reactions are particularly interesting because of their abundance and the importance of their products to the fate of the atmosphere.[12,16] These reactions are suggested to occur according to the Criegee mechanism.[18] The mechanism is initiated through the 1,3-cycloaddition of ozone to the double bond of the compound, forming a five-membered ring known as primary ozonide (POZ).[19−21] The POZ decomposes swiftly, which leads to the formation of a carbonyl oxide recognized as the Criegee intermediate (CI) and a carbonyl compound depending on the structure of the monoterpene. Collisions of the CI with nonreactive species in the atmosphere leads to its stabilization, corresponding to stabilized CI. The CI subsequently undergoes either unimolecular or bimolecular reactions. In unimolecular reactions, the CI passes through the vinyl hydroperoxide (VHP) channel via 1,4-proton transfer or the dioxirane ester pathway via cyclization.[22−25] Furthermore, the bimolecular reactions of the CI with the carbonyl compound produced from the POZ decomposition lead to the formation of a secondary ozonide (SOZ); see Figure .[23,26] Another main bimolecular channel occurs via reaction with other atmospheric species, that is, CO,[27] O3,[28−30] NO,[22,31,32] SO2,[31,33] and H2O and its clusters.[34−38] To assess the effects of CIs on the atmosphere, it is vital to increase our understanding of these reaction mechanisms. For a full overview of the ozonolysis reactions, mechanisms, CI orientations, and theoretical levels used, we refer the reader to our recent review of monoterpenes.[39]

Figure 1

SOZ formation and hydration of the anti-CI of sabinene. (I: intermediate, P: product).

Previous computational studies of several CIs of small alkenes reacting with H2O and 2H2O have been reported in the literature.[34−36] Further reactions of CIs of β-pinene and limonene have also been investigated, with different orientations, that is, syn-CI and anti-CI.[37,38] However, the SOZ formation from CIs of monoterpenes has only been studied in a few cases.[23,40] Furthermore, the lifetimes of small CIs are rather short and cannot be significantly stabilized. Therefore, the SOZs of monoterpenes that result from the reaction of the CI with formaldehyde are more important since they can be stabilized under 298 K and 1 atm because of their higher abundance.[2,7] For a mechanistic view of this study, see Figure .

To the best of our knowledge, the SOZ that results from the ozonolysis of sabinene along with the hydration reactions of the corresponding CI has not been investigated. Therefore, a detailed computational study of these reaction mechanisms and activation energies at different levels of theory has been performed to shed more light on their chemistry. The main objective is to elucidate the reaction mechanisms and identify the chemical products that result in high yields. Furthermore, this study will shed more light on different bimolecular reactions of the CI, that is, SOZ and α-hydroxy hydroperoxide formation, and will also increase our understanding of the hydration reactions of different mechanisms to provide more insights to atmospheric chemistry.

Results and Discussion

Infrared Spectrum of Sabina Ketone

Although the experimental detection of the products that result from the ozonolysis of sabinene can be difficult, the Fourier-transform infrared (IR) spectrum of the dominant product, sabina ketone, has been reported.[12,41,42] The spectrum reported by Chiappini et al.[42] is the first to be reported using a synthesized standard. The main absorption band ranges from 1700 to 1800 cm–1. Therefore, the main interest is to provide more insight into the main absorption band of sabina ketone; that is, the carbonyl group stretching. However, there is a range of 100 cm–1; hence, our focus is on getting a closer frequency view of the carbonyl stretching.

The total number of vibrational modes are 66. The calculated IR spectrum of sabina ketone is depicted in Figure , where the term epsilon exemplifies the coefficient of molar absorbance. Three weak absorption peaks with frequencies in the range of 2906–3099 cm–1 refer to the symmetric and asymmetric stretching of CH, CH2, and CH3 groups. A sharp and strong peak with a frequency of 1727 cm–1 corresponds to the carbonyl group (C=O) stretching. Thus, the calculated C=O frequency is in agreement with the experimental range. Moreover, another peak with a frequency value of 1158 cm–1 is conformable with the asymmetric vibration of the C=O group toward the adjacent CH and CH2 groups; this is in close agreement with the experimental frequency range of 1100–1150 cm–1.[42]

Figure 2

Calculated IR spectra of sabina ketone at B3LYP/6-311+G(2d,p). Epsilon refers to the coefficient of molar absorbance.

Formation of the SOZ (Pathways A1 and A2)

In a recent study,[5] we investigated the dissociation of the POZ that results from the ozonolysis of sabinene into a syn-CI or anti-CI and formaldehyde. The calculation at different levels of theory showed that the formation of anti-CI and formaldehyde is more plausible with activation energies ranging from 6 kJ mol–1 to barrierless. The formation of the SOZ from the resulting products of the POZ dissociation is also studied. This is due to the importance of SOZ, in which it leads to the formation of SOA through nucleation and condensation of the SOZ resulting products. The reaction begins with either the sabinene CI and formaldehyde (Figure ) or the sabina ketone and the CI (Figure S1 in the Supporting Information). In general, it proceeds from compounds that exhibit an oxygen moiety for the SOZ formation. Two main pathways, A1 and A2, were studied at different levels of theory. The reacting complex has been located in different conformers, and the lowest energy conformer has been selected as the main reacting complex (RA1).

Figure 3

Optimized geometries for SOZ formation at B3LYP/6-311G(3df,3pd) for pathway A1.

Because of the enhanced stability of the anti-CI of sabinene (RA1) relative to the syn-CI, it is considered to be the main source of the SOZ.[5,23,24] The reaction proceeds through a bimolecular complex of the formed CI and the carbonyl compound that results from dissociation of the POZ from ozonolysis of sabinene.[23,39] Both pathways, A1 and A2, lead to the same product (PA1), occurring via transition states TSA1 and TSA2. Pathway A1 involves the reaction of the sabinene CI with formaldehyde, whereas pathway A2 involves the reaction of the sabina ketone with formaldehyde oxide (CI). It must be noted that pathway A1 is mainly discussed herein because of the similarities in reaction mechanisms of A1 and A2. This is also based on the activation energies, where the difference is no more than 5 kJ mol–1 of both pathways at different levels of theory (Table ). Table shows the activation energies of both pathways at various levels of theory. The potential energy surface (PES) of pathway A1 is given in Figure , while the PES and optimized geometries of pathway A2 are provided in the Supporting Information (Figures S1 and S2, respectively), in which the PESs show the high exothermicity of the reactions. Figure shows that through TSA1, the sabinene CI approaches the formaldehyde by a nucleophilic addition with C–O bonds of 1.903 and 2.258 Å, forming the SOZ (PA1) adduct. The bond distances of TSA2 (Figure S1) between the C and O atoms in the sabina ketone and the CI amount to 2.299 and 2.033 Å, respectively. The described bond distances are significant in the determination of other SOZs recognized as cyclic adducts in the nucleophilic reaction of SO2 and NO2 with different CIs in the troposphere.[39]

Table 1

Activation Energies, Enthalpies of Activation, and Gibbs Energies of Activation for SOZ Formation (in kJ mol–1) at 298.15 K (Pathways A1 and A2)

	TSA1			TSA2
theory/basis set	Ea	ΔH‡	ΔG‡	Ea	ΔH‡	ΔG‡
B3LYP/6-31G(d)	9	6	14	11	7	19
B3LYP/6-311G(3df,3pd)	15	11	20	18	14	28
B3LYP/6-31+G(d)	15	11	22	17	13	27
M06-2X/6-31G(d)	7	3	11	4	0	9
MP2/6-31G(d)	4			9
MP2/6-311++G(d,p)	8			13
CCSD(T)/6-31G(d)	10			12
CCSD(T)+CF	6			8

Figure 4

PES for SOZ formation (pathway A1). Energies calculated at different levels of theory.

The activation energy values of TSA1 and TSA2 at CCSD(T)+CF are comparable, with values of 6 and 8 kJ mol–1, respectively. Furthermore, the energies of TSA1 and TSA2 at B3LYP/6-311G(3df,3pd) are slightly close, with values of 15 and 18 kJ mol–1, respectively. The activation energies for both pathways are within a range of approximately 3 kJ mol–1 at the B3LYP/6-31G(d), B3LYP/6-31+G(d), and M06-2X/6-31G(d) levels of theory. Hence, the CCSD(T)+CF results are more favorable compared to the density functional theory (DFT). Moreover, the activation energy value of TSA1 is lower than the energy reported for the SOZ formation from the syn-CI of substituted cyclohexenes, where its value is 21 kJ mol–1 at B3LYP/6-31G(d).[40] This is explained according to the steric hindrance and tethering of the compounds, in which the steric factor increases with the branching and the presence of various functional groups to the compound. The plausibility of the selected reactions is based on the calculated energy barriers; herein, pathways with the lowest energy barriers are selected as more favored. Furthermore, the low activation energies at different levels of theory explain and demonstrate the high reactivity of the SOZ formation. The SOA formation could also be affected on the basis of additional reactions of SOZ with multiple prevalent atmospheric species, i.e., H2O and NH3; determining their nucleation fate. The reaction of SOZ with H2O or NH3 could be initiated by a concerted or step-wise nucleophilic addition, leading to ring opening and simultaneous hydrogen transfer to one of the oxygens in SOZ. This leads to the formation of different harmful chemical compounds of organic acids, amines, nitriles, and amides.

Bimolecular Reaction of the Anti-CI with H2O PES (Pathway B1)

The hydration reactions of the CI with nH2O (n = 1, 2, 3, ..., 6) are considered the main and dominant reactions in the atmosphere because of the ubiquitous concentrations of H2O. Herein, the reaction is studied by the interaction of anti-CI of sabinene with H2O and 2H2O. Previous studies suggest that the anti-CI of monoterpenes is more stable than the syn-CI by no more than 4 kJ mol–1,[5,23,32,39,43] in which the terminal oxygen of the syn-CI and anti-CI is oriented toward and opposite the bicyclic ring, respectively. Our recent ozonolysis study of sabinene investigated the orientations and activation energies of the CIs using DFT and ab initio methods, confirming the different chemistries of the CIs by the VHP and ester channels.[5] It should be mentioned that pathways with the lowest calculated energy barriers are selected to be the most likely mechanism to occur in an atmospheric gas-phase reaction. However, there is still a possibility that the resulting product with a higher energy barrier will be formed or will contribute to the formation of other species. Moreover, this applies to the upcoming pathways of B2, C1, and C2. This is because other predominant atmospheric species, such as CO2, NO2, and SO2 might act as catalysts in the reactions and decrease the energy barriers, partially or significantly.

The reaction of anti-CI with H2O (pathway B1) is initiated by the formation of α-hydroxy hydroperoxide intermediates (I1B1 and I2B1) in TS1B1. TS1B1 involves the transfer of a hydrogen atom from H2O to the terminal oxygen of the CI. This is accompanied by a simultaneous nucleophilic addition of the OH group of H2O to the carbonyl carbon of the CI. This leads to delocalization of the positive charge on the central oxygen atom and hence forms α-hydroxy hydroperoxide (I1B1 and I1B2); see Figure . There are considerable changes in the important bond lengths of TS1B1. Particularly, the bond length of the terminal O atom of the CI decreases by 0.490–1.288 Å. Also, the hydroxyl group in the H2O molecule decreases by 1.127–2.052 Å. This is followed by an increase of 0.182 Å in the bond length of the OH group in the H2O.

Figure 5

Optimized geometries for the reaction of anti-CI with H2O at B3LYP/6-311G(3df,3pd) for pathway B1.

Notably, the DFT results show that the formed intermediates (I1B1 and I2B1) are both conformers with corresponding energies. However, the conformers differ by 11 kJ mol–1 at CCSD(T)+CF (Figure ). Moreover, there is a difference in the torsion angle of the OH groups in the formed intermediates, where the first is similar to a cis isomer while the second is similar to a trans one. In the second TS (TS2B1), the decomposition of α-hydroxy hydroperoxide occurs in a concerted step through dissociation of the O–OH group, where the bond is elongated from the molecule by 0.561–2.005 Å. This is followed by a simultaneous hydrogen transfer from the OH to the O–OH group. The bond length of the OH dissociation increases by 0.177 Å, while decreasing to 1.323 Å for the O–OH group. Furthermore, the C–O bond decreases by 0.1 Å to form a carbonyl group. This concerted step leads to the formation of sabina ketone and atmospheric hydrogen peroxide (H2O2) products (PB1); see Figure .

Table shows the barriers obtained at several theoretical levels. The activation energy of TS1B1 at CCSD(T)+CF is 48 kJ mol–1, which is similar to the one obtained at B3LYP/6-31G(d). The addition of a diffuse function to B3LYP/6-31G(d) increases the activation energy by 16 kJ mol–1 for TS1B1, whereas the addition of a polarization function leads to the same activation energy. Furthermore, increasing the size of the basis set of the B3LYP method leads to a slightly higher energy of 58 kJ mol–1. However, the lower energy value of 40 kJ mol–1 is obtained at the M06-2X/6-31G(d) level of theory (Table ). The reaction of the syn-CI of limonene with H2O, higher barriers of 62, 65, and 69 kJ mol–1 were determined at CCSD(T)+CF.[37] Moreover, the reaction of the anti-CI of β-pinene (with different orientations) and H2O was reported with energy values of 51, 61, and 69 kJ mol–1 at M06-2X/6-311+G(2d,p).[38] It is worth mentioning that the TS with the lowest energy value (51 kJ mol–1) is comparable not only with the CCSD(T)+CF energy but also with its orientation; in which it is similar to TS1B1 along with the optimized structure of the α-hydroxy hydroperoxide formed.

Table 2

Activation Energies, Enthalpies of Activation, and Gibbs Energies of Activation for the Reaction of Anti-CI with H2O (in kJ mol–1) at 298.15 K (Pathway B1)

	TS1B1			TS2B1
theory/basis set	Ea	ΔH‡	ΔG‡	Ea	ΔH‡	ΔG‡	overall
B3LYP/6-31G(d)	48	43	57	137	138	133	54
B3LYP/6-311G(3df,3pd)	58	52	69	135	136	131	64
B3LYP/6-31+G(d)	64	59	74	134	135	130	70
M06-2X/6-31G(d)	40	37	44	173	174	170	52
MP2/6-31G(d)	43			192			60
MP2/6-311++G(d,p)	47			189			59
CCSD(T)/6-31G(d)	52			190			72
CCSD(T)+CF	48			193			73

The overall activation energy (relative activation energies of the highest energy transition state in reference to the initial reactant) of TS2B1 at the CCSD(T)+CF is 73 kJ mol–1. The B3LYP results utilizing the 6-31+G(d) and 6-311G(3df,3pd) basis sets are in agreement with CCSD(T)+CF with respective values of 70 and 64 kJ mol–1. However, lower overall activation energies are obtained with respective values of 52 kJ mol–1 at M06-2X/6-31G(d) and 54 kJ mol–1 at B3LYP/6-31G(d); see Table . In a relative comparison, the activation energies of the syn-CI of limonene with H2O are significantly higher with values of 178, 179, and 220 kJ mol–1 at CCSD(T)+CF. This could be attributed to the steric factor of the limonene and the orientation of the CI compound along with its stability. However, for a comparable view of theoretical levels used for pathways B1 and B2; the PES for each pathway is given in Figures S3 and 6.

Figure 6

PES for the reaction of anti-CI with H2O (pathway B1). Energies calculated at different levels of theory.

According to the activation energies in Table , M06-2X/6-31G(d), in agreement with the B3LYP/6-31G(d), is the most reliable method in terms of computational cost for this reaction. This is consistent with the hydration reactions of the anti-CI of β-pinene.[38] However, in the hydration reactions in anti-CI of β-pinene, the authors did not consider the dissociation of α-hydroxy hydroperoxide into further reaction mechanisms. Therefore, the M06-2X method might be debatable in the overall step for upcoming reactions, and this is observed and discussed in the next reaction with 2H2O.

Trimolecular Reaction of the Anti-CI with 2H2O PES (Pathway B2)

The reaction of the anti-CI with 2H2O, pathway B2, along with the effect of water on the barrier, whether it acts as a mediator or a spectator, has been included. The mechanism of the 2H2O addition to the anti-CI is analogous to the mechanism in pathway B1. The corresponding H2O dimer plays a significant role in the reaction behaving as a mediator (Figure ). The second H2O molecule transfers one of the hydrogen atoms from the original H2O molecule to the terminal O atom of the CI. This step is accompanied by a simultaneous nucleophilic addition of the OH group of the original H2O molecule to the carbonyl group of the CI. Hence, the positive charge on the central O atom of the CI is delocalized, and α-hydroxy hydroperoxide and H2O are formed (I1B2 and I2B2). The intermediates are formed through a concerted water-catalyzed transition state defined as TS1B2. Different conformational changes led to locating the lowest energy conformers of I1B2 and I2B2 that proceed the reaction to the desired products. Figure shows that the bond lengths of TS1B2 are slightly similar compared to the lengths in the first step of pathway B1 (TS1B1). Furthermore, the bond length of H–OH (OH group is in the second H2O molecule) decreases from 1.781 to 1.318 Å. Followed by an elongation of 0.194 Å in the other hydrogen bond that is being transferred to the terminal O atom, forming I1B2 and I2B2. The intermediates are both conformers with energies differing by no more than 4 kJ mol–1; see Figure S5 in the Supporting Information. Moreover, there is a difference in the torsion angle of the OH groups and orientation of H2O; see Figure .

Figure 7

Optimized geometries for the reaction of anti-CI with 2H2O at B3LYP/6-311G(3df,3pd) for pathway B2.

In the last step, the second intermediate (I2B2) decomposes through TS2B2 to form the sabina ketone, H2O2, and H2O (PB2). The O–OH group is dissociated from α-hydroxy hydroperoxide, and hence, the bond is elongated from the molecule by 0.408–1.850 Å. Simultaneously, the hydrogen is transferred from the terminal OH to the O–OH group through the H2O molecule. Therefore, the H2O molecule acts as a catalyst, and the whole reaction mechanism is water-mediated. Furthermore, the bond length of the hydrogen dissociation from the OH group increases by 0.309 Å, while it decreases to 1.169 Å to reach the H2O molecule. Likewise, the mediator transfers the hydrogen to the O–OH group, producing the sabina ketone, H2O2, and H2O products (PB2); see Figure .

The activation energies of the reaction of anti-CI with water dimer 2H2O are lower than those of the anti-CI with H2O monomer; see Tables and 3. The activation energy of TS1B2 at CCSD(T)+CF and B3LYP/6-311G(3df,3pd) is the same with an energy value of 50 kJ mol–1. The energy calculated at B3LYP/6-31+G(d) is in agreement with CCSD(T)+CF and B3LYP/6-311G(3df,3pd) with a value of 53 kJ mol–1. However, results of B3LYP/6-31G(d), B3LYP/6-31G(2df,p), and M06-2X/6-31G(d) are lower with values of 36, 37, and 30 kJ mol–1 (Table ). Thus, the lowest activation energy values for the hydration reactions of the anti-CI of sabinene for TS1B1 and TS1B2 are calculated at M06-2X/6-31G(d). This is consistent with the hydration reactions of the syn-CI and anti-CI of β-pinene.[38] Lin et al.[38] reported eight TSs with different orientations for the reaction of the anti-CI of β-pinene with 2H2O, in which the energy barriers were calculated in the range of 33–40 kJ mol–1 at M06-2X/6-311+G(2d,p). These barriers are in good agreement with this study at B3LYP/6-31G(d), B3LYP/6-31G(2df,p), and M06-2X/6-31G(d). It should be noted that upon consideration of the dissociation of α-hydroxy hydroperoxide into further reactions, the M06-2X method may not be considerably reliable in the overall step for upcoming reactions. To our knowledge, there are no previous monoterpene studies in the literature that represent the dissociation of α-hydroxy hydroperoxide resulting from the CI reaction with nH2O (n = 1, 2, 3, ..., 6).

Table 3

Activation Energies, Enthalpies of Activation, and Gibbs Energies of Activation for the Reaction of Anti-CI with 2H2O (in kJ mol–1) at 298.15 K (Pathway B2)

	TS1B2			TS2B2
theory/basis set	Ea	ΔH‡	ΔG‡	Ea	ΔH‡	ΔG‡	overall
B3LYP/6-31G(d)	36	30	46	98	95	102	12
B3LYP/6-31G(d)a	59	54	67	147	147	147	61
B3LYP/6-311G(3df,3pd)	37	31	47	96	93	99	34
B3LYP/6-31+G(d)	50	43	63	103	99	197	41
M06-2X/6-31G(d)	53	46	65	107	104	110	–8
MP2/6-31G(d)	30	25	35	112	108	115	–4
MP2/6-311++G(d,p)	43			132			16
CCSD(T)/6-31G(d)	51			16			24
CCSD(T)+CF	58			135			3

Represents the nonmediated H2O role in the reaction.

The overall activation energy is interestingly low at CCSD(T)+CF with a value of 3 kJ mol–1. The B3LYP results utilizing 6-31G(d), 6-311G(3df,3pd), and 6-31G+(d) are higher with respective overall energy values of 12, 34, and 41 kJ mol–1. Thus, the addition of diffuse and polarized functions increase the energy values sufficiently, compared to the B3LYP/6-31G(d). M06-2X/6-31G(d) describes the dissociation in the final products as an unreliable one with an overall energy of −8 kJ mol–1, compared to the positive barriers at the other levels of theory in Table . This is also observed at MP2/6-31G(d), where the overall activation energy is −4 kJ mol–1.

To provide more insight on the hydration reactions of the CIs, the role of the second H2O molecule, where it acts as a spectator in the reaction with the anti-CI, has been investigated utilizing B3LYP/6-31G(d). The activation energy of the TS1B2 value of 59 kJ mol–1 is higher than the reaction as a mediator by 23 kJ mol–1; see Figure S4 in the Supporting Information. In a comparison of the mediator and the spectator, the barrier of TS2B2 where the H2O acts a spectator is overestimated with a value of 147 kJ mol–1, where the overall energy is 61 kJ mol–1; see Table . Hence, the water-mediated reaction is more favorable with a lower barrier than the spectator one. This might be attributed to the number of hydrogen bonds formed in the reaction. This is consistent with our previous work where the barriers drop significantly for the water-mediated reactions.[44−50] Furthermore, the presence of a second H2O molecule increases the electronegativity with the contribution of the lone pair of electrons with the hydrogen atom mediation.

Water-Mediated (H2O and 2H2O) VHP Channel PES (Pathways C1 and C2)

The reaction of anti-CI with nH2O (n = 1, 2, 3, ..., 6) is initiated through 1,4-proton transfer via the mediation of the proton in the H2O molecule. The VHP channel has been investigated in our recent study,[5] through the direct 1,4-proton transfer for the syn-CI and anti-CI to the final radical products. However, this channel must be given more attention because of the fact that it leads to the formation of sabina ketone and OH radicals. Therefore, the radicals’ formation will be investigated through a mediated mechanistic pathway. It should be noted that the H2O dimer (pathway C2) was determined by configuring a multiple number of geometries; the lowest energy conformer has been selected as the main source of the reaction. The reaction is based on the mechanism of the 1,4-proton transfer, where this reaction is H2O-mediated. The VHP channel is usually associated with the unimolecular dissociation, whereas herein, the reaction is categorized as a bimolecular one with H2O and trimolecular with 2H2O molecules. Both the H2O monomer (Figure ) and its 2H2O dimer (Figure S5 in the Supporting Information) were studied. However, the main focus of this discussion will be on the monomer because of its higher plausibility and lower activation energies. It should be noted that the reaction mechanisms of both pathways agree with each other in terms of bond lengths.

Figure 8

Optimized geometries for the VHP channel via the H2O molecule at B3LYP/6-311G(3df,3pd) for pathway C1.

In general, the reaction occurs by the dissociation of the anti-CI through the proton transfer from the methylene (CH2) group to the terminal oxygen of the CI via the H2O molecule; see Figures and S5 (in the Supporting Information). This step is connected by the VHP (I1C1) formation through TS1C1 via a seven-membered ring, followed by a significant conformational change to the second VHP (I2C1). Figure shows the change in bond lengths and torsion angles of the reaction. TS1C1 depicts the change in the bond length of the C–H bond in the CH2 group from 1.088 to 1.290 Å, while the distance of the proton reaching the H2O molecule decreases by 0.981–1.369 Å. As a mediator, the H2O molecule transfers a proton to the terminal oxygen of the CI. The bond length of this proton increases from 0.985 to 1.243 Å with a simultaneous decrease in the bond length of the proton reaching the O atom to 1.191 Å. In the sequence of this mechanism, the carbonyl group of the CI changes its chemistry by a tautomerization step, leading to the VHP formation. The conformational change is confirmed by the fact that there is a change in the torsion angle between the methine (CH) group and the hydrogen of the terminal OH group. The conformations differ by no more than 30 and 7 kJ mol–1 for pathways C1 and C2, respectively, at different levels of theory (Figure ). The bond lengths of structures in pathway C2 are in agreement with pathway C1; see Figures and S5 in the Supporting Information. The significant difference is in the nine-membered ring transition state of pathway C2 (TS1C2). The relative energies of pathways C1 and C2 are given in Figures and S6 in the Supporting Information.

Figure 9

PES for the VHP channel via the H2O molecule (pathway C1). Energies calculated at different levels of theory.

The second transition state (TS2C1) involves the dissociation of the OH group from the VHP, which includes a retro tautomerization of the C=C bond to become a carbonyl group. This leads to the radicals’ formation of sabina ketone and OH. The considerable change in bond lengths is mainly in the OH dissociation, in which the bond is elongated from 1.471 to 2.081 Å. Moreover, the C=C bond is elongated by 0.100–1.435 Å in the final product, while the C=O group is formed by the constriction of the bond from 1.369 Å in I2C1 to 1.234 Å in PC1. This channel corresponds with only one fate of the CI, that is, the radicals’ formation. The optimized structures along with selective bond lengths are given in Figure , at B3LYP/6-311G(3df,3pd). The bond lengths at B3LYP/6-311G(3df,3pd) are in agreement with the bond lengths of sabinene, limonene, α-pinene, and β-pinene CIs at the B3LYP/6-31G(d) and B3LYP/6-31G(d,p) levels of theory.[5,22,24,37]

The accessibility of the activation energies is mostly dependent on the overall energy. CCSD(T) affords a barrier that significantly overshoots the barrier of the M06-2X method. Bearing in mind that these reactions occur in the atmosphere, the likelihood of a lower barrier is more plausible. Hence, it follows that M06-2X gives a more realistic description than the more expensive CCSD(T) method. However, CCSD(T)/6-31G(d) proved to be significant in the case of this pathway (Figure ). Table shows that lower overall activation energies for the anti-CI with the H2O monomer (pathway C1) are obtained at different levels of theory. For example, the overall barrier for pathway C1 at B3LYP/6-31G(d), B3LYP/6-311G(3df,3pd), and B3LYP/6-31+G(d) is lower by 6, 22, and 18 kJ mol–1, respectively. Furthermore, the overall barrier of the M06-2X/6-31G(d) level suggests that the monomer reaction with a value of 124 kJ mol–1 is more favorable than the dimer reaction with a value of 144 kJ mol–1. Interestingly, M06-2X/6-31G(d) overestimates the energy barrier comparatively to other levels of theory. This is in agreement with our recent study of the direct 1,4-proton transfer.[5] Higher activation energies result from the calculation at CCSD(T)+CF, where the barrier is relatively at its highest respective values of 102 and 180 kJ mol–1 for pathways C1 and C2. By comparison, a previous study on the VHP channel from the syn-CI of limonene in the presence of H2O as a catalyst reported lower energy values by roughly 30 kJ mol–1, utilizing CCSD(T)+CF.[37] Intuitively, this is attributed to the chemistry of the CI (syn or anti) and most importantly, whether it is treated as a biradical or zwitterion.

Table 4

Activation Energies, Enthalpies of Activation, and Gibbs Energies of Activation for Water-Mediated (H2O and 2H2O) VHP Channel (in kJ mol–1) at 298.15 K (Pathways C1 and C2)

	TS1C1(TS1C2)			TS2C1(TS2C2)
theory/basis set	Ea	ΔH‡	ΔG‡	Ea	ΔH‡	ΔG‡	overall
B3LYP/6-31G(d)	50(45)	46(39)	58(56)	88(115)	86(115)	94(120)	74(80)
B3LYP/6-311G(3df,3pd)	51(53)	46(48)	61(63)	76(105)	75(105)	81(110)	45(67)
B3LYP/6-31+G(d)	64(61)	59(55)	73(70)	70(99)	69(99)	74(99)	61(79)
M06-2X/6-31G(d)	52(59)	49(55)	54(60)	144(177)	142(177)	148(180)	124(144)
MP2/6-31G(d)	72(76)			87(179)			47(112)
MP2/6-311++G(d,p)	63(66)			71(94)			14(25)
CCSD(T)/6-31G(d)	93(102)			63(144)			74(93)
CCSD(T)+CF	102(112)			79(229)			(180)

Conclusions

In this study, the mechanisms of the gas-phase SOZ and hydration reactions of the anti-CI that result from the ozonolysis of sabinene have been investigated using quantum-chemical calculations. The SOZ formation could proceed from two different reactions: the sabinene CI and formaldehyde or the sabina ketone and formaldehyde oxide (CI) with corresponding activation energies within the range of ±5 kJ mol–1. However, the calculations show that the SOZ formation is more plausible from the former reaction than the latter. Furthermore, CCSD(T)+CF is the most suitable level of theory in terms of the energy barrier, relative to the other methods of calculation in the SOZ pathway. However, in this pathway, further reactions are required to increase the understanding of the SOA phenomena.

Upon comparing the structural parameters and activation energies for the hydration reaction of the anti-CI with H2O and 2H2O acquired at different levels of theory, it was found that M06-2X/6-31G(d) is most reliable in describing the hydration reactions (lowest energy barrier). Interestingly, the overall activation energy of pathway B2 is barrierless at M06-2X/6-31G(d). Moreover, the reaction of the anti-CI with H2O is slower than with 2H2O, where the overall energy barrier of the latter is lower than the former by 60 kJ mol–1, at the M06-2X/6-31G(d) level of theory. Thus, the formation of sabina ketone, H2O, and H2O2 (pathway B2) is more favorable than the formation of sabina ketone and H2O2 (pathway B1) at different levels of theory. Furthermore, the role of the second H2O molecule in the reaction with 2H2O as a spectator at B3LYP/6-31G(d) reveals that the reaction is less favorable, as the overall activation energy is higher than the H2O mediator role by 49 kJ mol–1. This study sheds more light on the water monomer and dimer reactions: the fact that the reaction is governed by dissociation of α-hydroxy hydroperoxide by a second transition state rather than forming it only.

In the atmosphere, the formation of sabina ketone and OH radicals from the anti-CI of direct VHP formation and dissociation is interestingly more possible than the water-mediated VHP, with lower overall activation energies. The DFT calculations suggest that the direct VHP channel is more plausible roughly by 5 kJ mol–1. Furthermore, the VHP channel with the water monomer is significantly more attainable than the dimer at different levels of theory. Thus, the 1,4 proton transfer for the direct VHP leads to the rapid radicals’ formation compared with the mediated reactions. Furthermore, the DFT calculation shed more light on the level of theory used, in which most reliable in these channels is B3LYP/6-311G(3df,3pd), that is, comparative and more adequate than other methods. Although the reaction is water-mediated, M06-2X/6-31G(d) overestimates the barriers by about 77 kJ mol–1 relative to the other DFT methods.

Computational Methods

All of the geometry computations were performed using the Gaussian 09 (G09) suite.[51] All optimized structures were optimized at B3LYP and M06-2X, utilizing the basis sets of 6-31G(d), 6-31G(2df,p), and 6-311G(3df,3pd).[52−54] The 6-31+G(d) basis set has also been used to test the effect of diffuse functions on the energy barrier. Furthermore, single-point energy calculations using the coupled-cluster theory with triple excitation [CCSD(T)][55,56] at 6-31G(d) and the frozen core second-order Møller–Plesset perturbation theory (MP2) at 6-31G(d) and 6-311++G(d,p) were performed based on the B3LYP/6-31G(d) geometries. A correction factor (CF) from the difference in energy between the MP2/6-31G(d) and MP2/6-311++G(d,p) levels of theory was applied to evaluate the effect of basis sets on the activation energies. Subsequently, the energy values of the CCSD(T)/6-31G(d) level of theory were corrected by the CF, corresponding to CCSD(T)/6-31G(d)+CF [henceforth, identified as CCSD(T)+CF]. It should be noted that the B3LYP/6-31G(2df,p) level of theory was not used for the last two pathways of the hydration reactions of the anti-CI. This is due to high energy barrier calculated at B3LYP/6-31G(2df,p). Moreover, the optimized geometries of all stationary points for the proposed reactions depicted in the figures are selected at B3LYP/6-311G(3df,3pd). This is because the optimized structures were comparable at all the investigated levels of theory. Hence, within the B3LYP formalism, choosing higher basis set changes the geometries only very marginally.

The transition states were verified using the intrinsic reaction coordinate method, ensuring the connection of all stationary points on the PES.[57] Minima were confirmed as those geometries with no imaginary frequencies, and transition states were those with one imaginary frequency. Relative energies of all stationary points were corrected by the zero-point vibrational energies (ZPE). Furthermore, minima structures of radicals were optimized by applying the unrestricted wave function, UB3LYP, UM06-2X, UMP2, and UCCSD(T) with the use of the quadratically convergent self-consistent field (SCF = QC). Moreover, to provide a spectral insight, the IR spectra of sabina ketone was calculated by the vibrational frequency analysis, at the B3LYP/6-311+G(2d,p) level of theory. The peak heights were applied with 10 cm–1 of the half-width at half height, and a scaling factor of 0.9692 was used for the calculated frequencies.[58]