Ozonolysis of β-Phellandrene via Criegee Intermediates: Mechanistic Insights from DFT Calculations

Terpenes constitute a major class of biogenic volatile organic compounds (VOCs) that play a central role in atmospheric oxidation chemistry.^1-4 These compounds, emitted in large quantities by vegetation, are highly reactive with key atmospheric oxidants, including ozone (O₃), hydroxyl radicals (OH), and nitrate radicals (NO₃).⁵ Their oxidation contributes significantly to the formation of secondary organic aerosols (SOAs), which affect not only air quality but also climate through their influence on cloud condensation nuclei (CCN) activity and radiative forcing.^6-8

Among these compounds, β-phellandrene is a structurally unique monoterpene featuring a cyclic backbone and multiple double bonds.⁹ These structural features result in diverse reaction pathways, leading to a wide range of oxidation products. Gas-phase reactions of β-phellandrene with OH, NO₃, and O₃ were studied under atmospheric conditions (297 K, 1 atm), yielding rate constants of 1.68 × 10^-11, 7.96 × 10^-12, and 4.77 × 10^-16 cm³ molecule^-1 s^-1, respectively.⁹ These values correspond to atmospheric lifetimes ranging from approximately 1 to 8 hours, depending on oxidant levels. OH radicals dominate daytime degradation, while NO₃ and O₃ become more significant during nighttime.

The ozonolysis of β-phellandrene is particularly important in the formation of Criegee intermediates and biradicals, both of which serve as reactive intermediates capable of initiating secondary reactions. Criegee intermediates can abstract hydrogen atoms or form acids and peroxides, while biradicals may undergo rearrangements or oxygen abstraction to yield stable carbonyl products such as ketones and aldehydes.^10,11 These reactions contribute not only to SOA formation but also to broader atmospheric processes, such as oxidative capacity modulation and reactive oxygen species production.^10,12 Due to the transient nature of these reactive intermediates, direct experimental detection is often challenging. Therefore, computational chemistry—particularly density functional theory (DFT)— serves as a powerful tool for investigating their structures, energetics, and reaction pathways.¹³

In this study, we used the UB3LYP/6-311++G(d,p) level of theory to characterize biradical intermediates formed during the ozonolysis of β-phellandrene. The computed structures and energetics support proposed reaction mechanisms and provide new insights into biradical pathways and their role in terpene oxidation and secondary product formation.

The proposed mechanism for the ozonolysis of β-phellandrene is illustrated in Fig. 1. The initial reaction of β-phellandrene (BP) with ozone generates two primary ozonides (POZ-a and POZ-b) through the addition to different double bonds. Each primary ozonide subsequently undergoes cleavage via transition states (TR-1 to TR-4), yielding four distinct Criegee intermediates (CI-1 to CI-4). Following cleavage, CI-1 decomposes to produce 4-isopropyl-2-cyclohexanone (P1) along with dioxirane, while CI-2 rearranges to form an intermediate (IM-P2) with the concurrent release of formaldehyde (HCHO). Similarly, CI-3 and CI-4 undergo ring opening to yield IM-P3 and IM-P4, respectively. The potential energy diagram for the ozonolysis of β-phellandrene, illustrated in Fig. 2, presents the relative energies of the primary ozonides (POZs), Criegee intermediates (CIs), transition states (TRs), and other intermediates. Among these, the POZ-a pathway is approximately 2.6 kcal/mol lower in energy than POZ-b, which can be attributed to reduced steric hindrance and increased resonance stabilization when ozone adds to the terminal double bond.

Figure 1. Ozonolysis pathways of β-phellandrene, illustrating the formation of primary and secondary ozonides, intermediates, and final products.

Figure 2. Computed potential energy diagram for the ozonolysis of β-phellandrene.

Although the transition states (TSs) for the BP + O₃ → POZ-a/b reactions were not explicitly calculated in this study, analogous reactions in limonene exhibit very low TS barriers (–0.19 to 1.89 kcal mol^-1), suggesting that both POZ-a and POZ-b formation pathways are kinetically accessible.¹⁴

The transition states that mediate the conversion from primary ozonides (POZ-a and POZ-b) to their corresponding Criegee intermediates (CI-1 to CI-4) in the ozonolysis of β-phellandrene are presented in Fig. 3. These optimized structures, designated as TR-1 through TR-4, display characteristic features of asynchronous O–O bond cleavage. The O–O bond lengths in these transition states range from 2.772 Å to 2.995 Å, indicating varying degrees of bond elongation along the dissociation coordinate. This structural variation reflects the dynamic nature of the bondbreaking process and possible conformational effects inherited from the POZ frameworks.

Figure 3. Optimized geometries of transition states TR-1 to TR-4 involved in the cleavage of primary ozonides (POZ-a and POZ-b) to form Criegee intermediates during β-phellandrene ozonolysis. Key O–O bond distances (in Å) are labled.

Each transition state was confirmed to be a first-order saddle point by vibrational frequency analysis, with a single imaginary frequency corresponding to the O–O bond dissociation mode. This confirms that the geometries are true transition states on the potential energy surface leading from POZs to Criegee intermediates. These POZ→CI steps were selected for TS analysis because they are endothermic and likely represent key energetic bottlenecks in the reaction network. In contrast, subsequent rearrangements and product-forming steps are generally exothermic and have been shown in related systems to proceed with low to moderate barriers. Prioritizing the characterization of the POZ decomposition steps thus allows us to capture the most energetically critical features of the ozonolysis mechanism.

Table 1 summarizes the relative energy differences (ΔE) between selected pairs of intermediates and transition states along the proposed reaction pathway. The values represent the energy gap between each species pair (E₂ − E₁), highlighting key features such as the comparable activation barriers for the formation of CI-1 and CI-2 (1.2 kcal/mol), as well as the notably low energy differences between TR-1 and TR-2 (−0.7 kcal/mol) and between TR-3 and TR-4 (−0.6 kcal/mol). These small energy differences suggest possible energetic degeneracy or dynamic interconversion between respective species. As a result, decomposition of POZ-a yields the lowest-energy Criegee intermediates, CI-2 and CI-1, whereas CI-3 and CI-4, derived from POZ-b, lie about 6 kcal/mol higher in energy. This trend is also reflected kinetically: TR-1 and TR-2, leading to CI-1 and CI-2, have significantly lower activation barriers than TR-3 and TR-4.

Table 1. Energy differences (ΔE = E₂ − E₁, kcal/mol) between selected species pairs involved in the reaction pathway

To further assess the thermodynamic feasibility of the post-Criegee transformations, we evaluated the enthalpy (ΔH), Gibbs free energy (ΔG), and entropy (ΔS) changes for the overall reactions starting from β-phellandrene and ozone. These results are summarized in Table 2 and provide additional support for the dominance of the CI-1 → P1 pathway.

Table 2. Thermodynamic parameters (ΔH, ΔG, and ΔS) for the formation of reaction products from β-phellandrene and ozone at 300 K

The full thermodynamic profiles for reactions starting from β-phellandrene and ozone at 300 K are presented in Table 2. The formation of P1 and dioxirane exhibits the most favorable ΔG (–85.51 kcal/mol), with negligible entropy change (+0.24 cal/mol·K), suggesting the reaction is primarily driven by enthalpy.

Interestingly, the IM-P2 + HCHO pathway shows a modest entropy gain (+4.96 cal/mol·K), likely due to the liberation of a small volatile molecule (formaldehyde), which contributes to the free energy decrease. In contrast, the IM-P3 and IM-P4 channels display negative entropy changes (–24.78 and –33.62 cal/mol·K, respectively), indicating decreased disorder upon formation—possibly due to structural rigidity or decreased degrees of freedom. These unfavorable entropy terms partially offset their enthalpic contributions, making these routes thermodynamically less favorable overall.

Among the CIs, CI-1 undergoes a direct, concerted, and highly exergonic reaction to form P1 and a dioxirane without passing through any intermediate. In contrast, CI-2, CI-3, and CI-4 proceed via discrete biradical intermediates (IM-P2–4) before yielding stable products. Although the transition state energy from POZ-b to CI-2 is slightly lower than that of the POZ-a to CI-1 pathway, suggesting a marginally more favorable kinetic route, the electronic energy of the final product P1, derived from CI-1, is significantly lower than that of other products. Therefore, we anticipate that the CI-1 channel leading to P1 is overall more favorable due to the greater thermodynamic driving force inferred from electronic energy differences.

However, we acknowledge that our calculations did not include transition state structures for all subsequent reaction steps beyond the formation of Criegee intermediates. Although transition states for the Criegee intermediate → product or intermediate steps were not explicitly located in this study, their presence is well established in related systems such as limonene, where such pathways proceed via moderate barriers (~7–12 kcal mol⁻¹).¹⁴ In particular, the transition states connecting CI-1 to P1 and CI-2 to IM-P2 have not been explicitly characterized in this study. As a result, the present data alone are insufficient to definitively determine whether the P1 or IM-P2 pathway constitutes the dominant reaction channel.

Nevertheless, experimental evidence strongly supports the importance of the P1 pathway. In particular, Hakola et al. reported the detection of compound P1 as a major stable product in the atmospheric ozonolysis of β-phellandrene, with a yield of approximately 29%.¹⁵ In the same study, additional minor products were identified, including 3-isopropyl-6-oxoheptanal (3.5%) and 6-isopropyl-3-oxohexanal (2.5%), along with formaldehyde and other small carbonyl-containing species. Some of these products were not fully quantified due to their high reactivity and rapid transformation under ambient conditions. These findings support the interpretation that P1 is not only thermodynamically favorable but also chemically persistent in the atmosphere.

In contrast, the intermediate IM-P2 may not remain as a stable end product. Even if it undergoes cyclization, the resulting dioxirane is expected to be highly unstable and prone to further transformation. IM-P2 may also react with atmospheric oxidants, leading to the formation of more complex oxidation products or contributing to the generation of secondary organic aerosols. These subsequent reactions render the IM-P2 pathway more chemically diverse and potentially less selective than the CI-1→P1 pathway.

As this work is intended as a computational note, the present study does not include complete kinetic analyses or all transition states along the full reaction network. We plan to address this limitation in future work by performing a comprehensive kinetic analysis, including the calculation of transition states for the conversion of Criegee intermediates into final products.

Notably, the formation of IM-P2 from CI-2 involves the elimination of formaldehyde (HCHO), providing thermodynamic driving force. By contrast, the ring opening of CI-3 and CI-4 does not release a small stable molecule, resulting in lower exergonicity and less favorable pathways for product formation. Consequently, the POZ-a pathway via CI-1 and CI-2 is energetically preferred, while IM-P2, IM-P3, and IM-P4 remain in higher-energy states and are more likely to react with O₂ than to undergo unfavorable cyclization.

Although P1 is mainly formed via direct decomposition of CI-1, the biradical intermediate IM-P2, derived from CI-2, may also serve as an alternative route to P1 formation. This can occur through an oxygen abstraction process involving atmospheric oxidants, yielding P1 as a secondary product. Such a mechanism suggests that IM-P2, in addition to branching toward other oxidation routes, may contribute to P1 formation under oxidizing conditions. The transformation of IM-P2 into P1 via oxygen abstraction is supported by both theoretical and experimental evidence. Cremer et al. demonstrated that methylenebis(oxy)-type biradicals, similar in structure to IM-P2, can undergo low-energy rearrangements or oxygen transfer reactions to form stable products like esters or ketones.¹⁶ High-level CCSD(T) and MR-AQCC calculations indicated that these biradicals decompose into carbonyl-containing species with activation energies of 2–4 kcal/mol, making such transformations feasible even at ambient temperatures. This suggests that IM-P2 could also transform into P1 via intramolecular rearrangement or oxygen abstraction.

Similarly, Adam et al. showed that dimethyldioxirane, a strained cyclic peroxide, acts as an efficient oxygen donor in reactions with nucleophiles.¹⁷ By analogy, IM-P2 may acquire an oxygen atom from residual ozone-derived intermediates or atmospheric oxygen, converting into P1, a stable ketone product.

Our computed energy profile is fully consistent with these experimental findings, demonstrating that the pathway POZ-a→CI-1→P1 is both kinetically and thermodynamically favored. In contrast, routes involving POZ-b and CI-3/CI-4 are significantly less favorable. This strong agreement between theoretical and experimental results highlights the reliability of our mechanistic model and emphasizes the critical role of Criegee intermediate energetics in controlling product selectivity during β-phellandrene ozonolysis.

This study provides a comprehensive mechanistic understanding of the ozonolysis of β-phellandrene through detailed DFT calculations. Four distinct reaction pathways were identified, originating from two primary ozonides and leading to four final products via Criegee intermediates. Among them, the formation of P1 was found to be the most favorable both kinetically and thermodynamically. These findings underscore the critical role of Criegee intermediate stability in determining product selectivity and offer valuable insight into the atmospheric oxidation behavior of biogenic monoterpenes.

Computational details

Geometry optimization and energy calculations of all species were carried out using the UB3LYP/6-311++G(d,p) level of theory with Gaussian 16 software.¹⁸ Zero-point energies were obtained at the same level through vibrational frequency calculations. Relative energies of intermediates, transition states, and final products were presented with zero-point energy corrections. Transition state structures were validated via intrinsic reaction coordinate (IRC) calculations to confirm that each TS connects the appropriate primary ozonide and Criegee intermediate.