the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Jul 2026
An Overlooked Kinetic Relaxation in the Formation of Sesquiterpene-Derived Criegee Intermediates
Abstract. Criegee intermediates (CIs) from sesquiterpene ozonolysis contribute to secondary organic aerosol (SOA) formation. The ozonolysis rate constants of typical sesquiterpenes have been measured by prior experiments, but whether these values can represent the formation rate constants of sesquiterpene-derived CIs remains questionable. This study reports the overlooked kinetic relaxation in the CI formation from representative sesquiterpenes, including α-cedrene, α-copaene, β-caryophyllene, α-farnesene and β-farnesene. We found that the apparent formation rate constant of sesquiterpene-derived CIs is initially unstable but gradually approaches a plateau, which equals the rate constant of sesquiterpene ozonolysis. Such behavior arises because CI formation cannot instantaneously respond to sesquiterpene ozonolysis due to the finite time for the production of primary ozonides (POZs). Our results also reveal that the kinetic relaxation is sensitive to temperature variations, as cold surges extend the relaxation timescale from minutes to hours (or hours to days) for most sesquiterpenes while heatwaves reversely diminish the relaxation timescale. Exceptionally, β-caryophyllene exhibits the longest relaxation timescale (at least 2.6 days) even during the heatwaves. Our findings demonstrate that neglecting this kinetic relaxation may substantially overestimate the rate of sesquiterpene-derived CI formation and thus the CI-driven atmospheric oxidation capacity under extreme temperature conditions.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-3255', Anonymous Referee #1, 15 Jul 2026
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CC1: 'Comment on egusphere-2026-3255', Anonymous Refereee, 30 Jul 2026
The authors applied a kinetic model based on thermal equilibrium to a reaction system far from thermal equilibrium. The results are misleading.
(1) The kinetic model assumed thermal equilibrium for SPCs and POZs, and ignored collisional energy transfer within each species. This may be true for SPCs, and is invalid for POZs. POZs are formed with high excitations as POZs*, which can undergo prompt isomerization to CIs*. The authors calculated k3 using the equilibrium energy distribution in POZs. This is invalid unless the reactions are under extremely high pressure.
The kinetic processes are more often modelled using RRKM-ME method. Due to the large size of reaction system, there might be a fraction of POZ* being thermalized by collision before their prompt isomerization.
(2) The kinetic model is simply an example of consecutive reaction as “Reactant -> Intermediate -> Product” in all Physical Chemistry textbooks. The rate of reactant consumption and the rate of product formation are NOT always the same. This is a commonsense, particularly when “Intermediate -> Product” is slow. It is NOT a black box.
(3) Note that rate coefficient is an empirical parameter, and it is well-defined only for reactants with steady-state energy distribution (such as equilibrium distribution under high pressures). For system far from steady-state energy distribution such as POZ* here, the rate coefficient is just a phenomenological parameter and would vary with time.
(4) Line 167: “kCI is in principle proportional to the POZ concentration”. This statement is incorrect. kCI, if exist as stated in (3), should be a parameter of molecule and energy distribution. It is “the Formation Rate of CI is proportional to the POZ concentration”. Figure 1C is incorrectly interpreted.
Citation: https://doi.org/10.5194/egusphere-2026-3255-CC1 -
RC2: 'Comment on egusphere-2026-3255', Anonymous Referee #2, 31 Jul 2026
In this manuscript, the authors have evaluated “kinetic relaxation” in the ozonolysis process in atmospheric sesquiterpenes using computational methods. Here, they compared the reaction rate for forming primary ozonide (POZ) versus that for forming the Criegee intermediates (CIs). In both reactions, the reactants are the sesquiterpenes and ozone. The authors defined kinetic relaxation as the ratio of CI formation rate versus POZ formation rate. They performed theoretical calculations using M06-2X/def2-TZP geometries with DLPNO-CCSD(T) energy corrections.
The key issue in this manuscript is that the authors considered thermal POZ formation from ozone and sesquiterpene and CI formation from thermally equilibrated POZ as two independent processes for the calculation. I suggest that the authors properly show the calculated energies in Figures 2C and 2D. Whether POZ will be in equilibrium or not after passing the transition state from ozone and sesquiterpene depends on the exothermic energy of POZ relative to the reactants, ozone and sesquiterpenes. Many previous studies have mentioned that ozonolysis will produce “vibrationally excited” POZ, which can quickly produce CI under atmospheric pressure conditions. Therefore, the difference in the POZ formation rate and the CI formation rate is assumed to be small in atmospheric conditions.
Instead of using thermal approximation for each process, one should use energy-based master’s equation with buffer gas collision for energy activation and deactivation. Such protocols are available in the multiwell package that the authors used for calculating thermal rate coefficients.
In addition, schematic geometries of intermediates and CIs should be presented in the main text. Labels such as SPC1-1, SPC1-2, or CI isomer 1 are hard to follow without molecular structures in the main text.
Some conditions mentioned in the main text are not necessary. For example, on page 8, the authors assume steady-state SPC concentration for the reaction forming POZ. However, forming POZ from the reactants of ozone and sesquiterpene can occur by directly reaching the TS through collision.
Citation: https://doi.org/10.5194/egusphere-2026-3255-RC2
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- 1
Dear Editor:
This is a theoretical work which calculates related rate coefficients and analyzes temperature-dependent kinetics for a few systems of sesquiterpene ozonolysis. The main mechanism is copied below.
Terpene + 𝑂3 {𝑘1⇌𝑘−1} SPCs
SPCs {𝑘2→} POZs
POZs {𝑘3→} CIs
While the estimation for k1, k−1, and k2 in this work does not seem unreasonable, the very small values of k3 (as given in Figure 3 (B) and (C)) are surprising. Note: the y-axis unit is strange; k3 should be first-order.
It appears to me that this work assumes that the primary ozonide (POZ) is fully thermalized and calculates k3 accordingly. However, it is well known that the POZ formation is highly exothermic and the large energy release leads to ultrafast decomposition of the POZ.
Unless under a very high pressure, thermalized POZ is not expected.
At lines 242-244, the authors claimed:
“Once formed, sesquiterpene-derived POZs rapidly stabilize by colliding with the surrounding gas molecules (Chuong et al., 2004; Hakala and Donahue, 2023), mainly nitrogen and oxygen in the air, which inhibits rapid decomposition.”
However, both Chuong et al., 2004 and Hakala and Donahue, 2023 do not support this claim at all. The former mentions:
“… ozone adds to the double bond in a concerted [2 + 3] cycloaddition to produce a vibrationally excited primary ozonide (POZ), which then quickly decomposes to yield an excited carbonyl oxide [Criegee intermediate (CI)] and a carbonyl compound. The excited CI may either undergo further unimolecular reactions or be collisionally stabilized.”
And the later mentions:
“Here, we focus on gas-phase systems, where POZ decomposition is rapid, and also assume that concerted scission of C−C and O−O bonds gives bimolecular (or for endocyclic alkenes, unimolecular) products with unit yields.”
Therefore, I feel that the basic assumption of this work is in doubt. The authors should carefully consider the energy content of POZ, which has been addressed in a number of publications, but fully neglected in this work.