Kinetics of the Reactions of Ozone with Halogen Atoms in the Stratosphere

Abstract

It is well established that reaction cycles involving inorganic halogens contribute to the depletion of ozone in the atmosphere. Here, the kinetics of O₃ with halogen atoms (Cl, Br, and I) were investigated between 180 and 400 K, expanding the temperature range relative to prior studies. Canonical variational transition state theory including small curvature tunneling correction (CVT/SCT) were considered, following the construction of the potential energy surfaces. MRCI + Q/aug-ano-pVTZ//MP2/aug-cc-pV(T + d)Z and MRCI + Q/aug-ano-RCC-VTZP//MP2/aug-cc-pV(T + d)Z levels of theory were used to calculate the kinetic parameters. Calculated rate coefficients were used to fit the Arrhenius equations, which are obtained to be k₁ = (3.48 ± 0.4) × 10⁻¹¹ exp[(−301 ± 64)/T] cm³ molecule⁻¹ s⁻¹, k₂ = (3.54 ± 0.2) × 10⁻¹¹ exp[(−990 ± 35)/T] cm³ molecule⁻¹ s⁻¹ and k₃ = (1.47 ± 0.1) × 10⁻¹¹ exp[(−720 ± 42)/T] cm³ molecule⁻¹ s⁻¹ for the reactions of O₃ with Cl, Br, and I atoms, respectively. The obtained rate coefficients for the reactions of O₃ with halogen atoms using CVT/SCT are compared to the latest recommended rate coefficients by the NASA/JPL and IUPAC evaluations. The reactivity trends and pathways of these reactions are discussed.

1. Introduction

The importance of halogens (X = Cl, Br, and I) as catalysts in the destruction of ozone in the atmosphere is well recognized [1]. Halogen source gases are emitted at the surface both naturally and from human activities, and eventually can be photolyzed by sunlight or react chemically to convert their halogen content into inorganic forms. Ozone destruction takes place through a number of different chemical cycles in which halogen atoms are the key reactant in the ozone loss step.

ClO radicals are major contributors to stratospheric ozone loss in the Arctic and Antarctic poles [1,2]. During polar winter and spring, heterogeneous processes convert relatively inert chlorine reservoir species (ClONO₂ and HCl) into active, photolabile forms (Cl₂ and HOCl). These photolabile species are rapidly photolyzed in sunlight to produce Cl, which reacts with O₃ to form ClO. Subsequent reaction of ClO with another ClO molecule at cold temperatures to form ClOOCl initiates a catalytic reaction cycle [3,4], which repeatedly forms Cl in sunlight and subsequently destroys O₃ via the Cl + O₃ reaction. This is one of many catalytic ozone-loss cycles at work in the stratosphere, in which a single Cl atom can destroy numerous O₃ molecules [1].

BrO radicals are formed in the atmospheric breakdown of bromine-containing compounds and are similarly involved in ozone destruction occurring in the polar and midlatitude stratosphere [1,2]. Ozone-destroying Br is often formed in catalytic cycles that involve interhalogen reactions. The BrO + ClO reaction cycle in particular produces both Br and Cl atoms to react with O₃. The reactivity of bromine on a per atom basis is approximately 70 times more destructive to stratospheric ozone than is chlorine [1,5,6].

Cl + O₃ ⟶ ClO + O₂

(R1)

Br + O₃ ⟶ BrO + O₂

(R2)

I + O₃ ⟶ IO + O₂

(R3)

The iodine-catalyzed destruction of O₃ is through IO, formed directly in the reaction between I atoms and O₃. Recent work suggested that iodine plays a more significant role than previously believed in stratospheric ozone chemistry and, moreover, that iodine is approximately 400–1000 times more effective at destroying ozone than stratospheric chlorine in the lower stratosphere. In the future, the share of halogen-induced ozone loss in the stratosphere due to reactions of iodine will likely be greater than it is today [7,8].

Of significant recent interest in the literature, and providing additional motivation for this work, is the potential for co-injection of inorganic halogens along with sulfate into the stratosphere from explosive volcanic eruptions [1,9]. While once believed to be unimportant due to hydrometeor scavenging, it is now well established that halogens from volcanoes are transported to the stratosphere, with recent enhancements in chlorine [10], bromine [11], and iodine [12] all being reported.

Gas-phase reactions involved in ozone loss cycles can have significant temperature dependences [13]. Hence, kinetic studies must be carried out over a wide range of temperatures to fully describe the behavior of these processes. In particular, extremely cold temperatures are possible in the upper troposphere and lower stratosphere. Largely because of their importance in stratospheric chemistry, the kinetics of O₃ reactions with halogen atoms have been the subject of numerous experimental studies (e.g., Cl + O₃, Br + O₃, and I + O₃) [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. On the theoretical side, however, the number of kinetics studies of O₃ with halogen atoms are relatively sparse [38,39,40,41,42,43,44,45,46].

Farantos et al., 1978 [38] have studied the classical dynamics of the O₃ reaction with Cl and derived the rate coefficients from 220–300 K. Tyrrell et al., 2001 [40] have used B3 LYP/-311 + G* theories and found that the reaction between ozone and the Cl atom proceeds via an early transition state and a late transition state. Castillo et al., 2011 [41] have studied the dynamics of O₃ + Cl by means of quasi-classical trajectory (QCT) calculations using the UQCISD/aug-cc-pVDZ level of theory over the temperature range of 200–400 K. None of these studies used dual level calculations, which are known for more accurate kinetic parameters [47,48], especially at low temperatures. Very few groups have studied the reaction mechanism of O₃ with Br using theoretical methods [44,45,46], and theoretical rate coefficients have not been reported in the literature. While there are theoretical studies [49,50] of the reaction mechanism of O₃ with iodine oxides, there are no theoretical studies of the reaction mechanism and low temperature kinetics of O₃ with the I atom. To the best of our knowledge, the present study represents the first report of the theoretical temperature-dependent rate coefficients for the reactions of ozone with the bromine atom and the iodine atom.

The temperature ranges used to determine the recommended values in the most recent NASA/JPL [13] compendium for the reactions of O₃ with Cl, Br, and I atoms are 205–300 K, 195–422 K, and 230–370 K, respectively. The IUPAC [51]-recommended temperature ranges for the reactions of O₃ with Cl, Br, and I atoms are 180–300 K, 190–430 K, and 230–370 K, respectively. (Hereafter, NASA/JPL and IUPAC recommendations refer to [13,51], respectively, with superscript reference numbers not shown.) As the heterogeneous activation of inorganic chlorine primarily occurs when temperatures drop below ~195 K in the polar vortex, rate coefficients for the title reactions in the lower temperature range (especially < 200 K) are very important. The recommended temperature-dependent rate coefficients by both the NASA/JPL and IUPAC evaluations are limited, particularly for iodine. Both experimental and theoretical studies play important roles in improving our understanding of the chemical reactions that are occurring in the stratosphere, with theoretical calculations in particular providing valuable mechanistic insight. Our focus here is to improve the theoretical understanding of the title reactions and extend the temperature range beyond what is experimentally available, from 180 to 400 K for all three halogens with a primary focus on atmospherically relevant conditions.

In the present investigation, the kinetics of O₃ with halogen atom reactions have been studied using canonical variational transition state theory including small curvature tunneling corrections (CVT/SCT) over the temperature range of 180–400 K. To get more constrained and accurate kinetics parameters, dual level calculations were performed at the MRCI + Q/aug-ano-pVTZ//MP2/aug-cc-pV(T + d)Z and MRCI + Q/aug-ano-RCC-VTZP//MP2/aug-cc-pV(T + d)Z levels of theory with ZORA (zeroth-order regular approximation) using the ORCA program. Thermodynamic properties were studied at the CCSD(T)/aug-cc-pV(T + d)Z level of theory. Reactivity trends of O₃ with all the halogens (F, Cl, Br, and I) and reaction pathways are discussed.

2. Computational Methods

The geometries and harmonic frequency calculations of reactants (halogens and O₃), pre-reactive complexes (PRCs), transition states (TSs), product complexes (PCs), and products were performed at the Møller−Plesset level of theory with second order perturbation (MP2) in combination with the augmented correlation consistent polarized triple-ζ (aug-cc-pV(T + d)Z) basis set [52,53]. Møller−Plesset perturbation theory assumes Hartee-Fock Hamiltonian as the zero-order perturbation. The combination of the MP2 method with the aug-cc-pV(T + d)Z basis set is extensively used for atmospheric reactions in the literature [54,55]. Transition states were identified with one imaginary frequency. Reactants, pre-reactive complexes, product complexes, and products were identified with zero imaginary frequencies. All the electronic structure calculations were performed using Gaussian 09 program suite [56], and all the normal modes and structures were viewed in Gauss view [57]. Intrinsic reaction coordinates (IRCs) calculations were carried out at the MP2/aug-cc-pV(T + d)Z level of theory for all the transition states to verify that the transition states are connected to the reactants and products. Thermodynamic properties were studied using Coupled-cluster with single, double, and triple excitation (CCSD(T)) with the aug-cc-pV(T + d)Z level of theory. To obtain more refrained and accurate energies, single point energy calculations were performed. Dual level calculations were carried out at the Multireference configuration interaction (MRCI) method. For better accuracy, the Davidson correction, core-valence correlation, and spin-orbit coupling effects are included (+Q). MRCI + Q in combination with aug-ano-pVTZ, aug-ano-RCC-VTZP, and ZORA (zeroth-order regular approximation) were used for refining energies [58,59]. These dual level calculations were performed using the ORCA program, which is one of the most versatile quantum chemistry packages available [60,61]. DFT, single-reference correlation, and multi-reference correlation methods can be executed using ORCA. The lowest spin-orbit states, A₁ for O₃ and ²P_3/2 for Cl, Br, and I atoms, were used throughout the calculations in this study.

3. Kinetics

The temperature-dependent rate coefficients for the reactions of halogen atoms with O₃ were calculated with CVT/SCT using the POLYRATE 2016A program and GAUSSRATE [62,63]. The POLYRATE program is a well-known software package for calculating kinetics parameters for gas-phase reactions; a detailed procedure was given in our previous articles [64,65]. To get the canonical variational transition state rate coefficient, the generalized rate coefficients can be minimized by varying the transition state dividing surface along the reaction coordinate using the following expressions:

$$k^{CVT/SCT}\left(T\right)={\mathrm{Ƙ}}^{CVT/SCT}\left(T\right)k^{CVT}\left(T\right)$$

(1)

$$k^{GT}\left(T,s\right)=\sigma \frac{k_{B}T}{h}\left(\frac{Q^{GT}\left(T,s\right)}{{\varnothing }^R\left(T\right)}\right)exp\left(\frac{-V_{MEP}\left(s\right)}{k_{B}T}\right)$$

(2)

Here, k^CVT/SCT(T) is the tunneling corrected rate coefficient, which is obtained by multiplying k^CVT and a temperature-dependent transmission coefficient $\mathrm{Ƙ}$^CVT/SCT, σ is reaction path degeneracy, k_B is Boltzmann’s constant, T is temperature in Kelvin, h is Planck’s constant. Q^GT is the canonical partition function of the generalized transition state at “s”, and “s” is a reaction coordinate parameter that determines the location of the generalized transition dividing surface. ${\varnothing }^R$ is the partition function of the reactant. V_MEP(s) is the potential along the reaction path at “s”, and the minimum energy pathway (MEP) was constructed with a gradient step size of 0.01 Å. The canonical variational transition state is located by maximizing the free energy of activation with respect to “s”. The minimum energy pathway is obtained using direct dynamics for a small range of the reaction path with the mass scaled reaction coordinate “s” from –1.0 to 1.0 Å by using the Page-McIver integrator with a step size of 0.01 Å.

4. Results and Discussion

4.1. Reaction of Cl + O₃

The potential energy level diagram for the reaction of O₃ with Cl atoms (R1) is given in Figure 1 along with the optimized geometries at the MP2/aug-cc-pV(T + d)Z level of theory. All the structural parameters are given in the Supplementary Materials Table S1. This reaction goes through an early transition state (pre-reactive complex, PRC), is connected through a late transition state (product complex, PC), and leads to the products as shown in Figure 1. The Cl atom attack on a terminal oxygen of the ozone in both trans and cis pathways was identified, consistent with previous literature [38,39,40,41,42,43]. Among the trans and cis pathways, the trans pathway was found to be the lowest energy pathway. Hence, the trans pathway is considered in the present kinetics calculations. In the case of O atom abstraction by the Cl atom, the breaking O–O bond length in O₃ was stretched up to 32% when compared with the bond length in the reactant O₃.

The obtained bond lengths, bond angles, and vibrational frequencies of the Cl + O₃ reaction in the present study are compared with values in the available literature in

Table 1. The obtained bond lengths (r_e in Å) and bond angles (θ in deg) for the reaction of Cl + O₃ at various levels of theory.

Species		This Work	Hwang et al. [39]	Tyrrell et al. [40]		Castillo et al. [41]
		MP2/aug-cc-pV(T + d)Z	QCISD/ 6-311G*	pw91pw91/ aug-cc-pVQZ	pw91pw91/6-311 + G*	QCISD/aug-cc-pVDZ
O3	re	1.230	1.256	1.272	1.283	1.264
	θ	118.35	117.7	118.2	116.9	117.4
Pre-reactive complex	re Cl-O1	2.814	2.284	2.305	2.313	2.449
	θ	101.2	110.8	110.8	112.4	109.5
	re O1-O2	1.235	1.320	1.323	1.336	1.315
	θ O1-O2-O3	118.0	113.9	115.8	115.8	114.1
	re O2-O3	1.225	1.287	1.256	1.258	1.295
Transition state	re Cl-O1	1.634	1.705	2.284	2.302	2.449
	θ	105.8	105.4	112.9	114.1	109.5
	re O1-O2	1.627	1.433	1.326	1.329	1.315
	θ O1-O2-O3	108.6	107.7	118.7	118.7	114.1
	re O2-O3	1.198	1.239	1.254	1.256	1.295
Product complex	re Cl-O1	1.559	1.664	1.642	1.637	2.449
	θ	106.0	106.2	111.3	112.9	109.5
	re O1-O2	2.893	1.625	2.441	2.191	1.315
	θ O1-O2-O3	108.6	110.8	113.3	113.8	114.1
	re O2-O3	1.188	1.163	1.213	1.210	1.295
ClO	re Cl-O1	1.559		1.53	1.619	1.634
O2	re O2-O3	1.187		1.228	1.228	1.211

and

Table 2. Vibrational frequencies (cm⁻¹) for the reaction of Cl + O₃ at various levels of theory.

Species		This Work	Tyrrell et al. [40]	Castillo et al. [41]
		MP2/aug-cc-pV(T + d)Z	pw91pw91/aug-cc-pVQZ	QCISD/aug-cc-pVDZ
O3	v1	795.4	714	737
	v2	1375.0	1066	894
	v3	1379.9	1187	1219
Pre-reactive complex	v1	39.8	83
	v2	87.0	157
	v3	95.3	252
	v4	800.6	558
	v5	1350.4	790
	v6	1394.1	1475
Transition state	v1	396.8i	134i	90i
	v2	54.6	111	57
	v3	231.2	211	187
	v4	537.9	651	672
	v5	861.0	818	867
	v6	1520.8	1181	968
Product complex	v1	43.5	40
	v2	63.1	54
	v3	101.3	123
	v4	113.8	150
	v5	792.3	822
	v6	1521.6	1538
ClO	v1	916.4	829	803
O2	v1	1765.3	1558	1625

. There is variation in the level of agreement across the 42 intercompared variables shown, but our computed bond lengths, bond angles, and vibrational frequencies typically agree with the reported values in previous studies. The observed differences are most likely due to the different levels of theory and basis sets used in the computations by Hwang et al. [39] (QCISD/6-311G*), Tyrrell et al. [40] (PW91PW91/aug-cc-pVQZ and PW91PW91/6-311 + G*), and Castillo et al. [41] (QCISD/aug-cc-pVDZ) relative to the present study (MP2/aug-cc-pV(T + d)Z).

The energies of all the stationary points were refined at MRCI + Q/aug-ano-pVTZ using the optimized geometries obtained at the MP2/aug-cc-pV(T + d)Z level of theory. Thus, refined energies were used in dual level calculations to compute the rate coefficients for the reaction of R1 over the temperature range of 180–400 K. The rate coefficients from CVT/SCT at the MRCI + Q/aug-ano-pVTZ//MP2/aug-cc-pV(T + d)Z levels of theory are compared with the recommended rate coefficients by NASA/JPL and IUPAC in Figure 2. The obtained temperature-dependent rate coefficient (180–400 K) for R1 is k₁ = (3.48 ± 0.4) × 10⁻¹¹ exp[(−301 ± 64)/T] cm³ molecule⁻¹ s⁻¹. The reported uncertainties on the A factor and -E_a/R are, respectively, from the deviation in the intercept and slope of a two-parameter linear least squares fit of ln k versus 1/T.

Table 3. Rate coefficients (cm³ molecule⁻¹ s⁻¹) for the reaction of O₃ with Cl at the MRCI + Q/aug-ano-pVTZ//MP2/aug-cc-pV(T + d)Z levels of theory using CVT/SCT rate coefficients along with the recommended rate coefficients by NASA/JPL [13] and IUPAC [51] for comparison.

T(K)	k (Present Work)	k (JPL)	k (IUPAC)
180	6.54 × 10−12		6.98 × 10−12
200	7.73 × 10−12		8.02 × 10−12
210	8.30 × 10−12	8.87 × 10−12	8.51 × 10−12
230	9.40 × 10−12	9.64 × 10−12	9.44 × 10−12
250	1.04 × 10−11	1.03 × 10−11	1.03 × 10−12
270	1.14 × 10−11	1.10 × 10−11	1.11 × 10−11
298	1.27 × 10−11	1.18 × 10−11	1.21 × 10−11
300	1.28 × 10−11	1.18 × 10−11	1.22 × 10−11
350	1.47 × 10−11
400	1.64 × 10−11

shows the rate coefficients from this work compared with the recommended rate coefficients from NASA/JPL (2.3 × 10⁻¹¹ exp[−200/T] cm³ molecule⁻¹ s⁻¹) and IUPAC (2.8 × 10⁻¹¹ exp[−250/T] cm³ molecule⁻¹ s⁻¹).

The obtained rate coefficients in the present study for the reaction of R1 are in excellent agreement with the JPL- and IUPAC-recommended values, differing by only 7% and 5%, respectively, at 298 K. For comparison, the theoretically reported rate coefficient at 298 K by Farantos et al. (2.6 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹) is a factor of two higher than the recommended rate coefficient by the NASA/JPL evaluation, and the 298 K value of Castillo et al. (9.29 × 10⁻¹² cm³ molecule⁻¹ s⁻¹) is 21% lower. Our rate coefficients differ by 0–8% over the temperature range of 205–300 K when compared with JPL-recommended values and by 0–7% from 180–300 K when compared with IUPAC. Overall, the obtained rate coefficients in the present investigation are very close to the NASA/JPL and IUPAC-recommended rate coefficients when compared with previously reported theoretical rate coefficients, which shows the accuracy and reliability of the advanced theoretical methods used in the present calculations.

Further comparison of our theoretical rate coefficients with previous individual experimental studies generally yields good agreement. The obtained rate coefficients for the reaction of R1 differ by 0–4% when compared with Beach et al. [14] ((3.1 ± 1.35) × 10⁻¹¹ exp[–(280 ± 100)/T] cm³ molecule⁻¹ s⁻¹) over the temperature range of 184–298 K, 14–15% when compared with Kurylo and Braun [21] ((2.94 ± 0.49) × 10⁻¹¹ exp[−(298 ± 39)/T] cm³ molecule⁻¹ s⁻¹) over the temperature range of 213–298 K, 4% when compared with Leu and DeMore [22] ((1.3 ± 0.3) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹) at 295 K, 7–15% when compared with Nicovich et al. [23] ((2.49 ± 0.38) × 10⁻¹¹ exp[−(233 ± 46)/T] cm³ molecule⁻¹ s⁻¹) over the temperature range of 264–385 K, 0–30% when compared with Seely et al. [24] ((1.63 ± 0.34) × 10⁻¹¹ exp[−(91 ± 61)/T] cm³ molecule⁻¹ s⁻¹) over the temperature range of 206–296 K, and 0–25% when compared with Zahniser et al. [27] ((2.35 ± 0.5) × 10⁻¹¹ exp[−(171 ± 30)/T] cm³ molecule⁻¹ s⁻¹) over the temperature range of 210–360 K.

4.2. Reaction of Br + O₃

The potential energy level diagram for the reaction of O₃ with Br atoms (R2) is given in Figure 3 along with the optimized geometries at the MP2/aug-cc-pV(T + d)Z level of theory. All the structural parameters are given in the Supplementary Materials Table S2. This reaction goes through an early transition state (pre-reactive complex, PRC), is connected through a late transition state (product complex, PC), and leads to the products as shown in Figure 3. The Br atom attack on a terminal oxygen of the ozone in both trans and cis pathways was identified analogously to reaction R1. Among the trans and cis pathways, the trans pathway was found to be the lowest energy pathway. Hence, the trans pathway is considered in the present kinetics calculations. In the case of O atom abstraction by the Br atom, the breaking O–O bond length in O₃ was stretched up to 34% when compared with the bond length in the reactant O₃.

The obtained bond lengths, bond angles, and vibrational frequencies of the Br + O₃ reaction in the present study are shown, along with values from previous studies in

Table 4. The obtained bond lengths (r_e in Å) and bond angles (θ in deg) for the reaction of Br + O₃ at various levels of theory.

Species		This Work	Bing et al. [45]	A-Hussein et al. [46]
		MP2/aug-cc-pV(T + d)Z	MP2/6-31G(d)	PM3-CI (4 × 4)
O3	re	1.230	1.300
	θ	118.3	116.8
Pre-reactive complex	re Br-O1	2.963	2.655	2.981
	θ	102.2	107.5	107.31
	re O1-O2	1.235	1.311	1.937
	θ O1-O2-O3	118.0	113.0	116.86
	re O2-O3	1.226	1.305	1.172
Transition state	re Br-O1	1.781	2.248	2.357
	θ	106.4	108.4	104.7
	re O1-O2	1.649	1.434	1.627
	θ O1-O2-O3	108.6	111.1	103.8
	re O2-O3	1.195	1.276	1.191
Product complex	re Br-O1	1.711
	θ	84.4
	re O1-O2	3.114
	θ O1-O2-O3	85.9
	re O2-O3	1.188
BrO	re Br-O1	1.711	1.753
O2	re O2-O3	1.187	1.247

and

Table 5. Vibrational frequencies (cm⁻¹) for the reaction of Br + O₃ at various levels of theory.

Species		This Work	Bing et al. [45]
		MP2/aug-cc-pV(T + d)Z	MP2/6-31G(d)	MP2/6-311 + G(d)
O3	v1	795.4
	v2	1375.0
	v3	1379.9
Pre-reactive complex	v1	53.2	84.3	60.2
	v2	91.7	315.7	321.6
	v3	112.7	645.3	653.7
	v4	802.1	960.5	953.9
	v5	1351.3	1184.0	1213.9
	v6	1394.7	2145.8	1988.9
Transition state	v1	476.6i	55.7i
	v2	61.2	56.4
	v3	200.7	181.9
	v4	456.0	679.6
	v5	768.4	1035.1
	v6	1539.6	1063.0
Product complex	v1	39.5
	v2	45.8
	v3	83.0
	v4	93.5
	v5	778.7
	v6	1765.1
BrO	v1	791.9	765.4	750.6
O2	v1	1765.3

. When compared with Bing et al. [45] and A-Hussein et al. [46], our results represent the first reported values for the product complex of the Br + O₃ reaction. Where intercomparison with existing literature is possible, the computed bond lengths, bond angles, and vibrational frequencies exhibit some variation but are typically in agreement. The observed differences are most likely due to the different levels of theory and basis sets used in the computations by Bing et al. [45] (MP2/6-311 + G(d)) and A-Hussein et al. [46] (PM3-CI) relative to the present study (MP2/aug-cc-pV(T + d)Z).

The energies of all the stationary points were refined at MRCI + Q/aug-ano-RCC-VTZP using the optimized geometries obtained at the MP2/aug-cc-pV(T + d)Z level of theory. Thus, refined energies were used in dual level calculations to compute the rate coefficients for the reaction of R2 over the temperature range of 180–400 K. The obtained rate coefficients from CVT/SCT at the MRCI + Q/aug-ano-RCC-VTZP//MP2/aug-cc-pV(T + d)Z levels of theory are compared with the recommended rate coefficients by NASA/JPL and IUPAC in Figure 4. The rate coefficients from CVT/SCT were used to fit the Arrhenius expression, and the obtained temperature-dependent rate coefficient (180–400 K) for R2 is k₂ = (3.54 ± 0.2) × 10⁻¹¹ exp[(−990 ± 35)/T] cm³ molecule⁻¹ s⁻¹. The reported uncertainties on the A factor and –E_a/R are, respectively, from the deviation in the intercept and slope of a two-parameter linear least squares fit of ln k versus 1/T.

Table 6. Rate coefficients (cm³ molecule⁻¹ s⁻¹) for the reaction of O₃ with Br at the MRCI + Q/aug-ano-RCC-VTZP//MP2/aug-cc-pV(T + d)Z levels of theory using CVT/SCT along with the recommended rate coefficients by NASA/JPL [13] and IUPAC [51] for comparison.

T (K)	k (Present Work)	k (JPL)	k (IUPAC)
180	1.45 × 10−13
200	2.51 × 10−13	3.24 × 10−13	3.11 × 10−13
230	4.78 × 10−13	5.39 × 10−13	5.25 × 10−13
250	6.75 × 10−13	7.07 × 10−13	6.93 × 10−13
270	9.05 × 10−13	8.90 × 10−13	8.78 × 10−13
298	1.28 × 10−12	1.17 × 10−12	1.16 × 10−12
300	1.31 × 10−12	1.19 × 10−12	1.18 × 10−12
350	2.09 × 10−12	1.72 × 10−12	1.73 × 10−12
400	2.98 × 10−12	2.28 × 10−12	2.30 × 10−12

shows the rate coefficients from this work compared with the recommended rate coefficients from NASA/JPL (1.6 × 10⁻¹¹ exp[−780/T] cm³ molecule⁻¹ s⁻¹) and IUPAC (1.7 × 10⁻¹¹ exp[−800/T] cm³ molecule⁻¹ s⁻¹).

The obtained rate coefficient for the reaction of R2 at 298 K differs by 9% when compared with either the NASA/JPL-recommended value or IUPAC. As stated previously, there are no theoretical rate coefficients in the literature to compare with the obtained rate coefficients in the present study. Our rate coefficients differ by 0–33% over the temperature range of 195–400 K when compared with JPL-recommended values and by 0–31% from 190–400 K when compared with IUPAC. Our rate coefficients are smaller than the recommended rate coefficients in the temperature range of 195–250 K and larger in the temperature range of 250–400 K. The level of agreement is within the stated uncertainty range of the NASA/JPL and IUPAC recommendations and the uncertainty range of the present calculations.

Further comparison of our theoretical rate coefficients with previous individual experimental studies generally yields good agreement. The obtained rate coefficients using CVT/SCT for the reaction of R2 differ by maximum of 0–3% when compared with Leu and DeMore [29] ((3.34 ± 0.40) × 10⁻¹¹ exp[−(978 ± 36)/T] cm³ molecule⁻¹ s⁻¹) over the temperature range of 224−400 K, 0–33% when compared with Michael and Payne [31] ((9.45 ± 2.48) × 10⁻¹² exp[−(659 ± 64)/T] cm³ molecule⁻¹ s⁻¹) over the temperature range of 234−360 K, 6% when compared with Ninomiya et al.³² ((1.2 ± 0.1) × 10⁻¹² cm³ molecule⁻¹ s⁻¹) at 298 K, and 4–12% when compared with Toohey et al.³³ ((3.28 ± 0.40) × 10⁻¹¹ exp[−(944 ± 30)/T] cm³ molecule⁻¹ s⁻¹) over the temperature range of 248–400 K.

4.3. Reaction of I + O₃

The potential energy level diagram for the reaction of O₃ with I atoms (R3) is given in Figure 5 along with the optimized geometries at the MP2/aug-cc-pV(T + d)Z level of theory. All the structural parameters for the reaction of R3 are given in the Supplementary Materials Table S3. This reaction goes through an early transition state (pre-reactive complex, PRC), is connected through a late transition state (product complex, PC), and leads to the products as shown in Figure 5. Both trans and cis pathways for the I atom attack on a terminal oxygen of the ozone were identified analogously to reactions (R1) and (R2). Among the trans and cis pathways, the trans pathway was found to be the lowest energy pathway. Hence, the trans pathway is considered in the present kinetics calculations. In the case of O atom abstraction by the I atom, the breaking O–O bond length in O₃ was stretched up to 36% when compared with the bond length in the reactant O₃.

The obtained bond lengths, bond angles, and vibrational frequencies in the present study are shown in

Table 7. The obtained bond lengths (r_e in Å) and bond angles (θ in deg) for the reaction of I + O₃.

Species		This Work	Papayannis et al. [54]
		MP2/aug-cc-pV(T + d)Z	MP2/LANL2DZ
O3	re	1.230
	θ	118.3
Pre-reactive complex	re I-O1	3.133
	θ	109.9
	re O1-O2	1.235
	θ O1-O2-O3	118.1
	re O2-O3	1.225
Transition state	re Cl-O1	1.948
	θ	107.4
	re O1 -O2	1.674
	θ O1-O2-O3	108.9
	re O2-O3	1.193
Product complex	re I-O1	1.868
	θ	92.5
	re O1-O2	3.081
	θ O1-O2-O3	83.9
	re O2-O3	1.188
IO	re I-O1	1.870	1.877
O2	re O2-O3	1.187

and

Table 8. Vibrational frequencies (cm⁻¹) for the reaction of I + O₃.

Species		This Work	Papayannis et al. [54]
		MP2/aug-cc-pV(T + d)Z	MP2/LANL2DZ
O3	v1	795.4
	v2	1375.0
	v3	1379.9
Pre-reactive complex	v1	48.0
	v2	77.5
	v3	94.6
	v4	801.5
	v5	1355.1
	v6	1395.7
Transition state	v1	527.3i
	v2	65.3
	v3	183.9
	v4	418.6
	v5	718.4
	v6	1554.4
Product complex	v1	37.4
	v2	58.4
	v3	93.6
	v4	120.0
	v5	678.9
	v6	1768.2
IO	v1	662.7	597
O2	v1	1765.3

and are compared with the limited available literature data where possible. With all but two exceptions, our data represent the first reported values. Our computed I–O bond length is very close to the reported I–O bond length by Papayannis et al. [54] and our computed IO vibrational frequency is slightly higher than the reported value by Papayannis et al. [54]. The observed differences are most likely due to the different level of basis set used in the computations of IO by Papayannis et al.[54] (MP2/LANL2DZ) relative to the present study (MP2/aug-cc-pV(T + d)Z).

The energies of all the stationary points were refined at MRCI + Q/aug-ano-RCC-VTZP using the optimized geometries obtained at the MP2/aug-cc-pV(T + d)Z level of theory. Thus, refined energies were used in dual level calculations to compute the rate coefficients for the reaction of R3 over the temperature range of 180–400 K. The rate coefficients obtained in the present study for the reaction of R3 at the MRCI + Q/aug-ano-RCC-VTZP//MP2/aug-cc-pV(T + d)Z levels of theory are compared with the recommended rate coefficients by NASA/JPL and IUPAC in Figure 6. The rate coefficients from CVT/SCT were used to fit the Arrhenius expression, and the obtained temperature-dependent rate coefficient (180–400K) for R3 is k₃ = (1.47 ± 0.1) × 10⁻¹¹exp[(−720 ± 42)/T] cm³ molecule⁻¹s⁻¹. The reported uncertainties on the A factor and -E_a/R are, respectively, from the deviation in the intercept and slope of a two-parameter linear least squares fit of ln k versus 1/T.

Table 9. Rate coefficients (cm³molecule⁻¹s⁻¹) for the reaction of O₃ with I at the MRCI + Q/aug-ano-RCC-VTZP//MP2/aug-cc-pV(T + d)Z levels of theory using CVT/SCT along with the recommended rate coefficients by NASA/JPL [13] and IUPAC [51] for comparison.

T (K)	k (Present Work)	k (JPL)	k (IUPAC)
180	2.69 × 10−13
200	4.02 × 10−13
230	6.42 × 10−13	5.42 × 10−13	5.69 × 10−13
250	8.25 × 10−13	7.23 × 10−13	7.59 × 10−13
270	1.02 × 10−12	9.25 × 10−13	9.71 × 10−13
298	1.31 × 10−12	1.23 × 10−12	1.30 × 10−12
300	1.33 × 10−12	1.26 × 10−12	1.32 × 10−12
350	1.88 × 10−12	1.87 × 10−12	1.96 × 10−12
400	2.43 × 10−12

shows the rate coefficients from this work compared with the recommended rate coefficients from NASA/JPL (2.0 × 10⁻¹¹exp[−830/T] cm³ molecule⁻¹s⁻¹) and IUPAC (2.1 × 10⁻¹¹exp[−830/T] cm³ molecule⁻¹s⁻¹).

Our rate coefficient at 298 K is in very good agreement with the JPL- and IUPAC-recommended values, differing by 6% and 1%, respectively. There are no previous theoretical studies available for the reaction of R3 to compare with the obtained rate coefficients in the present study. This work provides rate coefficient data at significantly colder temperatures than in the NASA/JPL and IUPAC recommendations. For the overlapping temperature ranges, our rate coefficients agree within 0–16% relative to the NASA/JPL recommendation (230–370 K) and within 0–11% relative to IUPAC (230–370 K). The level of agreement at all temperatures is within the stated uncertainty range of the NASA/JPL and IUPAC recommendations and the uncertainty range of the present calculations.

Further comparison of our theoretical rate coefficients with previous individual experimental studies generally yields good agreement. The obtained temperature-dependent rate coefficients in the present study for the reaction of R3 differ by 0–13% when compared with Turnipseed et al. [37] ((2.3 ± 0.7) × 10⁻¹¹exp[−(860 ± 100)/T] cm³ molecule⁻¹s⁻¹) over the available temperature range of 240–370K. The obtained rate coefficient for the reaction of R3 differs by 2% and 28% at 298 K when compared with Tucceri et al. [35] ((1.28 ± 0.06) × 10⁻¹² cm³molecule⁻¹s⁻¹) and Sander [36] ((9.5 ± 1.5) × 10⁻¹³ cm³molecule⁻¹s⁻¹), respectively.

4.4. Feasibility of the Reactions

To understand the feasibility and spontaneity of the reactions R1, R2, and R3 in terms of thermodynamic parameters, the enthalpies (∆_rH°, kcal mol⁻¹), Gibbs free energies (∆_rG°, kcal mol⁻¹), and entropies (∆_rS°, cal mol⁻¹ K⁻¹) at different levels of theory and basis sets are collected in

Table 10. Enthalpies (∆_rH°, kcal mol⁻¹), Gibbs free energies (∆_rG°, kcal mol⁻¹) and entropies (∆_rS°, cal mol⁻¹ K⁻¹) for the reactions of O₃ with Cl, Br, and I atoms obtained at various levels of theory along with the reported values in the literature at 298 K.

	Cl + O3			Br + O3			I + O3
	∆rH°	∆rG°	∆rS°	∆rH°	∆rG°	∆rS°	∆rH°	∆rG°	∆rS°
a CCSD(T)/aug-cc-pV(T + d)Z	−36.01	−37.54	4.62	−31.22	−32.65	4.99	−29.86	−31.01	5.34
IUPAC51	−38.81			−32.26			−32.02
b Experimental	−38.9
c G2MP2	−37.5
c G2MP2 with HLC	−34.4
d Experimental				−32.3
e CCSD(T)/6-311 + G(3df)				−33.54	−35.67
e G2MP2				−26.70	−29.01
f PM3-CI				−36.9	−38.55

^a This work, ^b Molina and Rowland [66], ^c Hwang et al. [39], ^d Dyke et al. [67], ^e Bing et al. [45], and ^f A-Hussein et al. [46].^.

along with reported values in the literature at 298K. Our obtained enthalpy for the reaction of R1 at CCSD(T)/aug-cc-pV(T + d)Z (−36.01 kcal/mol) is within 8% of the recommended value by the IUPAC evaluation (−38.81 kcal/mol) and the experimental value of Molina and Rowland [66] (−38.9 kcal/mol), and within 1% of the mean theoretical value from Hwang et al. [39] using G2MP2 and G2MP2 with higher level correction (−35.95 kcal/mol). Our obtained enthalpy for the reaction of R2 at CCSD(T)/aug-cc-pV(T + d)Z (−31.22 kcal/mol) is within 3% of the recommended value by the IUPAC evaluation (−32.26 kcal/mol) and the experimental value of Dyke et al. [67] (−32.3 kcal/mol), and within 4% of the mean theoretical value from Bing et al. [45] and A-Hussein et al. [46] using CCSD(T)/6-311 + G(3df), G2MP2, and PM3-CI (−32.38 kcal/mol). Our obtained Gibbs free energy for the reaction of R2 at CCSD(T)/aug-cc-pV(T + d)Z (−32.65 kcal/mol) is within 5% of the mean theoretical value from Bing et al. [45] and A-Hussein et al. [46] (−34.41 kcal/mol). Finally, our obtained enthalpy for the reaction of R3 at CCSD(T)/aug-cc-pV(T + d)Z (−29.86 kcal/mol) is within 7% of the recommended value by the IUPAC evaluation (−32.02 kcal/mol). There are no previous theoretical studies available for the reaction of R3 to compare with the obtained values in the present study.

In addition to the data comparisons above, we provide a number of new thermodynamic parameters in Table 10 not previously reported in the literature to our knowledge. Based on the results in Table 10, the O atom abstractions by halogen atoms are feasible and spontaneous. Among these halogens, Cl atom abstraction reactions are more feasible and spontaneous than the Br and I atom abstraction reactions both kinetically and thermodynamically, which is consistent with the present kinetics findings.

4.5. Kinetics Analysis

From Figure 2, Figure 4 and Figure 6, it is clear that the reactions of R1, R2, and R3 show positive temperature dependencies, which is consistent with the NASA/JPL and IUPAC evaluations over the studied temperature range (180–400 K).

Table 11. Rate coefficients at 298 K (cm³molecule⁻¹s⁻¹), pre-exponential factors (cm³molecule⁻¹s⁻¹), and activation energies/R (K) for the reactions of O₃ with F, Cl, Br, and I atoms.

Reaction	k a	A a	Ea/R a	k b	A b	Ea/R b
F + O3				1.0 × 10−11	2.2 × 10−11	230
Cl + O3	1.27 × 10−11	3.48 × 10−11	301	1.18 × 10−11	2.3 × 10−11	200
Br + O3	1.28 × 10−12	3.54 × 10−11	990	1.17 × 10−12	1.6 × 10−11	780
I + O3	1.31 × 10−12	1.47 × 10−11	720	1.23 × 10−12	2.0 × 10−11	830

^a Results from this work. ^b NASA/JPL [13] recommended values.

shows that the room temperature (298 K) rate coefficient for the reaction of O₃ with F atoms is close to that of the reaction of O₃ with Cl atoms. Similarly, the room temperature (298 K) rate coefficient for the reaction of O₃ with Br atoms is close to that of the rate coefficient for the reaction of O₃ with I atoms. In addition, both the theory results from this work and the NASA/JPL recommendation show that the rate coefficient for the reaction of O₃ with Cl atoms is approximately a factor of 10 faster than the reaction of O₃ with Br or I atoms at 298 K. This may be explained based on pre-exponential factors and activation energies listed in Table 11; in particular, it is clear that the activation energy for the reaction of O₃ with a Cl atom is significantly lower than the activation energies of reactions of O₃ with Br and I atoms.

The obtained rate coefficients in the present study for the title reactions are very close to the recommended rate coefficients by NASA/JPL and IUPAC evaluations in the vicinity of room temperature (298 K). When the temperature range is extended to substantially colder and warmer temperatures, the rate coefficients deviate farther from the recommended rate coefficients by the NASA/JPL and IUPAC evaluations but are still in agreement within uncertainty. The overall consistency between our calculated values and the previous experimental studies supports the accuracy of the results presented here, which in turn, helps underpin the theoretical foundation of the X + O₃ title reactions over the considered temperature range.

5. Conclusions

In this study, the reactions of O₃ with Cl, Br, and I atoms were investigated using canonical variational transition state theory including small curvature tunneling corrections (CVT/SCT). Rate coefficients were computed at MRCI + Q/aug-ano-pVTZ//MP2/aug-cc-pV(T + d)Z and MRCI + Q/aug-ano-RCC-VTZP//MP2/aug-cc-pV(T + d)Z levels of theory. To our knowledge, this study represents the first reported temperature-dependent rate coefficients for the reactions of O₃ with Br and I using theoretical methods. Dual level calculations give more accurate and refined kinetics parameters, which had not been performed previously in the literature for any of the title reactions. The temperature range is also extended relative to previous experimental studies for the three reactions from 180 to 400 K. Overall, we find very good agreement between our temperature-dependent rate coefficients and the experimentally derived, recommended values from NASA/JPL and IUPAC for the three X + O₃ reactions studied here, thereby helping underpin the theoretical foundation for these important ozone-loss reactions. The reaction of O₃ with the iodine atom proceeds via an early transition state and a late transition state, which is analogous to reactions of O₃ with Cl and Br but had not previously been reported in the literature. Thermodynamically, these three reactions are feasible and spontaneous. Previous experimental values and our theoretical results show that the reaction of Cl atoms with O₃ is around a factor of 10 times faster than the reactions of O₃ with Br and I atoms.