High-accuracy theoretical studies on the gas-phase reaction mechanisms of sulfur mustard with reactive oxygen species (OH/O₂/HO₂/O)

Abstract

The gas-phase reaction mechanisms of sulfur mustard (HD) under oxygenated conditions constitute the theoretical foundation for understanding its environmental evolution processes and evaluating its incineration efficiency. In this work, the gas-phase reaction mechanisms and kinetics between HD and reactive oxygen species (OH, O₂, HO₂, O) were investigated at the CCSD(T)/aug-cc-pVTZ//M06-2X/6-311+G(d,p) theoretical level. The study reveals that all four oxygen species can participate in hydrogen abstraction reactions with HD, with the OH-mediated and O-mediated pathways being the most favorable. Furthermore, the research demonstrates that O₂ and O can directly oxidize HD to form mustard sulfoxide, which can be further oxidized to mustard sulfone – a compound exhibiting comparable toxicity to HD itself. The HD-OH adduct can be converted to mustard sulfoxide in the presence of O₂, and the resulting sulfoxide-OH adduct can subsequently be oxidized to mustard sulfone. Computational analysis of the reaction pathways employing the RS2C method indicates that both steps proceed via substantially high energy barriers. Kinetic simulations show that under typical incineration conditions, OH and O play dominant roles in HD degradation.

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Introduction

Sulfur mustard (HD) is a typical military blister agent that can cause vesication and erosion of skin tissues. It has been extensively produced and stockpiled worldwide.^1,2 Among the developed methods for the destruction of chemical warfare agents, incineration serves as a key disposal approach for HD.^3,4 The low aqueous solubility of HD, coupled with the formation of hydrolysis-induced polymeric products at the HD-water interface, contributes to its environmental persistence,⁵ posing significant threats to both human health and environmental safety. The evolution pathways of residual HD in natural environments directly influence its environmental persistence, with oxidation serving as a crucial driving force for the degradation of organic compounds in natural settings.^6–9 As a critical approach for HD neutralization, the oxidative destruction of HD during incineration constitutes a key determinant for both disposal completeness and operational safety.^3,4 Consequently, investigating the gas-phase oxidation mechanisms of HD represents a research priority—equally essential for evaluating its environmental persistence, assessing incineration efficiency, and optimizing destruction processes.

Previous studies have investigated some gas-phase reactions of HD under photochemical conditions.^10,11 However, these reactions typically occur through complex interactions with multiple atmospheric components, involving concurrent oxidation, pyrolysis, and photolysis processes, which consequently preclude clear elucidation of the fundamental gas-phase oxidation mechanisms of HD. In the liquid-phase and catalytic oxidation of HD,^12,13 significant oxidation products include sulfur mustard sulfoxide (SMO) and sulfur mustard sulfone (SMO₂). Notably, the oxidation products exhibit substantial variations in toxicity. In vitro toxicological studies demonstrate that compared to HD itself, SMO₂ exhibit higher toxicity, while SMO shows relatively lower toxicity.¹⁴

During combustion processes, the sequential thermal decomposition followed by oxidation of pyrolysis products often represents a critical reaction pathway for organic compounds.^15–18 Previous studies have investigated the pyrolysis characteristics of HD, with analytical results identifying ethylene and vinyl chloride as predominant thermal degradation products.¹⁹ Further in-depth studies on the gas-phase pyrolysis of HD have revealed that hydrogen abstraction represents a critical reaction pathway in its thermal decomposition. The resultant radicals formed through hydrogen abstraction subsequently undergo diverse fragmentation routes, thereby elucidating the fundamental mechanistic framework of HD pyrolysis.^20,21 However, the degradation mechanisms of HD in the presence of reactive oxygen species have attracted greater research attention, as they more directly reflect the degradation characteristics of HD under both natural environmental conditions and incineration scenarios. Regrettably, there remains a significant lack of both experimental and theoretical studies on HD degradation reactions under oxygenated gas-phase conditions.

Currently, two primary approaches have been developed to address the experimental limitations imposed by the high toxicity of chemical warfare agents: theoretical computational methods for investigating reaction characteristics of the agents,^22–24 and experimental studies employing less toxic chemical simulants. Previous studies have documented the oxidation of thioether compounds structurally analogous to HD (substances critically involved in atmospheric sulfur cycling),^25–32 where these thioethers primarily undergo oxidation through reaction pathways such as hydrogen abstraction and radical recombination with oxygen-containing species in the atmosphere. Researchers have theoretically and experimentally investigated the gas-phase oxidation of diethyl sulfide (DES), an HD simulant, demonstrating that hydrogen abstraction serves as the initial reaction pathway, with H atoms, hydroxyl radicals (OH), molecular oxygen (O₂), hydroperoxyl radicals (HO₂), and oxygen atoms (O) acting as potential hydrogen abstractors.¹⁹ These reactive oxygen species (OH, O₂, HO₂, and O) represent crucial reactive intermediates in both atmospheric chemistry and combustion processes, playing pivotal roles in the gas-phase decomposition and oxidative transformation of organic compounds.^33–37 The oxidation of organic compounds by reactive oxygen species typically proceeds via multiple competing pathways, primarily including: (i) hydrogen atom transfer, wherein reactive oxygen species abstract a hydrogen atom from the organic substrate, generating a carbon-centered or heteroatom-centered radical; (ii) oxygen atom transfer, wherein an oxygen atom is directly inserted into the substrate to form oxidized functionalities such as C=O or S=O bonds. In addition, depending on the specific nature of the reactive oxygen species and the substrate, other pathways—such as single-electron transfer or cycloaddition reactions—may also operate competitively.^34,35,38 As a structurally distinctive thioether compound, the reaction characteristics of HD under oxygenated conditions represent a scientifically significant research question worthy of systematic investigation.

This study conducts high-accuracy theoretical investigations into the reaction mechanisms between HD and reactive oxygen species (OH, O₂, HO₂, O) in the gas phase, aiming to elucidate potential reaction pathways under oxygenated conditions, enhance fundamental understanding of the environmental degradation processes, and establish theoretical foundations for revealing the incineration destruction mechanisms of HD.

Computational details

The minimum-energy structures of all species in the reaction system, along with frequency calculations and transition state searches, were computed at the M06-2X/6-311+G(d,p) level of theory.^39,40 Fig. S1 of SI presents the optimized minimum-energy structures and transition states obtained at this theoretical level. Previous studies have demonstrated that M06-2X represents an appropriate method for predicting accurate reaction transition states in organic systems.^20,41 The employed 6-311+G(d,p) basis set incorporates both polarization and diffuse functions, which is usually important in the geometry optimizations for weakly bonded complexes.

For HD, a conformational search was performed using the Molclus program,⁴² identifying the global minimum-energy structure (Fig. 1). Additional conformational details of HD, including relative energies and Boltzmann populations, are provided in Table S1 of the SI. The minimum-energy structures were confirmed by frequency analysis to exhibit no imaginary frequencies, while all transition states were characterized by the presence of exactly one imaginary frequency. Intrinsic reaction coordinate (IRC) calculations^43,44 (Fig. S2 of the SI) were performed for each transition state to verify proper connectivity between reactants and corresponding products. The potential energy surface (PES) was accurately determined through single-point energy calculations at the CCSD(T)/aug-cc-pVTZ level of theory,^45–47 with the relative Gibbs free energies incorporating both the CCSD(T)/aug-cc-pVTZ single-point energies and Gibbs free energy corrections computed at the M06-2X/6-311+G(d,p) level.

Fig. 1 Optimized minimum-energy structure of HD showing atomic numbering scheme.

T ₁ diagnostics were performed for all stationary points in the reaction system at the CCSD(T) level (Table S2 of the SI). The results demonstrate that all examined species exhibit T₁ diagnostic values below 0.044 except for OH-TS4 and OH-TS7, indicating that the single-reference approach employed in this study provides an appropriate description of the wavefunctions for this system.⁴⁸

In this study, all structural optimizations and energy calculations, except for reactions involving multiple reference states with high T₁ diagnostic values, were performed using the Gaussian 16 program.⁴⁹ The reaction rates were derived from thermal rate constants, which were evaluated employing transition state theory.⁵⁰ The influence of quantum tunneling effects was evaluated using the Eckart model.⁵¹ For reactions exhibiting significant multireference character, multireference calculations were performed using the Molpro2015 program,⁵² with the RS2C method⁵³ employed to determine reaction energy barriers.

The kinetic simulations were performed using the Chemkin program⁵⁴ to elucidate the roles of reactive oxygen species in the degradation of HD during incineration. These simulations employed the closed homogeneous constant-pressure reactor module and covered a temperature range of 973–1573 K.

Results and discussion

The molecular conformers of HD were systematically explored using the Molclus program,⁴² and the global minimum-energy structure was identified. The lowest-energy structure of HD optimized at the M06-2X/6-311+G(d,p) level, along with its atomic numbering, is shown in Fig. 1. The minimum-energy configuration of HD adopts a C₂ symmetric structure, in which the chloroethyl side chains on both sides of the sulfur atom exhibit a trans-antiperiplanar arrangement. This global minimum-energy structure is fully consistent with those reported in previous studies.^55,56

The reaction mechanism between OH and HD

The reaction between the OH radical and HD initially forms an prereactive complex or adduct which subsequently degrades HD through two distinct pathways: a hydrogen abstraction oxidation route and a oxygen atom transfer oxidation route (Fig. 2). The OH radical forms two prereactive complexes with HD, designated as OHrc1 and OHrc2. Analysis of the interaction region indicator (IRI)⁵⁷ for the HD-OH complexes reveals significant dispersion interactions between the sulfur atom and oxygen atom, as well as between the oxygen atom and the hydrogen atom at the C1 and C4 carbon position, indicating the presence of weak noncovalent interactions (Fig. S3 of the SI).

Fig. 2 PES for the OH + HD reactions. (a) Hydrogen abstraction pathway; (b) oxygen atom transfer pathway.

Hydrogen abstraction reaction mechanism. Due to the trans-symmetric configuration of HD, this study focuses on the four hydrogen atoms bonded to C1 and C2 in HD to investigate the hydrogen abstraction mechanism. The OH radical can form prereactive complexes OHrc1 and OHrc2 with HD, which are structurally analogous to those formed between vinyl sulfoxide and OH radicals.²⁶ All these complexes are stabilized through weak noncovalent interactions.

The complexes OHrc1 and OHrc2 can undergo hydrogen abstraction reactions from C1 and C2 of HD via the corresponding transition states OH-TS1 and OH-TS2, respectively (Fig. 2(a)). Among these two reaction pathways, the hydrogen abstraction from the C2 position exhibits lower free energy barriers compared to that from the C1 position. This trend is consistent with Hammond's postulate,⁵⁸ which suggests that the transition state for hydrogen abstraction structurally resembles the resulting radical intermediate. Compared to C1, the adjacent chloromethyl group and sulfur atom at C2 provide stronger hyperconjugative interactions and inductive stabilization, rendering the p-IM2 radical generated after hydrogen abstraction at C2 thermodynamically more stable than the p-IM1 radical formed at C1. Consequently, the transition state leading to the more stable p-IM2 radical is stabilized, ultimately manifested in the lower energy barrier of OH-TS2.

It is noteworthy that the Gibbs free energy change (ΔG) for the hydrogen abstraction reaction between the OH radical and HD is consistently negative, indicating the thermodynamic spontaneity of this reaction. This finding has significant implications for the natural environmental degradation of HD, suggesting that this reaction may serve as an important pathway facilitating HD decomposition in natural settings. The hydrogen abstraction by OH radicals represents one of the primary reaction pathways responsible for the environmental degradation and subsequent sulfur release from dimethyl sulfide (DMS), a key sulfur-containing compound involved in atmospheric cycling.^30,59 In the context of incineration disposal, such exothermic reactions can further promote the continuous degradation of HD.

Oxygen transfer reaction mechanism. The adduct OHad1, formed between HD and the OH radical, is structurally analogous to the DMS-OH adduct derived from DMS and OH. A structural and electronic analysis of OHad1 was performed using the Multiwfn program^60,61 (Table S3 in the SI), revealing that OHad1 also exhibits the characteristic two-center three-electron (2c–3e) bonding motif. OHad1 is stabilized by 49.79 kJ mol⁻¹ relative to the separated HD and OH, a value comparable to the stabilization energies reported for the DMS-OH adduct (37.66–58.58 kJ mol⁻¹).^62–64

The OHad1 adduct can undergo elimination of a chloroethyl group via the transition state OH-TS3 to yield 2-chloroethane sulfinic acid (P1) (Fig. 2(b)).

Similar to DMS-OH,^30,59 the OHad1 adduct can also undergo oxidation in the presence of O₂, proceeding through the transition state OH-TS4 to form SMO. During the reaction of OHad1 with O₂, a distinct molecular isomerization process occurs. O₂ approaches OHad1 from the side proximal to the OH group, followed by a pronounced rotation of the H atom in the OH moiety of OHad1. This rotation progressively shifts the H atom's orientation from facing away from O₂ to facing toward O₂. Upon completion of this conformational change, the H atom gradually dissociates from the OH group in the OHad1 adduct, proceeding through the transition state OH-TS4 to generate SMO. Notably, the T₁ diagnostic value of OH-TS4 reaches 0.0597, indicating significant multireference character, which suggests that single-reference methods may not accurately evaluate its reaction energy barrier. Multireference calculations were performed along the reaction pathway using the RS2C method to obtain the reaction energy barrier, with an active space of (7e, 8o) selected. The computational results reveal that the reaction between OHad1 and O₂ needs to overcome a notably high energy barrier of 562.00 kJ mol⁻¹, indicating an extremely slow process that is unlikely to occur under conventional conditions (Fig. 3(a)). As one of the primary oxidation products of HD, SMO can undergo further degradation through multiple reaction pathways. SMO can form P1 and chloroethylene (P2) via transition state OH-TS5 (Fig. 3(b)), with this unimolecular reaction being independent of other oxygen-containing reactive species. Similar to HD, SMO can also react with hydroxyl radicals to form the SMO-OH adduct (OHad2), which can subsequently eliminates a chloroethyl group through transition state OH-TS6 to yield chloroethylsulfinic acid (P3) (Fig. 3(b)). Analogous to the cases of DMS-OH and OHad1, the OHad2 adduct can also undergo oxidation in the presence of O₂via transition state OH-TS7 to produce SMO₂. It should be noted that the T₁ diagnostic value of OH-TS7 reaches 0.0511, indicating significant multireference character in this system. The reaction energy barrier was calculated using the RS2C method with an active space of (7e, 8o), yielding a barrier of 501.09 kJ mol⁻¹ (Fig. 3(c)). The energy barrier for the oxygen transfer pathway of HD by OH radicals is significantly higher than that of the hydrogen abstraction pathway, indicating that hydrogen abstraction represents the dominant reaction route between OH and HD.

Fig. 3 PES for the HD-OH adduct and SMO degradation. (a) PES of OHad1 and O₂ reaction, (b) PES of SMO degradation, (c) PES of OHad2 and O₂ reaction. (a) and (c) were determined using the RS2C method.

The reaction mechanism between O₂ and HD

Hydrogen abstraction reaction mechanism. In contrast to the OH, O₂ does not form prereactive complexes with HD during hydrogen abstraction. Instead, O₂ can directly abstract hydrogen atoms from C1 and C2 of HD via two distinct transition states (O₂-TS1 and O₂-TS2), yielding the products p-IM1 and p-IM2, respectively (Fig. 4(a)).

Fig. 4 PES for the O₂ + HD reaction. (a) Hydrogen abstraction pathway and (b) oxygen atom transfer pathway.

Analogous to the hydrogen abstraction by OH from HD, the abstraction of C2 position hydrogens exhibits lower free energy barriers than that of C1 position, demonstrating that O₂-mediated hydrogen abstraction from HD is predominantly influenced by carbon position. The free energy barriers for O₂-initiated hydrogen abstraction exceed those of OH by more than fivefold. In contrast to OH reactions, the O₂-mediated abstraction exhibits a substantial Gibbs free energy increase exceeding 180 kJ mol⁻¹, rendering this pathway non-competitive with OH radicals under ambient conditions due to its prohibitively high activation barrier. However, in incineration environments where both high O₂ concentrations and elevated temperatures provide sufficient energy input, these O₂-driven abstraction reactions may become feasible.

Oxygen transfer reaction mechanism. Theoretical calculations reveal that O₂ can undergo oxygen transfer reaction with HD via transition state O₂-TS3 to form SMO, which can be further oxidized by O₂ through transition state O₂-TS4 to yield SMO₂ (Fig. 4(b)). The oxygen atom transfer oxidation between O₂ and HD exhibits an exceptionally high free energy barrier of 337.36 kJ mol⁻¹, coupled with a positive ΔG value, rendering this reaction thermodynamically unfavorable under natural environmental conditions. Similarly, the subsequent oxidation of SMO by O₂ faces a substantial kinetic barrier of 309.95 kJ mol⁻¹ with an endergonic character (ΔG > 0), making this transformation equally improbable in ambient environments. In contrast, combustion systems provide both continuous thermal energy input and high O₂ concentrations, creating favorable conditions for these otherwise prohibitive oxidative transformations.

Oxidation mechanism of key intermediates by O₂. Despite the prohibitively high reaction barriers (both for hydrogen abstraction and oxygen atom transfer oxidation by O₂) that render these pathways non-competitive in HD degradation, the subsequent reactions of O₂ with the hydrogen abstraction products (p-IM1 and p-IM2) constitute a critical and non-negligible reaction channel.

Analogous to DMS,^30,31 O₂ can oxidize the hydrogen abstraction products of HD. This study focuses on p-IM1 (derived from C1 abstraction) and p-IM2 (derived from C2 abstraction). O₂ reacts with p-IM1 via transition state O₂-TS5 to form the O₂-IM1, and with p-IM2 through O₂-TS6 to yield O₂-IM2 (Fig. 5 and 6). These intermediates subsequently degrade via multiple reaction channels (Fig. 5). O₂-IM1 undergoes intramolecular hydrogen abstraction via two distinct pathways: (i) at the C1 of the chloroethyl side chain through transition state O₂-TS7 forming O₂-IM3, and (ii) at the C2 through O₂-TS8 yielding O₂-IM4. Alternatively, O₂-IM1 can eliminate an OH radical via hydrogen transfer at the same carbon position (O₂-TS9) to produce O₂-IM5, which subsequently cleaves the S–C bond through O₂-TS10 to generate P2 and O₂-IM6. A fourth pathway involves HO₂ elimination through neighboring carbon hydrogen abstraction (O₂-TS11) to form O₂-IM7, followed by further rearrangement via O₂-TS12 to produce O₂-IM8 and P2. Among these four degradation channels, the intramolecular hydrogen abstraction pathway through O₂-TS8 exhibits the lowest free energy barrier Fig. 6(a), establishing it as the predominant route.

Fig. 5 Reaction pathways of O₂ with HD-derived hydrogen abstraction products p-IM1 and p-IM2. The values adjacent to the arrows denote the Gibbs free energy barriers for the respective reaction pathways: for the degradation pathways of p-IM1, the energy reference (zero point) is set to p-IM1+O₂; for those of p-IM2, the zero point is set to p-IM2+O₂.

Fig. 6 PES for the reactions of O₂ with hydrogen abstraction products from HD. (a) p-IM1 and (b) p-IM2.

The O₂-IM2 intermediate undergoes competitive degradation pathways through: (1) intramolecular hydrogen abstraction at the C1 position via O₂-TS13 forming O₂-IM9, or (2) at the C2 position via O₂-TS14 yielding O₂-IM10. Parallel routes include (3) OH radical elimination through same-carbon hydrogen transfer (O₂-TS15 → O₂-IM11) followed by S–C bond cleavage (O₂-TS16 → P2 + O₂-IM12), and (4) HO₂ radical elimination via adjacent-carbon hydrogen abstraction (O₂-TS17 → O₂-IM7). The PES analysis reveals analogous behavior to O₂-IM1, with the C2 position abstraction pathway (O₂-TS14) being the predominant route (Fig. 6(b)). Notably, despite originating from oxidation intermediates of different carbon positions (O₂-IM1 vs. O₂-IM2), the intramolecular hydrogen abstraction barriers at equivalent carbon positions show remarkably small differences (<2 kJ mol⁻¹), indicating minimal steric or electronic influence from the original abstraction site.

In contrast to the prohibitively high activation barriers associated with direct hydrogen abstraction and oxidation of HD by O₂, the subsequent reactions of O₂ with HD-derived intermediates (p-IM1/p-IM2) to form O₂-IM1/O₂-IM2, along with their further degradation pathways, exhibit significantly reduced free energy barriers. The relative height of this energy barrier indicates that during both environmental degradation and incineration processes, O₂ preferentially oxidizes HD fragmentation intermediates rather than engaging in direct reactions with intact HD molecules.

The reaction mechanism between HO₂ and HD

Hydrogen abstraction reaction mechanism. Analogous to OH radicals, HO₂ radicals can form prereactive complexes (HO₂rc1 and HO₂rc2) with HD through noncovalent interactions, which subsequently mediate hydrogen abstraction from C1 and C2 via distinct transition states (HO₂-TS1 and HO₂-TS2, Fig. 7). The abstraction of hydrogen atoms at the C2 position exhibits lower free energy barriers compared to those at the C1 position, demonstrating that the carbon position is a crucial governing factor in hydrogen abstraction reactions. The HO₂-mediated abstraction barriers are 2–3 times higher than OH but significantly lower than O₂, with all pathways being endergonic (ΔG > 0), precluding spontaneous environmental degradation. Consistent with OH/O₂ chemistry, hydrogen abstraction through HO₂-TS1 yields p-IM1, while HO₂-TS2 produces p-IM2. Under combustion conditions where HO₂ serves as a key chain-propagating intermediate,⁶⁵ continuous thermal energy input enables these otherwise thermodynamically prohibited reactions to become viable HD degradation pathways.

Fig. 7 PES for the hydrogen abstraction reaction between HO₂ and HD.

Oxidation mechanism of key intermediates by HO₂. Analogous to O₂, HO₂ can oxidize HD-derived hydrogen abstraction products p-IM1 and p-IM2, forming respective HO₂-IM1 and HO₂-IM2 (Fig. 8). These intermediates subsequently undergo degradation through multiple competing reaction channels (Fig. 9). The HO₂-IM1 intermediate undergoes two distinct degradation pathways: (1) O–OH cleavage generates an aldehyde and OH, which abstracts H to form H₂O; the aldehyde then abstracts H from H₂O to yield a hydroxyl group and a second OH, which finally recombines with the carbon-centered radical to afford HO₂-IM3 (HO₂-TS3), and (2) an alternative hydrogen transfer process through transition state HO₂-TS4, where the OH group of the OOH moiety abstracts the hydrogen atom from the same carbon center, resulting in concurrent O–O bond rupture and formation of O₂-IM5 and H₂O as final products. The HO₂-IM2 intermediate undergoes four competitive degradation pathways: (1) intramolecular hydrogen transfer from the OOH-coordinated carbon to the OH group via transition state HO₂-TS5, inducing O–O bond cleavage to form O₂-IM11 and H₂O; (2) concerted O–O bond rupture, oxygen rearrangement, and hydrogen transfer through HO₂-TS6 yielding HO₂-IM4 and H₂O; (3) OH radical-mediated hydrogen abstraction from the chloroethyl side chain (HO₂-TS7) resulting in synchronous C–S and O–O bond cleavage to produce HO₂-IM5, p-IM3, and H₂O; and (4) direct O–O homolysis via HO₂-TS8 generating HO₂-IM5 and P1. Although the conversion from p-IM1 and p-IM2 to HO₂-IM1 and HO₂-IM2, respectively, is a thermodynamically favorable process accompanied by a significant decrease in Gibbs free energy, both HO₂-IM1 and HO₂-IM2 degradation pathways exhibit substantially high free energy barriers (ΔG > 165.35 kJ mol⁻¹), rendering these intermediates effectively persistent under ambient environmental conditions. While combustion environments provide continuous thermal energy input and high HO₂ concentrations that may overcome these kinetic limitations, the oxidative capacity of HO₂ towards p-IM1/p-IM2 remains non-competitive relative to O₂.

Fig. 8 PES for the distinct degradation pathways of HO₂-IM1 (a) and HO₂-IM2 (b).

Fig. 9 Reaction pathways for HO₂ with p-IM1 and p-IM2, the hydrogen abstraction products derived from HD. The values adjacent to the arrows represent the Gibbs free energy barriers for the respective steps: for the degradation pathways of HO₂-IM1, the energy reference (zero point) is set to HO₂-IM1; for those of HO₂-IM2, the zero point is set to HO₂-IM2.

The reaction mechanism between O and HD

Hydrogen abstraction reaction mechanism. O can abstracts hydrogen atoms from HD through respective transition states O-TS1 and O-TS2, yielding products p-IM1 and p-IM2 (Fig. 10(a)). The C2 position C–H abstractions exhibit lower free energy barriers than that of C1 position, demonstrating pronounced carbon position dependence in transition state stabilization. The hydrogen abstraction barriers for O reacting with HD are higher than those for OH but substantially lower compared to O₂ and HO₂. These O-mediated abstraction reactions are thermodynamically favorable (ΔG < 0), suggesting that O may serve as critical chain carriers promoting HD degradation in the gas phase, particularly in combustion systems and upper atmospheric conditions where O concentrations are significant.⁶⁶

Fig. 10 PES for the O + HD reactions. (a) Hydrogen abstraction pathway, (b) and (c) oxygen transfer pathway.

Oxygen transfer reaction mechanism. The oxygen transfer reaction between HD and O is a spin-forbidden process. Specifically, the reactant system (HD + O) lies on the triplet potential energy surface, whereas the product SMO resides on the singlet surface. To account for this spin crossover, the minimum energy crossing point (MECP) between the triplet and singlet states was located using the sobMECP program,⁶⁷ at the M06-2X/6-311+G(d,p) level of theory. Similarly, the oxygen transfer reaction between SMO and O is also spin-forbidden, as it involves a transition from the triplet (SMO + O) to the singlet (SMO₂) state. The corresponding barrier for SMO₂ formation was computed using the same methods. The reaction between HD and O (Fig. 10(b)) initially forms a reaction complex Orc1, followed by an intersystem crossing (ISC) at MECP-1 to yield SMO. According to the PES, this reaction is likely governed by the ISC process as the rate-determining step. Similarly, the reaction between SMO and O (Fig. 10(c)) proceeds via analogous steps. SMO and O first associate to form the reaction complex Orc2, and subsequent ISC at MECP-2 leads to the formation of SMO₂. The PES analysis suggests that this reaction may also be rate-limited by the ISC event.

Reaction kinetics

Hydrogen abstraction kinetics. The Arrhenius plots (lg k vs. 1000/T) for hydrogen abstraction from HD by various oxygen species (298–1673 K, Fig. 11) reveal that OH radicals exhibit the highest reactivity, particularly for C–H abstraction at C2, followed by C–H abstraction at C1. O demonstrates comparable rates for C2 position C–H abstraction, with C1 position C–H abstraction being marginally slower. The reactivity gap between OH and O narrows significantly above 1000 K, suggesting thermally activated O reactions become competitive in combustion environments. As a crucial hydrogen-abstracting species in combustion reactions, HO₂ exhibits substantial reactivity toward HD under typical incineration conditions (1373 K), with a rate constant of 5.6 × 10⁹ cm³ mol⁻¹ s⁻¹ for the overall hydrogen abstraction process. Among the four reactive oxygen species studied, O₂ exhibits the lowest hydrogen abstraction rate from HD across the temperature range investigated. However, its reactivity demonstrates strong thermal sensitivity, increasing exponentially with temperature. Under typical incineration conditions (1373 K), the O₂-mediated hydrogen abstraction rate reaches 3.9 × 10⁵ cm³ mol⁻¹ s⁻¹, representing a 10¹⁸ fold enhancement compared to ambient temperatures (298 K).

Fig. 11 Temperature-dependent rate coefficients (lg k) for H-abstraction from HD by oxygen-containing species, plotted against inverse temperature (1000/T). The hydrogen abstraction rates for each radical are differentiated according to the carbon site: C1 (labeled p) and C2 (labeled s).

Oxygen atom transfer kinetics. O₂ and O can oxidize HD to SMO via oxygen atom transfer reactions, and SMO can be further oxidized to SMO₂. Fig. 12 demonstrates the O₂-mediated oxidation kinetic data. Crucially, comparative analysis of oxidation rates (Fig. 12) versus hydrogen abstraction rates (Fig. 11) reveals that hydrogen abstraction dominates HD degradation for O₂ oxidants across the entire temperature range (298–1673 K), with rate constants exceeding those of oxidation pathways by more than five orders of magnitude. This pronounced kinetic preference establishes hydrogen abstraction as the principal degradation mechanism, with oxidative pathways contributing less than 0.01% to overall HD consumption under typical environmental and combustion conditions.

Fig. 12 Arrhenius plots of HD oxidation rates (lg k vs. 1000/T) for HD + O₂ reaction pathways.

Notably, O₂ exhibits substantially higher oxidation rates toward SMO compared to HD, demonstrating the enhanced oxidative susceptibility of SMO relative to HD. This phenomenon has been consistently observed in multiple experimental studies of HD oxidation, where under sufficient oxidizing conditions, HD predominantly undergoes complete oxidation to SMO₂ rather than stopping at intermediate SMO formation.^5,12 Although the oxygen atom transfer oxidation pathways of HD exhibit inherently low reaction rates, the substantial abundance of both O₂ and O atoms in combustion environments creates non-negligible risks associated with complete oxidation to SMO₂.

Oxidation kinetics of hydrogen abstraction products. Hydrogen abstraction represents a critical reaction pathway in HD degradation, with its products p-IM1 and p-IM2 serving as key intermediates. Both p-IM1 and p-IM2 undergo oxygen atom transfer reactions with O₂ exhibiting relatively low energy barriers (Fig. 6). Consequently, both O₂-IM1 and O₂-IM2 are identified as important intermediates in the oxidative degradation of HD.

Among the multiple degradation pathways of O₂-IM1, the hydrogen abstraction reaction from the C2 on the other chloroethyl chain by the oxygen in O₂-IM1 exhibits the highest reaction rate, followed by the hydrogen abstraction from the C1 on the same chloroethyl chain. In contrast, the pathway involving hydrogen abstraction from the carbon directly bonded to O₂, accompanied by OH elimination, shows the lowest reaction rate due to its higher steric hindrance (Fig. 13(a)). Among the multiple degradation pathways of O₂-IM2, the oxygen in O₂-IM2 exhibits comparable reaction rates for hydrogen abstraction from both the C2 and C1 on the other chloroethyl chain. Similar to O₂-IM1, the pathway involving hydrogen abstraction from the carbon directly bonded to O₂ shows the lowest reaction rate due to significant steric hindrance (Fig. 13(b)).

Fig. 13 Temperature dependence of degradation rate constants (lg k vs. 1000/T) for various decomposition pathways of the oxidation intermediates. (a) O₂-IM1 and (b) O₂-IM2.

Roles of reactive oxygen species in HD degradation during incineration

Under incineration conditions, the concentrations of reactive oxygen species vary significantly depending on reaction conditions. The relative contributions of these species to HD degradation are determined by both their respective reaction rate constants with HD and their in situ concentrations. To quantitatively evaluate these contributions during incineration processes, we systematically examined the degradation efficiencies of OH, O₂, HO₂, and O toward HD using a validated combustion kinetic model⁶⁸ (the reduced version is provided in the SI B) at 973–1573 K (Fig. 14).

Fig. 14 The mole fractions of reactive oxygen species during incineration as a function of temperature (a), and the contribution rates of reactive oxygen species to HD degradation as a function of temperature (b). In panel (a), the species concentrations were calculated based on the NUIGMech1.1 mechanism⁶⁸ under conditions specified in Table S4 of the SI; the arrows in panel (a) indicate their corresponding vertical axes. In panel (b), the contribution rates of reactive oxygen species represent the percentage of HD degradation rate of each species relative to the total HD degradation rate.

As temperature increases, the mole fraction of O₂ gradually decreases but remains the dominant species among the four reactive oxygen species. In contrast, the mole fractions of OH and O increase progressively with temperature, while HO₂ exhibits a trend of first increasing and then decreasing, peaking at approximately 1323 K (Fig. 14(a)).

The elementary reactions contributing to the total rate for each reactive oxygen species are listed in Table S5 of the SI. The calculated contribution rates of reactive oxygen species to HD degradation (Fig. 14(b)) reveal that below 923 K, O₂ dominates HD degradation due to the extremely low concentrations of OH, O, and HO₂. Above 923 K, OH and O become the primary contributors. With increasing temperature, the contribution of OH gradually decreases, whereas that of O increases, exceeding 30% at 1573 K. Since the oxygen-transfer reaction between O and HD was not taken into account in its effect on the reaction rate, the contribution of O to HD consumption reported in this study is likely a conservative estimate. HO₂ exhibits only a minor contribution across all temperature ranges. Although the mole fraction of O₂ remains significantly higher than other species at all temperatures, its contribution to HD degradation becomes negligible as other reactive oxygen species form, primarily due to its extremely low reaction rate with HD.

Conclusions

The gas-phase reaction mechanisms and kinetics between HD and reactive oxygen species (OH, O₂, HO₂, O) were investigated at the CCSD(T)/aug-cc-pVTZ//M06-2X/6-311+G(d,p) theoretical level. All four reactive oxygen species can undergo hydrogen abstraction reactions with HD, with the OH-mediated hydrogen abstraction representing the most favorable reaction pathway, followed by the O-mediated pathway. The hydrogen abstraction reactions by OH and O may serve as crucial factors promoting HD degradation in natural environments, owing to their relatively low free energy barriers and negative ΔG values. Kinetic simulations revealed that OH and O play dominant roles in HD degradation during incineration processes. Consequently, increasing the concentrations of OH and O while elevating reaction temperature would facilitate HD degradation, whether in natural environmental conditions or during incineration disposal. In the oxygen atom transfer pathway, both O₂ and O can directly oxidize HD to form SMO. SMO can be further oxidized by O₂ or O to yield SMO₂, a highly toxic product. The oxygen atom transfer pathway involving O₂ exhibits a prohibitively high energy barrier, whereas that mediated by O is likely governed by intersystem crossing as the rate-determining step. Similar to DMS, the adduct formed between HD and OH can be converted to SMO in the presence of O₂, and the resulting SMO-OH adduct can undergo further oxidation by O₂ to produce SMO₂. SMO demonstrates significantly higher oxidizability than HD. Although the oxygen atom transfer pathway exhibits much slower reaction rates than hydrogen abstraction pathways, the risk of HD being oxidized to SMO₂ remains non-negligible under incineration conditions where high concentrations of O₂, O, and OH are present.

Author contributions

Xuefeng Liu: writing – original draft, investigation, formal analysis, data curation, conceptualization. Shangpeng Hao: writing – original draft, investigation, formal analysis, data curation, conceptualization. Xin Gao: writing – original draft, formal analysis. Lin Yang: writing – original draft, investigation. Huanhuan Wang: writing – original draft, methodology, software, funding acquisition. Haitao Wang: writing – review & editing, conceptualization, investigation, funding acquisition.

Conflicts of interest

The authors declare that there are no conflicts of interest.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: more detailed calculation information. Tables S4 and S5, further simulation details and the elementary reactions incorporated. See DOI: https://doi.org/10.1039/d5cp03593g.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (21876202, 21177158, 52506001).

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Footnote

† The authors contribute equally in this article.

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