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The homogeneous gas-phase formation mechanisms of PCPTs/PCDTs/PCDFs from the radical/radical cross-condensation of 2-CPR and 2-CTPR: a theoretical, mechanistic and kinetics study

Polychlorinated phenoxathiins (PCPTs) are one group of dioxin-like compounds, which can be considered to be one-oxygen-substituted polychlorinated thianthrene (PCTA) compounds or one-sulfur-substituted polychlorinated dibenzo-p-dioxin (PCDD) compounds. Owing to their high toxicity and wide distribution, clarifying the formation and emission of PCPTs due to combustion and thermal processes can deepen our understanding of the dioxin formation mechanism and allow reduced-emission and dioxin-control strategies to be established. Chlorophenols (CPs) and chlorothiophenols (CTPs) are direct precursors in PCPT formation. In this paper, the homogeneous gas-phase formation mechanisms of PCPTs, as well as polychlorinated dibenzofurans (PCDFs) and polychlorinated dibenzothiophenes (PCDTs), from the cross-condensation of 2-chlorophenoxy radicals (2-CPRs) and 2-chlorothiophenoxy radicals (2-CTPRs) under thermal and combustion conditions were investigated theoretically using a density functional theory (DFT) method. The reaction priorities and effects of water molecules on the formation mechanisms were discussed. The rate constants of crucial elementary steps were calculated from 600–1200 K. The acute and chronic toxicities of the main products were predicted at three trophic levels. This study shows that routes starting with oxygen–carbon condensation are favored over those starting with sulfur–carbon condensation for PCPT formation, and routes ending with Cl loss can occur more easily than those ending with H loss. Water molecules have a negative catalytic effect on CH–S H-transfer steps but a positive catalytic effect on CH–O H-transfer steps.


Introduction
Polychlorinated dibenzo-p-dioxins/dibenzofurans (PCDD/Fs) belong to the oen-mentioned typical persistent organic pollutant (POP) family because of their carcinogenic, teratogenic, and mutagenic effects and ubiquitous contamination of the global environment via global distillation. 1,2 Polychlorinated thianthrenes/dibenzothiophenes (PCTA/DTs) are PCDD/F analogues in which all the oxygen atoms are replaced by sulfur atoms. The replacement of oxygen by sulfur can lower the toxicity of PCDT/TAs; however, the concentrations of PCDT/TAs in some typical regions are higher than those of PCDD/Fs. 3,4 Polychlorinated phenoxathiins (PCPTs) are another group of chlorinated tricyclic aromatic heterocycles, which can be considered as one-oxygen-substituted PCTA compounds or onesulfur-substituted PCDD compounds. Therefore, PCPTs and PCTA/DTs exhibit physicochemical, toxicological, ecotoxicological, and persistent properties similar to those displayed by PCDD/Fs, which can be viewed as dioxin-like compounds. [5][6][7][8][9][10] The structures of PCPT/DD/TAs and PCDF/DTs are depicted in Scheme 1. It is well-established that PCDD/DFs and PCTA/DTs are never intentionally synthesized for commercial aims but are instead generated via a variety of combustion or thermal processes as unwanted byproducts, with examples including municipal and hazardous waste incinerators, industrial incinerators, y ash, stack gas, and the metal reclamation industry. [11][12][13][14][15][16][17] The simultaneous occurrence and mutual transformation of PCPTs, PCDD/DFs, and PCTA/DTs 18-21 indicate their close correlation and possibly similar formation pathways. However, to our knowledge, there is no information available on the formation of PCPTs. Therefore, obtaining detailed insight into the formation of PCPTs will deepen our understanding of the formation mechanisms of dioxin-like compounds and could lead to emission-reduction and dioxin-control strategies being established.
The most direct route to the formation of PCDD/Fs and PCTA/DTs is homogeneous gas-phase reactions from chemical precursors. Chlorophenols (CPs) and chlorothiophenols (CTPs) are widely recognized to be the predominant precursors for PCDD/DT and PCTA/DT formation, respectively. 3,[22][23][24][25][26][27] CPs mainly arise from direct applications, such as biocides, emissions from operating facilities, bleaching operations, and woodproduct leaching. 28,29 CTPs have been widely used in various chemical industries, such as in polyvinyl chloride, insecticides, and the manufacturing of dyes, pharmaceuticals, and printing inks. 30 Under high-temperature conditions, CPs and CTPs can readily form chlorophenoxy radicals (CPRs) and chlorothiophenoxy radicals (CTPRs) through losing phenoxyl-H and sulydryl-H, respectively, via direct H loss or abstraction reactions involving H, OH, Cl, and O( 3 P). The homogeneous gasphase formation of PCDD/DFs and PCTA/DTs involves the radical/radical condensation of C(T)PRs and radical/molecule recombination of C(T)PR and C(T)P. 3,21,22,27,31 Radical/radical condensation plays a crucial role in PCDD/DF and PCTA/DT formation. 3,[22][23][24][25][26][27]31 Based on radical/radical routes, a series of theoretical studies of PCDD/DF and PCTA/DT formation mechanisms from the coupling of 2-C(T)PRs, 2,4,5-TC(T)PRs, 2,4-DC(T)PRs, and 2,4,6-C(T)PRs has been carried out, 3,27,[31][32][33][34][35][36] and the consensus has been reached that PCDD and PCTA formation require the condensation of two C(T)PRs with at least one chlorine substituent in the ortho position, while PCDT formation needs two C(T)PRs with at least one available ortho hydrogen. 3,27,[31][32][33][34][35][36] For PCDD and PCTA formation, pathways that end with the elimination of Cl are dominant over pathways ending with the elimination of H. 3,27,[31][32][33][34][35][36] The chlorine substitution pattern has a signicant effect on the self-dimerization of C(T)Ps. 3,27,[31][32][33][34][35][36] However, despite there being a lot of studies of the formation mechanisms of PCDD/DFs and PCTA/DTs from the radical/radical self-coupling of CPRs and CTPRs, as far as we know, there is no information available about the formation mechanisms of PCPT/DF/DTs from the cross-coupling of CPRs and CTPRs under high-temperature conditions. Considering the structural resemblance and similar properties of PCPTs and PCTA/DDs, and the coexistence of CTPs and CPs, the study of PCPT formation with both CP and CTP as precursors is signicant.
Owing to their ability to form hydrogen bonds, water molecules can participate in many chemical reactions in the environment, such as unimolecular reactions, bimolecular reactions, hydrolysis reactions, and isomerization reactions via increasing or decreasing the energy potentials and catalyzing these reactions. [37][38][39][40][41] Water molecules can also form hydrogenbond clusters in the atmosphere and enhance aerosol nucleation processes. 42,43 In real-world waste incineration, the original waste contains an amount of water. Additionally, in some plants, ue gases are quenched with cooling water at the end of furnace operations. Water vapor is abundant and ubiquitous in waste incineration and industrial operations. Therefore, the inuence of water on dioxin formation needs to be studied. Several experimental and theoretical studies have been performed to investigate the effects of water on PCDD/F and PCTA/ DT formation via de novo synthesis and precursor formation studies 36,[44][45][46][47][48] but no agreement has been reached. Stieglitz and Ross found that water can enhance the catalytic activity of y ash and promote the yields of PCDD/Fs. 44,45 However, Jay and Briois reported that the presence of water molecules can decrease the PCDD/F formation potential and isomer distribution. 46,47 Shi et al. found that water molecules can promote the formation of PCDD/DFs via two routes: water molecules can participate actively in abstraction reactions involving CPs and H/OH radicals via lowering the potential barrier of CPR formation and in the H-shi step for the formation of PDDFs as a positive catalyst through proton transfer reactions via a bridge ring. 48 However, Xu et al. indicated that water molecules have a negative catalytic effect on the H-shi step and hinder the formation of PCDTs from CTPs. 36 Hence, in this work, we used an overall density functional theory (DFT) approach to study PCPT/DF/DT gas-phase formation with 2-CP and 2-CTP as forerunners under hightemperature pyrolysis or combustion conditions. All possible formation pathways involved in PCPT/DF/DT formation from the cross-condensation of 2-CPR and 2-CTPR were studied. Furthermore, the effects of water molecules on the PCPT/DF/DT formation mechanism are discussed. Some energetically preferred routes with and without water molecules were proposed to explain the isomer patterns of the PCPT/DF/DT products. Moreover, rate constants for the key elementary reactions from 600-1200 K were evaluated. The acute and chronic toxicity properties of the main products were predicted at three trophic levels. The last aim is to compare the formation potentials of PCDD/DF, PCTA/DT, and PCPT/DF/DT products from self-and cross-condensation mechanisms involving 2-CPR and 2-CTPR. The results can be input into dioxin control and prediction models as detailed parameters, which can be used to conrm the formation routes of dioxin-like compounds, reduce dioxin emissions, and establish dioxin-control strategies.

Computational methods
All calculations relating to chemical structures, energies, and frequencies of reactants, transition states, and products were performed using the Gaussian 09 program suite, 49 along with the hybrid meta function MPWB1K. 50 The MPWB1K method is a hybrid DFT model with effective performance in quantum calculations relating to thermochemistry, thermochemical kinetics, hydrogen bonding, and weak interactions.
The geometry and vibrational frequency calculations were carried out at the MPWB1K level with a standard 6-31+G(d,p) basis set. The nature of the stationary points, the zero-point energy (ZPE), and the thermal contributions to the free energy of activation can be determined via vibrational frequency calculations. The overall reactions discussed in this paper were veried using intrinsic reaction coordinate (IRC) calculations and the minimum energy path (MEP) analysis of all transition states. 51 To calculate the rate constants, 40 non-stationary points near the transition state along the minimum energy path (20 points on the reactant side and 20 points on the product side) were selected for frequency calculations at the MPWB1K/6-31+G(d,p) level. A more exible basis set, 6-311+G(3df,2p), was used to determine the single-point energies of various species based on the optimized geometries. The proles of the potential energy surfaces were constructed at the MPWB1K/6-311+G(3df,2p)//MPWB1K/6-31+G(d,p) level, including ZPE correction. All the relative energies quoted and discussed in this paper include ZPE corrections. The rate constants of the key elementary steps involved in this study were calculated over the wide temperature range of 600-1200 K using canonical variational transition-state (CVT) theory with small-curvature tunneling (SCT) correction. [52][53][54][55] The rate constant calculations were performed using the POLYRATE 9.7 program. 56 ECOSAR V2.0 (Ecological Structure Activity Relationships Version 2.0), developed by the US EPA (Environmental Protection Agency), was selected to assess the ecotoxicity properties of PCPT/DF/DTs from the reactions of 2-CPR and 2-CTPR. 57

Results and discussion
The reliability and accuracy of the MPWB1K6-311+G(3df,2p)// MPWB1K/6-31+G(d,p) level for geometry and energy calculations were studied via comparison with experimental values, as shown in Table S1 of the ESI. † The optimized geometry of phenoxathiin at the MPWB1K/6-31+G(d,p) level is in reasonable accordance with the corresponding experimental values, and the largest discrepancies are within 2.1% and 2.9% for the bond lengths and bond angles, respectively, except for two abnormal values. 58 For the reaction C 6 H 5 OH + C 6 H 5 SH / C 12 H 8 OS + 2H 2 , the reaction enthalpy of 26.32 kcal mol À1 calculated at the MPWB1K/6-311+G(3df,2p) level and at 298.15 K agrees well with the experimental value of 26.12 kcal mol À1 , obtained from the measured standard enthalpy of formation (DH f,0 ) values of C 6 H 5 OH (À23.02 kcal mol À1 ), C 6 H 5 SH (26.85 kcal mol À1 ), C 12 H 8 OS (30.05 kcal mol À1 ), and H 2 (0.03 kcal mol À1 ). [59][60][61][62] The formation of 2-C(T)PR from 2-C(T)P is the initial and key step in the formation of PCPT/DF/DTs. In combustion and thermal processes, 2-C(T)PR can be produced through the loss of phenoxyl-H or sulydryl-H via the unimolecular cleavage of the O-H or S-H bond or abstraction by active radicals. The potential barrier (DE) and reaction heat (DH) values of 2-CP and 2-CTP abstraction by H, OH, O( 3 P), and Cl were calculated at the MPWB1K/6-311+G(3df,2p) level, as shown in Table 1. Data for 2-C(T)P abstraction by H and OH are cited from our previous studies. [63][64][65] The imaginary frequencies, zero-point energies, and total energies for the transition states involved in the formation of PCPT/DF/DTs from the cross-condensation of 2-CPR and 2-CTPR are shown in Table S2 of the ESI. † Cartesian coordinates for the reactants, intermediates, transition states, and products involved in the formation of PCPT/DF/DTs are depicted in Tables S4 and S5 of the ESI. † According to the different positions and numbers of Cl substituents on the benzene ring, PCPT/DF/DTs have different congeners. In this paper, PCPT congeners with zero to two chlorine substitutions are represented by phenoxathiins (PTs), Table 1 The potential barrier (DE (in kcal mol À1 )) and reaction heat (DH (in kcal mol À1 )) values of elementary reactions involved in the formation of 2-CPR and 2-CTPR from 2-CP and 2-CTP, respectively. DH is calculated at 0 K   chlorine of the chlorophenoxy radical (S/CCl condensation for short); and the dimerization of chlorothiophenolic sulfur with the ortho-carbon bonded to the hydrogen of the chlorophenoxy radical (S/CH condensation for short). In Fig. 2, eight PCPT formation routes (routes 9-16) and ve products (PT, 1-MCPT, 4-MCPT, 1,6-DCPT, and 1,9-DCPT) arise from sulfur-carbon condensation of 2-CPR and 2-CTPR. All four (O/CCl, O/CH, S/CCl, and S/CH) condensation modes are barrierless and strongly exothermic processes, resulting in IM1 (with a reaction heat of À15.73 kcal mol À1 ), IM2 (with a reaction heat of À17.03 kcal mol À1 ), IM15 (with a reaction heat of À31.85 kcal mol À1 ), and IM16 (with a reaction heat of À32.13 kcal mol À1 ). The sulfur-carbon condensations are more exothermic compared to the oxygen-carbon condensations. This indicates that the sulfur-carbon condensations are favored over the oxygen-carbon condensations. For the oxygen-carbon condensations, O/CH condensation is preferred over O/CCl condensation; for the sulfur-carbon condensations, S/CH dimerization is preferred over S/CCl condensation. This may result from the fact that the steric hindrance effects of Cl atoms are larger than those of H atoms. Of the four intermediates, IM1 and IM15 undergo Cl abstraction, and IM2 and IM16 undergo H abstraction. All the Cl and H abstraction steps involve abstraction by H, OH, SH, and Cl radicals and produce IM3, IM9, IM6, and IM19 with low energy barriers and strong release heats. In routes 1, 5, 9, and 13, the loop closure and Cl-loss steps occur as one-step reactions and are rate-determining steps due to having the highest potential barriers and strongest endothermicities. However, the loop closure and H-loss steps occur separately in routes 2, 6, 10, and 14, and the H-loss steps are the rate-determining steps. Routes 3,4,7,8,11,12,15, and 16 contain two Smiles rearrangement steps aer the H or Cl abstraction step. The rate-determining steps are the loop closure and Cl-loss or H-loss steps for routes 3, 4, 7, 8, 11, and 15, but are the rst Smiles rearrangement steps for routes 12 and 16.
In Fig. 1, routes 1-4 cover three, four, six, and ve elementary steps, respectively, and route 1 has the least elementary steps. Furthermore, the rate-determining step involved in route 1 has the lowest potential barrier (14.52 kcal mol À1 ) and is the least endoergic (16.57 kcal mol À1 ) among all four routes. Thus, route 1 is favored over routes 2-4. Similarly, route 5 (with a potential barrier of 13.03 kcal mol À1 and a reaction heat of 14.75 kcal mol À1 ) is preferred over routes 6-8. Therefore, the thermodynamically favorable PCPT formation routes are route 1 and route 5, resulting in the formation of PT and 4-MCPT. Comparing routes 1 and 5, the initiation step of route 5 is preferred, involving O/CH dimerization, over that of route 1, involving O/CCl dimerization. In addition, the rate-determining step involved in route 5 has a lower potential barrier and less endothermicity than that involved in route 1. Thus, route 5 is preferred over route 1. 4-MCPT is the main product from the oxygen-carbon condensation of 2-CPR and 2-CTPR, as seen in Fig. 1, followed by PT.
The comparison of reaction routes presented in Fig. 2 shows that route 9, ending with a loop-closure and Cl-loss step has one less elementary step than route 10, ending with a H-loss step. Furthermore, the rate-determining step involved in route 9 has a lower potential barrier and is much less endoergic than that involved in route 10. Thus, route 9 is favored over route 10. Route 11 and route 12 involve two more Smiles rearrangement steps compared with route 10 and route 9, respectively. For the same reason, route 12, ending with a loop-closure and Cl-loss step is favored over route 11, ending with a H-loss step. This indicates that routes ending with Cl loss are favored over those ending with H loss, owing to the C-Cl bond being weaker than the C-H bond. Comparing routes 9 and 12, the ratedetermining step of route 9 is the loop-closure and Cl-loss step (potential barrier: 27.05 kcal mol À1 , reaction heat: 16.13 kcal mol À1 ), whereas the rate-determining step of route 12 is the rst Smiles rearrangement step (potential barrier: 25.51 kcal mol À1 , reaction heat: 8.11 kcal mol À1 ). Although route 9 covers two less elementary steps than route 12, the ratedetermining step of route 12 has a lower potential barrier and less endothermicity than route 9. Therefore, route 9 and route 12 should be competitive, resulting in the formation of PT. Similarly, route 13 and route 16 should be competitive, and the dominant product is 1-MCPT. Comparing routes 1 and 5 from Fig. 1 and routes 9, 12, 13, and 16 from Fig. 2, the ratedetermining steps of the most favored routes in Fig. 1 contain lower potential barriers (13.03-14.52 kcal mol À1 ) than those in Fig. 2 (24.52-27.80 kcal mol À1 ). This means that routes 1 and 5 from Fig. 1 are preferred over routes 9, 12, 13, and 16 in Fig. 2, and the main products from routes starting with the oxygencarbon and sulfur-carbon condensation of 2-CPR and 2-CTPR are PT and 4-MCPT.
It is interesting to compare PCPT formation from the crosscondensation of 2-CPR and 2-CTPR with PCDD and PCTA formation from the self-condensation of 2-CPR and 2-CTPR. 32,36 Our study investigated the PCDD formation routes from the self-coupling of 2-CPR, and the potential barriers of the ratedetermining steps are 27.03-27.41 kcal mol À1 . 32 Fig. S1 in the ESI † shows the PCTA formation routes from the self-coupling of 2-CTPR, and the potential barriers of the loop-closure and Clloss steps are 12.28-14.60 kcal mol À1 . 36 This study shows that the potential barriers of the rate-determining steps from the oxygen-carbon condensation of 2-CPR and 2-CTPR are 13.03-14.52 kcal mol À1 . Thus, the PCPT/DD/TA formation potentials from the self-and cross-condensation of 2-CPR and 2-CTPR can be ranked as follows: self-condensation of 2-CTPR (resulting in TA and 1-MCTA) > cross-condensation of 2-CPR and 2-CTPR (resulting in PT and 4-MCPT) > self-condensation of 2-CPR (resulting in DD and 1-MCDD).

The formation of PCDF/DTs from the crosscondensation of 2-CPR and 2-CTPR
The homogeneous gas-phase formation routes of PCDFs and PCDTs from the cross-condensation of 2-CPR and 2-CTPR with potential barriers (DE (in kcal mol À1 )) and reaction heats (DH (in kcal mol À1 )) calculated at the MPWB1K/6-311+G(3df,2p)// MPWB1K/6-31+G(d,p) level are presented in Fig. 3-5. Six PCDF/ DT formation routes (routes [17][18][19][20][21][22] and four products (4,6-DCDF, 4,6-DCDT, 4-MCDF, and 4-MCDT), illustrated in Fig. 3-5, are proposed from the carbon-carbon condensation of 2-CPR and 2-CTPR. Three types of carbon-carbon condensation coupling mechanisms for PCDF/DT formation are presented in Fig. 3-5: the condensation of the ortho-carbon bonded to the hydrogen of the chlorophenoxy radical with the ortho-carbon bonded to the hydrogen of the chlorothiophenoxy radical (COH/ CSH condensation for short) in routes 17-20 of Fig. 3 and 4; the condensation of the ortho-carbon bonded to the hydrogen of the chlorophenoxy radical with the ortho-carbon bonded to the chlorine of the chlorothiophenoxy radical (COH/CSCl condensation for short) in route 21 of Fig. 5; and the condensation of the ortho-carbon bonded to the chlorine of the chlorophenoxy radical with the ortho-carbon bonded to the hydrogen of the chlorothiophenoxy radical (COCl/CSH condensation for short) Fig. 5 Formation routes of PCDF/DTs including potential barrier (DE (in kcal mol À1 )) and reaction heat (DH (in kcal mol À1 )) values via the carboncarbon condensation (COCl/CSH and COH/CSCl) of 2-CPR and 2-CTPR. DH is calculated at 0 K. The red route represents the favored route without the introduction of water molecules, and the blue route shows the favored route with the introduction of water molecules. in route 22 of Fig. 5. In Fig. 3 and 5, the routes colored red represent the favored routes without the introduction of water molecules and the blue routes are the favored routes with the introduction of water molecules. The green routes represent the favored routes both with and without the introduction of water molecules. The optimized geometries for selected transition states in the formation processes of PCPT/DT/DFs from the radical/radical cross-condensation of 2-CPR and 2-CTPR are showed in Fig. 6.
In Fig. 3 With the participation of water molecules, the ratedetermining step of route 17 is the bimolecular CH-S Htransfer reaction, but the rate-determining step of route 18 becomes the OH-loss step. The potential barrier of the ratedetermining step of route 17 (17.81 kcal mol À1 ) is higher than that of route 18 (16.58 kcal mol À1 ). Thus, route 18 was favored over route 17 under wet conditions. The main product with the aid of water molecules is 4,6-DCDT.
In Fig. 4 Fig. 4, the potential barrier of TS62 is higher than that of TS61, whereas the potential barrier of TS63 is lower than that of TS61. This means that water molecules participating in CH-S double H transfer have a negative catalytic effect on PCDF/DT formation, and water molecules participating in CH-O double H transfer have a positive catalytic effect on PCDF/DT formation. Routes 19 and 20 have the same rst two steps, and differences occur in the last three elementary steps. For route 19, the OH-loss step involves the highest barrier (16.58 kcal mol À1 ) and is more endoergic (9.64 kcal mol À1 ) than any elementary step in the last three elementary steps of route 19, e.g., the OH-loss step is the rate-determining step of route 19. For the same reason, the loop-closure step is the ratedetermining step of route 20 (potential barrier: 8.88 kcal mol À1 , reaction heat: À13.41 kcal mol À1 ). Obviously, under conditions both with and without water molecules, the rate-determining step of route 20 can occur via a lower potential barrier than that of route 19, which means that pathway 20 (resulting in 4,6-DCDF) is thermodynamically favored compared with pathway 19 (resulting in 4,6-DCDT). Thus, 4,6-DCDF is the main product from the double H transfer route of the cross-coupling of 2-CPR and 2-CTPR under both dry and wet conditions.
Two reaction routes, shown in Fig Fig. 3-5 that COH-CSCl/COCl-CSH coupling has higher potential barriers (10.76 and 7.53 kcal mol À1 ) and is less exothermic (À3.28 and À3.22 kcal mol À1 ) than COH-CSH coupling (potential barrier: 4.44 kcal mol À1 , reaction heat: À10.31 kcal mol À1 ). These results indicate that COH-CSH condensation is favored over COH-CSCl/COCl-CSH condensation. In route 21, water molecules have an inhibiting effect on CH-S H-transfer and restrain the formation of 4-MCDF, which increases the potential barrier by about 5 kcal mol À1 compared with direct CH-S H-transfer. Direct CH-S H-transfer (potential barrier: 12.05 kcal mol À1 , reaction heat: 4.66 kcal mol À1 ) and CS-H H-transfer with water (potential barrier: 17.10 kcal mol À1 , reaction heat: 4.66 kcal mol À1 ) are the rate-determining steps of route 21 under dry and wet conditions, respectively. However, in route 22, water molecules have a positive catalytic effect on CH-O H-transfer and promote the formation of 4-MCDF, which decreases the potential barrier by about 1.5 kcal mol À1 compared with direct CH-O H-transfer. The rate-determining step of route 22 both with and without water is the OH-loss step, which has the highest potential barrier (15.85 kcal mol À1 ) and is the most strongly endothermic (8.83 kcal mol À1 ) in route 22. Under conditions without water, the rate-determining step of route 21 (12.05 kcal mol À1 ) has a lower potential barrier than that of route 22 (15.85 kcal mol À1 ), i.e., route 21 is favored over route 22 and 4-MCDF is the main product in a dry incinerator from the CH-CCl coupling of 2-CPR and 2-CTPR. However, under conditions involving water, the rate-determining step of route 21 (17.10 kcal mol À1 ) requires crossing a higher potential barrier than route 22 (15.85 kcal mol À1 ), i.e., route 22 is favored over route 21 and 4-MCDT is the dominant product from the CH-CCl coupling of 2-CPR and 2-CTPR in a wet incinerator.
Under dry conditions, without the introduction of water molecules, for PCDF/DT formation from 2-CPR and 2-CTPR, the favored routes are route 17, route 20, and route 21, shown in Fig. 3-5, respectively. The potential barriers of the ratedetermining steps of route 17, route 20, and route 21 are 14.18, 8.88, and 12.05 kcal mol À1 , which indicates that route 20 can occur more easily than routes 17 and 21, resulting in the formation of 4,6-DCDF. Under wet conditions, with the introduction of water molecules, route 18, route 20, and route 22 are the energetically preferred routes, as shown in Fig. 3-5, and the potential barriers of the rate-determining steps of route 18, route 20, and route 22 are 16.58, 8.88, and 15.85 kcal mol À1 , respectively. Thus, under wet conditions, the most favored route is also route 20 for PCDF/DT formation from the crosscondensation of 2-CPR and 2-CTPR.
It is necessary to compare PCDF/DT formation from the cross-condensation of 2-CPR and 2-CTPR with our previous studies of PCDF formation from the self-coupling of 2-CPR and PCDT formation from 2-CTPR (Fig. S1 in the ESI †). 32,36 For PCDF formation from the self-coupling of 2-CPR, no matter with or without water molecules, the rate-determining steps are the ring-closure steps, with potential barriers of 28.12 and 29.17 kcal mol À1 and reaction heats of 8.73 and 9.56 kcal mol À1 . 32 For PCDT formation from the coupling of 2-CTPR, under both dry and wet conditions, the rate-determining Table 2 Arrhenius formulae for the formation of PCPTs from the cross-condensation of 2-CPR and 2-CTPR over the temperature range of 600-1200 K (the units are per s and cm 3 per molecule per s for unimolecular and biomolecular reactions, respectively)

Reaction
Arrhenius formula

Rate-constant calculations
In the environmental eld, kinetics models are used to account for the potential outcomes regarding contamination of the environment and gaseous routes during production processes. However, for combustion and thermal processes, owing to the strict high-temperature experimental conditions required for dioxin formation and the lack of effective detection methods for short-lifetime intermediates, the availability of kinetics parameters and data, such as pre-exponential factors, activation energies, and rate constants, is limited and insufficient. This causes inaccuracies in dioxin-formation prediction models and difficulties relating to further improving and optimizing dioxinformation models. Therefore, an alternative method is to use calculated rate constants or other dynamic information directly obtained from quantum calculations of electronic structures, frequencies, and energies. In this study, the rate constants of the crucial elementary reactions for PCPT/DF/DT formation from the crosscondensation of 2-CPR and 2-CTPR were calculated using the CVT/SCT method on the basis of the MPWB1K/6-311+G(3df,2p)//MPWB1K/6-31+G(d,p) energy, as seen in Table  S3 of the ESI. † The CVT/SCT values were obtained over a wide temperature range of 600-1200 K, which covers the possible formation temperatures of PCPT/DF/DTs in combustion and thermal processes. Our previous studies of PCDD/DF formation from CPs and PCTA/DT formation with CTPs as precursors have successfully proved the accuracy of the CVT/SCT method for Table 3 Arrhenius formulae for the formation of PCDF/DTs from the cross-condensation of 2-CPR and 2-CTPR over the temperature range of 600-1200 K (the units are per s and cm 3 per molecule per s for unimolecular and biomolecular reactions, respectively) calculating the rate constants for the elementary reactions involved in dioxin-like compound formation. [32][33][34][35][36] To be applied more effectively, the CVT/SCT rate constants were tted, and the Arrhenius formulae are presented in Table 2 for PCPT formation from the oxygen-carbon coupling and sulfur-carbon coupling reactions between 2-CPR and 2-CTPR and in Table 3 for PCDF/DT formation from the carbon-carbon coupling reactions between 2-CPR and 2-CTPR. The preexponential factors and activation energies can be obtained from these Arrhenius formulae.
In order to explore whether the favored routes change with increasing temperature, we t plots of the CVT/SCT rate constants in the temperature range of 600-1200 K for the ratedetermining steps of each PCPT/DT/DF formation route from the cross-condensation of 2-CPR and 2-CTPR, which is shown in Fig. S2 in the ESI. † As can be seen from Fig. S2, † in the range of 600-1200 K, the plot lines have no cross-points, which means that the ranking of CVT/SCT values for the rate-determining steps of the PCPT/DT/DF formation routes from the crosscondensation of 2-CPR and 2-CTPR is consistent. For example, for PCPT formation in routes 1-4, the CVT/SCT values of TS5 in route 1 are consistently larger than those of TS7 in route 2, TS 11 in route 3, and TS 13 in route 4, which agrees well with the thermal analysis that route 1 is favored over routes 2-4. For PCDF/DT formation from the cross-condensation of 2-CPR and 2-CTPR in the range of 600-1200 K via routes 17 and 18, the CVT/SCT values of TS50 in route 17 are consistently larger than those of TS60 in route 18. The favored routes under wet and dry conditions are uniform with increasing temperature in routes 17 and 18. A similar trend occurs for PCDF/DT formation via routes 19 and 20 and routes 21 and 22. Thus, it can be inferred that the favored routes labelled in color in Fig. 3-5 will not change with increasing temperature for PCDF/DT formation.

Ecotoxicity assessment
Using ECOSAR, the acute and chronic toxicity properties of the main products (PT, 4-MCPT, 1-MCPT, 1,6-DCPT, 4,6-DCPT, 1,9-DCPT, 4-MCDF, 4,6-DCDF, 4-MCDT, and 4,6-DCDT) in this study were predicted at three trophic levels (i.e., green algae, daphnia, and sh). The acute toxicity values were measured using LC 50 (50% lethal concentration of the tested compound Table 4 Predicted acute and chronic toxicities of products generated from the condensation of 2-CPR and 2-CTPR aer daphnia and sh were exposed for 48 and 96 h, respectively) and EC 50 (the concentration of the tested chemical at which half of green algae experience growth inhibition aer 96 h of exposure) values. The chronic toxicity values are expressed as ChV, representing the repeat dose of a substance that can initiate the development of adverse effects. It can be concluded from Table 4 that the toxicity levels of the products were consistent at the three trophic levels (i.e., green algae, daphnia, and sh) in an aquatic environment, and the toxicity order is 1,6-DCPT/4,6-DCPT/1,9-DCPT > 4,6-DCDT > 4,6-DCDF > 4-MCPT/1-MCPT > 4-MCDT > PT > 4-MCDF. In order to compare the acute and chronic toxicity properties of the products of PCPT formation from the cross-condensation of 2-CPR and 2-CTPR with the acute and chronic toxicity properties of PCDD and PCTA formation from the self-condensation of 2-CPR and 2-CTPR, 32,36 we added the toxicity values for DD, 1-MCDD, 2,7-DCDD, TA, 1-MCTA and 2,7-DCTA to Table 4. From Table 4, for the given chlorine substitutions, the toxicities of PCPTs are higher than those of PCDDs and PCTAs. Hence, more attention should be paid to controlling the emission of PCPTs and to the treatment of this pollution.

Conclusions
In this study, the mechanisms of the homogeneous gas-phase formation of PCPT/DF/DTs from the cross-condensation of 2-CPR and 2-CTPR were investigated theoretically using DFT electronic structure theory at the MPWB1K/6-311+G(3df,2p)// MPWB1K/6-31+G(d,p) level. The formation potentials of PCTA/ DT products and the roles of water molecules in the mechanisms were discussed. The mechanisms were compared with PCDD/DF formation from the self-coupling of 2-CPR and PCTA/ DT formation from 2-CTP. Kinetics calculations were carried out and the rate constants were calculated over the temperature range of 600-1200 K using the CVT/SCT method. The acute and chronic toxicity properties of the main products were predicted at three trophic levels. Four specic conclusions can be drawn, as follows.
(1) In PCPT formation from the cross-coupling of 2-CPR and 2-CTPR, routes 1 and 5 are the most favored routes, resulting in the formation of PT and 4-MCPT. Routes starting with oxygencarbon condensation are favored over those starting with sulfur-carbon condensation, and routes ending with the elimination of Cl are energetically preferred to routes ending with the elimination of H.
(2) In PCDF/DT formation from the cross-coupling of 2-CPR and 2-CTPR, route 20 is the energetically preferred route under both wet and dry conditions, resulting in the formation of 4,6-DCDF. Water molecules participating in CH-S transfer have a negative catalytic effect on PCDF/DT formation and a positive catalytic effect on PCDF/DT formation.

Conflicts of interest
There are no conicts to declare.