Theoretical Investigations on the Reactivity of Hydrogen Peroxide toward 2,3,7,8-Tetrachlorodibenzo-p-dioxin

Acquiring full knowledge of the reactivity of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) is crucial for the better understanding of the transformation and degradation of TCDD-like dioxins in the environment. To clarify the reactivity of the organic hydroperoxides toward TCDD, in this study, the reactions between the neutral/anion of the hydrogen peroxide (H2O2) and TCDD have been systematically investigated theoretically. It was found that the neutral H2O2 is relatively difficult to react with TCDD compared with its anion, exhibiting the pH dependence of the title reaction. As for the anion of H2O2, it reacts with TCDD through two reaction mechanisms, i.e., nucleophilic substitution and nucleophilic addition. For the former, the terminal O atom of HO2− nucleophilically attacks the C atom of the C-Cl bond in TCDD to form an intermediate containing an O-O bond, accompanying the dissociation of the chlorine atom. For the latter, the terminal O atom of HO2− can be easily attached to the C atom of the C-O bond in TCDD, resulting in the decomposition of C-O bond and the formation of an intermediate containing an O-O bond. For these formed intermediates in both reaction mechanisms, their O-O bonds can be homolytically cleaved to produce different radicals. In addition, the selected substitution effects including F-, Br-, and CH3- substituents on the above reactions have also been studied. Hopefully, the present results can provide new insights into the reactivity of the organic hydroperoxides toward TCDD-like environmental pollutants.


Results and Discussion
In view of the fact that neutral H 2 O 2 and its anion coexist due to the occurrence of the acid-base dissociation equilibrium in solution, the reactions of the neutral and anion of H 2 O 2 with TCDD are discussed respectively.

Reaction of Neutral H 2 O 2 with TCDD
Similar to the reaction between chlorinated benzoquinones and H 2 O 2 [33,34], the reaction between H 2 O 2 and TCDD is initiated by the formation of an initial intermediate. Then, nucleophilic attack of H 2 O 2 on TCDD occurs to produce an unstable intermediate containing an O-O bond. Finally, the unstable intermediate decomposes via the homolytical cleavage of the O-O bond, resulting in the production of radicals. The detailed reaction mechanisms are described as follows.

Direct Reaction of the Neutral H 2 O 2 with TCDD
For the direct reaction of the neutral H 2 O 2 with TCDD, four nucleophilic attack modes named as 1, 2, 3, and 4 have been constructed considering the D 2h symmetry of TCDD and the different orientations of the H atom in H 2 O 2 . As shown in Figure 1, the corresponding transition states TSn (n = 1-4) for each mode have been located. As displayed in Figure 1, the O atom of H2O2 nucleophilically attacks the C atom of the C-Cl bond in TCDD, accompanying the proton transfer (PT) from the attacking O atom of H2O2 to the dissociated chlorine atom of TCDD. As presented in Table 1, the free energy barriers for the four nucleophilic attack modes are 62. 43, 62.39, 64.04 and 61.63 kcal/mol, respectively. Similarly, the M06-2X/6-311++G(d,p) level of theory can also give consistent results. Obviously, such high energy barriers suggest that it is very difficult for the title reaction to occur under normal conditions. Can the bulk solvent effects promote the above processes? To clarify this point, the solvent effects in aqueous solution have been considered employing the SMD model. As presented in Table  1, the free energy barriers mentioned above have been changed slightly upon solvation, where the changes of the free energy barriers range from 1.20 to −1.07 kcal/mol. Therefore, it is still difficult for the direct reaction between neutral H2O2 and TCDD to take place even though solvent effects are included.

Water-Assisted Reaction of Neutral H2O2 with TCDD
In view of the fact that a water molecule plays an important catalytic role in promoting the PT process and the above NAP involves the PT process, the reaction of H2O2 with TCDD has been explored below with the assistance of different numbers of explicit water molecules ranging from one to three on the basis of the above nucleophilic attack mode 1. For simplicity, the symbols IMx(nw) and TSx(nw) have been employed to stand for the optimized intermediates (IMs) and transition states (TSs), where x and n denote the formation sequence of the mentioned species and the numbers of water molecules involved, respectively. For instance, IM1(1w) and IM2(2w) represent the first and second intermediates in the reaction pathways involving one and two water molecules, respectively. The selected distances are given in Å and the data in square brackets refer to the imaginary frequency of the transition state, which is true for the remaining figures.
As displayed in Figure 1, the O atom of H 2 O 2 nucleophilically attacks the C atom of the C-Cl bond in TCDD, accompanying the proton transfer (PT) from the attacking O atom of H 2 O 2 to the dissociated chlorine atom of TCDD. As presented in Table 1, the free energy barriers for the four nucleophilic attack modes are 62.43, 62.39, 64.04 and 61.63 kcal/mol, respectively. Similarly, the M06-2X/6-311++G(d,p) level of theory can also give consistent results. Obviously, such high energy barriers suggest that it is very difficult for the title reaction to occur under normal conditions. Can the bulk solvent effects promote the above processes? To clarify this point, the solvent effects in aqueous solution have been considered employing the SMD model. As presented in Table 1, the free energy barriers mentioned above have been changed slightly upon solvation, where the changes of the free energy barriers range from 1.20 to −1.07 kcal/mol. Therefore, it is still difficult for the direct reaction between neutral H 2 O 2 and TCDD to take place even though solvent effects are included.

Water-Assisted Reaction of Neutral H 2 O 2 with TCDD
In view of the fact that a water molecule plays an important catalytic role in promoting the PT process and the above NAP involves the PT process, the reaction of H 2 O 2 with TCDD has been explored below with the assistance of different numbers of explicit water molecules ranging from one to three on the basis of the above nucleophilic attack mode 1. For simplicity, the symbols IMx(nw) and TSx(nw) have been employed to stand for the optimized intermediates (IMs) and transition states (TSs), where x and n denote the formation sequence of the mentioned species and the numbers of water molecules involved, respectively. For instance, IM1(1w) and IM2(2w) represent the first and second intermediates in the reaction pathways involving one and two water molecules, respectively.
For the four reaction pathways involving zero, one, two, and three water molecules, they have been named as pathways A, B, C and D, respectively.

Formation of the Initial Intermediate
As the first step of the whole reaction, the initial intermediates have been explored based on the IRC analyses of the corresponding transition states TS1(nw) n=0-3 in the NAPs. As shown in Figure 2, different initial intermediates IM1(nw) n=0-3 have been located. Correspondingly, the molecular graphs and topological analyses of them are given in Figure S1 and Table S1  For the four reaction pathways involving zero, one, two, and three water molecules, they have been named as pathways A, B, C and D, respectively.

Formation of the Initial Intermediate
As the first step of the whole reaction, the initial intermediates have been explored based on the IRC analyses of the corresponding transition states TS1(nw)n=0-3 in the NAPs. As shown in Figure 2, different initial intermediates IM1(nw)n=0-3 have been located. Correspondingly, the molecular graphs and topological analyses of them are given in Figure S1 and Table S1 of the Supplementary Materials, respectively.  As displayed in Figure 2 and Figure S1, TCDD, H 2 O 2 , and H 2 O interact with each other via intermolecular H-bonds in the formed IMs, which can be confirmed by the presence of the corresponding BCPs. In IM1(0w), one of the H atoms of H 2 O 2 forms an intermolecular H-bond with the chlorine atom of TCDD. For the water molecules introduced, they interact with both TCDD and H 2 O 2 simultaneously via intermolecular H-bonds. As presented in Table S1, the above intermolecular H-bonds are mostly predominated by the electrostatic interactions as can be seen from the positive values of the ∇ 2 ρ bcp and H bcp of the electron density at the BCPs. Actually, this point is also be reflected by the large H-bonding distances shown in Figure 2.
As presented in Table 2, IM1(0w) has been stabilized by 1.52 kcal/mol relative to those of the separated reactants. Moreover, the stabilization energy increases with the increasing of the numbers of water molecules. For example, IM1(1w), IM1(2w), and IM1(3w) have been stabilized by about 6.83, 13.82 and 21.31 kcal/mol, respectively. Meanwhile, the enthalpy changes for these formation processes are negative values, suggesting that the formation processes of these IMs are exothermic reactions. Importantly, the released reaction heat increases with the increasing of the numbers of water molecules, which is necessary for the following NAP. a All the units are in kcal/mol. The data in parentheses are the results relative to the corresponding IM2(nw).

Nucleophilic Substitution Process
As displayed in Figure 2, all the transition states TS1(nw) n=0-3 in the NAPs have been located, which have been further verified by the IRC calculations. As shown in Figure 3, the microscopic details during the NAP can be observed. For example, for the direct reaction in the absence of water molecules, one of the O atoms (O25) of H 2 O 2 directly attacks the C atom (C12) of TCDD, accompanying the simultaneous dissociation of the H26 atom of H 2 O 2 and Cl18 atom of TCDD. As a result, the second intermediate IM2(0w) containing an O-O bond can be formed. Note that the O25-H26 bond of H 2 O 2 begins to increase significantly until the formation of the transition state, exhibiting the asynchrony of the nucleophilic substitution reaction. As for the process assisted by one water molecule, as shown in Figure 3, the introduced water molecule accepts the proton of H 2 O 2 and donates its own proton to the chlorine atom of TCDD simultaneously, reflecting the bridge role of water molecule in the assistance of PT. Moreover, no zwitterionic species have been located during the PT process. Therefore, the above PT processes should proceed concertedly. Similarly, the same is also true for the processes involving two and three water molecules. To better understand the catalytic role of water molecules in the above process, the selected distances involving the attacked C atom of TCDD in TSs have been analyzed. As displayed in Figure  2, the distances between the dissociated Cl atoms and its linked C atom (RC···Cl) in TS1(nw)n=0-3 decrease with the increasing of the numbers of water molecules. For instance, RC···Cl is 2.284, 2.192, 2.153 and 2.139 Å in TS1(nw)n=0-3 involving zero, one, two, and three water molecules, respectively. On the other hand, the opposite is true for the distance between the attacking O atom of H2O2 and the attacked C atom of TCDD. Obviously, less structural deformations occur for H2O2 and TCDD in the presence of water molecules compared with the direct reaction, implying the decrease of the energy barriers with the assistance of water molecules.
Expectedly, as shown in Table 2, the original electronic energy barrier in the NAP has been decreased significantly with the increasing of the numbers of water molecules. For example, it has been decreased by 28.38 to 23.72 kcal/mol with the assistance of three water molecules, exhibiting the positive catalytic role of water molecules. On the other hand, the free energy barriers have been changed slightly.

Cleavage of the O-O Bond
After the NAP, the second intermediates IM2(nw)n=0-3 containing an O-O bond have been formed. As shown in Figure 2, all of them have been characterized by the intermolecular H-bonds, which can be further confirmed by the presence of the BCPs as shown in Figure S1.
As shown in Figure 2, the O-O bonds in IM2(nw)n=0-3 have been elongated more or less compared to that of the H2O2, indicating the weakening of them. Actually, as presented in Table S1, this point can be further confirmed by the decreases of the electron density at the BCP of the O-O bonds upon the formation of IM2(nw)n=0-3. Moreover, to further evaluate the strength of the O-O bonds, the vertical and adiabatic bond dissociation energies (BDEs) of the O-O bonds have been calculated for IM2(nw)n=0-3 as well as that of H2O2 for comparison. Here, the vertical BDE is calculated as the energy difference between the optimized intermediate and the dissociated fragments without considering the structural relaxation. As for the adiabatic BDE, it is calculated as the enthalpy difference between the optimized species before and after dissociation. As presented in Table 3, the O-O bond has been significantly weakened upon the formation of IM2(nw)n=0-3. For example, the vertical BDE of the O-O bond of H2O2 (48.62 kcal/mol) has been decreased by about 28.30 to 20.32 kcal/mol in IM2(0w). Meanwhile, significant decreases for the adiabatic BDE have also been observed. Therefore, it is easy to homolytically cleave these O-O bonds in IM2(nw)n=0-3 thermodynamically. To better understand the catalytic role of water molecules in the above process, the selected distances involving the attacked C atom of TCDD in TSs have been analyzed. As displayed in Figure 2, the distances between the dissociated Cl atoms and its linked C atom (R C···Cl ) in TS1(nw) n=0-3 decrease with the increasing of the numbers of water molecules. For instance, R C···Cl is 2.284, 2.192, 2.153 and 2.139 Å in TS1(nw) n=0-3 involving zero, one, two, and three water molecules, respectively. On the other hand, the opposite is true for the distance between the attacking O atom of H 2 O 2 and the attacked C atom of TCDD. Obviously, less structural deformations occur for H 2 O 2 and TCDD in the presence of water molecules compared with the direct reaction, implying the decrease of the energy barriers with the assistance of water molecules.
Expectedly, as shown in Table 2, the original electronic energy barrier in the NAP has been decreased significantly with the increasing of the numbers of water molecules. For example, it has been decreased by 28.38 to 23.72 kcal/mol with the assistance of three water molecules, exhibiting the positive catalytic role of water molecules. On the other hand, the free energy barriers have been changed slightly.

Cleavage of the O-O Bond
After the NAP, the second intermediates IM2(nw) n=0-3 containing an O-O bond have been formed. As shown in Figure 2, all of them have been characterized by the intermolecular H-bonds, which can be further confirmed by the presence of the BCPs as shown in Figure S1.
As shown in Figure 2, the O-O bonds in IM2(nw) n=0-3 have been elongated more or less compared to that of the H 2 O 2 , indicating the weakening of them. Actually, as presented in Table S1, this point can be further confirmed by the decreases of the electron density at the BCP of the O-O bonds upon the formation of IM2(nw) n=0-3 . Moreover, to further evaluate the strength of the O-O bonds, the vertical and adiabatic bond dissociation energies (BDEs) of the O-O bonds have been calculated for IM2(nw) n=0-3 as well as that of H 2 O 2 for comparison. Here, the vertical BDE is calculated as the energy difference between the optimized intermediate and the dissociated fragments without considering the structural relaxation. As for the adiabatic BDE, it is calculated as the enthalpy difference between the optimized species before and after dissociation. As presented in Table 3, the O-O bond has been significantly weakened upon the formation of IM2(nw) n=0-3 . For example, the vertical BDE of the O-O bond of H 2 O 2 (48.62 kcal/mol) has been decreased by about 28.30 to 20.32 kcal/mol in IM2(0w). Meanwhile, significant decreases for the adiabatic BDE have also been observed. Therefore, it is easy to homolytically cleave these O-O bonds in IM2(nw) n=0-3 thermodynamically. Moreover, as shown in Figure 2, the corresponding TSs for the cleavage of the O-O bond have also been located. As presented in Table 2, for IM2(0w), the calculated free energy barrier is 6.27 kcal/mol relative to IM2(0w). Moreover, the energy barriers are 8.53, 14.09 and 16.37 kcal/mol in the presence of one, two, and three water molecules, respectively. In fact, these transition states are lower in energy relative to the initial reactants. For example, TS2(2w) and TS2(3w) are lower in energy by 9.04 and 12.01 kcal/mol than the initial reactants. Thermodynamically, the calculated Gibbs free energy changes in the conversion process from IM2(nw) n=0-3 to products are −3.42, −4.40, −3.87, and −2.77 kcal/mol for the pathways A, B, C, and D, corresponding to the equilibrium constants of 3.22 × 10 2 , 1.69 × 10 3 , 6.82 × 10 2 , and 1.07 × 10 2 , respectively. Therefore, it is feasible for the intermediates IM2(nw) n=0-3 to produce two radicals via the homolysis of the O-O bond.
Compared with the NAPs, as shown in Table 2, the energy barriers for the cleavage of the O-O bond are relatively small. Therefore, the NAP should be the rate-determining step for the above reaction.

Reaction of TCDD with HO 2 − Anion
Moreover, the reaction of the anion of H 2 O 2 with TCDD has also been explored. As a result, two reaction mechanisms, i.e., nucleophilic substitution and nucleophilic addition, have been verified below.

Nucleophilic Substitution Process
As shown in Figure 4, two different nucleophilic attack modes, i.e., modes S1 and S2, have been designed based on the structural symmetry of TCDD. Similar to the above reaction involving neutral H 2 O 2 , two initial intermediates IM1(S1) and IM1(S2) for the two modes have first been located. Subsequently, the nucleophilic attack of HO 2 − on TCDD occurs via transition states TS1(S1) and TS1(S2), leading to the production of the second intermediates IM2(S1) and IM2(S2) containing an O-O bond. As expected, the following process should proceed to produce radicals via the homolytic cleavage of the O-O bond. Especially, unlike the reaction of the neutral H 2 O 2 mentioned above, no explicit water molecules are required here. Moreover, as shown in Figure 2, the corresponding TSs for the cleavage of the O-O bond have also been located. As presented in Table 2, for IM2(0w), the calculated free energy barrier is 6.27 kcal/mol relative to IM2(0w). Moreover, the energy barriers are 8.53, 14.09 and 16.37 kcal/mol in the presence of one, two, and three water molecules, respectively. In fact, these transition states are lower in energy relative to the initial reactants. For example, TS2(2w) and TS2(3w) are lower in energy by 9.04 and 12.01 kcal/mol than the initial reactants. Thermodynamically, the calculated Gibbs free energy changes in the conversion process from IM2(nw)n=0-3 to products are −3.42, −4.40, −3.87, and −2.77 kcal/mol for the pathways A, B, C, and D, corresponding to the equilibrium constants of 3.22 × 10 2 , 1.69 × 10 3 , 6.82 × 10 2 , and 1.07 × 10 2 , respectively. Therefore, it is feasible for the intermediates IM2(nw)n=0-3 to produce two radicals via the homolysis of the O-O bond.
Compared with the NAPs, as shown in Table 2, the energy barriers for the cleavage of the O-O bond are relatively small. Therefore, the NAP should be the rate-determining step for the above reaction.

Reaction of TCDD with HO2 − Anion
Moreover, the reaction of the anion of H2O2 with TCDD has also been explored. As a result, two reaction mechanisms, i.e., nucleophilic substitution and nucleophilic addition, have been verified below.

Nucleophilic Substitution Process
As shown in Figure 4, two different nucleophilic attack modes, i.e., modes S1 and S2, have been designed based on the structural symmetry of TCDD. Similar to the above reaction involving neutral H2O2, two initial intermediates IM1(S1) and IM1(S2) for the two modes have first been located. Subsequently, the nucleophilic attack of HO2 − on TCDD occurs via transition states TS1(S1) and TS1(S2), leading to the production of the second intermediates IM2(S1) and IM2(S2) containing an O-O bond. As expected, the following process should proceed to produce radicals via the homolytic cleavage of the O-O bond. Especially, unlike the reaction of the neutral H2O2 mentioned above, no explicit water molecules are required here. Further energy analyses suggest that the two initially formed intermediates IM1(S1) and IM1(S2) have been stabilized by about 24.16 and 23.17 kcal/mol relative to the initial reactants, respectively. Similarly, the corresponding transition states are also lower in energy by about 16.08 and 15.39 kcal/mol relative to the initial reactants. As a result, the calculated free energy barriers for the nucleophilic attack of TCDD by HO2 − are 7.64 and 7.08 kcal/mol relative to the initial intermediates, Further energy analyses suggest that the two initially formed intermediates IM1(S1) and IM1(S2) have been stabilized by about 24.16 and 23.17 kcal/mol relative to the initial reactants, respectively. Similarly, the corresponding transition states are also lower in energy by about 16.08 and 15.39 kcal/mol relative to the initial reactants. As a result, the calculated free energy barriers for the nucleophilic attack of TCDD by HO 2 − are 7.64 and 7.08 kcal/mol relative to the initial intermediates, respectively.
In aqueous solution, the corresponding free energy barriers are 23.64 and 23.03 kcal/mol relative to the initial intermediates, respectively. Compared with the results in the gas phase, the important solvent effects should be stressed here.
Overall, for the nucleophilic substitution process, the reaction of HO 2 − with TCDD is more favorable than that of the reaction involving the neutral H 2 O 2 , exhibiting the dependence of the title reaction on the pH value of the media.

Nucleophilic Addition Process
Besides the nucleophilic substitution reaction, the nucleophilic addition reaction of HO 2 − has also been observed. As shown in Figure 5, Overall, the nucleophilic addition process is more favorable kinetically compared with the above nucleophilic substitution process. respectively. In aqueous solution, the corresponding free energy barriers are 23.64 and 23.03 kcal/mol relative to the initial intermediates, respectively. Compared with the results in the gas phase, the important solvent effects should be stressed here.
Overall, for the nucleophilic substitution process, the reaction of HO2 − with TCDD is more favorable than that of the reaction involving the neutral H2O2, exhibiting the dependence of the title reaction on the pH value of the media.

Nucleophilic Addition Process
Besides the nucleophilic substitution reaction, the nucleophilic addition reaction of HO2 − has also been observed. As shown in Figure 5 Overall, the nucleophilic addition process is more favorable kinetically compared with the above nucleophilic substitution process.

Substitution Effects
To further explore the reactivity of the organic hydroperoxides with TCDD and its derivatives, the substitution effects including F-, Br-, and CH3-substitutes have been investigated.
For the neutral H2O2, its reactions with the F-and Br-substituted TCDD have been investigated as well as the reaction between TCDD and the CH3-substituted H2O2. Here, the NAP involving three water molecules is considered since it is the rate-determining step as mentioned above. As shown in Figure 6, the located transition states are similar to the TS1(3w) mentioned above. For the reactions of F-and Br-substituted cases, the calculated free energy barriers are lower by 0.68 and 1.44 kcal/mol than those resulting before substitution. As for the reaction of the CH3-substituted H2O2 with TCDD, the free energy barrier is higher by 3.54 kcal/mol than that before substitution. Therefore, for the

Substitution Effects
To further explore the reactivity of the organic hydroperoxides with TCDD and its derivatives, the substitution effects including F-, Br-, and CH 3 -substitutes have been investigated.
For the neutral H 2 O 2 , its reactions with the F-and Br-substituted TCDD have been investigated as well as the reaction between TCDD and the CH 3 -substituted H 2 O 2 . Here, the NAP involving three water molecules is considered since it is the rate-determining step as mentioned above. As shown in Figure 6, the located transition states are similar to the TS1(3w) mentioned above. For the reactions of F-and Br-substituted cases, the calculated free energy barriers are lower by 0.68 and 1.44 kcal/mol than those resulting before substitution. As for the reaction of the CH 3 -substituted H 2 O 2 with TCDD, the free energy barrier is higher by 3.54 kcal/mol than that before substitution. Therefore, for the reaction involving neutral organic hydroperoxides, the energy barriers have not been significantly influenced upon substitution.
As for the above nucleophilic substitution reactions involving the anion of organic hydroperoxides, taking model S1 for example, the corresponding transition states have been given in Figure 6. For the reactions of HO 2 − with F-and Br-substituted TCDD, the calculated free energy barriers are higher by 1.32 and 0.27 kcal/mol than the reaction before substitution. Similarly, for the reaction of the CH 3 − substituted HO 2 − with TCDD, the calculated free energy barrier is higher by about 3.13 kcal/mol than the reaction before substitution. Therefore, it is also feasible for the reaction to take place between the anions of the organic hydroperoxides and TCDD as well as its derivatives.
Molecules 2018, 23, x 9 of 13 reaction involving neutral organic hydroperoxides, the energy barriers have not been significantly influenced upon substitution. As for the above nucleophilic substitution reactions involving the anion of organic hydroperoxides, taking model S1 for example, the corresponding transition states have been given in Figure 6. For the reactions of HO2 − with F-and Br-substituted TCDD, the calculated free energy barriers are higher by 1.32 and 0.27 kcal/mol than the reaction before substitution. Similarly, for the reaction of the CH3 − substituted HO2 − with TCDD, the calculated free energy barrier is higher by about 3.13 kcal/mol than the reaction before substitution. Therefore, it is also feasible for the reaction to take place between the anions of the organic hydroperoxides and TCDD as well as its derivatives. As for the nucleophilic addition reaction, the addition mode A2 has been explored. As shown in Figure 6, the corresponding transition states associated with the C-O bond cleavage have been located. Similar to the reaction before substitution, all the intermediates and transition states are lower in energy than the separated reactants. Moreover, the free energy barriers are only 0.29, 0.37, and 1.38 kcal/mol for the C-O bond cleavage process, respectively. Therefore, the feasibility of the nucleophilic addition reaction has been confirmed once again.
In summary, organic hydroperoxides, especially for their anions, can react with TCDD and its derivatives. Taking the reaction of ROO − (R=H or alkyl groups) with TCDD for example, the reaction mechanisms between them can be proposed below. As displayed in Figure 7, on the one hand, the reaction can occur through nucleophilic substitution mechanism to produce an intermediate containing an O-O bond. On the other hand, nucleophilic addition mechanism is also feasible for the reaction, leading to the decomposition of the C-O bond of TCDD and the formation of an intermediate containing an O-O bond. Finally, the O-O bond in these intermediates can be cleaved homolytically to produce different radicals depending on the introduced substitutes. Given the fact that these highly reactive radicals can cause oxidative damages to organisms, the above reaction mechanisms can be used to partially explain the potential toxicity mechanism of TCDD-like environmental contaminants. Certainly, more complicated experiments are required to further verify the above findings. As for the nucleophilic addition reaction, the addition mode A2 has been explored. As shown in Figure 6, the corresponding transition states associated with the C-O bond cleavage have been located. Similar to the reaction before substitution, all the intermediates and transition states are lower in energy than the separated reactants. Moreover, the free energy barriers are only 0.29, 0.37, and 1.38 kcal/mol for the C-O bond cleavage process, respectively. Therefore, the feasibility of the nucleophilic addition reaction has been confirmed once again.
In summary, organic hydroperoxides, especially for their anions, can react with TCDD and its derivatives. Taking the reaction of ROO − (R=H or alkyl groups) with TCDD for example, the reaction mechanisms between them can be proposed below. As displayed in Figure 7, on the one hand, the reaction can occur through nucleophilic substitution mechanism to produce an intermediate containing an O-O bond. On the other hand, nucleophilic addition mechanism is also feasible for the reaction, leading to the decomposition of the C-O bond of TCDD and the formation of an intermediate containing an O-O bond. Finally, the O-O bond in these intermediates can be cleaved homolytically to produce different radicals depending on the introduced substitutes. Given the fact that these highly reactive radicals can cause oxidative damages to organisms, the above reaction mechanisms can be used to partially explain the potential toxicity mechanism of TCDD-like environmental contaminants. Certainly, more complicated experiments are required to further verify the above findings.

Computational Details
All the geometries have been fully optimized at the B3LYP/6-311++G(d,p) level of theory, where the reliability of the method has been verified by numerous systems [39][40][41][42][43][44][45][46][47][48][49][50]. Subsequently, vibrational frequency analysis has been carried out to identify the nature of the optimized species. For the located transition states (TSs), intrinsic reaction coordinate (IRC) [51,52] calculations have also been performed to further verify their correctness. For comparison, M06-2X/6-311++G(d,p) level of theory has also been employed for the direct nucleophilic substitution process involving neutral H2O2. As mentioned below, the calculated results are well consistent with the results of the B3LYP level. Thus, considering the compromise between computational accuracy and cost, the results at the B3LYP/6-311++G(d,p) level of theory have been mainly discussed if not otherwise noted.
To evaluate bulk solvent effects on the nucleophilic attack process (NAP), full optimizations have been performed for the selected species in aqueous solution employing the solvent model density (SMD) [53] solvation model. To explore the positive role of water molecules in the reaction, one, two, and three explicit water molecules have been introduced. Here, similar to previous studies on water-assisted proton transfer systems [33,34,54], the introduced water molecules have been located between the proton donor and proton acceptor through intermolecular H-bonds. Note that more water molecules without participating in the proton transfer have a slight influence on the reduction of the barrier heights [54].
To characterize the formation and nature of the intermolecular H-bonds formed in the intermediates, atoms in molecules (AIM) theory was employed based on the optimized geometries. In the AIM analyses [55], the locations of the bond critical point (BCP) and ring critical point (RCP) denote the presence of the interatomic interactions and the formation of a ring structure, respectively. Moreover, the nature of the H-bonding interaction can be predicted from the topological parameters of the electron density (ρbcp) at the BCP of the H-bonds, e.g., the Laplacian of electron density (∇ 2 ρbcp) and energy density (Hbcp) including the kinetic and potential energy density (Gbcp and Vbcp).
All calculations were performed by using the Gaussian 09 program [56].

Conclusions
In this study, the reactivity of H2O2 and its anion toward TCDD and its selected derivatives has been systematically investigated theoretically. It was found that the neutral H2O2 is relatively difficult to react with TCDD even though the reaction process is assisted by explicit water molecules. On the contrary, the anion of H2O2 can easily react with TCDD, exhibiting the pH dependence of the title reaction. Overall, HO2 − can react with TCDD via two different reaction mechanisms, i.e., nucleophilic substitution and nucleophilic addition.

Computational Details
All the geometries have been fully optimized at the B3LYP/6-311++G(d,p) level of theory, where the reliability of the method has been verified by numerous systems [39][40][41][42][43][44][45][46][47][48][49][50]. Subsequently, vibrational frequency analysis has been carried out to identify the nature of the optimized species. For the located transition states (TSs), intrinsic reaction coordinate (IRC) [51,52] calculations have also been performed to further verify their correctness. For comparison, M06-2X/6-311++G(d,p) level of theory has also been employed for the direct nucleophilic substitution process involving neutral H 2 O 2 . As mentioned below, the calculated results are well consistent with the results of the B3LYP level. Thus, considering the compromise between computational accuracy and cost, the results at the B3LYP/6-311++G(d,p) level of theory have been mainly discussed if not otherwise noted.
To evaluate bulk solvent effects on the nucleophilic attack process (NAP), full optimizations have been performed for the selected species in aqueous solution employing the solvent model density (SMD) [53] solvation model. To explore the positive role of water molecules in the reaction, one, two, and three explicit water molecules have been introduced. Here, similar to previous studies on water-assisted proton transfer systems [33,34,54], the introduced water molecules have been located between the proton donor and proton acceptor through intermolecular H-bonds. Note that more water molecules without participating in the proton transfer have a slight influence on the reduction of the barrier heights [54].
To characterize the formation and nature of the intermolecular H-bonds formed in the intermediates, atoms in molecules (AIM) theory was employed based on the optimized geometries. In the AIM analyses [55], the locations of the bond critical point (BCP) and ring critical point (RCP) denote the presence of the interatomic interactions and the formation of a ring structure, respectively. Moreover, the nature of the H-bonding interaction can be predicted from the topological parameters of the electron density (ρ bcp ) at the BCP of the H-bonds, e.g., the Laplacian of electron density (∇ 2 ρ bcp ) and energy density (H bcp ) including the kinetic and potential energy density (G bcp and V bcp ).
All calculations were performed by using the Gaussian 09 program [56].

Conclusions
In this study, the reactivity of H 2 O 2 and its anion toward TCDD and its selected derivatives has been systematically investigated theoretically. It was found that the neutral H 2 O 2 is relatively difficult to react with TCDD even though the reaction process is assisted by explicit water molecules. On the contrary, the anion of H 2 O 2 can easily react with TCDD, exhibiting the pH dependence of the title reaction. Overall, HO 2 − can react with TCDD via two different reaction mechanisms, i.e., nucleophilic substitution and nucleophilic addition. Given the fact that the produced highly reactive radicals can lead to potential damage to organisms, the reaction mechanisms herein are expected to provide an alternative elucidation for the potential toxicity mechanism of TCDD-like environmental contaminants. Certainly, related experiments are highly desirable to further confirm the present findings.
Supplementary Materials: The following are available online. Figure S1: Molecular graphs of the intermediates (IM) and transition states (TS) in the different reaction pathways involving neutral H 2 O 2 . Table S1: Topological parameters for the intermediates in the different reaction pathways involving neutral H 2 O 2 . Table S2: Cartesian coordinates of the optimized species in the present study.

Conflicts of Interest:
The authors declare no conflict of interest.