Environ. Sci. Technol. 2010, 44, 6745–6751
Dioxin Formations from the Radical/Radical Cross-Condensation of Phenoxy Radicals with 2-Chlorophenoxy Radicals and 2,4,6-Trichlorophenoxy Radicals FEI XU, WANNI YU, RUI GAO, QIN ZHOU, QINGZHU ZHANG,* AND WENXING WANG Environment Research Institute, Shandong University, Jinan 250100, P. R. China
Received May 27, 2010. Revised manuscript received July 22, 2010. Accepted July 22, 2010.
It is important to understand the role of phenol in the dioxin formations because it is present in the high amount in municipal waste incinerators (MWIs). The formation mechanism of dioxins from the cross-condensation of PhRs with 2-CPRs and 2,4,6TCPRs was investigated by using hybrid density functional theory (DFT) and compared with the dioxin formation mechanism from the self-condensation of single chlorophenol precursors. The geometrical parameters were optimized at the MPWB1K level with the 6-31+G(d,p) basis set without symmetry constraints. Single-point energy calculations were carried out at the MPWB1K/6-311+G(3df,2p) level of theory. The rate constants were deduced by using canonical variational transition-state (CVT) theory with small curvature tunneling (SCT) contribution over the temperature range of 600-1200 K. The Arrhenius formulas were reported for the first time. Results show that phenol is responsible for the formation of dioxin congeners. This work, together with results already published from our group, provides a comprehensive investigation of the homogeneous gasphase formation of dioxins from (chloro)phenol precursors and should help to clarify the formation mechanism of dioxins in real waste combustion and to develop more effective control strategies.
1. Introduction Of the several groups of chlorinated materials found in the environment, none has given rise to more public concern than dioxinssthe set of polychlorinated dibenzo-p-dioxin (PCDDs) and polychlorinated dibenzofurans (PCDFs). Dioxins are considered as typical persistent organic pollutants (POPs) with the carcinogenic, teratogenic, and mutagenic effects (1). They are also suspected to be environment endocrine disruptors that disturb the balance of hormones and damage the metabolism, immunity, and reproduction of exposed organisms (2-4). PCDD/Fs have never been intentionally synthesized for commercial purposes. Studies on the dioxin formations are of interest because they can serve as a basis for minimizing dioxin emissions. It is well-established that combustion processes, especially those of municipal solid waste, are the principal origin of * Corresponding author fax: 86-531-8836 1990; e-mail: zqz@ sdu.edu.cn. 10.1021/es101794v
2010 American Chemical Society
Published on Web 08/09/2010
dioxins (5-7). In municipal waste incinerators (MWIs), dioxin byproducts can be formed by two general formation pathways, precursor pathway and de novo synthesis. The former is 102∼105 times faster than the latter (8, 9). The relative yields of dioxins produced from precursors are 72-99 000 times higher than those formed by de novo synthesis (8, 9). The formation pathway via precursors accounts for the majority of dioxin emissions from combustion sources (10, 11). Among the variety of precursors, chlorophenols (CPs) are structurally similar to dioxins and relatively easy to form dioxins during thermal treatment. Additionally, they are among the most abundant aromatic compounds found in MWI flue gases. CPs have been demonstrated to be the predominant precursors of dioxins in MWIs and are implicated as key intermediates in de novo pathway (12-14). Much attention has been devoted to the dioxin formations from the CP precursors. However, phenol is typically much more abundant than CPs in municipal waste incinerators. For example, the concentration of phenol in the MWI flue gases is 30-100 times higher than the sum of total CPs (15). Numerous studies have shown that phenol has the greatest propensity for the formation of PCDFs, especially DF and less chlorinated PCDF congeners (16, 17). Steric and electronic effects associated with chlorine substitution suppress the PCDF formations. The cross-condensation of phenol with CPs with ortho-chlorine substituent is also responsible for the distribution of PCDD homologues. It is somewhat surprising that there is relatively little information available in the literature on the dioxin formations from the phenol precursor. Precursor formation pathway can occur via homogeneous gas-phase reactions and heterogeneous metal-mediated reactions. The homogeneous gas-phase formation of dioxins was proposed that involve (chloro)phenoxy radical/radical condensation, radical/molecule recombination of (chloro)phenoxy and (chloro)phenol. It has been shown that the radical/molecule mechanism requires chlorine and hydroxyl displacement as first steps, and these steps are not energetically favored (18, 19). The radical/radical condensation is the dominant pathway in the homogeneous gas-phase formation of dioxins. The radical/radical condensation plays a significant role in the heterogeneous metal-mediated formation pathway as well. Transition-metal species promote the formation of surface-associated (chloro)phenoxy radicals that react to produce dioxins through radical/radical reactions (20). (Chloro)phenols readily form (chloro)phenoxy radicals, which are neutral ambient radicals capable of reacting at the phenolic oxygen atom as well as at ortho and para carbon sites, under the combustion conditions. Due to their significant resonance stabilization, (chloro)phenoxy radicals could build up considerable concentration in the combustion environment affording their condensation to dioxin congeners. Despite the large volume of research data related to the dioxin formations, the specific formation mechanism of PCDD/Fs remains unclear. This is due in part to their extreme toxicity and the lack of efficient detection schemes for radical intermediate species. Quantum calculation is especially suitable for establishing the feasibility of a reaction pathway. In this paper, therefore, we present a rather comprehensive computational study on the dioxin formations from the crosscondensation of phenoxy radicals (PhRs) with 2-chlorophenoxy radicals (2-CPRs) and 2,4,6-trichlorophenoxy radicals (2,4,6-TCPRs). 2-chlorophenol (2-CP) and 2,4,6-trichlorophenol (2,4,6-TCP) are among the most abundant CP congeners found in MWIs (16). This work is a continuation VOL. 44, NO. 17, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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of our studies on the dioxin formations. In the recently published papers, we investigated the PCDD/F formations from the self-condensation of single chlorophenol precursors (21-23). A second motivation for this work is to evaluate the rate constants of the elementary reactions involved in the dioxin formations. The absence of the kinetic parameters, such as the pre-exponential factors, the activation energies, and the rate constants, of the elementary reactions is the most difficult challenge in further improving dioxin formation models.
2. Computational Methods The present study is carried out in two stages. In the first stage, by means of the Gaussian 03 suite of programs (24), DFT calculations are performed on an SGI 2000 supercomputer. It is well-known that MPWB1K is an excellent method for prediction of transition state geometries and thermochemical kinetics, based on the modified Perdew and Wang exchange functional (MPW) and Becke’s 1995 correlation functional (B95) (25). The geometrical parameters and harmonic vibrational frequencies of reactants, intermediates, transition states, and products were optimized at the MPWB1K level with a standard 6-31+G(d,p) basis set. Stationary points were characterized as minima or transition states by diagonalizing their Hessian matrices and confirming that there are zero or one negative eigenvalue, respectively. The minimum energy path (MEP) was obtained by the intrinsic reaction coordinate (IRC) theory to confirm that the transition state really connects to minima along the reaction path. At some point along the MEP, the matrices of force constants were computed in order to do the following calculations of the canonical variational rate constants. To yield more reliable reaction heats and barrier heights, a more flexible basis set, 6-311+G(3df,2p), was used for single-point energy calculations. All the relative energies quoted and discussed in this paper include zero-point energy (ZPE) corrections. In the second stage, the electronic structure information is input in Polyrate-Version 9.3 to calculate canonical variational transition-state (CVT) theory rate constants and their temperature dependence (26-28). The CVT rate constant, kCVT(T), at a fixed temperature (T) that minimized the generalized transition-state theory rate constant, kGT(T, s), with respect to the dividing surface at s is expressed as kCVT(T) ) min kGT(T,s) s
(1)
The generalized transition-state theory rate constant kGT(T, s) for T and a dividing surface at s is kGT(T, s) )
σkBT QGT(T, s) -VMEP(s)/kBT e h ΦR(T)
(2)
where, σ is the symmetry factor accounting for the possibility of more than one symmetry-related reaction path, kB is Boltzmann’s constant, h is Planck’s constant. ΦR(T) is the reactant partition function per unit volume, excluding symmetry numbers for rotation, and QGT(T, s) is the partition function of a generalized transition state at s with a local zero of energy at VMEP(s) and with all rotational symmetry numbers set to unity. The rotational partition functions were calculated classically, and the vibrational modes were treated as quantum-mechanically separable harmonic oscillators.
3. Results and Discussion It is vital to clarify the reliability of the theoretical calculations, especially for a continuous work. The optimized geometries and the calculated vibrational frequencies of phenol, DD, and 1-MCDD at the MPWB1K/6-31+G(d,p) level are in good 6746
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agreement with the available experimental values (29-32), and the relative error remains within 1.5% for the geometrical parameters and 8.0% for the vibrational frequencies except for the lowest frequency of DD, with the relative error up to 11.5%. In order to verify the reliability of the energies, we calculated the reaction enthalpies for the reactions of Ph+2CPfDD+H2+HCl and Ph+2-CPf1-MCDD+2H2 at the MPWB1K/6-311+G(3df,2p)//MPWB1K/6-31+G(d,p) level. The calculated values of 17.79 and 35.18 kcal/mol at 298.15 K and 1.0 atm show good consistency with the corresponding experimental values of 18.12 and 33.87 kcal/mol obtained from the measured standard formation enthalpies (∆Hf,0) of phenol, 2-CP, DD, 1-MCDD, HCl (33-36), especially if the experimental uncertainties are taken into consideration. Under typical incinerator conditions, (chloro)phenoxy radicals can be produced from (chloro)phenols through loss of the phenoxyl-hydrogen via unimolecular, bimolecular, or possibly other low-energy pathways (including heterogeneous reactions). The unimolecular reaction contains the decomposition of (chloro)phenols with the cleavage of the OsH bond. The bimolecular reactions involve the phenolichydrogen abstraction homogeneously in the gas phase from (chloro)phenols by the active radicals, H, OH, O (3P), and Cl, which are abundant in the combustion environment. The heterogeneous reactions include the reactions catalyzed by transition-metal oxides and chlorides. The formation of (chloro)phenoxy radicals from (chloro)phenols has been investigated in detail in the literature (37-39). 3.1. Formation of PCDDs. 3.1.1. Formation of PCDDs from the Cross-Condensation of PhRs with 2-CPRs. Five possible reaction pathways, displayed in Figure 1, are proposed for the formation of PCDDs from the crosscondensation of PhRs with 2-CPRs. It can be seen from Figure 1 that pathway 1, pathway 2, and pathway 5 are similar, they involve four elementary steps: oxygen-carbon coupling, Cl or H abstraction, ring closure, and intra-annular elimination of H. The intra-annular elimination of H is the rate determining step. Pathway 3 includes six elementary reactions: oxygen-carbon coupling, H abstraction, Smiles rearrangement (two elementary steps), ring closure, and intraannular elimination of H (the rate determining step). Pathway 4 contains three elementary processes: oxygen-carbon coupling, H abstraction, ring closure and intra-annular elimination of Cl. The ring closure and intra-annular elimination of Cl are found to occur in one step and are the rate determining step. Apparently, pathway 4 covers relatively less elementary steps. Furthermore, the rate determining step involved in pathway 4 has a lower barrier height and is less endoergic than those involved in pathway 1, pathway 2, pathway 3, and pathway 5, respectively. So, pathway 4 is thermodynamically preferred route, resulting in the formation of DD, consistent with the experimental study (40). The rate determining step to the PCDD formation is intraannular elimination of Cl or H. Mechanisms described above and our previous study (21) show that the thermodynamically preferred routes proceed through intra-annular elimination of Cl. In general, there are two kinds of oxygen-carbon coupling modes, the coupling of the phenolic oxygen with the ortho carbon bonded to chlorine of a second (chloro)phenoxy radical (O/σ-CCl for short), and the coupling of the phenolic oxygen with the ortho carbon bonded to hydrogen of a second (chloro)phenoxy radical (O/σ-CH for short). Thus, two kinds of thermodynamically preferred routes can be identified for the PCDD formations. The first one contains the elementary steps of O/σ-CCl coupling, Cl abstraction, intra-annular elimination of Cl, or intra-annular elimination of Cl after a Smiles rearrangement by two chlorine losses. Here, the elementary step of intra-annular elimination of Cl involves the ring closure and intra-annular elimination of Cl because they are found to occur in one-step reaction.
FIGURE 1. PCDD formation routes embedded with the potential barriers ∆E (in kcal/mol) and reaction heats ∆H (in kcal/mol) from the cross-condensation of PhRs with 2-CPRs. ∆H is calculated at 0 K.
FIGURE 2. PCDD formation routes embedded with the potential barriers ∆E (in kcal/mol) and reaction heats ∆H (in kcal/mol) from the cross-condensation of PhRs with 2,4,6-TCPRs. ∆H is calculated at 0 K. The second one includes the elementary processes of O/σCH coupling, H abstraction, intra-annular elimination of Cl or intra-annular elimination of Cl after a Smiles rearrangement by the loss of one chlorine atom. As shown in Figure 1, the O/σ-CH coupling is more exothermic compared to the O/σ-CCl coupling. In order to further justify the result, we have carried out additional study on the oxygen-carbon coupling from the self-condensation of 19 CPRs and the crosscondensation of PhR with other 18 CPRs. Results indicate that the O/σ-CH coupling is favored over the O/σ-CCl coupling with a exception of the oxygen-carbon coupling from the self-condensation of 2,5-dichlorophenoxy radicals (2,5-DCPRs). Furthermore, the elementary steps of H abstraction have a lower barrier compared to the corresponding Cl abstraction steps. For example, the barrier height for the
H abstraction from IM2 by H atom is 3.87 kcal/mol, whereas the value is 5.43 kcal/mol for the Cl abstraction from IM1 by H atom. These results may provide an explanation for the experimental observation that one chlorine loss is favored over two chlorine losses in the PCDD formations (40, 41). Among all the (chloro)phenol precursors, only the selfcondensation of 2-CPRs and the cross-condensation of PhRs with 2-CPRs can produce DD, which is present in a high concentration in MWIs. Comparison of the mechanism displayed in Figure 1 with a previous study (23) shows that the formation of DD from the cross-condensation of PhRs with 2-CPRs by one chlorine loss is preferred over the DD formation from the self-condensation of 2-CPRs by two chlorine losses. In addition, phenol is much more abundant VOL. 44, NO. 17, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. PCDF formation routes embedded with the potential barriers ∆E (in kcal/mol) and reaction heats ∆H (in kcal/mol) from the cross-condensation of PhRs with 2-CPRs. ∆H is calculated at 0 K. than 2-CP in MWIs (15). Thus, phenol plays a crucial role in the formation of DD. 3.1.2. Formation of PCDDs from the Cross-Condensation of PhRs with 2,4,6-TCPRs. Similar to the cross-condensation of PhRs with 2-CPRs, three possible PCDD formation pathways are postulated from the cross-condensation of PhRs with 2,4,6-TCPRs. The formation schemes embedded with 6748
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the potential barriers and reaction heats are depicted in Figure 2. Pathway 6 involves four elementary steps: O/σ-CCl coupling, Cl abstraction, ring closure, and intra-annular elimination of H (the rate determining step). Pathway 7 contains the elementary reactions of O/σ-CCl coupling, Cl abstraction, Smiles rearrangement (two elementary steps), ring closure, and intra-annular elimination of H (the rate
FIGURE 4. PCDF formation route embedded with the potential barriers ∆E (in kcal/mol) and reaction heats ∆H (in kcal/mol) from the cross-condensation of PhRs with 2,4,6- TCPRs. ∆H is calculated at 0 K. determining step). Pathway 8 includes three elementary processes: O/σ-CH coupling, H abstraction, ring closure and intra-annular elimination of Cl (they are found to occur in one step and are the rate determining step). It is evident from Figure 2 that pathway 8 involving one chlorine loss is the thermodynamically most feasible PCDD formation route. This reaffirms the conclusion above that PCDDs are preferentially formed by O/σ-CH coupling, H abstraction, ring closure and intra-annular elimination of Cl. 1,3-DCDD is the only PCDD product obtained from the cross-condensation of PhRs and 2,4,6-TCPRs, supported by the experimental evidence (40, 42). Previous study demonstrated that only chlorophenols with chlorine at the ortho position were capable of forming PCDDs (21). So, the self-dimerization of phenol can not produce PCDDs. However, PCDDs can be formed from the crosscondensation of phenol with chlorophenols with orthochlorine substituent. That is, only one ortho-chlorine is needed to produce PCDDs. Thus, phenol can contribute to PCDD isomer distributions in MWIs. 3.2. Formation of PCDFs. Two PCDF congeners, 4MCDF and DF, can be formed from the cross-condensation of PhRs with 2-CPRs. Four possible formation pathways are illustrated in Figure 3 for 4-MCDF. Clearly, pathway 9 and pathway 10 are similar, and they cover five elementary steps: ortho-ortho coupling, H abstraction, tautomerization (H-shift), ring closure, and elimination of OH. The ring closure process requires crossing a large potential barrier and is strongly endoergic, and it is the rate determining step. Pathway 11 is analogous to pathway 12, which involves five elementary processes: ortho-ortho coupling, tautomerization (double H-transfer), H abstraction, ring closure (the rate determining step), and elimination of OH. One possible formation pathway, depicted in Figure 3, is proposed for DF. The intermediate IM21 can be regarded as a prestructure for 4-MCDF, and IM29 is a prestructure of DF. As shown in Figure 3, the formation of IM21 is more exothermic than the formation of IM29. Furthermore, the rate determining step involved in the formation of 4-MCDF has a lower barrier and is less endothermic compared to that involved in the formation of DF. Thus, the formation of 4-MCDF is preferred over the formation of DF. Comparison of the mechanism presented in Figure 3 with a previous study (23) tells us that the PCDF isomers formed from the crosscondensation of PhRs with 2-CPRs is favored over isomers formed from the self-condensation of 2-CPRs. The result supports the experimental result that phenol plays a significant role in the distributions of PCDF homologues (16). Due to the symmetry of 2,4,6-TCPR, only one PCDF, 2,4DCDF, can be produced from the cross-condensation of PhRs with 2,4,6-TCPRs. The formation route involves five elementary processes: ortho-ortho coupling, Cl abstraction, tautomerization (H-shift), ring closure (the rate determining step), and elimination of OH. Because both ortho-positions
of phenol are substituted with chlorine, no PCDFs can be formed from the self-condensation of 2,4,6-TCPRs. PCDF can be produced from the cross-condensation of PhRs with 2,4,6-TCPRs, however. It means that only one ortho-site without chlorine is needed to form PCDFs. 3.3. Rate Constant Calculations. It is difficult to measure experimentally the rate constants of the elementary reactions, especially relative to the radical intermediates, involved in the formation of dioxins. In such a situation, direct dynamics calculations, that is, the calculation of the rate constants or other dynamical information directly from electronic structure calculations without the intermediate stage of constructing a full analytical potential energy surface, can be an alternative. In this work, the rate constants of the elementary reactions involved in the formation of dioxins from the crosscondensation of PhRs with 2-CPRs and 2,4,6-TCPRs were evaluated by canonical variation transition-state (CVT) theory, which is among the most promising current avenues of approach in theoretical chemical kinetics, over the temperature range of 600-1200 K. Quantum tunneling effect is calculated by means of the small curvature tunneling (SCT) approximation. The CVT/SCT method has been successfully performed for the elementary reactions involved in the formation of PCDD/Fs from the self-condensation of 2-CPRs, 2,4-DCPRs, and 2,4,6-TCPRs, respectively (21-23). The reliability of the CVT/SCT method has been clarified in our published studies (37, 38). The CVT/SCT rate constants of C6H5OH+HfC6H5O+H2, C6H5OH+OHfC6H5O+H2O are in good agreement with the corresponding experimental values, respectively (37, 38). In the kinetic models of the dioxin formations, the rate constants for the elementary step of
was assigned to be the values for the reaction of CH3Cl+HfCH3+HCl (43, 44). The CVT/SCT rate constants for
are reasonable compared to the experimental values for the reaction of CH3Cl+HfCH3+HCl (21, 45). For example, at 800 K, the CVT/SCT rate constant for
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TABLE 1. Arrhenius Formulas (Units Are s-1 and cm3 Molecule-1 s-1 for Unimolecular and Bimolecular Reactions, Respectively) for Elementary Reactions Involved in the Thermodynamically Preferred Formation Pathway of PCDD/Fs from the Cross-Condensation of PhRs with 2-CPRs and 2,4,6-TCPRs over the Temperature Range of 600-1200 K reactions IM3+H f IM11+H2 IM11 f DD+Cl IM14+H f IM20+H2 IM20 f 1,3-DCDD+Cl IM21+H f IM22+H2 IM21+OH f IM22+H2O IM22 f IM23 IM23 f IM24 IM24 f 4-MCDF+OH IM21+H f IM25+H2 IM25 f IM26 IM26 f IM27 IM27 f 4-MCDF+OH IM21 f IM28 IM28+H f IM23+H2 IM28+H f IM26+H2 IM29+H f IM30+HCl IM29+OH f IM30+HOCl IM29+Cl f IM30+Cl2 IM30 f IM31 IM31 f IM32 IM32 f DF+OH IM33+H f IM34+HCl IM33+OH f IM34+HOCl IM33+Cl f IM34+Cl2 IM34 f IM35 IM35 f IM36 IM36 f 2,4-DCDF+OH
Arrhenius formulas k(T) ) (1.39 × 10-11)exp(-2532.2/T) k(T) ) (3.58 × 1011)exp(-13706.9/T) k(T) ) (1.36 × 10-11)exp(-3364.0/T) k(T))(7.92 × 1011)exp(-14283.4/T) k(T) ) (1.80 × 10-11)exp(-3053.7/T) k(T) ) (5.44 × 10-13)exp(-4840.4/T) k(T))(3.08 × 1013)exp(-9948.6/T) k(T) ) (1.50 × 1012)exp(-13859.2/T) k(T) ) (3.42 × 1013)exp(-10068.7/T) k(T) ) (1.03 × 10-11)exp(-2091.1/T) k(T) ) (2.11 × 1010)exp(-4657.5/T) k(T) ) (2.04 × 1012)exp(-14193.4/T) k(T))(2.34 × 1013)exp(-9511.2/T) k(T) ) (1.48 × 1012) exp(-8692.8/T) k(T))(7.22 × 10-13)exp(-7878.6/T) k(T) ) (4.63 × 10-13)exp(-7932.1/T) k(T) ) (5.40 × 10-11)exp(-4101.1/T) k(T))(1.00 × 10-12)exp(-7198.3/T) k(T))(2.45 × 10-11)exp(-2672.3/T) k(T) ) (1.89 × 1012)exp(-9098.9/T) k(T) ) (5.18 × 1012)exp(-16190.1/T) k(T) ) (2.77 × 1013)exp(-9374.2/T) k(T) ) (6.34 × 10-11)exp(-3883.6/T) k(T) ) (1.50 × 10-12)exp(-6595.0/T) k(T) ) (7.65 × 10-11)exp(-2910.0/T) k(T) ) (2.89 × 1012)exp(-10093.1/T) k(T) ) (5.04 × 1012)exp(-15753.8/T) k(T) ) (1.52 × 1013)exp(-10196.3/T)
is 2.08 × 10-13 cm3 molecule-1 s-1, whereas the experimental value for the reaction of CH3Cl+HfCH3+HCl is 1.77 × 10-13 cm3 molecule-1 s-1. The potential barrier for the reaction of
is lower than that of CH3Cl+HfCH3+HCl. To be used more effectively, the calculated CVT/SCT rate constants are fitted, and Arrhenius formulas are given in Table 1 for elementary reactions involved in the thermodynamically preferred formation pathway of PCDD/Fs from the cross-condensation of PhRs with 2-CPRs and 2,4,6-TCPRs. The pre-exponential factor, the activation energy, and the rate constants can be obtained from these Arrhenius formulas.
Acknowledgments This work was supported by NSFC (National Natural Science Foundation of China, project No. 20737001, 20777047, 20977059), Shandong Province Outstanding Youth Natural Science Foundation (project No. JQ200804), the Research Fund for the Doctoral Program of Higher Education of China (project No. 200804220046) and Independent Innovation Foundation of Shandong University (IIFSDU, project No. 2009JC016). The authors thank Professor Donald G. Truhlar for providing the POLYRATE 9.3 program.
Supporting Information Available The total energies (in a.u.), the zero-point energies (ZPE, in a.u.), and the imaginary frequencies (in cm-1) for the transition states. The geometries in terms of Cartesian coordinate (in Angstrom) for the reactants, products, intermediates, and transition states. The reaction enthalpies ∆H0, the changes of Gibbs free energies ∆G for the elementary reactions involved in the formation of dioxins from the cross6750
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condensation of PhRs with 2-CPRs and 2,4,6-TCPRs at 298.15 K and 1.0 atm. This material is available free of charge via the Internet at http://pubs.acs.org.
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