Quantum Chemical Examination of the Sequential Halogen

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Quantum chemical examination of the sequential halogen incorporation scheme for the modeling of speciation of I/Br/Cl-containing trihalomethanes Chenyang Zhang, Maodong Li, Xuze Han, and Mingquan Yan Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b03871 • Publication Date (Web): 22 Jan 2018 Downloaded from http://pubs.acs.org on January 24, 2018

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Environmental Science & Technology

1

Quantum chemical examination of the sequential halogen incorporation

2

scheme for the modeling of speciation of I/Br/ClI/Br/Cl-containing trihalomethanes trihalomethanes

3

Chenyang Zhang a, Maodong Li b, Xuze Han a, Mingquan Yan a, *

4 5

6

7

a

Department of Environmental Engineering, Peking University, The Key Laboratory of

Water and Sediment Sciences, Ministry of Education, Beijing 100871, China; b

Center for Quantitative Biology, Peking University, Beijing 100871, China

*

Corresponding author: Mingquan Yan, Department of Environmental Engineering,

8

College of Environmental Sciences and Engineering, Peking University, Beijing 100871,

9

China; Tel: +86 10 62758501. E-mail: [email protected]

1

ACS Paragon Plus Environment


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Abstract:

11

The recently developed three-step ternary halogenation model interprets the

12

incorporation of chlorine, bromine and iodine ions into natural organic matter (NOM)

13

and formation of iodine-, bromine-, and chlorine-containing trihalomethanes (THMs)

14

based on the competition of iodine, bromine and chlorine species at each node of

15

the halogenation sequence. This competition is accounted for using the

16

dimensionless ratios (denoted as γ) of kinetic rates of reactions of the initial attack

17

sites or halogenated intermediates with chlorine, bromine and iodine ions. However,

18

correlations between the model predictions made and mechanistic aspects of the

19

incorporation of halogen species need to be ascertained in more detail. In this study,

20

quantum chemistry calculations were firstly used to probe the formation mechanism

21

of ten species of Cl-/Br-/I- THMs. The HOMO energy (EHOMO) of each mono-, bi-, or

22

trihalomethanes were calculated by B3LYP method in Gaussian 09 software. Linear

23

correlations were found to exist between the logarithms of experimentally

24

determined kinetic preference coefficients γ reported in prior research and, on the

25

other hand, differences of EHOMO values between brominated/iodinated and

26

chlorinated halomethanes. One notable exception from this trend was that observed

27

for the incorporation of iodine into mono- and di-iodinated intermediates. These

28

observations confirm the three-step halogen incorporation sequence and the factor

29

γ in the statistical model. The combined use of quantum chemistry calculations and

30

the ternary sequential halogenation model provides a new insight into the

31

microscopic nature of NOM-halogen interactions and the trends seen in the

32

behavior of γ factors incorporated in the THM speciation models. 2


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33

Introduction

34

Chlorination is widely used in disinfection technology due to its effectiveness

35

against most pathogens, low cost and ease of implementation. However,

36

interactions of chlorine with natural organic matter (NOM) generate numerous

37

chlorine-containing disinfection byproducts (DBPs)

38

present in the source water, these ions are oxidized by chlorine or chloramine to

39

HOBr/HOI that react with NOM to form brominated and/or iodinated DBPs

40

which have been shown to be more geno- and cytotoxic than chlorinated DBPs 11-15.

41

Considerable efforts have been invested in elucidating and modeling effects of the

42

dissimilar halogen species on DBP generation

43

demonstrated that yields and speciation of I/Br/Cl-containing trihalomethanes

44

(THMs) depend on the competition of iodine, bromine and chlorine as well as other

45

conditions, for instance the nature and concentration of organic precursors,

46

ammonia, temperature, pH and contact time 9, 18-25.

47

Prior studies have developed a consistent approach to model the speciation of

48

THMs and haloacetic acids (HAAs) based on the concept of a kinetic preference

49

coefficients γ, which is defined as a dimensionless ratio of the kinetic rates of

50

bromine or iodine incorporation into THM precursors over that of chlorine. Cowman

51

and Singer 26 applied this concept in a relatively simple speciation model to interpret

52

effects of varying HOBr/HOCl ratios on HAAs and THMs speciation

53

et al. 29 utilized a more detailed three-step halogenation scheme to develop a formal

54

kinetic model that was used to interpret effects of Br concentrations on the

55

speciation of THMs found in seventeen waters from New Zealand. In that model,

1-4

. When bromide or iodide are

16, 17

3


2, 5-10

,

. These studies have

24, 27, 28

. Nokes


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relative yields of chlorinated and brominated products formed at each node of

57

halogen incorporation were defined by the respective γ coefficients, which were

58

somewhat different at different nodes of the halogen incorporation sequence.

59

Roccaro et al.

60

Br concentrations on the speciation of THMs and HAAs in surface waters from

61

South-East Australia.

62

This approach was recently expanded to include NOM iodination

63

model accounted for the competition between chlorine, bromine and iodine species

64

at each node of the ternary three-step halogenation scheme. The presented model

65

was successfully used to interpret the speciation of the entire group of 10 species of

66

CHCl3-i-jBriIj THMs formed at varying pHs in two major water sources from the

67

Beijing metropolitan area 31. The ternary THM speciation model employed eighteen

68

γ factors and nine intermediates that account for differences in the reactivity

69

between HOCl, HOBr and HOI in their interactions with the NOM reactive sites and

70

the entire set of relevant halogenated intermediates. The optimized γ coefficients

71

introduced to model and interpret the experimental THM speciation data differed by

72

up to several orders of magnitude depending on the number and nature of halogen

73

atoms incorporated in them.

74

Notwithstanding the success of the ternary halogenation model applied to interpret

75

the currently available experimental THMs data, further research is needed to

76

understand the nature of the prominent differences between the γ values observed

77

for different nodes of the ternary halogen incorporation scheme, to ascertain the

78

fundamental mechanisms of the involved reactions and to ultimately expand the

30

expanded the utility of this approach to examine effects of pH and

4


31

. The expanded

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ternary halogen incorporation model to any specific water matrix.

80

The complexity of reactions between NOM and halogen species makes it

81

challenging to generate exhaustively detailed experimental data for a wide range of

82

water matrixes and treatment conditions. This limitation can be circumvented based

83

on a theoretical modeling of the mechanistic aspects of reactions that define γ

84

values for halogen incorporation sites and representative DBP compounds. In this

85

study, we employed quantum chemical (QC) calculations to explore the selected

86

thermodynamic aspects and formation mechanism of the I/Br/Cl-containing THMs

87

and to examine the extent of the applicability of the ternary three-step halogen

88

incorporation scheme and the meaning of γ factors obtained based on this model.

89

Theory

90

The Eyring equation (also known as the Eyring–Polanyi equation) is widely used

91

in chemical

92

reaction with temperature 32.

93

kinetics

ln(ki / A ) = −

to

describe

changes

of

kT ∆H ≠ ∆S ≠ + + ln( B ) RT R h

the rate

of

a

chemical

(1)

94

In the equation, k, T, ∆H‡, R, kB, h and ∆S‡ are the reaction rate constant, absolute

95

temperature, activation enthalpy, universal gas constant, Boltzmann and Planck

96

constants and activation entropy, respectively. According to the transition state

97

theory, the absolute value of the kinetic constant can be determined if the enthalpy

98

and entropy values of reactants and intermediates are known. In the case of the

99

system discussed in this paper, the structures of intermediates are difficult to

100

determine, and similar or more pronounced limitations to determine the enthalpy 5



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101

and entropy values of these intermediates.

102

An alternative approach was firstly pursued in the case of THM formation based on

103

the frontier orbital theory which states that the chemical kinetics is determined by

104

the HOMO and LUMO of reactant molecules

105

separation between the HOMO of the donor and the LUMO of the acceptor, the

106

faster should be the reaction rate. Prior literature 28 has shown that the logarithm of

107

kinetic rate constant values of the reaction of ozone with organic compounds such

108

as aromatic compounds, olefins, amines and compounds containing sulfur (S) are

109

linearly correlated with quantum molecular orbital descriptors such as the energy of

110

HOMO. Zhuo et al

111

theory and the frontier orbital theory to derive Eq. (2) presented below:

112

ln(ki / A ) = −

34

32, 33

. The smaller the energy

combined the Eyring equation (Eq. (1)) of the transition state

∆S ≠ mA n C kT ELUMO i + A EHOMO A − A + i / A + ln( B ) RT RT RT R h

(2)

113

In Eq. (2), the EHOMO A is the HOMO energy of nucleophile A and ELUMO i is the LUMO

114

energy of electrophile i . m A and n A are defined as LUMO and HOMO sensitivity

115

factors for nucleophile A, respectively. CA is a constant for all these nucleophilic

116

reactions. The kB is the Boltzmann constant. ∆Si≠/ A is the difference of entropic

117

between nucleophile A and electrophile i . The last three terms in Eq. (2) can be

118

regarded as constants because all these reactions are conducted at the same

119

temperature and their activation entropies are very close 34.

120

Two additional approximations can be adopted to simplify the derivation of

121

expressions for the formation of THMs in the three-step halogen incorporation

122

scheme

123

are considered to be stable during the formation of the involved halogenated

29

. First, the concentrations of active chlorine, bromine and iodine species

6


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124

intermediates; hence the rates of reactions involving these intermediates are

125

pseudo-first order with respect to their concentrations. Second, the steady-state

126

approximation can be applied because the rates of change of the concentrations of

127

the mono- and di-halogenated intermediates during the reaction are likely to be

128

small.

129

On the basis of these approximations, the linear correlation between log(γ ) and

130

the ∆EHOMO values of the involved intermediates can be established. We can

131

present γ sB0r/ Cl values in the Cl/Br binary system as an example; the reaction

132

pathway and the definitions of kinetic constants were illustrated in Figure 1 in

133

literature 29.

134

Based on the steady state approximation for intermediate [ SCl ] , we can obtain Eq.

135

(3):

136

137

138

139

140

141

142

d ( SCl ) = k1[HOCl][ S0 ] − k3[ SCl ][HOCl] − k4 [ SCl ][HOBr]=0 dt

(3)

Eq. (3) can be simplified to Eq. (4): k1[HOCl][ S0 ]=k3 [ SCl ][HOCl]+k4 [ SCl ][HOBr]

(4)

Base on the steady state approximation for the intermediate [ S Br ] , we obtain Eq. (5):

d ( S Br ) = k2[HOBr][ S0 ] − k5[ S Br ][HOCl] − k6 [ S Br ][HOBr]=0 dt

(5)

Eq. (5) can be simplified to Eq. (6):

k2 [ HOBr ][ S0 ] = k5 [ S Br ][ HOCl ] + k6 [ S Br ][ HOBr ] 7


(6)


143

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Based on Eq. (4) and Eq. (6), the following equation is obtained:

144

k1 HOBr k3[SCl ][ HOCl ] + k4 [SCl ][ HOBr ] = × k2 HOCl k5[SBr ][ HOCl ] + k6 [S Br ][ HOBr ]

145

According to Eq. (2), the following equations are obtained:

(7)

146

log(k3 ) = −

∆S ≠ mA n C kT ELUMO HOCl + A EHOMO S − A + i / A + ln( B ) Cl RT RT RT R h

(8)

147

mA nA C A ∆Si≠/ A kT + + ln( B ) log(k4 ) = − ELUMO HOBr + EHOMO − SCl RT RT RT R h

(9)

148

log(k5 ) = −

∆S ≠ mA n C kT ELUMO HOCl + A EHOMO S − A + i / A + ln( B ) Br RT RT RT R h

149

log(k6 ) = −

mA n C kT ∆S ≠ ELUMO HOBr + A EHOMO S − A + i / A + ln( B ) Br RT RT RT R h

150

152

156

log(

k3 n ) = A ( EHOMO S − EHOMO S ) Cl Br k5 RT

(12)

log(

k4 n ) = A ( EHOMO S − EHOMO S ) Cl Br k6 RT

(13)

Then:

k3 k4 α k3 = = k5 k6 α k5

154

155

(11)

Then:

151

153

(10)

(14)

Then:

k1 k3[SCl ][ HOCl ] + α k3[SCl ][ HOBr ] k3[ SCl ]([ HOCl ] + α[ HOBr ]) k3[SCl ] = = = k2 k5[S Br ][ HOCl ] + α k5[SBr ][ HOBr ] k5[S Br ]([ HOCl ] + α [ HOBr ]) k5[SBr ] 8


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(15)

157

158

159

Thus:

log(γ SB0r/Cl ) = log(

k1 [S ] k n ) = log( Cl ) + log( 3 ) = A ( EHOMO S − EHOMO S ) + c Cl Br k2 [ S Br ] k5 RT

(16)

160

The above equation demonstrates that the logarithm of a kinetic preference

161

coefficient is proportional to the difference of the HOMO energy of the two

162

corresponding products.

163

Materials and Methods

164

Data sources. All kinetic preference constants (γ) examined in this study were

165

reported in prior literature

166

consistently applied the sequential three-step halogenation model to study THM

167

formation. Specifically, Roccaro et al.

168

values based on the results for binary Cl/Br halogenation of Australian and New

169

Zealand waters, respectively. Yan et al.

170

log(γ sIx Cl ) in the ternary halogenation system involving I, Br and Cl for Jingmi and

171

Miyun source waters in the Beijing metropolitan area. In view that the kinetic

172

preference coefficients for the halogens incorporation in Jingmi and Miyun waters

173

did not change considerably at pH from 6.5 to 8.5, the relevant log(γ ) values at

174

different pH conditions were averaged.

175

QC calculations. All calculations to determine the structures and molecular orbital

176

distributions (including the Highest Occupied Molecular Orbitals (HOMO) and the

29-31

. To the best of our knowledge, three studies have

30

and Nokes et al.

31

29

determined log(γ sBrx Cl )

derived the data of log(γ sBrx Cl ) and

9



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177

Lowest Unoccupied Molecular Orbitals (LUMO)) were performed based on Density

178

Functional Theory (DFT) at the B3LYP level in Gaussian 09 software 35. The B3LYP

179

global hybrid functional in DFT was used due to its recognized ability to compute the

180

energy of HOMO

181

satisfactory results for the energy of the HOMO, especially in the compound

182

containing I atom cases

183

algorithms without any symmetry constraints. The nature of minima was checked

184

via vibrational analysis. All the optimization calculations accounted for hydration

185

effects via the continuum polarizable solvation model (SMD) 43.

186

Data treatment and statistical model evaluation. We hypothesized that the

187

involved intermediates in the sequential three-step halogenation model are in the

188

form of R − CH i X 3−i , in which X is halogen ions (I, Br and/or Cl). The effect of R- on

189

HOMO energy of intermediates were examined as it is aryl-CH2CO-, aryl-CO-, CH3-

190

and H-, respectively, that were selected to represent the simplest radical, alkyl

191

radical, benzene ring with the carbonyl group and complicated aromatic compounds.

192

The results are presented in Table S1 in Supporting Information (SI) section.

193

The difference of HOMO energy ( ∆E HOMO ) were calculated using formulas

194

presented below.

195

For the first step,

196

197

198

28, 36-41

.The def2-TZVP basis set was used for all atoms for its

42

. Structural optimizations were realized using standard

∆EHOMO (SBr /Cl )=EHOMO R−CH Br − EHOMO R−CH Cl (i = 1) 3 i

3

∆EHOMO (SI /Cl )=EHOMO R−CH I − EHOMO R−CH Cl (i = 1) 3i

3

For the second step, 10


(17)

(18)

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199

200

201

202

203

∆EHOMO (SBr /Cl )=EHOMO R−CH Cl Br

− EHOMO R−CH Cl

(i + j + k = 1, i, j , k ≥ 0)

∆EHOMO (SI /Cl )=EHOMO R−CH Cl Br I − EHOMO R−CH Cl

(i + j + k = 1, i, j, k ≥ 0)

2 i

2 i

j +1I k

2 i +1Br j I k

2 i +1Br j Ik

j k +1

(19)

(20)

For the third step

∆EHOMO (SBr /Cl )=EHOMO R−CHCl Br i

j +1I k

∆EHOMO (SI /Cl )=EHOMO R−CHCl Br I i

j k +1

− EHOMO R−CHCl

(i + j + k = 2, i, j, k ≥ 0)

− EHOMO R−CHCl

(i + j + k = 2, i, j, k ≥ 0)

i +1Br j I k

i +1Br j I k

(21)

(22)

204

The HOMO energy of intermediates with R- as H- are best to fit with the

205

experimental logarithm of kinetic preference constants data reported in prior

206

literature and H- is a straightforward choice, then we would discuss the results of

207

HOMO energy with R- as H- in detail below. It would be further explained below.

208

∆EHOMO values of THMs compounds, obtained from QC calculations, were

209

correlated with the logarithm of the corresponding γ values to develop linear

210

models by least-squares regression: log(γ)= a × (∆ ) + y0, where a and y0 are

211

the slope and the y-intercept, respectively. The performance of the models was then

212

evaluated by R2 values, the mean unsigned error (MUE) and the root-mean-square

213

error (RMSE) for EHOMO in eV units.

214

Results

215

Molecular orbitals and HOMO energy values.

216

Molecular geometries and energy of all relevant mono-, di- and trihalomethanes

11



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217

were calculated, and the molecular geometries of CH2ClBr and CHClBrI are shown

218

in Figure 1 as examples. The bond lengths between halogen atoms and C atoms

219

are marked in this diagram, which are consistent with previous literature

220

C-halogen bond lengths increased in the sequence I, Br and Cl due to the increases

221

of the atomic radii and the decrease of the electronegativity 45, 46. The bond lengths

222

are also sensitive to the presence of competitive halogen ions. For instance, the

223

incorporation of I into CH2ClBr to form CHClBrI results in an increased distance

224

between the Br/Cl atoms and the central C atom compared with the bond lengths in

225

CH2ClBr. This demonstrates that the incorporation of I, Br and Cl would affect the

226

structure and electronic properties of THMs and the intermediates.

44

. The

227

Figure 1

228

The HOMO and LUMO molecular orbitals were calculated for each halomethane,

229

the wave functions of CHClBrI are shown in Figure 2 as examples. The contribution

230

of I, Br and Cl to the HOMO and LUMO orbitals are different significantly. HOMO

231

orbital is dominated by I, while LUMO orbital is dominated by both Br and I. As

232

shown in Table S1, the EHOMO values of halomethanes change from -8.54 eV for

233

CHCl3 to -6.57 eV for CHI3. This suggests, in accord with prior research, that CHI3 is

234

more nucleophilic than CHCl3 and likely to lose one or more electrons in redox

235

reactions.

236

Figure 2

237

Correlation between log(γ γ) and difference of EHOMO values.

238

The difference of EHOMO values denoted as

∆EHOMO and calculated for all

12


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239

relevant halomethanes together with the corresponding log(γ ) values reported in

240

prior literature are summarized in Table 1

241

log(γ ) for the second and third steps of halogen incorporation are shown in Figure

242

3 to Figure 6 for the New Zealand, Southeast Australia, Jingmi and Miyun waters,

243

respectively. The data in the first halogen step have not been involved in Figure 3-6

244

because the reactants in the first halogen step are different from those in the

245

second and third steps. In the first step the reactants are organic precursors without

246

any halogen atoms.

247

29-31

. Correlations between ∆EHOMO and

Table 1.

248

Figure 3.

249

Figure 4.

250

Figure 5.

251

Figure 6.

252

The presented data demonstrate that reasonably strong linear correlations exist

253

between log(γ ) and ∆EHOMO values. These phenomena can be ascertained by

254

other theoretical calculation methods also (Table S2) and the data for Jingmi water

255

are presented in Figure S4 in SI. We only discussed the data obtained by the

256

B3LYP method with the def2-TZVP basis set in detail in this study. In the case of

257

binary Cl/Br systems, R2 and MUE values of the linear correlations between

258

∆EHOMO and log(γ ) for New Zealand and Southeast Australia waters are 0.60 and

259

0.11, 0.82 and 0.06, respectively. In the ternary I/Br/Cl systems, R2 and MUE values

260

for Jingmi and Miyun waters are 0.94 and 0.09, 0.63 and 0.27, respectively. Two

261

outliers (CH2I2 and CHI3 in both Jingmi and Miyun waters shown as open markers in

262

Figure 5 and 6) are excluded in the statistical model evaluation. Possible reasons 13



263

associated with the presence of these outliers are discussed in more detail in the

264

following section.

265

Discussion

266

Effect of intermediates on theoretical calculation.

267

First of all, it is a great challenge to determine the structures of intermediates

268

involved in QC calculations because the intermediates of THM formation are

269

extremely complex. To examine the influence of the structure of intermediates on

270

the QC calculation results, we have calculated the HOMO energy for halogenated

271

intermediates with R- as aryl-CH2CO-, aryl-CO-, CH3- and H-, respectively. If the

272

HOMO energy could reflect the reactivity of the methyl in the intermediates with

273

halogen ions, a well plane-fitting as a function of the number of halogen ions

274

incorporated would exist 47-49. This is indeed observed for H- and CH3- in Figure S1

275

(a) and (b). However, this was not observed for aryl-CH2CO- and aryl-CO- (Figure

276

S1 (c) and (d)). This finding demonstrates that the HOMO energy could reflect the

277

stability of halogenated intermediates when the R- is sufficiently simple.

278

This observation is reasonable. The HOMO energy is defined by the properties of

279

the entire molecule rather than those of local reactive group. On the other hand,

280

effects of the halogen on HOMO energy are expected to be most prominent for the

281

methyl group into which one or more halogens are incorporated. As a result, HOMO

282

energy calculations reflect most clearly such changes for the simple case of the

283

unsubstituted methyl group. For more complex substituent R groups, the HOMO

284

energy is likely to be dominated by the substituent rather than the methyl group at 14


Page 14 of 36

Page 15 of 36


285

which the halogen incorporation occurs. In that situation the incorporation of

286

halogen atoms into the methyl group may be not accompanied by significant and/or

287

consistent changes of the HOMO energy and therefore the HOMO energy may not

288

be adequately reflective of the characteristics of the localized incorporation reaction.

289

Thus, when the HOMO energy is adequately sensitive and reflective of the halogen

290

substitution, the frontier orbital theory has an advantage in predicting relative

291

changes of kinetic rate constants associated with the presence of dissimilar halogen

292

atoms.

293

In agreement with the above reasoning, the linear correlations between log(γ ) and

294

∆EHOMO values determined for R substituents such as aryl-CH2CO- and aryl-CO-

295

were weaker than those for H- and CH3-, as illustrated by the data for the Jingmi

296

water, Figure S2. Thus, we only present the results of R- as H- in detail in this paper.

297

Interpreting the competition in I-/Br-/Cl- THM formation.

298

The existence of linear correlations between ∆EHOMO values of the examined

299

halomethanes and the corresponding log(γ ) values can be interpreted as a

300

confirmation of the correctness of the sequential three-step halogenation schemes

301

in both binary and ternary systems. On the other hand, the data presented above

302

can be used to develop a more detailed understanding of the mechanisms of

303

NOM-halogen interactions and the formation of l-/Br-/CI- THMs.

304

According to prior publications

305

suggests that halogen X (X=Br or I) is kinetically more active in the formation of

306

intermediates compared with chlorine. Given the existence of the negative slope of

29-31

, the positive value log(γ X Cl ) (X=Br or I)

15



Page 16 of 36

307

the linear relationship between ∆EHOMO and log(γ X Cl ) , we can introduce a concept

308

of the critical ∆EHOMO value that corresponds to the log(γ X Cl ) value of zero. When

309

the ∆EHOMO value is less than the critical ∆EHOMO , the log(γ X Cl ) value will be

310

positive and it suggests that X (X=Br or I) ion is more active than Cl with

311

intermediates. Based on the data in Figure 5 and 6, the critical ∆EHOMO is about

312

0.48 eV (0.39 eV for Jingmi and 0.58 eV for Miyun, respectively).

313

The results compiled in Table 1 demonstrate that in all cases Br has the highest

314

affinity among halogen ions to the examined intermediates. The all values of

315

∆EHOMO (γ sBr Cl ) and ∆EHOMO (γ sBr I ) are less than 0.48 eV. This demonstrates that Br

316

is expected to have a higher affinity towards the electrophilic substitution than Cl

317

and I. This is consistent with the previous studies showing that significant

318

concentrations of Br-DBPs form even at low background bromide concentrations

319

20, 22-25, 31

9,

and that bromine acts as a catalyst in the formation of THMs during

320

chlorination 23. This observation should be further studied to probe the mechanisims

321

of bromated DBP formation.

322

The affinity of I, Br and Cl to the intermediates formed in the second and third

323

halogen incorporation steps strongly depends on the type of halogen ions that have

324

been incorporated in prior halogenation steps. This is especially notable for I. In this

325

case, the preference toward the incorporation of an additional I atom depends on

326

whether or not the preceding intermediate already contains one or two I atoms. The

327

same phenomenon was also found in our previous study

328

affinity of I to the intermediates improves rapidly with the number of I atoms that 16


31

. It showed that the

Page 17 of 36


329

have already been incorporated into the reaction sites while the incorporation of Br

330

and Cl atoms in the intermediates involved in the generation of THMs impedes the I

331

incorporation reactions

332

greater than 0.48 eV for both X= Br and/or Cl. This demonstrates that Cl is relatively

333

more reactive than I if an I atom is not present in the intermediates. In contrast, the

334

∆EHOMO (γ sIIXCl ) values for the intermediates that already have an I atom incorporated

335

in them are all less than 0.48 eV. This is indicative that I has higher affinity to the

336

incorporation into such intermediates than Cl. In addition, the values of ∆EHOMO for

337

S X I Cl (X=Br, Cl), SIX I Cl (X=Br, Cl), S In I Cl (n=1, 2) decrease gradually. This shows

338

that the presence of I in the intermediates increases their affinity to further I

339

incorporation. This is entirely consistent with the results of energy barrier

340

calculations (Table S3) demonstrating that the presence of I in the intermediates

341

tends to reduce the energy barrier of further iodination.

342

It is notable that the log(γ ) values for the iodinated intermediates obtained via the

343

fitting of the experimental data using the ternary halogenation model are much

344

higher than those expected based on the data of the frontier orbital theory, as

345

demonstrated by the presence of two outliers in both Figure 5 and 6. We

346

hypothesize that this may be caused by the occurrence of a direct incorporation

347

pathway (which is potentially distinct from the sequential three steps incorporation)

348

in the cases of CH2l2 and CHI3 formation. These pathways can be possibly

349

associated with the involvement of ·I2 and I3- species which have been observed to

350

form in the halogenation-dehalogenation processes involving CHCl2I and CHI3 50-52.

351

Our prior electrochemical experiments also showed that I2 and I3- could directly

31

. Table 1 shows that the values of ∆EHOMO (γ sIx Cl ) are

17



352

incorporate into organic matter by rotating ring-disk electrode (RRDE) and

353

spectroscopy methods 53, 54.

354

In order to compare the log(γ ) values derived from different water sources, results

355

shown in Figure 3-6 are combined in Figure S3. This comparison demonstrates that

356

in general, the slopes of the linear correlation between the experimental log(γ )

357

and calculated ∆EHOMO values are somewhat different and tend to cluster into two

358

groups, with the values of log(γ ) derived in the ternary system applied to the

359

THMs speciation data for Jingmi and Miyun waters being smaller than those for the

360

binary system applied to the data generated for New Zealand and South-East

361

Australia waters. It demonstrates that the site-specific properties of NOM affect the

362

extent of the competition between I, Br and Cl in the halogenation reactions to a

363

small degree. It is reasonable that the ratio of kinetic preference coefficients of

364

halogens incorporation is mainly determined by the relative reactivity of chlorine,

365

bromine and iodine at given reaction conditions. However, the influence of

366

site-specific properties of NOM on the extent of the competition between I, Br and Cl

367

in the halogenation reactions needs to be studied further in the future, especially to

368

obtain the correlation between site-specific properties of NOM and at least one

369

absolute kinetic rate constant of Cl, Br or I halogenation.

370

A good relationship was found in this study between the HOMO energy of

371

halomethanes obtained from the QC approaches and the kinetic preference

372

coefficients in each halogen step. The agreement of the results of the QC

373

calculation and the ternary halogenation/THM speciation model allows us to

374

examine the complexity of halogenation reactions, a further understanding of the 18


Page 18 of 36

Page 19 of 36


375

mechanisms of NOM/halogen interactions, specific iodinated and brominated DBP

376

formation and prediction of the speciation of THMs formed at varying pH values and

377

other system conditions.

378

Acknowledgements

379

We thank our colleague Dr. Zhirong Liu, Peking University for his valuable

380

comments. The authors wish to acknowledge the financial support from the National

381

Natural Science Foundation of China (grants 51578007 and 21277005). The

382

contents of this paper and its conclusions have not been endorsed or approved by

383

the funding agencies and do not intend to reflect their views. Part of the analysis

384

was performed on the High Performance Computing Platform of the Center for Life

385

Science.

386

Supporting Information

387

This information is available free of charge via the Internet at http://pubs.acs.org.

388

Brief

389

Linear correlations were found to exist between the logarithms of experimentally

390

determined kinetic preference coefficients γ reported in prior research and, on the

391

other hand, differences of EHOMO values between brominated/iodinated and

392

chlorinated halomethanes.

393

394

References

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395

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27



576

Figures and Tables

577

578

Figure 1. Molecular geometries of representative halomethanes. (a) CH2ClBr

579

and (b) CHClBrI.

28


Page 28 of 36

Page 29 of 36


580

581

Figure 2. Geometries of (a) HOMO and (b) LUMO molecular orbitals for

582

CHBrClI. The red and green areas correspond to the positive and negative

583

values, respectively, of the Schrodinger equation for the wave function.

29



Page 30 of 36

584

2.00 Second step Third step

log(γ)

1.50

1.00

0.50

y = -1.07x + 1.12 R² = 0.60

0.00 0

0.1

0.2

0.3

0.4

EHOMO/eV

585 586

Figure 3. Correlation between ∆ values and logarithms of the

587

γ coefficients determined for the second and third halogenation steps in New

588

Zealand waters 29.

30


Page 31 of 36



log(γ)

1.50

1.00

0.50 y = -1.64x + 1.52 R² = 0.82 0.00 0

0.1

0.2

0.3

0.4

EHOMO/eV

589 590


591

γ coefficients determined for the second and third halogenation steps in

592

South-East Australia water 30.

31



Page 32 of 36


3.00

log(γ)

2.00 1.00 y = -1.52x + 0.59 R² = 0.94

0.00 -1.00 -2.00 0

0.5

1

1.5

EHOMO/eV

593 594


595

γ coefficients determined for the second and third halogenation steps in

596

Jingmi water

597

CH2I2 and CHI3 in the second and third halogen incorporation steps.

31

. Open markers correspond to the formation of precursors of

32


Page 33 of 36



3.00

log(γ)

2.00 1.00

y = -1.18x + 0.68 R² = 0.63

0.00 -1.00 -2.00 0

0.5

1

1.5

EHOMO/eV

598 599


600

γ coefficients determined for the second and third halogen incorporation

601

steps in Miyun water

602

precursors of CH2I2 and CHI3 in the second and third halogen incorporation

603

steps.

31

. Open markers correspond to the formation of

33



Page 34 of 36

604

Table 1. Comparison of the ∆ and logarithms of γ coefficients for mono-,

605

bi-, or tri- halogen-methanes (R- is H- radicals) Ref. 31

SXX/Cl

∆EHOMO (eV )

Formula

Jingmi

Miyun

log(γ )

log(γ )

Ref. 29 New Zealand

log(γ )

Ref. 30 SouthEast Australia

log(γ )

First step of halogen incorporation

/

EHOMO

− EHOMO CH Cl

/

EHOMO

− EHOMO CH Cl

CH3Br

CH3I

3

3

0.55

0.7043

0.7806

1.21

0.8319

1.1397

0.9031

1.9294

0.7782

0.8451

0.9542

1.4771

0.6021

1.0000

1.0000

1.0792

1.1761

1.0792

Second step of halogen incorporation

/

EHOMO

− EHOMO CH Cl

/

EHOMO

/

0.36

-0.2805

0.2608

− EHOMO CH Cl

1.21

-1.2635

0.0371

EHOMO

− EHOMO CH BrCl

0.01

0.5738

1.2673

/

EHOMO

− EHOMO CH BrCl

0.83

-0.6180

-0.3638

/

EHOMO

− EHOMO CH ICl

-0.02

0.6621

0.9293

/

EHOMO

− EHOMO CH ICl

0.32

3.1595

3.1595

CH 2ClBr

2 2

2 2

CH 2ClI

CH 2Br2

2

CH 2BrI

2

CH 2BrI

2

CH 2I 2

2

Third step of halogen incorporation

/

EHOMO

− EHOMO CHCl

/

EHOMO

/

/

0.38

0.0953

0.4854

− EHOMO CHCl

1.29

-1.3656

-0.5986

EHOMO

− EHOMO CHBr Cl

0.18

0.1144

0.4571

EHOMO

− EHOMO CHBr Cl

0.94

-0.6819

-0.9736

CHCl2Br

3

CHCl2I

CHBr3

3

2

2

CHBr2I

/

EHOMO CHClBr − EHOMO CHCl Br

0.12

0.7749

0.3030

/

EHOMO CHClBrI − EHOMO CHCl Br

0.77

-0.6403

-0.7993

/

EHOMO CHBr I − EHOMO

0.01

0.7862

0.5409

2

2

2

2

CHClBrI

34


Page 35 of 36

606


/

EHOMO CHBrI − EHOMO

/

EHOMO CHBrI − EHOMO

/

EHOMO CHI − EHOMO

2

2

3

CHClBrI

CHClI 2

CHClI 2

/

EHOMO CHIBrCl − EHOMO

/

EHOMO CHI Cl − EHOMO 2

CHCl2I

CHCl2I

0.38

-0.1802

-0.5340

0.00

0.6144

0.9520

0.27

2.8868

2.8868

0.03

0.5064

0.8295

0.41

0.4155

0.4749

* selected data of the upstream surface water under pH 10 in Australian.

607

35



Page 36 of 36

Graphical Abstract 𝐸𝐻𝐻𝐻𝐻𝐶𝐶𝐶𝐶 𝐵𝐵 𝑖

𝑗 𝐼𝑘+1

𝐸𝐻𝐻𝐻𝐻𝐶𝐶𝐶𝐶

𝑖+1 𝐵𝐵𝑗 𝐼𝑘

= a log (

𝑘𝐶𝐶𝐶𝑙𝑖 𝐵𝐵𝑗𝐼𝑘+1

𝑘𝐶𝐶𝐶𝑙𝑖+1 𝐵𝐵𝑗 𝐼𝑘 γ

CHICl2

γ SICl/ Cl2 CHCl3

γ

SCl

γ

Br / Cl SCl

I / Cl S0

γ

S0

γ

/ Cl γ SIBrCl

𝛾=

HOMO of 𝐶𝐶𝐶𝐶𝑖 𝐵𝐵𝑗 𝐼𝑘+1

HOMO of 𝐶𝐶𝐶𝐶𝑖+1 𝐵𝐵𝑗 𝐼𝑘 ACS Paragon Plus Environment

𝑘𝐶𝐶𝐶𝑙𝑖 𝐵𝐵𝑗𝐼𝑘+1 γ 𝑘𝐶𝐶𝐶𝑙𝑖+1 𝐵𝐵𝑗𝐼𝑘

SBrCl

Br / Cl S BrCl

γ SBrBr/ Cl CHBr2Cl

CHI2Br

γ SI IBr/ Cl

CHIBrCl

Br / Cl S0

γ SBrI 2 / Cl

Br / Cl S ICl

SBr

CHBrCl2

SI2

CHI3

γ SBrI / Cl

SI

γ SICl/ Cl

γ SBrCl2/ Cl

γ SI I/ Cl

SICl

SCl2

γ SI I/2Cl

CHI2Cl

I / Cl S ICl

)+b

γ SI Br/ Cl SBr2

γ SBrBr2/ Cl

SIBr

γ SI IBr/ Cl CHIBr2

γ SIBr/ Cl2 CHBr3

Three-step sequential halogenation model

Quantum Chemical Examination of the Sequential Halogen

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