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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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Quantum chemical examination of the sequential halogen incorporation
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scheme for the modeling of speciation of I/Br/ClI/Br/Cl-containing trihalomethanes trihalomethanes
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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,
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College of Environmental Sciences and Engineering, Peking University, Beijing 100871,
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China; Tel: +86 10 62758501. E-mail:
[email protected]
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Abstract:
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The recently developed three-step ternary halogenation model interprets the
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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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Introduction
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Chlorination is widely used in disinfection technology due to its effectiveness
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against most pathogens, low cost and ease of implementation. However,
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interactions of chlorine with natural organic matter (NOM) generate numerous
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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.
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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
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kinetic model that was used to interpret effects of Br concentrations on the
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speciation of THMs found in seventeen waters from New Zealand. In that model,
1-4
. When bromide or iodide are
16, 17
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,
. These studies have
24, 27, 28
. Nokes
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relative yields of chlorinated and brominated products formed at each node of
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halogen incorporation were defined by the respective γ coefficients, which were
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somewhat different at different nodes of the halogen incorporation sequence.
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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
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CHCl3-i-jBriIj THMs formed at varying pHs in two major water sources from the
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Beijing metropolitan area 31. The ternary THM speciation model employed eighteen
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γ factors and nine intermediates that account for differences in the reactivity
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between HOCl, HOBr and HOI in their interactions with the NOM reactive sites and
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the entire set of relevant halogenated intermediates. The optimized γ coefficients
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introduced to model and interpret the experimental THM speciation data differed by
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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
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the currently available experimental THMs data, further research is needed to
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understand the nature of the prominent differences between the γ values observed
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for different nodes of the ternary halogen incorporation scheme, to ascertain the
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fundamental mechanisms of the involved reactions and to ultimately expand the
30
expanded the utility of this approach to examine effects of pH and
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. The expanded
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ternary halogen incorporation model to any specific water matrix.
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The complexity of reactions between NOM and halogen species makes it
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challenging to generate exhaustively detailed experimental data for a wide range of
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water matrixes and treatment conditions. This limitation can be circumvented based
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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
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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.
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Theory
90
The Eyring equation (also known as the Eyring–Polanyi equation) is widely used
91
in chemical
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reaction with temperature 32.
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kinetics
ln(ki / A ) = −
to
describe
changes
of
kT ∆H ≠ ∆S ≠ + + ln( B ) RT R h
the rate
of
a
chemical
(1)
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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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and entropy values of these intermediates.
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An alternative approach was firstly pursued in the case of THM formation based on
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the frontier orbital theory which states that the chemical kinetics is determined by
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the HOMO and LUMO of reactant molecules
105
separation between the HOMO of the donor and the LUMO of the acceptor, the
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faster should be the reaction rate. Prior literature 28 has shown that the logarithm of
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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
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linearly correlated with quantum molecular orbital descriptors such as the energy of
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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)
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In Eq. (2), the EHOMO A is the HOMO energy of nucleophile A and ELUMO i is the LUMO
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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
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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
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intermediates; hence the rates of reactions involving these intermediates are
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pseudo-first order with respect to their concentrations. Second, the steady-state
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approximation can be applied because the rates of change of the concentrations of
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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):
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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
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Based on Eq. (4) and Eq. (6), the following equation is obtained:
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k1 HOBr k3[SCl ][ HOCl ] + k4 [SCl ][ HOBr ] = × k2 HOCl k5[SBr ][ HOCl ] + k6 [S Br ][ HOBr ]
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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)
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mA nA C A ∆Si≠/ A kT + + ln( B ) log(k4 ) = − ELUMO HOBr + EHOMO − SCl RT RT RT R h
(9)
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log(k5 ) = −
∆S ≠ mA n C kT ELUMO HOCl + A EHOMO S − A + i / A + ln( B ) Br RT RT RT R h
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log(k6 ) = −
mA n C kT ∆S ≠ ELUMO HOBr + A EHOMO S − A + i / A + ln( B ) Br RT RT RT R h
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152
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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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158
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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)
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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
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Data sources. All kinetic preference constants (γ) examined in this study were
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reported in prior literature
166
consistently applied the sequential three-step halogenation model to study THM
167
formation. Specifically, Roccaro et al.
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values based on the results for binary Cl/Br halogenation of Australian and New
169
Zealand waters, respectively. Yan et al.
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log(γ sIx Cl ) in the ternary halogenation system involving I, Br and Cl for Jingmi and
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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.
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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
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Lowest Unoccupied Molecular Orbitals (LUMO)) were performed based on Density
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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
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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.
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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
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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)
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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 tri- halomethanes
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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
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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
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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
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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)
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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
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. It showed that the
Page 17 of 36
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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
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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
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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
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Figures and Tables
577
578
Figure 1. Molecular geometries of representative halomethanes. (a) CH2ClBr
579
and (b) CHClBrI.
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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
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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.
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Environmental Science & Technology
2.00 Second step Third step
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
Figure 4. Correlation between ∆ values and logarithms of the
591
γ coefficients determined for the second and third halogenation steps in
592
South-East Australia water 30.
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Page 32 of 36
4.00 Second step Third step
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
Figure 5. Correlation between ∆ values and logarithms of the
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
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Environmental Science & Technology
4.00 Second step Third step
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
Figure 6. Correlation between ∆ values and logarithms of the
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
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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
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Environmental Science & Technology
/
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
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Environmental Science & Technology
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
