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Author's personal copy

Computational and Theoretical Chemistry 1031 (2014) 22–33

Contents lists available at ScienceDirect

Computational and Theoretical Chemistry
journal homepage: www.elsevier.com/locate/comptc

A G4MP2 and G4 theoretical study on reactions occurring during
the ozonation of bromide containing waters
Sierra Rayne a,⇑, Kaya Forest b
a
b

Chemologica Research, Mortlach, Saskatchewan, Canada
Department of Environmental Engineering, Saskatchewan Institute of Applied Science and Technology, Moose Jaw, Saskatchewan, Canada

a r t i c l e

i n f o

Article history:
Received 10 December 2013
Received in revised form 4 January 2014
Accepted 5 January 2014
Available online 11 January 2014
Keywords:
Ozonation
Drinking water treatment
Thermodynamic properties
Theoretical study
Quantum chemistry composite methods

a b s t r a c t
The thermodynamic properties of chemical reactions proposed to occur during the ozonation of bromide
containing waters were examined via high-level G4MP2 and G4 composite theoretical methods with the
SMD, PCM, and CPCM solvation models. Enthalpies and free energies of reaction for the sequential oxidation of bromide to bromate and related reactions were determined under standard state conditions. For a
select subset of reactions where entropic changes were significant, the effects of varying temperature in
the range of 0–100 °C were also considered. Based on the current work, previously proposed BrOO ,
BrOOO , and BrO
4 intermediates thought to exist during the bromide ozonation process are called into
question. Similarly, bromide oxidation reactions involving Br2O4, BrOH , and HO2Br appear to be speculative. Analogous to the chloramines, the aqueous phase production of bromamines from hypobromous
acid and ammonia is predicted to be highly energetically favorable.
Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction
Ozone (O3) has been widely employed worldwide in drinking
water treatment over the past several decades [1,2]. A substantial
body of knowledge has been developed on the mechanistic and kinetic details of ozonation [3–6]. At high pH values, in addition to
the direct reaction of ozone with substrates, the highly reactive hydroxyl radical (OH) may be formed and also contribute to the degradation of dissolved and particulate materials [7]. While
ozonation can remove color, taste, and odor problems, act as an
effective pre-treatment mechanism for subsequent processes, and
disinfect the potable water stream, there are concerns about disinfection byproducts (DBPs) [8,9]. In bromide (Br ) containing
waters, bromate (BrO
3 ) may be formed via sequential oxidation
of the starting material [10–13]. At sufficiently high concentrations, bromate is known to pose significant health risks (see, e.g.,
Refs. [14–18] and references therein) to consumers of finished
water supplies.
The reactions between bromide and derived brominated compounds with ozone and its related oxidants have been the subject
of much kinetic and mechanistic study, including the influence of
pH, temperature, and the concentrations of various reactants and
the creation of complex reaction modeling schemes [19–25]. These
collective investigations have revealed several possible methods

⇑ Corresponding author. Tel./fax: +1 306 690 0573.
E-mail address: sierra.rayne@live.co.uk (S. Rayne).
2210-271X/$ - see front matter Ó 2014 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.comptc.2014.01.002

for reducing bromate formation, such as pH depression, the addition of hydroxyl radical scavengers, and ammonia addition to promote bromamine formation [26–31]. However, relatively little
attention has been paid to the thermodynamic properties of these
known and proposed reactions [32]. Thus, in the current study we
undertake the first high level theoretical thermodynamic investigation on the primary reactions during the ozonation of bromide
containing waters. This work provides a better understanding of
the reaction thermodynamics during water treatment with ozone
and facilitates a more rigorous interpretation of proposed
mechanisms.

2. Materials and methods
Gas and aqueous phase calculations were performed at the
G4MP2 [33] and G4 [34] levels of theory using the Gaussian 09
(G09) [35] software program. A select group of reactions was also
studied using the B3LYP [36–38] density functional and the 6311+(d) and 6-311+(d,p) [39–43] basis sets. Aqueous phase studies
were conducted with the SMD [44], PCM [45–48], and CPCM [49]
solvation models. Natural Bond Orbital (NBO) analyses were performed with NBO v3 [50–55] within G09. Molecular structures
were visualized using Avogadro v1.0.3 [56] and Gabedit v2.4.3.
[57] All gas and aqueous phase optimized structures were confirmed as true minima by vibrational analysis at the same level. Calculations using the G4MP2 and G4 methods are expected to be at or
near thermochemical accuracy (±4.2 kJ/mol) [33,34,58–70].

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S. Rayne, K. Forest / Computational and Theoretical Chemistry 1031 (2014) 22–33

23

The BrOOO formed in Reaction (1) is thought to decompose
into BrO , yielding either singlet oxygen (spin allowed; Reaction
(2)) or triplet oxygen (lower energy but spin forbidden; Reaction
(3)):

monomolecular BrOOO intermediate in the aqueous phase reactions between bromide and ozone must be considered in doubt.
Similarly, the cyclical [BrOOOO] molecule, as well as linear
[OBrOOO] and [BrOOOO] compounds, proposed [32] as potential
intermediates in the aqueous phase reaction between BrO and O3
also appear to not be monomolecular intermediates at higher levels of theory (e.g., G4MP2 and G4) regardless of phase and/or multiplicity. These intermediates should also be considered
speculative.
Consequently, we restricted our initial investigations to the following overall reactions [10,75] known to occur during the ozonation of bromide:

BrOOO ! BrO þ 1 O2

ð2Þ

Br þ O3 ! BrO þ 3 O2

ð4Þ

BrOOO ! BrO þ 3 O2

BrO þ O3 ! BrO 2 þ 3 O2

ð5Þ

ð3Þ

BrO þ O3 ! Br þ 23 O2

ð6Þ

BrO 2 þ O3 ! BrO 3 þ 3 O2

ð7Þ

3. Results and discussion
During the ozonation of bromide containing waters, the following initial reaction between bromide and ozone has been postulated [32]:

Br þ O3 ! BrOOO

ð1Þ



The existence of BrOOO was investigated at the B3LYP/6311+(d) density functional level of theory in the gas and aqueous
solvent (using the CPCM solvent model) phases, whereby a stable
structure was reported [32]. We were unable to reproduce a reasonable (i.e., Br–O bond length on the order of 1.8 Å) singlet, triplet,
or mixed state gas or aqueous phase BrOOO structure absent
imaginary frequencies at the B3LYP/6-311+(d), B3LYP/6311+(d,p), G4MP2, or G4 levels. Instead, a structure with a bromine
anion dissociating from an ozone molecule was obtained. This does
not appear to be a single discrete BrOOO molecule. Instead, our final geometries at the G4MP2 and G4 levels of theory have the bromine anion at >2.6 Å from the nearest terminal oxygen atom
forming a Br O3 complex. As discussed below, this Br O interatomic distance is far longer than experimentally known Br–O single bonds (1.7–1.8 Å).
Liu et al. [71] also investigated the potential structure of
BrOOO using theoretical methods, employing the B3LYP/631G(d) level of theory. A proposed BrOOO structure having a
central O–O bond length of 2.03 Å was reported, in addition to
the Br O3 complex we found at the G4MP2 and G4 levels. This
bond length is much longer than is known experimentally for O–
O single bonds (hydrogen peroxide [H2O2], 1.48 Å [72], dichlorine
dioxide [Cl2O2], 1.43 Å [73], and hydrogen trioxide [H2O3], 1.43 Å
[74]), suggesting the presence of a BrO O2 complex rather than
a true BrOOO intermediate compound. These authors have argued
that the bromide ion is forming a Lewis acid–base adduct with
ozone as a kinetic intermediate appearing prior to the transition
state.
To examine the Lewis acid–base proposal further, we conducted
gas phase bond order/index calculations using the G4 method on
the Br O3 complex we find at this level of theory. The Wiberg
bond indices for the O[1]–O[2] and O[2]–O[3] bonds (numbering
increases with distance from the bromine atom) are 1.50 and
1.18, respectively, and only 0.18 for the Br–O interaction. The
atom–atom overlap-weighted natural atomic orbital (NAO) bond
orders are 0.08 (Br–O[1]), 0.95 (O[1]–O[2]), and 0.84 (O[2]–O[3]).
By comparison, a classic Lewis acid–base adduct is tetrahydrofuran–borane (THF:BH3). For this adduct, at the G4 level we obtain
a B–O bond length of only 1.63 Å (close to the neighboring C–O
bond lengths of 1.46 Å and only modestly longer than the B–O
bond length calculated for boric acid [1.37 Å; http://
www.cccbdb.nist.gov/]). In THF:BH3, the Wiberg bond index for
the B–O interaction is 0.45, about half the B–H bond indices
(0.94) and greater than half the O–C bond indices (0.83). The
atom–atom overlap-weighted NAO bond orders in THF:BH3 are
0.45 (B–O), 0.80 (B–H), and 0.66 (C–O). Thus, the B–O bonding
interaction in the THF:BH3 Lewis acid–base adduct is on the order
of a conventional covalent bond, whereas in Br O3 the Br–O
bonding interaction is very weak. As a result, the existence of a true

Naumov and von Sonntag [32] have calculated the aqueous
phase standard state (298.15 K, 1 M) enthalpies (Drxn H ðaqÞ ) and free
energies (Drxn G ðaqÞ ) for Reactions (4)–(7) at the B3LYP/6-311+(d)/
CPCM level of theory (Table 1). Our corresponding values at the
B3LYP/6-311+(d), G4MP2, and G4 levels of theory using the PCM,
CPCM, and SMD solvation models, as well as gas phase standard
state (298.15 K, 1 atm) enthalpies (Drxn H ðgÞ ) and free energies
(Drxn G ðgÞ ) of reaction at each of these three levels of theory, are
shown for comparison.
We obtain excellent agreement at the B3LYP/6-311+(d)/CPCM
level with the Drxn H ðaqÞ and Drxn G ðaqÞ reported in Ref. [32] for these
reactions. While there are significant enthalpy and energy differences for each reaction depending on the computational method
and solvent model chosen, all four reactions are predicted to be
highly exothermic/exergonic in both the gas and aqueous phases.
To determine the corresponding energies for the analogous reacP
tions yielding singlet (1Dg) oxygen, the experimental 1 Dg 3
g
singlet–triplet energy gap for dioxygen (94.3 kJ/mol [76]) can be
added to the reaction energies herein. Of note, the reaction between ozone and the molecular undissociated form of hypobromous acid (HOBr) is considered negligible [5,10].
In the presence of ammonia (NH3), HOBr reacts rapidly to form
the mono- through tri-bromamines [21]:

HOBr þ NH3 ! NH2 Br þ H2 O

ð8Þ

HOBr þ NH2 Br ! NHBr2 þ H2 O

ð9Þ

HOBr þ NHBr2 ! NBr3 þ H2 O

ð10Þ

The gas and aqueous phase DrxnH° and DrxnG° for these reactions are given in Table 2. As with the chloramines [77], formation
of the bromamines via the hypohalic acid is strongly exothermic
and exergonic with minimal temperature dependence due to the
isentropic nature of the reactions.
At sufficiently low pH values, the bromammonium ion (NH3Br+)
has been proposed to react with bromamine (pKa 6.5 [78,79])
[21]:

NH3 Brþ þ NH2 Br ! NHBr2 þ NHþ4

ð11Þ

Alternatively, the reaction between these two compounds could
yield the dibromammonium ion (NH2 Brþ
2 ) and ammonia:

NH3 Brþ þ NH2 Br ! NH2 Brþ2 þ NH3

ð12Þ

The G4MP2 and G4 calculations support the proposition of
Reaction (11) as the operative pathway. In the gas phase, Reaction
(11) is energetically favorable (Drxn G ðgÞ ¼ 47 to 46 kJ=mol),

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S. Rayne, K. Forest / Computational and Theoretical Chemistry 1031 (2014) 22–33

Table 1
Calculated gas (298.15 K, 1 atm) and aqueous phase (298.15 K, 1 M) standard state enthalpies (DrxnH°) and free energies (DrxnG°) of reaction for Reactions (4)–(7) at the B3LYP/6311+(d), G4MP2, and G4 levels of theory.
Reaction

Level of
theory

DrxnH° (kJ/mol)
Gas





3

Br þ O3 ! BrO þ O2

ð4Þ

DrxnG° (kJ/mol)

SMD

PCM

CPCM

CPCM (from
Ref. [32])

Gas

SMD

PCM

CPCM

CPCM (from
Ref. [32])

B3LYP/6311+(d)
G4MP2
G4

61.2

96.4

62.4

62.5

61

69.2

104.4

70.4

70.5

75

32.0
33.3

62.3
63.7

28.4
29.7

28.5
29.8

n/a
n/a

39.9
41.2

70.3
71.8

36.4
37.6

36.4
37.7

n/a
n/a

137.5

125.6

124.4

124.5

126

139.7

128.0

126.7

126.7

130

127.3
128.6

115.6
117.0

113.3
114.7

113.3
114.8

n/a
n/a

127.4
128.7

115.8
117.2

115.1
116.5

115.2
116.6

n/a
n/a

þ O2

ð5Þ

B3LYP/6311+(d)
G4MP2
G4

276.4

325.6

325.4

318

366.1

306.4

355.6

355.4

347

ð6Þ

B3LYP/6311+(d)
G4MP2
G4

336.1

BrO þ O3 ! Br þ 23 O2

248.0
250.1

200.2
202.3

244.7
247.0

244.6
246.9

n/a
n/a

278.0
280.2

230.2
232.3

274.8
277.1

274.7
277.0

n/a
n/a

215.7

186.0

196.2

196.2

194

208.9

179.4

189.6

189.5

187

ð7Þ

B3LYP/6311+(d)
G4MP2
G4

222.5
223.8

200.4
201.4

206.7
207.7

206.6
207.6

n/a
n/a

217.3
218.6

195.2
196.3

199.8
200.8

199.7
200.8

n/a
n/a



BrO þ O3 !

BrO 2

þ O3 !

BrO 2

BrO 3

3

3

þ O2

Table 2
Calculated gas (298.15 K, 1 atm) and aqueous phase (298.15 K, 1 M) standard state enthalpies (DrxnH°) and free energies (DrxnG°) of reaction for bromamine formation (Reactions
(8)–(10)) at the G4MP2 and G4 levels of theory.
Reaction

HOBr þ NH3 ! NH2 Br þ H2 O ð8Þ

HOBr þ NH2 Br ! NHBr2 þ H2 O ð9Þ

HOBr þ NHBr2 ! NBr3 þ H2 O ð10Þ

Level of theory

DrxnH° (kJ/mol)

DrxnG° (kJ/mol)

Gas

SMD

PCM

CPCM

Gas

SMD

PCM

CPCM

G4MP2
G4

54.6
52.7

70.4
68.7

60.7
58.8

60.7
58.8

53.9
52.0

69.7
68.0

60.0
58.1

60.0
58.1

G4MP2
G4

64.0
62.8

75.1
74.0

66.4
65.1

66.4
65.1

62.2
61.0

73.2
72.1

64.6
63.3

64.6
63.3

G4MP2
G4

65.7
65.9

77.0
77.3

66.5
66.5

66.5
66.5

62.8
63.1

74.2
74.6

63.7
63.7

63.7
63.7

becoming more favorable in the aqueous phase via the SMD
(Drxn G ðaqÞ ¼ 93 to 92 kJ=mol) and PCM/CPCM (Drxn G ðaqÞ ¼
66 kJ=mol) solvation models. In contrast, Reaction (12) is
unfavorable in both the gas (Drxn G ðgÞ ¼ þ21 kJ=molÞ and aqueous
(SMD: Drxn G ðaqÞ ¼ þ78 kJ=mol; PCM/CPCM: Drxn G ðaqÞ ¼ þ46 to þ
47 kJ=mol) phases.
Reactions involving bromine containing compounds thought to
occur in the presence of hydroxyl radicals and related oxidants include the following [11,80–84]:

Br þ Br ! Br 2

ð13Þ

Br 2 þ Br 2 ! Br 3 þ Br

ð14Þ

Br 2 þ BrO ! BrO þ 2Br

ð15Þ

OH þ BrO ! BrO þ OH

ð16Þ

OH þ HOBr ! BrO þ H2 O

ð17Þ

CO 3 þ BrO ! BrO þ CO2
3

ð18Þ

BrO 2 þ OH ! BrO2 þ OH

ð19Þ

BrO 2 þ CO 3 ! BrO2 þ CO2
3

ð20Þ

Gas and aqueous phase DrxnH° and DrxnG° at the G4MP2 and G4
levels for these reactions are shown in Table 3. Reactions 13, 14,
and 17 are predicted to be substantially exothermic/exergonic
regardless of phase or solvent model chosen. In contrast, for Reactions 15, 16, 18, 19, and 20, the direction and magnitude of the calculated DrxnH° and DrxnG° depends strongly on the phase and/or
solvent model.
For Reaction (15), the SMD and PCM/CPCM solvent models predict
widely differing (by 57 kJ/mol) Drxn H ðaqÞ that also vary in the sign (+23
to + 25 kJ/mol [SMD] vs. 34 to 32 kJ/mol [PCM/CPCM]). The gas
and SMD aqueous phase calculations predict a strongly endothermic
reaction, whereas the PCM/CPCM models suggest a significantly exothermic aqueous phase reaction. In the gas phase, Reaction (15) is predicted to have a Drxn G ðgÞ of 0 kJ/mol (G4MP2 = 1.7 kJ/mol;
G4 = +0.6 kJ/mol). In the aqueous phase, the SMD and PCM/CPCM solvent models are in very poor reaction free energy agreement. The
SMD calculations suggest a slightly endergonic reaction (+2.4 to
+4.8 kJ/mol) in comparison to highly exergonic predictions ( 55 to
53 kJ/mol) for the PCM/CPCM models. We must conclude there is
significant uncertainty as to whether this reaction is spontaneous under standard state conditions in aqueous solution.

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S. Rayne, K. Forest / Computational and Theoretical Chemistry 1031 (2014) 22–33

Table 3
Calculated gas (298.15 K, 1 atm) and aqueous phase (298.15 K, 1 M) standard state enthalpies (DrxnH°) and free energies (DrxnG°) of reaction for Reactions (13)–(20) at the G4MP2
and G4 levels of theory.
Reaction

Level of theory

DrxnH° (kJ/mol)

SMD

PCM

CPCM

G4MP2
G4

106.5
108.7

73.3
75.4

56.7
58.8

56.8
58.9

85.7
87.9

52.2
54.4

35.5
37.6

35.6
37.7

G4MP2
G4

96.7
96.3

105.4
105.1

112.3
112.3

112.1
112.1

70.1
69.7

92.6
92.4

88.0
88.0

88.3
88.2

G4MP2
G4

+18.5
+20.9

+22.8
+25.1

34.3
32.2

34.1
32.0

1.7
+0.6

+2.4
+4.8

54.9
52.8

54.7
52.6

G4MP2
G4

+59.4
+58.8

47.5
47.3

0.7
1.4

0.7
1.4

+60.0
+59.4

46.8
46.6

0.1
0.8

0.1
0.8

G4MP2
G4

81.4
81.8

81.0
81.4

81.2
81.5

81.2
81.5

81.7
82.0

81.3
81.7

81.5
81.8

81.5
81.8

G4MP2
G4

+558.7
+555.7

6.0
6.6

+80.3
+78.8

+80.3
+78.8

+561.3
+558.2

2.8
3.4

+83.1
+81.5

+83.1
+81.5

G4MP2
G4

+68.6
+69.2

48.2
46.7

18.0
17.1

18.0
17.2

+67.8
+68.4

48.9
47.4

17.1
16.3

17.1
16.3

G4MP2
G4

+567.9
+566.1

6.7
6.0

+63.1
+63.1

+63.1
+63.1

+569.0
+567.2

4.9
4.2

+66.0
+66.1

+66.0
+66.1

Gas

Br þ Br ! Br 2

ð13Þ

Br 2 þ Br 2 ! Br 3 þ Br

ð14Þ

Br 2 þ BrO ! BrO þ 2Br

ð15Þ

OH þ BrO ! BrO þ OH

ð16Þ

OH þ HOBr ! BrO þ H2 O ð17Þ

CO 3 þ BrO ! BrO þ CO2
3

ð18Þ

BrO 2 þ OH ! BrO2 þ OH

ð19Þ

BrO 2

þ

CO 3

! BrO2 þ

CO2
3

DrxnG° (kJ/mol)

SMD

PCM

CPCM

Gas

ð20Þ

Similar ambiguities are evident for Reaction (16), which involves an electron transfer from the hypobromite ion to the hydroxyl radical. In the gas phase, this reaction appears to be highly
endothermic/endergonic. In the aqueous phase, the SMD model
predicts a highly exothermic/exergonic reaction (on the order of
47 kJ/mol for both Drxn H ðaqÞ and Drxn G ðaqÞ ). The PCM and CPCM
models both predict an effectively energetically neutral reaction
(Drxn G ðaqÞ ¼ 0:8 to 0:1 kJ=mol).
We find the reverse aqueous phase solvent model discrepancies
for Reaction (18), with the SMD model predicting a slightly exergonic process (Drxn G ðaqÞ ¼ 3 kJ=mol) versus a highly endergonic
reaction via the PCM/CPCM models (Drxn G ðaqÞ ¼ þ81 to þ
83 kJ=mol). Reaction (20) has an analogous prediction difference
between solvation models, which is not surprising since both reactions involve the carbonate radical anion being reduced to the carbonate dianion (by the hypobromite ion in Reaction (18) and the
bromite ion in Reaction (20)). Both Reactions (18) and (20) are predicted to be highly unfavorable in the gas phase. This result is expected given the increased charge concentration on the carbonate
dianion in the products versus the more diffuse dianionic charge
distribution across two molecules in the reactants. In solution,
the SMD model predicts a modestly favorable Drxn G ðaqÞ ( 4 to
5 kJ/mol) for Reaction (20), whereas the PCM/CPCM models project a significantly unfavorable reaction (+66 kJ/mol). Reaction (19)
is calculated to be unfavorable in the gas phase
(Drxn G ðgÞ ¼ þ68 kJ=mol) but consistently favorable in the aqueous

phase (Drxn GðaqÞ ¼ 48 kJ=mol [SMD] to 17 kJ/mol [PCM/CPCM]).

It is difficult to determine which solvation model reaction energies are more accurate. Additional experimental investigations are
required. Based on our prior experience [85–87] with the SMD solvation model, and benchmarking efforts by the development team
[88,89], the prima facie assumption is that this model’s results may
be more accurate than those of the PCM/CPCM models, particularly
for reactions involving charged species.
For Reactions (13)–(15), there is a notable difference in entropy
between reactants and products, indicating we would expect to
find significant changes in DrxnG as a function of temperature.
Gas and aqueous phase G4MP2 and G4 calculations were conducted at 10 °C intervals between 0 °C and 100 °C for all reactions
to examine the DrxnG sensitivity towards temperature. Reactions
(16)–(20) are effectively isentropic and so exhibit negligible variation in DrxnG (<1.2 kJ/mol) over this temperature range. The temperature dependent DrxnG for Reactions (13)–(15) are shown in
Fig. 1. CPCM calculations were omitted as they yield essentially
equivalent values to those of the PCM solvent model.
The predicted change in DrxnG between 0 °C and 100 °C is up to
+9 kJ/mol for Reactions (13) and (14), and 7 kJ/mol for Reaction
(15). For Reaction (15), the changes in DrxnG with temperature
influence whether the reaction is spontaneous. In the gas phase,
Reaction (15) is predicted to be non-spontaneous at low temperatures, transitioning to spontaneity as the temperature increases.
The point of spontaneity depends on the level of theory. At the
G4MP2 level, the DrxnG(g) for this reaction is 0.0 kJ/mol at 0 °C,
declining to 0.7 kJ/mol at 10 °C and reaching 6.9 kJ/mol at

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S. Rayne, K. Forest / Computational and Theoretical Chemistry 1031 (2014) 22–33

Fig. 1. Temperature dependent gas (DrxnG(g)) and aqueous phase (DrxnG(aq)) free energies of reaction between 0° and 100 °C for Reactions (a) 13, (b) 14, and (c) 15.

Author's personal copy

S. Rayne, K. Forest / Computational and Theoretical Chemistry 1031 (2014) 22–33

100 °C. At the G4 level, the reaction transitions from non-spontaneous to spontaneous at about 35 °C, with end members of
+2.3 kJ/mol at 0 °C and 4.5 kJ/mol at 100 °C. In the aqueous phase
using the SMD solvation model, the reaction is projected to make
the spontaneity transition at 60 °C with the G4MP2 method and
at about 95 °C with the G4 method. The PCM solvation model predicts Reaction (15) will be highly spontaneous at all liquid water
temperatures under ambient air pressure.
The reactions Br + OH ? BrOH and Br + OH ? BrOH have
also been proposed [11,22,80,83], but we are unable to obtain a
gas or aqueous phase converged geometry at the G4MP2 or G4 levels for BrOH with the bromine atom bound to the oxygen atom
(i.e., the hypobromous acid anion). Instead, the converged gas
phase geometry is linear in the atomic order [BrHO] with interatomic distances of Br H at 2.26 Å and H O at 1.00 Å, and a
Br–H–O angle of 180.0°. This Br H interatomic distance is far
longer than the gas phase Br–H bond length (1.41 Å) in hydrogen
bromide [90]. The gas phase natural charges in BrHO are 0.48
on bromine, +0.21 on hydrogen, and +0.27 on oxygen. There is neligible bonding between the Br anion and the hydroxyl radical in
the gas phase, with a Wiberg bond index of only 0.006 for the
Br–O interaction and 0.01 for the Br–H interaction (as compared
to 0.19 for the O–H bonding), and an atom–atom overlap-weighted
NAO bond order of only 0.02 for Br–H and 0.00 for the Br–O interactions (compared to 0.30 for O–H). Thus, it appears that BrOH , if
it exists in the gas phase, is not the hypobromous acid anion but
rather a weakly interacting Br HO complex.
In aqueous solution using the PCM solvation model, a linear [Br
HO] complex is obtained with Br H and H O interatomic distances of 2.29 Å and 0.99 Å, respectively, and natural charges of
0.48 on bromine, +0.21 on hydrogen, and +0.28 on oxygen. Conversely, the SMD solvation model predicts the linear [Br OH] complex as a transition state (one imaginary frequency). The converged
SMD geometry has the bromine anion (q = 0.43) located 2.65 Å and
2.55 Å from the oxygen and hydrogen atoms, respectively, of the OH
molecule (O–H bond length = 0.97 Å; qO = +0.22; qH = +0.21), forming
a near isosceles triangle (O–Br–H bond angle = 21.3°; Br–O–H bond
angle = 73.6°; Br–H–O bond angle = 85.1°). The Br O interatomic distance is far longer than the gas phase Br–O bond length in bromine
monoxide (1.72 Å; NIST Diatomic Spectral Database; http://
www.nist.gov/pml/data/msd-di/index.cfm) and in hypobromous acid

27

(1.83 Å [91]). Formation of a [Br OH] complex is predicted to be
substantially energetically favorable in the
gas phase
(Drxn G ðgÞ ¼ 40 kJ=mol; Drxn H ðgÞ ¼ 65 to 64 kJ=mol) and modestly unfavorable in the aqueous phase using the PCM/CPCM
(Drxn G ðaqÞ ¼ þ1 to þ 2 kJ=mol; Drxn H ðaqÞ ¼ 22 to 21 kJ=mol) and
SMD
(Drxn G ðaqÞ ¼ þ3 to þ 7 kJ=mol;
Drxn H ðaqÞ ¼ 18 to 15
kJ=mol) solvation models.
The dimerization of bromine dioxide has been included in reaction models that describe the ozonation of bromide containing
waters [11]:

2BrO2 ! Br2 O4

ð21Þ

The structure of the lowest energy Br2O4 isomer is of substantial
interest from an atmospheric chemistry perspective [92], but it
does not appear to have been previously investigated in aqueous
solution. Li and Francisco [92] examined the structures and energies of four Br2O4 isomers using density functional theory (B3LYP
with the 6-311+G(2d) and 6-311+G(3df) basis sets) having the
structures BrOOOOBr (1), BrOOBr(O)2 (2), OBrOOOBr (3), and
OBr(O)2BrO (4). BrOOOOBr and BrOOBr(O)2 were estimated to be
essentially isoenergetic, but BrOOBr(O)2 was rationalized as the
likely lowest energy isomer based on structural and thermodynamic considerations.
Using set notation to describe the relative positions of the bromine and oxygen atoms, and denoting linking or terminal bromine
dioxide moieties (i.e., a bromine atom with two adjacent oxygen
substituents [R–BrO2 where R = Br,O]) as ‘‘O2,’’ we obtain 20 potential Br2O4 isomers whereby oxygen and bromine are not bound to
more than two or three other atoms, respectively (Fig. 2). The four
Br2O4 isomers (i.e., numbered 1, 2, 3, and 4 in Ref. [92]) studied by
Li and Francisco correspond to {Br,O,O,O,O,Br}, {Br,O,O,Br,O2},
{Br,O,O,O,Br,O}, and {O,Br,O2,Br,O} from Fig. 2, respectively. Our
initial screening of Br2O4 isomers occurred via gas phase calculations at the G4MP2 level. In order to be considered as a plausible
Br2O4 candidate, the isomer needed to converge absent imaginary
frequencies and have interatomic distances consistent with
experimentally known gas phase bond lengths in diatomic bromine (rBr–Br = 2.28 Å; NIST Chemistry WebBook; http://www.
webbook.nist.gov/chemistry/), bromine moxoxide (rBr–O = 1.72 Å;
NIST Diatomic Spectral Database; http://www.nist.gov/pml/data/
msd-di/index.cfm), hypobromous acid (rBr–O = 1.83 Å [91]),

Fig. 2. Structures and set notation formulas for the Br2O4 isomers under consideration.

Author's personal copy

28

S. Rayne, K. Forest / Computational and Theoretical Chemistry 1031 (2014) 22–33

diatomic oxygen (rO–O = 1.21 Å [93]), ozone (rO–O = 1.28 Å [94]),
hydrogen peroxide (rO–O = 1.48 Å [72]), dichlorine dioxide
(rO–O = 1.43 Å [73]), and hydrogen trioxide (rO–O = 1.43 Å [74]).
We were unable to find any Br2O4 isomers that met these basic
gas phase structural criteria, along with associated full bond order/
index requirements, at the G4MP2 level of theory. In addition, each
of the four Br2O4 isomers identified by Li and Francisco [92] at the
B3LYP/6-311+G(2d) and B3LYP/6-311+G(3df) levels of theory have
either O–O or Br–O bond lengths of sufficient length as to warrant
caution regarding the existence of a discrete molecule rather than
an intermolecular association, as well as less than full bond orders/
indices between a number of atoms. Thus, we must conclude that
the aqueous phase existence of Br2O4 is in doubt. Absent more
clear experimental evidence, the aqueous phase dimerization of
BrO2 to Br2O4 and subsequent postulated aqueous phase reactions

þ
þ
of
Br2O4
(e.g.,
Br2 O4 þ OH ½H2 O ! BrO
3 þ BrO2 þ H ½2H
[11,26,71,82]) should likely be excluded from reaction modeling
efforts.
Where ozonation is used in combination with hydrogen peroxide, the following additional reactions have been proposed [20]:

in the gas phase and aqueous solution. In the gas phase, the
G4MP2/G4 calculations yield Drxn H ðgÞ =Drxn G ðgÞ of 300/ 327 kJ/mol.
In water, the predicted Drxn H ðaqÞ =Drxn G ðaqÞ is 175/ 202 kJ/mol
using the SMD solvent model and 262/ 289 kJ/mol with the
PCM/CPCM models.
During the c-irradiation of bromide and hydrogen peroxide
containing solutions, the following reactions are believed to occur
[22,83,84,95,96]:

HO 2

Gas and aqueous phase standard state enthalpies and free energies for these reactions are shown in Table 4. Reactions (26) and
(30) are predicted to be highly exergonic regardless of phase or solvent model, whereas Reaction (28) is substantially energetically
unfavorable in all phase/solvent model combinations. The decomposition of the triatomic bromine anion (Reaction (25)) is highly
endergonic in the gas and SMD aqueous solvent phases, but predicted to be either slightly favorable (Drxn G ðaqÞ ¼ 0:1 kJ=molÞ or
unfavorable (Drxn G ðaqÞ ¼ þ0:3 to þ 4:6 kJ=mol) with the PCM/
CPCM solvation models. Reaction (27) is modestly unfavorable in
the gas phase (Drxn G ðgÞ ¼ þ7:7 to þ 9:0 kJ=mol), and either slightly
favorable (Drxn G ðaqÞ ¼ 2:1 to 0:8 kJ=mol) to modestly favorable
(Drxn G ðaqÞ ¼ 17:0 to 15:4 kJ=mol) in the aqueous phase using
the SMD and PCM/CPCM solvation models, respectively.
Reaction (29) is significantly unfavorable in the gas phase



þ HOBr ! HO2 Br þ OH

ð22Þ

HO2 Br ! O2 þ Hþ þ Br

ð23Þ

Reactions (22) and 23 sum to yield the following overall
reaction:

HO 2 þ HOBr ! H2 O þ O2 þ Br

ð24Þ

However, we are unable to find any gas or aqueous phase converged geometries absent any imaginary frequencies at the G4MP2
level for HO2Br. Syn, anti, and linear starting conformations were
investigated, and none yielded true minima. As a result, Reactions
(22) and (23) are necessarily called into question because of insufficient theoretical evidence for a HO2Br intermediate. Regardless,
Reaction (24) is predicted to be highly energetically favorable, both

Br 3 ! Br2 þ Br

ð25Þ

Br þ BrO ! BrO þ Br

ð26Þ

BrO þ BrO 2 ! BrO þ BrO2

ð27Þ

Br 2 þ BrO 2 ! BrO þ BrO þ Br

ð28Þ

O 2 þ HOBr ! 3 O2 þ Br þ OH

ð29Þ

O3 þ Br ! BrO þ 3 O2

ð30Þ

Table 4
Calculated gas (298.15 K, 1 atm) and aqueous phase (298.15 K, 1 M) standard state enthalpies (DrxnH°) and free energies (DrxnG°) of reaction for Reactions (25)–(30) at the G4MP2
and G4 levels of theory.
Reaction

Level of theory

DrxnH° (kJ/mol)
Gas

Br 3

! Br2 þ Br



ð25Þ



Br þ BrO ! BrO þ Br

BrO þ

BrO 2

Br 2

BrO 2

O 2

þ



ð26Þ



ð27Þ





! BrO þ BrO2

! BrO þ BrO þ Br

3

þ HOBr ! O2 þ Br þ OH

3

O3 þ Br ! BrO þ O2

ð30Þ



ð28Þ

DrxnG° (kJ/mol)

SMD

PCM

CPCM

Gas

SMD

PCM

CPCM

G4MP2
G4

120.6
124.8

64.5
68.7

39.0
43.3

39.0
43.3

79.9
84.1

37.3
41.5

0.1
4.2

0.3
4.6

G4MP2
G4

88.0
87.9

50.5
50.3

91.0
91.0

90.9
90.9

87.4
87.2

49.8
49.6

90.4
90.4

90.3
90.3

G4MP2
G4

9.2
10.4

0.7
0.6

17.3
15.7

17.3
15.7

7.7
9.0

2.1
0.8

17.0
15.4

17.0
15.5

G4MP2
G4

113.8
116.2

76.1
78.3

50.5
52.8

50.7
53.0

85.7
88.1

47.9
50.2

23.8
26.1

24.0
26.3

G4MP2
G4

66.6
70.7

24.8
28.6

35.3
39.3

35.3
39.3

38.2
42.3

3.5
0.3

7.0
11.0

6.9
10.9

G4MP2
G4

120.0
121.1

112.8
114.1

119.4
120.7

119.4
120.7

127.3
128.5

120.1
121.4

126.8
128.1

126.7
128.1

ð29Þ

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S. Rayne, K. Forest / Computational and Theoretical Chemistry 1031 (2014) 22–33

(Drxn G ðgÞ ¼ þ38 to þ 42 kJ=mol) and modestly unfavorable in the
aqueous phase according to the PCM and CPCM models
(Drxn G ðaqÞ ¼ þ6:9 to þ 11:0 kJ=mol), whereas the SMD model predicts either a slightly favorable (G4MP2; Drxn G ðaqÞ ¼ 3:5 kJ=mol)
or unfavorable (G4; Drxn G ðaqÞ ¼ þ0:3 kJ=mol) reaction depending
on the level of theory.
As was discussed above, where reactions are effectively isentropic, negligible change in the DrxnG is expected with temperature.
Even where significant entropy changes occur during the reaction,
for the species under investigation this generally results in only
reasonably small (i.e., <10 kJ/mol) changes in DrxnG between 0 °C
and 100 °C. Consequently, temperature variability in liquid water
under ambient pressures will not change the non-spontaneity (or
significantly alter the corresponding equilibrium constant) of Reaction (28) despite the substantial entropy change during the reaction, nor will temperature effects alter the spontaneity of
Reaction (25) in water using the SMD solvation model or Reaction
(27) in water using the PCM and CPCM solvation models. Thus, we
chose to only examine the temperature effects on Reaction (25)
using the PCM solvation model, Reaction (27) using the SMD solvation model, and Reaction (29) using both the SMD and PCM
models.
Reaction (25) is predicted to transition from non-spontaneous
to spontaneous at 25 °C at the G4MP2 level using the PCM solvation model, and at 55 °C with the G4 method (Fig. 3). The end
member DrxnG(aq) are +3.2/+7.5 kJ/mol at 0 °C and 9.9/ 5.7 kJ/
mol at 100 °C using the G4MP2/G4 methods, respectively. There
will be little variability in DrxnG(aq) with temperature for Reaction
(27), and it will not affect the predicted spontaneity of the reaction
using the G4MP2 and G4 methods with the SMD solvation model.
Reaction (29) undergoes a spontaneity transition at 28 °C with
the G4-SMD approach, and is predicted to be spontaneous across
the temperature range from 0 °C to 100 °C with the G4MP2-SMD
method. Using the PCM solvation model, Reaction (29) remains
non-spontaneous over the entire temperature range at the G4 level, and becomes spontaneous only above 97 °C at the G4MP2
level.
The exchange of bromine and chlorine atoms between the corresponding hypohalous acids (Reaction (31)) and monohalamines
(Reaction (32)) also has to be considered [30]:

HOCl þ Br ! HOBr þ Cl



ð31Þ


NH2 Cl þ Br ! NH2 Br þ Cl

ð32Þ

Reaction
(31)
is
only
slightly
endergonic
(Drxn G ðgÞ ¼ þ1:8 to þ 3:6 kJ=mol) in the gas phase, but strongly
exergonic in the aqueous phase (Drxn G ðaqÞ ¼ 46 to 17 kJ=mol)
using all three solvation models (Table 5). Reaction (32) is
significantly endergonic in the gas phase (Drxn G ðgÞ ¼ þ18 to
þ20 kJ=mol), whereas in aqueous solution we predict the reaction
will be either significantly exergonic (SMD: Drxn G ðaqÞ ¼ 30 to
28 kJ=mol) or near energetically neutral (PCM/CPCM:
Drxn G ðaqÞ ¼ 2 to 0 kJ=mol). Because of the isentropic nature of both
reactions, their respective DrxnG would be little affected by changing temperatures. However, given its predicted energetic neutrality,
even small temperature changes would induce relevant variations
(but still <1 kJ/mol) in DrxnG for Reaction (32) using the PCM/CPCM
solvation models.

While bromite (BrO
2 ½OBrO ) with a central bromine atom
and two adjacent oxygen atoms is a known oxybromine compound,
the BrOO analog to bromite (having a central oxygen atom) has
been proposed as an intermediate in the attack of ozone on hypobromite (BrO ) [9]. It is thought that BrOO decays to bromide
and diatomic oxygen after its formation, thereby regenerating bromide ions in solution. At the G4MP2 and G4 levels, we are unable to
find a plausible BrOO structure starting either from linear or bent

29

geometries in the gas and aqueous phases. In all cases, O2 separates
from Br and the calculations either fail to converge on a stable energy minimum, or converge on a bent [Br O2] complex with a Br–
O–O angle of 119° and a Br–O bond length of >2.61 Å in the gas
phase and >2.45/2.69 Å (SMD/PCM + CPCM) in the aqueous phase
that is too long for a bromine-oxygen single bond (see above for
known experimental ranges that vary between 1.72 and 1.83 Å).
Therefore, it appears unlikely that BrOO is present during the
ozonation of bromidic waters.
The reaction between two hypobromite radicals (BrO) to form

bromite (BrO
2 ) and hypobromite (BrO ) has been included in reaction models with a rate constant of 5 109 M 1 s 1:

BrO þ BrO ! BrO
[31]. This proposed reaction is neither
2 þ BrO
charge nor atom balanced, and should not be included in ozonation
reaction modeling.
Bromine radicals may react directly with ozone to give BrO and
diatomic oxygen [11,31]:

Br þ O3 ! BrO þ O2

ð33Þ

At the G4MP2/G4 levels, this reaction is highly energetically
favorable
in
the
gas
(Drxn H ðgÞ ¼ 121 to 120 kJ=mol;

Drxn GðgÞ ¼ 128 to 127 kJ=mol) and aqueous phases (SMD:
Drxn H ðaqÞ ¼ 114 to 113 kJ=mol,
Drxn G ðaqÞ ¼ 121 to 120 kJ=mol;
PCM/CPCM:
Drxn H ðaqÞ ¼ 121 to 119 kJ=mol,
Drxn G ðaqÞ ¼ 128 to 127 kJ=mol).
Monobromamine may also be attacked by hydroxide ions
(Reaction (34)) or disproportionate to dibromamine and ammonia
(Reaction (35)) [21,24,31]:

NH2 Br þ OH ! BrO þ NH3

ð34Þ

2NH2 Br ! NHBr2 þ NH3

ð35Þ

While hydroxide attack on monobromamine is energetically
favorable in the gas phase (Table 5; Drxn G ðgÞ ¼ 29 to
28 kJ=mol), it is substantially unfavorable in aqueous solution
(Drxn G ðaqÞ ¼ þ37 to þ 95 kJ=mol depending on solvation model).
The disproportionation of monobromamine into dibromamine
and ammonia is predicted to be highly unfavorable
(DrxnG° > +51 kJ/mol) regardless of phase, solvation model, or level
of theory. Pinkernell and von Gunten [31] have proposed and
utilized an equilibrium constant (K) of 2.5 for Reaction (35). Our
calculations would suggest a negligible K for this reaction (i.e.,
2.5) given its predicted substantial endergonicity.
Finally, it has been suggested [25] that hydrogen peroxide can
react with hypobromous acid (Reaction (36)) or its conjugate base
(Reaction (37)) via the following reactions:

HOBr þ H2 O2 ! Br þ H2 O

ð36Þ

BrO þ H2 O2 ! Br þ H2 O

ð37Þ

Unfortunately, neither reaction is atom balanced, and Reaction
(36) is not charge balanced. Such physically impossible reactions
cannot be energetically modeled and should be disregarded from
future reaction modeling work.
4. Conclusion
The gas and aqueous phase standard state thermodynamic
properties of the major reactions occurring during the ozonation
of bromide containing waters for drinking water treatment were
calculated at the G4MP2 and G4 levels of theory employing the
SMD, PCM, and CPCM solvation models. The primary reactions
for sequential bromide oxidation to bromate and bromamine formation via reactions between hypobromous acid and ammonia
are highly exothermic and exergonic in both the gas and aqueous


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