DFT studies on the water-assisted synergistic proton dissociation

Subscriber access provided by READING UNIV

Article

DFT studies on the water-assisted synergistic proton dissociation mechanism for the spontaneous hydrolysis reaction of Al in aqueous solution 3+

Shaonan Dong, Wenjing Shi, Jing Zhang, and Shuping Bi ACS Earth Space Chem., Just Accepted Manuscript • DOI: 10.1021/ acsearthspacechem.7b00142 • Publication Date (Web): 29 Jan 2018 Downloaded from http://pubs.acs.org on January 31, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

ACS Earth and Space Chemistry is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Earth and Space Chemistry

1

DFT studies on the water-assisted synergistic proton dissociation

2

mechanism for the spontaneous hydrolysis reaction of Al3+ in

3

aqueous solution

4 Shaonan Dong, Wenjing Shi, Jing Zhang, and Shuping Bi*

5 6 7

School of Chemistry and Chemical Engineering, State Key Laboratory of Coordination Chemistry of

8

China & Key Laboratory of MOE for Life Science, Nanjing University, Nanjing 210023, China

9 10

*

11

011-86-025-86205840; Fax: +011-86-025-83317761; E-mail: [email protected].

Corresponding author. Chemistry Department, Nanjing University, Nanjing 210023, China. Phone:

12 13

Keywords: Aluminum ion; spontaneous hydrolysis mechanism; synergistic proton dissociation;

14

water-assisted; density functional theory

1

ACS Paragon Plus Environment

ACS Earth and Space Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

15

Abstract

16

The kinetic mechanism of spontaneous aluminum ion (Al3+) hydrolysis reaction in aqueous solution is

17

investigated using the density functional theory – quantum chemical cluster model (DFT-CM) method.

18

Three typical reaction pathways for the spontaneous Al3+ hydrolysis reaction are modeled, including:

19

(1) the traditional spontaneous proton dissociation on the Al3+ inner-shell coordinated waters; (2) the

20

conventional bulk water-assisted proton dissociation; and (3) the second-shell water-assisted

21

synergistic dissociation of the protons on the Al3+ inner-shell waters. The results show that the

22

electrostatic effects between Al3+ and its coordinated waters alone can not fully account for the proton

23

loss on an inner-shell coordinated water. It is suggested that the main reaction pathway for natural

24

hydrolysis of aqueous Al3+ is the second-shell water-assisted synergistic proton dissociation, in which

25

the participation of the second hydration shell is crucially important. The calculated synergistic proton

26

dissociation rate constant, kH = 1.14×105 s-1, is in close agreement with the experimental results

27

(1.09×105 s-1 and 7.9×104 s-1). The first hydrolysis equilibrium constant pKa1 of Al3+ is calculated as

28

5.82, also well consistent with the literature value of 5.00. This work elucidates the molecular

29

mechanism of the spontaneous Al3+ hydrolysis reaction in natural waters, and has important

30

environmental implications.

+

2


Page 2 of 26

Page 3 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


31

1.

32

The hydrolysis chemistry of Al3+ in natural water is critical for environmental science, material

33

chemistry and medicine.1-3 In the pH range of 3 to 7, Al3+ undergoes hydrolysis from the hexahydrate

34

Al(H2O)63+ to monomeric and polymeric hydroxyl Al species such as Al(OH)2+, Al(OH)2+, Al(OH)3,

35

Al(OH)4-, Al2(OH)2(H2O)84+ and the Keggin ion AlO4Al12(OH)24(H2O)127+.2,4 Historically, the metal

36

ion hydrolysis is viewed as the stepwise removal of protons from hydrate water molecules (see S1 in

37

SI).4 Due to the complexity of the hydrolytic species of Al3+ and the experimental limitations, the

38

microscopic details of the proton removal pathways for Al3+ hydrolysis is poorly understood 2. In the

39

1960s, Eyring et al.

40

hydrolysis reaction by dielectric relaxation, while Fong and Grunwald 6 obtained the acid dissociation

41

rate constant of Al(H2O)63+, kH+ = 7.9×104 s-1 at 298 K by 1H NMR. However, these macroscopic rate

42

constants are actually measured for a collective of aqueous Al3+ ions, while the microscopic hydrolysis

43

dynamics of a single Al3+ ion can not be provided at the molecular level by these experiments.

44

Researchers have tried to draw the precise reaction pathway for aqueous Al3+ hydrolysis using

45

theoretical methods such as molecular dynamics simulations, but they did not find a pathway whose

46

kH+ agrees with the experimental data (see S1 in SI).7-13 So far, there still lacks clear and unified

47

understanding on the kinetic mechanism of the Al3+ hydrolysis reaction in aqueous solution.

48 49

Introduction

5

obtained the rate constant kH+ = 1.09×105 s-1 at 298 K for the first-order Al3+

In literature, the first-order spontaneous hydrolysis reaction of Al3+ in aqueous solution is usually expressed using the following three different chemical reaction equations:

50

Al3+ + H2O → Al(OH)2+ + H+

(1)

51

Al(H2O)63+ → Al(OH)(H2O)52+ + H+

(2)

52

Al(H2O)63+ + H2O → Al(OH)(H2O)52+ + H3O+

(3)

53

Equation (1) describes that Al3+ interacts with one bulk water to form Al(OH)2+ and H+.4 In acidic

54

aqueous solutions, Al3+ mainly exists in the form of Al(H2O)63+, not in the form of naked Al3+, thus it

55

is not accurate to use equation (1) to describe the hydrolysis reaction of Al3+ in aqueous solution.

56

Equation (2) describes that a proton in Al(H2O)63+ dissociates into the bulk water to form

57

Al(OH)(H2O)52+ and H+,14 which reflects a traditional view of the metal ion hydrolysis mechanism,

58

that is, the coordination of a metal ion to water molecules polarizes the water molecules and makes the

59

spontaneous proton loss easier by electrostatics (Scheme 1(a)).14 Equation (3) describes that a proton in 3



Page 4 of 26

60

Al(H2O)63+ dissociates and binds with a bulk solvent water molecule to form H3O+,15 which reflects

61

another conventional view of the metal ion hydrolysis mechanism, that is, the hydrolysis reactions

62

occur when the acidity of the protons on the coordinated water molecules reaches a level when a

63

surrounding free solvent water molecule itself becomes a sufficient Brønsted base to remove a proton

64

to form a hydroxyl metal species and H3O+ (Scheme 1(b)).16 Thus, equation (3) can also be viewed as a

65

bulk water-assisted proton dissociation mechanism of the Al3+ hydrolysis.

66

H O H

(a) H2O

e

Al

(b)

H

OH2 O

H2O

H

O

H

OH2

H2O OH2

OH2

67

e

Al

OH2

H2O

H

OH2

68

Scheme 1

Schematic representations of (a) the traditional spontaneous proton dissociation

69

mechanism and (b) the conventional bulk water-assisted proton dissociation mechanism of the

70

first-order hydrolysis reaction of Al3+

71 72

In previous general Car-Parrinello molecular-dynamics (CPMD) simulations of the Al3+

73

hydrolysis pathways under ambient conditions, no event of the proton dissociation has been observed

74

during the simulation timescale of tens of picoseconds,11-13 which is believed to due to the fact that the

75

spontaneous Al3+ hydrolysis is a rare event, and is far beyond the simulation timescale accessible by

76

present-day ab initio molecular dynamics.9,11 In this study, typical kinetic reaction pathways for Al3+

77

hydrolysis in aqueous solution are modeled using the density functional theory – quantum chemical

78

cluster model (DFT-CM) method, which has been proved feasible for any desired reaction pathways

79

independent of the reactivity of the systems, including fast and slow reactions on picoseconds to

80

seconds timescale.17-19 The purpose of this study is to clarify the reasonable reaction pathways for Al3+

81

hydrolysis in aqueous solution, and to lay a good foundation for further investigating the Al3+

82

hydrolysis and polymerization mechanisms.

4


Page 5 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


83

2.

84

2.1. Test three reaction pathways for Al3+ hydrolysis

85

Referring to the different mechanisms of the Al3+ hydrolysis reaction in aqueous solution in literature,

86

the following three reaction pathways for the first-order Al3+ hydrolysis would be tested in this work:

87 88

Computational method

Pathway-I: the traditional hydrolysis mechanism of the spontaneous proton dissociation from a coordinated water in Al(H2O)63+, in which the proton moves directly into the bulk water;

89

Pathway-II: the conventional hydrolysis mechanism of the bulk water-assisted proton dissociation

90

from a coordinated water in Al(H2O)63+, in which the proton moves into a bulk solvent water molecule

91

which acts as the Brønsted base to accept the dissociated proton. In both pathway-I and -II, only one

92

proton dissociates from the inner-shell of Al(H2O)63+;

93

Pathway-III: the second-shell water-assisted synergistic proton dissociation between the inner-

94

and second-hydration shells of Al3+. One solvent water molecule accepts the dissociating proton from

95

an inner-shell water, and donates one of its own protons to another solvent water molecule in the

96

second hydration shell. Two protons dissociate synergistically, which is quite different from pathway-I

97

and –II.

98 99

2.2. Treatment of the solvent effects

100

Four different solvation models including the gas phase model (GP), the gas phase-polarizable

101

continuum model (GP-PCM), the gas phase-supermolecule model (GP-SM) and the gas

102

phase-supermolecule-polarizable continuum model (GP-SM-PCM) are used to simulate the three Al3+

103

hydrolysis reaction pathways. The short-range H-bond interactions between Al(H2O)63+ and its

104

surrounding solvents are considered by adding explicit solvent water molecules in the second

105

hydration shell of the gas phase Al(H2O)63+ and constructing the gas phase-supermolecule (GP-SM)

106

clusters,20-22 while the long-range bulk solvent effect is considered by performing the optimizations

107

and energy calculations of the GP-SM clusters in the polarizable continuum model (PCM).23,24 The

108

results with GP-SM-PCM are discussed in the text while the testing results with GP, GP-PCM and

109

GP-SM are summarized in S2.1 in SI. In modeling different Al3+ hydrolysis pathways, the numbers

110

(Nm’) and the arrangements of the explicit solvent water molecules added in the second hydration shell

5



Page 6 of 26

111

of Al3+ are determined accordingly. The influences of different Nm’ on the three Al3+ hydrolysis

112

pathways are systematically examined and the results are shown in S2.2 in SI.

113 114

2.3. Computational details

115

All DFT-CM calculations are performed using Gaussian 03 suite of programs.25 In the tested Al3+

116

hydrolysis pathways, the optimizations and frequency calculations of the reactants (R), transition states

117

(TS) and products (P) are carried out in PCM using DFT at B3LYP/6-311+G(d,p) level.26,27 The TS

118

structures with one imaginary frequency are obtained from Berny optimizations, while the stable

119

structures of R and P with no imaginary frequencies are obtained by further optimizing the structures

120

achieved from the intrinsic reaction coordinate (IRC) calculations.28,29 All optimizations and frequency

121

calculations are conducted at 0 K. The electronic energies Eelect(0K) of the aqueous reaction species at 0

122

K are obtained from the single-point PCM calculations on the GP-SM clusters using

123

MP2/6-311+G(d,p) method. The thermodynamic parameters of the aqueous reaction species at 298.15

124

K such as the total energies E298, enthalpies H298 and Gibbs free energies G298 are calculated by adding

125

zero-point energies EZPE(0K), thermal corrections Ecorr, enthalpy corrections Hcorr, and entropy

126

corrections –TS298 onto Eelect(0K).25,30 EZPE(0K) is obtained from frequency calculations, while Ecorr, Hcorr

127

and S298 are obtained from the thermochemistry analysis performed at 298.15 K and 1 atm. The UAKS

128

radius and the dielectric constant ε = 78.39 are used for water in the PCM calculations.31

129

The rate constants kH+ of the reaction pathways are estimated with the transmission coefficients

130

γH+ and the transition state rate constants kTST using kH+ = γH kTST. The kTST value is calculated using the

131

Eyring equation:

132

kTST =

+

≠

≠

≠

ΔG298, a ΔS ΔH 298, a k BT kT exp(− ) = B exp( 298, a − ) h RT h R RT

(4)

133

where kB, T, h, R, ΔG298,a≠, ΔS298,a≠ and ΔH298,a≠ are Boltzmann’s constant, temperature, Planck’s

134

constant, gas constant, activation Gibbs free energy, activation entropy and activation enthalpy,

135

respectively. The transition coefficient γH+ includes three factors: the tunneling factor κ, the recrossing

136

factor Γ, and the non-equilibrium factor g, that is, γH+ = κΓg.32 In proton transfer reactions, the

137

tunneling effect on the reaction rate constant can be expected to be more significant due to the small

6


Page 7 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


138

mass of the proton.33 Thus, the recrossing factor Γ and non-equilibrium factor g are assumed to be 1 in

139

this study. The tunneling factor κ can be estimated with the Wigner tunneling approximation: 33,34

140

κ = 1+

1 h |ν ≠ | 2 ( ) 24 k BT

(5)

141

where v≠ is the imaginary frequency of TS. Although equation (5) describes approximately the nature

142

of the tunneling effect, it is sufficient since it usually yields the correct order of magnitude.35-37 The

143

hydrolysis constant pKa of Al3+ in aqueous solution is estimated from the total Gibbs free energy

144

change ΔGT° of the overall hydrolysis reaction:38,39

145

pKa =ΔGT°/2.303RT

(6)

146

7



147

3.

148

3.1. The traditional spontaneous proton dissociation mechanism (pathway-I)

149

The spontaneous proton dissociation pathway is obtained with eleven explicit solvent waters (Nm’ =

150

11). The solvent waters are arranged based on a complete second hydration shell of Al3+ containing

151

twelve solvent waters with S6 symmetry,40 by removing one solvent water molecule in the proton

152

dissociation direction to leave a hole for the dissociating proton moving from the inner hydration shell

153

into the bulk water. The optimized configurations of the R, TS and P species are listed in Figure 1, and

154

the structural parameters are listed in Table 1. In R, the distance R(O-H(I)) between the coordinated O

155

atom and the dissociating proton-(I) is 0.977 Å. As the reaction begins, proton-(I) moves towards the

156

bulk water through the leaving hole. In TS, the distance R(O-H(I)) stretches to 1.428 Å. Nevertheless,

157

in the following P, the proton binds back to its initially bonded O atom instead of further moving into

158

the bulk water, and the distance R(O-H(I)) shrinks to 0.977 Å. Table 2 lists the relative thermodynamic

159

parameters. The zero-point contributions and tunneling are both important quantum effects in

160

calculating reaction rate constants. For pathway-I, the zero-point contribution (ΔEZPE(0K),a≠ = -18.1

161

kJ/mol) and tunneling effect (κ = 11.415) each increases the kH+ by 3 and 1 orders of magnitude.

162

However, the electronic energy barrier is so high (ΔEelect(0K),a≠ = 126 kJ/mol) that even the two

163

quantum effects apparently accelerate the reaction rate constant, the estimated kH+ (6.52×10-6 s-1) from

164

γH+ and ΔG298,a≠ (109 kJ/mol, including the zero-point energy term) is far smaller than the experimental

165

data (~105 s-1).5,6 The results indicate that the probability of the protons on the Al3+ coordinated waters

166

spontaneously dissociating into the bulk water is quite small, since the ionized protons will soon return

167

to coordinated O atoms.

Results and discussion

168

8


Page 8 of 26

Page 9 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.861 1.651

1.911

0.977

1.670

1.859 1.710

1.680

1.688

1.701

1.882 1.880

1.946

proton-(I)

1.588

1.904

1.684

1.690

1.980

1.711 1.666

1.684

1.876

1.925

1.921

1.913

1.727 1.679

1.710

1.932 1.911 1.909

1.699 1.680

1.968

1.705

0.977

1.670

1.960

1.607

1.651

1.910

proton-(I)

1.913

1.698

1.883

1.946

1.930

1.863 1.889

1.666

1.879 1.930 1.918

1.927

1.711

1.684 1.684

1.682

1.701

1.992

1.862 1.730

1.428

1.705

1.916

1.588

1.913 1.881

proton-(I)

1.932 1.908 1.911 1.921 1.904

1.699 1.959

1.845

1.773

1.888

1.883

169 170

TS (3272.52i cm-1)

R

P (The dissociating proton returns)

171

Figure 1. The optimized reactant, transition state and product configurations in the spontaneous

172

proton dissociation pathway-I (Nm’ = 11)

173 174

Table 1

175

pathway-I (Å) R(Al-OH2)II d ⎯R(Al-OH2)II e 4.030, 3.958, 3.917, 3.970, 3.900, 3.966, 3.949 3.922, 3.947, 3.913, 3.941, 3.975 TS 1.918, 1.913, 1.927, 1.930, 1.930, 1.879 1.916 1.428 3.990, 3.979, 3.955, 4.008, 3.926, 3.985, 3.969 3.959, 3.989, 3.933, 4.001, 3.946 P 1.909, 1.904, 1.913, 1.921, 1.911, 1.932 1.915 0.977 4.031, 3.957, 3.919, 3.970, 3.900, 3.965, 3.949 3.922, 3.947, 3.913, 3.941, 3.976 a The distances between Al3+ and the inner-shell coordination waters; b The average distance between Al3+ and the inner-shell coordination waters; c The distance between the coordinated O atom and the dissociation proton; d The distances between Al3+ and the second hydration shell solvent waters; e The average distance between Al3+ and the second hydration shell solvent waters. R(Al-OH2)I a 1.908, 1.904, 1.913, 1.921, 1.911, 1.932

Species R

176 177 178 179

Structural parameters of the reaction species in the spontaneous proton dissociation

180

Table 2

181

dissociation pathway-I a Species

182 183

⎯R(Al-OH2)I b 1.915

R(O-H(I)) c 0.977

Relative thermodynamic parameters and reaction rate constant for the spontaneous proton

ΔEelect(0K) (kJ/mol)

ΔEZPE(0K) (kJ/mol)

ΔE0(0K) (kJ/mol)

ΔE298 (kJ/mol)

ΔH298 (kJ/mol)

ΔS298 (J/mol-K)

ΔG298

R

0.0

0.0

0.0

0.0

0.0

0.0

0.0

TS P

126 0.0

-18.1 0.1

108 0.1

107 0.1

107 0.1

-4.7 0.6

109 -0.1

a

γH+

kTST (s-1)

kH+ (s-1)

kH+(expt) 5,6 (s-1)

11.415

5.71×10-7

6.52×10-6

1.09×105, 7.9×104

(kJ/mol)

The thermodynamic values are relative to R.

9



184

3.2. The conventional bulk water-assisted proton dissociation mechanism (pathway-II)

185

The conventional bulk water-assisted proton dissociation mechanism is proposed to model using the

186

Al(H2O)63+·12H2O cluster which has a complete second hydration shell with S6 symmetry (Nm’ =

187

12).40 In this cluster, the solvent water molecule which is adjacent to the leaving proton is selected as

188

an approximation of the bulk water that assists the proton dissociation. The TS structure for the proton

189

on the coordinated water of Al3+ dissociating into the adjacent solvent water molecule is not found,

190

because the proton always comes back to its initially bonded O atom during the optimizations and

191

forms the stable Al(H2O)63+·12H2O structure without imaginary frequencies (Figure 2(a)). In order to

192

verify whether the conventional bulk water-assisted proton dissociation pathway can occur or not, we

193

break an O-H bond in Al(H2O)63+ and move the proton to an adjacent solvent water molecule to

194

construct the Al(OH)(H2O)52+·H3O+(H2O)11 cluster which is close to the product configuration for the

195

proton dissociation, and then optimize the structure to its stable configuration. It turns out that the

196

proton which is enforced to dissociate comes back and binds to the inner-shell OH- in the final

197

optimized stable configuration, reforming the initial Al(H2O)63+·12H2O geometry again (Figure 2(b)).

198

In the CPMD simulations by Coskuner et al., Liu et al. and Ikeda et al., it is observed that the protons

199

on the coordinated waters diffuse to their nearest water and form Zundel-like or H3O+-like structures

200

occasionally, and then the protons come back very quickly.8,9,11 In the AIMD simulations by Lubin et

201

al., the protons on the coordinated waters dissociate into surrounding solvent water molecules to form

202

H3O+ only at elevated temperatures of about 800 K.13 In summary, our calculation results and the

203

literature simulations demonstrate that it is hard for a proton on the inner-shell coordinated water of

204

Al3+ to dissociate into the bulk water through the spontaneous or the bulk water-assisted proton

205

dissociation mechanisms, indicating that the electrostatic effects between Al3+ and its coordinated

206

waters alone can not fully account for the spontaneous hydrolysis of Al3+.7

207

10


Page 10 of 26

Page 11 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.968

1.899

1.875 1.184

1.676

1.898

1.693

1.713

1.875

1.500

1.613

1.004

1.665 1.897

1.915 1.914 1.915

1.680

1.954

1.915

1.694

1.692

1.914

1.954

1.918

1.917

1.919

1.918

1.694

1.675

1.876

1.676

1.698

1.890

1.696

1.682 1.877

1.697

1.678 1.866

1.970

1.889

1.931

1.689

1.920

2.469 1.676

1.689

1.947 1.965

1.677

1.915 1.891

1.890 1.903

208 209

Initial structure for TS

210

Finally optimized structure for TS

(a) TS for the bulk water-assisted proton dissociation

1.890 1.897

1.677 1.721

1.692

1.968

1.915

1.693

1.676

1.914

2.469

1.694 1.898

1.916 1.917 1.915 1.915

1.693

1.692

1.916

1.678

1.947

1.916 1.876

1.680

1.676

1.678

1.946 1.954

1.899 1.693

1.692 1.875

1.695

1.915

1.682 0.994

1.690

1.888

1.942

1.879

1.680

1.877

1.696

1.914 1.915 1.915

1.675

1.947

1.956 0.980

1.680 1.694

1.891

1.943

1.954

1.681 1.690

1.878

1.879

211 Initial structure for Al(OH)(H2O)52+·H3O+(H2O)11

212

Finally optimized stable structure for Al(OH)(H2O)52+·H3O+(H2O)11

213

(b) The Al(OH)(H2O)52+·H3O+(H2O)11 cluster

214

The optimization results for TS and the Al(OH)(H2O)52+·H3O+(H2O)11 cluster in the bulk

215

Figure 2.

216

water-assisted proton dissociation pathway-II (Nm’ = 12)

217 218

3.3. The second-shell water-assisted synergistic proton dissociation mechanism (pathway-III)

219

For pathway-III, eight explicit solvent water molecules are added in the second hydration shell of Al3+

220

to consider the short-range solvent effects (Nm’ = 8). The arrangement of the eight waters meets the

221

condition that the dissociating proton is H-bonded to the O atom of a solvent water, and a proton on

222

this solvent water is H-bonded to the O atom of another solvent water. Figure 3 lists the optimized

223

configurations of the R, TS and R species and Table 3 lists their structural parameters.

224

In R, Al(H2O)63+ is an approximate octahedral. The bond length between Al3+ and the coordinated

225

water on which the dissociating proton-(I) readies to leave is 1.919 Å. The distance R(O-H(I)) between 11



Page 12 of 26

226

the coordinated O atom and proton-(I) is 1.006 Å, and the distance between proton-(I) to the O atom of

227

its acceptor, the solvent water-a, R(H(I)-Oa) = 1.611 Å. On water-a, proton-(II) is about to dissociate

228

synergistically with proton-(I), and it has a distance of R(Oa-H(II)) = 0.981 Å to the O atom of water-a

229

and a distance of R(H(II)-Ob) = 1.844 Å to the O atom of its acceptor, the solvent water-b. As the

230

synergistic proton dissociation begins, proton-(I) and proton-(II) move synchronously along the

231

H-bond wire from their donator waters to their acceptor waters, respectively. In TS, the coordinated

232

water on which proton-(I) dissociates transforms into OH-, and its distance to the central Al3+ shrinks

233

to 1.808 Å. The formation of OH- results in several O-Al-O bond angles in the octahedral deviating

234

from 90°. The distances R(O-H(I)) and R(H(I)-Oa) are 1.481 and 1.040 Å, respectively. The old O-H

235

bond between the coordinated O atom and proton-(I) is broken and the new O-H bond between

236

proton-(I) and the O atom of the solvent water-a is nearly formed. The distances R(Oa-H(II)) and

237

R(H(II)-Ob) are 1.318 and 1.116 Å, respectively. At this point, proton-(II) locates between the two O

238

atoms of the solvent water-a and -b, and this local structure is similar to the Zundel ion. In P, the

239

distance R(H(I)-Oa) further shortens to 1.016 Å, and the new O-H bond forms. The distance R(H(II)-Ob)

240

decreases to 1.057 Å, and the Zundel-like structure converts into H3O+-like structure. The overall

241

second-shell water-assisted synergistic proton dissociation process is similar to the Grotthuss

242

mechanism which describes the motion of an excess proton in water along a network of H-bonds.41

243

After the H3O+ forms in P, it leaves the second hydration shell and enters the bulk water in the

244

next step. It is assumed that the solvent water-a and the protonated water-b move into the bulk water

245

together

246

Al(OH)(H2O)53+·4H2O clusters are optimized to stable species, respectively (see S2.2 in SI). The

247

inner-shell of Al(OH)(H2O)53+·4H2O is a distorted octahedral with an Al-OH bond length of 1.772 Å.

248

The average bond length of the five inner-shell Al-OH2 bonds is 1.952 Å, longer than that of the six

249

Al-OH2 bonds in Al(H2O)63+ in R (1.913 Å), reflecting the labilizing effect of OH- on other inner-shell

250

coordinated waters. In the H3O+(H2O)3 cluster, H3O+ is unsymmetrical as the three O-H bond lengths

251

are 1.035, 0.979 and 1.052 Å, respectively, which is due to that the three O-H bonds have different

252

solvation environments.

with

their

directly

H-bonded

solvent

water-c

and

-d.

The

H3O+(H2O)3

and

253

Table 4 indicates that the ΔG298,a≠ for the second-shell water-assisted synergistic proton

254

dissociation is 44.2 kJ/mol and the estimated reaction rate constant kH (= γH kTST) is 1.14×105 s-1, in +

12


+

Page 13 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


255

close agreement with the experimental values of 1.09×105 and 7.9×104 s-1.5,6 The zero-point

256

contribution (ΔEZPE(0K),a≠ = -9.0 kJ/mol) accelerates the reaction rate constant by about 2 orders of

257

magnitude, while the tunneling effect (κ = 1.023) has very little influence on kH . Comparing with the

258

single proton dissociation pathway-I, the quantum effects show less influences on the synergistic

259

proton dissociation pathway-III, while the smaller electronic energy barrier for pathway-III

260

(ΔEelect(0K),a≠ = 54.2 kJ/mol) is the root cause for its much higher rate constant.

+

261

The ΔG298,r≠ from R to P is -19.2 kJ/mol, while ΔG° for the H3O+(H2O)3 cluster to move from the

262

second hydration shell of Al3+ in P into the bulk water is 52.4 kJ/mol. The total chemical reaction

263

equation for the second-shell water-assisted synergistic proton dissociation mechanism of the

264

first-order Al3+ hydrolysis reaction can be written as:

265

Al(H2O)63+·2H2O → Al(OH)(H2O)52+ + H3O+·H2O

(7)

266

Using similar approaches in literature,42,43 the total Gibbs free energy change ΔGT° for the overall

267

reaction pathway of equation (7) equals the sum of ΔG298,r≠ and ΔG°, and is calculated as 33.2 kJ/mol.

268

Based on equation (6), the pKa1 for the first-order hydrolysis of Al3+ is calculated as 5.82, which agrees

269

with the literature value of 5.00.15

270

Therefore, it is proposed that in acidic aqueous solution, the main reaction mechanism for natural

271

Al3+ hydrolysis is the second-shell water-assisted synergistic proton dissociation. This pathway is also

272

supported by cross-validation calculations with the BLYP optimization method (see S3 in SI for

273

details). The participation of the solvent water molecules in the second hydration shell of Al3+ is

274

crucially important in the synergistic proton dissociation pathway, and this is a characteristic difference

275

between the hydrolysis mechanisms of Al3+ and other metal ions (such as Fe3+ and Cr3+).7

276

13



a

proton-(I) 1.942

c

1.982

1.611

proton-(I)

0.975 0.981

1.908

1.600

3.935 1.919

1.696

1.481

1.724

1.882

d

1.968

1.731

1.003 1.041 1.479

1.981

d

d

1.917

1.882

1.734

1.735

1.575

b

1.057

1.905 1.882

proton-(II)

1.443

4.548

1.799 1.955

1.917

1.502

1.885

1.939

1.702

1.563

0.990

1.570

1.900

1.901

a

3.877

0.976 1.033

4.546

1.808 1.911 1.954 1.962 1.984

b

0.995 1.686

1.626

b

1.116

c 1.911 1.016

proton-(II)

1.318

3.837

0.975 1.591

1.893

0.973

1.844

3.919

1.897 1.930 1.933 1.915

1.616

proton-(I)

a

1.040

proton-(II)

1.006

2.120

c

Page 14 of 26

1.585

277 278

TS (152.40i cm-1)

R

a

proton-(I)

1.648

0.979

0.979 2.028

1.772 1.923 1.974

1.750

proton-(II)

1.496

c

1.947

1.035

1.983

1.931

b

0.979 1.052

1.775 1.896

P

1.794 1.430

1.599

d

279 Al(OH)(H2O)52+·4H2O

280 281

H3O+·3H2O

282

Figure 3

The optimized reactant, transition state, product configurations in the second-shell

283

water-assisted synergistic proton dissociation process and the finally formed stable Al(OH)(H2O)52+

284

and H3O+ configurations (Nm’ = 8) (The solvent waters that move into the bulk water are labeled gray)

285 286

Table 3

287

proton dissociation pathway-III (Å)

Structural parameters of the reaction species in the second-shell water-assisted synergistic

1.930, 1.915, 1.882, 1.936, 1.897, 1.919 1.954, 1.984, 1.900, 1.962, 1.911 1.955, 1.981, 1.905, 1.968, 1.917 1.947, 1.983, 1.931, 1.974, 1.923 -

P 2+

Al(OH)(H2O)5 ·4H2O +

295

H3O ·3H2O

b

R(Al-OH)I

c

R(O-H(I))

d

R(H(I)-Oa)

e

R(Oa-H(II))

f

R(H(II)-Ob)

1.913

-

1.006

1.611

0.981

1.844

1.942

1.808

1.481

1.040

1.318

1.116

g

R(Al-OH2)II

h

⎯R(Al-OH2)II

1.945

1.799

1.570

1.016

1.443

1.057

1.952

1.772

-

-

-

-

3.921, 3.942, 4.130, 3.808, 3.931, 4.698, 3.935, 3.919 3.909, 3.963, 4.144, 3.822, 3.965, 4.590, 3.837, 4.546 3.911, 3.985, 4.166, 3.808, 3.946, 4.602, 3.877, 4.548 3.782, 3.984, 4.195, 4.014

-

-

-

0.979

1.496

1.035

-

i

4.036 4.097 4.105 3.994 -

a

The distances between Al3+ and the inner-shell coordination waters; b The average distance between Al3+ and the inner-shell coordination waters; c The distance between Al3+ and the inner-shell OH-; d The distance between the coordinated O atom and the dissociation proton-(I); e The distance between the dissociation proton-(I) atom and the O atom of the solvent water-a; f The distance between the O atom of solvent water-a and the dissociation proton-(II); g The distance between the dissociation proton-(II) atom and the O atom of the solvent water-b; h The distances between Al3+ and the second hydration shell solvent waters; i The average distance between Al3+ and the second hydration shell solvent waters.

Table 4

Relative thermodynamic parameters and reaction rate constant for the second-shell

water-assisted synergistic proton dissociation pathway-III a Species

ΔEelect(0K)

ΔEZPE(0K)

ΔE0(0K)

ΔE298

ΔH298

ΔS298

ΔG298

(kJ/mol)

(kJ/mol)

(kJ/mol)

(kJ/mol)

(kJ/mol)

(J/mol-K)

(kJ/mol)

R

0.0

0.0

0.0

0.0

0.0

0.0

0.0

TS

54.2

-9.0

45.2

43.4

43.4

-2.7

44.2

P

-6.2

-13.1

-19.3

-19.7

-19.7

-1.8

-19.2

127

-21.7

105

111

113

268

33.2

2+

296 297

⎯R(Al-OH2)I

R(Al-OH2)I

R TS

288 289 290 291 292 293 294

a

Species

+

Al(OH)(H2O)5 ·4H2O + H3O ·3H2O

b

a

+

γH

-1

(s ) 1.023

1.11×10

+

kH

-1

(s )

+ 5,6 (expt)

kH

kTST

-1

(s ) 5

1.14×10

5

5

1.09×10 , 7.9×10

4

The thermodynamic values are relative to R; b The thermodynamic parameters of the reaction system after the H3O+·3H2O moving into the bulk water relative to R.

14


Page 15 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


298 299

3.4. Environmental significance

300

The results in this study have important environmental implications:

301

(1) Generally, environmental processes like the proton transfer reactions in the Al3+ hydrolysis are

302

difficult to simulate with molecular dynamics methods, due to that the reactions in aqueous solution

303

are sensitive to details of the solvation and H-bonding networks, and more importantly, most

304

environmental processes are rare events that are too infrequent to be simulated in a dynamic

305

calculation.44 In this study, the estimated kH for the second-shell water-assisted synergistic proton

306

dissociation reaction and the pKa calculated for Al3+ with the same pathway are both in excellent

307

agreement with the reported experimental values, demonstrating that the DFT-CM method is well

308

applicable in modeling rare events and aqueous reactions in the natural environment;

+

309

(2) The proton dissociation pathway for the spontaneous Al3+ hydrolysis is proposed to have the

310

important characteristics of synergistic and water-assisted. It is noticeable that this molecular

311

mechanism is quite different from the traditional view that only the inner-shell proton in Al(H2O)63+

312

dissociates to form Al(OH)(H2O)52+. It is actually difficult for the inner-shell protons to dissociate

313

without the synergistic proton dissociation on its H-bonded adjacent solvent water. The role of adjacent

314

solvent waters was indeed undervalued in the past. In other environmental processes, similar

315

water-assisted synergistic proton dissociation pathway has also been found for the acid-base reactions

316

such as the hydrolysis of SO2 and the formation of NH4HSO4.45,46 It is reasonable to believe that the

317

simple elementary reaction steps may have more complicated reaction mechanisms than expected;

318

(3) The results in this study are helpful in future deep investigating a series of fundamental issues

319

in the hydrolysis and polymerization chemistry of the aqueous Al species, such as the proton

320

dissociation mechanisms of the Al(OH)2+ to form Al(OH)2+, Al(OH)3, Al(OH)4- and further

321

polymerizes to Al2(OH)2(H2O)84+, Keggin-AlO4Al12(OH)24(H2O)127+ as well as other species. It is also

322

advantageous for the researches on the influences of the titration rates and OH- concentration on the

323

Al3+ hydrolysis and polymerization pathways in base titration processes, as well as the reverse

324

protonation mechanisms of the hydrolyzed Al species in the acidification reactions.47-49 For example,

325

in the polyoxocation Keggin-AlO4Al12(OH)24(H2O)127+, there are one type of oxo-bridge and two types

326

of hydroxo-bridges, but their formation pathways have not been known yet. We expect that studying 15



327

the proton dissociation kinetics on the coordinated O atoms will be helpful in establishing the

328

formation mechanisms of the oxo- and hydroxo-bridges in the Al polyoxocations. In addition, there are

329

three sets of structurally distinct protons in Keggin-AlO4Al12(OH)24(H2O)127+, and their lifetimes have

330

been estimated from 1H NMR experiments which is helpful in constraining the proton dynamics on

331

aluminum-hydroxide material surfaces.50 The lifetime of a proton on a bound water in

332

Keggin-AlO4Al12(OH)24(H2O)127+ is about 2×10-4 s at 298 K,50 about 1 order of magnitude larger than

333

the lifetime of a proton in Al(H2O)63+ (~10-5 s).5,6 Despite the small magnitude difference between the

334

two lifetimes, the protons on the Keggin-AlO4Al12(OH)24(H2O)127+ bound waters and the Al(H2O)63+

335

coordinated waters may have similar dissociation mechanisms. The lifetimes of the protons on the two

336

distinct sets of hydroxo-bridges are 0.013 and 0.2 s, respectively.50 However, these two kinds of

337

hydroxyl protons can not be distinguished in experiments. If the DFT-CM method is used to model the

338

kinetic dissociation reactions of the two kinds of hydroxyl protons, it would be possible to identify

339

their lifetimes reasonably. In future applications, the DFT-CM method can be extended to study the

340

micromorphology and elementary reaction kinetics of Al and other metal ion species in heterogeneous

341

or non-aqueous environments, such as mineral or material surfaces, aerosols, flocs and sediments, as

342

well as the biological organisms, to explore the problems that are difficult to solve with traditional

343

experimental methods.51-57

344 345

4.

346

In this study, the density functional calculations elucidate a second-shell water-assisted synergistic

347

proton dissociation mechanism as the main mechanism for the first-order spontaneous hydrolysis of

348

Al3+ in aqueous solution. The reaction pathway proceeds via a concerted dissociation of two protons

349

from two H-bonded inner- and second-shell waters. The magnitudes of the estimated proton

350

dissociation rate constant (kH+ = 1.14×105 s-1) and equilibrium constant (pKa1 = 5.82) are in good

351

agreement with the experimental data. The calculation results show that the electrostatic effects

352

between Al3+ and its coordinated waters alone can not fully account for the spontaneous hydrolysis of

353

Al3+, and the traditional spontaneous dissociation mechanism of a single inner-shell coordinated water

354

proton (direct dissociation or assisted by a bulk solvent water) is very unlikely to occur in real aqueous

355

solution. The results in this study provide new insights into the microscopic molecular mechanism of

Conclusion

16


Page 16 of 26

Page 17 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


356

the elementary hydrolysis reaction of aqueous Al3+, and lay foundation for future deep investigating

357

the hydrolysis and polymerization chemistry of aqueous Al species.

358 359

Acknowledgements

360

This project is supported by the National Natural Science Foundation of China (No. 21177054). We are

361

grateful to the High Performance Computing Center of Nanjing University for doing the numerical

362

calculations in this paper on its Blade cluster system.

363 364

Appendix Supporting Information (SI)

365

S1.

Summarization for previous theoretical studies of the Al3+ hydrolysis pathway in literature

366

S2.

Testing results with different solvation models

367

S3.

Testing results with BLYP method

368

S4.

Cartesian coordinates of all reaction species in Al3+ hydrolysis reaction pathways (Å)

17



369

References

370

(1)

371

through integrated urban water management. Science 2014, 345, 812-814.

372

(2)

373

for five-coordination in AlOH(aq)2+ ion. Science 2005, 308, 1450-1453.

374

(3)

375

in polluted streams. Science 2002, 297, 2245-2247.

376

(4)

377

p4/p112-113.

378

(5)

379

J. Phys. Chem. 1968, 72 (1), 301-304.

380

(6)

381

water in dilute acid. Participation of water molecules in proton transfer. J. Am. Chem. Soc. 1969, 91

382

(10), 2413-2422.

383

(7)

384

Angew. Chem. Int. Ed. 2007, 46 (41), 7853-7855.

385

(8)

386

Chem. A 2010, 114 (41), 10981-10987.

387

(9)

388

Si(OH)4 and Al(H2O)63+ in aqueous solution. Geochim. Cosmochim. Acta 2010, 74 (2), 510-516.

389

(10) Ikeda, T.; Hirata, M.; Kimura, T. Hydrolysis of Al3+ from constrained molecular dynamics. J.

390

Chem. Phys. 2006, 124 (7), 074503.

391

(11) Ikeda, T.; Hirata, M.; Kimura, T. Ab initio molecular dynamics study of polarization effects on

392

ionic hydration in aqueous AlCl3 solution. J. Chem. Phys. 2003, 119 (23), 12386-12392.

Pikaar, H.; Sharma, K. R.; Hu, S.; Gernjak, W.; Keller, J.; Yuan, Z. Reducing sewer corrosion

Swaddle, T. W.; Rosenqvist, J.; Yu, P.; Bylaska, E.; Phillips, B. L.; Casey, W.H. Kinetic evidence

Furrer, G.; Phillips, B. L.; Ulrich, K.-U.; Pöthig, R.; Casey, W.H. The origin of aluminum flocs

Base, C. F.; Mesmer, R. E. The Hydrolysis of Cations, John Wiley & Sons, Inc, New York, 1976,

Holmes, L. P.; Cole, D. L.; Eyring, E. M. Kinetics of aluminum ion hydrolysis in dilute solutions.

Fong, D.-W.; Grunwald, E. Kinetic study of proton exchange between the Al(OH2)63+ ion and

Coskuner, O.; Jarvis, E. A. A.; Allison, T. C. Water dissociation in the presence of metal ions.

Coskuner, O. Single ion and dimerization studies of the Al(III) ion in aqueous solution. J. Phys.

Liu, X. D.; Lu, X. C.; Meijer, E. J.; Wang, R. C.; Zhou, H. Q. Acid dissociation mechanisms of

18


Page 18 of 26

Page 19 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


393

(12) Amira, S.; Spångberg, D.; Hermansson, K. OD vibrations and hydration structure in an Al3+(aq)

394

solution from a Car-Parrinello molecular-dynamics simulation. J. Chem. Phys. 2006, 124 (10), 104501.

395

(13) Lubin, M. I.; Bylaska, E. J.; Weare, J. H. Ab initio molecular dynamics simulations of aluminum

396

ion solvation in water clusters. Chem. Phys. Lett. 2000, 322 (6), 447-453.

397

(14) Burgess, J. Ions in Solution. Basic Principles of Chemical Interactions, 2nd ed., Horwood

398

Publishing Chichester, 1999, p62-65.

399

(15) Nordstrom, D. K.; May, H. M. Aqueous equilibrium data for mononuclear aluminum species. In

400

The Environmental Chemistry of Aluminum, 2nd ed.; G. Sposito, Ed., CRC Press, New York, 1996,

401

p34-35.

402

(16) Richens, D. T. The Chemistry of Aqua Ions, John Wiley & Sons, New York, 1997, p44-47.

403

(17) Rotzinger, F. P. Treatment of substitution and rearrangement mechanisms of transition metal

404

complexes with quantum chemical methods. Chem. Rev. 2005, 105 (6), 2003-2037.

405

(18) Weinhold, F. Kinetics and mechanism of water cluster equilibria. J. Phys. Chem. B 2014, 118

406

(28), 7792-7798.

407

(19) Erras-Hanauer, H.; Clark, T.; van Eldik, R. Molecular orbital and DFT studies on water

408

exchange mechanisms of metal ions. Coord. Chem. Rev. 2003, 238-239 (3), 233-253.

409

(20) Zhan, C. G.; Landry, D. W.; Ornstein, R. L. Reaction pathways and energy barriers for alkaline

410

hydrolysis of carboxylic acid esters in water studied by a hybrid supermolecule-polarizable continuum

411

approach. J. Am. Chem. Soc. 2000, 122 (11), 2621-2627.

412

(21) Hanauer, H.; Puchta, R.; Clark, T.; van Eldik, R. Searching for stable, five-coordinated aquated

413

Al(III) species. Water exchange mechanism and effect of pH. Inorg. Chem. 2007, 46 (4), 1112-1122.

414

(22) Qian, Z. S.; Feng, H.; Yang, W. J.; Miao, Q.; He, L. N.; Bi, S. P. Supermolecule density

415

functional calculations on the water exchange of aquated Al(III) species in aqueous solution. Chem.

416

Comm. 2008, 3930-3932.

19



417

(23) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum mechanical continuum solvation models. Chem.

418

Rev. 2005, 105 (8), 2999-3093.

419

(24) Tomasi, J. Thirty years of continuum solvation chemistry: a review, and prospects for the near

420

future. Theor. Chem. Acc. 2004, 112 (4), 184-203.

421

(25) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.;

422

Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.;

423

Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.;

424

Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai,

425

H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.;

426

Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.;

427

Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich,

428

S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.;

429

Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu,

430

G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.;

431

Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.;

432

Gonzalez, C.; Pople, J. A. Gaussian 03 (Revision B.02), Gaussian, Inc.,Wallingford, CT, 2004.

433

(26) Becke, D. Density-functional thermochemistry: III. The role of exact exchange. J. Chem. Phys.

434

1993, 98 (7), 5648-5652.

435

(27) Yang, Lee, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a

436

functional of the electron density. Phys. Rev. B 1988, 37 (2), 785-789.

437

(28) Gonzalez, C.; Schlegel, H. B. Reaction path following in mass-weighted internal coordinates. J.

438

Phys. Chem. 1990, 94 (14), 5523-5527.

439

(29) Shi, W. J.; Jin, X. Y.; Dong, S. N.; Bi, S. P. Theoretical investigation of the thermodynamic

440

structures and kinetic water-exchange reactions of aqueous Al(III)-salicylate complexes. Geochim.

441

Cosmochim. Acta 2013, 121 (6), 41-53.

442

(30) Rotzinger, F. P. The water-exchange mechanism of the [UO2(OH2)5]2+ ion revisited: The 20


Page 20 of 26

Page 21 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


443

importance of a proper treatment of electron correlation. Chem. Eur. J. 2007, 13 (3), 800-811.

444

(31) Takano, Y.; Houk, K. N. Benchmarking the conductor-like polarizable continuum model (CPCM)

445

for aqueous solvation free energies of neutral and ionic organic molecules. J. Chem. Theory Comput.

446

2005, 1 (1), 70-77.

447

(32) Garcia-Viloca, M.; Gao, J. L.; Karplus, M.; Truhlar, D. G. How enzymes work: Analysis by

448

modern rate theory and computer simulations. Science 2004, 303, 186-195.

449

(33) Bao, J. L.; Truhlar, D. G. Vibrational transition state theory: theoretical framework and recent

450

developments. Chem. Soc. Rev. 2017, 46, 7548-7596.

451

(34) Wigner, E. Concerning the excess of potential barriers in chemical reactions. Z. Phys. Chem. Abt.

452

B 1932, 19 (2/3), 203-216.

453

(35) Romero, E. E.; Hernandez, F. E. Solvent effect on the intramolecular proton transfer of the

454

Watson and Crick guanine-cytosine and adenine-thymine base pairs: a polarizable continuum model

455

study. Phys. Chem. Chem. Phys. 2018, 20, 1198-1209.

456

(36) Pina, J.; Sarmento, D.; Accoto, M.; Gentili, P. L.; Vaccaro, L.; Galvão, A.; de Melo, J. S. S.

457

Excited-state proton transfer in indigo. J. Phys. Chem. B 2017, 121, 2308-2318.

458

(37) Arabi, A. A.; Matta, C. F. Effects of external electric fields on double proton transfer kinetics in

459

the formic acid dimer. Phys. Chem. Chem. Phys. 2011, 13, 13738-13748.

460

(38) Yang, W. J.; Qian, Z. S.; Miao, Q.; Wang, Y. J.; Bi, S. P. Density functional theory study of the

461

aluminium(III) hydrolysis in aqueous solution. Phys. Chem. Chem. Phys. 2009, 11 (14), 2396-2401.

462

(39) Kubicki, J. D. Self-consistent reaction field calculations of aqueous Al3+, Fe3+, and Si4+:

463

Calculated aqueous-phase deprotonation energies correlated with experimental ln(Ka) and pKa. J. Phys.

464

Chem. A 2001, 105 (38), 8756-8762.

465

(40) Bock, C. W.; Markham, G. D.; Katz, A. K.; Glusker, J. P. The arrangement of first- and

466

second-shell water molecules in trivalent aluminum complexes: Results from density functional theory

467

and structural crystallography. Inorg. Chem. 2003, 42 (5), 1538-1548. 21



468

(41) Geissler, P. L.; Dellago, C.; Chandler, D.; Hutter, J.; Parrinello, M. Autoionization in liquid water.

469

Science 2001, 291, 2121-2124.

470

(42) Mackenzie, R. B.; Dewberry, C. T.; Leopold, K. R. Gas phase observation and microwave

471

spectroscopic characterization of formic sulfuric anhydride. Science 2015, 349, 58-61.

472

(43) Hazra, M. K.; Sinha, A. Formic acid catalyzed hydrolysis of SO3 in the gas phase: A barrierless

473

mechanism for sulfuric acid production of potential atmospheric importance. J. Am. Chem. Soc. 2011,

474

133 (43), 17444-17453.

475

(44) Casey, W. H.; Rustad, J. R. Reaction dynamics, molecular clusters, and aqueous geochemistry.

476

Annu. Rev. Earth Planet. Sci. 2007, 35, 21-46.

477

(45) Li, L.; Kumar, M.; Zhu, C. Q.; Zhong, J.; Francisco, J. S.; Zeng, X. C. Near-barrierless

478

ammonium bisulfate formation via a loop-structure promoted proton-transfer mechanism on the

479

surface of water. J. Am. Chem. Soc. 2016, 138, 1816-1819.

480

(46) Liu, J. J.; Fang, S.; Wang, Z. X.; Yi, W. C.; Tao, F. M.; Liu, J. Y. Hydrolysis of sulfur dioxide in

481

small clusters of sulfuric acid: Mechanistic and kinetic study. Environ. Sci. Technol. 2015, 49,

482

13112-13120.

483

(47) Casey, W. H. Large aqueous aluminum hydroxide molecules. Chem. Rev. 2006, 106 (1), 1-16.

484

(48) Bi, S. P.; Wang, C. Y.; Cao, Q.; Zhang, C. H. Studies on the mechanism of hydrolysis and

485

polymerization of aluminum salts in aqueous solution: correlations between the “core-links” model and

486

“cage-like “Keggin-Al13 model. Coord. Chem. Rev. 2004, 248 (5-6), 441-455.

487

(49) Casey, W. H.; Swaddle, T. W. Why small? The use of small inorganic clusters to understand

488

mineral surface and dissolution reactions in geochemistry. Rev. Geophys. 2003, 41 (2), 381-393.

489

(50) Houston, J. R.; Phillips, B. L.; Casey, W. H. Residence times for protons bound to three oxygen

490

sites in the AlO4Al12(OH)24(H2O)127+ polyoxocation. Geochim. Cosmochim. Acta 2006, 70 (7),

491

1636-1643.

492

(51) Stack, A. G.; Kent, P. R. C. Geochemical reaction mechanism discovery from molecular 22


Page 22 of 26

Page 23 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


493

simulation. Environ. Chem. 2015, 12 (1), 20-32.

494

(52) Panasci, A. F.; McAlpin, J. G.; Ohlin, C. A.; Christensen, S. C.; Fettinger, J. C.; Britt, R. D.;

495

Rustad, J. R.; Casey, W. H. Cooperation between bound waters and hydroxyls in controlling

496

isotope-exchange rates. Geochim. Cosmochim. Acta 2012, 78 (2), 18-27.

497

(53) Wang, W. D.; Yang, H. W.; Jiang, J.; Zhu, W. P.; Jiang, Z. P. Reaction mechanisms of soluble

498

silicic acid with aluminum in natural water. Acta Chim. Sinica 2008, 66 (23), 2625-2630. (In Chinese)

499

(54) Jin, J.; Dong, S. N.; Hou, X. X.; Zhang, J.; Bi, S. P. Density functional theory studies on the

500

static structures and water exchange reaction of aluminum-8-hydroxyquinoline complexes. Environ.

501

Chem. 2016, 35 (6), 1125-1133. (In Chinese)

502

(55) Lemay, S.; White, H. Electrochemistry at the nanoscale: Tackling old questions, posing new

503

ones. Acc. Chem. Res. 2016, 49 (11), 2371-2371.

504

(56) D. L. Sedlak, Professor Einstein and the quantum mechanics. Environ. Sci. Technol., 2015, 49,

505

2585-2585.

506

(57) J. I. Schroeder, E. Delhaize, W. B. Frommer, M. L. Guerinot, M. J. Harrison, L. Herrera-Estrella,

507

T. Horie, L. V. Kochian, R. Munns, N. K. Nishizawa, Y.-F. Tsay, D. Sanders, Using membrane

508

transporters to improve crops for sustainable food production. Nature, 2013, 497, 60-66.

23



Page 24 of 26

Table of Content

(3.33 inch × 1.88 inch)

The main reaction pathway for natural hydrolysis of Al3+ in aqueous solution is the second-shell water-assisted synergistic proton dissociation on the Al3+ inner-shell coordinated water.

24


Page 25 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table of Contents

DFT studies on the water-assisted synergistic proton dissociation mechanism for the spontaneous hydrolysis reaction of Al3+ in aqueous solution Shaonan Dong, Wenjing Shi, Jing Zhang and Shuping Bi* School of Chemistry and Chemical Engineering, State Key Laboratory of Coordination Chemistry of China & Key Laboratory of MOE for Life Science, Nanjing University, Nanjing 210023, China a

proton-(I) 1.942

c

1.982

1.611 3.935 3.919

1.591

b

0.995 1.686

1.724

1.808 1.911 1.954 1.962 1.984

1.626

b

0.976 1.033

d

1.731

1.968

(II)

proton-(II)

1.057

b

1.003 1.041

4.548

1.479

1.981

d

d 1.882

1.917

1.882 1.734

1.735

1.575

1.443

1.905

1.885

1.939 1.702

(I) 3.877

1.799 1.917 1.955

1.502

a 0.990

1.570

1.900

1.882 1.901 1.563

1.116

4.546

c 1.911 1.016

proton-(II)

1.318

1.481

1.616

1.893

0.973

3.837

0.975

1.930 1.897 1.933 1.915

2.120 1.040

1.844

1.919

1.696

c 1.908 proton-(II)

1.006

1.600

proton-(I)

a

proton-(I)

0.975 0.981

1.585

R

TS

P


ACS Paragon Plus 1 Environment


Page 26 of 26

Table of Content



DFT studies on the water-assisted synergistic proton dissociation

Recommend Documents