DFT studies on the water-assisted synergistic proton dissociation

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Article Cite This: ACS Earth Space Chem. 2018, 2, 269−277

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 S Supporting Information *

ABSTRACT: The kinetic mechanism of spontaneous aluminum ion (Al3+) hydrolysis reaction in aqueous solution is investigated using the density functional theory−quantum chemical cluster model method. Three typical reaction pathways for the spontaneous Al3+ hydrolysis reaction are modeled, including (1) the traditional spontaneous proton dissociation on the Al3+ inner-shell coordinated waters; (2) the conventional bulk water-assisted proton dissociation; and (3) the second-shell water-assisted synergistic dissociation of the protons on the Al3+ inner-shell waters. The results show that the electrostatic effects between Al3+ and its coordinated waters alone cannot fully account for the proton loss on an inner-shell coordinated water. It is suggested that the main reaction pathway for natural hydrolysis of aqueous Al3+ is the second-shell water-assisted synergistic proton dissociation, in which the participation of the second hydration shell is crucially important. The calculated synergistic proton dissociation rate constant, kH+ = 1.14 × 105 s−1, is in close agreement with the experimental results (1.09 × 105 s−1 and 7.9 × 104 s−1). The first hydrolysis equilibrium constant pKa1 of Al3+ is calculated as 5.82, also consistent with the literature value of 5.00. This work elucidates the molecular mechanism of the spontaneous Al3+ hydrolysis reaction in natural waters and has important environmental implications. KEYWORDS: aluminum ion, spontaneous hydrolysis mechanism, synergistic proton dissociation, water assisted, density functional theory

1. INTRODUCTION The hydrolysis chemistry of Al3+ in natural water is critical for environmental science, material chemistry, and medicine.1−3 In the pH range of 3−7, Al3+ undergoes hydrolysis from the hexahydrate Al(H2O)63+ to monomeric and polymeric hydroxyl Al species such as Al(OH)2+, Al(OH)2+, Al(OH)3, Al(OH)4−, and Al2(OH)2(H2O)84+ and the Keggin ion AlO4Al12(OH)24(H2O)127+.2,4 Historically, the metal ion hydrolysis is viewed as the stepwise removal of protons from hydrate water molecules (see S1 in the Supporting Information).4 Due to the complexity of the hydrolytic species of Al3+ and the experimental limitations, the microscopic details of the proton removal pathways for Al3+ hydrolysis are poorly understood.2 In the 1960s, Eyring et al.5 obtained the rate constant kH+ = 1.09 × 105 s−1 at 298 K for the first-order Al3+ hydrolysis reaction by dielectric relaxation, while Fong and Grunwald6 obtained the acid dissociation rate constant of Al(H2O)63+, kH+ = 7.9 × 104 s−1 at 298 K by 1H NMR. However, these macroscopic rate constants are actually measured for a collective of aqueous Al3+ ions, whereas the microscopic hydrolysis dynamics of a single Al3+ ion cannot be provided at the molecular level by these experiments. © 2018 American Chemical Society

Researchers have tried to draw the precise reaction pathway for aqueous Al3+ hydrolysis using theoretical methods such as molecular dynamics simulations, but they did not find a pathway whose kH+ agrees with the experimental data (see S1 in the Supporting Information).7−13 So far, there still lacks clear and unified understanding of the kinetic mechanism of the Al3+ hydrolysis reaction in aqueous solution. In literature, the first-order spontaneous hydrolysis reaction of Al3+ in aqueous solution is usually expressed using the following three different chemical reaction equations: Al3 + +H 2O → Al(OH)2 + +H+

(1)

Al(H 2O)6 3 + → Al(OH)(H 2O)52 + +H+

(2)

Al(H 2O)6 3 + +H 2O → Al(OH)(H 2O)52 + +H3O+

(3)

Received: Revised: Accepted: Published: 269

December 9, 2017 January 28, 2018 January 29, 2018 January 29, 2018 DOI: 10.1021/acsearthspacechem.7b00142 ACS Earth Space Chem. 2018, 2, 269−277

Article

ACS Earth and Space Chemistry Equation 1 describes that Al3+ interacts with one bulk water to form Al(OH)2+ and H+.4 In acidic aqueous solutions, Al3+ mainly exists in the form of Al(H2O)63+, not in the form of naked Al3+, thus it is not accurate to use eq 1 to describe the hydrolysis reaction of Al3+ in aqueous solution. Equation 2 describes that a proton in Al(H2O)63+ dissociates into the bulk water to form Al(OH)(H2O)52+ and H+,14 which reflects a traditional view of the metal ion hydrolysis mechanism; that is, the coordination of a metal ion to water molecules polarizes the water molecules and makes the spontaneous proton loss easier by electrostatics (Scheme 1a).14 Equation 3 describes that a

Al(H2O)63+, in which the proton moves directly into the bulk water. Pathway II: The conventional hydrolysis mechanism of the bulk water-assisted proton dissociation from a coordinated water in Al(H2O)63+, in which the proton moves into a bulk solvent water molecule which acts as the Brønsted base to accept the dissociated proton. In both pathways I and II, only one proton dissociates from the inner-shell of Al(H2O)63+. Pathway III: The second-shell water-assisted synergistic proton dissociation between the inner-shell and second hydration shell of Al3+. One solvent water molecule accepts the dissociating proton from an inner-shell water and donates one of its own protons to another solvent water molecule in the second hydration shell. Two protons dissociate synergistically, which is quite different from pathways I and II. 2.2. Treatment of the Solvent Effects. Four different solvation models, including the gas phase model (GP), the gas phase polarizable continuum model (GP-PCM), the gas phase supermolecule model (GP-SM), and the gas phase supermolecule polarizable continuum model (GP-SM-PCM) are used to simulate the three Al3+ hydrolysis reaction pathways. The short-range H-bond interactions between Al(H2O)63+ and its surrounding solvents are considered by adding explicit solvent water molecules in the second hydration shell of the gas phase Al(H2O)63+ and constructing the GP-SM clusters,20−22 whereas the long-range bulk solvent effect is considered by performing the optimizations and energy calculations of the GP-SM clusters in the polarizable continuum model (PCM).23,24 The results with GP-SM-PCM are discussed in the text, and the testing results with GP, GP-PCM, and GP-SM are summarized in S2.1 in the Supporting Information. In modeling different Al3+ hydrolysis pathways, the numbers (Nm′) and the arrangements of the explicit solvent water molecules added in the second hydration shell of Al3+ are determined accordingly. The influences of different Nm′ on the three Al3+ hydrolysis pathways are systematically examined, and the results are shown in S2.2 in the Supporting Information. 2.3. Computational Details. All DFT-CM calculations are performed using Gaussian 03 suite of programs.25 In the tested Al3+ hydrolysis pathways, the optimizations and frequency calculations of the reactants (R), transition states (TS), and products (P) are carried out in PCM using DFT at B3LYP/6311+G(d,p) level.26,27 The TS structures with one imaginary frequency are obtained from Berny optimizations, whereas the stable structures of R and P with no imaginary frequencies are obtained by further optimizing the structures achieved from the intrinsic reaction coordinate calculations.28,29 All optimizations and frequency calculations are conducted at 0 K. The electronic energies Eelect(0K) of the aqueous reaction species at 0 K are obtained from the single-point PCM calculations on the GPSM clusters using MP2/6-311+G(d,p) method. The thermodynamic parameters of the aqueous reaction species at 298.15 K such as the total energies E298, enthalpies H298, and Gibbs free energies G298 are calculated by adding zero-point energies EZPE(0K), thermal corrections Ecorr, enthalpy corrections Hcorr, and entropy corrections −TS298 onto Eelect(0K).25,30 EZPE(0K) is obtained from frequency calculations, and Ecorr, Hcorr, and S298 are obtained from the thermochemistry analysis performed at 298.15 K and 1 atm. The UAKS radius and the dielectric constant ε = 78.39 are used for water in the PCM calculations.31 The rate constants kH+ of the reaction pathways are estimated with the transmission coefficients γH+ and the

Scheme 1. Schematic Representations of (a) Traditional Spontaneous Proton Dissociation Mechanism and (b) Conventional Bulk Water-Assisted Proton Dissociation Mechanism of the First-Order Hydrolysis Reaction of Al3+

proton in Al(H2O)63+ dissociates and binds with a bulk solvent water molecule to form H3O+,15 which reflects another conventional view of the metal ion hydrolysis mechanism; that is, the hydrolysis reactions occur when the acidity of the protons on the coordinated water molecules reaches a level when a surrounding free solvent water molecule itself becomes a sufficient Brønsted base to remove a proton to form a hydroxyl metal species and H3O+ (Scheme 1b).16 Thus, eq 3 can also be viewed as a bulk water-assisted proton dissociation mechanism of the Al3+ hydrolysis. In previous general Car−Parrinello molecular dynamics (CPMD) simulations of the Al3+ hydrolysis pathways under ambient conditions, no event of the proton dissociation has been observed during the simulation time scale of tens of picoseconds,11−13 which is believed to be due to the fact that the spontaneous Al3+ hydrolysis is a rare event and is far beyond the simulation time scale accessible by present-day ab initio molecular dynamics.9,11 In this study, typical kinetic reaction pathways for Al3+ hydrolysis in aqueous solution are modeled using the density functional theory−quantum chemical cluster model (DFT-CM) method, which has been proven to be feasible for any desired reaction pathways independent of the reactivity of the systems, including fast and slow reactions on a time scale of picoseconds to seconds.17−19 The purpose of this study is to clarify the reasonable reaction pathways for Al3+ hydrolysis in aqueous solution and to lay a good foundation for further investigating the Al3+ hydrolysis and polymerization mechanisms.

2. COMPUTATIONAL METHODS 2.1. Three Reaction Pathways for Al3+ Hydrolysis. Referring to the different mechanisms of the Al3+ hydrolysis reaction in aqueous solution in literature, we tested the following three reaction pathways for the first-order Al3+ hydrolysis in this work: Pathway I: The traditional hydrolysis mechanism of the spontaneous proton dissociation from a coordinated water in 270

DOI: 10.1021/acsearthspacechem.7b00142 ACS Earth Space Chem. 2018, 2, 269−277

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Figure 1. Optimized reactant, transition state, and product configurations in the spontaneous proton dissociation pathway I (Nm′ = 11).

Table 1. Structural Parameters of the Reaction Species in the Spontaneous Proton Dissociation Pathway I (Å) R(Al−OH2)Ia

species R

R̅ (Al−OH2)Ib R(O−H(I))c

1.908, 1.904, 1.913, 1.921, 1.911, 1.932 1.918, 1.913, 1.927, 1.930, 1.930, 1.879 1.909, 1.904, 1.913, 1.921, 1.911, 1.932

TS P

1.915

0.977

1.916

1.428

1.915

0.977

R(Al−OH2)IId

R̅ (Al−OH2)IIe

4.030, 3.958, 3.917, 3.970, 3.900, 3.966, 3.922, 3.947, 3.913, 3.941, 3.975 3.990, 3.979, 3.955, 4.008, 3.926, 3.985, 3.959, 3.989, 3.933, 4.001, 3.946 4.031, 3.957, 3.919, 3.970, 3.900, 3.965, 3.922, 3.947, 3.913, 3.941, 3.976

3.949 3.969 3.949

a

The distances between Al3+ and the inner-shell coordination waters. bThe average distance between Al3+ and the inner-shell coordination waters. The distance between the coordinated O atom and the dissociation proton. dThe distances between Al3+ and the second hydration shell solvent waters. eThe average distance between Al3+ and the second hydration shell solvent waters. c

Table 2. Relative Thermodynamic Parameters and Reaction Rate Constant for the Spontaneous Proton Dissociation Pathway Ia species

ΔEelect(0K) (kJ/mol)

ΔEZPE(0K) (kJ/mol)

ΔE0(0K) (kJ/mol)

ΔE298 (kJ/mol)

ΔH298 (kJ/mol)

ΔS298 (J/mol K)

ΔG298 (kJ/mol)

γH+

kTST (s−1)

kH+ (s−1)

R TS

0.0 126

0.0 −18.1

0.0 108

0.0 107

0.0 107

0.0 −4.7

0.0 109

11.415

5.71 × 10−7

6.52 × 10−6

P

0.0

0.1

0.1

0.1

0.1

0.6

−0.1

a

kH+(expt)5,6 (s−1) 1.09 × 105, 7.9 × 104

The thermodynamic values are relative to R.

where v⧧ is the imaginary frequency of TS. Although eq 5 describes approximately the nature of the tunneling effect, it is sufficient since it usually yields the correct order of magnitude.35−37 The hydrolysis constant pKa of Al3+ in aqueous solution is estimated from the total Gibbs free energy change ΔGT° of the overall hydrolysis reaction:38,39

transition state rate constants kTST using kH+ = γH+kTST. The kTST value is calculated using the Eyring equation: k TST

−

⧧⎞ ⧧ ⎛ ΔG ⎛ ΔS kBT kBT 298, a 298, a ⎜ ⎟ ⎜ = = exp⎜ − exp⎜ h RT ⎟⎠ h ⎝ ⎝ R

ΔH298, a⧧ ⎞ ⎟ RT ⎟⎠

pK a = ΔGT °/2.303RT (4) ⧧

⧧

3. RESULTS AND DISCUSSION 3.1. Traditional Spontaneous Proton Dissociation Mechanism (Pathway I). The spontaneous proton dissociation pathway is obtained with 11 explicit solvent waters (Nm′ = 11). The solvent waters are arranged based on a complete second hydration shell of Al3+ containing 12 solvent waters with S6 symmetry,40 by removing one solvent water molecule in the proton dissociation direction to leave a hole for the dissociating proton moving from the inner hydration shell into the bulk water. The optimized configurations of the R, TS, and P species are listed in Figure 1, and the structural parameters are listed in Table 1. In R, the distance R(O−H(I)) between the coordinated O atom and the dissociating proton (I) is 0.977 Å. As the reaction begins, proton (I) moves toward the bulk water through the leaving hole. In TS, the distance R(O−H(I)) stretches to 1.428 Å. Nevertheless, in the following P, the

⧧

where kB, T, h, R, ΔG298,a , ΔS298,a , and ΔH298,a are Boltzmann’s constant, temperature, Planck’s constant, gas constant, activation Gibbs free energy, activation entropy, and activation enthalpy, respectively. The transition coefficient γH+ includes three factors: the tunneling factor κ, the recrossing factor Γ, and the nonequilibrium factor g, that is, γH+ = κΓg.32 In proton transfer reactions, the tunneling effect on the reaction rate constant can be expected to be more significant due to the small mass of the proton.33 Thus, the recrossing factor Γ and nonequilibrium factor g are assumed to be 1 in this study. The tunneling factor κ can be estimated with the Wigner tunneling approximation:33,34 2 1 ⎛ h ν⧧ ⎞ ⎟ ⎜ κ=1+ 24 ⎝ kBT ⎠

(6)

(5) 271

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Figure 2. Optimization results for TS and the Al(OH)(H2O)52+·H3O+(H2O)11 cluster in the bulk water-assisted proton dissociation pathway II (Nm′ = 12).

12).40 In this cluster, the solvent water molecule which is adjacent to the leaving proton is selected as an approximation of the bulk water that assists the proton dissociation. The TS structure for the proton on the coordinated water of Al3+ dissociating into the adjacent solvent water molecule is not found because the proton always comes back to its initially bonded O atom during the optimizations and forms the stable Al(H2O)63+·12H2O structure without imaginary frequencies (Figure 2a). In order to verify whether the conventional bulk water-assisted proton dissociation pathway can occur or not, we break an O−H bond in Al(H2O)63+ and move the proton to an adjacent solvent water molecule to construct the Al(OH)(H2O)52+·H3O+(H2O)11 cluster, which is close to the product configuration for the proton dissociation, and then optimize the structure to its stable configuration. It turns out that the proton which is enforced to dissociate comes back and binds to the inner-shell OH− in the final optimized stable configuration, reforming the initial Al(H2O)63+·12H2O geometry again (Figure 2b). In the CPMD simulations by Coskuner et al., Liu et al., and Ikeda et al., it is observed that the protons on the coordinated waters diffuse to their nearest water and form Zundel-like or H3O+-like structures occasionally, and then the protons come back very quickly.8,9,11 In the AIMD simulations

proton binds back to its initially bonded O atom instead of further moving into the bulk water, and the distance R(O− H (I) ) shrinks to 0.977 Å. Table 2 lists the relative thermodynamic parameters. The zero-point contributions and tunneling are both important quantum effects in calculating reaction rate constants. For pathway I, the zero-point contribution (ΔEZPE(0K),a⧧ = −18.1 kJ/mol) and tunneling effect (κ = 11.415) each increases the kH+ by 3 and 1 orders of magnitude. However, the electronic energy barrier is so high (ΔEelect(0K),a⧧ = 126 kJ/mol) that even the two quantum effects apparently accelerate the reaction rate constant, the estimated kH+ (6.52 × 10−6 s−1) from γH+ and ΔG298,a⧧ (109 kJ/mol, including the zero-point energy term) is far smaller than the experimental data (∼105 s−1).5,6 The results indicate that the probability of the protons on the Al3+ coordinated waters spontaneously dissociating into the bulk water is quite small because the ionized protons will soon return to coordinated O atoms. 3.2. Conventional Bulk Water-Assisted Proton Dissociation Mechanism (Pathway II). The conventional bulk water-assisted proton dissociation mechanism is proposed to model using the Al(H2O)63+·12H2O cluster, which has a complete second hydration shell with S6 symmetry (Nm′ = 272

DOI: 10.1021/acsearthspacechem.7b00142 ACS Earth Space Chem. 2018, 2, 269−277

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Figure 3. Optimized reactant, transition state, product configurations in the second-shell water-assisted synergistic proton dissociation process, and the finally formed stable Al(OH)(H2O)52+ and H3O+ configurations (Nm′ = 8) (the solvent waters that move into the bulk water are labeled gray).

into OH−, and its distance to the central Al3+ shrinks to 1.808 Å. The formation of OH− results in several O−Al−O bond angles in the octahedral deviating from 90°. The distances R(O−H (I) ) and R(H (I) −O a ) are 1.481 and 1.040 Å, respectively. The old O−H bond between the coordinated O atom and proton (I) is broken, and the new O−H bond between proton (I) and the O atom of the solvent water a is nearly formed. The distances R(Oa−H(II)) and R(H(II)−Ob) are 1.318 and 1.116 Å, respectively. At this point, proton (II) locates between the two O atoms of the solvent waters a and b, and this local structure is similar to the Zundel ion. In P, the distance R(H(I)−Oa) further shortens to 1.016 Å, and the new O−H bond forms. The distance R(H(II)−Ob) decreases to 1.057 Å, and the Zundel-like structure converts into an H3O+like structure. The overall second-shell water-assisted synergistic proton dissociation process is similar to the Grotthuss mechanism, which describes the motion of an excess proton in water along a network of H-bonds.41 After the H3O+ forms in P, it leaves the second hydration shell and enters the bulk water in the next step. It is assumed that the solvent water a and the protonated water b move into the bulk water together with their directly H-bonded solvent waters c and d. The H3O+(H2O)3 and Al(OH)(H2O)53+·4H2O clusters are optimized to stable species (see S2.2 in the Supporting Information). The inner-shell of Al(OH)(H2O)53+· 4H2O is a distorted octahedral with an Al−OH bond length of 1.772 Å. The average bond length of the five inner-shell Al− OH2 bonds is 1.952 Å, longer than that of the six Al−OH2 bonds in Al(H2O)63+ in R (1.913 Å), reflecting the labilizing effect of OH− on other inner-shell coordinated waters. In the H3O+(H2O)3 cluster, H3O+ is unsymmetrical as the three O−H bond lengths are 1.035, 0.979, and 1.052 Å, which is due to that the three O−H bonds have different solvation environments.

by Lubin et al., the protons on the coordinated waters dissociate into surrounding solvent water molecules to form H3O+ only at elevated temperatures of about 800 K.13 In summary, our calculation results and the literature simulations demonstrate that it is hard for a proton on the inner-shell coordinated water of Al3+ to dissociate into the bulk water through the spontaneous or the bulk water-assisted proton dissociation mechanisms, indicating that the electrostatic effects between Al3+ and its coordinated waters alone cannot fully account for the spontaneous hydrolysis of Al3+.7 3.3. Second-Shell Water-Assisted Synergistic Proton Dissociation Mechanism (Pathway III). For pathway III, eight explicit solvent water molecules are added in the second hydration shell of Al3+ to consider the short-range solvent effects (Nm′ = 8). The arrangement of the eight waters meets the condition that the dissociating proton is H-bonded to the O atom of a solvent water, and a proton on this solvent water is H-bonded to the O atom of another solvent water. Figure 3 lists the optimized configurations of the R, TS, and P species, and Table 3 lists their structural parameters. In R, Al(H2O)63+ is an approximate octahedral. The bond length between Al3+ and the coordinated water on which the dissociating proton (I) readies to leave is 1.919 Å. The distance R(O−H(I)) between the coordinated O atom and proton (I) is 1.006 Å, and the distance between proton (I) to the O atom of its acceptor, the solvent water a, R(H(I)−Oa) = 1.611 Å. On water a, proton (II) is about to dissociate synergistically with proton (I), and it has a distance of R(Oa−H(II)) = 0.981 Å to the O atom of water a and a distance of R(H(II)−Ob) = 1.844 Å to the O atom of its acceptor, the solvent water b. As the synergistic proton dissociation begins, proton (I) and proton (II) move synchronously along the H-bond wire from their donor waters to their acceptor waters, respectively. In TS, the coordinated water on which proton (I) dissociates transforms 273

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1.496 0.979 1.772 1.952 1.947, 1.983, 1.931, 1.974, 1.923 Al(OH)(H2O)52+·4H2O H3O+·3H2O

The distances between Al3+ and the inner-shell coordination waters. bThe average distance between Al3+ and the inner-shell coordination waters. cThe distance between Al3+ and the inner-shell OH−. The distance between the coordinated O atom and the dissociation proton (I). eThe distance between the dissociation proton (I) atom and the O atom of the solvent water a. fThe distance between the O atom of solvent water a and the dissociation proton (II). gThe distance between the dissociation proton (II) atom and the O atom of the solvent water b. hThe distances between Al3+ and the second hydration shell solvent waters. iThe average distance between Al3+ and the second hydration shell solvent waters.

1.035

1.057 1.443 1.016 1.570 1.799 1.955, 1.981, 1.905, 1.968, 1.917 P

1.945

1.116 1.318 1.040 1.481 1.808 1.942 TS

1.913

1.930, 1.915, 1.882, 1.936, 1.897, 1.919 1.954, 1.984, 1.900, 1.962, 1.911 R

Table 4 indicates that the ΔG298,a⧧ for the second-shell water-assisted synergistic proton dissociation is 44.2 kJ/mol, and the estimated reaction rate constant kH+ (=γH+kTST) is 1.14 × 105 s−1, in close agreement with the experimental values of 1.09 × 105 and 7.9 × 104 s−1.5,6 The zero-point contribution (ΔEZPE(0K),a⧧ = −9.0 kJ/mol) accelerates the reaction rate constant by about 2 orders of magnitude, while the tunneling effect (κ = 1.023) has very little influence on kH+. Comparing the single proton dissociation pathway I, the quantum effects show less influences on the synergistic proton dissociation pathway III, while the smaller electronic energy barrier for pathway III (ΔEelect(0K),a⧧ = 54.2 kJ/mol) is the root cause for its much higher rate constant. The ΔG298,r⧧ from R to P is −19.2 kJ/mol, whereas ΔG° for the H3O+(H2O)3 cluster to move from the second hydration shell of Al3+ in P into the bulk water is 52.4 kJ/mol. The total chemical reaction equation for the second-shell water-assisted synergistic proton dissociation mechanism of the first-order Al3+ hydrolysis reaction can be written as Al(H 2O)6 3 + ·2H 2O → Al(OH)(H 2O)52 + +H3O+ ·H 2O (7) 42,43

Using similar approaches in literature, the total Gibbs free energy change ΔGT° for the overall reaction pathway of eq 7 equals the sum of ΔG298,r⧧ and ΔG° and is calculated as 33.2 kJ/mol. Based on eq 6, the pKa1 for the first-order hydrolysis of Al3+ is calculated as 5.82, which agrees with the literature value of 5.00.15 Therefore, it is proposed that, in acidic aqueous solution, the main reaction mechanism for natural Al3+ hydrolysis is the second-shell water-assisted synergistic proton dissociation. This pathway is also supported by cross-validation calculations with the BLYP optimization method (see S3 in the Supporting Information for details). The participation of the solvent water molecules in the second hydration shell of Al3+ is crucially important in the synergistic proton dissociation pathway, and this is a characteristic difference between the hydrolysis mechanisms of Al3+ and other metal ions (such as Fe3+ and Cr3+).7 3.4. Environmental Significance. The results in this study have important environmental implications: 1. Generally, environmental processes like the proton transfer reactions in the Al3+ hydrolysis are difficult to simulate with molecular dynamics methods, due to the fact that the reactions in aqueous solution are sensitive to details of the solvation and H-bonding networks, and more importantly, most environmental processes are rare events that are too infrequent to be simulated in a dynamic calculation.44 In this study, the estimated kH+ for the second-shell water-assisted synergistic proton dissociation reaction and the pKa calculated for Al3+ with the same pathway are both in excellent agreement with the reported experimental values, demonstrating that the DFT-CM method is well applicable in modeling rare events and aqueous reactions in the natural environment. 2. The proton dissociation pathway for the spontaneous Al3+ hydrolysis is proposed to have the important characteristics of synergistic and water-assisted. It is noticeable that this molecular mechanism is quite different from the traditional view that only the inner-shell proton in Al(H2O)63+ dissociates to form Al(OH)(H2O)52+. It is actually difficult for the innershell protons to dissociate without the synergistic proton dissociation on its H-bonded adjacent solvent water. The role of adjacent solvent waters was indeed undervalued in the past.

d

a

3.994

4.105

4.097

4.036

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 1.844 1.006

1.611

0.981

R(Al−OH2)IIh R(H(II)−Ob)g R(Oa−H(II))f R(H(I)−Oa)e R(O−H(I))d R̅ (Al−OH2)Ib R(Al−OH)Ic R(Al−OH2)Ia species

Table 3. Structural Parameters of the Reaction Species in the Second-Shell Water-Assisted Synergistic Proton Dissociation Pathway III (Å)

R̅ (Al−OH2)IIi

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1.09 × 105, 7.9 × 104

In other environmental processes, similar water-assisted synergistic proton dissociation pathway has also been found for the acid−base reactions such as the hydrolysis of SO2 and the formation of NH4HSO4.45,46 It is reasonable to believe that the simple elementary reaction steps may have more complicated reaction mechanisms than expected. 3. The results in this study are helpful in future deep investigating a series of fundamental issues in the hydrolysis and polymerization chemistry of the aqueous Al species, such as the proton dissociation mechanisms of the Al(OH)2+ to form Al(OH)2+, Al(OH)3, and Al(OH)4− and further polymerizes to Al2(OH)2(H2O)84+, Keggin-AlO4Al12(OH)24(H2O)127+, as well as other species. It is also advantageous for the research on the influences of the titration rates and OH− concentration on the Al3+ hydrolysis and polymerization pathways in base titration processes, as well as the reverse protonation mechanisms of the hydrolyzed Al species in the acidification reactions.47−49 For example, in the polyoxocation KegginAlO4Al12(OH)24(H2O)127+, there is one type of oxo bridge and two types of hydroxo bridges, but their formation pathways are not known yet. We expect that studying the proton dissociation kinetics on the coordinated O atoms will be helpful in establishing the formation mechanisms of the oxo and hydroxo bridges in the Al polyoxocations. In addition, there are three sets of structurally distinct protons in Keggin AlO4Al12(OH)24(H2O)127+, and their lifetimes have been estimated from 1H NMR experiments, which is helpful in constraining the proton dynamics on aluminum hydroxide material surfaces.50 The lifetime of a proton on a bound water in Keggin AlO4Al12(OH)24(H2O)127+ is about 2 × 10−4 s at 298 K,50 about 1 order of magnitude larger than the lifetime of a proton in Al(H2O)63+ (∼10−5 s).5,6 Despite the small magnitude difference between the two lifetimes, the protons on the Keggin AlO4Al12(OH)24(H2O)127+ bound waters and the Al(H 2 O) 6 3+ coordinated waters may have similar dissociation mechanisms. The lifetimes of the protons on the two distinct sets of hydroxo bridges are 0.013 and 0.2 s.50 However, these two kinds of hydroxyl protons cannot be distinguished in experiments. If the DFT-CM method is used to model the kinetic dissociation reactions of the two kinds of hydroxyl protons, it would be possible to identify their lifetimes reasonably. In future applications, the DFT-CM method can be extended to study the micromorphology and elementary reaction kinetics of Al and other metal ion species in heterogeneous or nonaqueous environments, such as mineral or material surfaces, aerosols, flocs, and sediments, as well as the biological organisms, to explore the problems that are difficult to solve with traditional experimental methods.51−57

4. CONCLUSION In this study, the density functional calculations elucidate a second-shell water-assisted synergistic proton dissociation mechanism as the main mechanism for the first-order spontaneous hydrolysis of Al3+ in aqueous solution. The reaction pathway proceeds via a concerted dissociation of two protons from two H-bonded inner- and second-shell waters. The magnitudes of the estimated proton dissociation rate constant (kH+ = 1.14 × 105 s−1) and equilibrium constant (pKa1 = 5.82) are in good agreement with the experimental data. The calculation results show that the electrostatic effects between Al3+ and its coordinated waters alone cannot fully account for the spontaneous hydrolysis of Al3+, and the traditional spontaneous dissociation mechanism of a single inner-shell

a

−19.2 33.2 −1.8 268 −19.7 113 −19.7 111 −19.3 105 −13.1 −21.7 −6.2 127 P Al(OH)(H2O)52+·4H2O + H3O+·3H2Ob

R TS

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

1.14 × 105 1.11 × 105 1.023 0.0 44.2 0.0 −2.7 0.0 43.4 0.0 43.4 0.0 −9.0 0.0 54.2

0.0 45.2

kH+ (s−1) kTST (s−1) γH+ ΔG298 (kJ/mol) ΔS298 (J/mol K) ΔH298 (kJ/mol) ΔE298 (kJ/mol) ΔE0(0K) (kJ/mol) ΔEZPE(0K) (kJ/mol) ΔEelect(0K) (kJ/mol) species

Table 4. Relative Thermodynamic Parameters and Reaction Rate Constant for the Second-Shell Water-Assisted Synergistic Proton Dissociation Pathway IIIa

kH+(expt)5,6 (s−1)

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coordinated water proton (direct dissociation or assisted by a bulk solvent water) is very unlikely to occur in real aqueous solution. The results in this study provide new insights into the microscopic molecular mechanism of the elementary hydrolysis reaction of aqueous Al3+ and lay foundation for future investigation of the hydrolysis and polymerization chemistry of aqueous Al species.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsearthspacechem.7b00142. Summarization of previous theoretical studies of the Al3+ hydrolysis pathway in the literature; testing results with different solvation models; testing results with the BLYP method; Cartesian coordinates of all reaction species in the Al3+ hydrolysis reaction pathways (PDF)

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AUTHOR INFORMATION

Corresponding Author

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

Shuping Bi: 0000-0003-4437-7769 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project is supported by the National Natural Science Foundation of China (No. 21177054). We are grateful to the High Performance Computing Center of Nanjing University for doing the numerical calculations in this paper on its Blade cluster system.

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REFERENCES

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