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Nov 13, 2009 - The water exchange reactions on the gibbsite surface are simulated by density functional theory combining the supermolecular and PCM ...
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Environ. Sci. Technol. 2009 43, 9281–9286

Density Functional Investigation of the Water Exchange Reaction on the Gibbsite Surface Z H A O S H E N G Q I A N , †,‡ H U I F E N G , †,‡ XIAOYAN JIN,† WENJING YANG,† Y I N G J I E W A N G , † A N D S H U P I N G B I * ,† School of Chemistry and Chemical Engineering, State Key Laboratory of Coordination Chemistry of China and Key Laboratory of MOE for Life Science, Nanjing University, Nanjing 210093, China, and College of Chemistry and Life Science, Zhejiang Normal University, Jinhua 321004, China

Received May 30, 2009. Revised manuscript received October 1, 2009. Accepted October 28, 2009.

The water exchange reactions on the gibbsite surface have been investigated by density functional calculations (B3LYP/631G(d) level) combining the supermolecular model and PCM model in this paper, and the water exchange rate constants on the gibbsite surface have also been predicted. In the proposed reaction pathways, the clusters Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are used as the models of gibbsite surface and protonated gibbsite surface respectively to examine the effect of protonation of gibbsite surface on the water exchange rate constants. The activation energy barriers ∆E* s (aq) for Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are 28.6 and 27.2 kJ mol-1, respectively. The reaction energies ∆Es(aq) for Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are 2.9 and 14.4 kJ · mol-1, respectively, indicating that hexacoordinate aluminum in the gibbsite surface is more stable. The log kTST for Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are 6.5 and 7.5 respectively, and the log kex calculated by the given transmission coefficient for Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are 2.4 and 3.4 respectively, indicating that the protonation of gibbsite surface promotes the water exchange reaction of gibbsite surface and accelerates the dissolution rate of gibbsite. The relationship between the calculated free energy and experimental rate constants was explored, and according to this relationship, the log kex for Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are 2.5 and 3.1 respectively, close to the corresponding values calculated by the given transmission coefficient. The water exchange rate constant of gibbsite surface is close to those of K-MAl12(M ) Al, Ga, and Ge) polyoxocations, but deviates from that of Al(H2O)63+, implying that the same reactions with similar structure have similar water exchange rate constants.

1. Introduction Water exchange reactions between water and mineral surfaces are the key questions in geochemistry and environmental chemistry since these reactions control the over solution chemistry and nearly all of the environmental and geochemistry processes involving dissolution and transfor* Corresponding author phone: +86 25 86205840; fax: +86 25 83317761; e-mail: [email protected]. † Nanjing University. ‡ Zhejiang Normal University. 10.1021/es901583m CCC: $40.75

Published on Web 11/13/2009

 2009 American Chemical Society

mation of minerals, transport and degradation of pollutants (1-3). However, since the experimental techniques are difficult to study the reactions of mineral surface at present, the information on the reactions of mineral surface is scarce. Recent studies indicate that aqueous aluminum polyoxocations are very helpful to understand the mineral surface reactions and explore the reaction mechanism (4, 5). To study the dissolution processes of mineral at the molecular level and predict the water exchange rate constant of hydroxide aluminum mineral surface, K-MO4Al12(OH)24(H2O)12n+(M ) Al, Ga, n ) 7; M ) Ge, n ) 8) (K-MAl12) have been used as the ideal experimental models of hydroxide aluminum mineral surface. Casey et al. (6-8) determined the water exchange rate constants and activation parameters of K-MAl12(M ) Al, Ga, and Ge) polyoxocations, and studied the proton exchange reaction between K-Al13 and bulk solution (9). For exploring the microscopic mechanism of the water exchange reactions of K-MAl12(M ) Al, Ga, and Ge) polyoxocations, Pophristic et al. (10) and Tossell (11) using ab initio methods and molecular dynamics studied the structure and NMR properties of K-Al13 respectively. Stack et al. (12) and Rustad et al. (13) simulated the water exchange reactions of K-Al13 and K-GaAl12 respectively. Wang et al. (14) employing molecular dynamics predicted the water exchange rate constants of aluminum species involving K-Al13 polyoxocation. In our recent work (15, 16), we simulated the water exchange reactions of K-Al13, K-GaAl12, and K-GeAl12 polyoxocations using a supermolecular model, and calculated the transmission coefficients of the three water exchange reactions. Aluminum trihydroxides Al(OH)3 are gibbsite, bayerite and nordstrandite, in which gibbsite and bayerite are natural solids. Theoretical studies on the stability of aluminum trihydroxides Al(OH)3 indicate that gibbsite is the most stable form (17). The crystal structure of gibbsite has been determined by Megew (18). Gibbsite forms by the polymerization of the monomer Al(OH)3, and its basic unit is the six-member cycle Al6(OH)18. It has been proved that the surface of gibbsite involves a coordinated water molecule except the five coordinated hydroxyl ligands of the aluminum (19). Although the aluminum polyoxocations can be used as the experimental model to simulate the water exchange reactions of the hydr(oxide) aluminum mineral surfaces, the surfaces of hydr(oxide) aluminum minerals are different from these aluminum polyoxocations in the detailed structure, chemical environment, and charge. Therefore, people began to directly investigate the surface reactions of hydroxide aluminum minerals by the theoretical methods. Wang et al. (14) predicted the rate constants of the water exchange reactions of the hydroxide aluminum minerals surface using the molecular dynamics. Although the prediction of the rate constants by Wang et al. (14) is not very accurate, their study provides a means for estimating kinetic parameters for sites at aqueous polynuclear ions and oxyhydroxide surfaces. It has been shown that the mineral surface will be protonated when the mineral is immersed in the bulk solution (20), but the influences of the protonation of the mineral surface on the water exchange rate constants and the dissolution rate constants are not clear. Therefore, it is important to simulate the water exchange reactions on the mineral surface for understanding the dissolution and transformation of mineral and the formation of the nanominerals. In the present work, we simulated the water exchange reaction on the gibbsite surface, predicted the water exchange rate constant, and examined the influence of the protonation on the water exchange rate constant of the gibbsite surface VOL. 43, NO. 24, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Structures of the model clusters of gibbsite surface: Al6(OH)18(H2O)60 (a) and Al6(OH)12(H2O)126+ (b). combining the supermolecular model and PCM model by density functional theory. Ten explicit water molecules were included in the supermolecular model to estimate the explicit solvent effect, and the remaining water was modeled as a polarizable dielectric continuum medium surrounding the supermolecules to estimate the bulk solvent effect. For comparison, the water exchange reaction was also simulated by the gas-phase model. To examine the influence of the protonation of the gibbsite surface on the water exchange rate constant, we constructed two model clusters Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+.

2. Mechanistic Approach 2.1. Model Reactions. In order to explore the gibbsite mineral surface reactions, different model clusters have been adopted to simulate the mineral surface. Ladeira et al. (21) and Paul et al. (22) adopted the model clusters Al2(OH)6 and Al2(OH)5(H2O)5+ to simulate the gibbsite surface respectively, whereas Frenzel et al. (23) and Oliveira et al. (24) adopted the model clusters Al6(OH)18 and Al6(OH)17(H2O)7+ to simulate the gibbsite surface respectively. The proposed model cluster with positive charge is consistent with the results by molecular dynamics (25), i.e., the mineral surface will be protonated when the mineral is immersed in the bulk solution. In this present paper, we modeled the clusters Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ to simulate the gibbsite surface and protonated gibbsite surface respectively in order to examine the influence of the protonation of gibbsite surface on the water exchange rate constant. 2.2. Notation. In order to describe the complexes consistently, the following notation is adopted. The water exchange reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are denoted as Reaction 1 and Reaction 2 respectively, and the reactants, transition states and products in the gas-phase reaction system and supermolecular reaction system are denoted as R1, TS1, P1, R2, TS2, P2, and Rs1, TSs1, Ps1, Rs2, TSs2, Ps2 respectively. The parameters used to characterize structural changes during the reaction process comprise the average bond length between the reacted aluminum and its coordinated oxygen r(AlsO), the bond distance between the reacted aluminum and the leaving water molecule r(AlsOL), the bond distance between the hydrogen atom of the leaving water molecule and its neighboring hydroxyl bridge r(OsHL), the distance between the leaving water molecule and the hydrogen atom of its neighboring hydroxyl bridge, and the sum of the distances between the reacted aluminum atom and its coordinated oxygen atoms ∑r(AlsO). 2.3. Computational Details. The Gaussian 03 suite of programs was used throughout this paper (26). Ten solvent 9282

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water molecules with hydrogen bonds with the solutes are explicitly included in the supermolecule model to simulate the explicit solvent effect, and the bulk solvent effect was simulated by calculations using the polarizable continuum model (PCM) (27). All the stable structures of the gas-phase species and supermolecular species were fully optimized at the B3LYP/6-31G(d) level by density functional theory. Vibrational frequency calculations were carried out to confirm the stable structures optimized and the transition states, and intrinsic reaction coordinate (IRC) (28) calculations were performed to verify the expected connections of the firstorder saddle points with the local minima found on the potential energy surfaces. To obtain accurate energies for the reaction surfaces, the single-point energies were further calculated at the MPWKCIS1K/6-31+G(d,p) level (16), and the single-point PCM calculations were also performed to estimate the bulk solvent effect accurately. A dielectric constant  ) 78.39 and the UAKS radii model were used in the calculations for water at 298.15 K and 1 atm. For confirmation of the sufficiency of the explicit solvent water molecules included in the supermolecular model, we also modeled the supermolecules with the consideration of 9 and 11 explicit water molecules for the water exchange reaction of Al6(OH)12(H2O)126+. The activation entropy ∆S* and activation enthalpy ∆H* for the water exchange reactions were obtained by frequency calculations, and then the transition-state rate constant was calculated according to the Eyring equation (29): kTST ) (kBT/h) · exp(∆S* /R-∆H* /RT)

(1)

The rate constant was calculated on the base of transitionstate rate constant and transmission coefficient (30): kex ) κkTST

(2)

3. Results and Discussion 3.1. Benchmarking of the Methods. Three kinds of models, i.e., the gas-phase model, supermolecular model (the gasphase model with several explicit solvent molecules) and combined supermolecular model and PCM model, have been applied on the static calculations of water exchange reactions of aluminum ions and clusters until now. The gas-phase model can not consider the solvent effect (31), but is able to simulate the water exchange pathways reasonably except for some metal clusters with high positive charges (32). Hanauer et al. (33) and Evans et al. (34) constructing the supermolecular model showed the obvious influence of explicit solvent effect on the energy barriers. However, the results of Evans et al. (34) also showed that the chosen model

TABLE 1. Energy Barriers (kJ mol-1) with Consideration of 9, 10, and 11 Explicit Water Molecules for the Water Exchange of Al6(OH)12(H2O)126+ no. waters

n)9

n ) 10

n ) 11

*

23.4

27.2

26.9

∆Es (aq)

with different explicit water molecules leads to varied energy barriers. One can see that the supermolecular models of Hanauer et al. (33) and Evans et al. (34) include the explicit solvent effect, but don’t consider the bulk solvent effect, and it is not confirmed whether the included explicit water molecules in their models are sufficient to describe the explicit solvent effect. In the combined supermolecular model and PCM model, both of the explicit and bulk solvent effects are included, and the energy barriers are nearly constant when enough explicit water molecules are included. From our previous studies (15, 16, 32, 35), one can see that the combination of the supermolecular model and PCM model is creditable, and the energy differences induced by the different converged numbers of the included explicit water molecules are about (5 kJ mol-1, within the DFT systematic errors. Our previous studies (15, 16, 32, 35) on the water exchange reactions of aluminum species indicate that the adopted methods B3LYP for the optimization of the structures and MPWKCIS1K/6-31+G(d,p) for the calculation of the energies are suitable to simulate these water exchange reactions. For confirmation of the sufficiency of the explicit solvent water molecules included in the supermolecule model, we also modeled the supermolecules with the consideration of 9 and 11 explicit water molecules for the water exchange reaction of Al6(OH)12(H2O)126+. As shown in Table 1, the calculated energy barriers with the consideration of 10 and 11 explicit water molecules are very close, and thereby the convergence with respect to the number of water molecules is satisfactory for n g 10. Therefore, one can see that our adopted supermolecule model and methods would model the water exchange reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ accurately. 3.2. Structural Characteristics. The fully optimized structures and the selected structural parameters of the supermolecular species involved in the water exchange reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are shown in Figure 2 and Table 2, respectively. As shown in Figure 2, for the water exchange reaction of Al6(OH)18(H2O)60, 10 additional solvent water molecules simultaneously form strong hydrogen bonds with the hydroxo-bridges and the water ligands in the first coordination sphere. In the reactant Rs1, the leaving water molecule forms a hydrogen bond with the neighboring hydroxyl-bridge with the bond length of 1.632 Å. Dissociating the leaving water molecule from its coordinated aluminum leads to the transition state TSs1. In the transition state TSs1, the leaving water molecule forms one hydrogen bond, r(H-OL) ) 1.763 Å, with the neighboring water molecule in the first coordination sphere, and is located between the first and second coordination spheres at a distance of 2.833 Å. When the distance between the reacted aluminum and the leaving water molecule lengthens to 3.697 Å, the leaving water molecule becomes part of the second coordination sphere, and the product Ps1 with a five-coordinated aluminum atom forms. The leaving water molecule in the product Ps1 forms hydrogen bond with the neighboring hydroxyl-bridge and the hydroxyl ligand. Table 2 shows that the average bond length between aluminum and coordinated water molecules decreases from 1.931 Å in the reactant Rs1, to 1.873 Å in the transition state TSs1, and finally to 1.859 Å in the product Ps1 as reaction proceeds.

For the water exchange reaction of Al6(OH)12(H2O)126+, the leaving water molecule neighbors with one of the water molecules in the first coordination sphere in the reactant Rs2. Lengthening the distance between the leaving water molecule and the aluminum to 3.018 Å, the transition state TSs2 is achieved. In the transition state TSs2, the hydrogen bond between the leaving water molecule and the neighboring water molecule in the first coordination sphere is 1.755 Å. As the reaction proceeds, the leaving water molecule enters into the second coordination sphere, and locates in the distance of 3.981 Å to the central aluminum in the product Ps2. As shown in Table 2, the average bond length between aluminum and coordinated water molecules decreases stepwise as the reaction proceeds, which may be induced by the decrease of the coordinated water molecules. 3.3. Calculations of the Rate Constants for the Water Exchange Reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+. The computed energy barriers and reaction energies for the water exchange reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are summarized in Table 3. For the gas-phase reaction system, the energy barriers for the water exchange of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are 39.0 and 8.8 kJ mol-1, respectively, and the reaction energies are 34.1 and -50.3 kJ mol-1, respectively. The reaction energy of -50.3 kJ mol-1 indicates there is a trend from hexacoordinated aluminum to pentacoordinated aluminum for the water exchange of protonated Al6(OH)12(H2O)126+ in the gas phase. This is different with the conclusions of Swaddle et al. (36) and Qian et al. (35) about the coordination change of Al(OH)2+ since their conclusions are based on the data including the solvent effect. For the supermolecular reaction system, the energy barriers for the water exchange of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are 23.7 and 13.3 kJ mol-1 respectively, and the reaction energies are -7.2 and -22.6 kJ mol-1 respectively. After considering the bulk solvent effect, the energy barriers for the water exchange of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are increased to 28.6 and 27.2 kJ mol-1, respectively, and the reaction energies are increased to 2.9 and 14.4 kJ mol-1, respectively, which underscores the importance of the bulk solvent effect. According to the papers of Truhlar et al. (30, 37, 38), the rate constant is linked to the transition-state rate constant by the transmission coefficient, and transmission coefficient is not going to be 1. The generalized transmission coefficient includes the recrossing factor, tunneling factor and nonequilibrium factor (38), and the recrossing and nonequilibrium factors are proved to be important in liquid (39). The transmission coefficients induced by the recrossing factor of the water exchange reactions of aquated sodium and aluminum species were calculated by Rey and Hynes (40) and Wang et al. (14), respectively. However, there is no effective method to estimate the transmission coefficient induced by both the recrossing and nonequilibrium factors at present, and thereby it is useful to explore the possible relationships between the calculated data including transmission coefficient and activation free energy and the experimental rate constant to estimate the rate constant of the water exchange on mineral surface. According to the transition-state theory, we calculated the transition-state rate constants of the water exchange reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+. As shown in Table 4, log kTST for the water exchange reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are 6.5 and 7.5 respectively. In our recent paper, we proposed that the water exchange reactions of aluminum species with similar structure have nearly same transmission coefficients (32). Since gibbsite surface has similar structure and charges with K-Al13 polyoxocation (41), the transmission coefficients of their water exchange reactions can be regarded as a constant (log κ ) -4.1). According to the equation kex ) κ kTST, the rate VOL. 43, NO. 24, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 2. Structures of the supermolecules in the water exchange reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+. The oxygen atoms of the leaving water molecule are colored in white to distinguish them from the others. constants for the water exchange reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are calculated, and log kex for Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are 2.4 and 3.4 respectively, which indicates that the protonation of the gibbsite surface promotes the water exchange rate constants. Comparing the rate constants for gibbsite surface (log kex ) 2.4), Al(H2O)63+(log kex ) 0.1) and K-MAl12(M ) Al, Ga and 9284

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Ge) (log kex ) 3.0, 2.4, and 2.3), one can note that the rate constant for the water exchange on the gibbsite surface is close to those for the water exchange reactions of K-MAl12(M ) Al, Ga, and Ge) polyoxocations, and deviates largely from that for the water exchange reaction of Al(H2O)63+, indicating that K-MAl12(M ) Al, Ga, and Ge) as the experimental models for the hydr(oxide) aluminum mineral surfaces are reasonable.

TABLE 2. Selected Structural Parameters (Å) of the Supermolecules for the Water Exchange Reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ complex

r(Al-OL)

r(O-HL)

Rs1 TSs1 Ps1 Rs2 TSs2 Ps2

2.062 2.833 3.697 2.086 3.018 3.981

1.632 1.763 1.740

6.5

-4.1

2.4

Key questions in environmental chemistry and geochemistry focus on reactions between bulk solution and mineral surfaces since these reactions nearly control the overall solution chemistry and all the Earth’s surface environments (42). For collecting the microscopic information of the environmental processes, a series of investigations on the dissolution of minerals have been carried out (43, 44), and the catalysis of the protonation on the dissolution of the minerals were also explored in detail (45), which is consistent with the finding of the acceleration of protonation on the exchange rate constant. This framework provides a new method for the exploration of the environmental processes and mineral surface reactions and the prediction of the water exchange rate constants of the mineral surfaces. The combination of the supermolecular and PCM model in this paper is expected to apply on the related surface reactions in environments, and the proposed relationship between the activation free energy and experimental rate constant is useful to predict the rate constants of dissolution of aluminum minerals and clusters in future.

7.5

-4.1

3.4

Acknowledgments

r(H-OL)

r(Al-O)

∑r(Al-O)

1.755 1.936

1.931 1.873 1.859 1.936 1.876 1.857

11.584 12.198 12.991 11.618 12.399 13.268

TABLE 3. Calculated Relative Energies and Rate Constants of the Water Exchange Reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ complex

∆E (g)a ∆Es(g)b ∆Es(aq)c log kTSTd log kexf (kJ mol-1) (kJ mol-1) (kJ mol-1) (s-1) log Ke (s-1)

R1/Rs1 TS1/TSs1 P1/Ps1 R2/Rs2 TS2/TSs2 P2/Ps2

0 39.0 34.1 0 8.8 -50.3

0 23.7 -7.2 0 13.3 -22.6

a

0 28.6 2.9 0 27.2 14.4

4. Environmental relevance

b

For the gas-phase species. For the supermolecular species. c Bulk solvent effect on the supermolecular species. d The transition-state rate constant. e From ref 16. f Calculated rate constants.

TABLE 4. Calculated Energy Parameters and Experimental Rate Constants for the Water Exchange Reactions of Al(H2O)63+, K-Al13, K-GaAl12, and K-GeAl12 complex

∆H*a (kJ mol-1)

∆S*a (J mol-1 K-1)

∆G*a (kJ mol-1)

log kexb

Al(H2O)63+ K-Al13 K-GaAl12 K-GeAl12

70.1 29.1 31.3 37.0

32.8 -11.1 -10.1 -11.5

60.3 32.4 34.3 40.4

0.1 3.0 2.4 2.3

a The calculated activation enthalpy, activation entropy, and activation free energy (Data from ref 32). b Log value of the experimental rate constants from ref 2.

In order to explore the possible relationship between the calculated activation free energies and the experimental rate constants for the water exchange of aluminum species, as shown in Table 4, we summarized the calculated energy parameters and the corresponding experimental rate constants for the water exchange reactions of Al(H2O)63+, K-Al13, K-GaAl12 and K-GeAl12 (15, 16, 32, 35) in the solution. The relationship between the activation free energies and the corresponding experimental rate constants (log kex) was shown in SI Figure S2. The relationship can be expressed in the following equation: log kex ) 6.06 - 0.0981 ∆G*, in which R2 ) 0.970. One can see that the calculated activation free energies (∆G*) have a reasonably linear relationship to the log value of experimental rate constants (log kex). The calculated activation free energies for the water exchange reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+ are 35.8 and 30.1 kJ mol-1, respectively. According to this relationship, we calculated the log kex from the corresponding activation energies for the water exchange reactions of Al6(OH)18(H2O)60 and Al6(OH)12(H2O)126+, and their log kex are 2.5 and 3.1, respectively, close to the corresponding values 2.4 and 3.4 calculated by the formula kex ) κ kTST in which κ is given as a constant. Comparing the log kex data by the two kinds of methods, we presume the calculated log kex may have an error of (0.3.

This project is supported by the NSFC (No. 20777030 and NFFTBS-J063042) and grant from Nanjing University (No. 2009PL04). We are also grateful to the High Performance Computing Center of Nanjing University for the award of CPU hours to accomplish this work.

Supporting Information Available The structures and the selected structural parameters of the gas-phase species, the relationship between the activation free energy and experimental rate constant, and the related references.This material is available free of charge via the Internet at http://pubs.acs.org.

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