Hybridization-reactivity relationship in Pb(II) adsorption on α-Al2O3

ARTICLE pubs.acs.org/JPCC

Hybridization-reactivity relationship in Pb(II) adsorption on r-Al2O3-water interfaces: A DFT Study Sara E. Mason,*,†,§ Thomas P. Trainor,‡ and Anne M. Chaka† † ‡

Physics Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States Department of Chemistry and Biochemistry, University of Alaska Fairbanks, Fairbanks, Alaska 99775, United States ABSTRACT: We report on a density functional theory study aimed at comparing the reactivity of differently structured R-Al2O3-water interfaces as probed through adsorption of the Pb(II) cation. We assign the Pb-O bonding in Pb(II)/Al2O3 geometries to in-plane and out-of-plane orbital contributions. From our analysis, the empirically known greater Pb(II) reactivity of R-Al2O3(1102) over R-Al2O3(0001) is ascribed to the ability of oxygen functional groups in the corrugated (1102) interface to hybridize more effectively with Pb(II) electronic states than oxygen functional groups in the topographically flat (0001) interface. The theoretical evidence of a Pb-O hybridization-reactivity relationship goes beyond bondvalence predictions that cite oxygen functional group coordination as a key predictor of mineral-water interface reactivity. We also report the details of adsorption-induced surface relaxations, including an example of surface hydrogen bond rearrangement, as well as evidence of long-range Pb-O interaction. To further assess the bonding saturation of lead in the optimized Pb(II)/Al2O3 structures, molecular H2O adsorption studies are carried out and shown to support that the cation coordination is largely satisfied through interactions with surface functional groups.

’ INTRODUCTION A persistent barrier that remains to solving a wide rage of environmental and technological problems is the limited molecular-level understanding of reactivity at mineral-water interfaces. The inherent complexity of oxide surfaces1,2 combined with the ubiquitous role that hydrated oxides play in natural and engineered systems3-7 motivates the ongoing study of heterogeneous chemical processes at mineral-water interfaces. The uptake of aqueous cations to form inner-sphere (chemically bound) surface complexes is critical to applications ranging from environmental transport to catalysis. The adsorption of metal cation contaminants at hydrated metal oxide and hydroxide particles is perhaps the most significant process responsible for controlling contaminant sequestration and mobility and finds widespread use in remediation technologies8-10 and catalyst preparation.11-13 Divalent lead, Pb(II), is a notably toxic metal cation contaminant14 that is known to partition strongly with solid phases, resulting in persistent contamination issues associated with slow leaching from soils and mine tailing environments.15 While the importance of Pb(II) interactions with environmental interfaces is recognized, the adsorption process is not well understood at a fundamental level. Owing to the intrinsic relationship between structure and reactivity, well-characterized mineral-water interfaces are ideal choices for controlled, comparative reactivity studies. Furthermore, the natural abundance and the diverse technical applications of aluminum oxides and hydroxides16,17 lead to substantial interest in the interfacial properties of these substrates. The wealth of previous structural characterization studies on alumina (R-Al2O3)-water interfaces through both experimental (see, for r 2011 American Chemical Society

example, refs 18-27) and theoretical (see, for example, refs 28-38) methods makes these systems accessible and relevant candidates for studies aimed at forming an understanding of underlying mineral-water reactivity considerations. The chemical properties of the alumina-water interface arise from structural and compositional constraints associated with the bulk oxide geometry, the electronic structure, and steric features of the potential terminations. The bulk corundum structure of R-Al2O3 and the surface structure of different surface planes under pristine laboratory conditions are well-studied and only briefly reviewed here. Bulk R-Al2O3 is described as alternating planes of oxygen and aluminum layered along the (0001) direction. All of the Al(III) cations are octahedrally coordinated with O(II) anions, with 2/3 occupation of the available sites.39 Electrostatic repulsion results in distortions of the Al-bilayer sandwiched between the oxygen double layers. As discussed and depicted in Guo et al.,40 there are several ways to terminate bulk R-Al2O3 to form the prevalent (0001) and (1102) growth faces. Under UHV conditions, the (0001) surface is found to be Al-terminated, exhibiting extensive relaxation in the outermost Al-O atomic layers,30,41-48 with reconstructed surfaces reported at high temperatures.49 The (1102) surface is less extensively studied than the (0001) surface but is also reported to be clean, chemically stable, and well-ordered under UHV conditions50 and is predicted to be oxygen terminated with 5-fold coordinated Al surface species.40 Received: August 29, 2010 Revised: December 27, 2010 Published: February 22, 2011 4008

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Under hydrous conditions, many experiments report strong interactions between water and R-Al2O3, leading to hydroxylation of the surfaces.51,52 On the (0001) surface, experimental21,53 and theoretical28,30,31,54 evidence supports the formation of a fully hydroxylated, oxygen terminated surface, with a (1
1) stoichiometry of (HO)3-Al-Al-Rc, where Rc denotes the continuing stoichiometric (0001) atomic stacking sequence O3-Al-Al. We refer to this hydrated R-Al2O3(0001) model as the “c-cut” model throughout the remainder of the paper. The hydrated (1102) surface structure has been reported to exist in a hydroxylated stoichiometric structure25 or in a predominantly “missing-Al” hydroxylated structure22 depending on preparation conditions. We recently carried out an ab initio thermodynamics analysis of the R-Al2O3(1102) surface,55 including model structures consistent with both of the experimentally posed structures. Abbreviating the stoichiometric (1
1) (1102) atomic stacking sequence (O2-Al2-O2-Al2-O2) as Rr, our hydroxylated stoichiometric model ((HO)2-(HO)2-Al2-O2-Al2-O2-Rr) and our hydroxylated missing-Al model ((H2O)2-X-(HO)2Al2-O2-Rr) (referred to as the “A3 r-cut” and “C4 r-cut” models in the remainder of the paper, consistent with a previously established model naming scheme56) are found to be nearly thermodynamically equivalent at room temperature under ambient gas-phase water and oxygen pressures.55 Other theoretical studies also report thermodynamic stability of analogous models for hydroxylated R-Al2O3(1102) surfaces.34,38 Side views of the c-cut and A3 and C4 r-cut models are shown in Figure 1, illustrating the structural variety of alumina-water interfaces. The reactive sites at mineral-water interfaces are typically defined in terms of the oxygen functional groups formed by the surface oxygen atoms and dissociated (or molecularly adsorbed) H2O. The coordination of the exposed oxygen groups with surface cations and the extent of surface oxygen protonation are both key factors that dictate the reactivity of a particular interface.57,58 The structural interpretation of interface reactivity is based largely on the understanding of surface complex structures arising from spectroscopic and X-ray scattering experiments and via the crystal chemistry bond-valence theory of ionic and covalent bonding, which grew from Pauling’s rules of ioniccrystal stability.59 The bond-valence model of Brown60-64 provides simple expressions to calculate the relative strength of metal-oxygen bonds using input metal-oxygen distances and tabulated parameters and delineates theorems and rules for predicting structure stability. Example analytical expressions for the bond-valence s of atom type i, developed from bond-valence to bond length correlations, are given by  N R ð1Þ si ¼ R0 or

si ¼ expððR0 - RÞ = bÞ

ð2Þ

where R is the observed or input bond length and R0, b, and N are fitted bond-valence parameters. Values of si computed using literature empirical parametrization60-62 are often reported in “valence units”, or v.u., where 1 v.u. is equivalent to one unit of charge in the atomic valence.64 An expression for O-H bonds developed by Bargar et al.,65 in which the O-H distance is denoted as ROH, is given by sOH ¼

0:241 ROH - 0:677

ð3Þ

Figure 1. Side views of the c-cut (top), r-cut A3 (middle), and r-cut C4 (bottom) mineral-water interface structures. Singly, doubly, and triply coordinated surface oxygen atoms are labeled as AlO, Al2O, and Al3O, respectively. Oxygen atoms are shown in large red, aluminum atoms in small blue, and hydrogen in medium-sized gray spheres.

The bond-valence model can be used to place constraints on the stoichiometry and local coordination environments of mineral-water interface species (e.g., adsorbed cations), hence providing some simple constraints useful in the interpretation of X-ray scattering and spectroscopy experiments.66-69 The partitioning behavior of Pb(II) to R-Al2O3 single crystal (0001)70 and (1102) surfaces65 and alumina powders,71 as well as the hematite (R-Fe2O3) analogue (0001) and (1102) surfaces72 and powders,73 has been studied via X-ray absorption spectroscopy measurements. A summary of these experimental studies74 indicates that the Pb(II) reactivity follows the sequence: R-Fe2O3(0001) > R-Al2O3(1102) ≈ R-Fe2O3(1102) . R-Al2O3(0001). In all cases, Pb(II) is bound in an inner-sphere manner to the surface (hydr)oxo moieties, with the possible exception of the (0001) surface in which an outer-sphere hydrated complex is suspected to predominate.70 This empirically determined reactivity trend is interpreted to be a result of differences in the types of surface functional groups (in terms of O-Al coordination and the degree of O protonation) terminating the substrates.74 For example, as shown in Figure 1, the R-Al2O3(0001)-water interface structure consists of only doubly Al-coordinated oxygen functional groups, while the R-Al2O3(1102)-water interface can 4009

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The Journal of Physical Chemistry C have singly, doubly, and triply Al-coordinated oxygen functional groups, labeled as AlO, Al2O, and Al3O, respectively. The protonation state of the functional group can be used to further characterize the potential reactivity. Bond-valence predictions suggest that the -OH groups formed with doubly coordinated surface oxygen atoms, Al2OH, are relatively inert, with bondvalence sums near to the ideal value of the atomic valence of oxygen. Furthermore, from a bond-valence perspective, Al2O-Pb configurations are predicted to be less stable than Al2OH due to oversaturation of the oxygen valence in the former. On the other hand, AlO and Al3O surface functional groups are predicted to form stable bonds with Pb(II), leading to a high affinity for surface complex formation.65,71 Comparison of these bond-valence predictions with more accurate electronic structure calculations will provide a framework to assess the strengths and weaknesses of bond-valence predictions for Pb(II) surface complex geometries. In the present study, we use density functional theory (DFT) to model the adsorption of Pb(II) onto the hydrated (0001) and (1102) alumina faces using previously determined aluminawater interface structural models.30,55,75 This work follows up on our earlier study in which we carried out a similar DFT investigation of Pb(II) adsorption on isostructural hydrated R-Fe2O3 and R-Al2O3(0001) surfaces, focusing on the role of substrate composition for a common surface structure on Pb(II) reactivity,75 and adds to the growing information about metals adsorbed on hydrated minerals from electronic structure methods (see, for example, refs 76-81). The aim of the present study is to determine how the coupling of interface geometry and electronic structure impacts the relative stability of Pb(II) complexes on differently structured R-Al2O3 substrates. To provide a molecular-level understanding of observed reactivity trends, we assign Pb-interface bonding to orientation-dependent Pb-O orbital interactions. We also use our DFT Pb(II)/ Al2O3 structural results in bond-valence model calculations and discuss the strengths and weaknesses of bond-valence predictions for Pb(II) surface complexation.

’ METHODOLOGY AND COMPUTATIONAL DETAILS DFT calculations are carried out using the DMol3 software82 developed by Delley.83,84 All-electron calculations using a double-numeric-plus-polarization, atom-centered basis set with a converged real-space cutoff of 3.5 Å are performed using the generalized gradient approximation (GGA) to the exchangecorrelation functional of Perdew, Burke, and Ernzerhof.85 Previously reported bulk lattice constant optimizations for R-Al2O3, with differences from experiment indicated in parentheses, yielding a = 4.823 Å (þ1.3%) and c = 13.111 Å (þ0.9%), are in good agreement with experiment86 and other DFT-GGA results.30,35,41,87,88 For this Pb(II) adsorption study, we focus on the thermodynamically most stable, and hence most prevalent, aluminawater interfaces over a broad range of environmental conditions, as identified by ab initio thermodynamics30,55 and experimental results.21,22,25 As discussed in the Introduction, the (0001) face exhibits a single hydrated surface stoichiometry, while the (1102) face exhibits several thermodynamically competitive structures. To limit the present study on reactivity, while still representing a reasonable range in (1102) structure and surface functional groups, we model Pb(II) adsorption on both the A3 and C4 r-cut models. The details of these three surface models have been presented previously55,75 and are only briefly reviewed here.

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The c-cut model DFT simulation slab consists of 6 O layers and 10 Al layers, with images along the surface normal separated by more than 25 Å. The A3 (and C4) r-cut simulation slabs consist of 14 (12) O and 8 (6) Al layers, also with an excess of 25 Å separating periodic images along the surface normal. All of the simulation slabs have two equivalent surfaces related by inversion symmetry, and in all geometry optimizations the full slab is allowed to relax with no additional constraints. A force tolerance of 0.01 eV/Å is used in optimizing the geometry of both the clean and Pb(II)-adsorbed surfaces. To reproduce the experimentally observed range of Pb(II) surface concentrations,71 it is necessary to use (2
2) supercells for the c-cut and r-cut models, sampled using a converged (2
2
1) gamma-centered Monkhorst-Pack k-point grid,89 and with Pb(II) adsorption modeled on both sides of the simulation slab to maintain inversion symmetry. To determine how surface oxygen functional group Al coordination influences cation adsorption, we model inner-sphere Pb(II) adsorption at the c-cut and the A3 and C4 r-cut models, spanning Pb(II)-interface bonding at surface -OH functional groups with single Al-coordination (as in A3 and C4), double Alcoordination (as in c-cut and C4), and triple Al-coordination (as in A3). The Al-coordination of different surface oxygen atoms is indicated in the side view of the three interface models shown in Figure 1. (While the C4 model does have terminal triply Alcoordinated oxygen functional groups, they are sterically inaccessible to Pb(II).) The substrates chosen for adsorption studies allow us to examine the bond-valence-based prediction that Al2OH groups, which fully terminate the c-cut model, are less reactive than the AlOH groups terminating the two r-cut models.71 We also test the prediction of relatively high reactivity of aquo groups (OH2) due to the highly labile proton.58 Both of these predictions rely on the oxygen Al-coordination and level of protonation, which are known reactivity factors.90,91 We note an additional gross feature of contrast between the c-cut and two r-cut models, shown in Figure 1: While the c-cut model has a flat topography, both of the r-cut models are corrugated, with high rows of AlOH2 or AlOH groups separated by low-lying rows of Al2OH or Al3OH groups, present in the C4 or A3 structures, respectively Generating initial Pb(II) binding geometries on the previously studied c-cut model is relatively simple as the experimental prediction of predominant distorted trigonal pyramidal Pb(II)/ Al2O3 structures71 and the c-cut model terminal oxygen layer, which forms a triangular sublattice, leads to inherently welldefined, high-symmetry adsorption sites. The adsorption sites, defined by the centers of the surface oxygen sublattice triangles, are distinguished by considering what type of atom, and at what atomic layer number, is encountered going along the surface normal direction into the bulk. Each adsorption site defined in this manner is surrounded by three surface OH groups, two of which lose a hydrogen atom to balance the charge (i.e., maintaining overall charge neutrality). As the orientations of the OH groups are not equivalent (and in fact as we found two energetically degenerate yet chemically distinct hydrogen bond network structures for the c-cut model75), there are multiple ways to displace hydrogen atoms at each adsorption site, quickly scaling up the number of initial geometries to be considered. As previously reported, the hydrogen bonding in the c-cut model is competitive with the adsorption of Pb(II) such that a different Pb(II) site preference is predicted on two different hydrogenbonded surfaces.75 The overall minimum-energy Pb(II)/Al2O3 4010

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Figure 2. Optimized geometry of the Pb(II)/c-cut structure. The top panel is a side view showing three repeats of the full (2
2) simulation slab with two exposed symmetry-related surfaces. The lower panel is a top view of the local Pb(II) geometry, with Pb-O bond lengths indicated in Å. Lead is shown in extra large dark gray, oxygen atoms in large red, aluminum atoms in small blue, and hydrogen in mediumsized gray spheres.

structure we find on the c-cut model has Pb(II) occupying the bulk cation site. That is, the Pb(II) prefers the site corresponding to where the next Al atom would go in a continuation of the bulk structure. This minimum-energy c-cut Pb(II)/Al2O3 structure, referred to as “Pb(II)/c-cut” from here on and shown in Figure 2, was previously reported.75 Here, the Pb(II)/c-cut structure is revisited and characterized in more detail and also used for comparison against the r-cut Pb(II)/Al2O3 structures. Careful testing for changes in the calculated properties as a function of the theoretical treatment of Pb is carried out through a series of benchmarking against reference structures, as fully reported previously.75 The definition of initial Pb(II) adsorption sites is complicated on the r-cut A3 and C4 models owing to the corrugated interface geometries. We therefore take a different approach in constructing initial Pb(II)/Al2O3 structures on the r-cut models: a large number (about 50 for each A3 and C4) of distinct Pb(II)/Al2O3 structures are generated by using bond-valence considerations and a minimum Pb-O bond length of 1.5 Å. For each Pb(II) geometry, hydrogen displacements from surface functional groups within 3.0 Å of Pb(II) are considered. This large pool of potential Pb(II)/Al2O3 geometries are then subjected to precursory geometry optimization in which only ten structural optimization steps are made. The results are then tabulated, and 1/2 of the structures is discarded based on the DFT total energy results. This farming procedure is repeated, each time discarding about half of the highest-energy structures, until a manageable

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subset of 5 Pb(II)/Al2O3 structures for each of the two r-cut models is left and fully optimized; of these, only the minimumenergy structures are reported in detail here. While it is possible that some low-energy Pb(II)/Al2O3 were missed in this procedure, the approach taken here avoids thermal molecular dynamics simulations that are judged to be computationally prohibitive to the present study. Another modeling consideration is how to calculate an adsorption energy for Pb(II) that can be compared between the (varying stoichiometry) R-Al2O3 c- and r-cut interfaces. This matter is further complicated by the desire to have a consistent level of computational accuracy for all species that contribute to the adsorption energy. While periodic DFT-GGA is well-suited for the description of the interface and the formation of Pb(II) surface complexes, it is not an ideal methodology for describing the properties of the solvated cation. Furthermore, theoretical descriptions of the hydration properties of aqueous Pb(II) and other geochemically relevant metals are still active research topics.92-96 This leads to complications that include disagreement between theoretical studies on fundamental factors such as the number of water molecules in the first coordination shell of divalent lead.92,97,98 Therefore, we find it to be advantageous in the present study to circumvent explicit treatment of the cation hydration, especially since the adsorption energy can be partitioned such that this information could be added in at a later time. The overall reaction of interest is the adsorption of the lead cation coming from a hydrated aqueous source, [Pb(H2O)nþ2]2þ, where nþ2 is the total number of waters in the hydration sphere of Pb2þ. In the present study, we are targeting the reaction for a bidentate charge-neutral surface complex. To balance the stoichiometry, the lead cation displaces two surface hydrogen atoms from reactive surface functional group(s) labeled as Al(OH2), forming the overall neutral surface complex species denoted as ([Al(O2)]2-, [Pb(H2O)n]2þ). The displaced hydrogen atoms stay attached to two of the lead waters of hydration as H3Oþ. AlðOH2 Þ þ ½PbðH2 OÞn þ 2 2þ f ð½AlðO2 Þ2 - , ½PbðH2 OÞn 2þ Þ þ 2H3 Oþ

ð4Þ

Computing the reaction energy as written in eq 4 directly using periodic DFT-GGA is complicated both by the presence of charged species and by the difficulty in accurately describing the solvated cation. We therefore partition the overall reaction into two steps AlðOH2 Þ þ Pb½ðOHÞ2 , H2 On  f ð½AlðO2 Þ2 - , ½PbðH2 OÞn 2þ Þ þ 2H2 O ðaÞ 2H2 O þ ½PbðH2 OÞn þ 2 2þ f Pb½ðOHÞ2 , H2 On  þ 2H3 Oþ ðbÞ ð5Þ

where Pb[(OH)2, H2On] is a neutral intermediate species that may or may not be realistic under environmental conditions. The energy of the reaction in eq 5a is readily accessible through periodic DFT-GGA. The complications arising from charged species and the hydrated cation are all contained in step 5b; therefore, for the purpose of comparing the relative reactivity of different interfaces, the energy of step 1 is sufficient. Such relative energies can then be transformed to absolute energies through the addition of the cation-dependent (but interface-independent) step 5b. It is worth emphasizing that the equations for the adsorption energy (eqs 4-6) are intended to be generic 4011

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The Journal of Physical Chemistry C and do not assume details about the Al(OH2) functional group(s) involved. Here, we make the assumption that the value of n in eq 5 is 0. In other words, we assume that surface-bound Pb(II) has no H2O or OH ligands from solution and is only coordinated to the surface oxygen functional groups. In doing so, we effectively use the gas-phase Pb(OH)2 complex (of known atmospheric interest99) as a reasonable reference in determining surface adsorption energies. Taking into account the two inversion-related surfaces in our modeled slab, and under our sign convention of more positive values representing more favorable adsorption, our expression for the Pb(II) adsorption energy, Eads, is 1 Eads ¼ ½ðEsurf þ 2EPbðOHÞ2 Þ - ðEsurf = Pb þ 4EH2 O Þ ð6Þ 2 where Esurf and Esurf/Pb are the DFT total energies of the c-cut and r-cut models and the models with two hydrogen atoms displaced by Pb(II), respectively. EH2O and EPb(OH)2 are the DFT total energies of the isolated gas-phase water and Pb complex, respectively. Values of Eads for Pb(II) on R-Al2O3(0001) from eq 6 are reported in our previous Pb(II) adsorption study.75 Here, we elect to emphasize that using the energy partitioning in eq 5 we are only computing relative adsorption energies. We reference the most favorable value of Pb(II) Eads on R-Al2O3(0001) to zero, and report values of ΔEads. Using the inner-sphere adsorption energy of Pb(II) on R-Al2O3(0001) as an energetic point of reference is a reasonable choice based on reports that weakly bound outer-sphere Pb(II) adsorption dominates on this interface.70 To characterize the cation-interface interactions and to provide a molecular-level understanding of the empirically observed Pb(II)/Al2O3 reactivity trends, we apply several electronic structure analysis methods. To visualize the bonding interactions of adsorbed Pb, we examine the deformation density Fd defined within DMol3 as ð7Þ Fd ¼ Fr - ΣR FR ðr - RR Þ where Fr is the system charge density and FR(r - RR) is the density of the free atom R located at coordinates RR. Regions of Fd > 0 indicate bond formation, while Fd < 0 indicate electron loss relative to the gas-phase neutral atomic species. A particularly helpful analysis in assigning bonding interactions to specific electronic states of specific atoms is the use of state-by-state atom-projected density of states (PDOS). This semiquantitative method projects the single-electron KohnSham orbitals onto atomic orbitals centered at the atomic positions determined in the geometry optimization. Using PDOS analysis, intensity from different states and different atoms at common energies below the Fermi level (εF), indicative of covalent bonding, can be related to the s, p, and d contributions of participating atoms. Likewise, surface atoms with PDOS unaffected by Pb(II) adsorption, as determined by comparison with the clean interfaces, can be identified and thus shown to not play a significant role in adsorption. In our previous study, we used PDOS analysis to characterize a Pb(II)-O covalent interaction in the Pb(II)/c-cut system. Covalent resonances were noted at about 0.7 eV below εF, consistent with the experimental observation that the c-cut Al2O3 is relatively nonreactive toward Pb(II). In the present study, we carry out PDOS analysis of optimized Pb(II)/Al2O3 structures to assign bonding interactions as a function of interface geometry. To improve upon the character-

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Table 1. Relaxations for the Pb(II)/c-Cut Structurea ΔEads = 0.00 d

Δsurf

Δbulk

O1-Al2

0.910

8.6

0.2

Al2-Al3

0.336

-33.8

6.0

Al3-O4

0.932

11.2

0.1

O4-Al5

0.844

0.7

3.3

Al5-Al6

0.517

1.7

6.2

Al6-O7

0.831

-0.9

3.4

O7-Al8

0.836

-0.2

0.3

a

The interplanar separations d are reported in Å along with the percent changes relative to the hydrated surface (Δsurf) and bulk R-Al2O3 (Δbulk) values. Atomic layers are labeled numerically and consistently with our previous study.75 The relative adsorption energy (ΔEads, as defined in the text) is reported in eV.

ization of Pb(II)/Al2O3 bonding previously determined75 and to identify the role of orbital directionality and overlap, here we exploit a PDOS decomposition by both the l and m quantum numbers of each atomic orbital. The utility of such an “orbitalspecific” PDOS analysis has been demonstrated in other adsorption systems.100 Here, we refer to this more detailed analysis as “lmDOS”.

’ RESULTS The results of modeled Pb(II)/Al2O3 systems are analyzed and presented in terms of geometry, energy, and electronic structure. We focus on the common substrate identity but varying geometries of the three modeled R-Al2O3-water interfaces to extract how structure controls reactivity. Optimized Geometry of Pb(II)/Al2O3. We detail the DFToptimized geometries of four Pb(II)/Al2O3 structures: the previously reported Pb(II)/c-cut structure, two nearly degenerate (but structurally distinct) Pb(II) surface complexes on the A3 interface (referred to as “Pb(II)/A3a” and “Pb(II)/A3b”), and the minimum-energy Pb(II) surface complex found on the r-cut C4 model, referenced as “Pb(II)/C4.” The previously reported75 Pb(II)/c-cut structure, shown in Figure 7, forms two shorter Pb-O bonds (2.17 and 2.19 Å) and one longer Pb-OH bond (2.36 Å). The shortest Pb-Al distance is 3.50 Å. These details of geometry are in good agreement with the postulated local Pb(II) coordination environment based on powder Pb(II)/R-Al2O3 X-ray studies71 that predict a trigonal pyramid geometry with Pb-O distances in the range of 2.182.35 Å and Pb-Al distances ranging from 3.16-3.32 Å. The DFT-optimized interlayer spacings in the Pb(II)/c-cut structure are presented in Table 1. The layers in the slab are referred to by numerical order, starting at the outermost atomic layer, made up of oxygen atoms and designated as O1. The percent differences with respect to the DFT-optimized c-cut interface geometry and theoretical bulk spacings are also reported as Δsurf and Δbulk, respectively. As listed in Table 1, the value of Δsurf for the topmost Al-Al bilayer (formed between Al2-Al3) is -33.8%. The result that Pb(II) adsorption has a relatively large impact on the Al2-Al3 bilayer has been found to persist for a number of Pb(II)/c-cut systems as well as hematite analogues.75 The value of Δsurf for the outermost layers (O1-Al2) is positive. This finding is expected, as the interaction with Pb(II) satisfies a portion of the bond-valence of nearby surface oxygen atoms. Therefore, the oxygen atoms participating in Pb-O bonding 4012

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Figure 3. Optimized geometry of the Pb(II)/A3a structure. The top panel is a side view showing 3 repeats of the full (2
2) simulation slab with two exposed symmetry-related surfaces. The lower panel is a top view of the local Pb(II) geometry, with Pb-O bond lengths indicated in Å. Lead is shown in extra large dark gray, oxygen atoms in large red, aluminum atoms in small blue, and hydrogen in medium-sized gray spheres.

interact less with surface Al atoms, resulting in relaxations outward from the surface. The optimized geometries of the (nearly degenerate) Pb(II)/ A3a and Pb(II)/A3b surface complexes are shown in Figure 3 and Figure 4, with interplanar spacings reported in Table 2. Again, the layers in the slab are referred to by numerical order starting with the terminal layer of oxygen atoms labeled O1. For both Pb(II)/A3a and Pb(II)/A3b, Pb(II) adsorption expands the outermost O1-Al2 layer separation with respect to the hydrated surface, consistent with the outward surface relaxation in the Pb(II)/c-cut system. The positive values Δsurf for the outermost atomic layers in Pb(II)/A3a and Pb(II)/A3b are expected, as in the adsorbed systems Pb(II) partially satisfies the bond valence of nearby terminal oxygen atoms, leading to decreased O-Al interaction and outward adsorption-induced surface relaxation. The initial geometry for Pb(II)/A3a was formed by approximating an edge-sharing bidentate configuration, as suggested by bond-valence analysis and by extended X-ray absorption fine structure interpretation of Pb(II)/Al2O3 powder studies.71 In the initial geometry, Pb(II) forms bonds of 2.1 and 2.3 Å with singly Al-coordinated and triply Al-coordinated surface oxygen atoms, respectively. The formal charge on Pb(II) is balanced by removing two hydrogen atoms from two Al3OH groups near the Pb(II) adsorption site and within the same “valley” between the outermost row of AlOH groups. In the optimized geometry, Pb(II)/

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Figure 4. Optimized geometry of the Pb(II)/A3b structure. The top panel is a side view showing three repeats of the full (2
2) simulation slab with two exposed symmetry-related surfaces. The lower panel is a top view of the local Pb(II) geometry, with Pb-O bond lengths indicated in Å. Lead is shown in extra large dark gray, oxygen atoms in large red, aluminum atoms in small blue, and hydrogen in mediumsized gray spheres. The adsorption-induced surface hydrogen rearrangement is highlighted by circling the formed bare doubly coordinated oxygen and the formed aquo group.

Table 2. Relaxations for the Pb(II)/A3a and Pb(II)/A3b Structuresa Pb(II)/A3a

Pb(II)/A3b

ΔEads = 0.56

ΔEads = 0.67 Δsurf

d O1-Al2

1.367

Al2-O3 O3-Al4

0.293 0.779

Δbulk

5.4 -17.8 1.6 -4.7

8.1 3.1

d 1.365 0.310 0.756

Δsurf

Δbulk

5.3 -13.0 7.6 -7.2

5.2 3.6 -5.2

Al4-O5

0.743

1.2

-7.5

0.747

1.8

O5-O6

0.329

5.2

0.5

0.338

7.9

0.2

O6-Al7

1.381

-0.9

-2.7

1.376

-1.3

-1.7

Al7-O8

0.346

1.9

-0.2

0.350

2.9

-0.1

a

The interplanar separations d are reported in Å along with the percent changes relative to the hydrated surface (Δsurf) and bulk R-Al2O3 (Δbulk) values. Atomic layers are labeled numerically and consistently with our previous study.55 The relative adsorption energy (ΔEads, as defined in the text) is reported in eV.

A3a exhibits a high degree of coordination with the interface, forming five Pb-O bonds ranging from 2.42 to 2.66 Å. The 4013

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The Journal of Physical Chemistry C DFT-optimized distances between Pb(II) and the edge-sharing triply and singly Al-coordinated oxygen atoms are 2.58 and 2.45 Å, respectively. Pb(II) forms two other bonds to AlOH groups: one Pb-O bond of 2.55 Å is formed with an AlOH group in the same row (going into the surface from the perspective of Figure 4) of surface AlOH atoms as the Pb(II) complex edge-sharing OH group. The other Pb-O bond is 2.66 Å and is formed with an AlOH group in an adjacent row of AlOH groups. The Pb-Al distance formed with the Al atom defining the edge-sharing AlO6 octahedra is 3.23 Å, while the Pb-Al distance to the neighboring AlO6 octahedra (containing the AlOH group that forms a 2.66 Å bond with Pb(II)) is 3.05 Å. It is worth noting that the shortest Pb-Al distance is not formed with the same AlO6 octahedron that participates in the shortest Pb-O bonds, as was assumed in the interpretation of X-ray absorption fine structure (XAFS) Pb-Al separations in powder Pb(II)/R-Al2O3 studies.71 The evolution of Pb(II)/A3b from its starting to optimized geometry (shown in Figure 4) exhibits unique characteristics relative to the (nearly degenerate) Pb(II)/A3a structure. In the initial geometry, Pb(II) was again assumed to be in an edgesharing configuration, forming short Pb-O bonds to triply and singly coordinated surface oxygen atoms participating in the same AlO6 octahedron. To balance the charge of the adsorbing cation, one hydrogen atom was removed from the Al3OH group of the edge-sharing configuration. The second hydrogen atom removed comes from a neighboring row AlOH group. In the optimized geometry, significant rearrangement of surface hydrogen atoms occurs: An Al3OH group, in the same row as the edgesharing Al3O group, effectively donates its hydrogen to an AlOH group in the row to the left of the Pb(II) site in the perspective of Figure 4. In the starting geometry, the distance this migrating hydrogen atom forms with the involved Al3O and AlOH group oxygen atoms is 1.01 and 1.80 Å, respectively. In the optimized geometry, these lengths are nearly reversed: The Al3O-H distance elongates to 1.71 Å, and the AlOH-H distance reduces to 1.02 Å, which effectively forms an AlOH2 group (highlighted as the left-most circled functional group in the top view of Figure 4). Furthermore, the oxygen of a bare (deprotonated) AlO group in the starting geometry recovers a hydrogen atom from an Al3OH group in the “valley” to the left of the Pb(II) site in the perspective of Figure 4. The result of this adsorptioninduced hydrogen rearrangement is that there is a bare Al3O group 5.14 Å away from the lead atom in the final Pb(II)/A3b geometry (highlighted as the right-most circled functional group in the top view of Figure 4). The electronic structure of and reactivity implications for this surface functional group are considered in later sections. The fourth optimized surface complex geometry that we discuss in detail is Pb(II)/C4, shown in Figure 5 and formed from modeling Pb(II) adsorption on the r-cut C4 interface structure. The interplanar distances of Pb(II)/C4 are provided in Table 3. The terminal atomic layer of oxygen atoms is labeled as O1. The C4 model is missing an atomic layer of Al, and the next present atomic layer is made up of oxygen and is labeled O3. In contrast to Pb(II)/c-cut, Pb(II)/A3a, and Pb(II)/A3b, Δsurf of the outermost layer spacing in Pb(II)/C4 is negative. This is counterintuitive to the prediction that Pb-O interactions at the surface will decrease surface O-Al interactions and result in surface outward relaxations. The initial Pb(II)/C4 geometry is a Pb(II) bidentate structure involving AlOH2 and AlOH functional groups from different AlO6 octahedra. The hydrogen

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Figure 5. Optimized geometry of the Pb(II)/C4 structure. The top panel is a side view showing three repeats of the full (2
2) simulation slab with two exposed symmetry-related surfaces. The lower panel is a top view of the local Pb(II) geometry, with Pb-O bond lengths indicated in Å. Lead is shown in extra large dark gray, oxygen atoms in large red, aluminum atoms in small blue, and hydrogen in mediumsized gray spheres.

Table 3. Relaxations for the Pb(II)/C4 Structurea ΔEads = 0.79 d

Δsurf

Δbulk

O1-O3

1.381

-3.1

0.5

O3-Al4 Al4-O5

0.680 0.368

54.5 8.2

-5.7 3.3 -1.0

O5-O6

1.360

-1.3

O6-Al7

0.369

3.7

3.7

Al7-O8

0.726

-0.5

0.6

a

The interplanar separations d are reported in Å along with the percent changes relative to the hydrated surface (Δsurf) and bulk R-Al2O3 (Δbulk) values. Atomic layers are labeled numerically and consistently with our previous study.55 The relative adsorption energy (ΔEads, as defined in the text) is reported in eV.

atoms removed to balance the adsorbing cation charge come from two different AlOH2 groups, one participating in the initial bidentate structure and the other from a neighboring group. In the optimized geometry, Pb(II) is fairly well centered above an Al2OH group connecting two neighboring surface AlO6 octahedra. The Pb-OH bond distance of the shared Al2OH group is 2.39 Å. The other Pb-OH bond formed with the Al2OH on the bidentate edge site is 2.45 Å. The Pb-OH bonds formed with 4014

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The Journal of Physical Chemistry C the neighboring AlOH groups (each of which existed as AlOH2 groups in the r-cut C4 interface structure) are 2.43 and 2.45 Å, with Pb-Al distances of 3.20 and 3.43 Å in each AlO6 associated octahedra, respectively. The details of the Pb(II)/C4 structure provide an explanation for the unexpected negative value of Δsurf for the terminal O1O3 atomic layers. As shown in Table 3, the O1-O3 value of Δsurf is -3.1%, and the O3-Al4 value of Δsurf is þ54.5%. Therefore, the surface inward relaxation of the O1-O3 layers is small relative to the large expansion in the O3-Al4 layer spacing. Therefore, the expected adsorption-induced surface relaxation is fulfilled by the large outward O3-Al4 relaxation. This highlights another unexpected finding: the relatively large value of Δsurf for the O3-Al4 spacing, 54.5%, is larger than any other value of Δsurf in the minimum-energy Pb(II)/Al2O3 structures reported in this study, begging the question as to how Pb(II)/C4 can also be a minimum-energy configuration. The explanation of how Pb(II)/C4 can energetically “afford” the relatively large interplanar O3-Al4 surface relaxation lies in the orientation of the OH groups of the O3 layer. As can be seen in Figure 1, the Al2OH groups have hydrogen directed into the surface, forming surface hydrogen bonds with deeper (layer 5) surface oxygen atoms (05). In addition to the values of Δsurf reported in Table 3, the values of ROH can also be compared before and after the Pb(II) adsorption. In the C4 geometry, the Al2OH value of ROH is 1.01 Å, and the distance between the hydrogen and the O5 atom at which it is directed is 1.65 Å. In the optimized Pb(II)/C4 geometry, the average Al2OH value of ROH (for the two A2OH groups at the Pb(II) adsorption site) is 1.045 Å, and the corresponding H-O5 distance is 1.52 Å. Therefore, the relatively large adsorption-induced relaxations in Pb(II)/C4 appear to be compensated for energetically by adjustments in the surface hydrogen bonding. While the details of the minimum-energy Pb(II)/Al2O3 geometries vary and span Pb-O interactions across several O-Al and O-H coordinations, a notable commonality among the three detailed minimum-energy Pb(II)/r-cut geometries is that Pb(II) always occupies “valleys” between rows of AlOH or AlOH2 functional groups. A number of metastable Pb(II)/Al2O3 structures were found on both the A3 and C4 interfaces, the energetics of which are detailed in the next section. However, we consistently find that structures with Pb(II) occupying the topographical valleys are preferred over structures in which Pb(II) surface complexes form on “hills” of surface oxygen functional groups The structural results also show that the average DFT Pb-O bond distance RPb-O on the r-cut interfaces is longer than those on the c-cut interface. The average RPb-O in the Pb(II)/c-cut structure is 2.24 Å, in good agreement with the range of 2.18-2.35 Å reported in powder studies of Pb(II)/ Al2O3.71 The average value of RPb-O spanning the Pb(II)/A3a, Pb(II)/A3b structures is 2.48 Å. This is longer than the best-fit value obtained using a single shell of oxygen atoms in a study of single-crystal Pb(II)/Al2O3(1102).65 However, in the same study, a fit using a second shell of oxygen atoms yielded RPb-O = 2.28 and 2.48 Å, where the longer distance is attributed to a separate Pb(II) coordination environment. Therefore, our DFT values of RPb-O are overall in reasonable agreement with experiment. It is possible that our inability to find a Pb(II)/rcut geometry with RPb-O closer to the shorter experimental value of 2.28 Å arises from the difficulty to computationally explore the complicated r-cut potential energy surface, which gives rise to several metastable minima. Furthermore, given the known

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Table 4. ΔEads, in eV, Calculated by Equation 6 and Referencing Eads of Pb(II)/c-cut to Zeroa ΔEads Pb(II)/c-cut

0.00

Pb(II)/A3a Pb(II)/A3b

0.56 0.67

Pb(II)/C4

0.79

a

Values for the four minimum-energy Pb(II) surface complexes are given, with ranges of values for metastable geometries detailed in the text.

dependence of mineral-water interface structural details on surface preparation in similar substrates25,27,56,101,102 and the theoretical prediction of several thermodynamically competitive structures of hydrated R-Al2O3(1102),55 it is possible that the shorter experimentally observed rPb-O occurs at interface geometries (or defects) not included in the present modeling. DFT Energetics of Pb(II)/Al2O3. Relative Pb(II) adsorption energies, ΔEads, calculated using eq 6 and referencing Eads of Pb(II)/c-cut to zero, are presented in Table 4 for the four minimumenergy Pb(II)/Al2O3 structures. As noted in the Methodology and Computational Details section, numerous starting geometries of Pb(II) on both the A3 and C4 interface models were considered, with high-energy structures excluded through incremental geometry optimizations. Ultimately, a total of 7 Pb(II)/A3 and 8 Pb(II)/C4 were fully optimized, leading to the Pb(II)/A3a, Pb(II)/A3b, and Pb(II)/C4 structures detailed above and 12 additional metastable Pb(II)/r-cut geometries. The range of ΔEads for different fully optimized Pb(II)/r-cut structures is -0.31 to 0.67 eV for Pb(II)/ A3 and 0.16-0.79 eV for Pb(II)/C4. From our previous study and the current definition of ΔEads, the range found on the R-Al2O3(0001) interface is -1.13 to 0.00 eV. Our DFT-based adsorption energetics are therefore consistent with the experimentally based observation that Pb(II) reactivity follows the sequence R-Al2O3(1102) . R-Al2O3(0001).74 Electronic Structure of Pb(II)/Al2O3. We begin the results for the electronic structure of the sorbate systems by plotting isosurfaces of Fd for Pb(II)/Al2O3 structures. We employ Fd visualization prior to more detailed electronic structure analysis to first qualitatively identify key features of interface bonding, and as such we compute Fd using truncated slab models with the atomic positions fixed at the optimized values for the full simulation cells. The qualitative interpretation of Fd is unaffected by the use of these more computationally convenient structural models. We note that Fd of all three minimum-energy Pb(II)/ r-cut structures is similar and detail the results for Pb(II)/C4. The calculated Fd of the Pb(II)/c-cut model (we previously reported Fd for the full Pb(II)/c-cut simulation cell but repeat the analysis here for a truncated slab model for a consistent comparison with Fd calculated for truncated Pb(II)/r-cut geometries) is shown in the upper panel of Figure 6. The positive isosurface above Pb(II) and directed away from the surface clearly shows an asymmetric electron distribution around lead, consistent with a stereoactive Pb(II) lone pair such as is reported in Pb(II) bulk103,104 and surface complex73 structures. The positive isosurfaces on Pb(II)-bound oxygen atoms are spatially back-toback with negative isosurface intensity on Pb(II), indicative of ionic Pb-O bonding relative to gas-phase neutral O and Pb atomic species. Additionally, the shape of the isosurfaces centered about Pb(II) are suggestive of sp hybridization, while the shape of the isosurfaces centered about Pb(II)-bound oxygen 4015

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Figure 7. lmDOS of the Pb(II)/c-cut structure. The projections onto Pb are shown in the left panel; projections onto oxygen atoms of doubly Al-coordinated functional groups (Al2O) bound to Pb are shown in the middle panel; and the projection onto the oxygen atom of the doubly Alcoordinated OH group (Al2OH) weakly bound to Pb is shown in the right panel.

Figure 6. Isosurfaces of the deformation density Fd calculated for Pb(II)/c-cut. The values shown are within a sphere of 5.50 au (2.91 Å) centered about Pb. Dark (turquoise) isosurfaces show areas of charge gain, while light (gray) isosurfaces show ares of charge loss, relative to gas-phase neutral species. The atomic positions (not including hydrogen, which is left out to better show the isosurfaces) are indicated by large (dark gray) spheres for Pb, medium (red) spheres for oxygen, and small (blue) spheres for aluminum. Top: Pb(II)/c-cut. Bottom: Pb(II)/C4.

atoms indicates that the oxygen p states are interacting with the Pb(II) sp-hybrid. The calculated Fd of Pb(II)/C4 is shown in the lower panel of Figure 6 and shows many characteristics similar to that of Pb(II)/ c-cut. One notable difference is that in Pb(II)/C4 the asymmetric charge density in Pb(II) is not oriented directly along the surface normal but instead is slightly tilted toward the surface plane. While the shape of the isosurfaces centered about Pb(II)-bound oxygen atoms still shows that oxygen p states are interacting with Pb(II), the Fd of Pb(II)/C4 shows that the directionality of the O p states interacting with Pb(II) is not the same for all Pb-O interactions. Specifically, the oxygen atoms below Pb(II) show charge pointed roughly in the direction of the surface normal toward Pb(II), while the oxygen atoms on either side of Pb(II) have charge directed along the surface plan. This foreshadows the importance of differentiating between in-plane and out-of-plane Pb-O interactions. The next electronic structure analysis we carry out is atomcentered lmDOS. Our surface cells are oriented with the surface normal along the z-direction. Therefore, in the lmDOS, the inplane p-projection (referred to as p1) is the sum of the l = 1, m = (1 projections, while the out-of-plane p-projection (referred to as p0) is the l = 1, m = 0 projection. The lmDOS of the Pb(II)/c-cut structure is presented in Figure 7 and provides a more detailed description of the covalent

Pb-O interactions than previously reported.75 The projections onto the oxygen atoms in both of the doubly Al-coordinated functional groups bound to Pb(II), but not to hydrogen, (Al2O) are shown as an average in the middle panel of Figure 7. The PbO distances with Al2O are 2.21 and 2.22 Å. The right-hand panel of Figure 7 shows the projection onto the oxygen atom of a third doubly Al-coordinated OH functional group (Al2OH) that is 2.31 Å from Pb. Comparing the Pb and Al2O lmDOS, a resonance made up of Pb s, Pb p0 (but with no contribution from Pb p1), and O p0 (but not O p1) has intensity centered about the Fermi level. As this state is at εF, it can be interpreted to be inert and likely made up of the asymmetric Pb(II) electrons. A second Pb-O resonance is noted at 0.7 eV below εF and is made up of contributions from Pb s and Pb p0. The Al2O oxygen contributions to this state come from O p1 O p0, in an approximate 3:1 ratio. Another resonance at 0.3 eV below εF arises from O-O interaction without participation from lead, a detail made more clear under the present lmDOS analysis. The lmDOS of the oxygen atom in the Al2OH group shows far less interaction with Pb states, consistent with bond-valence predictions.65 Finally, we note that there is an absence of Pb s-Pb p1 or Pb p0-Pb p1 interaction either above or below εF. The lmDOS of Pb(II)/A3a and Pb(II)/A3b are shown in Figure 8 and Figure 9. As noted in the above description of the optimized Pb(II)/A3a geometry, Pb(II) forms bonds with several AlOH groups and two Al3O groups. The sum of projections onto each differently coordinated oxygen atom is calculated and divided by the number of participating atoms in the presented plots. Similar to the Pb(II)/c-cut lmDOS is the fact that the in- and out-of-plane Pb and O contributions play distinct roles. Also, the inert Pb-O resonance centered at εF is again observed in both Pb(II)/A3a and Pb(II)/A3b. A stark contrast between the lmDOS of Pb(II)/c-cut and Pb(II)/A3b is the existence of a low-lying Pb-O bonding resonance found only in the latter. This resonance is made up of mostly Pb s and oxygen p1 of the AlO group, with weak contribution from oxygen p0 of AlO and oxygen p of Al3O, at 7.0 eV below εF. For comparison, we repeat that the lowest-energy Pb-O resonance seen, the Pb(II)/c-cut lmDOS, is at 0.7 eV below εF, roughly ten times higher in energy than the Pb-O bonding seen in Pb(II)/A3b. We note that this low-lying Pb-O 4016

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Figure 8. lmDOS of the Pb(II)/A3a structure. The projections onto Pb are shown in the left panel, the projections onto oxygen atoms of triply Al-coordinated functional groups (Al3O) bound to Pb in the middle panel, and projections onto oxygen atoms of singly Al-coordinated OH functional groups (AlOH) bound to Pb in the right panel.

Figure 9. lmDOS of the Pb(II)/A3b structure. The projections onto Pb are shown in the left panel, the projections onto oxygen atoms of triply Al-coordinated functional groups (Al3O) bound to Pb in the middle panel, and projections onto oxygen atoms of singly Al-coordinated OH functional groups (AlOH) bound to Pb in the right panel.

covalent resonance is also present in the R-PbO PDOS reported in DFT studies of the bulk oxide.103,104 Furthermore, recent DFT work characterizing Pb(II) surface complexes at edge sites in birnessite nanoparticles reveals Pb-O orbital overlap in the energy range of -6 to -3 eV below the Fermi level,79 further suggesting that the absence of coincident Pb and O PDOS intensity at lower energies in the topographically flat Pb(II)/ccut structure is a sign of relative instability. Another difference in comparing the Pb(II)/c-cut lmDOS with that of Pb(II)/A3a and Pb(II)/A3b is the appearance of Pb s-Pb p1 and Pb p0-Pb p1 interactions, particularly above εF. The lmDOS of Pb(II)/A3b in Figure 9 is similar to that of Pb(II)/A3a, again showing more oxygen contribution from the Pb(II)-bound AlOH group to the relatively low-lying Pb-O resonance. The geometry shown in Figure 4 shows that the Al3O groups participating in Pb-O bonding are oriented vertically relative to Pb(II), while the AlOH groups participating in Pb-O bonding are offset sideways with respect to Pb(II). As detailed in the discussion of Pb(II)/A3b, an adsorption-induced surface hydrogen rearrangement results in a bare (not protonated) Al3O group 5.15 Å away from the adsorbed Pb(II). The lmDOS of the adsorbed lead and the bare Al3O oxygen atom are presented in

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Figure 10. lmDOS of the Pb(II)/A3b structure. Projections onto Pb are shown in the left panel. The projections onto oxygen in Al3O and Al3OH functional groups are shown in the middle and right panels. The middle panel shows the lmDOS of the oxygen from the functional group that donates its hydrogen atom to an AlOH group during the geometry optimization trajectory. The right panel shows the lmDOS of an oxygen from an Al3OH group from the same row of surface oxygen atoms, for comparison. The Pb-O distances (RPb-O) are indicated.

Figure 11. lmDOS of the Pb(II)/C4b structure. The projections onto Pb are shown in the left panel, the projections onto oxygen atoms of doubly Al-coordinated OH functional groups (Al3OH) bound to Pb in the middle panel, and projections onto oxygen atoms of singly Alcoordinated OH functional groups (AlOH) bound to Pb in the right panel.

Figure 10. Despite the relatively large spatial separation, the bare Al3O group oxygen shows strong overlap with Pb-O resonances near εF. The lmDOS of an Al3OH oxygen atom in the same row as the bare Al3O group, 4.40 Å away from the adsorbed Pb(II), is also shown in Figure 10. Despite being closer to the adsorbed cation than the bare Al3O group oxygen, the oxygen in the Al3OH group does not show significant overlap with the covalent Pb-O resonances. Finally, the lmDOS of Pb(II)/C4 is shown in Figure 11. Again, bonding resonances at energies lower than what is present in Pb(II)/c-cut are observed. In the case of Pb(II)/C4, there are two low-lying Pb-O bonding resonances, one at 7.25 eV below εF and one at 8.0 eV below εF. The atomic contributions to the resonance at -8.0 eV are made up of Pb s and oxygen p1 of the AlOH group interacting with lead. The resonance at -7.25 eV has more diverse contributions, spanning Pb s and p, oxygen p1 and p0 from the Pb(II)-bound AlOH group, and oxygen p1 and p0 from the Pb(II)-bound Al2OH group. As in the Pb(II)/A3 4017

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The Journal of Physical Chemistry C structures, Pb s-Pbp1 and Pb p0-Pb p1 interactions above εF and weak O p and Pb p1 interactions below εF are seen.

’ DISCUSSION The presence of low-lying Pb-O bonding resonances in all three of the detailed Pb(II)/r-cut geometries but absent in the Pb(II)/c-cut geometry, along with the in-plane and out-of-plane lmDOS analysis, suggests a hybridization-reactivity relationship in Pb(II)/Al2O3: On the corrugated r-cut substrates, Pb(II) prefers adsorption sites within “valleys” of oxygen functional groups because these sites allow for simultaneous side-to-side and vertical overlap with nearby oxygen atoms. On the topographically flat c-cut substrate, the Pb-O overlap is limited, resulting in weaker Pb(II) adsorption. Therefore, the coupling of interface geometry and electronic structure gives rise to stronger Pb(II) adsorption on the modeled (1102) interfaces than on the (0001) interface. We summarize the role of directional Pb-O bonding in Pb(II)/Al2O3 stability through a schematic orbitalgeometry representation detailed below. Orbital Interpretation of Pb(II)/Al2O3. The Pb-O bonding in the Pb(II)/Al2O3 surface complexes is highly ionic, but the varying Pb-O covalent interactions, as detailed in the lmDOS, can be used to interpret and explain the variations in ΔEads. To summarize the detailed lmDOS descriptions of Pb-O covalent interactions in a simplified chemical interpretation, we create Hoffmann105,106-inspired schematics of Pb-O orbital interactions. While Fd of Pb(II)/r-cut does show some tilt in the asymmetric Pb(II) charge, for simplicity we represent the interacting Pb orbital as an spz hybrid. On the basis of the lmDOS, we distinguish the oxygen px/py orbitals from the oxygen pz. We assume a planar geometry with Pb(II) and four oxygen atoms, two roughly sideways to Pb(II) and two roughly below Pb(II). The sideways oxygen atoms are labeled Oh and represent the “hills” of oxygen functional groups present on the (1102) interfaces. The low-lying oxygen atoms are labeled Ov and represent the “valley” oxygen functional groups in the (1102) or the single surface plane of oxygen function groups in the (0001) interface. The resulting four classes of Pb-O interactions are Pb spz and Ohpx/Ohpy, Pb spz and Ohpz, Pb spz and Ovpz, and Pb spz and Ovpx/ Ovpy, drawn in Scheme 1 panels (a), (b), (c), and (d), respectively. Using this representation to determine the Pb-O interactions on the R-Al2O3 interfaces, we note that all four interactions are possible in the three minimum-energy Pb(II)/r-cut geometries, while only the latter two interactions are possible in the Pb(II)/c-cut geometry. Thus, this DFTguided simple orbital analysis can be used to interpret the Pb(II) reactivity trend, and we suggest that the same approach could be used in the prediction or interpretation of a variety of mineralwater reactivity problems. Bond-Valence Analysis of DFT Pb(II)/Al2O3 Structures. The variety of Pb(II)/Al2O3 structures found in the present study through DFT geometry optimization provides an opportunity to test the agreement between DFT and the bond-valence model. We use eq 2 with literature values taken from Brown62 to compute the valence sums of Pb, O, and Al atoms and eq 3 to compute OH contributions. For the latter, we impose a tolerance of 2.5 Å above which the OH valence contribution is set to zero. This effectively limits the counted OH contributions to neighboring surface oxygen atoms. The resulting valence sums for all four Pb(II)/Al2O3 structures studied in detail have near-ideal (within 0.1 v.u.) average values for O, Al, and H atoms. However, the computed valence sums for Pb vary greatly between the

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c-cut and r-cut surface complexes, resulting in values of 2.30, 1.71, 1.76, and 1.87 v.u. for Pb(II)/c-cut, Pb(II)/A3a, Pb(II)/ A3b, and Pb(II)/C4, respectively. In all structures analyzed, the compensation of the bond-valence over- and under-saturation of Pb(II) is not localized but instead is spread out over many surface oxygen atoms. The nonideal valence sums for DFT-optimized geometries are interpreted as bond-valence model breakdown as opposed to a failure of DFT. However, we note a number of factors that could contribute to the obtained nonideal sums: A possible source of systematic error in the computed valence sums is the choice of employed bond-valence parameters. While other literature parameters are available,64 changing the parameters will not change the overall result of a larger valence sum on Pb(II) in Pb(II)/ c-cut than in the three closely studied Pb(II)/r-cut complexes. Additionally, the DFT-GGA bond lengths could also lead to systematic variations in the computed bond-valence sums. Again, refitting the bond-valence model to DFT-GGA reference structures would not change the qualitative result that the Pb(II) valence sum varies notably between the c-cut and r-cut complexes. Therefore, the nonideal valence sums suggest a breakdown of the bond-valence model as applied to these Pb(II) surface complex geometries. In the rest of this section, the bondvalence results are further detailed, and a potential cause for model breakdown is suggested. The bond-valence prediction of oversaturation in the Pb(II)/ c-cut structure indicates instability, while the lower saturation of Pb(II)/r-cut can be interpreted as being plausible though nonideal configurations. This is in qualitative agreement with the experimentally noted trend that R-Al2O3(1102) is much more reactive toward Pb(II) than R-Al2O3(0001).74 However, it is surprising that the Pb(II)/r-cut valence sums on the adsorbed cation are so far from the ideal value of 2.0 v.u. We suspect that a limitation of employing the bond-valence model to surface complexation geometries is the parametrization, which relies on well-characterized bulk reference structures. As we have seen through studying the Fd and lmDOS of Pb(II)/Al2O3, the Pb-O bonding has a strong directional dependence. As summarized in ref 12, Pb-O interactions are maximized if Pb(II) is able to participate in bonding through both side-to-side and top-tobottom overlap with oxygen p states. It has been previously noted that tetrahedral and octahedral structures in which the coordination environment allows for equal interactions between cations and the three oxygen p orbitals are lowest in energy,107 and this is built into the bond-valence model implicitly. However, as currently implemented, the bond-valence model relies only on interatomic distances. We suggest that the DFT Pb(II)/r-cut geometries are not severely under-coordinated as suggested by the valence sums. Instead, because the geometry of adsorbed cations at mineral-water interfaces may vary from the bulk counterparts used to parametrize the model, the bond-valence model may not be sufficient to accurately assess the relative stability of Pb(II)/Al2O3 surface complexes. We suggest that an extension from bulk bond-valence models is necessary for more accurate assessment of surface complex stability, such as a model term which can explicitly take into account the angles between the central atom and all coordinating species. Explicit Hydration Effects in Pb(II)/Al2O3. An important consideration for our approach to modeling mineral-water reactivity by adsorbing the Pb(II) cation onto the hydrated RAl2O3 surface is whether or not the results are sensitive to the addition of molecular water. While it is beyond the scope of the 4018

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Scheme 1. Schematic Representations of the Orbital Interactions in Pb(II)/Al2O3a

a

In this model, the Pb(II) is cradled by four surface oxygen atoms, shown in red, all in the same plane (arbitrarily xz or yz) as Pb. On the basis of the lmDOS, the interacting Pb(II) state is taken to be an sp hybrid. Interactions between oxygen px/py and pz are listed separately for low-lying “valley” oxygen atoms (Ov) and higher “hill” oxygen atoms (Oh). (a) Pb spz and Ohpx/Ohpy. (b) Pb spz and Ohpz. (c) Pb spz and Ovpz (d) Pb spz and Ovpx/Ovpy.

present study to exhaustively consider the effects of explicit hydration, it is briefly considered here, similar to the H2O adsorption results presented in our previous study on Pb(II)/ R-Al2O3(0001).75 The main goal in this part of the study is to support that the coordination of Pb(II) in the reported DFToptimized structures is satisfied by surface functional groups, even though the valence sums using literature bond-valence model parametrization suggest under-coordination. If the reported Pb(II)/Al2O3 structures result in significantly undercoordinated lead, then it is reasonable to expect that the cation will be reactive toward an introduced water molecule. As noted, the Pb(II) cation has asymmetric charge density directed away from the surface, and as previously reported, molecular water is largely repelled by Pb(II) in the Pb(II)/ccut structure.75 To span both studied r-cut interface models, a single molecule of water is added to the Pb(II)/A3a and Pb(II)/ C4 structures. On each, three initial H2O/Pb(II)/Al2O3 geometries are considered: one with H2O donating a hydrogen bond to an AlOH group atom also bound to Pb(II), one with H2O accepting a hydrogen bond from a surface OH group proximal to Pb(II), and one with H2O acting as a ligand to Pb(II). In five out of the six H2O/Pb(II)/Al2O3, the adsorption energy of the molecular water is less than 0.18 eV. In one H2O/Pb(II)/ Al2O3 structure, in which the added water donates a hydrogen bond to a singly coordinated OH proximal to Pb(II), the adsorption energy is 0.28 eV. However, in all of the H2O/ Pb(II)/Al2O3, the Pb(II) still stays in the valley sites, and the calculated Pb valence sums are changed by less than 0.04 v.u. Consistent with the bond-valence analysis of the Pb(II)/Al2O3

structures prior to H2O adsorption, the low Pb(II) valence sum is compensated by slight changes in the valence sums of many of the outermost interface oxygen atoms. The subtle changes in the Pb valence sum as a function of molecular water adsorption in a variety of sites indicate that the Pb(II)/r-cut structures reported here are not highly under-coordinated, and thus the Pb(II) bonding is well satisfied through interactions with surface oxygen functional groups. This result further suggests a breakdown in the bond-valence model as applied to these systems. While clearly more work is needed to fully understand hydration effects on Pb(II)/Al2O3, the testing reported here supports the validity of our modeling approach.

’ CONCLUSIONS Our DFT-based study of Pb(II)/Al2O3 supports the observation that the R-Al2O3(1102)-water interface is more reactive toward Pb(II) than the R-Al2O3(0001)-water interface. The DFT results suggest that the corrugation of surface oxygen functional groups in the (1102) structures, but absent in the topographically flat (0001) structure, enables more effective PbO orbital interaction. In particular, the coexistence of Pb-O overlap between the cation and surface groups both in-plane and along the surface normal direction in Pb(II)/r-cut gives rise to a covalent bonding resonance 6-7 eV below εF. The low-lying Pb-O interaction in Pb(II)/r-cut structures is similar to what is seen in bulk R-PbO but is absent in Pb(II)/c-cut structures. In an attempt to simplify and generalize the hybridization-reactivity relationship, we cast the Pb-O bonding into a schematic representation of orbital interactions. 4019

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The Journal of Physical Chemistry C We also find that the Pb(II) valence sum computed using empirical bond-valence models and literature parametrization for Pb(II)/c-cut is greater than 2.0 v.u., while that of Pb(II)/r-cut is less than 2.0 v.u. This is in qualitative agreement with the experimentally observed trend that R-Al2O3(1102) is much more reactive toward Pb(II) than R-Al2O3(0001).74 However, we note that the bond-valence model includes no explicit angular dependence, which based on our orbital interpretation may be a key factor in predicting the relative stability of surface complex geometries. Future development of such extensions to the existing bond-valence model will require more extensive DFT training sets. In addition to the prominent effects of surface corrugation, we also report a Pb(II)/Al2O3 structure with long-range Pb-O interaction and adsorption-induced surface hydrogen rearrangement. These results support our previously reported result75 that the dynamic nature of surface hydrogen bonding may influence cation-surface partitioning. Surface hydrogen bonding also appears to be able to energetically compensate for relatively large adsorption-induced interlayer relaxations, as highlighted in the case of Pb(II)/C4. These results suggest that molecular dynamics simulations may be required to further understand adsorption (or thermally) induced changes in mineral-water interface hydrogen bonding. To address the possibility of under-coordinated Pb(II) in our model, we tested the impact of adding H2O to the Pb(II)/Al2O3 structures. In doing so, we consider H2O in three possible roles of H-bond donor, H-bond acceptor, and Pb(II) ligand. The molecular water makes a small impact on the Pb(II)/Al2O3 geometry and system bond-valence sums, and we attribute this result to the ability of Pb(II) to satisfy its bond valence through surface interactions, thus additional coordinating water molecules do not interact strongly with the cation. The foundational understanding provided in this study provides a basis for future research aimed at addressing more complicated Pb(II) surface complexation scenarios and dynamic effects. In particular, we note that as the hybridization-reactivity relationship predicts surface corrugation as a key reactivity factor, defects and features which result in increased roughness will likely exhibit enhanced reactivity.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Present Addresses §

Department of Chemistry, University of Iowa.

’ ACKNOWLEDGMENT This work was supported by NSF Grants CBWT-0404400 and CHE-0431425 and SERDP Grant ER-1770 and utilized the high-performance computational capabilities of the Arctic Region Supercomputing Center at the University of Alaska Fairbanks and Helix Systems Biowulf cluster at the National Institutes of Health, Bethesda, MD. S.E.M. was supported by a National Research Council (NRC) Postdoctoral Fellowship. We acknowledge Dr. Christopher R. Iceman for insightful research discussions. ’ REFERENCES (1) Henrick, V. E.; Cox, P. A. The surface science of metal oxides; Cambridge University Press: Cambridge, 1994.

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