DFT Study of Antimony(V) Oxyanion Adsorption on Î±-Al2O3(11Ì02

Article pubs.acs.org/JPCC

DFT Study of Antimony(V) Oxyanion Adsorption on α‑Al2O3(11̅02) Sai Kumar Ramadugu and Sara E. Mason* Department of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States S Supporting Information *

ABSTRACT: Density functional theory (DFT) calculations using periodic slab models are carried out to study the reactivity of aqueous Sb(OH)6− on model α-Al2O3(110̅ 2) surfaces. The strength of inner-sphere (specific) adsorption between Sb(OH)6− and surface models is ranked using DFT adsorption energies, Eads. Trends in Eads in terms of surface structure, adsorbing functional group identity, and oxyanion coordination to the surface are determined and analyzed in terms of geometry and electronic structure. The results show that not all Sb−Osurf interactions involve the same type of Sb and O orbital interactions, which explains why trends in Eads cannot be rationalized by universal Sb−O bond length−bond strength relationships. The DFT results show a preference for Sb(V) bidentate and tridentate geometries in which Sb bonds through the corners of AlO6 groups in the surface. Less favorable adsorption involving edge sites is associated with adsorption-induced surface relaxations of oxygen groups from deeper layers of the surface.

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INTRODUCTION While arsenic and antimony are both group 15 elements, the current state of knowledge of the toxicity and chemistry of Sb in the environment trails that of its periodic table neighbor. Reviews of Sb in the environment1−3 identify the need to fill in knowledge gaps such as details of Sb global cycling through different environmental compartments. In terms of health and safety interests, Sb is classified as a priority pollutant by the US Environmental Protection Agency, and has a stringent drinking water standard of 6 ppb.4 Aqueous Sb(V) can form innersphere surface complexes on the surfaces of mineral and clay mineral phases.5−7 In this sense, the reactive sites of mineral surfaces can be thought of as long-term “docking stations”8 that can effectively sequester contaminant ions. The partitioning reactions between aqueous Sb and natural solid phases influence the speciation, transport, and fate of Sb in the environment. Thus, obtaining a molecular-level understanding of Sb adsorption to the mineral surface is of fundamental importance. Under oxic conditions, Sb exists mainly as the Sb(V) oxyanion, Sb(OH)6−.9,10 The adsorption of Sb(OH)6− onto hematite has been shown to occur in an inner-sphere bidentate fashion by McComb et al.11 using attenuated total reflectance infrared spectroscopy. The study compared the IR normal modes of free Sb(OH)6− in solution and in complex with αFe2O3, and confirmed earlier Möessbauer spectroscopy results by Okada et al.12 who found that Sb(V) adsorbs onto hematite forming Sb−O−Fe bonds. Luez et al. have shown that Sb(III) and Sb(V) adsorb on the surface of geothite as inner-sphere complexes at pH < 7.13 Subsequently, extended X-ray adsorption fine structure (EXAFS) studies by Scheinost et al. on adsorption of Sb(OH)6− onto geothite have shown the © 2015 American Chemical Society

formation of inner-sphere edge-sharing and corner-sharing complexes.14 An EXAFS study4 of antimony in mining environments of Kashtina Hills of Alaska reported that Sb(V) adsorbs on α-Fe2O3 in bidentate inner-sphere corner- and edgesharing configurations. Recent studies by Ilgen and Trainor15 of the adsorption of Sb(OH)6− on hydrous Al oxides report that the adsorption is predominantly bidentate corner-sharing, whereas for clays, mono- and bidentate corner and edgesharing modes are reported with Sb(V)−O distances in the range of 1.98−2.04 Å. Further molecular-level understanding of Sb adsorption to mineral surfaces, and comparisons of structural information from experiments can be obtained using various modeling approaches. Empirical models commonly employed to assess plausible surface complex geometries at mineral−water interfaces are based on the bond-valence concept of bonding from Pauling’s rules of ionic crystal stability.16 Such bondvalence (BV) models17,18 employ bulk parametrization and simple mathematical bond length−bond strength relationships. The resulting BV sums for surface atoms and adsorbing species can then be used to assess whether surface complex geometries are plausible.19−22 Surface complexation models (SCMs) attempt to fill the niche of connecting macroscopic geochemical behavior to microscopic understanding and include the concept of site-specific bonding coefficients as well as a description of the electrical double layer that forms at charged coefficients.23−26 As SCMs rely on parametrization using experimentally obtained (or matched) information, their application Received: March 2, 2015 Revised: July 10, 2015 Published: July 14, 2015 18149

DOI: 10.1021/acs.jpcc.5b02061 J. Phys. Chem. C 2015, 119, 18149−18159

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The Journal of Physical Chemistry C

Figure 1. Side views of the Al2O3(110̅ 2) surfaces modeled in (2 × 2) supercells. Key: (a) A3, (b) C3, and (c) C4. The A3 model is stoichiometric, while the C models have a missling Al layer. Oxygen, aluminum, and hydrogen atoms are shown as red, aquamarine, and gray spheres, respectively.

vibrational spectra for various oxyanions adsorbed onto metal (hydr)oxides.27−30 A second geometry that lends itself to readily to periodic boundary condition DFT calculations are slab models. In periodic calculations, mineral surfaces are represented by a finite number of atomic layers of cations and anions with periodicity in the surface plane. The periodic cell length in the surface normal direction includes vacuum tested to be sufficient to prevent spurious interactions between images. An advantage of periodic slab models is the ability to achieve qualitative and quantitative agreement with experimental measurements of surface relaxations and stable surface stoichiometries.31−43 Classical and ab initio molecular dynamics

to different conditions must be done carefully and evaluated for accuracy. Essential chemical information about surface complexation is now becoming available through computational modeling employing quantum mechanical methods such as density functional theory (DFT). Within atomistic computational modeling there exist choices in the model geometry used to represent surface complexation. One option is to use small molecular cluster models. For example, a cluster model for alumina could be comprised of a few edge-sharing AlO6 octahedra. Calculations on these systems have been carried out to yield reaction energies, Gibbs free energies and 18150


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Figure 2. Initial geometries for all of the considered Sb(V)/Al2O3 structures on the A3, C3 and C4 surfaces. The color scheme and atom representation is same as Figure 1, with Sb shown as magenta. The model names are defined in Table S2.

previous studies of ion adsorption on alumina and hematite surfaces.33−35,65 Further details of convergence studies of the basis set cut off are given in Table S1. The theoretical α-Al2O3 lattice constants have been previously reported and compared to literature values.33 Three α-Al2O3(11̅02) surface models previously detailed by ab initio thermodynamics59 and compared to experimental structures57,58 are used as substrates. Using the alpha-numeric surface stoichiometry naming scheme of Lo et al.,32 the surface models are referred to as A3, C3, and C4. All of the model slabs (including those with Sb(OH)6−) are modeled with two equivalent surfaces, related by inversion symmetry. The C3 and C4 surfaces have a missing layer of Al cations whereas the A3 surface has stoichiometric full layers of Al cations. Due to this difference in the number of layers, the A3, C3, and C4 slabs consist of 14, 12, and 12 oxygen and 8, 6, and 6 aluminum layers, respectively, all with an excess of 25 Å separating periodic images along the surface normal. In order to reduce inplane adsorbate interactions, we model adsorption using (2 × 2) supercells of the surface models, which results in in-plane Sb−Sb distances of at least 9.5 Å. Side views of the surface models, including layer labeling and numbering, are shown in Figure 1. Geometry optimizations using a force tolerance of 0.05 eV/Å are carried out, and the total energy is sampled using a converged (2 × 2 × 1) gamma-centered Monkhorst−Pack kpoint grid.66 To model aqueous effects, the continuum solvation model COSMO developed by Klamt et al.67 and as implemented by Delley in DMol3 68 is applied. It is reported that accurate DFT calculations of aquo-metal ion pKa values is known to require at least two explicit solvation shells.69 It is also the case that some mineral surfaces exhibit strong ordering of near-surface water.70 However, modeling explicit hydration atomistically is computationally demanding. As we are interested in assessing surface-

simulations can also be applied to geochemical surface science and allow for the prediction of pKa values. In classical dynamic simulations, force field parameters are applied to describe the interactions in the system. A few recent examples include the development and application of CLAYFF force field for layer alumino-silicates44,45 and simulations of uranium-ion adsorption.45,46 In ab initio molecular dynamics (AIMD) simulations, the equations of motion are integrated based on a firstprinciples potential energy surface. AIMD simulations have been used to study ion adsorption, acidity constants, and to study the behavior of water on the surface of the metals and metal oxides.47−56 The overarching goal of this study is to provide molecularlevel information on aqueous Sb(V) adsorption to mineral surfaces, for which there is limited experimental information. We carry out DFT calculations on periodic slab model geometries of Sb(V) adsorption on α-Al2O3(11̅02), including neutral aqueous effects. α-Al2O3(110̅ 2) was selected because this mineral-water interface has been well-detailed in previous experimental and theoretical characterizations of the surface stoichiometry.57−61 Furthermore, unlike the Fe atoms in ironbearing minerals, the Al atoms in alumina do not have any d electrons. Therefore, assigning Sb−Osurf interactions through electronic structure analysis is relatively accessible.

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METHODOLOGY, COMPUTATIONAL DETAILS, AND SB(V)/AL2O3 MODEL GEOMETRIES DFT calculations were carried out using the DMol3 software developed by Delley.62,63 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.64 Similar computational details were used (and justified) in 18151


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The Journal of Physical Chemistry C driven trends in Sb(V) adsorption, including aqueous effects through continuum solvent is put forth as a reasonable compromise between model accuracy and tractability. The COSMO screening charge compensates for the charge of the Sb(OH)6− in the periodic slab modes, and the energy derivatives used during geometry optimization of all slab and surface complex models include COSMO. Upon optimization, the Sb(V)/Al2O3 structures were fed into a BV model employing tabulated parameters from Brown et al.17 For the BV contributions from O−H bonds, the functional form from Bargar et al. was utilized.71 The adsorption complex geometries modeled in this work include corner-sharing and edge-sharing bidentate and tridentate modes of Sb(OH)6− on A3, C3, and C4 surfaces. For each surface, we generated both corner- and edge-sharing complexes to model possible bidentate adsorption. We denote oxygen functional groups that are doubly or triply coordinated to surface Al as O(II) and O(III), respectively. To model tridentate surface complexes, the three Sb−O bonds can be formed by either two O(I) and one O(II) or two O(II) and one O(I) in the case of C3 and C4 surfaces, or through a combination of O(I) and O(III) on the A3 surface. Figure 2 shows the starting geometries for all of the models generated. We generate bidentate models with two O(I) and two O(II/ III) for all the surfaces. In other words, bidentate models for each mode are generated that allow us to compare Sb(V) bonding through oxygen atoms from the corners of neighboring AlO6 octahedra, which are part of the outermost layer of oxygen atoms in the surface, or through edge-sharing, which must involve oxygen atoms from deeper surface layers. The names and abbreviations of the Sb(V)/Al2O3 models are given in Table S2, and the naming convention used for all the models generated in this study is explained as follows: Considering the bidentate adsorption C4 surface as an example, corner-sharing models are referred to as C4-(bi-corner-i) (see Figure 2, panel c, left-most structure for reference), where “C4” identifies the surface model, “bi” specifies the adsorption mode (with “bi” for bidentate and “tri” for tridentate), “corner” indicates that Sb forms bonds to oxygen atoms on the corners of two neighboring AlO6 in the surface (while “edge” would indicate that Sb bonds to two oxygen atoms of a single AlO6), and the lower case Roman numeral “i” was used to number the model of this kind, as for some adsorption classes two structures were generated. The same naming convention applies to all the bidentate models across A3 and C3 surfaces. For the tridentate complexes, we generated two structures for each surface. Again, considering tridentate adsorption model on C4 surface as an example, C4-(tri2corner) (see Figure 2, panel c, right-most structure for reference), C4 represents the surface, “tri” represents the mode of adsorption, and 2corner represents that there are two O(I) functional oxygen atoms and one O(II) and C4-(tri2edge) refers to the tridentate model with two O(II) and one O(I). The same convention applies to C3 and A3 surfaces. We calculate the adsorption energy, Eads, using the DFT total energy information (weighted appropriately by stoichiometric coefficients) and model concerted reactions for Sb(V)/Al2O3 surface complexes. The bidentate adsorption reaction is written as

while that for tridentate adsorption is written as 2Al(OH)3 + 2Sb(OH)6− → 2AlO3 Sb(OH)3− + 6 H 2O (2)

In eqs 1 and 2, surface species are underlined. The stoichiometry as written represents the double-sided slab models with adsorption occurring on both exposed surfaces, while all values of Eads are reported as per surface values by dividing through by two. The reacting surface moiety is written generically as Al(OH)3. The surface complex product is written as Al(OH,O2)Sb(OH)41− for bidentate adsorption and as AlO3Sb(OH)31− for tridentate adsorption. All molecular and surface species are modeled including COSMO to model aqueous effects. As discussed previously, computing aqueous surface reactions directly from DFT is complicated by the presence of charged species and the difficulty of accurately describing solvated ionic species.34 Furthermore, as noted in previous work,35 we do not need to reply on the sign of Eads to support the plausibility of Sb(V)/Al2O3 surface complexes as Sb inner-sphere adsorption has been reported on various aluminum hydroxides.15,72 Therefore, we focus on relative values of Eads in our analysis of the results.

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RESULTS AND DISCUSSION Surface Structures. While the surface models employed in this study have been previously studied using the same DFT methods,59 the addition of COSMO causes (sometimes negligible) structural changes. We track changes in the hydrogen bonding between surface OH/H2O groups and surface oxygen atoms. In A3, the distances are 1.82 (1.86) Å for the hydrogen bond distance among the layer-i hydroxyl groups. In C3, the distance among the layer-1 hydroxyl groups is 1.97 (1.98) Å, while the distance between the layer-5 hydroxyl and layer-3 oxygen is 1.49 Å, unchanged by the addition of COSMO. Finally, for C4, the distances of the geometries optimized with (and without) COSMO are 1.96 (1.95) Å among the layer-1 water groups in C4 and 1.65 (1.64) Å between the layer-3 hydroxyls and layer-5 oxygen atoms. Details of the layer spacings for all of the surface models reoptimized in the presence of COSMO are reported in Table S4. DFT Adsorption Energies. The values of Eads are reported in Table 1. Upon geometry optimization, some of the surface complex geometries deviated from their initial design. For example, on the C3 surface, edge-sharing bidentate models (C3Table 1. DFT Adsorption Energies, Eads, Based on Eq 1 for Bidentate Adsorption and Eq 2 for Tridentate Adsorptiona Bidentate

2Al(OH)3 + 2Sb(OH)6− → 2Al(OH, O2 )Sb(OH)4 − + 4H 2O

model

bi-corner-i

bi-corner-ii

biedge-i

biedge-ii

A3 C3 C4

1.12 0.10 0.05

− − 0.56 Tridentate

RC RC 1.26

2.08 RC 0.92

model

tri2corner

tri2edge

A3 C3 C4

0.42 −0.44 0.83

0.92† 1.07† 2.54

a

The reaction energies are reported in eV per surface. RC refers to the model that reduced coordination. The tridentate models that started as 2edge and optimized to 2corner structures are indicated by †.

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Figure 3. Side views of the optimized bidentate models of Sb(V)/Al2O3 structures. The top panel shows the structural models for A3 surface, middle panel shows the structural models on C3 surface whereas the bottom panel shows the structural models on C4 surface. The color scheme and atom representation is the same as Figure 2. The A3-(bi-corner-i) structure shows an oxygen atom in green that accepts an H atom from another surface functional group over the course of geometry optimization, as discussed in the text.

has the least favorable values for Eads. In terms of Sb(V) coordination to the surface, tridentate adsorption is the most favored mode on the C3 surface, while on A3 and C4, bidentate adsorption is preferred. The stability of the bi-corner-i models relative to the bi-corner-ii models is likely due to steric factors, as in the latter the O(I) groups bonding to Sb are separated by rows of oxygen atoms not bound to Sb (see C4 models panel, second model in Figure 3). The results of Eads can also be compared in terms of adsorption through corner- or edge-sharing oxygen functional groups. For the A3 surface, from the structures that successfully optimize, the bi-corner-i structure is preferred relative to the biedge-ii structure, with Eads values of 1.12 and 2.08 eV, respectively. On the C3 surface, an optimized biedge geometry could not be obtained, but the bi-corner-i structure has a relatively favorable value of Eads = 0.10 eV. The tri2corner geometry is favored relative to the tri2edge, by 0.5, 1.51, and 1.71 eV for the A3, C3, and C4 surfaces, respectively. Collectively, the results suggest that it is preferable (if not necessary) for Sb(V) to adsorb in corner-sharing configurations for bidentate complexes. In the following subsections looking at aspects of Sb(V)/Al2O3 geometry and electronic structure, we consider explanations for the apparent preference for Sb to bond through corner sites relative to edge sites.

(biedge-i) and C3-(biedge-ii)) effectively reduced Sb coordination over the course of geometry optimization, resulting in monodentate complexes with relatively high corresponding DFT total energies. All the structures that deviated from original geometry by reducing coordination are labeled as “RC” in Table 1. Other structures deviated from their initial design by maintaining the number of Sb−O bonds but with changes in which oxygen atoms bond to Sb. Specifically, the tridentate models C3-(tri2edge) and A3-(tri2edge) had Sb lose coordination with the O(II)/O(III) from the initial geometry but formed bonds with O(I) in the final geometry (these are referred to with the symbol † in Table 1). In this way, these models for tri2edge configurations resulted in tri2corner geometries similar to C3-(tri2corner) and A3-(tri2corner). For both the A3 and C3 surfaces, the tri2corner structures that result from initial tri2edge geometries are higher in energy than the tri2corner geometries that result from structures that are initially tri2corner. In subsequent presentation and discussion of results, we include only the results for the lower-energy tri2corner geometries. The the results in Table 1 show that in terms of surface model, the C3 surface has the most favorable value of Eads (for the tri2corner model). For bidentate adsorption, the A3 surface 18153


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Figure 4. Side views of the optimized tridentate models of S(V)/Al2O3. From left to right: A3-(tri2corner), C3-(tri2corner), C4-(tri2corner), and C4-(tri2edge) models after structural optimization. The color scheme and atom representation is the same as Figure 2. The A3-(tri2corner) structure shows an oxygen atom in green that accepts an H atom from another surface functional group over the course of geometry optimization, as discussed in the text.

Table 2. Sb(V)/Al2O3 Sb−O Distances (in Å) and BV Sums for Sb and O (in Parentheses, in Units of v.u.)a A3 model

atoms

distance

bi-corner-i

Sb−O(I) Sb−O(I) Sb−O(I) Sb−O(I) Sb−O(I) Sb−O(II) Sb−O(I) Sb−O(II) Sb−O(III) Sb−O(I) Sb−O(I) Sb−O(II) Sb−O(III) Sb−O(II) Sb−O(II) Sb−O(I)

2.224 2.028 − − − − 2.044 − 2.328 1.961 2.001 − 2.322 − − −

bi-corner-ii biedge-i biedge-ii

tri2corner

tri2edge

a

C3

BV sum (Sb, O) (4.78, (4.78, − − − − (4.48, − (4.48, (4.95, (4.95, − (4.95, − − −

1.73) 1.73)

distance 1.979 1.992 − − − − − − − 1.972 1.994 2.424 − − − −

1.67) 1.56) 1.90) 1.90) 1.72)

C4

BV sum (Sb, O) (5.17, (5.17, − − − − − − − (4.92, (4.92, (4.92, − − − −

2.16) 2.16)

1.99) 1.99) 2.17)

distance 2.030 2.038 2.064 2.211 2.079 2.084 2.079 1.991 − 2.11 2.033 1.984 − 1.992 2.062 2.154

BV sum (Sb, O) (4.94, (4.94, (4.74, (4.74, (4.91, (4.91, (4.88, (4.88, − (4.88, (4.88, (4.99, − (4.99, (4.99, (4.99,

1.89) 1.89) 1.85) 1.85) 2.17) 1.64) 2.09) 1.70) 1.96) 1.96) 1.91) 1.87) 1.87) 1.66)

Results for the models that either reduced coordination or changed to a different structure are left blank. The model names are defined in Table S2.

Sb(V)/Al2O3 Geometry. The optimized geometries of the bidentate and tridentate Sb(V)/Al2O3 are shown in Figure 3 and Figure 4, respectively. The structures in which Sb reduced coordination or in which the identity of the oxygen atoms bonding to Sb changed, as indicated in Table 1, are not shown. The Sb(V)/Al2O3 geometries are summarized in terms of the range of Sb−Osurf bond distances for each type of oxygen functional group. For Sb−O(I), the range is 1.96 to 2.22 Å, while for Sb−O(II) and Sb−O(III) it is 1.99 to 2.42 Å and 1.96 to 2.33 Å, and the individual results are reported in Table 2. Similar to what was reported in a previous DFT study of Sb(III)/Sb(V) adsorption on (0001) alumina and hematite surfaces,35 the overlapping ranges in Sb−O distances makes it difficult to identify trends based on the oxygen function group coordination alone. While there is little directly comparable experimental information available, we note that the experimentally determined values of Sb−Osurf distances reported for Sb(V) on hydrous Al oxides by Ilgen and Trainor15 (1.98−2.04 Å) fall within the broader range of Sb−Osurf distances reported here (1.96−2.42 Å). While the DFT results include some longer Sb−Osurf distances, that could be due to the fact that we only modeled the Al2O3(11̅02) surface, while the samples studied by Ilgen et al. may have exhibited different types of adsorption sites. Thus, it is possible that the experimental

samples contained sites with greater reactivity toward Sb and shorter associated Sb−O bond distances. In some cases, the optimization of initial Sb(V)/Al2O3 geometries resulted in significant H atom rearrangements on the surface. For example, in the A3-(bi-corner-i) structure, a layer-1 OH group donates H to one of the layer-i groups bound to Sb, resulting in a Sb−OsurfH group with a relatively long Sb− O(I) bond distance of 2.224 Å. The oxygen atom of the Sb− OsurfH group is highlighted in green in Figure 3. A similar arrangement occurs in the A3-(tri2corner) structure, and the affecting oxygen group bound to Sb is also highlighted in green in Figure 3. On the C4 surface, hydrogen bonding between the surfacebound aquo groups is disrupted by Sb. Before adsorption, the intermolecular water hydrogen bonding distance is 1.962 Å while in the optimized C4 Sb(V)/Al2O3 structures the distances range from 1.88 to2.12 Å. The results for the C4-(bi-corner-i) and -(bi-corner-ii) models, (as shown in Figure 3), raise a point of contrast: Despite both being labeled as bi-corner structure, the respective Eads values of 0.05/eV and 0.56 eV vary significantly. However, details of the bi-corner-ii reveal that the distance between Sb− O(I) is 2.064 Å (as reported in Table 2), but the distance between the corresponding Al and O(I) is increased from the distance in the surface of 2.200 Å to 2.951 Å. This large 18154


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Figure 5. Projected density of states for bidentate Sb(V)/Al2O3 on A3 and C3 surfaces. Key: (a) A3-(bi-corner-i) (b) A3-(biedge-ii), and (c) C3-(bicorner-i). The Fermi level is at 0 eV in all plots.

Figure 6. Projected density of states for bidentate Sb(V)/Al2O3 (a) C4-(bi-corner-i), (b) C-4(bi-corner-ii), C4-(biedge-i), and (d) C4-(biedge-ii). The Fermi level is at 0 eV in all plots.

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Figure 7. Projected density of states for tridentate Sb(V)/Al2O3 surfaces. Key: (a) A3-(tri2corner) and (b) C3-(tri2corner) (c) C4-(tri2corner), and (d) C4-(tri2edge). The Fermi level is at 0 eV in all plots.

We also note that the formation of Sb(V)/Al2O3 can induce variations from the ideal octahedral Sb(V) geometry. We detail the O−Sb−O angles in the geometry-optimized surface complexes in Table S3, and highlight a representative snapshot from each of C4-(bi-corner-i) and C4-(biedge-i) in Figure S2. A visual analysis of the geometry of corner- and edge-sharing models, particularly the angle formed between O(I)−Sb-O(I)/ (II) in C4-(bi-corner-i) and C4-(biedge-i) clearly shows that this angle deviates from the ideal value of 90° observed in octahedral complexes. While there are examples of apparent agreement between Sb(V) angular distortion and Eads values (for example, on the A3 surface, the (tri2corner) model has nearly ideal O−Sb−O angles and Eads of 0.42 eV, while the (biedge-ii) has a strained O(I)−Sb-O(II) angle of 76° and a relatively unfavorable Eads of 0.92 eV), the O−Sb−O and Eads values are not universally correlated. Electronic Structure. Electronic structure analysis of the Sb(V)/Al2O3 geometries is used to characterize the orbital interactions responsible for the Sb−O bonding on the surface. We use projected density of states (PDOS) analysis, an atomby-atom and state-by-state decomposition of Sb(V)/Al2O3 charge density. Covalent interactions are identified by PDOS intensity from different orbital contributions at the same energy. The hybridization of Sb(V) in Sb(OH)−6 is sp3d2, and we plot the Sb s, p, and d states along with the O p states of surface oxygen atoms bound to Sb. The PDOS of the four optimized bidentate Sb surface complexes on the A3 and C3 surfaces are shown in Figure 5, while those for the C4 and A3 bidentate structures are shown in Figure 6. The PDOS for all of the successfully optimized tridentate Sb surface complexes are presented in Figure 7.

distortion of the AlO6 octahedra is likely the reason for the relatively unfavorable value of Eads for the C4-(bi-corner-ii) structure. We report the surface layer spacings and percent relaxations (relative to the theoretical bulk values) for all of the optimized Sb(V)/Al2O3 structures in Table S3. When averaged over the full atomic layers of the supercells, the effects of adsorptioninduced relaxations are unclear. However, significant surface relaxations local to the surface complex geometry can be noted and interpreted. For example, in the C4 bidentate models, outward O(II) relaxations along the surface normal direction of 0.5 Åin C4-(biedge-i) and 0.2 Å in the case of C4-(biedge-ii) are noted. These surface relaxations are visually highlighted in Figure S1. The extensive adsorption-induced surface relaxation in bidentate adsorption at edge sites demonstrates a structure− reactivity relationship that provides an explanation for why bidentate adsorption through corner sites is preferable. Considering the surface structures, the layer-1 corner oxygen atoms are above the missing Al layer C3/C4models, and are therefore less sterically hindered than the layer-3 oxygen atoms of the edge sites. Similarly, in the A3 model, the layer-i corner oxygen atoms (which are not part of the Al2O3 lattice) are less structurally constrained than the layer-3 edge oxygen atoms. The argument can be generalized to interpret why on all of the surfaces, bidentate adsorption at edge sites (or tridentate adsorption through 2/3 edge sites relative to 2/3 corner sites) is unfavorable, as it incurs an energetic penalty for outward relaxation of lattice oxygen. This interpretation may also lend itself to the recent experiments by Ilgen et al.15 who did not observe any bidentate edge-sharing complexes on hydrous aluminum oxide. 18156


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relaxations of edge site oxygen atoms in deeper surface layers. This result is opposite to what was previously reported for divalent lead adsorption on the same surface models.34 The adsorbates are intrinsically different as Sb(V) exists as an oxyanion. The contrast can also be discussed in terms of electronic structure. For Pb(II), the hybridization is sp, and it was shown using charge density analysis that Pb had favorable overlap when interacting simultaneously with outermost and deeper surface oxygen functional groups. Pb(II) adsorption was also modeled without any distal ligands on Pb. With its sp3d2 hybridization, the Sb(V) bonding environment is less flexible/ more directionally dependent than that of Pb(II), and furthermore the distal OH ligands impose a steric factor not included in the Pb(II) modeling. The PDOS analysis of Sb(V)/Al2O3 shows that energy matching and overlap between adsorbate and surface states is associated with favorable adsorption. This is to be expected based on the theoretical measure of interaction from perturbation theory. Consider a system described by a Hamiltonian that can be expressed as Ĥ = Ĥ 0 + H′ where the H′ = 0 case is assumed to be solvable and with associated eigenvalues ϵ0i . For H′ ≠ 0 and |H′ij| ≪ (ϵ0i − ϵ0j ), perturbation theory yields

Owing to the complexity of Sb bonding to multiple surface atoms of varying functional group identity, we focus on comparisons of the PDOS of contrasting Sb(V)/Al 2 O 3 structures. First, we note the salient features of the PDOS for C3-(tri3corner) and C4-(bi-corner-i), the two most favorable structures with Eads = −0.44 and 0.05 eV, respectively. In the C3-(tri2corner) PDOS (Figure 7b)), Sb s and O p overlap appears in narrow and intense PDOS peaks near −8 and +4 eV. Sb p and O p overlap occurs over a wider range of energies, with notable intensity near −3 and −5.5 eV for both O(I). The O(II) p PDOS exhibits common intensity with Sb d near −1.5 eV and with Sb p near −5.5 eV. The O(I) density is shifted closer to the Fermi level relative to that of O(II), however, there are no Sb states above −1 eV available for bonding interactions. The fact that the differently coordinated oxygen functional groups interact with different Sb states means that the Sb−O interactions would show distinct variations as a function of Sb−O separation. The variable nature of Sb−O interactions as shown in the PDOS therefore provides insight as to why BV bond length−bond strength arguments may not be applicable to surface bonding. The PDOS for C4-(bi-corner-i) in Figure 6a) shows O(I) p overlaps with Sb p near −7 and −4 eV, while overlap with Sb d is seen near −3 eV. The PDOS of both O(I) are similar, and are shifted lower in energy relative to the O(I) PDOS in the C3-(tri2corner) structure. While the details of the PDOS for the two structure with the most favorable values of Eads vary, they both exhibit good energy matching and overlap between surface and adsorbate states. With this in mind, we next compare the PDOS of the four optimized C4 bidentate structures, show in Figure 6. This set of Sb(V)/Al2O3 structures is convenient because as Eads is based on a concerted reaction, we can expect the surface bondbreaking will be similar in all four structures. This set is also useful to consider because it allows comparison between corner- and edge-sharing configurations. The details of the C4(bi-corner-i) PDOS are given above, and that of the C4-(bicorner-ii) (Figure 6b) are qualitatively similar. In the C4(biedge-i) and C4-(biedge-ii) PDOS (Figure 6, parts c and d), there is diminished Sb p intensity between −7 and −8 eV relative to the C4 corner-sharing structures, and most of the O(I) and O(II) p overlap with Sb p occurs near −4 eV. In both of the edge structures, the O(II) p PDOS is shifted closer to the Fermi level, away from regions of Sb states that are available for bonding. While the Sb−O(II) bond distances (2.084 and 1.991 Å) are similar to the Sb−O(I) bond distances (2.079 Åin both), it is again clear that the actual Sb−O interactions are distinct.

ΔE =

|Hij′|2 |ϵi0 − ϵ0j |

(3)

where Hij′ is shorthand for ⟨i||Ĥ ′||j⟩ terms, referred to as “hopping integrals” to reflect that these matrix elements involve transfer of charge between states. Often, approximations or empirical fits for Hij′ terms are employed in conceptual models,73 and hopping integrals also roughly scale with orbital overlap, which can be obtained numerically from simulation data. As discussed in eloquent detail by Hoffmann,74 this theoretical term can be used to chemically decider variations in metal surface-molecule interactions. While the Sb(V)/Al2O3 system is more complex, the conceptualization of Sb-surface interactions through eq 3 is more robust than bond length− bond strength arguments. In particular, the numerator in eq 3 captures the importance of considering how overlap and directional bonding at the surface affect reactivity. The role of adsorption-induced surface relaxations and oxyanion distortion discussed in the present study point to the need to consider how surface complexes are modeled at the atomistic level. In particular, cluster models using a few AlO6 octahdera to represent the surface are inherently more floppy than periodic slab models. The comparison of cluster and slab modes is also highlighted in the literature: For example, the adsorption of SO42− on to the surface of Fe(hydroxide)−H2O interface studied75 using cluster models as well as periodic slab models show that the deviation of O−Fe−O angle is greater in the former (80° for the cluster versus 85° for the periodic slab model). The local nature of the surface relaxations demonstrates the value of the structural details available from DFT modeling to provide information difficult to attain by experimental means.

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CONCLUSIONS The analysis of Eads in terms of surface complex geometry, adsorption-induced surface relaxations, and electronic structure provided in this study demonstrates that the trends in Eads cannot be delineated through oxygen functional group coordination alone. Specifically, the electronic structure reveals several distinct Sb−O interactions in individual Sb(V)/Al2O3 structures, which undermines any universal Sb−O bond length−bond strength relationship. However, many of the results can be rationalized in chemical terms that allow for some generalization. Furthermore, the results provide some guidance as to what adsorbate and surface factors govern reactivity trends. The comparison of edge- and corner-sharing configurations suggests a structure−reactivity relationship in which corner sites are favorable because they avoid adsorption-induced

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ASSOCIATED CONTENT

* Supporting Information S

Convergence testing of the real-space basis set cutoff (Table S1), Sb(V)/Al2O3 model definitions/naming scheme (Table S2), surface layer-averaged relaxations (relative to bulk) of the A3, C3, and C4 surfaces and all of the optimized Sb(V)/Al2O3 18157


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structures (Table S3), O−Sb−O bonds in optimized Sb(V)/ Al2O3 geometries (Table S4), and figures highlighting adsorption-induced surface relaxation (Figure S1) and showing select Sb(V)/Al2O3 geometries (Figure S2). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b02061.

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AUTHOR INFORMATION

Corresponding Author

*(S.E.M.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by NSF Grant CHE-1254127 and the University of Iowa College of Liberal Arts and Sciences. We acknowledge Prof. Thomas P. Trainor for research discussions and the Arctic Region Supercomputing Center for computational resources. Dr. Diane Neff is acknowledged for carrying out pilot geometry optimizations of Sb(V)/Al2O3 geometries.

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