Computational Molecular Simulation of the Oxidative Adsorption of

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Computational Molecular Simulation of the Oxidative Adsorption of Ferrous Iron at the Hematite (001)-Water Interface Sebastien Kerisit, Piotr Zarzycki, and Kevin M. Rosso J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 13 Apr 2015 Downloaded from http://pubs.acs.org on April 14, 2015

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The Journal of Physical Chemistry

Computational Molecular Simulation of the Oxidative Adsorption of Ferrous Iron at the Hematite (001)-Water Interface Sebastien Kerisit,*,1 Piotr Zarzycki,2 and Kevin M. Rosso1 1

Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA

2

Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland

*

Corresponding author: Sebastien Kerisit; Address: Physical Sciences Division, Pacific

Northwest National Laboratory, P.O. Box 999: MSIN K8-96, Richland, WA 99354 USA; Phone: 509-371-6382; E-mail: [email protected].

ABSTRACT The interaction of Fe(II) with ferric oxide/oxyhydroxide phases is central to the biogeochemical redox chemistry of iron. Molecular simulation techniques were employed to determine the mechanisms and quantify the rates of Fe(II) oxidative adsorption at the hematite (001)-water interface. Molecular dynamics potential of mean force calculations of Fe(II) adsorbing on the hematite surface revealed the presence of three free energy minima corresponding to Fe(II) adsorbed in an outersphere complex, a monodentate innersphere complex, and a tridentate innersphere complex. The free energy barrier for adsorption from the outersphere position to the monodentate innersphere site was calculated to be similar to the activation enthalpy for water exchange around aqueous Fe(II). Adsorption at both innersphere sites was predicted to be unfavorable unless accompanied by release of protons. Molecular dynamics umbrella sampling simulations and ab initio cluster calculations were performed to determine the rates of electron transfer from Fe(II) adsorbed as an innersphere and outersphere complex. The electron transfer rates were calculated to range from 10-4 to 102 s-1, depending on the adsorption site and the 1 ACS Paragon Plus Environment


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potential parameter set, and were generally slower than those obtained in the bulk hematite lattice. The most reliable estimate of the rate of electron transfer from Fe(II) adsorbed as an outersphere complex to lattice Fe(III) was commensurate with the rate of adsorption as an innersphere complex suggesting that adsorption does not necessarily need to precede oxidation.

Keywords: iron oxides; iron redox; molecular dynamics; electron transfer; Marcus theory.

INTRODUCTION The redox transformation of iron oxide/oxyhydroxide minerals in aqueous solutions is of great geochemical importance due to its major role in the cycling of iron. Notably, many iron oxide/oxyhydroxide phases are semiconductors that can exhibit significant charge carrier mobilities.1 In turn, charge carrier mobility can lead to the coupling of redox reactions between remote surface sites via bulk charge transport. Indeed, the reductive transformation of hematite (α-Fe2O3) has revealed the coupling between oxidative adsorption of Fe(II) at the (001) surface and internal reductive dissolution of Fe(III) at edge surfaces through bulk charge transport.2 This circuit is driven by the potential gradient generated across the crystal from divergent charge accumulation at structurally distinct surface types. Key individual processes involved in this reaction cycle have been identified as Fe(II) adsorption, interfacial electron transfer between adsorbed Fe(II) and lattice Fe(III), bulk electron transfer, and Fe(II) release; however, a fundamental understanding of the feasibility of these processes at the molecular scale has not yet been comprehensively developed. Multiple lines of evidence have emerged to support the concept of interfacial electron transfer between adsorbed Fe(II) and lattice Fe(III) without changes in mineralogy. In particular,

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Fe Mössbauer spectroscopy showed that electron transfer following Fe(II) adsorption onto

hematite surfaces can lead to the formation of an oxidized iron surface layer.3-7 Interestingly, although Fe(II) adsorption onto iron oxide/oxyhydroxide surfaces is not expected to occur at pH 3 based on macroscopic observations,8-12 Catalano et al.13 showed evidence, based on X-ray reflectivity measurements, of significant reaction between Fe(II) and three hematite surfaces at this pH. Similar conclusions were drawn by following Fe(II) interaction with hematite by the Eisenthal-3 variant of second harmonic generation spectroscopy that reports on interfacial potentials.14 These observations suggest that there can be interaction between Fe(II) and iron oxide/oxyhydroxide minerals without any net change in the overall apparent iron concentration in solution. This is consistent with the isotope tracer studies of Handler et al.15-16, which demonstrated that isotope exchange between aqueous Fe(II) and goethite crystallites proceeded at conditions where no uptake of aqueous Fe(II) is observed. Computational work in our group has shown that, following electron transfer into the hematite lattice, electrons could cover large lateral distances in the near-surface region before diffusing in the bulk or being trapped at energetically favored surface sites.17 The electron transfer model used in our work is based on a polaron model whereby conduction occurs via a hopping mechanism and hence can be treated within the framework of Marcus’ theory.18 Our initial work showed that it was appropriate to model an extra electron in the hematite lattice as localized in the form of a small polaron centered on an iron site.19 Further validation of the electron transfer model for hematite was obtained in a subsequent study,20 in which the known anisotropy of the electron mobility between the directions perpendicular and parallel to the c axis in hematite21-22 was closely reproduced with this model. Later, a kinetic Monte Carlo study23



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showed that the electron transfer model yielded good quantitative agreement with experimental data on the temperature dependence of the electrical conductivity of hematite. In this contribution, we utilize the electron transfer model further to shed light on the mechanisms and quantify the rates of electron transfer between adsorbed Fe(II) and lattice Fe(III). One important aspect of this approach is determining the relative affinity for forming innersphere versus outersphere Fe(II) complexes. Indeed, the preference for innersphere versus outersphere adsorption nominally will impact the rates of interfacial electron transfer through their exponential dependence on distance. Therefore, classical and quantum-mechanical calculations are employed to compute the free energy profile of Fe(II) adsorbing at the hematite (001)-water interface as well as the rates of subsequent electron transfers to surface sites from both innersphere and outersphere positions. This study focuses on the (001) hematite surface, which is the most frequently occurring surface in hematite mineral crystals24 and, therefore, has been extensively studied both experimentally25-29 and computationally30-35. Yanina and Rosso2 observed oxidative adsorption of Fe(II) and homoepitaxial growth on the (001) surface; consequently, several subsequent studies have featured this surface.7,13,36-38 The hematite structure along the [001] direction consists of alternating hexagonal close-packed oxygen layers and iron bilayers and, therefore, the (001) surface can be terminated either by a layer of oxygen or iron atoms. An X-ray photoemission study39 showed that a low water pressure was sufficient for full hydroxylation of the oxygen termination thus strongly suggesting that this termination is fully hydroxylated when in contact with bulk water. Scanning tunneling microscopy40 and crystal truncation rod28-29 studies have indicated that the two terminations can occur on a same crystal surface in distinct domains but that the hydroxylated termination, which will be considered in this work, is


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predominant. Previous work37 demonstrated that the surface charge of the (001) surface in aqueous solutions is close to neutral over a wide pH range (4-14) because of the stability of the doubly-coordinated surface hydroxyls. In addition, the first two hydrolysis constants of aqueous Fe(II) are 9.5 and 20.6.41 Therefore, the adsorption reaction studied in this work ([Fe(H2O)6]2+ adsorbing on a neutral, fully-hydroxylated hematite (001) surface) is expected to be representative of conditions that occur over a wide pH range.

COMPUTATIONAL METHODS In the approach used in this work, classical molecular dynamics simulations are used to calculate the potential of mean force of Fe(II) adsorbing on the (001) hematite surface, identify the adsorption sites of Fe(II) at the surface, and calculate two of the three electron transfer parameters (λ and ΔG0, see description below), whereas the third electron transfer parameter (VAB, see description below) is obtained via ab initio electronic structure calculations. Molecular dynamics simulations. All MD calculations were carried out with the computer program DL_POLY,42 at 300 K, and in the NVT ensemble (constant number of particles, constant volume, and constant temperature). The temperature was kept constant via the use of the Nosé-Hoover thermostat.43 The electrostatic forces were calculated by means of the Ewald summation method.44 A 8 Å cutoff was used for the short-range interactions and the real part of the Ewald sum. The Verlet leapfrog integration algorithm was used to integrate the equations of motion with a time step of 1 fs or 0.2 fs for rigid-ion and shell model simulations, respectively. In the simulations that made use of a shell model, the shells were given a mass of 0.2 a.u. and their motion treated as that of the cores following the adiabatic shell model first introduced by Mitchell and Fincham.45 The geometry of the water molecules was held fixed by the SHAKE



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algorithm46 in the simulations with the SPC/E model. The hematite slab had a thickness of approximately 25 Å (i.e. two unit cell-thick) and had a surface area of 20.3 × 17.6 Å2. A gap of approximately 25 Å was created between opposing surfaces and filled with water molecules. The (001) hematite surface was modeled as terminated by a full layer of bidentate hydroxyl ions. A snapshot of one of the MD simulations is shown in Figure 1.

Figure 1. Snapshot of a MD simulation of the hematite (001)-water interface. Iron atoms are shown in purple, oxygen atoms in red, and hydrogen atoms in white. Potential models. In the potential models reported in this work, the particles of a system are represented as point charges, which interact via long-range Coulombic forces and short-range interactions. The latter are represented as parameterized potential functions and represent the electron-cloud repulsion, the van der Waals attraction forces, and, where appropriate, covalent effects by means of distance- and angle-dependent terms. The atomic charges and the short-range parameters constitute the potential parameter set.


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In this work, we make use of three potential parameter sets (Models 1, 2, and 3 in Table 1) for describing Fe(II) adsorption and electron transfer at the hematite-water interface in an effort to identify the model dependent properties. This is motivated by the fact that, by and large, the models for the solid and liquid parts of the interface have been derived independently. These three potential parameter sets were previously used in a computational study focused on the structure of water at hematite-water interfaces38 and their compositions from the individual models for hematite, water, and iron-water interactions are given in Table 1. The potential parameter set derived by Lewis and Catlow47 was used to model hematite. This model was used previously in our work on charge transfer rates in iron oxide lattices.17,48 As previously,38 we used both shell model and rigid-ion versions of this model whereby, in the latter, the oxygen shells were removed and a formal charge of -2.0 e was used for the oxygen cores. The hydroxyl ion model of Baram and Parker49 was also employed to model the surface hydroxyl ions. In addition, two potential parameter sets were considered for simulating water, namely, the shell model of de Leeuw and Parker,50 with the modified hydrogen bond potential of Kerisit and Parker,51 and the extended simple point charge model (SPC/E) of Berendsen et al. 52 Finally, the potential parameters of Kerisit and Rosso17 and those of Curtiss et al.53 were used to represent the iron-water interactions. The three potential parameter sets are given in Tables S1 to S5 of the Supporting Information.



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Table 1. Potential parameter sources for the three models considered in this work (S = shell model; R = rigid-ion model). Model

Water

Iron Oxide

Iron-Water

1

De Leeuw and Parkera

Lewis and Catlowb (S)

Kerisit and Rossoc

2

SPC/Ed

Lewis and Catlowb (R)

Curtiss et al.e

3

SPC/Ed

Lewis and Catlowb (S)

Curtiss et al.e

a

Reference 50 Reference 47 c Reference 17 d Reference 52 e Reference 53 b

As the surface of interest is terminated by hydroxyl groups, the energetics of Fe(II) adsorption are expected to be dominated by the relative strength of the Fe(II)-water and Fe(II)hydroxyl bonds. Therefore, we evaluated the ability of the potential parameters derived previously17 for reproducing the length and strength of these two bonds. A first test consisted in comparing the calculated and experimental lattice parameters and inter-atomic distances of white rust (Fe(OH)2). The lattice parameters of white rust were calculated from an energy minimization of the bulk structure with the computer code METADISE54 with the potential parameters of Lewis and Catlow47 and of Baram and Parker49 and were compared with the neutron diffraction data of Parise et al.55 at 10 K (a=b=3.25919(5) Å and c=4.5765(1) Å). The calculated lattice parameters are significantly shorter than the experimental values (percentage differences with respect to the experimental values are shown in parentheses): a=b=3.155 (-3.2%) Å and c=4.097 (-10.5%) Å. Therefore, the Fe(II)-hydroxyl oxygen potential was modified to increase the Fe(II)hydroxyl oxygen bond length from 2.06 to 2.14 Å (expt.=2.141(1) Å). In addition, the hydroxyl hydrogen-hydroxyl oxygen potential was modified to increase the hydroxyl hydrogen-hydroxyl


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oxygen distance from 2.16 to 2.58 Å (expt.=2.490(3) Å). As a result, the new lattice parameters are significantly improved: a=b=3.295 (+1.1%) Å and c=4.705 (+2.8%) Å. In a second test, three gas-phase clusters were considered, namely [Fe(OH2)6]2+, [Fe(OH2)5(OH)]+, and [Fe(OH)3]-, and their gas-phase formation energies from the constituent species (i.e., Fe2+, H2O, and OH-) were evaluated both with the three potential parameter sets and at the density functional theory (DFT) level. Both sets of calculations were performed without periodic boundary conditions to simulate gas-phase conditions. The DFT calculations were carried out with NWChem.56 In these calculations, the B3LYP exchange correlation potential was employed and the Ahlrichs valence triple-zeta57 and 6-31G*58-59 basis sets were used for iron and for oxygen and hydrogen atoms, respectively. The formation energies calculated with Model 1 for [Fe(OH2)6]2+, [Fe(OH2)5(OH)]+, and [Fe(OH)3]- were 60, 77, and 85% of the DFT/B3LYP energies showing that the strength of the Fe(II)-water bond is underestimated relative to that of the Fe(II)-hydroxyl bond in this model. In contrast, the same energies for Models 2 and 3 were 78, 84, and 84% of the DFT/B3LYP energies and thus better reproduced the relative stabilities. Therefore, in addition to the modifications to the potential model described in the previous paragraph, the Fe(II)-water oxygen potential of Model 1 was modified to increase the Fe(II)water bond strength. The resulting gas-phase formation energies were 78, 84, and 83% of the DFT/B3LYP energies, thus showing an improved agreement with the relative stabilities. Additionally, the formation energy of the second hydration shell was determined by considering [Fe(OH2)18]2+ and was found to be 70% and 77% of the DFT/B3LYP energy for Model 1 and Models 2/3, respectively. The formation energies of all the gas-phase clusters and the Fe-O bond lengths are given in Tables S6 and S7 of the Supporting Information, respectively.



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Potential of mean force calculations. For each of the three models, constrained MD simulations were carried out to model the adsorption of Fe(II) on the (001) hematite surface. The reaction coordinate was taken to be the normal to the surface, whereby the surface (z=0) is defined as the average height of the hydroxyl oxygen atoms. A total of 66 runs were performed for each model from z=0.5 Å to z=7.0 Å with an interval of 0.1 Å. Each simulation was run for 1,000,000 steps after an equilibration period of 10,000 steps. The starting configurations were generated by substituting Fe(II) for a water molecule at the desired height in an equilibrated system, thus allowing for a relatively short equilibration period. The free energy difference between Fe(II) at a height z and Fe(II) in the middle of the water slab (i.e., at height z0) was obtained by integrating the average force in the direction perpendicular to the surface, fz, acting on Fe(II) from z0 to z: z

A( z )  A( z )  A( z 0 )   f z ( z ) dz

(1)

z0

Electron transfer model. The approach used in this work to calculate electron transfer rates across the hematite-water interface follows that introduced in previous work (see reference 17 and references therein). Therefore, this approach is only briefly described here. The electron transfer of interest is that between aqueous Fe(II) in the vicinity of the surface and a surface Fe(III), whereby the ‘extra’ electron thus introduced in the mineral is considered to be localized on a surface iron site. We showed previously that it is appropriate to model electrons in the hematite lattice as localized in the form of small polarons centered at an iron site.17,19,23 The electron transfer between the two sites is described by three parameters: the reorganization energy, λ, the free energy of reaction, ΔG0, and the electronic coupling matrix element, VAB. These electron transfer parameters are illustrated in Figure 2. The reorganization energy is the


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energy to distort the configuration of the reactants into that of the products, and vice versa, without changing the electronic distribution; the free energy of reaction is the change in free energy upon electron transfer; and the electronic coupling matrix element is the amount of electronic interaction between the reactants and products states at the transition state. The reorganization energy and the free energy of reaction are obtained using MD simulations and an umbrella sampling approach first introduced by Warshel and co-workers60-62 for evaluating the free energy surfaces as a function of the reaction coordinate, which is defined as the energy gap, that is, the energy difference between the reactants and products charge distributions for a particular configuration of the system (see reference 17 for details of the approach). VAB is defined as half the energy difference between the upper and lower adiabatic surfaces at the crossing point configuration63 and is obtained using ab initio electronic structure cluster calculations as described in detail below. GP(E)

Free Energy (G)

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l GR(E)

VAB

G* ' G0

A

C

B

Reaction Coordinate (E)

Figure 2. Free energy diagram of an electron transfer reaction.



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Electron transfer can take place in two different regimes, namely, adiabatic and nonadiabatic, depending mainly on the strength of the electronic coupling. When the coupling is strong, the electron transfer is adiabatic and the rate expression is as follows:

k et  n n exp(G* / k BT )

(2)

where G * 

(l  G 0 ) 2  V AB 4l

(3)

n is the number of sites available for electron transfer, νn is a typical frequency for nuclear motion, kB is the Boltzmann constant, and T is the temperature. However, if the electronic coupling is weak, the electron transfer is nonadiabatic and the rate constant takes the following expression instead.18

2 k et  V AB 

2

 (G 0  l ) 2  exp  4lk B T  4l k B T  1

(4)

where ħ is the Planck constant. Ab initio cluster calculations. Ab initio calculations were performed to compute VAB for electron transfers from Fe(II) adsorption sites identified in the potential of mean force calculations. First, an energy optimization with the steepest-descent approach was carried out for each Fe(II) adsorption free energy minimum of interest, whereby only the hematite slab and the first or the first and second Fe(II) hydration shells were retained. The geometry optimizations were performed with the charges of the donor and acceptor irons set to +2.5 e in order to obtain a configuration as close as possible to the crossing point. Because of the asymmetry of the mineral-water interface, setting both charges to +2.5 e does not guarantee obtaining a crossing point configuration. The donor and acceptor irons were excised from the geometry-optimized configurations together with their first coordination shell. The clusters were then protonated 12 ACS Paragon Plus Environment

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using a protonation scheme described elsewhere19-20 for use in ab initio cluster calculations. Next, calculations of the electronic coupling matrix elements were carried out with NWChem56 at the spin unrestricted HF level with the Ahlrichs valence triple-zeta basis set for iron,57 which was augmented with three diffuse functions (function/exponent = s/0.01257, p/0.04184, d/0.11330)17 and the 6-311+G basis set for the oxygen and hydrogen atoms.64-66 Following an approach previously employed for interfacial VAB calculations,67 hydrogen atoms were removed either fully or partially, by replacing them with fixed partial charges, from the coordination shell of the donor iron to bring the reactants and products energies to be degenerate and thus allow for calculating VAB. The effect of electron correlation on the values of VAB was not included as these calculations were based on the UHF wave functions of the reactant and product states.

RESULTS AND DISCUSSION Fe(II) adsorption at the hematite (001) surface. The free energy profiles obtained from the potential of mean force calculations with the three potential models are shown in Figure 3. The three profiles display a number of similarities. Firstly, all three profiles predict a shallow minimum at approximately 4 Å above the surface with a free energy around 0 kJ·mol-1 (-0.3, 0.1, and 2.1 kJ·mol-1 for Models 1, 2, and 3, respectively). Iron-water oxygen and iron-hydroxyl oxygen radial distribution functions (RDF) were computed at each height and the iron coordination number with both oxygen types were extracted from integration of the RDF up to the first minimum. The resulting coordination profiles obtained with Model 1 are shown in Figure 4. Figure 4 clearly shows that, at this height above the surface, Fe(II) is coordinated to six water molecules and that therefore this shallow minimum corresponds to Fe(II) in an outersphere configuration, which will be referred to as the outersphere adsorption site. Models 2 and 3 show



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very similar results. It should be noted that, beyond approximately 3.2 Å above the surface, the iron-water oxygen RDFs all show a region between the first and second hydration shells where g(r) is zero, which signifies that no water exchange took place around Fe(II) above that height. This finding is consistent with previous work on the rate and mechanism of water exchange around aqueous ferrous iron68 and experimental data,69-70 which both indicated that the residence time of water in the first hydration shell of Fe(II) is on the order of microseconds. Consequently, water exchanges are not expected to be observed during the 200-ps MD simulations.

Figure 3. Free energy profiles for the adsorption of Fe(II) onto the (001) hematite surface obtained with all three models. Also shown are the electron density profiles obtained from MD simulations of the hematite (001)-water interface with Models 1 and 2.


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Figure 4. Fe(II)-water oxygen and Fe(II)-surface hydroxyl oxygen coordination number profiles for the adsorption of Fe(II) onto the hematite (001) surface with Model 1. Secondly, the position and the size of the main energy barrier for adsorption are very similar for the three models. The barrier heights are 48.0, 49.4, and 48.4 kJ·mol-1, which is remarkably similar to the experimental enthalpy of activation for water exchange ( H ‡ex = 41.4 kJ·mol-1).69 All three transition states are positioned at 2.8 Å above the hematite surface, which corresponds to the distance at which Fe(II) begins to exchange a water molecule for a surface hydroxyl in its first coordination shell (Figure 4). This finding is in agreement with previous work on the adsorption of alkaline-earth cations on the (104) calcite surface.51 Finally, all three models predict the presence of a second shallow minimum at 2.4, 2.4, and 2.7 Å for Models 1, 2, and 3, respectively, and a deeper minimum at 1.4, 1.3, and 1.2 Å for Models 1, 2, and 3, respectively. The former corresponds to Fe(II) attaching to one surface hydroxyl whereas, in the later, Fe(II) is coordinated to three surface hydroxyls and three water molecules (Figure 4). These two sites will be referred to as the monodentate and tridentate adsorption sites, respectively. The main discrepancy between the three profiles is the free energy for adsorption at the tridentate site, which is predicted to be 55.7, 25.4, 65.5 kJ·mol-1 for Models 1, 2, and 3, 15 ACS Paragon Plus Environment


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respectively. However, all three models predict the free energy of adsorption at the two innersphere positions to be unfavorable for the conditions considered in this work. The rate of adsorption over the main free energy barrier from the outersphere complex to the monodentate complex can be calculated from transition state theory as follows:

k  k TST

(5)

where kTST is the transition state rate constant k TST 

k B T exp(  WPMF (r*) k B T ) 2 r*  exp(  WPMF (r ) k B T )dr

(6)

0

where μ simplifies to the mass of the adsorbing ion in this case, kB is Boltzmann constant, T is the temperature, WPMF is the free energy determined from the potential of mean force calculations, and r* is the transition state distance. The rate calculation was done for Models 1 and 3 as the electron transfer rate calculations were carried out for these two models only, as explained later. The transition state rate constants were calculated to be 5.5×103 and 1.8×104 s-1 for Models 1 and 3, respectively. The transmission coefficient, κ, was determined from the plateau value of the normalized reactive flux, which can be computed as k (t ) 

r(0) [r (t )  r*] c r(0) [r(0)] c

(7)

where θ[x] is the Heaviside function, which is 1 if x is larger than 0 and 0 otherwise, and r(0) is the initial velocity of the Fe(II) ion along the reaction coordinate. The subscript c means that the initial configurations have been generated in the constrained reaction coordinate ensemble. To compute κ, a pool of initial configurations was produced by running a 1,125-ps MD simulation where Fe(II) was constrained at the transition state distance and collecting a configuration every 1.5 ps for a total of 750 configurations. Each configuration was run both backward and forward 16 ACS Paragon Plus Environment

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in time for 2.0 ps and values of κ of 0.002 and 0.013 were determined for Models 1 and 3, respectively, from averaging k(t) over the last 1.0 ps (Figure S1). For comparison, previous work51 on the adsorption of divalent alkaline-earth cations at the (104) calcite surface resulted in values of κ ranging from 0.006 to 0.029. As a result, the adsorption rate constants were calculated to be 1.3×101 and 2.3×102 s-1, for Models 1 and 3, respectively. The PMF calculations show that Fe(II) adsorption as an innersphere complex is not favorable on a neutral, flat, and fully-hydroxylated (001) surface. As described in detail in the next section, Fe(II) is bound to three doubly-coordinated hydroxyl groups when adsorbed as a tridentate innersphere complex. Therefore, adsorption as an innersphere complex on other hematite surfaces with different surface functional groups is expected to yield different adsorption free energies. Indeed, this is consistent with the favorable free energies calculated with Model 1 for Fe(II) adsorbing at several goethite surfaces.71 Moreover, it should be noted that the presence of step edges could lead to the formation of adsorption sites with configurations and protonation states72 distinct from those considered in this work and thus with different adsorption free energies. Unlike the reactive force field developed by Rustad and co-workers73 for the Fe-O-H system, the potential models used in this work do not allow for spontaneous proton dissociation and, therefore, multiple simulations with different protonation schemes have to be performed when considering the effects of protonation/deprotonation. Therefore, the PMF simulations were repeated for Models 1 and 2 with two surface hydroxyl groups deprotonated. Figure 5 shows that, as expected, deprotonation of surface hydroxyls renders adsorption at all three sites significantly favorable, with both models predicting similar free energy profiles. This result suggests that protons could be released from the surface either following Fe(II) adsorption or as



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part of a concerted mechanism, and that the residence time of adsorbed Fe(II) would be significantly increased in such a scenario. Additionally, this result implies that, at high pH, the driving force for Fe(II) adsorption and the residence time of adsorbed Fe(II) on the surface will be much greater than near the point of zero surface charge (that is, the pH value at which the surface charge density is zero).

Figure 5. Free energy profiles obtained with Models 1 and 2 for the adsorption of Fe(II) onto a fully hydroxylated (001) hematite surface and onto the same surface with two surface hydroxyl groups deprotonated. Fe(II) adsorption complexes at the hematite (001) surface. In this section, we discuss the structure of Fe(II) complexes adsorbed at the hematite (001) surface and compare the ironoxygen bond lengths with those obtained in bulk calculations to evaluate to what extent adsorption affects the structure of the iron coordination shell. For the purposes of this section, additional MD simulations were carried out with the three models with Fe(II) initially positioned in the three energy minima determined in the potential of mean force calculations for the neutral surface. All MD simulations were run for 5 ns; however, in the simulations of Fe(II) adsorbed as a monodentate complex, Fe(II) desorbed from the surface after approximately 160 ps, 130 ps, and 5 ps for Models 1, 2, and 3, respectively. Therefore, not enough data was available to 18 ACS Paragon Plus Environment

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determine iron-oxygen distances for the monodentate complex for Model 3. Similarly, in the simulations of Fe(II) adsorbed as an outersphere complex, Fe(II) desorbed after approximately 500 ps and 1.4 ns for Models 1 and 2, respectively. Also, the tridentate complex with Model 3 desorbed after approximately 900 ps. All the calculated iron-oxygen bond distances are summarized in Table 2. For reference, the Fe(II)-water oxygen and the Fe(II)-hydroxyl oxygen distances obtained with each model from a simulation of Fe(II) immersed in bulk water and that of bulk Fe(OH)2, respectively, are also shown in Table 2. The calculated Fe(II)-water oxygen distances (2.07-2.09 Å) are at the shorter end of the range of the distances derived experimentally from extended X-ray absorption fine structure spectroscopy (EXAFS) measurements (2.09 ± 0.06 Å74 and 2.12 ± 0.01 Å75), X-ray diffraction (2.120 and 2.124 Å),76 and neutron diffraction (2.13 ± 0.02 Å).77 The calculated Fe(II)-hydroxyl oxygen distances (2.142.15 Å) reproduce well the experimental data of Parise et al.55 at room temperature (2.143 ± 0.001 Å), as expected since the Fe(II)-hydroxyl oxygen potential parameters were fitted to reproduce the experimental data of Parise et al.55 at 10 K.

Table 2. Fe(II) adsorption complexes at the hematite (001) surface. Distances are in Å and coordination numbers are shown in brackets. Model Distance

1

2

3

Fe-OW

Fe-OH

Fe-OW

Fe-OH

Fe-OW

Fe-OH

Tridentate

2.07 (3.0)

2.22 (3.0)

2.10 (3.0)

2.23 (3.0)

2.06 (3.0)

2.25 (3.0)

Monodentate

2.07 (5.0)

2.44 (1.3)

2.07 (5.0)

2.39 (1.0)

-

-

Outersphere

2.07 (6.0)

-

2.09 (6.0)

-

2.09 (6.0)

-

Fe2+(aq)

2.07 (6.0)

-

2.09 (6.0)

-

2.09 (6.0)

-

-

2.14 (6.0)

-

2.15 (6.0)

-

2.14 (6.0)

Fe(OH)2



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The upper FeO6 octahedron of the surface iron bilayer shares a face with a FeO6 octahedron from the iron bilayer immediately below and shares edges with three FeO6 octahedra in the same iron bilayer. The lower FeO6 octahedron of the surface iron bilayer shares edges with three FeO6 octahedra of the same iron bilayer. Therefore, there are two potential adsorption sites at the surface that correspond to extensions of the hematite lattice. If Fe(II) adsorbs in the first site, the Fe(II)O6 octahedron is in a face-sharing configuration with a lower FeO6 octahedron of the surface iron bilayer; whereas, if Fe(II) adsorbs in the second site, the Fe(II)O6 octahedron shares corners with three surface octahedra. Figure 6 displays a projection of the atomic densities onto the surface plane from the simulation of Fe(II) adsorbed in the tridentate site with Model 1 (similar results were obtained with Models 2 and 3). Figure 6 shows that the tridentate complex adsorbs in the latter of the two sites just described. When adsorbed in this site, Fe(II) is coordinated to three surface hydroxyl groups and three water molecules. The Fe(II)-water oxygen distances are essentially the same as for the aqueous complex whereas the Fe(II)hydroxyl oxygen distances are approximately 4-5% longer than in Fe(OH)2.


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Figure 6. Surface density contour plot from the simulation of Fe(II) adsorbed as a tridentate innersphere complex with Model 1. Fe(III) ions are shown in gray, Fe(II) in green, hydroxyl oxygens in orange, and water oxygens in blue. Color intensity increases with density. When adsorbed as a monodentate complex, the Fe(II)-hydroxyl oxygen distances increase further to approximately 2.4 Å whereas, again, the Fe(II)-water oxygen distances remain similar those obtained in the bulk (2.07 and 2.09 Å for Models 1 and 2/3, respectively). When adsorbed as an outersphere complex, the iron-water oxygen distances (2.07 and 2.09 Å for Models 1 and 2/3, respectively) are identical to those obtained in bulk aqueous solution. It is interesting to note that although the free energy barrier for desorption from the outersphere position is comparable with the thermal energy (Figure 3), Fe(II) remains in an outersphere configuration for long periods of time (0.5, 1.4, and at least 5 ns for Models 1, 2, and 3, respectively). This is explained by the observation that the outersphere complex adopts specific configurations on the surface. As shown in Figure S2 from a MD simulation with Model 3 of Fe(II) adsorbed as an outersphere



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complex, Fe(II) occupies, for the most part, two sites at the surface; one situated directly above a surface Fe(III) ion and a second site positioned between two surface hydroxyl oxygens. If the free energy barrier between these outersphere sites is lower than that for desorption, Fe(II) can remain adsorbed at the surface for longer periods of time that would be expected strictly based on the one-dimensional free energy profiles shown in Figure 3. This finding is consistent with the study of Bargar et al.78 on Pb(II) adsorption onto the (001) surface of α-Al2O3, which is isostructural to hematite, in which Pb(II) was suggested to adsorb as an outersphere complex at specific sites based on the presence of a Pb-Al peak in the Pb LIII EXAFS spectrum. No direct experimental data on the structure of Fe(II) adsorbed complexes on the (001) hematite surface is available for comparison with the calculated bond lengths presented in Table 2. This is due to the apparent facile oxidation of adsorbed Fe(II) on the (001) hematite surface on the time scale of laboratory experiments. Tanwar et al.29 used crystal truncation rod X-ray diffraction to probe the structure of the hematite (001)-water interface after reaction with Fe(II). The derived bond distances for the adsorbed Fe were found to be consistent with Fe(III)-O bond lengths for Fe(III) in octahedral coordination, thus strongly suggesting that adsorbed Fe(II) had been oxidized on the timescale of the experiments. The same observation was made by the same workers for Fe(II) adsorption on the (012) hematite surface using the same technique.79 Similarly, Fe K-edge resonant anomalous X-ray reflectivity measurements of Fe(II) reacted with three hematite surfaces, namely, the (001), (012), and (110) surfaces, indicated that Fe(II) surface coverages were within error of zero for all three surfaces.13 A DFT study of Fe(II) adsorption as an innersphere complex on two goethite (α-FeOOH) surfaces80 reported Fe(II)-hydroxyl oxygen (OOH) distances ranging from 1.94 to 2.03 Å. These distances are much shorter than the Fe(II)-OOH distances calculated in this work; however, they


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are also short compared to the experimental value of the Fe(II)-OOH distance in Fe(OH)2 (2.143 ± 0.001 Å)55 and to the Fe(III)-OOH distances in α-FeOOH (2.100 and 2.106 Å)81 and more closely resemble Fe(III)-OOH distances in β-FeOOH (2.048 Å),82 γ-FeOOH (2.019 Å),83 and δ-FeOOH (2.039 Å).84 The Fe(II)-water oxygen distances were not reported. Oxidation of adsorbed Fe(II) at the hematite (001) surface. Electron transfer parameters were calculated for electron transfer reactions from the tridentate innersphere and outersphere adsorption sites to surface iron sites (see Table 3). Precisely, electron transfer rates were calculated to the nearest topmost iron site (upper iron of the iron bilayer) in each case. There are three and one symmetrically equivalent acceptor sites from the tridentate innersphere and outersphere adsorption sites, respectively. The monodentate innersphere site was not considered as this minimum was predicted to be very shallow by all three models, which leads to very short residence time of Fe(II) in this position. Calculations were carried out solely with Models 1 and 3 as rigid-ion models were shown previously to be inadequate for calculating reorganization energies of electron transfer in iron oxides.48 For each electron transfer reaction, free energy surfaces similar to that shown in Figure 2 were constructed using the umbrella sampling technique described in the Computational Methods section and following the same approach as used in previous work on similar systems.17,48



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Table 3. Electron transfer parameters and rates of electron transfer reactions between adsorbed Fe(II) and surface Fe(III). Model

λ (eV)

VAB (eV)

d VAB (Å)

κ

k (s-1)

Tridentate innersphere 1

3.20

0.071

3.58

0.88

1.9×100

3

3.69

0.066

3.55

0.83

1.4×10-2

Outersphere 1

3.89

0.001

4.75

0.001

3.6×10-4

3

3.06

0.011

5.16

0.07

1.4×102

For electron transfer from an outersphere adsorbed complex, the length of the electron transfer calculation is on the order of the residence time of Fe(II) in a given surface site; therefore, it is likely that Fe(II) would not reside in that site throughout the whole simulation, which would lead to erroneous results. Therefore, a weak tether was added between the adsorbed Fe(II) donor and the surface Fe(III) acceptor. The tether distance was set to the distance between the two ions obtained from a simulation free of constraints. The tether was a harmonic potential with a force constant of 1 eV·Å-1. A control calculation was performed with Model 1 for the electron transfer from the outersphere position with a force constant reduced by half and showed no significant difference indicating that, given a low enough force constant, the tether does not significantly affects the results. The values of the reorganization energies obtained with Models 1 and 3 for the two adsorption sites are shown in Table 3. We first note that all the reorganization energies are high compared to those obtained previously with similar potential models for electron transfers within the hematite lattice. For example, the reorganization energies obtained for the basal and cdirection transfers in bulk hematite with Models 1 and 3 (which use the same model for the iron 24 ACS Paragon Plus Environment

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oxide phase) are 1.75 and 1.88 eV, respectively.17 These values are slightly overestimated relative to the reorganization energies obtained from electronic structure calculations for the same transfers (1.42 and 1.47 eV, respectively).20 For Fe2+/Fe3+ electron transfer in aqueous solution, the reorganization energy can be divided into an innersphere contribution due to the relaxation of the first hydration shell and an outersphere contribution mostly due to the polarization of water molecules in the vicinity of the electron transfer couple. The four-point method applied to hexaaquo clusters leads to an innersphere reorganization energy of 2.78 eV with Model 1. This is much greater than previous estimates of 0.6-0.7 eV obtained using density functional theory and the B3LYP exchange-correlation potential.85 However, Rustad et al.86 obtained 1.93 eV with a polarizable water model. Rustad et al.86 also explained that the difference between their model and the DFT results could be accounted for mostly by the difference in the calculated wavenumbers for the ν1 symmetric breathing mode of Fe3+(aq) and that the experimental value for ν1 was half-way between the model and DFT values, suggesting that the average of the two values (~1.3 eV) would be a more accurate prediction. The innersphere reorganization energy obtained with Model 3 (0.82 eV) was in better agreement with the DFT values. The overall reorganization energy for the Fe2+/Fe3+ electron transfer in aqueous solution, as obtained from an umbrella sampling calculation in which the Fe2+ and Fe3+ ions were in separate simulation cells, were calculated to be 5.41 and 3.62 eV for Models 1 and 3, respectively. Subtracting the innersphere reorganization energies just mentioned, this leads to outersphere reorganization energies of 2.63 and 2.80 eV for Models 1 and 3, respectively. For comparison, Rosso and Rustad85 calculated the outersphere reorganization energy to be 1.50 eV from Marcus’ continuum formula.87



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Two conclusions can be drawn from this discussion. Firstly, the interfacial reorganization energies obtained in this work are likely to be somewhat overestimated as the potential model calculations lack the full electronic degrees of freedom compared to the electronic structure calculations, with Model 3 offering the best quantitative agreement with previous electronic structure calculations. Secondly, despite this limitation, the simulations demonstrate that the interfacial reorganization energies are higher than those for electron transfers within the hematite lattice because of the larger reorganization energy of the aqueous Fe ions and the fact that the interfacial electron transfers take place over longer distances (3.55 to 5.16 Å, Table 3) than the electron transfers in the bulk of the lattice (2.98 and 2.93 Å for the basal plane and c-direction transfers), which is consistent with previous work showing that the reorganization energy generally increases with increasing electron transfer distance.88 The reorganization energies calculated in this work are in agreement with the range of reorganization energies obtained with Model 1 for several interfacial Fe(II)/Fe(III) electron transfers at several goethite surfaces.71 It should be noted that there is a direct correlation, in the MD simulations, between the free energy of interfacial electron transfer and the difference in enthalpy of hydration of Fe2+ and Fe3+ (ΔΔHhydr.), whereby the driving force for electron transfer from adsorbed Fe(II) to a surface Fe(III) increases the greater ΔΔHhydr.. Indeed, as ΔΔHhydr. increases, and thus Fe3+(aq) becomes more stable relative to Fe2+(aq), the reaction products, which consist of Fe(III) at least partially hydrated, become energetically more favorable and hence ΔG0 becomes more favorable. As shown in Figure S3 of the Supporting Information, using Models 1 and 3 as well as Model 1 before the changes to the potential parameter set introduced in the Computational Methods section, linear correlations with R2 values of 0.97 and 0.98 were found for ΔG0 versus ΔΔHhydr., for the tridentate innersphere and outersphere adsorption sites, respectively. The values of


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ΔΔHhydr. were obtained from MD simulations of one ferric or ferrous ion in simulation cell containing 255 water molecules. In these simulations, the corrections described by Kastenholz and Hünenberger89-90 were used to account for the effects of the finite size and periodicity of the system on water polarization as well as the summation scheme used to determine the potential at the ion site. Using the correlation between ΔG0 and ΔΔHhydr. and the experimental value for ΔΔHhydr. (2456.5 kJ·mol-1)91 led to corrected ΔG0 values of 12.7 and -35.9 kJ·mol-1 for electron transfers from the tridentate innersphere and outersphere adsorption sites, respectively. This result is consistent with the model of Rustad and co-workers,92 which also pointed to the high hydration of Fe(III) as a driving force for electron transfer at the (012) hematite surface. To obtain VAB, an energy optimization with the steepest-descent approach was carried out for the tridentate innersphere and outersphere minima in the Fe(II) adsorption free energy profile. For the tridentate innersphere complex, only the first shell water was retained whereas for and outersphere complex both the first and second shells were used in the geometry optimization. The energy minimizations and the VAB calculations were performed as described in the Computational Methods section. The VAB values thus obtained are shown in Table 3. The two models lead to larger VAB values for electron transfer from the tridentate innersphere complex than from the outersphere complex, as expected based on the differences in electron transfer distances. The VAB values of the two models are in good quantitative agreement for the tridentate innersphere complex, whereas a reduced electronic coupling is calculated with Model 1 compared to Model 3 for the outersphere complex. A potential source of this difference is the fact that VAB is sensitive to the relative orientation of the two iron octahedra67,93 and, whereas this orientation is likely to be more constrained and similar between the two models for the tridentate innersphere complex, it could differ more for the outersphere complex.



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Both models predict the electron transfers from the tridentate innersphere sites to be adiabatic and the electron transfer from the outersphere position to be nonadiabatic and therefore Equations (2) and (4) were used to calculate the electron transfer rates, respectively. The average of the hematite highest infra-red active longitudinal optic mode phonon (i.e., 1.85×1013 s-1)20 and the frequency factor for aqueous Fe(II)/Fe(III) electron transfer obtained from ab initio cluster calculations (i.e., 1.16×1013 s-1)85 was used to determine νn. Electron transfer rates obtained with Models 1 and 3 differ by two orders of magnitude for electron transfer from the tridentate innersphere site. There is a five-to-six-order-of-magnitude difference between the rates calculated by Models 1 and 3 for the outersphere position. This is due to sizeable differences in both the reorganization energy and the electronic coupling matrix element between the two models for this transfer. As discussed above, the reorganization energy predicted by Model 3 is likely to be more accurate and therefore the electron transfer rate from the outersphere position is likely to be on the upper end of the range predicted by the two models. By and large, the interfacial electron transfer rates are orders of magnitude slower that those calculated in the bulk hematite lattice (3.2×109 s-1 and 6.5×105 s-1 for electron transfers in the basal plane and c direction, respectively).17 In a previous publication,17 we reported molecular dynamics calculations of electron transfer reactions in the top few atomic layers of several hematite surfaces including the hydroxylterminated (001) surface. This work addressed the fate of an electron already injected into the lattice. For the hydroxyl-terminated (001) surface, the simulations predicted a small overall driving force for the electron to remain in the topmost iron bilayer and no significant free energy barrier for diffusion to and from the bulk. In addition, the rates of electron transfer were found to only differ slightly from those obtained in the bulk hematite lattice. Because of the orientation of


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the (001) surface, with the slow c-direction transfer only occurring in the direction normal to the surface and the rapid basal electron transfer only occurring in the direction parallel to the surface, electrons are predicted to diffuse more rapidly within an iron bilayer than between two such layers. It was therefore concluded that electrons would be able to diffuse over long lateral distances.

CONCLUSIONS Combined classical molecular dynamics and ab initio cluster calculations were carried out to simulate the adsorption and oxidation of ferrous iron at the hematite (001) surface. The simulations indicate that Fe(II) can adsorb in three different sites at the surface, namely, tridentate innersphere, monodentate innersphere, and outersphere complexes. Adsorption in both innersphere sites was found to be unfavorable, although release of protons upon adsorption renders the free energy of adsorption more favorable. In addition, a large free energy barrier, commensurate with the enthalpy of activation for water exchange around Fe(II) in aqueous solution, exists for adsorption as an innersphere complex from the outersphere position. Indeed, an adsorption rate constant on the order of 101-102 s-1 was calculated using the reactive flux method. The simulations predict that electron transfer to a surface Fe(III) is slightly unfavorable from the tridentate innersphere complex but favorable from the outersphere complex. In addition, the simulations indicate the driving force for electron transfer to the lattice depends on a subtle balance between the energetics of Fe(II)/Fe(III) substitution at the hematite surface and the difference in hydration between Fe(II) and Fe(III). Therefore, the magnitude of this driving force is likely to be very sensitive to changes in surface structure and solution chemistry. The rate of



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electron transfer from the outersphere position obtained with Model 3, which was found to be the most reliable prediction of the models considered here, was commensurate with the rate of adsorption, suggesting that adsorption onto the hematite surface does not necessarily have to precede oxidation. Previous work with a similar model than those used in this study indicates that, once injected into the hematite lattice, electrons are able to rapidly diffuse away from the site of interfacial electron transfer. Importantly, three different potential parameter sets were used in the molecular dynamics simulations and, despite some quantitative differences, all three models predicted the same general behavior of Fe(II) at the hematite (001)-water interface. The findings are consistent with experimental observations of oxidative adsorption of Fe(II) at hematite (001)-water interfaces and elucidate the mechanism in terms of a competition of adsorption and interfacial electron transfer pathways.

ACKNOWLEDGEMENTS The authors acknowledge the two anonymous reviewers for their insightful comments. This research was supported by the Geosciences Research Program in the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences. PZ also acknowledges the Polish Ministry of Science and Higher Education (grant MNiSW IP2012 059872). The computer simulations were performed in part using the Molecular Science Computing (MSC) facilities in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by the U.S. Department of Energy’s Office of Biological and Environmental Research (OBER) and located at Pacific Northwest National Laboratory (PNNL). PNNL is operated for the DOE by Battelle Memorial Institute under Contract DE-AC05-76RL01830.


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Supporting Information Available. Complete list of all potential parameters, reactive fluxes for Fe(II) adsorption, surface density contour plots for Fe(II) adsorbed as an outersphere complex, and free energy of interfacial electron transfer as a function of Fe(II)/Fe(III) hydration enthalpy difference. This material is available free of charge via the Internet at http://pubs.acs.org.



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REFERENCES (1) Leland, J. K.; Bard, A. J. Photochemistry of Colloidal Semiconducting Iron Oxide Polymorphs. J. Phys. Chem. 1987, 91, 5076-5083. (2) Yanina, S. V.; Rosso, K. M. Linked Reactivity at Mineral-Water Interfaces through Bulk Crystal Conduction. Science 2008, 320, 218-222. (3) Williams, A. G. B.; Scherer, M. M. Spectroscopic Evidence for Fe(II)-Fe(III) Electron Transfer at the Iron Oxide Water Interface. Environ. Sci. Technol. 2004, 38, 4782-4790. (4) Larese-Casanova, P.; Scherer, M. M. Fe(II) Sorption on Hematite: New Insights Based on Spectroscopic Measurements. Environ. Sci. Technol. 2007, 41, 471-477. (5) Larese-Casanova, P.; Scherer, M. M. Morin Transition Suppression in Polycrystalline 57

hematite (-Fe2O3) Exposed to 56Fe(II). Hyperfine Interact 2007, 174, 111-119.

(6) Silvester, E.; Charlet, L.; Tournassat, C.; Géhin, A.; Grenèche, J.-M.; Liger, E. Redox Potential Measurements and Mössbauer Spectrometry of FeII Adsorbed onto FeIII (Oxyhydr)Oxides. Geochim. Cosmochim. Acta 2005, 69, 4801-4815. (7) Rosso, K. M.; Yanina, S. V.; Gorski, C. A.; Larese-Casanova, P.; Scherer, M. M. Connecting Observations of Hematite (-Fe2O3) Growth Catalyzed by Fe(II). Environ. Sci. Technol. 2010, 44, 61-67. (8) Zhang, Y.; Charlet, L.; Schindler, P. W. Adsorption of Protons, Fe(II) and Al(III) on Lepidocrocite (-FeOOH). Colloids Surf. 1992, 63, 259-268. (9) Coughlin, B. R.; Stone, A. T. Nonreversible Adsorption of Divalent Metal Ions (Mn II, CoII, NiII, CuII, and PbII) onto Goethite: Effects of Acidification, FeII Addition, and Picolinic Acid Addition. Environ. Sci. Technol. 1995, 29, 2445-2455.


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Computational Molecular Simulation of the Oxidative Adsorption of

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