Theoretical Study of Small Iron-Oxyhydroxide Clusters and Formation

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Theoretical Study of Small Iron-Oxyhydroxide Clusters and Formation of Ferrihydrite Bidisa Das J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b09470 • Publication Date (Web): 20 Dec 2017 Downloaded from http://pubs.acs.org on December 25, 2017

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The Journal of Physical Chemistry

Theoretical Study of Small Iron-oxyhydroxide Clusters and Formation of Ferrihydrite BIDISA DAS*,† Technical Research Centre (TRC). Indian Association for the Cultivation of Science (IACS). 2A & 2B Raja S. C. Mullick Road. Jadavpur. Kolkata 700032. India.

*Email:[email protected]

Abstract

Hydrolysis of iron compounds in water, leads to the formation of Fe(III) oyxhydroxide based minerals like Ferrihydrite, which act as natural scavengers of inorganic contaminants in the environment. Though studied widely, experimental identification of these oxyhydroxides remains to be very difficult due to their extreme reactivity. Present study theoretically investigates the formation of Fe(III) oxyhydroxides starting from a single hydrated Fe(III) ion, modelling the formation of larger clusters gradually. The structures, formation enthalpies and free energies of dimers, trimers, tetramers and even larger Fe(III) oxyhydroxide clusters comprising of Fe5, Fe7 and Fe13-Keggin ions in gaseous phase and in aqueous medium (using

†

Past Address: Center for Advanced Materials (CAM). Indian Association for the Cultivation of Science (IACS). 2A & 2B Raja S. C. Mullick Road. Jadavpur. Kolkata 700032. West Bengal. India.

1 ACS Paragon Plus Environment

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self-consistent reaction field method) are systematically studied using Density Functional Theory. Spontaneous formation of certain multinuclear Fe(III) oxyhydroxide clusters with clear structural signatures of Ferrihydrite highlights their potential as pre-nucleation clusters in the course of mineralization.

Introduction Iron based compounds and minerals are present in numerous geological, biological and industrial systems, thus aqueous chemistry of iron had been studied extensively since early sixties.1 Hydrolysis of iron, which dictates the aqueous chemistry is understood to be a multi-step process and proceeds via the formation of lowmolecular-weight species followed by the segregation of an intermediate cationic polymeric phase. This phase may eventually be converted to the oxide phase with aging, or the oxide phase may also be precipitated from the low-molecular-weight precursors. Though occurring in almost all environmental and many metallurgical and biological processes, identification of some hydrolysis products of Fe(III) were greatly underestimated earlier because of their poorly crystalline nature, which remained uncharacterized and were commonly designated as 'colloidal amorphous iron hydroxides'. Continued research efforts gradually helped in identifying at least fourteen well-defined Fe(III) oxides, hydroxides and oxyhydroxide phases among which goethite, hematite, and magnetite are known to occur most abundantly in nature.2 Certain minerals like lepidocrocite, ferrihydrite, and maghemite are also very common in soils, surface-waters and mine drainages but were termed as intermediate phases which later on transformed into more stable phases like hematite or magnetite.2 That many of these metastable minerals occurred in nanophases having variable compositions with in-built point-defects, added to their characterization woes.


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Recently with new experimental characterization techniques and more quantitative approach to phase stability enabled in understanding the stability, and transformation of many of these complex materials.3 Fe(III) oxyhydroxides, like goethite, lepidocrocite, akaganeite or ferrihydrite are ubiquitous in nature and may occur in anhydrous (FeO(OH)) or hydrated (FeO(OH). nH2O) forms and this study focuses on ferrihydrite (nominal chemical formula 5Fe2O3. 9H2O) specifically, which has the smallest particle size of all and is widespread in natural environments. Due to the small particle size and consequently large surface area (>340 m2/g) and high reactivity; ferrihydrite is an important adsorbent of various trace metals, anions, and organic species in both surface and groundwater systems acting as natural scavenger and its structure, formation and growth is of great importance.2 It was pointed out by J. F. Banfield et al that Fe(III) oxyhydroxide phases, like ferrihydrite grow via an aggregation-based pathway under natural conditions by assembly of multinuclear molecular clusters.4 It was observed that, the crystals grow from the assembly of increasingly larger and larger particles (of few nm diameter) to gradually even bigger ones. The occurrence of meta-stable solute phases during the crystallization process was later understood in the form of pre-nucleation clusters which occur in case of numerous bio-mineralization products.5 There are debates regarding the structure of ferrihydrite and it is still characterized experimentally by the number of X-ray diffraction lines: typically '2-line' ferrihydrite for material exhibiting little crystallinity and '6-line' ferrihydrite for best crystallized samples.2 Though formation of ferrihydrite had been studied earlier, a recent study by J. S. Weatherill et al addressed the formation mechanism in greater detail and they tried to explore the pathways of ferrihydrite formation including the an intermediate Fe13 Keggin cluster using various experimental techniques.6 A related study attempted



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to explore the nucleation pathways of iron oxyhydroxide formation and concluded that the nucleation is governed by the dynamics of the clusters formed, based on the chemistry of the linkages within the clusters.7 To gain a complete understanding of the hydrolysis of Fe(III) in aqueous systems, identifying and understanding the structures of the species present in solution is important, which offers possibilities of tailoring materials for a wide range of utilizations. In absence of adequate experimental evidence of small oligomeric Fe(III) oxyhydroxide clusters, related theoretical modeling studies are extremely important. The small Fe(III) oxyhydroxide clusters, although are not minerals, they can be used to examine bond breakings / dissociations at a truly molecular scale and these nanometre-sized ions may serve as models for the more complicated minerals.8 There are earlier experimental and theoretical studies of small Fe(III) oxyhydroxide clusters

9-13

along with some studies involving molecular

dynamics simulation of Fe(II)/Fe(III) ions in water

15,16

offering insights into the

mechanism. Theoretical investigation of larger Fe(III) oxyhydroxide clusters may help in understanding various nucleation pathways for the formation of solid mineral phases like ferrihydrite/goethite/akaganeite and the present study aims to bridge this gap. Here, the focus is on the gradual formation of Fe(III) oxyhydroxide clusters from a single hydrated Fe(III) ion, which first forms the dimeric oxyhydroxide cluster. Then we looked into the formation enthalpies of stable trimeric, tetrameric or larger stable oligomeric clusters [Fe3, Fe4 , Fe5 , Fe7 and Fe13 oxyhydroxide clusters], with more number of Fe(III) ions connected to the dimeric or trimeric oxyhydroxides via FeO or FeOH linkages, which are potential pre-nucleation clusters for formation of the mineral ferrihydrite. The formation of Fe(III) oxyhydroxide clusters were studied both


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in gaseous phase and in aqueous medium (using self-consistent reaction field model), so that realistic estimates of formation enthalpies and free energies could be made.

Computational Details The electronic structure studies for all Fe(III) oxyhydroxide clusters and related species were performed using density functional theory (DFT) as implemented in the Gaussian 09 suite of programs.17 Studies were performed using the B3LYP18-20 hybrid functional with the 631G** basis sets for all atoms as implemented in G09 program.17 To ascertain the stable structures, a re-check was carried out using the B3PW9121 functional along with 6-31G** basis set and it was observed that the bond-distances calculated using this method are slightly shorter. The stable clusters were determined by full geometry optimization in the gas-phase and consequent harmonic frequency calculations were performed to ascertain the stationary points. For any reaction, Reactants → Products, the enthalpy of formation is calculated as;

∆ = ∑ ∆ − ∑ ∆ where, ∆H represents the sum of electronic and thermal enthalpies of the corresponding species. The reaction enthalpies and free energies for all reactions studied in the gas phase are tabulated in Table 1. Along with studies in gaseous phase, we have done single-point solvent-phase studies on the B3LYP/6-31G** optimized structures using the self-consistent reaction field (SCRF) method employing implicit solvation based conductor-like polarizable continuum model (CPCM)22,23 and density-based solvation model (SMD)24 in aqueous medium ( using dielectric constant, ε = 78.39). Computing solvation free energy as a single-point calculation on the gas phase optimized structure implicitly, as done in CPCM and SMD methods, assume that the molecule undergoes little structural changes between the two phases. This is strictly true for small rigid molecules only and is approximate in complex environments, we however adopt these methods so that we can conveniently study large Fe(III) oxyhydroxide clusters. The 5 ACS Paragon Plus Environment


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aqueous phase free energies (Gs) are obtained by adding the corresponding solvation free energies to the gas phase free energies, Gs = Ggas + ∆Gsolv (see Supporting Information, SI for more details about calculation of ∆Gsolv).25 In this study, all data obtained for Fe(III) oxyhydroxide clusters in the gas phase are for 298 K and 1 atm pressure. All calculated solvation free energies are calculated for an ideal gas at a concentration of 1 mol/L dissolving as an ideal solution at a liquid-phase concentration of 1 mol/L. The relationship26,27 between these two standard states is: ∆Ggas→soln = RT ln(24.46)∆n where ∆n = change in number of moles of products and reactants (more details in SI). At 298 K ∆Ggas→soln equals 1.89 kcal/mol if ∆n = 1. Since the SMD model is known to achieve lower mean unsigned errors in calculation of solvation free energies of tested neutrals and ions,24 the aqueous phase free energies using SMD methods are reported here (Table 2) and the same obtained using CPCM method (Table S1) are included in the SI. The small Fe(III) complexes with more than one Fe centers reported here are generally lowspin, while high-spin cases were also studied. In principle, for multinuclear Fe clusters, there may be many structures with differing spin-states, but we study generally the lowest spinstate (singlet for all clusters with even numbered Fe atoms, and sextet (Ms=6) for clusters with odd numbered Fe atom clusters) along with the spin-states where all spins are parallel. For Fe(III) clusters consisting of more than five atoms, the low-spin structures were very difficult to optimize due to convergence issues. For the Fe7 cluster, two different high-spin states (all seven spins parallel, Ms=36, and only five spins parallel, Ms=26) and for Fe13 cluster, two high-spin states (all thirteen spins parallel, Ms=66, and only nine spins parallel, Ms=46) could only be stabilized. The important changes in structural parameters for small clusters like dimer through pentamer with the high- and low-spin magnetic states are that, the low-spin structures are more compact and Fe-Fe and Fe-O bond-distances are shorter but overall structures remain mostly unaffected by the magnetic states of the clusters (structural 6 ACS Paragon Plus Environment

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comparison for dimers, trimers, pentamers, heptamers and Keggin ion in different spin-states are given in SI). The formation of a new mineral phase from solution is a dynamic process, sometimes with bacterial intervention, which is beyond the scope of this study. On the contrary, present work looks into the detailed structural parameters, reaction free energies and enthalpies of small, isolated Fe(III) oxy-hydroxide clusters in equilibrium state and compares them structurally with bulk mineral phases of ferrihydrite.

Results & Discussions Ferrihydrite & Iron Oxyhydroxide Clusters

In order to study the formation of nanocrystalline ferrihydrite, through small pre-nucleation clusters it is necessary to start with the proposed crystal structure of mineral ferrihydrite. 28,29 A detailed DFT study by Pinney et al had compared the thermodynamical stabilities of bulk ferrihydrite with respect to other bulk iron oxyhydroxide polymorphs.30 The bulk model used in this study shows that in its ideal, defect-free bulk form, ferrihydrite has a hexagonal unit cell comprising of two types of octahedrally coordinated iron atoms referred to as Fe1 and Fe2 (see Figure 1). There are tetrahedrally coordinated iron atoms too in the unit cell referred to as Fe3. The edge-sharing Fe-octahedra forming layers consisting exclusively of same type of iron atoms Fe1, resemble the structure of brucite-type hydroxides M(OH)2 (with M = Mg, Ca, Mn, Fe, Co, Ni, Zn or Cd) which are model layered hydroxides. In the brucite structure the layers are well-separated but in ferrihydrite the interlayer space is occupied by iron tetrahedra (comprised of Fe3 atoms) and a rotated Fe octahedra comprised of Fe2 atoms.30 Figure 1 shows the relationship between the brucite structure with ferrihydrite, which becomes clear when the top views are compared. In ferrihydrite, these layers are separated by a mixed layer of octahedrally and tetrahedrally coordinated Fe(III) atoms (Fe2 & Fe3 respectively)30 , which



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Figure 1. a) Crystal structure of Brucite, Mg(OH)2, Mg atoms are green balls and O atoms are red balls and H atoms are not shown. b) Crystal structure of Ferrihydrite.29 The top view of the first layer marked by the box. The iron atoms 30marked by arrows are to be identified with Fe1, Fe2 and Fe3 respectively from the top (by Pinney et al ) . The small clusters which are identified in the ferrihydrite stucture. c) trimer-T, Fe3O(OH)3(H2O)94+ d) Heptamer-H, Fe7O(OH)12(H2O)127+, e) δ-Keggin cluster Kδ , FeO4(Fe(OH)2(H2O))127+. Iron atoms are represented by brown/drak red balls and Oxygen atoms are bright red balls. Hydrogen atoms are small bluish white balls.

are marked by arrows in Figure 1. The theoretically calculated bond-distances30 of bulk ferrihydrite are Fe3O(tetrahedral): 1.91-1.92A, Fe2O (octahedral): 1.95-2.20A and Fe1O (octahedral): 1.98-2.07A which have small discrepancies with experimentally obtained parameters depending on crystallinity. The pre-nucleation clusters of ferrihydrite formation may be identified as meta-stable phases, which are thermodynamically stable but highly dynamic entities and may have encoded structural motifs resembling corresponding crystalline counterpart.5 Thus to look for stable pre-nucleation clusters of ferrihydrite formation, it is extremely important to study the


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formation energies and free energies of all possible stable dimeric, trimeric, tetrameric and larger oligomeric Fe(III) oxyhydroxide clusters and find the signatures of bulk ferrihydrite in them. Herein, we study the formation of small Fe(III) oxyhydroxide clusters Fe2 through Fe13, gradually increasing in size, employing an atom-by-atom 'bottom-up' approach. Previous experimental evidences have shown that, solvated Fe(III) ion undergoes hydrolysis with subsequent formation of low-molecular-weight cationic species such as hydrated and hydrolyzed dimers,9-12,15,16 trimers31,32 and other small oligomers33 releasing protons in solution. The solution of Fe(III) in water readily becomes acidic, due to the release of protons, as observed experimentally. Fe oxyhydroxide particles may then nucleate from the polynuclear species and grow via 'atom-by-atom addition' or 'oriented aggregation'.4 The resultant Fe oxyhydroxide phases formed depend on the anion type and pH of the solution and the impact of anions in phase organization originates from their Fe(III) binding ability. A review article by J-P. Jolivet et al looked into the iron oxide chemistry, via formation of molecular clusters in finer details.32 It was mentioned that Fe(III) complexes condense very rapidly due to high reactivity32 and it is difficult to stop the process at molecular level, though few polycationic species with strongly complexing polydentate ligands33-36 were isolated. Present study successfully identifies various smaller molecular clusters of Fe(III) oxyhydoxide, shown in the following sections, some of which have similar structures as that of bulk ferrihydrite and these smaller clusters can be formed spontaneously as indicated by their gas-phase formation enthalpies. The trimeric T and heptameric H structures (see Figure 1), to be discussed in the later sections, could easily be identified in the bulk Ferrihydrite structure besides the δ-Keggin (Kδ) structure as proposed by others.37,38 In aqueous medium (using SMD/CPCM model within DFT), the reaction free energies calculated are higher, but for larger Fe(III) oxyhydroxide clusters the reactions are found to be spontaneous.



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Fe2 , Fe3 & Fe4 Oxyhydroxide Clusters Iron oxyhydroxides are generally obtained as a precipitate from the aqueous solution of Fe(III) salts and consist of both FeO and FeOH linkages systematically arranged in octahedral networks in which each iron atom is surrounded by six oxygen atoms. It is well known that Fe3+ ions in water remain as octahedral, hexahydrated complex Fe(H2O)63+ (M in Figure 2a), and consequently two molecules of Fe(H2O)63+ may dimerize to form the small oxyhydroxide clusters, Fe2(H2O)6(OH)42+ (D1, D2 shown in Figure 2b), with two hydroxy/aqua bridge bonds between two Fe atoms or Fe2(H2O)6(OH)24+(D3 shown in Figure 2b) with two hydroxy bridge bonds between two Fe atoms. The dimeric oxyhydroxide structures are flexible with hydroxy (OH) or aqua (H2O) bridges between the Fe atoms and the ligands connected to the Fe-atoms may also be hydroxo or water depending of the pH of the solution. Our results show that the complex with two aqua bridge bonds (Figure 2b, D2) is energetically less stable compared to the complex with two hydroxy bridge bonds (Figure 2b, D1) even if their chemical formulae are identical.39,40 The modelling of various possible dimeric Fe(III) oxyhydroxide clusters (D1, D2 and D3, Figure 2b) shows that both hydroxo and aqua bridged dimers can be formed spontaneously in gas phase, showing negative values of reaction free energies (Table 1). In the dimeric oxyhydroxide D1, there are two -OH bridges between the two central Fe atoms, Fe-Fe distance is 2.90 A and Fe-O (-OH bridge) distance is 1.86 A, whereas other Fe-O (ligand H2O) distances range from 2.01-2.04 A. Structurally it is seen that the dimers D1, D2 and D3 with varying number of water molecules only differ in certain structural parameters (D2: Fe-Fe: 3.18 A, Fe-O(-H2O bridge): 2.05 A, Fe-O (ligand H2O) : 1.97 A; D3: Fe-Fe: 2.98 A, Fe-O (-OH bridge): 1.87 A, Fe-O (ligand


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Figure 2. Optimized structure of a) hexaaqua-Fe(III) ion M, b) the Fe(III) oxyhydroxide dimers D1,D2 and D3 c) the cyclic Fe(III) oxyhydroxide trimer T , the top view (top) and the side view (bottom), d) the linear Fe(III) oxyhydroxide trimer L. Large dark red balls represent Fe(III), smaller red balls represent Oxygen and smallest white balls represent Hydrogen atoms.

H2O): 1.97 A). hydroxo

bridge

We have also studied two dimeric clusters with single oxo and bonds

between

two

Fe

atoms

(Fe2O(H2O)104+,

D4

and

Fe2OH(H2O)105+, D5), following previous molecular dynamics studies16 but found their formation unfavourable in gaseous phase (Table 1, D4, D5). The molecular dynamics studies15,16 which look into aqueous Fe(III) systems report other dimeric clusters along with monomers, but the structures reported are dynamic, over coordinated and unstable which are absent experimentally. Though formation of dimers had been discussed in literature,

9-16

only one later quantum mechanical study38

looked into higher order polynuclear species like Keggin cluster, likely to form



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spontaneously when excess of Fe(III) is present in aqueous medium. We find that it is possible to spontaneously form the trimeric Fe(III) cluster Fe3O(OH)3(H2O)94+, T (see Figure 2c) as the reaction enthalpy is highly exothermic and free energy negative (∆H -147.9 kcal, ∆Ggas -169.2 kcal/mol, Table 1). On the other hand the formation of a linear trimeric cluster, Fe3(OH)4(H2O)105+, L (see Figure 2d) is not favoured with positive values for formation enthalpy and free energy in gas phase (∆H: 36.4 kcal,

∆Ggas 24.7 kcal, Table 1). The trimeric Fe(III) core of T (Figure 2c) has C3 symmetry and Fe-Fe distances range from 2.90-2.92 A. The central O atom is bound to three Fe atoms and the Fe-O distances are 1.89-1.92 A. The Fe-O (bridge) bonds are 1.881.90A. All the Fe-O distances from co-ordinated water molecules range from 1.952.15 A. The trimeric complex T that we found has been studied in literature in connection with iron containing biological systems.41 The trimeric T unit with all octahedrally connected Fe atoms, can be also readily identified from the ferrihydrite structure (see Figure 1c).

It is not surprising that the cyclic cluster, Fe3O(OH)3

(H2O)94+ may interact with another Fe(III) monomer to give a tetrameric Fe4O2(OH)4(H2O)104+, TT1 ion (shown in Figure 3a) and the formation enthalpy is negative (-60.1 kcal, Table 1), indicating the process to be generally spontaneous in gaseous state. The TT1 complex possesses inversion symmetry (see Figure 3a) and it can readily be identified as a portion of a brucite [Mg(OH)2] like layer in three dimensions. The important bond-distances of Fe4O2(OH)4(H2O)104+ complex are Fe-O: 1.87A, Fe-O(-OH bridge ):1.93A, Fe-O(H2O): 2.02A, Fe(OH)-Fe(O): 2.93A, Fe(O)Fe(O): 2.84A. Another tetrameric Fe(III) oxyhydroxide, Fe4(OH)8(H2O)84+ (TT2, shown in Figure 3b), which has a cubic structure, may also be formed from two dimeric Fe2(OH)4(H2O)62+ (D1) complexes interacting in orthogonal fashion and the formation enthalpy is highly positive (283.9 kcal, Table 1) indicating that it is a non12 ACS Paragon Plus Environment

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spontaneous reaction in gas phase. The cluster TT2 is however, stable and the important bond-distances are; Fe-O(H): 1.96 A, Fe-O(H2O): 2.00 A but there are short Fe-Fe distances (2.97 A) where two bridging -OH ligands and two co-ordinated -OH ligands are involved, which form a intra-molecular hydrogen bond, and a longer Fe-Fe distance 3.12 A where only the bridging -OH ligands are present.

Fe5 , Fe7 & Fe13 Oxyhydroxide Clusters This section discusses about Fe(III) oxyhydroxide clusters in high-spin states which are bigger than tetrameric clusters though the details of few lower-spin clusters have been included in the SI. The trimeric cluster T, Fe3O(OH)3(H2O)94+, may fuse with another dimer and form an oxyhydroxide consisting of five Fe(III) atoms to form P, Fe5O3(OH)5(H2O)114+, (Figure 3c) or an even larger cluster Fe7O6(OH)6(H2O)123+, H1 (Figure 3d) consisting of seven Fe atoms. So we looked into the condensation reaction in gas phase (with D1) showing the possibility of formation of small brucite layer like structure. Results indicate that, though it is possible to form small layer like structures, P or H1 by introducing more Fe atoms, there is a gradual fall in formation enthalpy (compared to P) in gas phase as given in Table 1. In the low-spin cluster P, Fe5O3(OH)5(H2O)114+ (Figure 3c), the Fe-Fe distances vary from 2.84-2.88A and the Fe-O distances are 1.86 A and Fe-O(H) distances are 1.94 A and Fe-O(H2O) distances are 2.15 A (Figure 3c). Formation of a similar cluster had already been discussed by J. Rose et al which indicated the presence of trimers, formed by double corner sharing of a third Fe octahedron with a dimer, as a minor species along with a Fe5 cluster, from partially hydrolyzed acidic ferric nitrate solutions through their local structure analysis by using X-ray absorption spectroscopy.31



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Figure 3. Optimized structure of Fe(III) oxyhydroxide clusters. a) tetramers of Fe(III) oxyhydroxide TT1 (top & side views shown) b) tetrameric Fe(III) oxyhydroxide TT2 (two views shown) c) Pentameric Fe(III) oxyhydroxide P (top & side views shown) , d) heptameric Fe(III) oxyhydroxide cluster H1 (top & side views shown) , e) heptameric Fe(III) oxyhydroxide cluster H (top & side views shown. Large dark red balls represent Fe(III), smaller red balls represent Oxygen and smallest white balls represent hydrogen atoms f) Fe13 Keggin ion (right) is shown with marked T (left) and H (middle) units in different colour.

Though there is a possibility of formation of small layer like Fe(III) oxyhydroxide structures, such as P or H1, the transformation of layered structure to particle-like ferrihydrite structure can only be brought about by introducing Fe(III) tetrahedra or rotated (out of brucite plane) Fe(III) octahedra into the network. These two aspects actually drive the structure away from layered structure, in spite of the presence of the basic trimeric unit mimicking the brucite lattice (see Figure 1). This was earlier shown for Aluminum Keggin cluster which consists of a central tetrahedral Al(OH)4- unit.42 So it is important to strategically include the tetrahedral Fe atoms into Fe(III) oxyhydroxide clusters, and indeed in case of the heptameric Fe(III) cluster H,


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Fe7O(OH)12(H2O)127+ (see Figure 3e) with one central tetrahedral Fe(III) connected to one trimeric T unit at the top and surrounded by three six co-ordinated octahedral Fe(III) atoms, the layer structure is successfully converted into a hemispherical structure. H is indeed found to be a stable cluster, can be readily identified as fragment of Fe13 δ-Keggin ion (shown using different colors in Figure 3f) and the enthalpy of formation from the trimeric Fe3O(OH)3(H2O)94+ unit is highly negative in gas phase (∆H

-84.5

kcal)

indicating

its

spontaneous

formation.

The

cluster

Fe7O(OH)12(H2O)127+ has a C3v symmetry with one tetrahedral Fe(III) positioned along the C3 axis. The novel cluster H, may be considered as an essential

unit

of

ferrihydrite consisting of all three types of Fe environments as discussed by Pinney et

al30 and is shown in Figure 1d. The central Fe-O bond passing through the C3 axis is shortest, 1.88 A, but the other Fe-O bonds in the trimeric unit are 2.10 A. The Fe-Fe distances in the central trimeric fragment is 3.12 A, with other longer Fe-Fe distances (3.70 A) which is observed with only one direct bridge bond. The Fe(tetrahedral)Fe(Octahedral) distance is somewhat shorter ~3.5 A. The formation enthalpy of Fe7O(OH)12(H2O)127+ (H) may readily be compared with the formation enthalpy of Fe7O6(OH)6(H2O)123+ (H1) with layer structure and it is seen that the hemispherical cluster H is more likely to be formed (Table 1). The recent laboratory synthesis of the iron oxo-keggin ion cluster had conclusively shown that it is possible to form bigger Fe(III) oxyhydroxide cluster (Fe13) with both hydroxo bonds connected to Fe(III) atoms using suitable bulky counterions.43 Keggin ions (based on P, Si, S, Ge, As, Co) have been isolated possessing the general formula [XM12O40]n−, where X is a heteroatom connected to four O atoms in a tetrahedral fashion.44 The Fe13 δ-Keggin cluster is understood to be the building unit of ferrihydrite crystal in a cross-linked and fused fashion.37 The X-ray structure of the iconic



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Figure 4. Schematic representation of the δ-Keggin Fe13 cluster is shown, by gradually incorporating trimeric cluster T along each Fe-O direction of the central tetrahedral Fe(III) for better understanding of the structure in three dimensions. Large dark red balls represent Fe(III), smaller red balls represent Oxygen and hydrogen atoms are not shown for better clarity.

Polyoxometalate-based Keggin compounds was first established in 1933, Keggin ion for ammonium phosphomolybdate ((NH4)3[PMo12O40]).45 Later, various other Keggin structures existing as α, β, γ, δ, and ε isomers, resulting from the 60° rotation of the four basic [M3O13] units were proposed, by Baker and Figgis.46,47 Figure 4 shows schematically the Fe13 δKeggin cluster formation with gradual incorporation of trimeric Fe3O(OH)3(H2O)94+ cluster, T to the Fe-O bonds of the central tetrahedral Fe(III), one by one which helps in the understanding of the complex structure in three dimensions (not to be confused with formation pathways). The central FeO4 unit of Kδ Keggin cluster is connected to four Fe3O(OH)3 units which are fused to each other by -OH- linkages. The present study explores all six isomers of Fe13 Keggin ion [FeO4(Fe(OH)2(H2O))12]7+ in high-spin states (Spin multiplicity, 2s+1=66, see Figure 5 for structures of all isomers). It is to be noted that this ion is positively charged due to the presence of -OH bridges instead of only oxo (FeO) linkages and neutral water molecules as co-ordinated ligands. We have also studied the Fe13 Keggin 16 ACS Paragon Plus Environment

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cluster with fluorine (F-) ions as ligands, [Fe13O4(OH)12F24]5- with overall charge of the cluster being -5. The comparison of energies of all isomers of Fe13 Keggin ion shows that the ε-Fe13 Keggin ion is the most stable one with the δ-Fe13 Keggin cluster (Kδ) coming a close next (energy difference 6 kcal) and the α, β and γ isomers are 14-15 kcal less stable than ε isomer in gas

Figure 5. Optimized structures for high-spin Fe13 Keggin clusters, all isomers are shown. The δ-Keggin isomer is also shown rotated, for better understanding as it is thought to be the essential nucleation cluster of Ferrihydrite. Large dark red balls represent Fe(III), smaller red balls represent Oxygen and smallest white balls represent hydrogen atoms.



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∆Hg (kcal)

∆ Gg (kcal)

-213.2 (Ms=1) -300.7 (Ms=11) -170.0(Ms=1)*

-216.7 (Ms=1) -255.4 (Ms=11) -172.9(Ms=1)*

2Fe(H2O)63+→ Fe2(H2O)8(OH)24+(D3) + 2H3O+

70.2 (Ms=1) -30.1 (Ms=11)

65.9 (Ms=1) -40.7 (Ms=11)

4

2Fe(H2O)63+ + 2H2O → Fe2O(H2O)104+(D4) + H2O+ 2H3O+

20.3 (Ms=1) -72.6 (Ms=11)

26.2 (Ms=1) -74.8 (Ms=11)

5

2Fe(H2O)63+ → Fe2OH(H2O)105+(D5) + H3O+

309.2 (Ms=1) 191.8 (Ms=11)

315.5 (Ms=1) 192.5 (Ms=11)

6

3Fe(H2O)63+ → Fe3O(OH)3(H2O)94+ (T) + 5H3O+

7

3Fe(H2O)63+ → Fe3(OH)4(H2O)105+(L) + 4H3O+

8

Fe3O(OH)3(H2O)94++Fe(H2O)63+→ Fe4O2(OH)4(H2O)104+ (TT1) + 3H3O+

-147.9 (Ms=6) -211.4 (Ms=16) 36.4 (Ms=6) -32.9 (Ms=16) -60.1 (Ms=1) -164.2 (Ms=21)

-169.2 (Ms=6) -239.6 (Ms=11) 24.7 (Ms=6) -50.8 (Ms=16) -72.8 (Ms=1) -182.4 (Ms=21)

9

2Fe2(H2O)6(OH)42+ → Fe4(OH)8(H2O)84+ (TT2) + 4H2O

10

Fe3O(OH)3(H2O)94+ + Fe2(H2O)6(OH)42+→ Fe5O3(OH)5(H2O)114+ (P)+ 2H3O++ 2H2O Fe3O(OH)3(H2O)94++2Fe2(H2O)6(OH)42+→ Fe7O6(OH)6(H2O)123+ (H1) + 5H3O+ + 4H2O Fe3O(OH)3(H2O)94+ + 4Fe(H2O)63+ + 9H2O → Fe7O(OH)12(H2O)127+ (H) + 9H3O+ + 12H2O 4Fe3O(OH)3(H2O)94++Fe(H2O)63+→ [FeO4(Fe(OH)2(H2O))12]7+ (Kδ) + 12H3O+ + 6H2O

Reaction enthalpies and free energies in gas phase 2Fe(H2O)63++ 2H2O → Fe2(OH)4(H2O)62+(D1) + 4H3O+ 1 2Fe(H2O)63+ + 2H2O → Fe2(H2O)6(OH)42+(D2) + 4H3O+ 2 3

11

12 13

283.9 (Ms=1)

258.0 (Ms=1)

-63.9 (Ms=26)

-131.1 (Ms=26)

-46.8 (Ms=36)

-102.7 (Ms=36)

-84.5 (Ms=36)

-247.3 (Ms=36)

-199.4 (Ms=66)

-314.1 (Ms=66)

Table 1. The formation of various Fe(III) oxyhydroxide clusters in gaseous phase. The reaction enthalpies and free energies are shown in gaseous phase. Corresponding spin-states of the clusters are mentioned by Ms values in the parentheses. *No high-spin state.

phase (all energy differences correspond to for Ms=66 state of the isomers). In case of various Keggin clusters the bond-distances do not vary much. The size of the δ-Fe13 cluster is ~ 11 A in diameter (with co-ordinated water molecules, without water molecules ~7.5 A for Ms=66 state) and the closest Fe-Fe distances calculated are 2.98-3.05 A (identical to dimeric cluster as in Fe2(OH)2(H2O)8]4+). The Fe-O distances in the central FeO4 unit are 1.88-1.90 A whereas Fe-O distances in case outer FeO6 octahedra are 2.00-2.12 A. The Fe-O(H) distances range from 1.90-1.98 and the Fe-O(H2O) distances are 2.12-2.20 A which are all in the periphery of the cluster. There are another set of longer non-bonded Fe-Fe distances found between the central tetrahedral Fe atom with the peripheral octahedral Fe atoms, which are 18 ACS Paragon Plus Environment

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3.5-3.6 A. The structures of Fe(III) oxyhydroxide clusters, P, H, and Kδ in other spin-states are provided in the SI and it is observed that the low-spin structures are more compact, showing shorter Fe-Fe distances.

A previous report38 about Fe(III) oxyhydroxide

nanoparticles earlier studied the Keggin cluster (Kδ) in high-spin state theoretically using a smaller basis-set and found similar structure. Present study emphasizes the formation of the Kδ structure, as it is directly related to ferrihydrite mineral with Fe(III) atoms present in two different octahedral and one tetrahedral environments.30 The formation enthalpy of Kδ ion from the stable trimeric T, Fe3O(OH)3(H2O)94+ cluster is highly exothermic and spontaneous in gaseous phase (∆H 199.4 kcal, ∆Ggas -314.1 kcal, Table 1 ) indicating rapid formation.

Formation of Fe(III) Oxyhydroxide Clusters in Water

It is well known that the formation of Fe(III) oxyhydroxides in water is always associated with release of protons, and the process starts with the spontaneous hydrolysis of Fe(H2O)63+ ion in water. So we first studied the free energies of hydrolysis of Fe(H2O)63+, stepwise in aqueous medium (SMD, CPCM model) using gas-phase optimized structures and obtained correct trends known experimentally.1,8 Then using the same theoretical approach, aqueous phase free energies (∆Gs) are calculated, for all gas phase reactions discussed in the previous section from the respective solvation free energies.24-26 While studying various steps of the Fe(III) hydrolysis we find that, Fe(H2O)63+ and the first hydrolysis product, Fe(H2O)5(OH)2+ are more stable in Ms=6 state, while less stable Ms=4 states were also studied. For the hydrolysis product obtained in the step two, Fe(H2O)4(OH)2+, there may be cis trans isomerism along with sextet (Ms=6) and quartet (Ms=4) spin states, giving rise to four structures very close in energies. The hydrolysis 19 ACS Paragon Plus Environment


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product after step three, Fe(H2O)2(OH)3 , is more stable in sextet state while Fe(OH)4- may exist as sextet and quartet states as gas-phase energies are similar (energies of all structures are reported in SI, Tables S2-S3). The free energies calculated for different steps of Fe(III) hydrolysis reactions in water are given below. In the following reactions, corrections for standard states made are ∆Ggas→soln and the activity of water was taken in ideal solution limit i.e. 55.5 mol L-1 (SI); Fe(H2O)63+ + H2O → Fe(H2O)5(OH)2+ + H3O+, ∆Gs= 4.26 kcal/mol Fe(H2O)5(OH) 2+ + H2O → Fe(H2O)4(OH)2+ + H3O+, ∆Gs= 20.72 kcal/mol Fe(H2O)4(OH)2 + → Fe(H2O)2(OH)3 + H3O+, ∆Gs= 20.34 kcal/mol Fe(H2O)2(OH)3 → Fe(OH)4- + H3O+, ∆Gs= 24.10 kcal/mol These free energy values may be compared with the experimental values of 3, 7.8, 18.5 and 21.5 kcal/mol for four steps respectively as reported in literature.

1,8

The discrepancies in the

hydrolysis constants are partly due to the inaccuracy in estimating solvation energy of H3O+ which is known to be very tricky25-27,48 along with errors arising due to gas-phase structures adopted. Especially in the second step of hydrolysis all four conformers contribute as the gasphase energies are comparable and the predicted free energies are much overestimated compared to the experimental value because in this case conformational entropy term not considered here may also be significant.27 The results from aqueous state studies show that the gas-phase reactions which have very large negative ∆Ggas values are less spontaneous in water and (∆Gs) values are positive. The free energies calculated in aqueous medium are given in Table 2, where it is generally seen that for high-spin states the reaction free energies are smaller. The reaction free energies


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Sl. No.

Reactions in aqueous medium using SMD method (all aqueous phase free energies calculated from Gsolv)

∆Gs in aqueous medium (kcal)

1

2Fe(H2O)63++ 2H2 O → Fe2(OH)4(H2O)62+(D1)+ 4H3O+

142.28 (Ms=1) 41.92 (Ms=11)

2

2Fe(H2O)63+ + 2H2O → Fe2(H2O)6(OH)42+(D2)+ 4H3O+

173.42 (Ms=1)*

3

2Fe(H2O)63+ → Fe2(H2O)8(OH)24+(D3) + 2H3O+

121.44 (Ms=1) 11.0 (Ms=11)

4

2Fe(H2O)63+ + 2H2O → Fe2O(H2O)104+(D4) + H2O + 2H3O+

110.26 (Ms=1) 26.22 (Ms=11)

5

2Fe(H2O)63+ → Fe2OH(H2O)105+(D5) + H3O+

124.7 (Ms=1) 19.88 (Ms=11)

6

Fe2(H2O)8(OH)24+(D3)+ Fe(H2O)6 3+ → Fe3O(OH)3(H2O)94+(T)+ 3H3O+

23.35 (Ms=6) 22.0 (Ms=16)

7

3Fe(H2O)63+ → Fe3(OH)4(H2O)105+(L) + 4H3O+

8

Fe3O(OH)3(H2O)94++ Fe(H2O)63+→ Fe4O2(OH)4(H2O)104+(TT1)+ 3H3O+

100.26 (Ms=6) 31.66 (Ms=16) 135.8(Ms=1) -42.3 (Ms=21)

9

Fe3O(OH)3(H2O)94+ + Fe2(H2O)8(OH)24+→ Fe5O3(OH)5(H2O)114+ (P) + 4H3O+

-25.70 (Ms=6) 47.67 (Ms=26)

10

Fe3O(OH)3(H2O)94++ 2Fe2(H2O)8(OH)24+→ Fe7O6(OH)6(H2O)123+ (H1) + 9H3O+

115.56 (Ms=36)

11

Fe3O(OH)3(H2O)94+ + 4Fe(H2O)6 3+ → Fe7O(OH)12(H2O)127+(H)+ 9H3O+ + 3H2O

-8.5 (Ms=36)

12

4Fe3O(OH)3(H2O)94+ + Fe(H2O)63+ → [FeO4(Fe(OH)2(H2O))12]7+ (Kδ) + 12H3O+ + 6H2O

-176.95 (Ms=66)

Table 2. The formation of Fe(III) oxyhydroxide clusters in water using SMD model. The reaction free energies are calculated form solvation free energies and corrected for standard states (ideal gas-phase concentration of 1 mol/L dissolving as an ideal solution at concentration of 1 mol/L, details in SI) are reported in water for spin-states mentioned in the parantheses.* No high-spin state. obtained using CPCM model are given in Table S1 in the SI, where similar trends are found. The free energy of formation of the hydroxo bridged Fe(III) oxyhydroxide dimer D3 is 11 kcal/mol and the free energy of formation of trimeric cluster T in aqueous medium is 22 kcal/mol (see Table 2). The formation of the linear trimer (L) and heptamer H1 in water are inhibited due to larger values of reaction free energies compared to the clusters in the gaseous phases, whereas tetramer TT1, pentamer P show negative free energies in aqueous medium (42.3 and -25.7 kcal/mol respectively, Table 2). The results show that, in water the free 21 ACS Paragon Plus Environment


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energy of formation for the heptamer H from trimer T is -8.52 kcal/mol and the same for the Keggin cluster, Kδ is -176.95 kcal/mol indicating their spontaneous formation in aqueous medium. Table 2 shows the formation of the larger clusters, like P, H, Kδ from the trimer T , because the trimeric unit is easily relatable to the Ferrihydrite structure. The Keggin cluster (Kδ) may also be formed via other pathways involving different starting clusters listed in Table 3. It is possible to form the Keggin cluster from only the monomer Fe(H2O)63+ or dimer D3, likewise, it also is possible to form the Keggin cluster from H reacting with either cluster D3 or T as shown in Table 3. In all these reactions the starting reactant is Fe(H2O)63+ which first forms D3, T or H clusters, which then act as stable intermediate clusters giving rise to Kδ as the final product. Formation of Kδ from Fe(OH)-4, proposed earlier in case of Al13 Keggin cluster,42 could also be imagined as an alternative favorable pathway (shown in Table 3), though formation of Fe(OH)-4 (hydrolysis end-product of Fe(H2O)63+) is not likely in water. It is important to note that the formation of Kδ directly from the monomer/dimer have very high positive free energies, showing the processes as highly improbable and the formation becomes favorable when larger clusters associate to form the Keggin cluster. The trend in Table 3 clearly establishes that the reactions involving the association of larger clusters are more favorable, indicating their highly reactive, spontaneous association in water as observed experimentally. The modelling of the plausible pathways presented here must be considered with caution as there are numerous stable species involved and also various isomers of Keggin clusters may complicate the pathways further. Additionally, it is an oversimplification to examine only the thermodynamics of an isolated reaction in aqueous medium, many other competing reactions may occur and the real situation is more complex than it has been presented here.


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Sl. No.

Reactions in aqueous medium using SMD method (all aqueous phase free energies calculated from Gsolv)

∆Gs in aqueous medium (kcal)

1.

13Fe(H2O)63+ →[FeO4(Fe(OH)2(H2O))12]7+ (Kδ) + 32H3O++ 6H2O

245.5

2.

6 Fe2(H2O)8(OH)24+ (D3) + Fe(H2O)63+ → [FeO4(Fe(OH)2(H2O))12]7+ (Kδ) + 20H3O+ + 6H2O Fe7O(OH)12(H2O)127+(H) + 3Fe2(H2O)8(OH)24+ (D3)→ [FeO4(Fe(OH)2(H2O))12]7+ (Kδ) + 12H3O+ + 3H2O Fe7O(OH)12(H2O)127+(H) + 2 Fe3O(OH)3(H2O)94+(T) → [FeO4(Fe(OH)2(H2O))12]7+ (Kδ) + 8H3O+ + 3H2O Fe(OH)4 - + 4 Fe3O(OH)3(H2O)94+ → [FeO4(Fe(OH)2(H2O))12]7+ (Kδ) + 8H3O+ + 8H2O

173.6

3. 4. 5.

-215.8 -62.8 -245.7

Table 3. The formation of Keggin cluster Kδ in water is shown using various pathways (SMD model). The reaction free energies are calculated form solvation free energies and corrected for standard states (ideal gas-phase concentration of 1 mol/L dissolving as an ideal solution at concentration of 1 mol/L, details in SI) .

Conclusion

The present study theoretically investigated the formation of small Fe(III) oxyhydroxide clusters starting from a single hydrated ion, stepwise modelling the formation of larger clusters gradually. The reaction free energies for the Fe2, Fe3, Fe5, Fe7 and Fe13-Keggin oxyhydroxide clusters in gas phase and in aqueous medium using SCRF model are calculated and their structural relationships with Ferrihydrite are established. Various probable pathways for the formation of the Keggin cluster, the potential nucleation cluster of Ferrihydrite are suggested from the dimeric, trimeric and heptameric oxyhydroxide clusters.

The stable

oxyhydroxides studied here may actually act as pre-nucleation clusters themselves or may further aggregate to form bigger clusters for the formation of the mineral phase Ferrihydrite. That Fe(III) oxyhydroxides consist of both iron-oxo, iron-hydroxo and sometimes aqua linkages too arranged in octahedral networks, it is imperative that the structure of these clusters might change slightly depending on the pH of the surrounding medium and the number of co-ordinated water molecules may vary depending on the environment. The



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widely reported nominal formula of ferrihydrite, is thought to be excessively hydrous, and it has been demonstrated that almost all of the water molecules can be replaced by adsorbed species, which explains partly the difficulty in the determination of exact crystal structure of ferrihydrite formed naturally.2 In the form of nanoparticles with an excess of specific surface area, iron oxyhydroxides are interesting from a technological point of view as adsorbents for large amounts of contaminant ions in water remediation and chemical industries. Since ferrihydrite is a very important natural scavenger, once we know the small stable molecular clusters which exist in hydrated Fe(III) environment, we can explore how these clusters may react with other hydrated contaminant ions like arsenic, lead or antimony 'in-situ' to give other minerals and use them for contaminant fixation. Supporting Information

Details of theoretical methodologies, all optimized structures, energies, enthalpies, free energies (B3LYP/6-31G** & B3PW91/6-31G**) of the Fe(III) oxyhydroxide clusters in various spin-states are provided. Details of solvation energies using CPCM method are also given.

Acknowledgements

This work acknowledges the useful inputs from discussions with Professor A. Paul and Professor S. Ray of IACS, Kolkata. The athour acknowledges funding from DST, Government of India, through fellowship from TRC project. The author also acknowledges DST project no. DST/TM/WTI/2K15/74 (G) for additional computational support.

References [1] Flynn, C. M.; Hydrolysis of Inorganic Iron(III) Salts. Chem. Rev., 1984, 84, 31-41. [2] Jambor, J. L.; Dutrizac, J. E.; Occurrence and Constitution of Natural and Synthetic Ferrihydrite, a Widespread Iron Oxyhydroxide. Chem. Rev., 1998, 98, 2549-2586.


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[3] Navrotsky, A.; Mazeina, L.; Majzlan, J.; Size-driven Structural and Thermodynamic Complexity in Iron Oxides. Science, 2008, 319, 1635-1638. [4] Banfield, J. F.; Welch, S. A.; Zhang, H.; Ebert, T. T. ; Penn, R. L.; Aggregation-based Crystal Growth and Microstructure Development in Natural Iron Oxyhydroxide Biomineralization Products. Science, 2000, 289, 751-754. [5] Gebauer, D.; Kellermeier, M.; Gale, J. D.; Bergstrom, L.; Colfen, H.; Pre-nucleation Clusters as Solute Precursors in Crystallisation. Chem. Soc. Rev., 2014, 43, 2348-2371. [6] Weatherill, J. S.; Morris, K.; Bots, P.; Stawski, T. M.; Janssen, A.; Abrahamsen, L.; Blackham, R.; Shaw, S.; Ferrihydrite Formation: The Role of Fe13 Keggin Cluster. Environ. Sci. Technol., 2016, 50, 9333-9342. [7] Scheck, J.; Wu, B.; Drechsler, M.; Rosenberg, R.; Van Driessche, A. E. S.; Stawski, T. M.; Gebauer, D.; The Molecular Mechanism of Iron(III) Oxide Nucleation. J. Phys. Chem. Lett., 2016, 7, 31233130. [8] Ohlin, C. A.; Villa, E. M.; Rustad, J. R.; Casey, W. H.; Dissolution of Insulating Oxide Materials at the Molecular Scale. Nature Materials, 2010, 9, 11-19. [9] De Abreu, H. A.; Guimaraes, L.; Duarte, H. A. ; Density-Functional Theory Study of Iron(III) Hydrolysis in Aqueous Solution. J. Phys. Chem. A, 2006, 110, 7713-7718. [10] Farrell, J.; Chowdhury, ; Understanding Arsenate Reaction Kinetics with Ferric Hydroxides. J. Environ. Sci. Technol.,2013, 47, 8342-8347. [11] Zhang , N.; Bowlers , P.; Farrell, J.; Evaluation of Density Functional Theory Methods for Studying Chemisorption of Arsenite on Ferric Hydroxides. J. Environ. Sci. Technol., 2005, 39, 4816-4822. [12] Li, X. F.; Liu, Y.; First-principles Study of Ge Isotope Fractionation During Adsorption onto Fe(III)Oxyhydroxide Surfaces. Chemical Geology, 2010, 278, 15-22. [13] Zhu, M.; Legg, B.; Zhang, H.; Gilbert, B.; Ren, ; Banfield, J. F. ; Waychunas, G. A.; Early Stage Formation of Iron Oxyhydroxides during Neutralization of Simulated Acid Mine Drainage Solutions. J. Environ. Sci. & Technol., 2012, 46, 8140-8147. [14] Zhu, M.; Puls, B. W.; Frandsen, C.; Kubicki, J. D.; Zhang, H.; Waychunas, G. A.; In Situ Structural Characterization of Ferric Iron Dimers in Aqueous Solutions: Identification of μ-Oxo Species. Inorg. Chem., 2013, 52, 6788-6797. [15] Guardia, E.; Padro, J. A.; Molecular Dynamics Simulation of Ferrous and Ferric Ions in Water. Chem. Phys., 1990, 144, 353-362. [16] Zhang, H. ; Waychunas, G. A.; Banfield, J. F.; Molecular Dynamics Simulation Study of the Early Stages of Nucleation of Iron Oxyhydroxide Nanoparticles in Aqueous Solutions. J. Phys. Chem. B, 2015, 119, 10630-10642. [17] Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;Robb, M. A.; Cheeseman, J. R.; Scalmani, G. ; Barone, V.; Mennucci, B.; Petersson, G. A., et. al. Gaussian 09, Revision A.02, Gaussian Inc., Wallingford CT, 2009. [18] Becke, A. D.; Density-functional Exchange-energy Approximation With Correct Asymptotic Behavior. Phys. Rev. A,1988, 38 , 3098-3100. [19] Becke, A. D.; Density-functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys, 1993, 98, 5648-5652. [20] Lee, C.; Yang, W.; Parr, R. G. ; Development of the Colle-Salvetti Correlation-energy Formula into a Functional of the Electron Density. Phys. Rev. B, 1988, 37, 785-789. [21] Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M.R.; Singh, D.J.; Fiolhais, C.; Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Phys. Rev. B, 1992 , 46, 6671-6687. [22] Cossi, M.; Rega, N.; Scalmani, G.; Barone, V.; Energies, Structures, and Electronic Properties of Molecules in Solution with the C-PCM Solvation Model. J. Comp. Chem.,2003, 24, 669-681. 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Theoretical Study of Small Iron-Oxyhydroxide Clusters and Formation

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