Electron Exchange and Conduction in Nontronite from First

Article pubs.acs.org/JPCC

Electron Exchange and Conduction in Nontronite from FirstPrinciples Vitaly Alexandrov,*,† Anke Neumann,‡ Michelle M. Scherer,‡ and Kevin M. Rosso† †

Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States Civil and Environmental Engineering, University of Iowa, Iowa City, Iowa 52242, United States

‡

ABSTRACT: Fe-bearing clay minerals serve as an important source and sink for electrons in redox reactions in various subsurface geochemical environments. We apply first-principles calculations using a small polaron hopping approach and Marcus electron transfer theory to examine electron exchange mobilities in an Ferich smectite, nontronite Fe2Si4O10(OH)2. GGA+U calculations provide rates of electron hopping that agree very well with values deduced from variabletemperature Mössbauer data (Schaefer et al. Environ. Sci. Technol. 2011, 45, 540), indicating a surprisingly fast electron mobility at room temperature. Evaluation of the electron transfer (ET) rates within the Hartree−Fock cluster framework for the Fe2+/Fe3+ electron hopping in tetrahedral (TS) and octahedral sheets (OS), as well as across the sheets (TS−OS), shows that the dominant contribution to the bulk electronic conductivity should come from the ET within the OS. Deprotonation of structural OH groups mediating ET between the Fe ions in the OS is found to decrease the internal reorganization energy and to increase the electronic coupling, whereas protonation (to OH2 groups) has the opposite effect. Our calculations suggest that the major factors affecting ET rates are the nature and structure of the nearest-neighbor local environment and the degree of covalency of the bonds between Fe and ligands mediating electron hops. The generally higher reorganization energy and weaker electronic coupling found in Fe-bearing clay minerals lead to electron mobilities much lower than in iron oxides.

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INTRODUCTION Fe-bearing minerals are known to play an important role in biogeochemical cycling of various transition metals, organic matter, contaminants, and radionuclides in water, soils, and subsurface environments. A rapid reduction of iron oxide minerals by dissimilatory metal-reducing bacteria widespread in the natural environment has been previously demonstrated,1−4 and some studies suggested that microbes can also use iron minerals as natural sinks of electrons for efficient interspecies electron transfer.5 The change of oxidation state of structural Fe has a profound impact on physicochemical characteristics of clay minerals.6,7 Specifically, reduction−oxidation has important consequences for ion exchange and ion adsorption to clay minerals, dissolution and precipitation,6,8 weathering processes,6 and swelling behavior.9,10 However, compared to the iron-oxide mechanisms of redox transformation, Fe-bearing clay minerals are poorly understood. This is partly due to a large compositional variability in clay minerals that can tolerate various isomorphic substitutions in both tetrahedral and octahedral sheets, with excess charge compensated by a wide range of counterions in the interlayer region. This leads to a large parameter space in experiments and associated difficulties/ambiguities when interpreting experimental data. From a theoretical standpoint, it is also due to the lack of microscopic information on the site localization of electron density and the kinetics of electron exchange in clay minerals. Therefore, to quantify redox reactivity of different Fe entities in © 2013 American Chemical Society

various local environments and thus help deliver an adequate overall kinetic model of reduction mechanism, we undertake first-principles calculations of the rates of Fe2+−Fe3+ electron transfer in a clay mineral. We focus on nontronite as a representative of the Fe-rich smectites that have been studied experimentally during the past few decades.11−16 Smectite minerals such as nontronite are characterized by a 2:1 layer structure with an octahedral sheet (OS) sandwiched between two tetrahedral sheets (TS), commonly referred to as a TOT unit (Figure 1). Depending on the nature of cations in the TOT unit, TOT layers may bear some permanent electric charge that is compensated by interlayer species such as alkali cations. The ideal chargeneutral nontronite has monoclinic C2/m space group symmetry and the general formula Fe2Si4O10(OH)2.17 In the structure, Si4+ and O2− ions form hexagonal siloxane rings of the tetrahedral sheet, while Fe3+ ions serve as the coordinating cations in the octahedral sheet that also has a hexagonal honeycomb pattern (Figure 1). Nontronite has the dioctahedral layer structure characterized by the Fe3+ cation to oxygen ratio of 1:3, with only two out of three cation sites occupied, as opposed to the fully occupied octahedral sheet in the trioctahedral structure of, e.g., the mica annite. The octahedral Received: November 8, 2012 Revised: January 7, 2013 Published: January 11, 2013 2032

dx.doi.org/10.1021/jp3110776 | J. Phys. Chem. C 2013, 117, 2032−2040

The Journal of Physical Chemistry C

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model in the bulk and on surfaces of iron oxides, including wüstite (FeO),20 hematite (α-Fe2O3),21−24 and magnetite (Fe3O4).25 In contrast to iron oxides, there have been a very limited number of computational studies addressing electron transfer in Fe-bearing clay minerals.26−28 For instance, in a study of charge transport in annite,26 activation barriers of Fe2+−Fe3+ electron hopping along different pathways within the OS were computed using a molecular cluster approach and the Hartree−Fock method. It was shown that room-temperature charge transport should occur along the M2 iron sublattice with the predicted electron transfer (ET) rate of about 106 s−1, while the M1 sites are expected to act as efficient electron traps. This frequency is much smaller than previously calculated for ET in hematite (∼1012 s−1) using the same approach.21 It has also been demonstrated29 that substitution of Al or Mg for Fe in M1 sites of annite has very little impact on ET rates for the electron hopping on the M2 iron sublattice, whereas the substitution of Fe for structural OH bridges substantially decreases the hopping rate, effectively closing an ET channel relative to nonfluorinated cases. Because Fe-bearing clay minerals and iron oxides have structural similarities such as close Fe−Fe distances bridged via similar shared-edge Fe octahedra topologies and differences such as the presence of structural hydroxyls in clay minerals, the comparison is valuable for a broader understanding of what factors control ET rates in Fe minerals. In this study, we present the results of computational modeling of Fe2+−Fe3+ ET properties for the nontronite clay mineral using both periodic GGA+U plane-wave and molecular cluster UHF approaches combined with the Marcus electron transfer theory.

Figure 1. Top view of the 2:1 layer of idealized nontronite structure in polyhedral representation. Only the top tetrahedral sheet (TS) comprised of siloxane rings and the middle octahedral sheet (OS) comprised of iron−oxygen rings are shown, while the bottom TS is obscured from view. Structural protons in the OS located in trans positions with respect to the vacant M1 iron sites are depicted as white balls.

sheet has two structural hydroxyl groups on opposite sides of the (M1 site) cation vacancy (trans-vacant). These two hydroxyls are believed to play an important role in the electron transfer (ET) transition between Fe3+ and Fe2+ bridging two adjacent (M2 site) iron atoms in the octahedral sheet, thereby mediating the electron hopping between Fe ions, and are known to be susceptible to a dehydroxylation reaction due to their protonation upon reduction of the clay mineral.14 There have been a range of experimental studies using various spectroscopic and diffraction techniques to examine atomic structure, crystal chemistry, and oxidation−reduction processes of nontronites.12−19 A series of studies by Manceau and co-workers13,14,19 aimed at elucidating the oxidation− reduction mechanism of iron in dioctahedral smectites. This produced a conceptual model for reduction that involves migration of the reduced Fe ions from cis to adjacent trans octahedra with an accompanying dehydroxylation due to the protonation of structural hydroxyls. This model results in the formation of trioctahedral Fe2+ clusters separated by domains of vacancies in the OS. A number of studies have specifically focused on Fe redox reactivity and the kinetics of Fe oxidation−reduction in dioctahedral smectites including nontronite.15,16 By means of infrared spectroscopy,15 several structurally distinct reactive Fe2+-containing entities were identified. It has been shown that the formation and reactivity of the Fe2+ sites depend on the cationic composition and the location of the excess charge during Fe reduction. The reduction process was found to be accompanied by intense dehydroxylation and structural changes, however, preserving the overall clay mineral structure. Following these insights into the bulk reactivity, a 57Fe Mössbauer spectroscopic study16 has provided evidence of interfacial ET between sorbed Fe2+ and structural Fe3+ in nontronite. Importantly, based on temperature-dependence data, the study constrained the rate of Fe2+−Fe3+ electron hopping relative to the Mössbauer characteristic time of ∼10−7 s, information that can be directly compared with theoretical calculations. Recently, progress has been made in applying first-principles approaches coupled with Marcus electron transfer theory to predict electron hopping mobilities within the small polaron

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THEORETICAL METHODS Periodic Structure Calculations. Periodic structure calculations were performed within the density functional theory (DFT) GGA+U plane-wave formalism, using the generalized gradient approximation Perdew−Burke−Ernzerhof (GGA-PBE)30 exchange-correlation functional in conjuction with projector augmented wave (PAW)31 potentials as implemented in the VASP simulation package.32,33 A planewave cutoff energy of 500 eV and the potentials labeled “H”, “Si”, “O”, and “Fe” from the VASP PBE library were employed throughout the study. Structural optimizations (ionic positions, cell volume, and cell shape) were carried out applying a conjugate-gradient algorithm until atomic forces were less than 0.02 eV/Å and the total energy was converged to better than 10−5 eV. We used a Monkhorst−Pack34 scheme for the Brillouin zone integration. To describe the localized nature of the Fe valence 3d electrons we employ the effective on-site Hubbard Ueff correction as proposed by Dudarev.35 Since the exact value of Ueff best suited for nontronite is not known, we examine structural and ET properties by varying Ueff in the range from 4 to 8 eV. In the past, Ueff = 4−5 eV was shown to be successful in describing bulk and surface properties of other mixed-valence iron compounds, such as Fe3O4 (magnetite).36−38 All calculations were done spin-polarized imposing a ferromagnetic configuration of the local magnetic moments on Fe atoms in the octahedral sheet. To examine the kinetics of ET between the Fe2+ and Fe3+ ions in the nontronite lattice, we used a 2 × 2 surface supercell and optimized the initial and final states with small-polaron centers formed on the neighboring Fe ions in OS. A subsequent linear interpolation of the nuclear reaction coordinate between 2033



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Figure 2. Side (left) and top (right) view of the working molecular cluster excised from the nontronite structure (see Figure 1) before the protonation scheme was applied.

investigate the influence of the basis set quality on the values of electronic coupling matrix element VAB, we perfomed a number of VAB calculations using the improved basis sets with an addition of polarization and diffuse functions, namely, aug-ccpVDZ on the two Fe atoms (the rest of the Fe atoms Ahlrichs VTZ) and 6-311++G** on the two mediating OH groups (the other O, Si, and H atoms6-311G). An initial guess for the open-shell electron density of each cluster was calculated using the UHF orbitals of iron, silicon, oxygen, hydroxyl, and water fragments, with the Fe ions being treated spin-parallel and assigning the initial magnetic moments of 5 μB to Fe3+ and 4 μB to Fe2+ ions. Electron Transfer Model. Molecular-orbital formulation of an ET problem43 combined with the Marcus model44 allows one to obtain the electronic coupling matrix element VAB in terms of molecular-orbital eigenvectors at the crossing-point configuration and to thus discriminate between adiabatic (strong electronic interaction, large VAB) and diabatic (weak electronic interaction, small VAB) regimes of the electron transfer. While the reader is referred to the available literature for greater detail,45−49 Figure 3 summarizes the relevant ET parameters for a typical cross section of an energy profile between initial and final states for a symmetrical ET reaction. The ET rate can be computed according to the following expression50

the obtained configurations allows us to calculate an energy profile for the electron hopping along the migration path by performing a series of static total-energy calculations. These small polaron hopping calculations were performed using Γpoint total energies converged to better than 10−6 eV. The calculated electron hopping activation barriers can then be compared with the results from the molecular cluster approach discussed below. Molecular Cluster Calculations. The use of a molecular cluster as an alternative approach to describe properties of a solid provides the opportunity to employ virtually any of the existing ab initio molecular-orbital electronic structure methods for localizing electrons and computing ET properties. This approach also gives a direct way to discriminate between adiabatic and nonadiabatic regimes of electron transfer by evaluating the magnitude of electron coupling between the initial and final states. Within the cluster approach, there should be a reasonable compromise between the size of a cluster and the size of an atomic-orbital basis set to properly capture ET properties. In the present study, we have chosen a cluster of nontronite containing two complete siloxane rings and six iron−oxygen octahedra in such a way that the ET reaction between the two neighboring Fe ions mediated by the two structural hydroxyls can be considered symmetric. The model of the working cluster is shown in Figure 2. This cluster has the advantage of being large enough for the central octahedral Fe ions to have not only the nearest-neighbor local environment but also beyond, which seems to be important as most previous calculations have been restricted to using relatively small (dimers and trimers of iron) clusters when modeling Fe-bearing mineral systems.24−26 Addition of terminal protons to saturate the dangling bonds after the cluster was excised from the nontronite structure has been performed using Pauling electrostatic bond strength analysis that yielded an overall cluster composition of Fe6Si12O50H42 with a net charge of +8, provided that all six octahedral Fe ions are in the trivalent oxidation state. The effect of protonation/deprotonation of structural hydroxyls on ET rates was examined by adding/removing protons to/from the cluster. The effect of tetrahedral substitution of Si(IV) by Fe3+ was studied by replacing all six Si ions by Fe ions in one of the TSs. All cluster calculations were carried out as all-electron at the spin unrestricted Hartree−Fock (UHF) level with the Ahlrichs valence triple-ζ (VTZ) basis set for Fe39 and 6-311G basis set for O, Si, and H40,41 using the NWChem package.42 To

Figure 3. Schematic showing a cross section of an energy profile for electron hopping between initial (ξ = 0) and final (ξ = 1) states in a typical symmetric electron-transfer reaction. 2034



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Table 1. Lattice Constants a, b, and c (Å) and an Angle β (deg) for Ideal Nontronite Structure Calculated Using GGA+U Periodic Structure Calculations for Two Values of Ueff and from Experiment17a Ueff = 4 Ueff = 8 experiment17 a

a

b

c

β

5.336 (1.1%) 5.331 (1.0%) 5.277

9.179 (0.4%) 9.163 (0.2%) 9.140

9.940 (1.6%) 9.886 (1.1%) 9.780

112.1 (9.9%) 112.1 (9.9%) 101.0

The values in parentheses give the deviation of the theoretical values from experimental data.

Table 2. Selected Interatomic Distances (Å) and Angles (deg) in the Ideal Nontronite from Molecular Cluster UHF and Periodic GGA+U Calculations, As Well As from Experiment17 cluster (UHF) periodic (GGA+U, Ueff = 4) periodic (GGA+U, Ueff = 8) experiment17

τ = nτ0 exp( −ΔG*/kBT )

Fe1−Fe1

Fe1−Fe2

Fe1−O(H)

(Fe1)O−H

Fe1−O(H)−Fe1

3.283 3.057 3.054 3.047

3.170 3.077 3.072 3.047

2.030 2.013 1.995 2.033

0.945 0.977 0.975 −

108.1 98.8 99.9 97.1

fall systematically into the trend. It is clearly seen that the structural parameters turn out to be insensitive to the value of Ueff in the range of 4−8 eV, resulting in fair agreement with available experimental data.17 In Table 2 we compare some of the structural parameters that are particularly critical for examining ET properties in nontronite. It is seen that the periodic GGA+U calculations provide very good agreement with available experimental data for the structural parameters listed. The cluster approach gives rise to larger Fe−Fe distances and Fe−O(H)−Fe angles that are likely due to the absence of the surrounding lattice, the presence of the net positive charge, and the Hartree−Fock level of the description of electron interaction. The deviations, however, are reasonably small and consistent with those previously found in calculations of annite.26 We also note that the Fe−Fe and Fe−O distances calculated here for nontronite are rather close to those found for annite in both periodic and cluster calculations. As will be discussed below, because of the structural similarities, the electron hopping rates predicted for the OS of dioctahedral nontronite and trioctahedral annite turn out to be quite similar.

(1)

where n is the number of possible acceptor sites for electron hopping that can be taken as three for the number of nearestneighbor sites adjacent to the donor site for the ET in nontronite TS and OS, and τ0 = VAB/ℏπ is the frequency of electron oscillation between the two sites.51 It should be noted that there are various expressions available in the literature for the rate of electron transfer. Here, we are utilizing the approach used in a series of previous studies26,29 that allows us to directly compare our results for nontronite with those obtained previously for annite. To determine the adiabaticity for an ET reaction, the electron transfer probability P for ET at the crossing point was calculated as 2 ⎛ ⎞1/2 VAB π P= ⎜ ⎟ ℏν0 ⎝ 4ΔG*kBT ⎠

(2)

where ℏ is Planck’s constant; kB is Boltzmann’s constant; T is the temperature; and ν0 is the highest frequency for a longitudinal optical phonon. If P ≥ 1, the system is considered as adiabatic, and P can be taken as 1, whereas if P < 1 the system is nonadiabatic and the ET rate τ is reduced by a factor of P. Evaluation of the electronic coupling matrix element VAB at the crossing-point configurations was done according to the quasi-diabatic approach43 implemented in the electron transfer module of the NWChem code. The crossing-point geometry was found using the linearized reaction coordinate approximation according to q(ξ) = (1 − ξ)qA + ξqB

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ET FROM PERIODIC GGA+U CALCULATIONS Following our geometry optimization of the nontronite structure, we calculate the activation energy of electron small polaron hopping between two adjacent Fe ions in the OS. To create a polaron center on an Fe site, we added one additional electron to the neutral supercell of nontronite that was compensated by introducing a neutralizing background. To properly account for the strong electron correlations in the Fe 3d shell so that stable small polarons can be formed, we employ the GGA approach with the Hubbard U correction on Fe sites. It has been previously demonstrated that charge disproportionation on the octahedral Fe sublattice in the mixed-valence iron oxide, Fe3O4, takes place beyond Ueff = 2 eV,37 and a series of recent studies have proved to be most successful in describing structural, magnetic, and electronic properties of Fe3O4 using Ueff from 4 to 5 eV.36−38,52 Here, we examine the activation barrier of electron transfer in nontronite as a function of Ueff in the range of 4−8 eV to test the sensitivity of the barriers to the magnitude of Ueff and to find out what Ueff value provides the best agreement with recent Mössbauer data on the ET rates. An analysis of the atomic on-site occupancy matrices of the fully relaxed nontronite structure shows substantial charge disproportionation on the octahedral Fe sublattice and confirms

(3)

where qA (ξ = 0) and qB (ξ = 1) are the reaction coordinates of the reactant and product. For a symmetrical ET, as for the case of electron hopping between Fe2+ and Fe3+ in the OS, the crossing-point geometry is exactly halfway (ξ = 0.5) between the initial and final configurations.

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ATOMIC STRUCTURE OF IDEAL NONTRONITE We report the crystal structure of bulk nontronite calculated using both the periodic GGA+U plane-wave method and molecular cluster approach. Table 1 lists the optimized lattice parameters of the charge-neutral nontronite with no interlayer species from GGA+U calculations for the Ueff values of 4 and 8 eV, while the parameters obtained using in-between Ueff values 2035



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Figure 4. Energy profiles for electron migration in the nontronite octahedral sheet between two adjacent iron sites bridged by hydroxyls (left panel) and by siloxane oxygens (right panel), as calculated by GGA+U using Ueff = 6 eV.

barriers along both pathways of electron migration turn out to be similar for a given Ueff being within the thermal energy at room temperature. This suggests the absence of an energetic preference between the two ET pathways within the OS of idealized nontronite. Note that this situation can be changed under conditions where a progressive oxidation/reduction of Fe atoms would require charge compensation, for instance, through the loss/gain of structural protons. This point will be specifically addressed in detail below. Variable-temperature Mössbauer spectroscopy used in a recent investigation of electron exchange kinetics in nontronite16 offers one way of constraining the ET rates relative to the Mössbauer characteristic time of approximately 10−7 s (the mean lifetime of the nuclear excited state of 57Fe).54 An analysis of the temperature-dependent behavior of the spectra indicates the temperature region ∼120−150 K where electron hopping becomes sufficiently slow (∼107 hops per second) for Fe2+ and Fe3+ ions to be discriminated from each other through the appearance of a distinct Fe2+ doublet in the spectra. Knowledge of this temperature allows us to estimate a crossover activation barrier and what Ueff is thus most appropriate to describe the electron transfer in nontronite. By using expression 1 with the magnetite value of τ0 = 1.85 × 1013 s−1,55 site multiplicity n = 3, and the Mössbauer characteristic time of 10−7 s, we find that the temperature crossover at 150 K occurs for ΔG* values of about 200 meV. Therefore, using the activation energy dependence on Ueff from Figure 5, we show that the best agreement between theoretical predictions and Mössbauer data on the ET rates in nontronite is achieved for Ueff = 4−4.3 eV. This is in excellent agreement with prior GGA+U investigations showing that the best description of electronic and magnetic properties of magnetite Fe3O4 can be obtained using Ueff = 4−5 eV,36−38,52 as well as with the recent study28 of the catalytic properties of nontronite using similar Ueff.

the formation of small polaron centers on Fe sites. A degree of electron localization clearly varies with the value of Ueff, with the magnetic moments of the Fe3+ and Fe2+ ions being 4.30 μB and 3.79 μB for Ueff = 4 eV and 4.61 μB and 3.92 μB for Ueff = 8 eV, respectively. To obtain the activation energy of an electron small polaron hop, we performed a series of static self-consistent calculations along a polaron migration path between the equilibrium initial and final configurations with the polarons formed on the two adjacent Fe sites. In the OS of nontronite, two symmetric pathways for polaron migration can be distinguished. The first one (Figure 4, left panel) involves the ET between Fe sites bridged by structural hydroxyl groups. The second path, however, involves the migration of a polaron between Fe sites bridged by O atoms shared with the siloxane rings of the TS (Figure 4, right panel). Therefore, we calculate the activation barrier of the ET for both cases. Figure 4 shows the calculated energy profiles of a polaron migration using Ueff = 6 eV as a special case, while Figure 5 summarizes the results obtained for

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Figure 5. Activation energy barrier for two possible pathways of electron migration in nontronite OS as a function of Ueff parameter.

ET FROM MOLECULAR CLUSTER CALCULATIONS To gain further insight into the ET properties of nontronite, we also employ molecular-cluster UHF calculations. This approach allows us to not only compare our results for nontronite with previous investigations of the ET properties of other Fe-bearing mineral oxides using UHF method but also directly assess the electronic coupling matrix element VAB and to examine various structural substitutions in the nontronite lattice that would be more difficult within the periodic approach because of the charge imbalance. In addition, although the absolute values of ET rates might be underestimated at the UHF level due to

the activation barrier as a function of Ueff. It is clear that as the degree of electron localization on Fe sites increases at higher Ueff leading to a decrease in wave function overlap between adjacent Fe ions the activation energy barriers for the ET significantly increase. The presence of two regions characterized by linear dependences of the activation barrier on Ueff with two different slopes observed in Figure 5 can be attributed to different degrees of electron localization and was previously found for electron migration in other Fe-containing compounds such as olivine phosphates.53 Figure 5 also shows that activation 2036



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Table 3. Electron Transfer Rate Parameters for Fe2+−Fe3+ Electron Hopping in the Tetrahedral (TS) and Octahedral (OS) Sheets from Molecular Cluster Calculations of the Idealized Nontronite Computed for T = 298.15 Ka R, Å TS OS OS (in annite26)

3.622 3.246 3.21

ΔG*, eV 1.45 0.54 0.48

λI, eV 5.79 2.16 2.01

VAB, eV

τ0, s−1

τ, s−1

0.081 0.014 0.064

3.9 × 10 6.8 × 1012 3.1 × 1013 13

4.8 × 10−11 1.7 × 105 8.3 × 105

a

Parameters for ET in OS are presented for the case of electron hopping between Fe ions bridged by structural hydroxyls. The values from a previous computational study of annite26 using a similar approach but a smaller cluster of Fe3O13H22 to probe the M2−M2 ET in OS are given for comparison.

Note that here we only evaluate the internal reorganization energy λI, that is, the energy required to distort the reactants into the nuclear configuration of the products maintaining the reactants’ electronic state. Evaluation of the external part defined as the energy needed to repolarize the surrounding lattice requires knowledge of the optical and static dielectric constants that are not known for nontronite. Nevertheless, the external contribution in the case of annite was previously estimated using hematite dielectric constants to constitute about 12% of the total reorganization energy26 and can be expected to be on the same order for nontronite. Using the relaxed geometries for Fe2+ in the TS and OS as the initial and final configurations, we also estimate the ET parameters for electron hopping from TS to OS by calculating potential energy curves for the ET as a function of linearly extrapolated reaction coordinate q. In this case, the ET reaction is asymmetric with the state of Fe2+ in the OS having about 0.9 eV lower energy than the one with tetrahedral Fe2+. The reaction coordinate for the crossing-point configuration turns out to be displaced slightly closer to a higher-energy state (Fe2+ in the TS), and the activation barrier for the ET from TS to OS is found to be on the order of 1 eV. Due to the nature of the working cluster chosen in this study, evaluation of the activation energy for polaron hopping from TS to OS should be regarded as quite approximate. Nevertheless, the obtained ΔG* value of about 1.1 eV that involves the energy to distort both tetrahedral and octahedral local environments of iron atoms seems to be meaningful, lying between 1.45 eV for ET in TS and 0.54 eV for ET in OS. Thus, we show that the transport of electrons within the TS and from the TS to OS is predicted to be extremely slow as compared to ET in OS. We should note that we do not consider here the case of electron transport from Fe2+ species in solution to Fe3+ ions in TS of the nontronite, while this might turn out to be quite facile and be a mechanism of obtaining tetrahedral Fe2+. Overall, our results are consistent with recent observations15 suggesting that Fe2+ might exist in the TS remaining within the reduced nontronite structure. Effect of Protonation/Deprotonation of Structural OH Groups. Although the charge-compensating mechanism upon redox transormations of clay minerals might involve various processes including heterovalent cationic substitutions in the clay mineral sheets and exchange of counterions in the interlayer region, there is strong evidence for the involvement of structural protons.56 Also, it is believed that protonation of the nontronite structural hydroxyls facilitates a dehydroxylation reaction accompanied by the migration of reduced Fe ions from cis- to adjacent trans-octahedra, leading to the formation of trioctahedral Fe2+ clusters separated by vacancy domains.14 As our calculations suggest the involvement of tetrahedral Fe ions in the overall redox transformation of nontronite to be energetically unfavorable, one plausible scenario might be

overlocalization, it is reasonable that relative ET rates can provide good insight into the mechanism of electron transfer in metal oxides. ET Within and Across the Nontronite Sheets. In this section we present the results of ET calculations using the molecular cluster of nontronite as discussed in the Theoretical Methods (see Figure 2). We particularly focus here on the ET between Fe3+ and Fe2+ in the OS as the formation of a Fe2+ entity in the nontronite tetrahedral environment is expected to be energetically unfavorable. However, tetrahedral Fe3+ ions can be present in some smectites including Fe-rich nontronites,15 and questions of their accessibility for ET reactions and involvement into the overall charge transport still remain. Therefore, we will also provide estimates of the activation energy barrier for electron hopping in the TS and from the TS to the OS. Table 3 summarizes the ET parameters obtained in calculations of electron hopping between Fe ions in the nontronite sheets. First of all, it is seen that τ0 values estimated as VAB/ℏπ are remarkably close to a value of 1.85 × 1013 s−1 for the highest longitudinal optical phonon in magnetite.55 We also see that the ET in the OS is characterized by three times lower electron hopping activation barrier (ΔG*) and almost three times smaller internal reorganization energy (λI) than for ET in the TS, resulting in a much higher ET rate. The extremely small ET rate for the TS suggests almost negligible electronic conductivity in the TS. The electronic coupling at the crossing point configuration is found to be much stronger (larger VAB) for the tetrahedral ET that, as will be dicussed below, might be associated with the more covalent nature of the unprotonated mediating oxygen atoms as compared to hydroxyl groups in the OS. A possible protonation of oxygen atoms of the basal plane in aqueous solutions is expected to lead to smaller VAB, thus increasing even further the activation barrier of the ET in the TS. In the table, we also compare the parameters for ET in the dioctahedral nontronite OS with the values previously predicted using the same computational approach for trioctahedral annite for best-available literature comparison. It is seen that the calculated activation and internal reorganization energies are just slightly higher for nontronite than for annite. This difference, however, might be associated with different sizes of the working clusters, the absence of Si−O tetrahedra in the annite cluster, and a different degree of cluster rigidity for the dioctahedral structure of nontronite versus trioctahedral structure of annite. Note that the rates of M2−M2 electron transfer for nontronite and annite (∼105−106 s−1) calculated by the UHF method within the cluster approach are substantially lower than the frequencies of Fe2+/Fe3+ electron transfer predicted using a similar model for α-Fe2O3 hematite (∼1012 s−1)21 and Fe3O4 magnetite (∼1010−1012 s−1).25 The reasons for such a dramatic difference will be discussed in more detail in the next section. 2037



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Table 4. Electron Transfer Rate Parameters from Molecular Cluster Calculations for Electron Hopping in OS between Fe2+ and Fe3+ Bridged by Mediating Ligands for T = 298.15 Ka R, Å one OHstruct two OHstruct two H2Ostruct

2.931 3.246 3.899

ΔG*, eV 0.51 0.54 0.65

λI, eV 2.04 2.16 2.6

VAB, eV

τ0, s−1

τ, s−1

0.045 0.014 0.013

2.2 × 10 6.8 × 1012 6.3 × 1012 13

2.1 × 105 1.7 × 105 2.7 × 103

a

In addition to the case of idealized nontronite with two structural OH groups (two OHstruct), the systems with one deprotonated OH (one OHstruct) and two protonated OH (two H2Ostruct) groups are presented.

for nontronite, the case when Fe3+ replaces some amount of tetrahedral Si4+ is interesting, as Fe ions can change their redox state and potentially have a pronounced influence on the ET process in OS. Also, this case has been recently studied for the example of Fe-rich synthetic nontronite with different contents of tetrahedral Fe.15 Here, we look at the effect of the tetrahedral substitutions on the characteristics of ET in OS focusing specifically on the case of complete substitution of Si4+ by Fe3+ in one of the two TS (50% tetrahedral Fe). We find that the activation energy for electron hopping between Fe ions bridged by hydroxyls in OS increases by only 0.01 eV with respect to the original case with no tetrahedral Fe for which the activation barrier was found to be 0.54 eV. The magnitude of VAB is computed to increase by about 0.01 eV. These two effects are thus expected to largely cancel each other out so that the resulting ET rate should not change noticebly as compared to the original case. These findings suggest that the major factor affecting the ET parameters is the structure and topology of the immediate surroundings to the electron hopping, mainly of the Fe ions participating in ET and the mediating ligands. We should note that a similar conclusion about the shortrange nature of the effects of compositional defects on ET rates has been drawn in the computational study of annite.29 It has been shown that, although substitution of Al or Mg for Fe in M1 sites perturbs the structure of the neighboring Fe-occupied M2 sites, this distortion has very little influence on ET rates through these M2 sites. The main effect of such an M1 substitution is thus to occlude ET pathways and reduce the directional degrees of freedom for electron transport in the annite lattice. Basis Set Effect. In ab initio approaches involving calculations of molecular orbitals built as a linear combination of atomic orbitals, it is crucial to ensure convergence of properties of interest with respect to the basis set. In regard to electron transfer properties, it is believed to be important to use an all-electron basis set rather than a pseudopotential approach. Also, an accurate estimate of the electronic coupling matrix element VAB, used to distinguish between adiabatic and nonadiabatic regimes in the Marcus model, might require an addition of polarization and/or diffuse functions to properly describe the electronic state at the crossing point. In a recent paper,57 a rigorous analysis of the basis set effect on the magnitude of VAB was carried out on the example of an aqua complex of the iron dimer. In this case, the ligandmediating electron transfer between adjacent octahedral Fe ions is a water molecule. It was demonstrated that VAB increases with the basis set size, being particularly sensitive to the improvement of the valence shell description. The major factor affecting the magnitude of VAB was expectedly found to be the quality of the description of the donor and acceptor Fe ions and the bridging ligands. Quantitatively, however, the largest difference in VAB was computed to be no more than 0.025

penetration of a solution-phase electron donor through the siloxane cavity into the vacancy domain for a subsequent ET in the nontronite OS. In addition, protonation of structural hydroxyls might also be coupled with the ET between octahedral Fe ions. Since the protonation/deprotonation of structural OH groups appears to be very important for redox transformations in smectites, we investigate the influence of this process on the ET rates in the case of nontronite. Table 4 lists the ET characteristics of polaron hopping in the OS between Fe ions bridged by structural hydroxyls. Here, we consider three cases of ET in nontronite with two structural OHs (two OHstruct), with both the hydroxyls protonated to give two structural H2Os and with one deprotonated OH to give OH and O2− as the bridging ligands (one OHstruct). This allows us to examine the effects of both protonation and deprotonation on the ET parameters. First of all, it is seen that the Fe3+−Fe2+ distance increases quite significantly upon protonation, about 1 Å across the cases considered. We can also observe that the general trend for activation and reorganization energies is to increase upon protonation which in turn leads to a decrease of the ET rate, particularly in the case of two water molecule bridges. Regarding the effect of protonation/deprotonation on the magnitude of the electronic coupling matrix element (VAB), we can see that the addition of protons to structural hydroxyls has almost no effect on VAB, whereas deprotonation of one of the hydroxyls leads to a substantial increase in VAB. For the sake of comparison, we also studied the case of doubly deprotonated OH groups, thus leaving behind two oxygen atoms as the bridging ligands mediating ET between Fe ions. This case turns out to be very energetically unfavorable as the bridging oxygen ions tend to displace considerably toward Fe octahedra yielding an activation energy on the order of 4 eV, while the electronic coupling was found to be approximately twice stronger than in the case of singly deprotonated OH groups. Such a significant increase in VAB and its magnitude for the case of mediating oxygen atoms are consistent with the VAB values found in modeling ET properties of the bulk magnetite where no structural protons are present.25 These findings appear to be quite general, in excellent agreement with a previous theoretical study29 showing that the substitution of F for structural OH groups increases the internal reorganization energy and decreases the electronic coupling matrix element, thereby resulting in a substantial decrease of the ET rate. Therefore, it is the higher reorganization energy and the weaker electronic coupling that are responsible for a much slower electron transport in nontronite and likely other smectites than in iron oxides. Effect of Tetrahedral Fe3+ Substitutions. Since clay minerals are known to be prone to various cationic substitutions in the clay sheets, it is important to understand how sensitive the ET parameters are to these compositional changes. Among a number of cationic substitutions observed 2038



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nature and structure of the nearest-neighbor local environment and the degree of covalency of the bonds between Fe and ligands mediating electron hops.

eV (25%) and thus less than the thermal energy at room temperature. The basis set effect on the reorganization energy was also found to be relatively small, leading to an increase of the diabatic crossing-point energy by 0.02 eV. Although this dimer and nontronite have different structures, they indeed have several common structural features relevant to the ET process: 6-fold coordination of the iron ions, similar Fe2+−Fe3+ distance (∼3 Å), and the presence of protonated bridging ligands (H2O molecule in the dimer and OH groups in the nontronite) mediating electron hopping between neighboring Fe ions. In the calculations of VAB in nontronite, we found that the use of the 6-311++G** basis set on bridging H and O atoms and aug-cc-pVDZ on two Fe ions (the rest is 6-311G on H, Si, and O and Ahlrichs VTZ on Fe) increased the VAB by 0.009 eV for the cluster with two structural protons and by 0.006 eV for the cluster with one structural proton. Such an increase in VAB is expected to be rather systematic across different ET pathways and thus should not have a noticeable effect on the relative electron mobilities. This increase is consistent with the fact that an addition of diffuse functions to the basis set should increase the degree of covalency of the system and therefore lead to an increase of VAB.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported in part by the U.S. Department of Energy Office of Biological and Environmental Research (OBER) Subsurface Biogeochemical Research (SBR) program through a grant to PNNL and through the PNNL Science Focus Area. The computations were performed using PNNL Institutional Computing at Pacific Northwest National Laboratory. NWChem Version 6.1, as developed and distributed by PNNL, and funded by the DOE, was used to obtain some of these results. The authors acknowledge Eugene Ilton for discussions and valuable comments.

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CONCLUSIONS Rates of Fe2+−Fe3+ electron transfer in the typical Fe-rich dioctahedral smectite, nontronite, were investigated by using GGA+U plane-wave and UHF molecular cluster approaches in combination with the Marcus electron transfer theory within the small-polaron hopping model. We computed the rates of electron exchange between Fe ions in the tetrahedal and octahedral sheets, as well as from TS to OS. We examined the effects of protonation/deprotonation of structural hydroxyls and tetrahedral Fe substitutions on the ET properties and also the basis set effect on the magnitude of the electronic coupling matrix element. Electronic conductivity of bulk nontronite is predicted to be dominated by the electron transport within the OS. By varying Ueff in GGA+U calculations, we show that the best agreement with the recent variable-temperature Mössbauer data on the ET rates in nontronite is obtained at Ueff = 4−4.3 eV. On the basis of UHF calculations, we find that the state with tetrahedral Fe2+ in the nontronite lattice is about 0.9 eV higher in energy than the one with Fe2+ in OS, with the activation energy for ET from the TS to the OS estimated to be nearly 1.1 eV. Protonation of the O atoms of structural hydroxyls mediating ET between the nearest-neighbor Fe ions in OS is found to increase the internal reorganization energy and to decrease the magnitude of the electronic coupling matrix element. A substantial weakening of the electronic coupling at the crossing-point configurations upon protonation of the bridging O atoms may reflect an increase in ionicity of the Fe−O bonds participating in ET. This is thought to be one of the reasons, along with a much higher internal reorganization energy, for several orders of magnitude slower Fe electron exchange in clay minerals like nontronite and annite than in iron oxides. Substitution of Si4+ by Fe3+ ions in the nontronite TS is found to have only a small effect on the rates of ET between octahedral Fe ions bridged by structural hydroxyls. Such a substitution, however, might have a larger effect on the rates of the ET involving basal planes (i.e., mediated by O atoms belonging to siloxane rings of the TS). This is consistent with the notion that the major factors affecting ET rates are the

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Electron Exchange and Conduction in Nontronite from First

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