Mechanisms and Rates of U(VI) Reduction by Fe(II) in Homogeneous

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Mechanisms and Rates of U(VI) Reduction by Fe(II) in Homogeneous Aqueous Solution and the Role of U(V) Disproportionation Richard N. Collins, and Kevin M. Rosso J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b05965 • Publication Date (Web): 15 Aug 2017 Downloaded from http://pubs.acs.org on August 17, 2017

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The Journal of Physical Chemistry

Mechanisms and Rates of U(VI) Reduction by Fe(II) in Homogeneous Aqueous Solution and the Role of U(V) Disproportionation

Richard N Collins1,* and Kevin M Rosso1,2

1

UNSW Water Research Centre, School of Civil and Environmental Engineering, UNSW Australia, Sydney, NSW, Australia 2052.

2

Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99336, USA.

* Corresponding author: [email protected]

ACS Paragon Plus Environment


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ABSTRACT Molecular-level pathways in the aqueous redox transformation of uranium by iron remain unclear, despite the importance of this knowledge for predicting uranium transport and distribution in natural and engineered environments. As the relative importance of homogeneous versus heterogeneous pathways is difficult to probe experimentally, here we apply computational molecular simulation to isolate rates of key one electron transfer reactions in the homogenous pathway.

By comparison to experimental

observations the role of the heterogeneous pathway also becomes clear. Density functional theory (DFT) and Marcus theory calculations for all primary monomeric species at pH values ≤ 7 show for UO22+ and its hydrolysis species UO2OH+ and UO2(OH)20 that reduction by Fe2+ is thermodynamically favorable, though kinetically limited for UO22+. An inner-sphere encounter complex between UO2OH+ and Fe2+ was the most stable for the first hydrolysis species and displayed an electron transfer rate constant ket = 4.3 x 103 s-1.

Three stable inner- and outer-sphere encounter complexes between

UO2(OH)20 and Fe2+ were found, with electron transfer rate constants ranging from ket = 7.6 x 102 s-1 to 7.2 x 104 s-1. Homogeneous reduction of these U(VI) hydrolysis species to U(V) is, therefore, predicted to be facile. In contrast, homogeneous reduction of UO2+ by Fe2+ was found to be thermodynamically unfavorable, suggesting the possible importance of U(V)-U(V) disproportionation as a route to U(IV). Calculations on homogeneous disproportionation, however, while yielding a stable outer-sphere U(V)U(V) encounter complex, indicate that this electron transfer reaction is not feasible at circumneutral pH. Protonation of both axial O atoms of acceptor U(V) (i.e., by H3O+) was found to be a prerequisite to stabilize U(IV), consistent with the experimental observation that the rate of this reaction is inversely correlated with pH. Thus, despite prevailing notions that U(V) is rapidly eliminated by homogeneous disproportionation, this pathway is irrelevant at environmental conditions.


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1. INTRODUCTION There is significant interest in understanding the rates and mechanisms of uranium(VI) reduction to U(IV), as the latter is only sparingly soluble under anoxic conditions. For example, this process is seen as a potential immobilization mechanism for subsurface sediments contaminated with uranium1,

2

or

those surrounding deep geological repositories planned to be used for the long-term storage of nuclear waste.2-4 In such environments, ferrous iron, Fe(II), is considered to be a major potential abiotic reductant of U(VI).5 Indeed, there have been numerous studies demonstrating U(VI) reduction by either aqueous or mineralogic Fe(II) phases, which typically show the formation of two principle reduced U phases, uraninite (UO2) and sorbed molecular U(IV).2, 5-9 Other, less often, reduced phases that have been reported to form are metastable U(V) sorption complexes or solid phases,1,

10, 11

and U(V)

incorporated into the structure of goethite (α-FeOOH), arising from the Fe(II)-catalyzed crystallization of ferrihydrite,12, 13 or magnetite.14 While these experimental studies have unequivocally established that U(VI) reduction can be facilitated by Fe(II), substantial uncertainty still exists with regards to the chemical and redox conditions required for this reaction to be thermodynamically favorable, as well as the exact electron transfer (ET) pathways and their kinetics. For example, the homogeneous reduction of U(VI) to U(IV) by Fe(II) has long been considered to be thermodynamically favorable but kinetically inert.15

Recently, however, this

predisposition has been challenged16 where it was demonstrated that homogeneous reduction of U(VI) to U(IV) by Fe(II) is relatively rapid at pH values > 5 at relatively high U(VI) and Fe(II) concentrations. Subsequent experiments by Stylo et al.9 also produced similar results to that of Du et al.16 Elsewhere, however, Taylor et al.17 produced computational evidence that the outer-sphere one electron reduction of U(VI) by Fe2+ (i.e., in homogeneous aqueous solution) via the UO2(OH)20 species is thermodynamically favorable, but the reaction is kinetically inert with a rate constant of ~10-19 s-1, as originally indicated by Liger et al.15 Experimental evidence detailed in Taylor et al.17 further supported the conclusion that homogeneous reduction of U(VI) to U(IV) by Fe(II) does not occur on laboratory time-scales. It was thus suggested that the results obtained by Du et al.16 may have been caused by oversaturation with respect to meta-schoepite, thereby creating conditions conducive to heterogeneous reduction mechanisms. In addition, after the one electron reduction of U(VI) to U(V), it remains unclear if Fe(II) can further reduce U(V) to U(IV)16 or if continued reduction results from U(V) disproportionation to U(IV) and U(VI).9 Computational studies by Skomurski et al.11 on trimer cluster models of Fe(II)-U(VI)-Fe(II)



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surface complexes indicated that while reduction to U(V) by the first Fe(II) is favorable, further reduction to U(IV) by the second Fe(II) is strongly uphill. It has likewise been reported that the homogeneous reduction of triscarbonato-U(VI) within a di-iron ternary complex, i.e., [Fe2U(VI)(CO3)3]0 by the two available Fe(II) is thermodynamically unfavorable beyond U(V).18 Both studies suggest that further reduction to U(IV) would have to result from either different structural environments than those considered or by U(V) disproportionation. Because of the tendency of the system to continue to U(IV) precipitation in relevant experiments, U(V) has been notoriously difficult to isolate and its elimination by disproportionation has long been considered fast.

However, almost all of the experimental studies examining the kinetics of

homogeneous U(V) disproportionation have necessarily been conducted in extremely acid conditions (i.e., < pH 2) to avoid condensation of U(IV) species.19-26 Reported disproportionation rate constants in these studies have varied from ~1 – 11 600 M-1 s-1, being strongly influenced by concentrations of H+, U(VI) and complexing anions, such as sulfate and chloride. While some of the pioneering studies observed a first-order rate relationship with respect to H+, later studies did not observe such a phenomenon.19, 20 Nevertheless, it is generally agreed that solvent H+ promotes U(V) disproportionation though the mechanism(s) through which it does so have not been clearly articulated.19 Evidently, the slowest disproportionation rates have been observed at the higher end of pH values examined (i.e., pH 2 - 3).24,

27

In fact, Kraus et al.24 were able to stabilize U(V) in solution for a “very long time” until,

presumably, U(IV) polymerization occurred facilitating rapid heterogeneous U(V) disproportionation. These early studies thus established that U(V) disproportionation in homogenous solution accelerates with decreasing pH, suggesting by extension to circumneutral pH that the homogeneous disproportionation pathway may be intrinsically slow and elimination of U(V) at these conditions must therefore occur by the heterogeneous disproportionation pathway. Despite its obviously important role on the microscopic details of uranium reduction, no prior theoretical simulation studies have addressed pH dependent speciation on homogeneous uranium reduction and disproportionation kinetics. A recent theoretical study suggested that the outer-sphere homogeneous disproportionation of U(V) would be slow, with an estimated rate constant of ~ 10-1 M-1s-1,28 using an ad hoc encounter complex but without examining the importance of acidity for facilitating electron transfer. In addition, it was earlier suggested that homogeneous U(V) disproportionation occurs through a very different inner-sphere “cation-cation” encounter complex, though no electron transfer kinetics were computed in that study.29


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The goal of the present work is to provide a detailed and systematic study into the thermodynamics and kinetics of electron transfer involved in the homogeneous reduction of U(VI) by Fe(II) and U(V) disproportionation and so to provide insights for resolving many of the apparent discrepancies described above. Clearly, in experiments, assigning the one electron transfer pathways to either homogeneous or heterogeneous reactions is difficult as both U(IV) and Fe(III) are sparingly soluble and once nucleated the system immediately enables parallel pathways. Computational techniques are, therefore, a natural choice to overcome this limitation. Here we isolate and predict reaction rates of key species available to the homogeneous pathway alone. We apply a combination of density functional theory (DFT) and Marcus theory to determine the thermodynamics and electron transfer kinetics of U(VI) reduction to U(V) by Fe2+(aq) and homogeneous U(V) disproportionation, for the aqueous U and Fe species that would be present at environmentally-relevant concentrations (0.1 µM U(VI) and 200 µM Fe(II)) at pH values ≤ 7. These species include UO22+, UO2(OH)+, UO2(OH)20, Fe2+ (Fig. S1, Supporting Information (SI)) and UO2+. At such low U(VI) concentrations, only the monomeric species would be expected to be present.30 We furthermore explore the role of acidity in facilitating disproportionation, to establish correspondence with and to elaborate mechanisms pertaining to historical experimental precedent. By addressing and understanding rates of processes possible in solution, the role of the heterogeneous pathway can also be inferred. 2. COMPUTATIONAL METHODS 2.1 Energy minimization of aqueous species and encounter complexes Molecular orbital theory first principles calculations were performed with NWChem 6.3,31 to determine energy-minimized structures of aqueous U, Fe and stable U-Fe and U-U encounter complexes. The methods we employed are well established through a range of computational studies including benchmarking on these specific ions as monomeric aquo complexes.32-36 To evaluate likely encounter complex structures, where less experimental information is available, a wide range of complexes were constructed for testing on the basis of bond valence analysis, and where possible, experimentally informed topologies. Inner shell solvation was explicitly treated; second shell and beyond was modelled using the COSMO dielectric continuum method as a robust approach to include solvent screening of charge redistribution associated with all solvent beyond first shell. Ground-state geometry optimizations were undertaken using the open-shell Kohn-Sham DFT formalism and the B3LYP hybrid exchangecorrelation functional, first in the gas phase and then again in the continuum solvation model.37 No



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symmetry restrictions were imposed on the geometry optimizations. Ahlrichs pVDZ was used as the Fe atom basis set and 6-31G** was used for H and O. The Stuttgart relativistic large-core basis set with effective core pseudopotentials was used for U, which has been shown to be robust for U DFT computations38 and has provided good results on prior U(VI) electron transfer computations.18 All basis sets were obtained from the EMSL Basis Set library.39, 40 Concatenated fragment molecular orbitals were used to precondition the initial guess wavefunction of the U and Fe species and their encounter complexes with a range of possible initial spin distributions to test, however, other than to fix the total spin multiplicity, no spin restrictions were imposed. High-spin states on both Fe and U species were always found to be most stable, consistent with expectations. The DFT-optimized monomeric U and Fe species (Table S1 and Fig. S2, SI) were used to form a starting guess for encounter complexes and, depending on the rate of convergence, pre-optimizations were often first performed for complexes in vacuo at the Hartree-Fock level of theory and these structures and converged wavefunctions were then used as starting guesses for DFT optimizations in vacuo and then ultimately including the use of the COSMO dielectric continuum solvation model. COSMO is a standard approach to enable inclusion of the screening effects of surrounding bulk water in the final calculated structure and total energy.41 In many cases, multiple initial guess wavefunctions were optimized to test for proper convergence to the same thermodynamically most stable structure. Default NWCHEM convergence criteria were used for the calculations. Similar trends and results were obtained among the pre-optimization calculations as all final reported results and trends at the DFT+COSMO level. Vibrational frequencies of the optimized structures were then obtained and thermochemical contributions to enthalpy and entropy were computed at 298.15 K and 1 atm to obtain the total energy at this standard condition. This standard state, conventional in molecular orbital theory codes, includes a small error with respect to the condensed solution phase that must be corrected in absolute total energies of aqueous species, but cancels through total energy differences of species,32 such as exclusively used here. Total DFT energy differences were, therefore, used to compute the values of ∆G° for electron transfer (ET). Multiple (inner- and outer-sphere) encounter complexes were optimized to examine the likelihood of two (or more) thermodynamically stable structures coexisting. We used the Boltzmann distribution to calculate probabilities for various possible species based on their number and relative energies according to:

⁄ /

= ∑


(1)

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which gives the probability of species i of energy Ei among total number of allowed species N of types jM, where the Boltzmann constant (k) = 8.6173324 x 10-5 eV/K and T = 298.15 K. Table 1: Thermodynamics of U(VI)-Fe(II) encounter complexes as computed by DFT with the COSMO model at standard conditions. (IS) refers to an inner-sphere encounter complex (number of bridging OH groups highlighted in bold) whereas (OS) refers to an outer-sphere encounter complex. Total DFT energies for the monomeric species and encounter complexes are shown in Table S1, SI. species/encounter complex UO2(H2O)52+ U(VI)O2(H2O)5 | Fe(II)(H2O)6 (OS) UO2(OH)(H2O)4+ U(VI)O2(H2O)4-(OH)-Fe(II)(H2O)5 (IS) + H2O U(VI)O2(H2O)4 | Fe(II)(H2O)5 (OS) UO2(OH)2(H2O)20 U(VI)O2(H2O)2(OH)-(OH)-Fe(II)(H2O)5 (IS) + H2O U(VI)O2(H2O)2(OH)2 | Fe(II)(H2O)6 (OS) U(VI)O2(H2O)2-(2OH)-Fe(II)(H2O)4 (IS) + 2H2O a

∆G° (eV)a

species abundance (%)b

0.08243

96.0 4.0

0.00423 0.05638

51.3 43.7 4.6

Assuming G° is equal to Total DFT energy (Table S1, SI), ∆G° is between an encounter complex and the thermodynamically most stable

encounter complex. The determination of ∆G° is based on mass balanced equations (i.e. inclusion of H2O molecules). b

Based on the Boltzmann distribution.

2.2 Electron transfer calculations The approach used to calculate electron transfer rates was based on that reported by Rosso and coworkers17, 18, 33-36 and is only briefly reiterated here with modifications noted. Once the structures of the U-Fe/U-U encounter complexes (both pre- and post-ET) had been optimized by DFT, intermediate structures based on linear combinations of the nuclear coordinates of both electronic states were calculated based on the linear synchronous transit (LST) method: Xn = αXp + (1 - α)Xr

(2)

where Xn represents a linear combination of the nuclear coordinates of the pre- (Xr) and post-ET (Xp) optimized structures based on a given mixing parameter (α) having a value between 0 and 1. Total DFT energies were calculated for nine intermediate structures (as well as the pre- and post-ET optimized structures), as described above, using the corresponding ground state wavefunctions for either the pre-ET or post-ET case as pre-conditioning initial guesses. Mulliken spin density distributions were used to confirm that the correct state had been maintained upon energy convergence and these



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intermediate energies were combined with the ground state energies to construct the pre- and post-ET potential energy surfaces. These energies were fitted with parabolic functions to estimate the crossingpoint at which the pre- and post-ET potential energy surfaces were equal, namely the diabatic activation energy (∆G*′). A linear combination structure based on the mixing parameter at the crossing point was then calculated for computation of the electronic-coupling matrix element (VAB), which is a measure of the electronic interaction between the pre- and post-ET states at the crossing-point, and reduces ∆G*′ to the activation energy ∆G*. The magnitude of VAB determines if ET occurs diabatically (weak electronic coupling; VAB < kT) or adiabatically (strong electronic coupling; VAB > kT) where kT at 25 °C is 0.0257 eV. The VAB was determined for each crossing-point structure using Hartree-Fock wavefunctions as implemented in the ET module of NWChem. It was observed during initial VAB computations that the Stuttgart relativistic small-core basis set was required to obtain reliable VAB values, as previously noted by Taylor et al.17 The reorganization energy (λ), a critical parameter of ET kinetics, is composed of the sum of two contributions, the first from bond distortion in the encounter complex (internal part, λI) and the second from changing the polarization of the surrounding solvent (external part, λE).35 The internal part was calculated as the difference between the energy of the post-ET encounter complex and the potential energy surface of the pre-ET encounter complex distorted into the post-ET geometry without electron transfer (e.g. Fig. S3, SI). The external reorganization energy (λE) was calculated from total DFT energies of the pre- and post-ET encounter complex geometries that were computed with two different dielectric constants corresponding to the optical (εopt) and static (εs) dielectric constant, respectively, 1.77 and 78.39.

Four electrostatic solvation energies were, therefore, computed where (∆Gsolv) =

ε – E(in vacuo). The external reorganization energy was then calculated as 41:

λE = ∆G†solv(post-ET) – ∆G†solv(pre-ET), where

(3)

∆G†solv = ∆Gsolv(εs) – ∆Gsolv(εopt)

(4)

When electronic coupling is weak (i.e., VAB < 0.0257 eV at 25 °C) the rate constant of ET (kET) can be determined by:

kET =

ℏ

(VAB)2

√λ

(∆!° " λ)$ %λ


(5)

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where ℏ is Planck’s constant at 1 bar = 6.58 x 10-16 eV s. When electronic coupling is strong, ET occurs adiabatically and kET can be determined by: kET = ν

∆ ! ∗

(6)

where ν is the typical frequency for nuclear motion (1013·s-1). All ET reactions in this study were found to involve weak coupling, so were treated as nonadiabatic. Where desirable for evaluating ET rate constants that can be compared with experimental values, the steady state approximation values of kET were multiplied by estimates of the equilibrium constant for encounter complex formation (Kenc) computed as described in Rosso and Rustad,35 for a condition of zero ionic strength. Kenc was calculated with the following equation: Kenc = 4πNR2 dR exp(-w/RT)

(7)

where N is Avogadro’s number, R is the distance between the two reactants at their closest approach, dR is the reaction zone thickness and w is the Coulombic work to bring the reactants together. The latter term (w) depends on the charges of the reactants, the distance between the reactants and the dielectric properties of the solvent (corrected for ionic strength). w = (1/4πε0)Z1Z2e2N/εsRm(1 + BRÅµ1/2)

(8)

where (1/4πε0) is equal to 8.988 x 109 Nm2/C2, Z1 and Z2 are the charges of the reactants, e is the electron charge (1.602 x 10-19 C), Rm is R expressed in meters, The factor BRÅ is a unitless parameter on the order of unity.35 In the case of the U(V)-U(V) disproportionation reaction, which was found to necessarily involve solvent H3O+ molecules for donating protons to the axial oxygens of the acceptor U(V) moiety, ET calculations were performed using alternative methods related to those above, as specifically noted. As noted elsewhere17,

18

ET in an encounter complex can often be accompanied by spontaneous

intermolecular proton transfer (PT), where an H+ dissociates from a donor ligand (e.g., H2O) on the side of the encounter complex that becomes more electropositive after ET to an acceptor ligand (e.g., OH−) on the new more electronegative side. In this study, like those previous, several post-ET ground states involved an accompanying intramolecular PT (i.e., proton-coupled electron transfer, PCET). In such cases, the PT makes a significant contribution to the thermodynamic driving force for ET, but the extent



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of coupling of the PT to the ET process along the reaction coordinate is an unknown. ET and PT can be simultaneous in nature, such as in hydride transfer, or sequential (ET followed by PT or vice versa). The methods applied in the present study, and also in related prior work,17,

18

do not allow for an

unambiguous determination in this regard. Specifically, PT is often mediated by other H2O molecules, and the absence of explicit second-shell water surrounding the encounter complex precludes simulation of solvent-mediated PT.

Furthermore, the LST method used to approximate the nuclear reaction

coordinate, while allowing the ET to follow a low potential energy surface, does not do so for the PT. Reorganization energies for ET with a simultaneous PT computed using the LST method thus typically overestimate the activation energy, often greatly, due to the unrealistic trajectory for the PT. Thus, in the present study, for all ET processes found to be accompanied by intramolecular PT, the reorganization energy was calculated as that associated with the ET process alone. In such cases the internal and external reorganization energies were computed using fixed O-H distances to eliminate the PT process and its artificial contribution to the activation energy. This strategy avoids the unnecessary ambiguities of ET/PT coupling, includes the PT contribution to the ET driving force, avoids overestimation of the activation energy, and treats all ET reactions throughout on an equal basis. 3. RESULTS AND DISCUSSION 3.1 Uranium(VI) reduction by Fe(II) 3.1.1 UO22+ reduction by Fe2+ No stable outer-sphere encounter complex was found to form between UO2(H2O)52+ and Fe(H2O)62+. This is primarily due to the strong repulsive electrostatic interaction between these two +2 species, which is not completely screened by water (as included via the COSMO solvation model). For example, on the basis of purely electrostatic interactions in water, the equilibrium constant Kenc estimated for a hypothetical encounter complex at typical outer-sphere contact separations in this study (e.g., 5.0 Å) is only 5.2 x 10-4 M-1, smaller than any estimated for the encounter complexes discussed below. It was, therefore, concluded that UO2(H2O)52+ reduction by Fe(H2O)62+ is kinetically insignificant, though this reduction step is predicted to be thermodynamically favorable by more than 0.47 eV (Table 2). 3.1.2 UO2(OH)+ reduction by Fe2+ For the first hydrolysis species of U(VI), which has a concentration maximum at pH ~ 5 (Fig. S1, SI), DFT energy minimizations resulted in both a stable inner- and an outer-sphere pre-ET encounter complex (Fig. 1). The inner-sphere encounter complex was computed to be the most thermodynamically


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stable however, comprising 96% of the probable encounter complexes, whereas only 4% of the encounter complexes would be outer-sphere (Table 1). Kenc for both species was estimated to be 2.6 x 10-3 M-1 and 1.1 x 10-2 M-1, respectively. Both values are higher than that for UO22+ because of the markedly decreased donor-acceptor electrostatic repulsion. Despite similar charges on the donor and acceptor species, the lower equilibrium constant for the inner-sphere complex arises because the donoracceptor separation distance needed to form this complex is smaller (3.95 Å) than that for the outersphere complex (5.25 Å) (Fig. 1). Thus, although the inner-sphere complex is predicted to more thermodynamically stable once formed, the electrostatic work that has to be overcome to form this complex is also higher, relative to the outer-sphere complex. This aspect is captured in Kenc. ET for a single electron, as confirmed by the Mulliken spin density distributions, was computed to be thermodynamically favorable for both encounter complexes (Table 2). The ET rate constant for the inner-sphere complex was calculated to be moderately fast at 4.3 x 103 s-1, indicating that reduction of UO2(OH)(H2O)4+ by Fe(H2O)62+ should be facile, with an overall rate of ~11.2 M-1 s-1. Electron transfer in the outer-sphere encounter complex was found to be coupled with the spontaneous transfer of one proton from a water ligand bound to the Fe cation to the lone equatorial OH group of U (Fig. 1). This PT is an intramolecular response to the new charge density distribution associated with the post-ET state. This ET reaction has a stronger thermodynamic driving force, a larger electronic coupling matrix element, and a lower total reorganization energy than the IS encounter complex (Table 2), thus yielding a lower activation barrier and a much faster overall ET rate of 7.5 x 106 s-1. Combined with Kenc, this yields an overall electron transfer rate of 8.2 x 104 M-1 s-1. Thus although this outer-sphere complex is less stable than the IS one, its much faster overall rate makes this ET process an active parallel channel for reduction of U(VI) monohydroxo species.



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Table 2: Mulliken spin densities, thermodynamics, ET parameters and rate constants of U(VI) reduction by Fe(II) computed with the COSMO solvation model at standard conditions. (IS) refers to an inner-sphere encounter complex (number of bridging OH groups highlighted in bold) whereas (OS) refers to an outer-sphere encounter complex. species/encounter complex Fe(H2O)62+ Fe(H2O)63+ UO2(H2O)52+ UO2(H2O)5+ UO22+ UO2(H2O)52+ + Fe(H2O)62+ → UO2(H2O)5+ + Fe(H2O)63+ UO2(OH)+ U(VI)O2(H2O)4-(OH)-Fe(II)(H2O)5 (IS) U(V)O2(H2O)4-(OH)-Fe(III)(H2O)5 U(VI)O2(OH)(H2O)4 | Fe(II)(H2O)5 (OS) U(V)O2(H2O)5 | Fe(III)(OH)(H2O)5 PCET UO2(OH)20 U(VI)O2(OH)(H2O)2-(OH)-Fe(II)(H2O)5 (IS) U(V)O2(H2O)3-(OH)-Fe(III)(OH)(H2O)4 PCET U(VI)O2(OH)2(H2O)2| Fe(II)(H2O)6 (OS) U(V)O2(H2O)4 | Fe(III)(OH)2(H2O)4 PCET U(VI)O2(H2O)2-(2OH)-Fe(II)(H2O)4 (IS) U(V)O2(H2O)2-(2OH)-Fe(III)(H2O)4

Mulliken spin density Fe U 3.85 4.36 0.00 1.14

a

∆G°

b

VAB

λI

λE

ket s-1

eV

-0.4713 3.84 4.32 3.88 4.28

0.02 1.16 0.00 1.15

3.83 4.26 3.84 4.28 3.86 4.29

0.01 1.17 0.00 1.15 -0.09 1.14

-0.1128

0.007391

1.83

0.32

4.3 x 103

-0.3025

0.019784

1.47

0.46

7.5 x 106

-0.1002

0.001233

1.35

0.53

1.4 x 103

-0.4610

0.001564

1.75

0.87

7.6 x 102

-0.3891

0.001234

1.69

0.29

7.2 x 104

a

Includes entropy and enthalpy contributions and these values are, therefore, different to the energy minima shown in Figure S3, SI.

b

Determined from the parabolic functions shown in Figure S3, SI.


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Figure 1: Pre- and post-ET encounter complexes for inner- (top) and outer-sphere (bottom) U(VI) reduction by Fe(II) for the first U(VI) hydrolysis species (UO2(OH)+). Values represent bond distances (Å) of the oxygen atoms to the metal centers.



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3.1.3 UO2(OH)20 reduction by Fe2+ Structural optimizations of the monomeric second hydrolysis species of U(VI) indicated that only four OH/H2O molecules were preferred in the equatorial plane, with the two OH molecules being in a ‘cis’ position (Fig. S2, SI). Three stable pre-ET encounter complexes with Fe(H2O)62+ were found for this hydrolysis species (in order of decreasing thermodynamic stability): an inner-sphere monodentate complex bridged through one OH group; an outer-sphere complex and; an inner-sphere bidentate complex bridged through the two cis OH groups (Table 1 and Fig. 2). Given the neutral acceptor species, Kenc for these encounter complexes are similar, at 9.3 x 10-2 M-1, 1.5 x 10-1 M-1, and 6.7 x 10-2 M-1, respectively. The first and second thermodynamically most stable encounter complexes were calculated to be present in almost equal proportions (Table 1).

However, the third and least

thermodynamically stable encounter complex was expected to be only sparingly present at 4.6 % species abundance. These results significantly differ from those obtained in the theoretical studies of Taylor et al.17 In that study, in vacuo DFT calculations indicated that, of the two encounter complexes examined an outer-sphere complex and an inner-sphere bidentate complex, only the outer-sphere complex would be present in solution. In fact, the in vacuo structure optimizations performed here were in good agreement with the results of Taylor et al.17 (Table S2, SI). However, inclusion of the COSMO solvation model during DFT structural optimizations includes the important electrostatic screening effects of surrounding bulk water.

Thus, a lower tendency for

intramolecular hydrogen bonding would be expected within the solvated encounter complexes. In fact, comparison of the O...H distances in the encounter complexes optimized in vacuo (Fig. S4, SI) and with COSMO (Fig. 2) showed that this was indeed the case (Fig. S5, SI). The greatest reduction in hydrogen bonding distances was observed for the outer-sphere complex, then the monodentate inner-sphere complex (Fig. S5, SI) with essentially no differences in the O-H distances of the bidentate inner-sphere complexes.

As such, the change in hydrogen bonding when energy minimized including solvent

screening effects influences the relative thermodynamic stability of the encounter complexes, resulting in structures that are more isoenergetic. As discussed below, this effect has important implications for theoretical computations on the homogeneous Fe(II) reduction kinetics of this U(VI) hydrolysis species to U(V).


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Figure 2: Pre- and post-ET encounter complexes for U(VI) reduction by Fe(II) for the second U(VI) hydrolysis species (UO2(OH)20). a) monodentate inner-sphere encounter complex; b) outer-sphere encounter complex and; c) bidentate inner-sphere encounter complex. Values represent bond distances (Å) of the oxygen atoms to the metal centers.



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Electron transfer from Fe(II) to U(VI) was thermodynamically favorable for all three of the encounter complexes (Table 2). Mulliken spin density distributions show a remarkable consistency in the extent of internal charge redistribution between the metal centers. ET was coupled with spontaneous PT for the inner-sphere monodentate and outer-sphere encounter complexes (Fig. 2). These two most prevalent encounter complexes have similar ET rates, with ket = 1.4 x 103 s-1 (inner-sphere monodentate) and ket = 7.6 x 102 s-1 (outer-sphere). The ET rate determined for the inner-sphere bidentate encounter complex is predicted to be fastest, with ket = 7.2 x 104 s-1, while being the least prevalent encounter complex in this group. Combined with Kenc, overall rates are 1.3 x 102 M-1 s-1, 1.1 x 102 M-1 s-1, and 4.8 x 103 M-1 s-1, respectively. Based on the collective ET processes discussed so far, it would be expected that the homogeneous one electron reduction of U(VI) by Fe(II) should be rapid for both its first and second hydrolysis species, but not for UO22+. Previous computational studies have reported that the homogenous one electron reduction of the aqueous U species, UO2(CO3)34- and UO2(OH)20, by Fe2+ is thermodynamically favorable but the kinetics are either slow or virtually zero, respectively.17, 18 Direct comparisons can be made with the study of Taylor et al.17 as we have performed computations for the same aqueous U(VI) species. While the ET kinetics calculated for the outer- and inner-sphere complexes are largely in agreement in vacuo,17 the inclusion of the screening effects of the surrounding bulk water reduces H bonding contributions to the final calculated structures and total energies.

As such, our results are more likely to be

representative of these phenomena in situ. Furthermore, in a broader sense, the results we have obtained are in line with the experimental results of Du et al.16 where U(VI) reduction by Fe(II) at low pH values was not observed (i.e. for the UO22+ cation) but occurred at pH values where U(VI) (polymeric) hydrolysis species were prevalent. Although Taylor et al.17 demonstrate that U(VI) polymerization is rapid at the U concentrations employed by Du et al.,16 which could certainly lead to the opening of heterogeneous ET pathways, this experimental result does not necessarily preclude (possibly initial) homogeneous ET pathways. 3.2 Uranium(V) reduction by Fe(II) The homogeneous reduction of monomeric U(V) to U(IV) by Fe(II) was examined based on the U(V) cation, UO2(H2O)5+, yielding an optimized structure as shown in Figure S2, SI. This is the only species expected to be present at pH values < 7, although the pKa of UO2(H2O)5+ has not been formally measured.24 Here, we assume that after the initial one electron reduction of U(VI) via its hydrolysis species, upon encounter complex dissociation the monomeric U(V) cation rapidly converts to its most


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stable form UO2(H2O)5+. For the interaction of this species with Fe2+, a stable outer-sphere pre-ET encounter complex was found through hydrogen bonding to one of the axial O atoms (Fig. S6, SI). Kenc was estimated to be 1.6 x 10-2 M-1, similar to that for the outer-sphere complex of UO2(OH)+/Fe2+ because of the similar donor-acceptor distances and charges. As for several of the ET reactions reported above, ET was coupled to PT, in this case from an adjacent water ligand on Fe2+ to the H-bonded axial O atom (Fig. S6, SI). However, ET was found to be strongly thermodynamically unfavorable, by 1.26 eV, which precludes any forward ET rate of significance. As will be discussed in further detail in the following section on U(V) disproportionation, U(V) reduction by Fe(II) where the U(V) molecule possessed a protonated axial O atom (in this case H+ being donated by solvent H3O+) was also investigated. However, no stable outer-sphere pre-ET encounter complex could be obtained. Our results show that homogeneous U(V) reduction to U(IV) by Fe(II) is a thermodynamically unlikely pathway, which suggests that further reduction could depend on U(V) disproportionation. Our results indicate that the homogeneous one electron reduction of UO2+ by Fe2+ is significantly thermodynamically uphill and corroborates all previous computational studies that have examined various aspects around U(V) reduction by Fe(II).11, 18 Our computational results are also consistent with thermodynamic calculations that have indicated that homogeneous reduction of U(VI) to U(IV) by Fe(II) would not be thermodynamically favorable without the free energy reduction associated with precipitation of Fe(III) solid phases.17, 42 In a notionally similar ET system, density functional theory calculations on the oxidation states of Fe and U in the crystal structure of FeUO4 also showed that the pairing of U(V) and Fe(III) is substantially more thermodynamically stable than U(VI) and Fe(II), even in the presence of additional lattice Fe(II).43 These results unanimously support the notion that further reduction of UO2+ in the aqueous phase, with Fe2+ as the sole electron donor, could only occur potentially through disproportionation. 3.3 Uranium(V) disproportionation Two pre-ET U(V)-U(V) encounter complexes, based on the DFT-optimized monomeric U(V) specie shown in Figure S2 (SI), were investigated: an outer-sphere complex (Fig. 3a), and an inner-sphere ‘cation-cation’ complex proposed by Steele and Taylor29 whereby an axial O atom from one U(V) is inserted into the equatorial plane of the other U(V) (Fig. S7a). The outer-sphere encounter complex was substantially thermodynamically favored (0.12 eV) resulting in a predicted 99 % predominance by the Boltzmann distribution (Table 3).



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As for many of the ET pathways discussed so far, it was observed that PT, in this case to an axial O atom, was required to obtain a stable post-ET outer-sphere encounter complex (Fig. S8b, SI). However, PT was not spontaneous during structural optimizations and this PCET pathway was computed to be highly thermodynamically unfavorable (1.71 eV). As noted in section 1, ample evidence exists showing that solvent H+ plays a role in U(V) disproportionation. Therefore, further structural optimizations of the pre-ET inner- and outer-sphere encounter complexes were undertaken by sequentially protonating, from an included H3O+ molecule, the axial O atoms of the U(V) molecule that would eventually be the recipient of electron transfer (i.e., converted to U(IV)). It was found that the initial protonation of the axial O atom not (hydrogen-) bonded to the other U atom was thermodynamically more favorable (Figs. S8c and S7b, SI). In this case, the energy difference between the protonated outer- and inner-sphere encounter complexes becomes such that the outer-sphere complex is the only one of significance; U(V) disproportionation through the inner-sphere ET pathway is extremely unlikely. As such, no further calculations on the inner-sphere complex were undertaken.

Nevertheless, once again, ET was thermodynamically

unfavorable (0.96 eV) for the outer-sphere encounter complex when coupled to PT from the electron donor (Figs. S8c-d).

In fact, U(V) disproportionation was only found to be thermodynamically

favorable (-0.54 eV) when a second H3O+ molecule served as a proton donor to the second axial O atom during PCET (Figs. 3a, b). The single ET converts the two doublet U(V) states into a triplet U(IV) and a singlet U(VI) (Table 4). The collective calculations on U(V)-U(V) disproportionation clearly show that for the forward rate to be significant, both axial oxygens on the acceptor U(V) must first be protonated. In this case the ET rate was computed to be 3.4 x 103 s-1 (Table 4), and when combined with its Kenc of 5.1 x 10-2 M-1 yields an overall rate constant of 1.7 x 102 M-1 s-1. This calculated rate lies within the range of those observed, which, as mentioned in the Introduction, required low pH to be measurable (e.g., pH 2-3). As will be discussed, based on these results the most plausible ET pathway in U(V) disproportionation would appear to be one in which H3O+ is integral to its occurrence, i.e., extremely acidic conditions. The results here show that outer-sphere U(V)-U(V) encounter complexes are significantly more thermodynamically stable than the inner-sphere complex proposed by Steele and Taylor.29 In that study, an inner-sphere encounter complex derived from the crystal structure of NpO2ClO4(H2O)4 was used for U(V)-U(V) and treated in the gas-phase. As such, we conclude that disproportionation through an innersphere complex is not important in homogeneous systems. Wander et al.28 have also theoretically


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examined outer-sphere disproportionation kinetics and found that ET was slow (ket ~ 10-1 M-1 s-1). However, they only considered internal rearrangements to achieve proton transfer within the encounter complexes.

Given the overwhelming evidence of the role of solvent H+ in accelerating U(V)

disproportionation,19-26 the PCET proposed by Wander et al.28 may not accurately reflect the disproportionation ET pathway. The PCET rate constant that we obtained, which requires two protonation steps of axial oxygens by solvent H+, is consistent with the assertions in Steele and Taylor29 and Kubicki et al.44 that acid attack of axial oxygens is a necessary process to stabilize the product states of U(IV) and U(VI). Table 3: Thermodynamics of U(V)-U(V) encounter complexes as computed by DFT with the COSMO model at standard conditions. (IS) refers to the inner-sphere encounter complex whereas (OS) refers to the outer-sphere encounter complex. Total DFT energies for the monomeric species and encounter complexes are shown in Table S1, SI. species/encounter complex Initial encounter complexes U(V)O2(H2O)5 | U(V)O2(H2O)5 (OS) U(V)O2(H2O)4-(O)-U(V)O(H2O)5 (IS) + H2O Encounter complexes (one protonated axial O atom) U(V)O(OH)(H2O)5 | U(V)O2(H2O)5 (OS) U(V)O2(H2O)4-(O)-U(V)OH(H2O)5 (IS) + H2O Encounter complex (one protonated axial O atom + H3O+) U(V)(OH)2(H2O)5 | U(V)O2(H2O)5 (OS) + H3O+ a

∆G° (eV)a

species abundance (%)b

0.1226

99.1 0.9

0.4754

100 1 x 10-6

Assuming G° is equal to Total DFT energy (Table S1, SI), ∆G° is between an encounter complex and the thermodynamically most stable

encounter complex. The determination of ∆G° is based on mass balanced equations (i.e. inclusion of H2O molecules). b

Based on the Boltzmann distribution.



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Figure 3: Outer-sphere U-U encounter complexes pre- (a) and post-ET (b) for the thermodynamically favorable U(V) disproportionation pathway. Values represent bond distances (Å) of the oxygen atoms to the metal centers.

While earlier studies demonstrated that U(V) is indeed metastable, rate constants as slow as ~1 M-1 s-1 have been reported at very acidic pH values,19,

20, 24, 27

suggesting that U(V) could have significant

lifetimes under certain chemical conditions. Similar, in the crystal structure of FeUO4, two U(V) oxidation states were computed to be substantially more stable than disproportionation into U(VI) and U(IV).43 Nevertheless, there is a pervasive conception that because U(V) is metastable its chemistry is unimportant in uranium (geo)chemistry. The collective results suggest that this notion may possibly be erroneous and the lack of U(V) detection in many studies may have resulted from rapid U(V) oxidation arising from sampling issues or a lack of rigorous analysis,10 or simply because it was thought to be nonexistent.


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Table 4: Mulliken spin densities, thermodynamics, ET parameters and rate constants of the thermodynamically favorable U(V) disproportionation pathway for the outer-sphere encounter complex computed with the COSMO solvation model at standard conditions. Mulliken spin oxidation state/encounter complex density U

a

∆G°

U

U(VI)

0.00

U(V)

1.14

U(IV)

2.18

U(V)O(OH)(H2O)5 | U(V)O2(H2O)5 (OS) + H3O+

1.20

1.15

U(IV)(OH)2(H2O)5 | U(VI)O2(H2O)5 (OS) + H2O PCET

2.18

0.00

b

c

VAB

λI

d

λE

s-1

eV

-0.5356

0.00058

ket

0.95

1.43

3.4 x 103

a

Includes entropy and enthalpy contributions and these values are, therefore, different to the energy minima shown in Figure S3, SI.

b

Approximated using the relationship VAB(r)=VAB(r0)exp(-α(r-r0)) with average calculated VAB values from Table 2 and average corresponding metal-metal distances in pre-ET

complexes to estimate r0 and VAB(r0), and using α=1.9 as given in Zarzycki et al.41 along with the calculated U(V)-U(V) pre-ET distance of 5.483 Å as r. c

Calculated using the four-point method, as given in Rosso and Dupuis.36

d

Approximated using Marcus’ continuum model, using the calculated U(V)-U(V) pre-ET distance of 5.483Å and half of this distance as the two respective cavity radii, using bulk

water dielectric and optical constants.



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3.4 Reconciling computational and experimental results In contrast to Du et al.,16 there have been at least three experimental studies which have shown that U solution concentrations remain stable for relatively long periods of time in the presence of Fe(II).15, 17, 45 For example, it has been reported that U concentrations did not decrease significantly for 40 minutes in solutions at pH 7.5 containing 5 x 10-3 Fe(II) and 1 x 10-5 M U(VI).45 Similarly, in another study,17 it has been shown for a solution containing 1 x 10-3 M Fe(II) and 2 x 10-5 M U(VI) that U concentrations remained stable for 10 hr until concentrations decreased coincident with the formation of partiallyreduced U solid phases. Finally, Liger et al.15 have reported stable U(VI) concentrations over 3 days for solutions at pH 7.5 containing 1.6 x 10-4 M Fe(II) and 5 x 10-7 M U(VI). In all of these studies, substantial concentrations of Fe2+, Fe(OH)+ and UO2(OH)20 would be expected to be present leading to the formation of similar encounter complexes shown in Figure 2. Therefore, it would be predicted that rapid reduction to U(V) should proceed under these conditions. While the presence of aqueous U(V) in the studies of Zeng et al.45 and Taylor et al.17 cannot be ruled out as they used inductively-coupled plasma-mass spectrometry (ICP-MS), which is indiscriminate to oxidation state, the use of laser-induced fluorescence to measure aqueous U(VI) concentrations by Liger et al.15 would seem to counter the idea that the oxidation state of U in these studies was U(V). However, U(V) oxidation by molecular O2 is extremely rapid.24 While it is difficult to ascertain whether the solution samples analyzed by Liger et al.15 were protected from O2 during storage and analysis, the prevailing notion that U(V) disproportionation is rapid resulting in U(IV) precipitation probably would have precluded any thought that soluble U could have been present in the (V) oxidation state. As such, it is possible that reduction to U(V) occurred in all of these experiments and then remained in solution due to very slow disproportionation kinetics as a result of a lack of readily available H3O+ molecules to protonate the axial oxygens. Indeed, it would be of interest to redo studies similar to that of Liger et al.15 and compare total U and U(VI) concentrations measured by, respectively, ICP-MS and laserinduced fluorescence spectroscopy on temporal samples that have simply been kept anoxic. Noting the strong influence of solvent H+ on disproportionation kinetics,19-26 and assuming a first-order relationship to H+ concentrations,21, 22, 24-26 it is entirely plausible that the rate constant of homogeneous U(V) disproportionation at pH 7 - 8 could be five to seven orders of magnitude slower than that experimentally reported to occur at pH values < 2. The predicted stability of U(V) is not unprecedented as it has previously been shown that U(V) can remain as a stable surface species on magnetite for at least 56 days1 or as an aqueous UO2(CO3)35- complex for at least 14 days.46 Indeed, in earlier studies


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first exploring the existence of U(V), it was found that U(V) solutions could be prepared that were stable for a “very long time” between pH 2 - 3 before disproportionation commenced rapidly, presumably due to the autocatalytic effects of U(IV) polymerization.24 5. CONCLUSIONS The application of density functional theory (DFT) and Marcus theory to determine the thermodynamics and electron transfer kinetics of homogeneous U reduction by Fe(II) and U(V) disproportionation of environmentally-relevant monomeric U species suggests that only one electron reduction by Fe2+ is thermodynamically favorable and kinetically feasible, and this occurs via the monomeric hydrolysis species. The homogeneous one electron reduction of U(V) by Fe(II) is predicted to be thermodynamically unfavorable. Homogeneous uranium(V) disproportionation occurs only at low pH, via an outer-sphere PCET pathway and solvent H+ (i.e. H3O+) plays an important role in facilitating electron transfer, the latter being in agreement with that observed in experimental studies. Calculated homogeneous U(V) disproportionation rates are consistent with those observed at low pH, involving protonation of axial oxygens by solvent H+. U(V) is thus predicted to be an aqueous species with appreciable lifetime, and the cascade to equilibrium is by surface catalysis, either through heterogeneous reduction of sorbed U(V) by sorbed Fe(II) or heterogeneous U(V)-U(V) disproportionation. These results suggest that the U(V) oxidation state certainly has the potential to exist as a long-lived intermediate, requiring consideration in the aqueous redox chemistry of uranium. Instead of being a surface product, trace U(V) on or trapped in product Fe(III)/Fe(IV) solids may just be a residual from solution. Although heterogeneous ET pathways are known to accelerate U reduction, it should be noted that experimental evidence is accumulating that the one electron reduction of U(VI) and the chemistry of U(V) has the potential to impart a significant influence on the fate of U in the environment.1, 10-14, 46, 47 ASSOCIATED CONTENT Supporting Information Figure S1: Thermodynamic equilibrium speciation of 0.1 µM U(VI) and 200 µM Fe(II) between pH 3 to 7 as calculated with Visual MINTEQ version 3.1. Figure S2: DFT-optimized structures of the relevant U(VI), U(V) and Fe(II) monomeric species computed with use of the COSMO solvation model. Table S1: Thermodynamics of monomeric species, U(VI)-Fe(II) and U(V)-U(V) encounter complexes as computed by DFT with the COSMO model at standard conditions. Figure S3: Linear synchronous



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transit (LST) results for the one electron transfer from Fe(II) to U(VI) for the encounter complexes optimized with the COSMO solvation model involving UO2(OH)+ and UO2(OH)20. Table S2: Thermodynamics of monomeric species and UO2(OH)20 / Fe(H2O)62+ encounter complexes optimized by DFT in vacuo at standard conditions. Figure S4: in vacuo DFT-optimized structures of the U(VI)-Fe(II) encounter complexes for the second U(VI) hydrolysis species (UO2(OH)2(H2O)20). Figure S5: O-H interatomic distances of the DFT-optimized encounter complexes formed by UO2(OH)20 and Fe(H2O)62+ as optimized in vacuo or with the COSMO solvation model. Figure S6: DFT-optimized encounter complexes pre- and post-ET for Fe(II) reduction of U(V) to U(IV).

Figure S7: DFT-optimized

structures of: a) the inner-sphere U(V)-U(V) encounter and; b) the same complex with one axial O atom protonated.

Figure S8: Outer-sphere U-U encounter complexes pre- and post-ET for the

thermodynamically unfavorable U(V) disproportionation pathways. Figure S8 is followed by Cartesian atomic coordinates for all COSMO optimized pre- and post-ET encounter complexes and intermediate structures for which electron transfer rates were calculated. ACKNOWLEDGEMENTS Richard Collins acknowledges the Australian Research Council for funding of a Future Fellowship (FT110100067) and the Australian-American Fulbright Commission for a Senior Scholarship in Nuclear Science and Technology. Kevin Rosso acknowledges support from the U.S. Department of Energy’s (DOE) Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, & Biosciences (CSGB) Division through its Geosciences program at Pacific Northwest National Laboratory (PNNL). The computations described in this paper were performed using either EMSL, a national scientific user facility sponsored by the U.S. DOE Office of Biological and Environmental Research and located at PNNL or the Leonardi Engineering Research Computing Cluster, UNSW Australia. REFERENCES 1. Ilton, E. S.; Boily, J.-F.; Buck, E. C.; Skomurski, F. N.; Rosso, K. M.; Cahill, C. L.; Bargar, J. R.; Felmy, A. R., Influence of dynamical conditions on the reduction of UVI at the magnetite-solution interface. Environ. Sci. Technol. 2010, 44, 170-176. 2. Chakraborty, S.; Favre, F.; Banerjee, D.; Scheinost, A. C.; Mullet, M.; Ehrhardt, J.-J.; Brendle, J.; Vidal, L.; Charlet, L., U(VI) sorption and reduction by Fe(II) sorbed on montmorillonite. Environ. Sci. Technol. 2010, 44, 3779-3785. 3. Privalov, T.; Schimmelpfennig, B.; Wahlgren, U.; Grenthe, I., Reduction of uranyl(VI) by iron(II) in solutions: An ab initio study. J. Phys. Chem. A 2003, 107, 587-592.


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Mechanisms and Rates of U(VI) Reduction by Fe(II) in Homogeneous

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