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Toward a Reliable Energetics of Adsorption at Solvated Mineral Surfaces: A Computational Study of Uranyl(VI) on 2:1 Clay Minerals Alena Kremleva, Sven Krueger, and Notker Roesch J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b09902 • Publication Date (Web): 07 Dec 2015 Downloaded from http://pubs.acs.org on December 15, 2015

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The Journal of Physical Chemistry

Toward a Reliable Energetics of Adsorption at Solvated Mineral Surfaces: A Computational Study of Uranyl(VI) on 2:1 Clay Minerals

Alena Kremleva,a Sven Krüger,a Notker Röscha,b,c,* a b

c

Department Chemie, Technische Universität München, 85747 Garching, Germany Catalysis Research Center, Technische Universität München, 85747 Garching, Germany Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore

Abstract

We developed an efficient computational protocol for studying adsorption at solvated solid surfaces by a quantum mechanical method. We combine first-principles molecular dynamics at low temperature with simulated annealing and optimization steps to allow relaxation of the solvent structure without strongly perturbing the geometry of adsorption complexes. On the example of uranyl(VI) adsorption at the (110) edge surface of smectite minerals we show by density functional calculations using periodic slab models that our approach yields more reliable energies than direct optimization. In this way we were able to identify the preferred adsorption complex at this surface. By decomposing the complex formation energies into deprotonation energies of the surface and adsorption energies as well as by a charge analysis of the adsorption sites, we rationalize this result as well as the composition and the structures of less stable adsorbed species. Our computational results are compatible with available experimental structural data of uranyl(VI), adsorbed at montmorillonite.

* Corresponding author. Email: [email protected]

1

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1. Introduction

The interaction of ions at solid-liquid interfaces, especially with solvated mineral surfaces, is of general importance in geochemistry, soil, and environmental science. An important application is the risk assessment of potential deep geological repositories for radioactive waste that consists to a large extent of actinides.1,2 In this context, a common strategy for predicting the distribution of cations of radioactive elements between solid and liquid phases in the environment is thermodynamic modeling3,4 where one typically fits experimental data by a model with various parameters, e.g., complexation constants for species in solution and adsorbed at various sites on the surface.4 The parameters derived from such models are then used for describing more complex cases at relevant conditions. Yet, the quality of such modeling depends very much on the microscopic information available, e.g., knowledge about adsorbed species and the surface sites they occupy as well as the corresponding sorption energies and preferred reaction pathways. In part, such information on the atomic scale can be gained by spectroscopic methods, like extended Xray absorption fine structure (EXAFS), time-resolved laser fluorescence spectroscopy (TRLFS), Fourier transform infrared spectroscopy (FTIR), and resonant anomalous X-ray reflectivity (RAXR).2,3,5-9 Computational modeling offers an attractive complementary approach to basic information for thermodynamic modeling.10-17 A major complication of such modeling is the proper treatment of surface solvation for which various methods are available. Classical molecular dynamics (MD) allows investigating model systems with many thousands of molecules of water, e.g., as used for studying solvation of clays,18,19 swelling20 and adsorption, such as the interaction of U(VI) with the basal surfaces of 2:1 clay minerals.11 Classical molecular dynamics is based on a force field with empirical parameters and in general is not appropriate for describing processes where bonds are formed or broken; such processes are important on edge surfaces of clay minerals as water may dissociate and protons may rearrange dynamically.21 Therefore, quantum chemical (QC) modeling14,15,16,17 as well as first-principles MD (FPMD) calculations13,22 are applied more commonly in studies of actinide adsorption at mineral surfaces. Early QC studies modeled adsorption on bare surfaces without accounting for surface solvation.23-25 Later on, a water monolayer adsorbed on the surface was included in QC models.26,27 Describing surface solvation in such a way was found important when one addressed edge surfaces of clay minerals whereas solvation effects were minor when treating basal surfaces.14,15,22 To the best of our knowledge, there is only one Car-Parrinello MD study on actinide 2


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adsorption for the example of U(VI) on the solvated (001) gibbsite surface;13 it addressed the free energy profile of the transition between inner- and outer-sphere adsorption modes. Thus far, this computational approach is the best one for estimating adsorption energies, although computationally very costly; simulations of in total ~150 ps were required to establish a single profile.13 More often quasi-static DFT calculations, including geometry optimization, are invoked.14,15,17,23,28 However, treating solvent molecules explicitly leads to uncertainties in energies due to the somewhat arbitrary initial structure of the water overlayer.29 Recently we studied the adsorption of U(VI) on edge surfaces of 2:1 clay minerals.29 Comparing structural parameters to experiment, we were able to identify favorable adsorption complexes.29 However, this identification was only tentative in view of uncertainties in the calculated energies. The relative energies of various adsorption complexes varied by up to 100 kJ mol-1 for the same surface; no clear trends were noticeable.29 More reliable energies of adsorption complexes should be achievable by a carefully equilibrated water overlayer. In the present work, we are suggesting a low-temperature partial equilibration (LTPE) procedure for arriving at the structures of various adsorption complexes and for calculating the corresponding adsorption energies. Compared to a costly full FPMD treatment, this procedure is efficient enough to allow a systematic study of various adsorption complexes at several sites of mineral surfaces. In this way, we extended our previous work29 specifically with respect to energy aspects of adsorption: (i) we suggest an approximate equilibration procedure for solvated surfaces as a novel approach to improved energies of adsorption and (ii) we rationalize the resulting energy preferences for adsorption at specific sites with the help of surface deprotonation and a charge analysis of the various sites. As a case study, we examine the adsorption of uranyl UO22+ on (110) edge surfaces of three 2:1 model clay minerals.

2. Model Surfaces of 2:1 Clay Minerals and Adsorption Sites

As we study the same adsorption complexes as in our previous work, we only briefly describe the models used; for details, see Ref. 29. Dioctahedral clay minerals show a layered structure where an octahedral Al sheet is sandwiched between two tetrahedral Si sheets. Negatively charged defects, typically cationic substitutions of Al3+ by Mg2+/Fe2+ or of Si4+ by Al3+, are neutralized by interlayer cations, e.g., Na+ and Ca2+.30 The interlayer cations may bind water ligands and in this way increase the interlayer spacing (swelling).20 We examined

model

clay

minerals

of

the

stoichiometric

formula 3



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Naq(Si4-nAln)(Al2-mMgm)O10(OH)2, where q e is the (negative) charge of the mineral layer per formula unit (f.u.) of the layer compensated by q sodium cations; n and m are the numbers of substitutions in tetrahedral and octahedral sheets per f.u., respectively. We modeled q = 0.25 e by means of a single substitution per four f.u. In the present work, we use the optimized bulk structures and the same models of edge surfaces as previously.29 In the following, we consider adsorption on (110) surfaces. The structures of six model surfaces are shown in Fig. 1. The pyrophyllitic neutral model (Fig. 1a) does not include any substitutions. Figs. 1b–d present beidellitic models with tetrahedral substitutions of Si4+ by Al3+ resulting in Na(Si15Al)Al8O40(OH)8. Figs. 1e and 1f show montmorillonitic models with an Al3+ ion substituted by Mg2+ in the octahedral sheet, resulting in NaSi16(Al7Mg)O40(OH)8. Subsurface substitutions, i.e., in the second outermost cation layer from the surface (Fig. 1, column 1), do not directly affect the surface groups.29 Edge surfaces with subsurface substitutions exhibit surface groups of the types SiOH, AlOH2+1/2, AlOmSi-1/2 (a mixed center Om connects Al and Si cations), and Al2OH (Figs. 1a, c, e). The formal charges, noted as upper indices, of the surface oxygen centers Os involved, derived from Pauling’s bond valence theory,31 are helpful for interpreting the results.32 A substitution directly at the surface affects the surface groups and sometimes even leads to a rearrangement of the protons on the surface.29 The resulting adsorption sites involving Os centers coordinated to the substituted cation are defined as substituted sites. When an Al cation is substituted for Si (Fig. 1b), we determined that a proton of the AlOH2+1/2 group moves to the O center connecting two Al ions to form an Al2OH+1/4 group.29 No other surface substitution affects the proton arrangement on the surface (Figs. 1d, f). To account for solvation, the model edge surfaces were covered by 16 H2O molecules per unit cell. When modeling the solvation of adsorbed uranyl, the same number of water molecules was used in addition to three aqua ligands in the first solvation shell of uranyl. We focused our models on bidentate inner-sphere adsorption complexes, as postulated from experiments.6,33 We examined adsorption at aluminol, silanol, and mixed sites (Fig. 2). Aluminol (silanol) sites include only aluminol (silanol) groups. Mixed sites are formed by an aluminol group and a neighboring silanol group, AlO(H)-SiO(H). For a beidellitic substitution on the surface (Fig. 2b), we considered only sites of aluminol type. They can be classified as tetrahedral AlOO(t) or octahedral sites AlOO(o), according to the position of the Al cation in the tetrahedral or octahedral sheet, or as long-bridge sites AlOH-AlO and AlO-AlOH, involving Os centers of two neighboring Al cations (Fig. 2b). For a montmorillonitic surface substitution, an Al cation of an adsorption site is substituted by a 4


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Mg center (Fig. 2c). 3. Computational Method

We carried out first-principles density functional calculations on supercell slab models of smectite edge surfaces, using the plane-wave based Vienna ab initio simulation package (VASP).34-38 We applied the GGA (generalized gradient approximation) exchangecorrelation potential as parameterized by Perdew and Wang (PW91).39 The effect of core electrons was accounted for by the projector-augmented wave (PAW) method, as implemented in VASP.40,41 Scalar relativistic effects were incorporated in the PAW potential via mass-velocity and Darwin corrections.42 For the surface models we adopted an energy cutoff of 400 eV. Integrations over the Brillouin zone were carried out using the Γpoint only. In geometry optimizations the total energy was converged to 10–4 eV and forces acting on ions were required to be less than 2×10–4 eV/pm. To arrive at a pre-equilibrated arrangement of the 16 water molecules used to model surface solvation, we invoked FPMD according to the following simulated annealing protocol. The system was first equilibrated for several ps, using the NVE microcanonical ensemble and adjusting the temperature to 200 K every 50 steps of 0.2 fs. Next the system was cooled down to 0 K by decreasing the temperature linearly every 50 steps. The rather low starting temperature was chosen (i) to preserve the structures also of metastable adsorption complexes (not only of the most stable complexes), but (ii) to allow nevertheless a rearrangement of the hydrogen bond network of the solvation layer. In this way, one also avoids the evaporation of water molecules into the space between the slabs. The plane-wave energy cutoff was set to 300 eV. To check the degree of equilibration, an optimization step was carried out after each picosecond of the NVE run. If the total energies of two subsequent optimizations agreed within 10 kJ mol-1, then the system was regarded as sufficiently equilibrated. The equilibration phase took 3–6 ps, typically 4 ps. As final stage of the protocol, the pre-equilibrated system was optimized with the accuracy parameters given above. Some examples of the “equilibration” procedure, as we refer to the complete protocol for simplicity, are given in Section S1 of the Supporting Information (SI). The program VASP provides compensating corrections for charged unit cells of cubic lattices only.43 For our calculations of uranyl adsorbed at edge surfaces, we used neutral unit cells.14,29 Restricting our study to sites with an overall charge of -2 e, we removed two protons from neighboring groups at the surface to compensate the charge of the adsorbed uranyl ion (Fig. 2). Thus, by its very nature, an adsorption site of uranyl is two-fold deprotonated. Sometimes it will be convenient to refer also to the protonated variant of the involved surface group(s) as “site”. From the context it will always be clear when the latter 5



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form of a site is implied. For all adsorption complexes studied we calculated complex formation energies Eform defined as the exchange of two protons at the mineral surface by the uranyl ion: Surface-(OH)2 + UO2(H2O)52+ → Surface-(O)2UO2(H2O)3 + 2 H3O+

(1)

The calculation of formation energies is based on neutral extended systems only, circumventing the problem of charged unit cells. The solvation energy of the initial uranyl complex and the resulting hydronium ions were determined by means of a polarizable continuum model44 as in our earlier studies.29 The adsorption energy Eads of a uranyl aqua complex on a deprotonated surface site is the reaction energy of the process Surface-(O–)2 + UO2(H2O)52+ → Surface-(O)2UO2(H2O)3 + 2 H2O

(2)

As Eq. (2) implies a charged unit cell, it cannot be used directly. Instead, we determine the adsorption energy of uranyl at various sites as the difference Eads = Eform – Edepr

(3)

where the site deprotonation energy Edepr is defined as the energy change of the reaction Surface-(OH)2 + 2 H2O → Surface-(O–)2 + 2 H3O+

(4)

We evaluate Edepr in an approximate way as described in Section 4.2.2. 4. Results and Discussion

We started the LTPE protocol with previously optimized structures29 of the adsorption complexes (Section 2). Preferentially we treated complexes of five-fold coordinated adsorbed uranyl. For the sites AlOmOH and SiOmO, we inspected the adsorption of [UO2(OH)]+ as we were unable to optimize UO22+ as adsorbate on these sites.29 In the following subsections we first discuss the species determined (Section 4.1) and then turn to surface complex formation energies and their interpretation (Section 4.2). We divide these formation energies into the energy for deprotonating the solvated surface without adsorbate (Section 4.2.2) and the adsorption energy proper (Sections 4.2.3). Finally, we compare the resulting structure parameters to our previous computational results (Section 4.3) and to available experimental data (Section 4.4). 4.1. Adsorbed species

Table 1 lists optimized initial as well as equilibrated and subsequently optimized final species for various sites and surface models. We observe two types of deviations from fivecoordinated uranyl – hydrolysis and change of coordination number. Hydrolyzed species were optimized already earlier29 on AlOmOH and SiOOm sites, and they were used here as initial structures for equilibration. The more accurate LTPE approach confirms these species 6


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with the only exception of the substituted AlOO(t) site, where UO22+ resulted as adsorbate after equilibration. A change of coordination number as a result of equilibration appears commonly for adsorption on substituted sites of montmorillonite. For the unsubstituted sites we found the same adsorbed species before and after equilibration, with the only exception of UO22+ on the AlOH-SiO site which changes the CN from 5 to 4. For the montmorillonitic model we managed to equilibrate both CN = 5 and CN = 4, the latter being 16 kJ mol-1 more favorable. In our previous study we noticed that CN = 4 is characteristic for mixed sites with longer Os-Os distances.29 This preference of CN = 4 is confirmed by applying the equilibration protocol for the adsorption on AlOH-SiO sites, but not on AlO-SiOH, where CN = 5 is preserved after equilibration. In the case of adsorption on AlO-SiOH sites, 3–5 ps of equilibration possibly do not suffice for achieving a change in coordination number. For the optimized five-coordinated adsorption complexes29 on AlOH-SiO sites the angle Os-UOs is 77° on average while it amounts to 73° for AlO-SiOH sites which is very close to the ideal O-U-O angle of 72° for five-coordinated uranyl. Thus, the adsorption complex on the AlOH-SiO site is expected to have a higher propensity for CN = 4 than the one on the AlOSiOH site. Substituted sites commonly showed changes of the adsorbed species compared to the results of simple optimization (Table 1). For the beidellitic model with surface substitution, the initially adsorbed uranyl on the AlOO(o) site converged to [UO2(OH)]+ on the AlOOH(o) site; a proton of a water ligand of uranyl moved to form an AlOH surface group. The adsorption complexes on aluminol sites generated by substitution, AlOH-AlO and AlOAlOH, both converged to four-coordinated uranyl. For the montmorillonitic model with a Mg substitution on the surface, the complexes on MgOmO and MgOmOH sites also converged to CN = 4 (Table 1). Already in our earlier study, we noted CN = 4 for the site MgOmO.29 Mg-Os bonds are longer than the corresponding Al-Os bonds. Therefore the distance Os-Os = 301 pm of the adsorption sites MgOmO(H) is considerably longer than OsOs of unsubstituted AlOmO(H) sites, 260–270 pm. A longer Os-Os distance of the adsorption site increases the propensity of CN = 4 for adsorbed uranyl (see above). In our earlier study29 we first optimized the adsorption complexes at unsubstituted sites and then optimized again after having placed the substitution at the surface position to obtain the adsorption complexes on substituted sites. Such a procedure aimed at getting comparable energetics by disturbing the solvation layer as little as possible. As a result, the adsorbate and the solvation layer did not change much due to surface substitution, and the species found on the substituted sites were the same as on unsubstituted sites. The 7



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equilibration protocol introduces a perturbation that suffices for leaving this local minimum. 4.2. Energies of adsorption 4.2.1. Formation energies of adsorption complexes

We start our discussion of energy aspects of adsorption with the formation energies Eform, Eq. (1) (Fig. 3; Table 2), which subsequently will decomposed into the deprotonation energy of the adsorption site and the adsorption energy proper; see Sections 4.2.2 and 4.2.3. All formation energies are endothermic (positive) as they include the two-fold deprotonation of the surface [Eq. (1), Table 2]. To show the effect of LTPE

on the

formation energies, we compare two sets of data: (i) Eform from our earlier static DFT calculations (Fig. 3a and SI of Ref. 29) and (ii) as calculated here via the equilibration protocol (Fig. 3b). In contrast to the almost randomly distributed formation energies of the first set (Fig. 3a), the Eform values calculated after pre-equilibration exhibit clear trends (Fig. 3b). The adsorption on the pyrophyllitic model is less favorable compared to beidellite and montmorillonite, at least by 24–34 kJ mol-1 for aluminol and silanol sites and by 9 kJ mol-1 for the mixed sites (Fig. 3b). The formation energies of the same complexes at the same unsubstituted adsorption sites of beidellitic and montmorillonitic models (i.e. substitution in a subsurface layer, see Section 2) are rather close; they differ by 10 kJ mol-1 on average (Fig. 3b, Table 2). Adsorption on substituted sites is more favorable compared to the corresponding unsubstituted sites with the single exception of adsorption on the AlOO(t) site of beidellite (Fig. 3b, Table 2). The rather high deprotonation energy of that site, compared to the unsubstituted SiOOm site, induces this exception; see Section 4.2.2. Interestingly, the adsorption on the AlOH-SiO site is most favorable for all surface models (Fig. 3b, Table 2). The second most stable type of complexes, at SiOOm, exhibits Eform values which are at least 27 kJ mol-1 higher in energy (Table 2). Complexes at AlOSiOH are the least favorable for all surface models. These trends corroborate the reliability of our computational procedure for achieving more accurate energies. Thus, we confidently conclude that, independent of the mineral model used, the most stable adsorption complexes on (110) surfaces with reference to the protonated surface of dioctahedral smectites are those at the AlOH-SiO site or analogous substituted sites. 4.2.2. Deprotonation energies

To determine adsorption energies, (Eq. 3), we first need to estimate the site deprotonation energies Edepr, Eq. (4). We circumvent the problem of charged surface systems in Eq. (4) by evaluating model site deprotonation energies instead: 8


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model model model E depr = E depr (1) + E depr (2)

(5)

In the first step involving only neutral systems, two protons are moved from the surface to the “bottom” of the slab model: model E depr (1) :

Surface-(OH)2 → (H+)2-Surface-(O–)2

(5a)

In the second step, the protons from the bottom of the slab are released to the solution: model E depr (2) : (H+)2-Surface-(O‾)2 + 2 H2O → Surface-(O–)2 + 2 H3O+.

(5b)

As the final state of the first step, Eq. (5a), we selected for each surface the same site at the model bottom of the surface slab models; therefore, E depr (2) is approximately constant for a given

surface. model Consequently, for incorporating the effect of E depr (2) , it suffices to determine the

absolute deprotonation energy of a single site. We chose the one with the lowest model model deprotonation energy. Again, it is not possible to calculate directly the value of E depr (2) as

Eq. (5b) involves charged surface systems. As an alternative, we resorted to deprotonation energies of single surface groups as recently determined by an accurate FPMD approach and represented there via pKa values.45 For using these data, we assumed that the reaction energy for the two-fold deprotonation of each mineral surface can approximately be equated with the sum of the (single) intrinsic deprotonation energies of the corresponding surface groups. So-called “intrinsic” deprotonation energies are ideal deprotonation energies of surface groups with reference to the neutral surface while real deprotonation events of all groups, but that with the lowest deprotonation energy, take place when other groups are already deprotonated. In this way we approximately corrected our model deprotonation energies and we arrive at model realistic estimates E depr of absolute site deprotonation energies, Eq. (5). In the following we

comment on three aspects of this procedure. (i) In the final state for determining the model deprotonation energies, we always placed each of the two protons at the same Om centers at the fixed (unrelaxed) bottom of the slab model, specifically at positions optimized on the example of two deprotonated AlOH2 groups. (ii) The geometry optimization of a partially deprotonated surface leads to proton rearrangements so that only more stable protonation states can be obtained. For example, two-fold deprotonation of an AlOH2 surface group and subsequent optimization of the surface results in a re-protonation of the highly charged AlO group by a proton from a neighboring SiOH group. To overcome this difficulty we calculated approximate 9



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model deprotonation energies E depr (1) by restricted optimizations, relaxing only the surface O(H)

groups from which the protons had been removed (Table 2). For comparison we also determined deprotonation energies without structure relaxation. Both approaches yield similar trends, as discussed in Section S2 of the SI. (iii) The energy shift for estimating absolute values from calculated site deprotonation model energies E depr (1) for the three surface models without surface substitutions is 62 kJ mol-1

(Table S3 of the SI), i.e., twice the energy required for deprotonating an AlOH2 group according to the FPMD calculations.45 Among all mineral models without surface substitution, the AlOH2 surface group was determined to show the lowest pKa value, 5.5.45 The energy shift for surfaces with surface substitution for the sites on the beidellitic model is estimated at 89 kJ mol-1 and for the sites of the montmorillonitic model at 77 kJ mol-1; see Table S3 of the SI. A detailed table of relevant pKa values and the derived reference deprotonation energies is given in Table S3 of the SI. model The resulting model deprotonation energies E depr of all adsorption sites studied are

collected in Table 2. On the unsubstituted surfaces, the sites AlOmOH and AlOH-SiO exhibit the lowest deprotonation energies of all surface models groups show an acidity constant of ~8.45 Thus, the AlOH2+1/2 group most probably will deprotonate already at acidic pH, followed by SiOH, whereas AlO-3/2 surface groups are, the second lowest value was determined for the site SiOOm. To classify the sites at unsubstituted surfaces, one may refer to the intrinsic pKa values of various OH groups on the (110) surfaces of 2:1 clay minerals.45 AlOH2+1/2 surface groups on (110) surfaces exhibit the lowest pKa, ~5.5, while silanol expected to occur much less likely at environmental conditions due to their high pKa. According to these considerations, AlOmOH, AlOH-SiO, and SiOOm sites are most likely on unsubstituted (110) surfaces at common pH conditions. Concomitantly their deprotonation energies are always lower than those of all other sites (Table 2). The acidities of the substituted surface groups were determined higher, by 2–9 pKa units, than those of the corresponding aluminol and silanol surface groups.45 This is also reflected in the data of Table 2. Deprotonation energies of substituted sites are always higher than those of the analogous unsubstituted sites, e.g., 111 kJ mol-1 vs. 75 kJ mol-1 and 117 kJ mol-1 vs. 62 kJ mol-1 for AlOH-SiO sites and their substituted analogues on beidellite and montmorillonite, respectively. As mentioned, the energies required for creating the sites AlOmO and AlO-SiOH by two-fold deprotonation are the highest, as the same aluminol group is deprotonated in two consecutive events. Also the substituted site AlOO(t) of the beidellitic model exhibits a very 10


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high deprotonation energy (Table 2). To create that site two aluminol groups, AlOH and Al2OH, have to be deprotonated (Figs. 1b, 2). Both groups result from surface substitution of Si4+ by Al3+ which leads to enhanced deprotonation energies. The intrinsic pKa of these groups have been determined to 17.5 and 10.2, respectively, compared to 8.3 and 1.7 for the corresponding unsubstituted SiOH and OmH surface groups.45 Thus, the formation of the site AlOO(t) seems unlikely, in agreement with the rather high deprotonation energy, 158 kJ mol-1, estimated in the present work (Table 2). This relatively high deprotonation energy may be the reason for the large complex formation energy mentioned before (Section 4.2.1, Fig 3b). Although our approximate site deprotonation energies are determined without solvent relaxation, they correctly reproduce the expected trends and agree with trends expected from calculated intrinsic pKa values45 of single surface groups. 4.2.3. Adsorption energies

Formation energies, Eq. (1), give the relative energy of uranyl and proton binding to the surface. They are useful, e.g., for comparing the same type of complexes on various adsorption sites of a given mineral. In contrast, the interaction energy Eads, Eq. (2), between the adsorbate and the deprotonated surface can be used to assess the inherent strength of the bond of an adsorbate at a surface. The adsorption energies Eads at analogous sites of beidellite and montmorillonite with subsurface substitutions are rather similar. The corresponding Eads values for pyrophyllite are significantly higher (Table 2), indicating a weaker binding on this neutral substrate. On beidellite and montmorillonite surfaces with subsurface substitutions, the most favorable adsorption is calculated for the AlOmO sites, -17 kJ mol-1 and -45 kJ mol-1, followed by the sites SiOOm, AlOH-SiO, and AlO-SiOH, with Eads values of -10 mol-1 to 29 kJ mol-1. On pyrophyllite the most favorable adsorption occurs at the sites AlOH-SiO with Eads = 29 kJ mol-1; adsorption at all other sites is notably less favorable, with Eads = 69–121 kJ mol-1. For all mineral models, substituted sites are calculated more favorable than their unsubstituted analogues (Table 2). Many Eads values are positive, indicating that adsorption is an endothermic process, hence unfavorable, even at a doubly deprotonated surface. Note, however, that the absolute values of the resulting adsorption energies are uncertain to some degree. Besides the approximate way of estimating deprotonation energies (Section 4.2.2), another important uncertainty is the solvation correction for molecular species in Eq. (1), which is estimated at 46 kJ mol-1 using a polarizable continuum solvation model (PCM).23 This model yields the solvation energy of the hydronium ion at -376 kJ mol-1, while the experimental value is -430 11



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kJ mol-1.46 With the experimental value of the solvation energy of H3O+ in Eq. (1), all energies Eads shift by -108 kJ mol-1, thus turning exothermic for all sites studied, except for the site AlOmOH on pyrophyilite. As an aside, we briefly comment on the solvation energy of uranyl. The experimental value is not accurately known. Results range from -1225 kJ mol-1 to -1827 kJ mol-1;47-49 see the derived Gibbs free energies as collected in Table 5 of Ref. 50. Based on the latest experimental solvation energy of uranyl,49 -369±15 kcal mol-1, the solvation energy of UO2(H2O)52+ is estimated at -724±63 kJ mol-1 while our calculated result is -799 kJ mol-1. Together with the experimental solvation energy of H3O+ this yields a rough estimate of the solvation correction of the molecular species in Eq. (1), -136±63 kJ mol-1. Compared to the PCM value of 46 kJ mol-1, that solvation correction shifts all formation energies by -182 kJ mol-1, rendering most of them endothermic. However, the relatively large uncertainty of 63 kJ mol-1 makes a reliable estimate of solvation energies based on experimental results difficult. For consistency, we apply a solvation correction derived from PCM calculations, 46 kJ mol-1. The binding of a uranyl ion to a clay mineral surface can be expected to have a notable ionic character. Thus, the adsorption energy is expected to correlate with the charge of the adsorption site. As an example, we compare the sites AlOmOH and AlOmO with formal charges of -1 e and -2 e, respectively. Adsorption on AlOmO sites is always more favorable than on AlOmOH sites, with adsorption energies of 69 kJ mol-1 vs. 121 kJ mol-1, -17 kJ mol-1 vs. 90 kJ mol-1, and -45 kJ mol-1 vs. 81 kJ mol-1 for pyrophyllite, beidellite, and montmorillonite models, respectively (Table 2). To corroborate the ionic character of uranyl adsorption, we inspected the correlation between adsorption energies and charges of the adsorption sites. In previous studies29,32 we used Pauling31 charges of the oxygen centers of the various surface groups, but here we employed a specifically designed scheme of effective charges that, instead of formal valences and bond strength values as in the Pauling scheme, combines Bader charges51 of the oxygen centers with an empirical measure, borrowed from the bond-valence method,52 of the strengths of the involved bonds of the oxygen centers. For details, see Section S3 of the SI. These novel effective charges of the oxygen centers (Table 2) allow one to differentiate groups that are characterized by identical Pauling charges. The total charges of unsubstituted sites on beidellite and montmorillonite tend to be more negative, by up to 0.22 e, than those of their analogues of pyrophyllite (Table 2). The site charge is always slightly more negative for substituted sites. The substitution on the montmorillonitic surface changes the total charge qtot of the AlOmO(H) sites by about -0.2 e, while the changes of qtot of all 12


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other substituted montmorillonitic sites do not exceed -0.07 e (Table 2). The beidellitic surface substitution renders the negative charge of unsubstituted sites more negative by 0.1– 0.2 e. The general trend of the qtot values correlates with the trend of the adsorption energies. Adsorption of uranyl on montmorrilonite and beidellite is more favorable (as charges are more negative) than on pyrophyllite and the substituted surface sites are more favored compared to unsubstituted ones. Fig. 4 illustrates the weak correlation with R2 = 0.56 between the site charges and the corresponding adsorption energies. The unsubstituted sites correlate with R2 = 0.53, while substituted sites exhibit R2 = 0.46. The weak correlation may in part be due to the approximate nature of estimating site deprotonation energies. Other factors could be covalent contributions to the uranyl surface bonds. The trend lines in Fig. 4 show that adsorption on substituted sites is ~30 kJ mol-1 more favorable compared to adsorption at unsubstituted sites, concomitant with the more negative charges of the former sites. Two factors, easy deprotonation and a strong negative charge of the resulting adsorption site, lead to the most favorable adsorption complexes on (110) smectite surfaces. Table 2 shows that the sites AlOmOH and AlOH-SiO and their substituted analogues exhibit the lowest deprotonation energies of all surface models. However, the effective charges of the AlOH-SiO sites are ~0.3 e more negative than those of the AlOmOH sites. This difference of charge is less than expected, as the AlOH-SiO site is locally two-fold deprotonated, but the AlOmOH site only singly deprotonated (Fig. 2). This difference allows one to rationalize the energy preference for adsorption at AlOH-SiO sites (Fig. 3b). 4.3. Structural parameters of uranyl adsorption complexes

In adsorbed uranyl ions, the uranium center remains in oxidation state (VI). Bader charges calculated for the UO2 moiety vary between 0.96 and 1.16 e, close to the charge in the corresponding aqua ion, 1.24 e. Only a slight bending is observed for adsorbed UO2 moieties; the Ot-U-Ot angle is always larger than 170°. Therefore, the adsorption complexes described are properly referred to as adsorbed uranyl(VI) ions, bound to surface O centers. In our earlier study29 we concluded that the main structural parameters of adsorption complexes on smectite edge surfaces do not depend on the variant of the mineral, but mainly on the surface groups of the adsorption site.29 The ionic character of uranyl-surface binding also implies a correlation between the charges of the surface groups and the corresponding bond lengths U-Os; such a correlation was suggested earlier based on formal Pauling charges.32 In Fig. 5 we present the correlation of U-Os values of the various adsorption complexes with the effective charges of the Os centers; see Figure S3 of the SI for the correlation with the Pauling charges. The R2 value of the correlation with the Pauling 13



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charges is 0.79. The correlation is slightly better, R2 = 0.83, for the effective charges (Fig. 5). This agreement supports our procedure of estimating the effective charges and the chemical reliability of the results. Both R2 values are smaller than the value R2 = 0.92 determined earlier for various smectite edge surfaces.32 Recall that in Ref. 32 only more favorable adsorption complexes were taken into account, whereas we consider here all complexes studied. The structural parameters of adsorption complexes on a given unsubstituted site at various mineral models are, as shown earlier,29 very similar for results obtained by optimization alone; see Section S3 of the SI. Thus, structural parameters of the same species at an unsubstituted site of pyrophyllitic, beidellitic, and montmorillonitic mineral models can be reliably averaged for further analysis (Table 3). In Table S4 of the SI, we also compare these averaged bond distances to corresponding averaged values as derived earlier by optimization.29 Differences in geometry between both approaches are small. The terminal uranyl bonds U-Ot almost do not change. The average equatorial distances U-Oeq change by at most 2 pm, other distances change by 5 pm at most (Table S4 of the SI). Notable structure changes are determined for adsorption complexes at substituted sites when one compares LTPE results to those of direct optimization as in these cases commonly changes of the coordination number are obtained; see Table 1 and Section 4.1. Nevertheless, the main trends of adsorption on substituted sites compared to unsubstituted ones as obtained from an analysis of optimized structures29 without equilibration still hold (Table 3). The U-Os bonds to the surface O centers attached to substituted cations shorten significantly, by up to 25 pm, due to the increased charge of the corresponding surface O centers (Table 3). As a result of these shorter and thus stronger bonds to the surface, the terminal uranyl bonds U-Ot elongate by up to 3 pm and U-Al/Si distances shorten in most cases (Table 3).29 In line with this interpretation, only small changes of bond lengths of less than 5 pm (Table 3) are calculated for the substituted sites MgOH-SiO and MgO-SiOH, which exhibit only a marginal increase of negative charge of 0.03 e (Table 2). For more details, see the discussion of geometries in Ref. 29. 4.4. Comparison with experiment

To the best of our knowledge, no EXAFS experiments on the adsorption of U(VI) on pyrophyllite or beidellite are documented in the literature. Rather, EXAFS data for comparing the present results to experiment are available only for montmorillonite (Table 3).3,6,53,54 EXAFS experiments have been carried out on clay particles exposing various surface orientations. Although at a pH > 4 uranyl is assumed to adsorb mainly as inner-

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sphere complex at the reactive edge surfaces of montmorillonite,3,6,53,54 sorption at ionexchanged sites in the interlayer space or at basal faces cannot be excluded. EXAFS averages over all complexes in a probe, whereas we treated only the exemplary ideally terminated (110) edge surface. Therefore one does not expect that our results cover the whole spectrum of possible surface complexes on montmorillonite29 as would be necessary for reproducing the EXAFS results. On the other hand, all our results for the various models of smectite surfaces are relevant in this comparison because they can be regarded as local models of montmorillonite, including subsurface as well as surface substitutions at octahedral and, to a small extent, also tetrahedral positions. Thus, in the following we regard our results for montmorillonitic models as particularly relevant, whereas pyrophyllitic and beidellitic models cover the less important features of unsubstituted sites of montmorillonites of low layer charge and the less common tetrahedral substitutions. From our comparison we exclude experimental data sets3,6,53,54 that show adsorbed uranyl carbonato complexes (U-C distance resolved in EXAFS) or adsorption of multinuclear complexes and precipitation (U-U distance resolved). The measured U-Ot bond lengths of adsorbed uranyl are 178–180 pm, featuring an elongation by 2–4 pm compared to the solvated UO22+ ion (Table 3). U-Oeq distances vary between 234 pm and 239 pm and are shorter than for the solvated uranyl ion (241 pm, Table 3).55 The corresponding CN varies between 4 and 6 for adsorbed complexes and equals 5 for the solvated ion. As we have shown earlier,29,56 U-Oeq correlates with the coordination number of uranyl. Thus, the experimentally observed shortening of U-Oeq points to a decreased CN. As CN = 5 is established for the solvated ion, for adsorption complexes one expects CN = 4–5, rather than CN = 5–6 as measured. In some EXAFS studies3,6,54 two shells of equatorial U-O distances, ~230 pm and ~248 pm, were resolved (Table 3). The shorter of these distances were interpreted as U-Os contacts to the surface and the longer ones as U-Ow bonds to aqua ligands.33 For the pH range of 6–8 no significant geometry variations have been observed in the experiments.3,6,53,54 Our analysis of adsorption energies of uranyl complexes at (110) surfaces of model smectites suggests four-coordinated complexes at AlOH-SiO sites and its substituted analogues as most favorable. These complexes exhibit U-Ot bonds of 183 pm (and 186 pm for AlOH-AlO) and U-Oeq values of 229–231 pm (Table 3). The distances U-Os to the surface measure about 220–230 pm, with the exception of the less relevant substituted site AlOH-AlO where U-OAl = 207 pm. U-Ow bonds to the aqua ligands are calculated at ~240 pm (Table 3). 15



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On first glance, these calculated structural parameters do not agree well with experiment. When comparing our computed geometry parameters to experiment, one should take into account the tendency of GGA functionals to overestimate bond lengths.57 Thus, differences between calculated results for solvated uranyl and adsorption complexes often are more accurate than absolute values. As a reference we use results for the uranyl ion at the same level of theory, equilibrated for 4 ps and optimized in a cubic box (edge 12.56 Å), filled with 64 H2O molecules. The final optimized structure of solvated uranyl shows U-Ot = 181 pm and U-Oeq = 243 pm. Due to adsorption on the AlOH-SiO and MgOH-SiO sites of (110) surfaces U-Ot elongates by 2 pm and U-Oeq shortens considerably, to 230–231 pm (Table 3). This calculated elongation of U-Ot due to adsorption agrees well with the corresponding experimental change of 2-4 pm (Table 3), while U-Oeq is calculated too short, due to the change of the coordination number from 5 for the solvated ion to 4 in the adsorption complex.29 Also, the experimental results suggest the coexistence of adsorption complexes with CN = 4 and CN = 5, in contrast to the measured CN of 5–6 (see above). Besides the average U-Oeq, also calculated U-Os and U-Ow bond lengths can be compared to experiment. The shorter U-Os bonds to the AlOH and SiO groups at the surface were calculated at 220–230 pm, which is comparable or slightly shorter than the experimental U-O bond resolved at ~230 pm (Table 3). Longer U-O bonds of ~240 pm are calculated for the water ligands. These U-Ow bonds are about 8 pm shorter than the corresponding EXAFS results, 248 pm (Table 3).3,6,54 This underestimation of U-O bond lengths can again be traced back to the coordination number of 4 for the adsorbed species on AlOH-SiO sites. For the montmorillonitic mineral model the uranyl adsorption complex on the AlOH-SiO site with CN = 5 was also calculated and determined to be by 16 kJ mol-1 less favorable than the species with CN = 4 (Table S4 of SI). For the five-coordinated species UOw bonds average to 256 pm and U-Oeq amounts to 243 pm. These longer bonds compared to CN = 4 are the result of increased bond competition between the aqua ligands and the surface. Assuming that adsorption complexes with CN = 4 and 5 coexist, the corresponding geometry parameters may be averaged, leading to U-Ow = 248 pm and U-Oeq = 237 pm. These values agree very well with the experiment. The experimentally resolved U-Al/Si distances vary significantly. Earlier EXAFS experiments determined a single distance of 331–342 pm,6,53,54 while a recent study resolved two distances of 309 pm and 328 pm.3 Our calculated U-Si distances for the adsorption complexes at the sites AlOH-SiO and MgOH-SiO are somewhat longer, 355–362 pm (Table 3). Shorter U-Al/Si distances were calculated for other sites like SiOOm, 300–308 pm. Note that U-Al/Si distances do not represent chemical bonds. These distances fall in the range of 16


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multiple scattering, and they are experimentally not always observed. Therefore, the uncertainty of these distances may be substantial. Taking into account these uncertainties as well as our current and earlier results29 for other uranyl surface complexes, the U-Si distances of our preferred complex can still be regarded as compatible with experiment. Overall, we conclude from this comparison of geometry parameters to experiment that the calculated energetically preferred adsorbed uranyl species at the (110) surface of the montmorillonitic model are in line with the experimental results, but other species at other surface orientations with coordination numbers of 4–5 are necessary to rationalize the EXAFS results in a quantitative fashion. 5. Conclusions

To determine reliable energies for adsorption complexes on solvated mineral surfaces, we suggested a partial equilibration procedure that combines a first-principles molecular dynamics run of a few picoseconds for the system under study, realizing a microcanonical ensemble at low temperature, with a cooling step of 1 ps followed by conventional geometry optimization. In this way, we attempted to obtain more accurate formation energies of the adsorption complexes than by straightforward optimization. As a case study, we reexamined uranyl(VI) complexes of a preceding work,29 adsorbed at edge surfaces of 2:1 smectites, on the example of the ideal (110) surfaces of pyrophyllite, montmorillonite, and beidellite models. In this way, we determined uranyl adsorption on AlOH-SiO sites of (110) smectite surfaces and their substituted analogues to be preferred compared to other sites. To rationalize this preference, we partitioned formation energies into (i) energies required for two-fold deprotonating a site and (ii) adsorption energies proper of the uranyl ion on the deprotonated sites. We found the adsorption energies to correlate with the effective charges of the adsorption sites, in agreement with the mostly ionic character of the uranyl binding to the surface. The ionic aspect of the interaction of uranyl with the surface was corroborated by the correlation of U-Os bond distances to surface oxygen centers Os with the effective charges of the latter. The AlOH-SiO sites were determined to exhibit relatively low deprotonation energies, compared to the other sites, and rather negative effective charges. This combination of features allows one to rationalize the particularly favorable capability of these sites to form uranyl adsorption complexes. The structures of the most preferred adsorption complexes on (110) smectite surfaces compare only in part with experimental geometry data for montmorillonite.3,6,53,54 The adsorption complexes on the sites AlOH-SiO and MgOH-SiO exhibit shorter U-Oeq bonds and longer U-Si distances compared to the EXAFS results.3,6,53,54 The terminal uranyl bonds 17



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U-Ot and the shorter U-Os bond lengths agree very well with experiment. Further preferred adsorption complexes on other edge surfaces, contributing to the EXAFS results, but not considered in the present study, may improve this comparison. In view of the averaged nature of structure parameters furnished by EXAFS, our more special results can be considered to agree satisfactorily with the available experimental findings. Associated Content Supporting Information Exemplary data on the convergence of the equilibration procedure, discussion of estimates of Edepr, estimate of effective charges, structural data of all complexes studied. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.xxxxxxx. Author Information Corresponding Author E-mail [email protected] (N.R.). Note The authors declare no competing financial interest. Acknowledgments. This work was supported by the German Bundesministerium für Wirtschaft und Energie (grant no. 02E11001). The authors gratefully acknowledge a generous grant of computing resources by the Gauss Centre for Supercomputing (www.gauss-centre.eu), provided on the SuperMUC platform of Leibniz Supercomputing Centre Garching (www.lrz.de).

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References

1.

Butler, D., France Digs Deep for Nuclear Waste. Nature 2010, 466, 804-805.

2.

Gückel, K.; Rossberg, A.; Müller, K.; Brendler, V.; Bernhard, G.; Foerstendorf, H.,

Spectroscopic Identification of Binary and Ternary Surface Complexes of Np(V) on Gibbsite. Environ. Sci. Technol. 2013, 47, 14418-14425. 3.

Marques Fernandes, M.; Baeyens, B.; Dähn, R.; Scheinost, A. C.; Bradbury, M. H.,

U(VI) Sorption on Montmorillonite in the Absence and Presence of Carbonate: A Macroscopic and Microscopic Study. Geochim. Cosmochim. Acta 2012, 93, 262-277. 4.

Bradbury, M. H.; Baeyens, B., Experimental Measurements and Modeling of

Sorption Competition on Montmorillonite. Geochim. Cosmochim. Acta 2005, 69, 41874197. 5.

Křepelová, A.; Brendler, V.; Sachs, S.; Baumann, N.; Bernhard, G., U(VI)-Kaolinite

Surface Complexation in Absence and Presence of Humic Acid Studied by TRLFS. Environ. Sci. Technol. 2007, 41, 6142-6147. 6.

Schlegel, M. L.; Descostes, M., Uranium Uptake by Hectorite and Montmorillonite:

A Solution Chemistry and Polarized EXAFS Study. Environ. Sci. Technol. 2009, 43, 85938598. 7.

Park, C.; Fenter, P. A.; Nagy, K. L.; Sturchio, N. C., Hydration and Distribution of

Ions at the Mica-Water Interface. Phys. Rev. Lett. 2006, 97, 016101. 8.

Park, C.; Fenter, P. A.; Sturchio, N. C.; Nagy, K. L., Thermodynamics, Interfacial

Structure, and pH Hysteresis of Rb+ and Sr2+ Adsorption at the Muscovite (001)-Solution Interface. Langmuir 2008, 24, 13993-14004. 9.

Müller, K.; Förstendorf, H.; Meusel, T.; Brendler, V.; Lefevre, G.; Comarmond, M.

J.; Payne, T. E., Sorption of U(VI) at the TiO2-Water Interface: An in situ Vibrational Spectroscopic Study. Geochim. Cosmochim. Acta 2012, 76, 191-205. 10.

Geckeis, H.; Lützenkirchen, J.; Polly, R.; Rabung, T.; Schmidt, M., Mineral-Water

Interface Reactions of Actinides. Chem. Rev. 2013, 113, 1016-1062. 11.

Greathouse, J. A.; Cygan, R. T., Water Structure and Aqueous Uranyl(VI)

Adsorption Equilibria onto External Surfaces of Beidellite, Montmorillonite, and Pyrophyllite: Results from Molecular Simulations. Environ. Sci. Technol. 2006, 40, 38653871.

19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

12.

Page 20 of 30

Kerisit, S.; Liu, C., Molecular Dynamics Simulations of Uranyl and Uranyl

Carbonate Adsorption at Aluminosilicate Surfaces. Environ. Sci. Technol. 2014, 48, 38993907. 13.

Lectez, S.; Roques, J.; Salanne, M.; Simoni, E., Car-Parrinello Molecular Dynamics

Study of the Uranyl Behaviour at the Gibbsite/Water Interface. J. Chem. Phys. 2012, 137, 154705. 14.

Kremleva, A.; Krüger, S.; Rösch, N., Uranyl Adsorption at (0 1 0) Edge Surfaces of

Kaolinite: A Density Functional Study. Geochim. Cosmochim. Acta 2011, 75, 706-718. 15.

Kremleva, A.; Martorell, B.; Krüger, S.; Rösch, N., Uranyl Adsorption on Solvated

Edge Surfaces of Pyrophyllite: A DFT Model Study. Phys. Chem. Chem. Phys. 2012, 14, 5815-5823. 16.

Polly, R.; Schimmelpfennig, B.; Flörsheimer, M.; Rabung, T.; Kupcik, T.; Klenze,

R.; Geckeis, H., Quantum Chemical Study of Inner-Sphere Complexes of Trivalent Lanthanide and Actinide Ions on the Corundum (110) Surface. In Radiochim. Acta, 2013; Vol. 101, p 561. 17.

Alexandrov, V.; Rosso, K. M., Insights into the Mechanism of Fe(II) Adsorption and

Oxidation at Fe–Clay Mineral Surfaces from First-Principles Calculations. J. Phys. Chem. C 2013, 117, 22880-22886. 18.

Morrow, C. P.; Yazaydin, A. Ö.; Krishnan, M.; Bowers, G. M.; Kalinichev, A. G.;

Kirkpatrick, R. J., Structure, Energetics, and Dynamics of Smectite Clay Interlayer Hydration: Molecular Dynamics and Metadynamics Investigation of Na-Hectorite. J. Phys. Chem. C 2013, 117, 5172-5187. 19.

Wang, J.; Kalinichev, A. G.; Kirkpatrick, R. J., Asymmetric Hydrogen Bonding and

Orientational Ordering of Water at Hydrophobic and Hydrophilic Surfaces: A Comparison of Water/Vapor, Water/Talc, and Water/Mica Interfaces. J. Phys. Chem. C 2009, 113, 11077-11085. 20.

Katti, D. R.; Srinivasamurthy, L.; Katti, K. S., Molecular Modeling of Initiation of

Interlayer Swelling in Na-Montmorillonite Expansive Clay. Can. Geotech. J. 2015. 21.

Churakov, S. V., Structure and Dynamics of the Water Films Confined between

Edges of Pyrophyllite: A First Principle Study. Geochim. Cosmochim. Acta 2007, 71, 11301144. 22.

Churakov, S. V.; Dähn, R., Zinc Adsorption on Clays Inferred from Atomistic

Simulations and EXAFS Spectroscopy. Environ. Sci. Technol. 2012, 46, 5713-5719.

20


Page 21 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


23.

Kremleva, A.; Krüger, S.; Rösch, N., Density Functional Model Studies of Uranyl

Adsorption on (001) Surfaces of Kaolinite. Langmuir 2008, 24, 9515-9524. 24.

Moskaleva, L. V.; Nasluzov, V. A.; Rösch, N., Modeling Adsorption of the Uranyl

Dication on the Hydroxylated alpha-Al2O3(0001) Surface in an Aqueous Medium. Density Functional Study. Langmuir 2006, 22, 2141-2145. 25.

Perron, H.; Domain, C.; Roques, J.; Drot, R.; Simoni, E.; Catalette, H., Periodic

Density Functional Theory Investigation of the Uranyl Ion Sorption on the TiO2 Rutile (110) Face. Inorg. Chem. 2006, 45, 6568-6570. 26.

Martorell, B.; Kremleva, A.; Krüger, S.; Rösch, N., Density Functional Model Study

of Uranyl Adsorption on the Solvated (001) Surface of Kaolinite. J. Phys. Chem. C 2010, 114, 13287-13294. 27.

Veilly, E.; Roques, J.; Jodin-Caumon, M.-C.; Humbert, B.; Drot, R.; Simoni, E.,

Uranyl Interaction with the Hydrated (001) Basal Face of Gibbsite: A Combined Theoretical and Spectroscopic Study. J. Chem. Phys. 2008, 129. 28.

Pan, Q.-J.; Odoh, S. O.; Asaduzzaman, A. M.; Schreckenbach, G., Adsorption of

Uranyl Species onto the Rutile (110) Surface: A Periodic DFT Study. Chem. Eur. J. 2012, 18, 1458-1466. 29.

Kremleva, A.; Krüger, S.; Rösch, N., Uranyl Adsorption at Solvated Edge Surfaces

of 2 : 1 Smectites. A Density Functional Study. Phys. Chem. Chem. Phys. 2015, 17, 1375713768. 30.

Emmerich, K.; Wolters, F.; Kahr, G.; Lagaly, G., Clay Profiling: The Classification

of Montmorillonites. Clays Clay Miner. 2009, 57, 104-114. 31.

Pauling, L., The Principles Determining the Structure of Complex Ionic Crystals. J.

Am. Chem. Soc. 1929, 51, 1010-1026. 32.

Kremleva, A.; Krüger, S.; Rösch, N., Assigning EXAFS Results for Uranyl

Adsorption on Minerals via Formal Charges of Bonding Oxygen Centers. Surf. Sci. 2013, 615, 21-25. 33.

Sylwester, E. R.; Hudson, E. A.; Allen, P. G., The Structure of Uranium (VI)

Sorption Complexes on Silica, Alumina, and Montmorillonite. Geochim. Cosmochim. Acta 2000, 64, 2431-2438. 34.

Kresse, G.; Furthmüller, J., Efficient Iterative Schemes for Ab Initio Total-Energy

Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169-11186.

21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

35.

Page 22 of 30

Kresse, G.; Furthmüller, J., Efficiency of Ab-Initio Total Energy Calculations for

Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15-50. 36.

Kresse, G.; Hafner, J., Ab Initio Molecular Dynamics Simulation of the Liquid

Metal Amorphous Semiconductor Transition in Germanium. Phys. Rev. B 1994, 49, 1425114269. 37.

Kresse, G.; Hafner, J., Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev.

B 1993, 47, 558-561. 38.

Kresse, G.; Hafner, J., Ab Initio Molecular Dynamics for Open Shell Transition

Metals. Phys. Rev. B 1993, 48, 13115-13118. 39.

Perdew, J. P.; Wang, Y., Accurate and Simple Analytic Representation of the

Electron Gas Correlation Energy. Phys. Rev. B 1992, 45, 13244-13249. 40.

Blöchl, P. E., Projector Augmented Wave Method. Phys. Rev. B 1994, 50, 17953-

17979. 41.

Kresse, G.; Joubert, D., From Ultrasoft Pseudopotentials to the Projector

Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758-1775. 42.

Macdonald, A. H.; Vosko, S. H., Relativistic Density Functional Formalism. J. Phys.

C 1979, 12, 2977-2990. 43.

Lo, C.; Trout, B. L., Density-Functional Theory Characterization of Acid Sites in

Chabazite. J. Catal. 2004, 227, 77-89. 44.

Fuchs, M. S. K.; Shor, A. M.; Rösch, N., The Hydration of the Uranyl Dication:

Incorporation of Solvent Effects in Parallel Density Functional Calculations with the Program Paragauss. Int. J. Quantum Chem 2002, 86, 487-501. 45.

Liu, X. D.; Cheng, J.; Sprik, M.; Lu, X. C.; Wang, R. C., Surface Acidity of 2:1-

Type Dioctahedral Clay Minerals from First Principles Molecular Dynamics Simulations. Geochim. Cosmochim. Acta 2014, 140, 410-417. 46.

Pearson, R. G., Ionization Potentials and Electron Affinities in Aqueous Solution. J.

Am. Chem. Soc. 1986, 108, 6109-6114. 47.

Cornehl, H. H.; Heinemann, C.; Marçalo, J.; Pires de Matos, A.; Schwarz, H., The

“Bare” Uranyl(2+) Ion, UO22+. Angew. Chem. Int. Ed. 1996, 35, 891-894. 48.

Marcus, Y.; Loewenschuss, A., Standard Thermodynamic Functions of the Gaseous

Actinyl Ions Mo and for Their Hydration. J. Chem. Soc. Faraday Trans. 1986, 82, 28732886.

22


Page 23 of 30

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49.

Gibson, J. K.; Haire, R. G.; Santos, M.; Marçalo, J.; Pires de Matos, A., Oxidation

Studies of Dipositive Actinide Ions, An2+ (an = Th, U, Np, Pu, Am) in the Gas Phase:• Synthesis and Characterization of the Isolated Uranyl, Neptunyl, and Plutonyl Ions UO22+(G), NpO22+(G), and PuO22+(G). J. Phys. Chem. A 2005, 109, 2768-2781. 50.

Li, B.; Matveev, A. V.; Krüger, S.; Rösch, N., Uranyl Solvation by a Reference

Interaction Site Model. Comput. Theor. Chem. 2015, 1051, 151-160. 51.

Tang, W.; Sanville, E.; Henkelman, G., A Grid-Based Bader Analysis Algorithm

without Lattice Bias. J. Phys.: Condens. Matter 2009, 21, 084204. 52.

Brown, I. D.; Altermatt, D., Bond-Valence Parameters Obtained from a Systematic

Analysis of the Inorganic Crystal-Structure Database. Acta Crystallogr. Sect. B: Struct. Sci. 1985, 41, 244-247. 53.

Hennig, C.; Reich, T.; Dähn, R.; Scheidegger, A. M., Structure of Uranium Sorption

Complexes at Montmorillonite Edge Sites. Radiochim. Acta 2002, 90, 653-657. 54.

Catalano, J. G.; Brown, G. E., Uranyl Adsorption onto Montmorillonite: Evaluation

of Binding Sites and Carbonate Complexation. Geochim. Cosmochim. Acta 2005, 69, 29953005. 55.

Allen, P. G.; Bucher, J. J.; Shuh, D. K.; Edelstein, N. M.; Reich, T., Investigation of

Aquo and Chloro Complexes of UO22+, NpO2+, Np4+, and Pu3+ by X-Ray Absorption Fine Structure Spectroscopy. Inorg. Chem. 1997, 36, 4676-4683. 56.

Krüger, S.; Schlosser, F.; Ray, R. S.; Rösch, N., Uranyl Complexation by Carboxylic

Acids: A Relativistic Density Functional Model Study for Actinide Complexation by Humic Acids. In Recent Progress in Computational Sciences and Engineering, Simos, T., Maroulis, G., Eds. 2006; Vol. 7A-B, pp 904-907. 57.

Görling, A.; Trickey, S. B.; Gisdakis, P.; Rösch, N., A Critical Assessment of

Density Functional Theory with Regard to Applications in Organometallic Chemistry. In Topics in Organometallic Chemistry, Brown, J., Hofmann, P., Eds. Springer: Heidelberg, 1999; Vol. 4, pp 109-163.

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Table 1. Adsorbed uranyl species on various two-fold deprotonated sites at (110) edge surfaces of 2:1 model smectite as determined by optimizationa or simulated annealing. For each site the adsorbed species and its coordination number (CN) are given. Method

Optimization

Models

Site

Adsorbate

CN

Adsorbate

Unsubstituted Aluminol

AlOmO

UO22+

5

UO22+

b

AlOmOH Silanol Mixed

SiOOm

[UO2(OH)]

+

[UO2(OH)]

+

Simulated annealing

5 5

CN 5

[UO2(OH)]

+

5

[UO2(OH)]

+

5

AlOH-SiO

UO2

2+

2+

5(4)

UO2

4c

AlO-SiOH

UO22+

5(4)

UO22+

AlOO(o)

UO22+

5

-

5

[UO2(OH)]+

5

Substituted beidelitic AlOOH(o) AlOO(t)

[UO2(OH)]

+

[UO2(OH)]

+

UO2

2+

AlO-AlOH

UO2

2+

MgOmO

UO22+

AlOH-AlO

5

UO2

2+

5

UO2

2+

4

5(4)

UO2

2+

4

4

UO22+

5 5(4)

Substituted montmorillonitic MgOmOH SiOOm MgOH-SiO MgO-SiOH

[UO2(OH)]

+

[UO2(OH)]

+

UO2

2+

UO2

2+

5 5 4(5) 5(4)

4

[UO2(OH)]

+

4

[UO2(OH)]

+

5

UO2

2+

4

UO2

2+

5

a

Ref. 29. In parentheses given the CN of the less energetically favorable isomers. b See text for details. c Both isomers, with CN = 4 and 5, were equilibrated and optimized for the montmorillonitic model.

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Table 2. Calculated formation energies Eform, estimated deprotonation energies Edepra, and adsorption energies Eads (kJ mol-1) as well as effective chargesb (e) of oxygen centers at various adsorption sitesc on (110) edge surfaces of 2:1 model smectites.d Without substitution on the surface Model

Site

Pyro

AlOmO

Eform

Edepr

Eads

With substitution on the surface

q1 -0.07

q2 -0.61

qtot -0.68

-0.74 -0.67

-0.90 -0.83

Site

Eform

Edepr

Eads

q1

q2

qtot

MgOmO

128

203

-75

-0.14

-0.87

-1.01

177

108

69

Beid

143

160

-17

Mont

129

174

-45

-0.16 -0.16

183

62

121

-0.14

-0.13

-0.27

Beid

152

62

90

-0.14

-0.19

-0.33

AlOOH(o)

123

89

34

-0.19

-0.24

-0.43

Mont

159

78

81

-0.15

-0.26

-0.41

MgOmOH

146

77

69

-0.21

-0.37

-0.58

165

91

74

-0.44

-0.04

-0.48

Beid

135

117

18

-0.40

-0.08

-0.48

AlOO(t)

160

158

2

-0.55

-0.13

-0.68

Mont

118

106

12

-0.38

-0.11

-0.49

SiOOm

103

123

-20

-0.44

-0.12

-0.56

100

71

29

-0.22

-0.41

-0.63

-0.37

-0.64

AlOH-AlO

57

111

-54

-0.25

-0.55

-0.80

MgOH-SiO

68

117

-49

-0.43

-0.38

-0.81

Pyro

Pyro

Pyro

AlOmOH

SiOOm

AlOH-SiO

Beid

88

75

13

-0.27

Mont

91

62

29

-0.37

-0.41

-0.78

186 177

108 160

78 17

-0.61

0.14

-0.47

-0.62

0.10

-0.52

AlO-AlOH

147

128

19

-0.66

-0.08

-0.74

164

174

-10

-0.60

0.08

-0.52

MgO-SiOH

169

203

-34

-0.63

0.08

-0.55

Pyro Beid Mont a

AlO-SiOH

Calculated by relaxing only the deprotonated surface group; for details, see text and Section S2 of the SI.

b

q1 is the charge of the first surface group of the site, q2 the charge of the second group, in the order indicated by the site label as given in column 2. For example, for the site AlOH-SiO q1 is the charge of OH of the AlOH group, q2 is the charge of the O center of the SiO group of the site. qtot = q1 + q2. For details regarding the determination of effective charges, see the Supporting Information, Section S3. c

For the sites, see Figure 2 and Table 1. d Pyrophyllitic (Pyro), beidellitic (Beid), and montmorillonitic (Mont) models.

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Table 3. Calculated structure parametersa of uranyl adsorption complexes at various sites of (110) edge surfaces of 2:1 model smectites.b Calculated data for the solvated uranyl ion, as well as experimental data for montmorillonite are also shown for comparison. Site Modelb UO2(H2O)64 AlOmO All MgOmO Mont

CN 5 5 4

U-Ot U-Os U-Os 181 186 (1) 252 (7) 204 (2) 187 233 201

U-OH U-Ow

AlOmOH All AlOOH(o) Beid MgOmOH Mont

5 5 4

182 (1) 257 (5) 234 (1) 185 232 244 182 233 227

221 (2) 254 (7) 244 (1) 355 (3) 221 251 240 343 231 246 234 354

SiOOm AlOO(t) SiOOm

All Beid Mont

5 5 5

184 (1) 222 (4) 258 (2) 185 211 239 183 230 243

232 (5) 252 (5) 243 (0) 257 244 300 232 254 242

308 (2)

AlOH-SiO All AlOH-AlO Beid MgOH-SiO Mont

4 4 4

183 (1) 229 (2) 217 (2) 186 231 207 183 226 219

240 (4) 231 (1) 240 229 353 238 230

355 (1)

AlO-SiOH All AlO-AlOH Beid MgO-SiOH Mont

5 4 5

186 (1) 200 (2) 260 (10) 189 197 239 187 196 262

257 (8) 246 (1) 243 231 367 260 248

379 (3)

Exp. Mont

pH 8 7 6.6 6.4 4

U-Ot 180(2.2) 180(2.0) 179(2.3) 178(2.0) 176(2)

U-Ow U-Oeq U-Al/Si 248(2.9) 239(6.0) 328(0.9) 309(0.9) 248(2.1) 234(5.0) 342(0.2) 247(2.1) 238(4.2) 331(0.6) 236(6.2) 343(0.6) 241(5)

UO22+

Ref. 3 54 6 53 55

U-Os 230(3.1) 232(2.8) 229(2.1)

U-Oeq U-Al/Mgc U-Sic 243 256 (7) 245 (1) 333 (1) 253 235 334

305

362

391

a

Average terminal uranyl bond length U-Ot, bond lengths U-Os to surface oxygen centers, in the order of the site label, U-OH distance to OH ligands, average bond lengths U-Ow to aqua ligands, average equatorial U-O bond length U-Oeq, U-Al and U-Si distances to the nearest surface Al and Si centers, respectively. The MAD values of averaged data and the coordination numbers of experimental data are given in parentheses. b Surface models included in the average: “All” – all models with subsurface substitutions studied, “Beid” – beidellitic, “Mont” – montmorillonitic models. c Only relevant U-Al/Si/Mg distances (shorter than 370 pm or the shortest available) are given for comparison with experiment.

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Figure 1. Schematic representation of various models of 2:1 clay minerals: (a) pyrophyllitic model; (b) beidellitic model, substitution at the surface. The optimized structure shows a proton arrangement that deviates from that of other surfaces; (c) beidellitic model, sub-surface substitution; (d) beidellitic model, substitution at the surface; (e) montmorillonitic model, subsurface substitution; (f) montmorillonitic model, substitution at the surface.

Figure 2. Schematic representation of adsorption sites studied in the present work. (a) unsubstituted sites on pyrophyllitic, beidellitic, and montmorillonitic models (subsurface substitution), (b) substituted sites at the surface of the beidellitic model, (c) substituted sites at 27 ACS Paragon Plus Environment


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the surface of the montmorillonitic model.

Figure 3. Formation energies, estimated from Eq. (1). Results (a) for the directly optimized structures (Ref. 29) and (b) for equilibrated systems.


Page 29 of 30

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Figure 4. Adsorption energies as a function of the effective charges of the corresponding adsorption sites. All complexes R2 = 0.56 (y = 208.55 x + 145.57); unsubstituted sites R2 = 0.53 (y = 187.92 x + 142.88); substituted sites R2 = 0.46 (y = 180.1 x + 111.27).

Figure 5. Calculated U-O bond lengths to surface oxygen centers of adsorption complexes of uranyl (VI) on pyrophyllitic, beidellitic, and montmorillonitic 2:1 smectite (110) surfaces as a function of the effective charges q of the surface oxygen centers Os.



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