Coordination and Hydrolysis of Plutonium Ions in Aqueous Solution

Article pubs.acs.org/JPCA

Coordination and Hydrolysis of Plutonium Ions in Aqueous Solution Using Car−Parrinello Molecular Dynamics Free Energy Simulations Samuel O. Odoh, Eric J. Bylaska, and Wibe A. de Jong*,† Environmental and Molecular Science Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States S Supporting Information *

ABSTRACT: Car−Parrinello molecular dynamics (CPMD) simulations have been used to examine the hydration structures, coordination energetics, and the first hydrolysis constants of Pu3+, Pu4+, PuO2+, and PuO22+ ions in aqueous solution at 300 K. The coordination numbers and structural properties of the first shell of these ions are in good agreement with available experimental estimates. The hexavalent PuO22+ species is coordinated to five aquo ligands while the pentavalent PuO2+ complex is coordinated to four aquo ligands. The Pu3+ and Pu4+ ions are both coordinated to eight water molecules. The first hydrolysis constants obtained for Pu3+ and PuO22+ are 6.65 and 5.70, respectively, all within 0.3 pH unit of the experimental values (6.90 and 5.50, respectively). The hydrolysis constant of Pu4+, 0.17, disagrees with the value of −0.60 in the most recent update of the Nuclear Energy Agency Thermochemical Database (NEA-TDB) but supports recent experimental findings. The hydrolysis constant of PuO2+, 9.51, supports the experimental results of Bennett et al. [Radiochim. Acta 1992, 56, 15]. A correlation between the pKa of the first hydrolysis reaction and the effective charge of the plutonium center was found.

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INTRODUCTION

regarding the aqueous chemistry of Np and Pu, especially the latter, and other actinides. The coordination and structures of plutonium ions in aqueous solution are particularly important as these reflect the nature of this radioactive element in the environment as well as the ease with which it interacts with different ligands in the environment. Experimentally, the structures of aqueous phase complexes are often probed with extended X-ray absorption fine structure (EXAFS) and high-energy X-ray spectroscopy (HEXS).5 These local X-ray techniques are able to provide the first hydration shell parameters from model fittings of the experimental spectra. In many cases, the equilibrium coordination number of aquo complexes of plutonium obtained with these X-ray absorption spectroscopies by various workers diverge by as much as ±2.5a,6 For example, Allen et al.6b have reported coordination numbers of 10.2 ± 0.96b and 9.2 ± 0.96a for the Pu3+ aqua ion while Reich et al.7 obtained 7.6 for the same ion. As a result, there is no clear understanding of the underlying thermodynamics affecting the speciation of these species. The thermodynamics and kinetics of the hydrolysis of the plutonium aquo complexes are also not fully understood.4b,8 The hydrolysis of plutonium, as well as other actinide elements, is particularly interesting given the role of such processes in the formation of polymeric structures.1b,8b,c,9 Surprisingly, there is still some disagreement in the literature regarding the first and

The speciation of actinide and actinyl ions in aqueous solutions is extremely important in understanding their mobility and reactivity under environmental conditions.1 This is because an adequate understanding of the aqueous chemistry of these elements is crucial in the design, maintenance, and remediation of nuclear waste repositories.1c There is significant interest in the properties of actinide and actinyl aqua ions as the processes that drive radionuclide transport in the environment are dictated by molecular-scale processes such as speciation, oligomerization in complex solutions, adsorption to mineral surfaces, and colloid formation. Of these properties, the most basic chemical behavior of these ions involves the coordination of several water molecules and the hydrolysis of the resulting aqua ions at higher pH values. It is however the case that the chemistry of uranium complexes has been significantly more studied than that of any other actinide element.1b,2 For plutonium, there are other barriers to studying its aqueous complexes, in addition to the general issues of chemical safety, expensive materials, and radiological toxicity.3 As an example, the Pu(IV) ion is not only readily hydrolyzed in aqueous solutions but also readily disproportionates at modest to high concentrations.4 This in addition to the difficulty of obtaining solutions containing one oxidation state3 makes experimental attempts to study its aqueous chemistries at environmentally relevant concentrations fraught with complications. Generally, multiple oxidation states of plutonium coexist at pH values greater than 1.1b However, their importance to the nuclear industry means that it is crucial that information be obtained © 2013 American Chemical Society

Received: September 26, 2013 Revised: October 26, 2013 Published: October 29, 2013 12256

dx.doi.org/10.1021/jp4096248 | J. Phys. Chem. A 2013, 117, 12256−12267

The Journal of Physical Chemistry A

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second hydrolysis constants of the Pu4+ ion. The first and second hydrolysis constants of Pu4+ contained in the most recent update of the Nuclear Energy Agency Thermochemical Database (NEA-TDB) are −0.60 and −0.63 (log K° values), respectively.10 These values10 imply that the ion occurs as Pu(OH)22+ at room temperature. However, it has been previously noted that the interference of colloidal precipitates could be responsible for the rather low log K° values obtained from these older experimental works.4b,11 When these effects were corrected for in their experimental work, the first hydrolysis constant of Pu4+ was found to be 0.59 by Yusov et al.12 and 0.00 ± 0.20 by Yun et al.8f The previous interpretation10 implied spontaneous hydrolysis in solution while the new experimental works8f,12 suggest that the hydrolysis of Pu4+ is an activated process that costs energy. It should also be noted that the study of the aqueous properties of the plutonyl cation, PuO2+, could provide some insights into the chemistry of the elusive uranyl cation, UO2+. The UO2+ ion has not been characterized in aqueous solution as it rapidly disproportionates to the +6 and +4 oxidation states.13 Although the PuO2+ ion also disproportionates in solution,8b,14 there is some experimental data regarding its aqueous phase shell structure5a,6,7 and first hydrolysis constant.4b,10b,15 At the very least, a study of this ion will give us insights into the degree of error associated with any simulations on its uranyl counterpart, UO2+.16 The aqueous chemistry of plutonium and other actinides can be studied by using tools afforded by computational chemistry.1d,17 The inclusion of the effects of the second solvation sphere remains one of the limitations to computational actinide chemistry. It is recognized that implicit solvation methods18 tend to provide good trends for calculated bond distances, vibrational frequencies, reaction energies, and transition state barriers of events in aqueous solution.17b,c,19 The inclusion of the effects of the second coordination sphere can be achieved with the aid of ab initio molecular dynamics (AIMD) approaches. The Car−Parrinello20 variant of AIMD is used in this work. This approach elegantly combines classical molecular dynamics (CLMD) with a density functional theory (DFT) description of the electronic structure at every time step. There is an ongoing surge in the use of the CPMD simulation method in studying the structural, electronic, and dynamic properties of actinides in solution.16,21 This method when combined with various free energy simulation approaches has been used in successfully predicting the hydrolysis constants of actinide species.16 In this work, we have employed the CPMD simulation method to study the solvent structures of Pu3+, Pu4+, PuO2+, and PuO22+. To map out the energy landscape of the aquo complexation of these ions, the free energy differences and transition barriers between the various aquo complexes of each of these species were determined by combining the CPMD simulations with metadynamics free energy simulations. This approach was also used in determining the first hydrolysis constants of the plutonium species. The trends in the first hydrolysis constants that were obtained are interpreted with a charge-based model.

studies as it has been found to perform well in the prediction of the solvation structure and acidities of UO22+, UO2+, and U4+.16 Generalized norm-conserving pseudopotentials modified into a separable form as suggested by Kleinman and Bylander24 were used to approximate the valence electron interactions. The hydrogen and oxygen atoms were described with softened Hamman pseudopotentials25 generated with the PBE96 exchange correlation functional while employing the following core radiiH: rcs = 0.8 au and rcp = 0.8 au and O: rcs = 0.7 au, rcp = 0.7 au, and rcd = 0.7 au. A Troullier−Martins26 pseudopotential was used for the plutonium atoms. To generate this potential, the 6s and 6p core electrons were removed from the core and placed in the valence space. By removing redundant orbital angular momentum components of the potential, we were able to skip the inclusion of semicore corrections. This however comes with the expense of adding extra valence electrons to the overall calculation. The radial cutoffs of the Pu pseudopotentials were set at 1.600, 1.800, 2.500, and 1.300 for the s, p, d, and f functions, respectively. This combination of pseudopotentials results in a Pu−Oyl bond length of 1.703 Å for the plutonyl dication, in good agreement with nonperiodic calculations employing Gaussian-type orbitals.27 Overall, the approach used in generating the plutonium pseudopotential is similar to that used for the uranium atom by Bühl et al.28 and Nichols et al.29 Other simulation parameters employed include a Γ-point sampling of the Brillouin zone, an energy cutoff of 120 Ry, a density cutoff of 240 Ry, a time step of 0.12 fs, and a fictitious mass of 600 au. A periodic cubic cell with lengths of 12.42 Å was used in the simulations, in which all the hydrogen atoms were replaced by deuterium. The plutonium atoms in the simulation cells possess 5, 4, 3, and 2 unpaired 5f electrons for Pu3+, Pu4+, PuO2+, and PuO22+, respectively. All the low-spin states of these species are found at higher energies. The temperature, set at 300 K, was controlled by using the Nose−Hoover thermostat.30 The starting structures were equilibrated for 2−3 ps, after which statistics were collected over the next 14−20 ps with the NVT ensemble for each system. These methods have been used to successfully describe the structural and hydration properties of highly charged actinide and transition metal ions.16,21a,29,31 A combination of this functional and temperature has resulted in nearly quantitative agreement between the experimental and simulated XAFS spectra of UO21/2+, U4+, and transition metal cations.16,21a,29,31d Although it has been noted that the use of generalized gradient approximation (GGA) functionals such as PBE does not accurately describe the liquid nature of bulk water,32 it is important to note that we are working on highly charged hydrated metal ion clusters. The residence times of the aquo ligands around the actinide ions are known to be on the order of hundreds of nanoseconds.33 Moreover, the electrostatic (and covalent) interactions between the charged actinide/ actinyl ions and the solvent molecules are significantly larger than the energies associated with the diffusion of the solvent molecules. The deficiencies of DFT+GGA are well-known.34 The most dramatic being that early water simulations that used low-density cutoffs (≪150 Ry) sometimes resulted in an amorphous-like state. However, since DFT+GGA calculations are reasonably efficient, this is the level of calculation used in essentially every ab initio molecular dynamics simulation. Results suggest that inclusion of exact exchange, e.g. PBE0, improves the general accuracy of DFT+GGA.31d Unfortunately, the high cost of the exact exchange calculation35 would make it impossible to perform free energy calculations with this level of

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COMPUTATIONAL METHODS CPMD simulations20 with pseudopotential plane waves were carried out with the NWChem22 computational chemistry package. The PBE functional,23 a generalized gradient approximation (GGA) functional, was employed in these 12257



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RESULTS AND DISCUSSION Coordination of Plutonium Species. Hexavalent Plutonyl. CPMD metadynamics simulations were used to examine the speciation of PuO22+ in aqueous solution. The free energy profile for its equatorial aquo coordination is presented in Figure 1. The equatorial regions of actinyl groups are

theory. Even with this limitation, our experience has shown that the PBE functional, when used with a proper density cutoff, describes the hydration properties and hydrolysis of the aquo complexes of the actinide/actinyl cations very well.16,21a,29,31 The free energy profiles corresponding to the equilibrium coordination number of the plutonium ions as well as their first hydrolysis constants are determined using metadynamics36 simulations. A coordination number collective variable was used to study both the equilibrium complexation as well as the first hydrolysis reactions. The description of the collective variable is according to Sprik37 and is defined as ξij =

1 1 + exp[n(rij − r0)]

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(1)

where r0 is the cutoff distance, n is set at 10 Ǻ −1, and rij is either the Pu−O distance (for equilibrium coordination number studies) or the O−H distance (for examination of the energetics of the hydrolysis reactions). For the former, we used the number of oxygen atoms within a Pu−O cutoff distance of 3.0 Ǻ while for the latter, we used the number of protons that are within 1.2 Ǻ of a specific aquo ligand that is directly coordinated to the metal center. The collective variable used in studying the hydrolysis reactions included all the protons in the cubic simulation box.16 The other sampling parameters used in generating the history-dependent biasing potentials are: the height of the repulsive Gaussian hills is set at 0.063 kcal/mol, the width of the Gaussian hills is set at 0.10, and the time interval between adding hills to the potential was set at 20 MD steps for all reactions except the hydrolysis of Pu4+, which was set at 50 MD steps. The longer interval was used for Pu4+ as the reaction energy associated with its hydrolysis is expected to be very small.4b,8a,d,e,15a The initial structures used in the metadynamics simulations are obtained at about 5−10 ps into the original CPMD simulations. These structures were then additionally equilibrated at 300 K for 1−5 ps before starting the metadynamics simulations. The selection of the collective variables used in the metadynamics simulations and the approach used in determining the convergence of free energy profiles have been previously discussed.16 The trends in the simulated hydrolysis constants of Pu3+, Pu4+, PuO2+, and PuO22+ are related to the effective charges of the actinide center obtained from Mulliken charge analysis.38 These were carried out on 14 snapshots of each aquo system obtained at picosecond intervals in the CPMD simulations. To complement this, we also calculated Hirshfeld charges39 on the gas phase cluster complexes that only account for the first-shell water molecules surrounding the ion. Although the gas-phase calculations represent a change of model from the AIMD simulations, they allow us to cheaply compare the aquo complexes of the plutonium ions with those of their analogous uranium and neptunium species. The DFT-optimized TZVP40 basis sets were used for the hydrogen and oxygen atoms while the small-core relativistic Stuttgart pseudopotential41 was used for the actinide atoms. Finally, we note that our simulations were performed at the scalar-relativistic level. As the ion hydration and hydrolysis reactions considered in this work do not constitute redox reactions, spin−orbit coupling effects can be expected to be minimal.17a,b,19b It was also found that the unpaired 5f electrons were highly localized and contribute little to the AnOyl, An− OH, and An−OH2 bonds (Supporting Information).

Figure 1. Radial distribution function, gPuO(r), and its integral, nPuO(r), of PuO22+ obtained from CPMD simulations with a cubic box containing 64 water molecules. The bottom panel contains the freeenergy profile for the equatorial coordination of PuO22+.

populated by 4, 5, or 6 aquo ligands during fitting of experimental spectroscopic data. 5a,b We observed both [PuO2(H2O)4]2+ and [PuO2(H2O)4]2+ in our metadynamics simulations but did not observe the formation of [PuO2(H2O)6]2+. The tetraaquo species was found to be about 2.55 kcal/mol higher in energy than the pentaaquo species, with a transition barrier of about 7.09 kcal/mol. The magnitude of the energy difference between these two species suggests facile interconversion between the two species even though the pentaaquo complex would be predominant at 300 K. Atta-Fynn et al.16 using a similar method obtained a free energy of 0.7 kcal/mol and a barrier of 4.7 kcal/mol for the transformation of [UO2(H2O)5]2+ to [UO2(H2O)4]2+. Those results agree well with recent experimental data42 showing an energy preference for [UO2(H2O)5]2+ over [UO2(H2O)4]2+ by 1.2 ± 0.4 kcal/mol. This gives us confidence regarding the value of 2.55 kcal/mol obtained from our simulations on [PuO2(H2O)4]2+ and [PuO2(H2O)5]2+. The radial distribution function (RDF) of PuO22+ obtained from the CPMD simulations is presented in Figure 1. The average Pu−Oyl bond length obtained from the simulation is in 12258



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Figure 2. Second-shell structure of [PuO2(H2O)5]2+ (left) and [PuO2(H2O)4]+ (right) showing their second coordination sphere structures. Several atoms in the second coordination sphere were omitted for clarity.

sampled. The results of these simulations show that the tetraaquo complex is more stable than the triaquo complex by about 13.42 kcal/mol and that there is a transition barrier of about 10−15 kcal/mol between these species. The transformation of the triaquo complex to the tetraaquo species is thermodynamically and kinetically favored, suggesting that the proportion of triaquo species in aqueous solutions will be minimal. Prior to commencing simulations on [PuO2(H2O)3]+ in a cubic box containing 64 water molecules, the solvent shell around the ion was equilibrated for about 12 ps. However, the insertion of a second coordination sphere water molecule into the first coordination sphere occurs after 2−3 ps during unconstrained NVT simulations on [PuO2(H2O)3]+. The energy difference between the tetraaquo and pentaaquo complexes is found to be 3.10 kcal/mol with the former being more stable. The implication is that that conversion of the latter to the former is favored. There was no ejection of a water molecule from the first coordination sphere during 18 ps NVT simulations on [PuO2(H2O)5]+. This suggests that the pentaaquo species is metastable. Overall, it appears that aqueous solutions of PuO 2 + will be dominated by [PuO2(H2O)4]+. The proportions of the tetraaquo and pentaaquo species in aqueous solutions are expected to be significantly larger than that of the triaquo complex. The calculated relative energies of the tetraaquo and pentaaquo species agree with the fact that nearly all experimental reports on PuO2+ have reported equatorial aquo coordination numbers of 3.3−4, with none reporting a coordination number greater than 4.5a,43a,c,44 The radial distribution of oxygen atoms around the plutonium atom of PuO2+ are presented in Figure 4. The simulations were started with either 4 or 5 equatorial aquo ligands and lasted similar time scales, 18 ps. The number of equatorial aquo ligands did not change during the course of each simulation. Examination of the average structural parameters from both simulations reveals that the axial Pu− Oyl bonds are tighter (by about 0.03 Å) for the tetraaquo complex. Similarly, the equatorial Pu−Ow bonds are about 0.07 Å shorter for the tetraaquo complex (Table 1). The origin of this contraction is most likely a “crowding-out” effect in which there is greater competition for the actinyl 5f and 6d orbitals in the pentaaquo species, resulting in longer Pu−Oyl bonds, as

reasonable (0.02−0.04 Å) agreement with available experimental results.5a,7,43 In this work, the first coordination sphere (region between 2.2 and 3.0 Å) around the plutonyl moiety contains five aquo ligands. The average Pu−O bond distance to these aquo ligands is 2.46 Å, also in good agreement with most experimental results.5a,7,43a,c The second coordination sphere is found between 3.5 and 5.25 Å of the PuO22+ ion (Figure 1). This region contains 16.6 water molecules with an average Pu−O distance of 4.62 Å. There are ten water molecules in the equatorial region of the second shell and between six and eight molecules in the apical region (Figure 2). The equatorial region, in which the protons of the first-shell water ligands are hydrogen bound to the oxygen atoms of the second-shell water, is far more structured than the apical region, in which the protons of the second-shell water ligands are only weakly bound to the axial oxo atoms of the plutonyl group. Pentavalent Plutonyl. The equatorial coordination of PuO2+ was probed with metadynamics simulations, and the free energy profiles obtained are presented in Figure 3. The range encompassing the triaquo and pentaaquo complexes was

Figure 3. Free-energy profile for the equatorial coordination of PuO2+ obtained from metadynamics simulations. This profile was made by amalgamating profiles obtained from a 3 ↔ 4 and a 4 ↔ 5 simulation. 12259



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than that found in [PuO2(H2O)5]2+ (Figure 2). There is direct hydrogen bonding between two of the apical second sphere water molecules and each axial oxo atom of the plutonyl group. This region is more structured that it is for the hexavalent analogue. The average distance between the oxygen atoms of the apical water molecules and the actinyl center is 4.59 Å. The mean residence times46 of the second-shell water molecules in the apical region of PuO2+ (7.0 ps) are larger than that obtained for PuO22+ (5.6 ps) but less than that obtained for UO2+ (7.9 ps).16 This would indicate that the axial oxo atoms of PuO2+ have weaker negative charges than those of UO2+ and are by inference less susceptible to oxo-functionalization. A similar situation is obtained for the second-shell water molecules in the equatorial region (PuO2+: 17.1 ps; PuO22+: 19.2 ps; and UO2+: 17.4 ps16). These values suggest that the actinide center and the protons of the first-shell aquo ligands have smaller effective positive charges in PuO2+ than in UO2+. Tetravalent Plutonium Ion. The free energy profile of the equatorial coordination number around the Pu4+ ion is shown in Figure 5. The energy difference between [Pu(H2O)8]4+ and [Pu(H2O)9]4+ is about 1.40 kcal/mol with a small barrier of about 3.78 kcal/mol. These species are essentially isoenergetic and can readily undergo interconversion. We note that with such small energy differences it is possible that the nature of the aqueous media vis-á-vis pH and counterions might play a role in determining the dominant species that is observed experimentally. The number of aquo ligands around the Pu4+ ion is found to be eight. To further check the stability of the 8fold structure, simulations were carried out with initial structures possessing 9 aquo ligands in the first coordination sphere. One of these ligands is ejected after about 6−8 ps (Figure S1). There was no reintegration of another water ligand into the first coordination sphere during the lifetime of our simulations (up to 20 ps). Even so, the average Pu−Ow distances obtained for the [Pu(H2O)9]4+ (prior to ejection of one aquo ligand) is 2.47 Å. This is about 0.08−0.09 Å greater than the available experimental bond lengths of 2.39,43a 2.3847 and 2.39 ± 0.02 Å.48 In contrast, the average Pu−Ow distance in the simulations with eight water molecules in their initial structures is 2.41 Å (Figure 6). We note in passing that AttaFynn et al. obtained a coordination number of 8.7 and an average U−Ow distance of 2.45 Å in their recent CPMD simulations on U4+.16 Using the calculated energy difference

Figure 4. Radial distribution functions, gPuO(r), and their integrals, nPuO(r), of PuO2+ obtained from CPMD simulations with a cubic box containing 64 water molecules.

well as sharing of the donated actinyl electron density over more ligands, resulting in longer Pu−Ow bonds. The average Pu−Oyl and Pu−Ow bond lengths obtained from the simulation with four equatorial ligands are in better agreement with available experimental results. It is should be noted that the PBE functional used in this work, like most GGA functionals tend to favor electron delocalization or overestimation of bond lengths.45 On the other hand, our previous work29 on UO22+ as well as PuO22+ (Table 1) suggests an error range of about 0.01−0.03 Å relative to experimental data. This would suggest that the simulation initiated with four aquo ligands better reflects the experimental conditions. Conradson et al.5a,43a,44 and Panak et al.43c have previously reported that aqueous PuO2+ has fewer equatorial aquo ligands. They noted not only that the hexavalent species has a larger number of aquo ligands but also that these ligands are found at shorter distances. The second coordination sphere of [PuO2(H2O)4]+ contains an average of 16.1 water molecules. In most cases, the number of water molecules found between 3.50 and 5.25 Å ranges from 15 to 17. The average Pu−OII (subscript II indicates second coordination sphere) distance between these water molecules and the actinyl center is 4.59 Å. There are about 8 second sphere water molecules that form hydrogen bonds to the four aquo ligands found in the first coordination sphere. The apical region contains 6−8 water molecules and is more structured

Table 1. Average First Hydration Shell Parameters of the PuO22+ and PuO2+ Moieties Obtained from CPMD Simulations in Aqueous Solutionsa PuO2

2+

expt43b expt7 expt43c expt5a expt43a PuO2+ expt44 expt43c expt5a expt43a a

method

NH2O

Pu−Oyl

Oyl−Pu−Oyl

Pu−Ow

Ow−H

H−Ow−H

tilt angle

this work this work EXAFS EXAFS EXAFS EXAFS EXAFS this work this work EXAFS EXAFS EXAFS EXAFS

5 4 4.1 4.4 4.7 6 6 5 4 3.3 3.8 4 4

1.77 1.77 1.79 1.74 1.76 1.74 1.74 1.82 1.85

174.9 174.2

2.45 2.38 2.31 2.42 2.42 2.40 2.45 2.55 2.47 2.47 2.48 2.47 2.45

0.97 0.97

107.4 107.7

33.2 33.5

0.97 0.98

106.6 107.2

33.6 34.1

174.5 173.5

1.82 1.81 1.84

The bond distances are given in Å while the bond angles are given in deg. 12260



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metal center and the oxygen atoms of the water molecules in the second solvation sphere, is 4.58 Å. This is slightly shorter than the average U−OII distance of 4.65 Å obtained for [U(H2O)9]4+.16 This is most likely a reflection of the tighter inner coordination sphere in the plutonium octahydrate species. Close examination of the structure reveals that the second-sphere water molecules are hydrogen bonded to the inner-sphere ligands. The distances between the protons of the inner-sphere aquo ligands and the oxygen atoms of the secondsphere molecules, HI−OII, are usually about 1.45−2.13 Å. Trivalent Plutonium Ion. The free-energy profile of the coordination number of Pu3+ is shown in Figure 5. [Pu(H2O)8]3+ is predicted to be about 4.90 kcal/mol more stable than [Pu(H2O)9]3+. Previous DFT calculations on gas-phase Pu3+ clusters have shown that the [Pu(H2O)8·(H2O)]3+ species, with one water molecule in the second solvation sphere, is about 7.84 kcal/mol more stable than the [Pu(H2O)9]3+ complex.49 The role of the second-sphere water molecules was not fully included in the DFT calculations49 and might be responsible for the disparity with the results presented here. The [Pu(H2O)7]3+ complex is about 3.73 kcal/mol higher in energy than [Pu(H2O)8]3+ (Figure 5). This on the whole suggests that the coordination number of Pu3+ can vary between 7 and 9 but with the octaaquo complex being the dominant species. As a result of the calculated energy difference between the heptaaquo, octaaquo, and nonaaquo species, the average equilibrium aquo coordination number of Pu3+ is essentially 8 in aqueous solutions. According to available experimental reports, the coordination number of Pu3+ in aqueous solution is between 7.6 and 10. Allen et al. have revised their previous work which showed a 10.2 ± 0.9 water molecules6b in the first coordination sphere to 9.2 ± 0.9 by using different fitting parameters.6a Reich et al.7 obtained a coordination number of 7.6 and suggested that the nature of the aqueous media (10 mM LiCl and 1 M HClO4) might be responsible for the discrepancy between the experimental data sets.5a,b,6,7,43a,50 Our calculated coordination number of 8 supports the findings by Reich et al.7 The simulations carried out in this work predict an average Pu−Ow distance of 2.56 Å for [Pu(H2O)9]3+ and 2.53 Å for [Pu(H2O)8]3+. The calculated Pu−Ow bonds of [Pu(H2O)8]3+ better match the available experimental data than those in [Pu(H2O)9]3+ (Table 2). The best evidence for the existence of the nonaaquo complex was obtained by Matonic et al.51 Although they have reported detailed structural analysis of the single crystal of [Pu(H2O)9][CF3SO3]3, it should be noted that our simulations were carried out in solution and do not account for the role of large strongly coordinating counterions. Finally, similar to the case of Pu4+, there is a diffusion of one innersphere water ligand into the second coordination sphere after about 8 ps in simulations of [Pu(H2O)9]3+. This suggests similar dynamics to that observed by Leung et al. in their work on [U(H2O)9]3+ in which there was a stabilization to the octaaquo complex after 6.8 ps.52 The radial distribution function of [Pu(H2O)8]3+ is shown in Figure 7, and it shows a well-formed second solvation sphere between 3.50 and 5.25 Å. The average number of water molecules in this region is 14.7. There are 14−16 water molecules in this region for about 70% of all events. The average Pu−OII distance is 4.69 Å. This is only about 0.04 Å longer than that obtained by Duvail et al. in their classical MD simulations.53 We however note that their model potentials predicted a coordination number of 9 for Pu3+. The second

Figure 5. Free-energy profile for the aquo coordination of Pu4+ (top) and Pu3+ (bottom).

Figure 6. Radial distribution function, gPuO(r), and its integral, nPuO(r), of Pu4+ obtained from CPMD simulations with a cubic box containing 64 water molecules.

between [Pu(H2O)8]4+ and [Pu(H2O) 9]4+, the average equilibrium aquo coordination number of Pu4+ is 8.1. This would suggest a contraction of the first coordination sphere on going from U4+ to Pu4+. The origin of the contraction of the Pu−Ow bond length on going from [Pu(H2O)9]4+ to [Pu(H2O)9]4+ is most likely the same as that seen on going from [PuO2(H2O)5]+ to [PuO2(H2O)4]+ (Table 1). The second coordination sphere (where Pu−O is between 3.5 and 5.2 Å, Figure 6) of [Pu(H2O)8]4+ contains an average of 15.6 water molecules. The range of these second sphere water molecules is 13−18 with about 66.4% being between 15 and 16. The average Pu−OII distance, the distance between the 12261



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Table 2. Average First Hydration Shell Parameters of the Pu4+ and Pu3+ Ions Obtained from CPMD Simulations in Aqueous Solutions Pu4+ expt47 expt43a expt48 Pu3+ expt7 expt5a expt43a expt6a expt50 a

method

NH2O

Pu−Ow (Å)

Ow−H (Å)

H−Ow−H (deg)

tilt angle (deg)

this work this work EXAFS EXAFS EXAFS this work this work EXAFS EXAFS EXAFS EXAFS EXAFS

8 9a 8.4 8 7.8 8 9a 7.6 8−9 9 9.2 ± 0.9 9.9

2.41 2.47 2.38 2.39 2.39 ± 0.02 2.53 2.56 2.48 2.49 2.48 2.51 2.51

0.98 0.98

105.9 106.3

25.4

0.97 0.97

106.3 106.5

23.2

One aquo ligand is ejected from the first solvation sphere after about 8 ps. The average structural features were obtained prior to this process.

sphere of U4+ with the QM/MM and AIMD approaches, respectively.16 The second-sphere water molecules of [Pu(H2O)8]3+ are hydrogen-bonded to the inner-sphere water ligands, similar to the case in [Pu(H2O)8]4+ (Figure 8). The average angle of tilt of the first-shell aquo ligands of the PuO22+, PuO2+, Pu4+, and Pu3+ species are presented in Tables 1 and 2. These angles are interpreted in terms of hydrogen bonding between the coordinated aquo ligand and the water molecules of the second coordination sphere. The definition of the tilt angle used in this work follows the geometric model previously described by one us54 and is shown in Figure 9. The tilt angles of the plutonyl systems are comparable at 33.2° and 33.6° for the hexavalent and pentavalent species, respectively. The magnitude of these angles is representative of the tetrahedral character of the hydrogen bonding near the first shell. In contrast, the tilt angles obtained for the Pu4+ and Pu3+ species are much lower, 25.4° and 23.2°, respectively. This indicates trigonal hydrogen bonding near the first shell. First Hydrolysis Constants of Plutonium Species. The calculated free energies for the hydrolysis reactions as well as the computed pKa values of PuO22+, PuO2+, Pu4+, and Pu3+ are given in Table 3, where they are compared to available experimental data. The free energy profiles obtained for the

Figure 7. Radial distribution function, gPuO(r), and its integral, nPuO(r), of Pu3+ obtained from CPMD simulations with a cubic box containing 64 water molecules.

coordination sphere in their simulations contained 21.6 water molecules. This disparity with our results is not surprising as it appears that classical MD and QM/MM approaches predict greater numbers of second-sphere water molecules than the AIMD approach used in this work. For example, Atta-Fynn et al. found 19 and 15.2 water molecules in the second solvation

Figure 8. Second-shell structure of [Pu(H2O)8]3+ (left) and [Pu(H2O)8]4+ (right) showing their second coordination sphere structures. Several atoms in the second coordination sphere were omitted for clarity. 12262



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Figure 9. A geometric model definition of the tilt angle in terms of the structural parameters of the first coordination sphere.

hydrolysis of the plutonium ions from our metadynamics simulations are presented in Figure 10. Hexavalent Plutonium Ion. The free-energy profile for the hydrolysis of PuO22+ yields a ΔF value of 8.78 kcal/mol. The pentaaquo species of PuO22+ was used in the metadynamics simulations. An entropic correction of −kBln5 is used to account for the fact that any of the five equatorial water molecules could be hydrolyzed under realistic conditions. This results in a corrected ΔF value of 7.82 kcal/mol. This agrees well with the value of 7.98 ± 0.67 kcal/mol that was obtained by Rao et al.8c from potentiometric titrations at 298 K. At 300 K, the ΔF value of 7.82 kcal/mol obtained from our simulation corresponds to a pKa value of about 5.7, which is in good agreement with the experimental values of 5.5 ± 0.515b and 5.85 ± 0.49.8c The hydrolysis of PuO22+ follows the Grotthuss mechanism in which a proton hops from a coordinated ligand to a second-sphere water molecule.55 This is accompanied by a simultaneous elongation of the O−H bond of the recipient water molecule and reorganization of the hydrogen bond network around both the recipient and acceptor oxygen atoms. We note that there is an increase in the ΔF value by about 1.03 kcal/mol on going from UO22+ to PuO22+.16 This is consistent with, but slightly overestimates, the experimental ΔΔFUO22+→PuO22+ value of 0.62 kcal/mol.8c,g From a methodological perspective, the choice of the −kB ln(n) as an entropic correction factor was based on the observation of the general hydrolysis mechanism of the actinide and actinyl aquo complexes during our simulations. At certain points (initial expansion of the O−H bond and a return of the O−H bond back to 0.96 Ǻ ), we noticed slight elongation/ contraction of the second proton attached to the hydrolyzed water ligand. The logarithmic portion of this entropic correction, −kB ln(n), reflects the treatment of one aquo ligand as a source of two potentially hydrolyzable protons and the slight coupling between them observed at the onset and conclusion of each hydrolysis.

Figure 10. Free-energy profile for the hydrolysis of aqueous plutonium and plutonyl ions.

Pentavalent Plutonium Ion. The raw ΔF value of PuO2+ hydrolysis from the metadynamics simulations was found to be 13.89 kcal/mol. The tetraaquo complex was used in these simulations as it was found to be more stable than the triaquo and pentaaquo species (Figure 3). Accounting for the entropic correction results in a ΔF value of 13.06 kcal/mol, which corresponds to a pKa value of 9.51. Bennett et al. have obtained a lower limit of 9.73 ± 0.10 for the experimental pKa value of PuO2+.8a On the other hand, Lemire et al. have proposed a value of 11.3 ± 1.5 as the lower limit by extrapolating from available data for NpO2+.15b The value obtained from our simulations is significantly lower than the estimate provided by Lemire et al.15b Given our good agreement with experimental data for PuO22+ (and Pu3+, as discussed in a later section), we conclude that PuO2+ has a much lower first hydrolysis constant than the estimate of Lemire et al.15b To support this conclusion, we note that the hydrolysis constant of NpO2+ was recently found to be 8.98 ± 0.09 by Rao et al.56 In addition, given that we have previously obtained an hydrolysis constant of 8.51 for UO2+ using metadynamics simulations,16 a pKa value in excess of 11.3 for PuO2+ would be improbable, with the value of 9.51 obtained from our simulations (Table 3) and Bennett et al.’s8a limit of 9.73 ± 0.10 being more realistic. Tetravalent Plutonium Ion. In the case of Pu4+, the raw ΔF value was predicted to be 1.48 kcal/mol for [Pu(H2O)8]4+. This aquo species was used in the metadynamics simulations as it was found to be more stable than [Pu(H2O)9]4+. Correction for entropic effects results in a ΔF value of 0.24 kcal/mol, a value that corresponds to a pKa of 0.17. We however note that a raw ΔF value of 2.13 kcal/mol was obtained for [Pu(H2O)9]4+. This

Table 3. pKa, Free Energies (ΔF, kcal/mol), and Correction Factors of PuO22+, PuO2+, Pu4+, and Pu3+ Obtained Experimentally and from Metadynamics Simulations at 300 K ΔF value

entropic correction

corrected ΔF value

simulated pKa

exptl estimates of ΔF

exptl pKa

PuO22+

8.78

−0.96

7.82

5.70

PuO2+ Pu4+

13.89 1.48

−0.83 −1.24

13.06 0.24

9.51 0.17

Pu3+

10.37

−1.24

9.13

6.65

7.50 7.98 ± 0.678c ≥13.36 0.62 0.00 ± 0.28 −0.82 9.41

5.5 ± 0.510a 5.85 ± 0.498c ≥9.738a 0.5912 0.00 ± 0.208f −0.6010a 6.910a

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collective variable is however not able to do this. In the limit of straightforward thermodynamic integration and at longer simulations, the use of the O−H distance constraint will inevitably find the proton-hopping pathway and yield the same results as metadynamics simulations using the coordination collective variable used in this work. It is also important to note that the ability or inability of GGA functionals to properly general liquid structure of bulk water is simply not the dominant source of error for the kinds of simulations carried out in this work. In the case of the simulations of the hydrolysis constants, where a proton drifts from the first shell and transiently becomes a Zundel cation (before rearrangement of the hydrogen bond network), it might be expected that the liquid-like nature of bulk water might play a role.55 However, we expect the energies associated with this error to be rather small (in actual fact, infinitesimally so when compared to the energy to dissociate the O−H bond!). As previously noted,31d although there are differences between the second-shell water− water interactions as described by the PBE0 and PBE96 functionals, these differences are not large. Trends in Hydrolysis Constants and Effective Charges. The pK a values obtained from our simulations and from experimental work (Table 3) follow the trend PuO2+ > Pu3+ > PuO22+ > Pu4+. This trend also reflects the relative endothermicities of the hydrolysis reactions. This is supported by the calculated Hirshfeld charges39 obtained for the plutonium atoms in gas-phase [PuO2(H2O)4]+, [Pu(H2O)8]3+, [PuO2(H2O)5]2+, and [Pu(H2O)8]4+ cluster complexes. The values of these charges are 0.75, 1.08, 1.15, and 1.33, respectively, implying that the ΔF and pKa values decrease with increasing charges at the metal center. A similar trend is observed after Mulliken charge analysis of snapshots obtained from the CPMD simulations. The geometries of [PuO2(H2O)4]+, [Pu(H2O)8]3+, [PuO2(H2O)5]2+, and [Pu(H2O)8]4+ cluster complexes were used as the initial structures during the gas-phase geometry optimizations of their uranium and neptunium analogues. The calculated charges for the An(V), An(III), An(VI), and An(IV) centers are 0.82, 1.10, 1.17, and 1.40 for uranium and 0.77, 1.09, 1.23, and 1.35 for neptunium, respectively. This is similar to the trend observed for the plutonium ions. The calculated charges also suggest that for each oxidation state the ΔF and pKa values would be smallest for uranium and largest for plutonium.

value illustrates the fact that the coordination number has little overall effect on the energy difference (≤1.0 kcal/mol) between the hydrolyzed product and the reactant (Table S1). The pKa obtained for [Pu(H2O)8]4+ from the metadynamics simulations is vastly different from a value of −0.60 obtained from older experimental data sets10 and the NEA-TDB,10 suggesting spontaneous hydrolysis. This value is however in good agreement with the values of 0.59 obtained by Yusov et al.12 and 0.00 ± 0.20 obtained by Yun et al.8f It also agrees with the estimated values obtained by Silver.8d,e,57 We note that as a result of the discrepancies between the various experimental studies on Pu4+ hydrolysis, Lemire et al.15b have previously suggested a rather large value of 0.78 ± 0.60. The reaction ΔF obtained from our simulations indicates the hydrolysis of Pu4+ is not spontaneous, a situation suggested by the older experimental data.10 The reaction ΔF obtained for [Pu(H2O)8]4+ is however very small. Trivalent Plutonium Ion. For Pu3+, the metadynamics simulations were carried out on [Pu(H2O)8]3+. The raw and corrected ΔF values were found to be 10.37 and 9.13 kcal/mol, respectively. The corrected ΔF value corresponds to a pKa of about 6.7. This is within 0.2 pH units of the experimental value of 6.9. The hydrolysis reaction follows a similar mechanism to that of PuO22+. Collective Variable for Actinide Hydrolysis. Two approaches were used in simulating the hydrolysis constant of PuO2+ with metadynamics. The first approach employed a collective variable describing the coordination of the oxygen atom of an aquo ligand with all protons in the periodic box. This (labeled as ξ(O′−Hall)) approach is exactly the same as was used for all the other plutonium ions. The results obtained with this approach are presented in Table 3. The second approach employs a collective variable corresponding to the coordination number of the oxygen atom of an aquo ligand with a specific proton attached to it. This is for all intents a bond-stretching collective variable. We label this collective variable as ξ(O′−H′). The raw ΔF and pKa values of PuO2+ obtained with this approach are 18.88 kcal/mol and 13.15, respectively. These values are significantly larger than those obtained with the ξ(O′−Hall) approach. For Pu3+, the reaction energy obtained with the ξ(O′−H′) approach, 14.20 kcal/mol, is also significantly larger than that obtained with the ξ(O′−Hall) approach (Table 3). The simulated pKa value, 9.44, is far greater than the value obtained by the ξ(O′− Hall) approach as well as the available experimental data (Table 3). Overall, the accuracy of metadynamics simulations in predicting the hydrolysis constants of actinide species appears to be very sensitive to the choice of collective variable. It is thought that the ξ(O′−H′) approach or a simple bond length (O−H) collective variable does not adequately capture the dynamics occurring in the second coordination sphere during hydrolysis of the plutonium/plutonyl aquo complexes. The mechanism of the hydrolysis of the complexes of plutonium ions studied in this work follows the Grotthuss mechanism.55 A coordination number collective variable (between a particular oxygen atom and all the protons in the cubic box) touches all the neighboring protons whose hydrogen bond networks have to be reorganized immediately after the lysis of the PuO−H bond. As such, this order parameter can add energy to a key degree of freedom in the reaction mechanism (the hopping of the dissociated proton to a secondsphere water molecule and consequent hop of a proton initially on that second-sphere water molecule). The O−H distance

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CONCLUSIONS Car−Parrinello molecular dynamics simulations of the Pu3+, Pu4+, PuO2+, and PuO22+ ions have been carried out in aqueous solutions at 300 K while employing periodic boundary conditions. Metadynamics free energy simulations were used to probe the equilibrium number of aquo ligands in the first coordination shell of these ions as well as their first hydrolysis reactions. The number of aquo ligands in the first coordination sphere of Pu3+, Pu4+, PuO2+, and PuO22+ is 8, 8−9 (average of 8.10), 4, and 5, respectively, in aqueous solution. For the trivalent and tetravalent ions, the octaaquo complexes are respectively about 4.90 and 1.40 kcal/mol more stable than their nonaaquo counterparts. In any case, a first-shell aquo ligand is ejected into the second shell after about 8 ps during simulations on [Pu(H2O)9]3+ and [Pu(H2O)9]4+. In the case of PuO2+, there is a barrier of about 10−15 kcal/mol between [PuO2(H2O)3]+ and [PuO2(H2O)4]+, with the latter being about 13.42 kcal/mol more stable. [PuO2(H2O)5]+ was also found to be less stable 12264



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than [PuO2(H2O)4]+ by about 3.10 kcal/mol. These results agree with spectroscopic data that have indicated an equatorial coordination number of 3.3−4.0 for PuO2+. The hexavalent complex PuO22+ most likely has five equatorial aquo ligands, although the energy difference between [PuO2(H2O)5]2+ and [PuO2(H2O)4]2+ is 2.55 kcal/mol, with the former being more stable. The apical region of the second shell of PuO2+ is more structured than that of PuO22+. There are hydrogen bonds between each axial oxo atom of PuO2+ and two apical water molecules. The mean residence time of apical and equatorial second-shell waters correlates with the overall electron density at the axial oxo atoms and the actinide center, respectively. The mean residence time of apical water molecules is higher for PuO2+ than for PuO22+, although the former is lower than that of UO2+. This indicates that the axial oxo atoms of PuO2+ have smaller negative charges and are less susceptible to oxofunctionalization than those of UO2+. In addition, the residence times of the second-shell water molecules in the equatorial region are smaller for PuO2+ than UO2+. This indicates that the actinide center has a smaller positive charge in the former than in the latter. The average distances between the plutonium ion and the first-shell water molecules are 2.53 and 2.41 Ǻ for Pu3+ and Pu4+, respectively. This is most likely indicative of the fact that Pu4+ has a greater effective positive charge, with attendant contraction of the Pu−Ow bonds. This contraction is also reflected in the second coordination sphere, for which the Pu− O bond lengths are 4.69 and 4.58 Ǻ , respectively, for these ions. The average second-shell coordination number for Pu4+ is 15.6 while that of Pu3+ is 14.7. The average tilt angles for the firstshell aquo ligands of the Pu4+ and Pu3+ species are around 23°− 26°, much smaller than those obtained for the plutonyl species, 33°−34°. The hydrogen bonding around the first-shell water molecules are trigonal for the Pu4+ and Pu3+ species and tetrahedral for the plutonyl species. The simulated pKa values for the first hydrolysis reactions of Pu3+, Pu4+, PuO2+, and PuO22+ are 6.65, 0.17, 9.51, and 5.70, respectively. For Pu3+ and PuO22+, the values obtained from the simulations are within 0.30 pH unit of the best experimental estimates. In the case of Pu4+, a positive pKa value indicates that the first hydrolysis reaction is endothermic. Our results disagree with older experimental values in the NEA-TDB. Our results support the more recent estimates by Yusov et al. (pKa of ∼0.59) and Yun et al. (pKa of ∼0.00 ± 0.20). The simulated pKa value for PuO2+ agrees well with the value of >9.73 by Bennett et al.8a but disagrees with the previously proposed value of ≥11.3 ± 1.5 which was obtained by extrapolating from NpO2+ data. The hydrolysis constants of these ions in aqueous solution correlate well with the effective charge at the plutonium center. It appears that the greater the charge at the metal center, the lower the free energy and pKa value associated with the first hydrolysis reaction. The overall effect of this is a trend of PuO2+ > Pu3+ > PuO22+ > Pu4+ and Pu > Np > U in the pKa values.

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material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (W.A.d.J.). Present Address

† Scientific Computing Group, Lawrence Berkeley National Laboratory, Berkeley, CA.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was funded by the BES Heavy Element Chemistry program in the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy. All calculations were performed using the Molecular Science Computing Capability in the William R. Wiley Environmental Molecular Science Laboratory, a national scientific user facility sponsored by the U.S. Department of Energy’s Office of Biological and Environmental Research and located at the Pacific Northwest National Laboratory, operated for the Department of Energy by Battelle.

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ASSOCIATED CONTENT

S Supporting Information *

The Pu−Ow bond lengths of [Pu(H2O)9]4+ over an 8 ps time scale; charge localization and electronic structures of the plutonium aquo complexes; convergence of the free energy landscapes obtained from the metadynamics simulations. This 12265



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