Molecular Dynamics Study of the Coordination Sphere of Trivalent

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Molecular Dynamics Study of the Coordination Sphere of Trivalent Lanthanum in a Highly Concentrated LiCl Aqueous Solution: a Combined Classical and Ab Initio Approach L. Petit,† R. Vuilleumier,*,‡ P. Maldivi,† and C. Adamo§ Laboratoire de Reconnaissance Ionique et de Chimie de Coordination, CEA-INAC/LCIB (UMRE 3 CEA-UJF), 17 rue des Martyrs, F-38054 Grenoble Cedex 9, France, Laboratoire de Physique The´orique de la Matiere Condense´e, UMR7600, UniVersite´ Pierre et Marie Curie, Paris, Tour 24 Boite 121, 4 place Jussieu, F-75252 Paris CEDEX 05, France, and Laboratoire d’Electrochimie et de Chimie Analytique, CNRS UMR-7575, Ecole Nationale Supe´rieure de Chimie de Paris, 11 rue P. et M. Curie, F-75231 Paris Cedex 05, France ReceiVed: February 27, 2008; ReVised Manuscript ReceiVed: May 30, 2008

The first coordination sphere of trivalent lanthanum in a highly concentrated (14 M) lithium chloride solution is studied with a combination of classical molecular dynamics and density functional theory based first principle molecular dynamics. This method enables us to obtain a solvation shell of La3+ containing 2 chloride ions and 6 water molecules. After refinement using first principle molecular dynamics, the resulting cation-water and cation-anion distances are in very good agreement with experiment. The 2 Cl- and the 6 water molecules arrange in a square antiprism around La3+. Exchange of water molecules was also observed in the firstprinciple simulation, with an intermediate structure comprising 7 water molecules stable for 2.5 ps. Finally, evaluation of dipole moments using maximally localized Wannier functions shows a substantial polarization of the choride anions and the water molecules in the first solvation shell of trivalent lanthanum. 1. Introduction Trivalent rare earths have been much studied over the past decade because of their implication for nuclear waste disposal. In this regard, it is of importance to be able to determine their coordination sphere in solution, in order to understand their properties and so to allow the improvement of current reprocessing avenues. Experimentally, this is a difficult task because the hydration sphere of trivalent f elements is known to be quite labile, and results can also be dramatically dependent on the technique used or on the experimental conditions. For instance, numerous experimental studies have focused on the determination of the stability constant of chloride complexes of trivalent f elements1–3 because such systems are assumed to be formed in geological salt formations when nuclear waste are being stored. Yet, inconsistencies between results from different experimental works show that the coordination chemistry of these compounds is still an open question. In the 1960s, Shiloh et al. have studied the evolution of the UV-vis spectra of several actinides as a function of chloride concentration.4,5 They found that neptunium and plutonium III exhibit a strong 5f n f 5f n-1 6d transition in concentrated lithium chloride (|LiCl| ) 14 M) due to the coordination of two chlorides to the metal center.4 Few years ago, Allen et al. used EXAFS spectroscopy (extended X-ray absorption fine structure) under similar experimental conditions.6,7 In contrast to Shiloh et al., they did not identify any chloride within the plutonium(III) first coordination sphere, even for a high concentration in LiCl. We have felt relevant to investigate such a contradiction with theoretical tools, and recently, we have studied the coordination * Corresponding author. E-mail: [email protected]. † Laboratoire de Reconnaissance Ionique et de Chimie de Coordination, CEA-INAC/LCIB (UMRE 3 CEA-UJF). ‡ Laboratoire de Physique The ´ orique de la Matiere Condense´e, UMR7600, Universite´ Pierre et Marie Curie. § Laboratoire d’Electrochimie et de Chimie Analytique, CNRS UMR7575, Ecole Nationale Supe´rieure de Chimie de Paris.

sphere of several trivalent f elements in a highly concentrated LiCl solution in order to determine whether chloride ions could enter plutonium(III) first coordination sphere. Our first approach was to follow Shiloh’s spectroscopic study by reproducing theoretically f-f and f-d intrametal transitions.8 Unfortunately, even though we managed to describe quite well f-f transitions, our method [ligand field density functional theory, LFDFT, see refs 9 and 10] was found to be unworkable to deal with f-d transitions that are more sensitive to the metal environment. In the following, we have thus decided to study the first coordination sphere of trivalent f elements with an alternative approach: molecular dynamics (“MD” thereafter). In classical molecular dynamics, interatomic interactions are calculated with empirical potentials derived from experimental data or quantum calculations, so electronic properties cannot be described. For trivalent lanthanides and heavy actinides that are known to be hard acid in the HSAB principle,11 soft sphere models combined with polarization or charge transfer effects are quite reliable.12–15 For actinides, with the exception of uranyl UO22+,12,16–19 fewer studies are available because their 5f orbitals are often involved in the chemical bonding which requires to treat f electrons explicitely. First principle molecular dynamics (FPMD) include a description of the electrons since the trajectories of the nuclei are obtained by on the fly DFT calculations,20,21 and offer the possibility of simulating a variety of environments. However, FPMD rely on transferable pseudopotentials to describe core electrons. To date, some pseudopotentials have been proposed for actinides and lanthanides,22,23 and first simulations of lanthanides in water have provided encouraging results.24–28 Such studies still remain rather scarce because of the well-known limitations of actinide systems: large number of electrons, open-shell systems, relativistic effects, quasi-degeneracy of f orbital levels, etc. Moreover, FPMD calculations require large computer-time that drastically limit both the size of the system and the length of the simulation.

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Figure 1. FPMD radial distribution functions (full line) gLa-Cl (on the left) and gLa-O (on the right) and corresponding coordination number cn (dashed line).

TABLE 1: Structural Parameters for the First Coordination Sphere of Trivalent Lanthanum in |LiCl| ) 14 Ma FPMD La-Cl, 1st peak La-Cl, 2nd peak La-O, 1st peak La-O, 2nd peak

CMD

experiment

r, Å

cn

r, Å

cn

r, Å

cn

| LiCl |, mol · L-1

ref

2.88 4.9 2.55 4.7

2.0

2.75 5.0 2.42 4.6

2.0

2.92 ( 0.005

2.1 ( 0.2

14

7

6.0

2.57 ( 0.003

6.5 ( 0.37

14

7

6.2

a r is the interatomic distance, and cn is the coordination number. Experimental data are from EXAFS measurements, ref 7. FPMD: first principle molecular dynamics. CMD: classical molecular dynamics.

In the present work, we study the coordination sphere of trivalent lanthanum in a highly concentrated LiCl aqueous solution with Car-Parrinello MD29 combined with classical MD. This is a simpler system than trivalent plutonium and we consider this study as a first step in that direction. Indeed, f orbitals in La(III) are empty, making La3+ a closed-shell system, and reducing considerably the computer time. Moreover, the coordination properties of lanthanum(III) are close to that of actinides(III) as they feature the same charge and similar ionic radii. Lanthanum(III) is thus an interesting system to check that our approach provides reasonable results to study plutonium(III) next. We have chosen [LiCl] ) 14 M in agreement with experimental references.4–7 We have already studied such a solution30 and we have shown that FPMD provide a good agreement with experimental data but cannot fully reorganize the structuring of the electrolyte. To overcome such a problem, an approach borrowed from amorphous material consists in combining classical MD with FPMD: the system is first preorganized with classical MD, and the resulting configuration is then refined with FPMD.31,32 Herein, we have applied this procedure and then we have checked the refined structures by comparison with experimental data. This has allowed the determination of the three-dimensional structure of the hydration shell. Water rearrangement in the first solvation shell could also be observed on one instance in the simulation. Finally, we have studied the influence of the trivalent cation on the electronic distribution in its surroundings through the dipole moments of the chloride anions and of water molecules. 2. Computationals Details A preliminary classical molecular dynamics simulation was performed with the Moldy package33 to get a reliable initial configuration for the first principle simulation as well as to determine an adequate size for the periodic box. The LennardJones 12-6 potential for the La-O interaction was taken from previous molecular dynamics works by Kowall et al. in which the authors derive a 8-6 potential for the Nd-O interaction.13 This potential was then adapted for lanthanum into a 12-6 form using Maple software.34 Missing parameters for La-Li and

Figure 2. Angular distribution of θ ) ∠Cl-La-Cl from FPMD.

La-Cl interactions were calculated from Lorentz-Berthelot rules. Various sizes of box were tested according to our previous study on 14 M LiCl solution.30 Simulations were carried out for 400 ps at 300K, with 2 previous equilibration steps of 100 ps each, at 800K and 300K respectively, in order to avoid too slow dynamics due to the high concentration in LiCl. Each time, we checked that the mean pressure was in the order of that found for a reference system of 243 H2O, 56 Cl-, 32 Li+, and 8 La3+ (reference box for lanthanum in 14 M lithium chloride solution). As mentioned above, water molecules in lanthanum first coordination sphere may be quite mobile, whereas chloride ions may stay longer nearby the metal center. We have thus chosen the box giving the best agreement with the experimental number of chloride ions surrounding lanthanum,7 that is a charged box with 30 H2O, 7 Cl-, 5 Li+, and 1 La3+. With respect to a neutral box, this should also avoid a too strong structuration of the system. To refine this configuration, the first principle simulation was performed with the Car-Parrinello molecular dynamics code (CPMD).35 We chose the BP86 functional36 as it has already proved to provide a reliable description of trivalent lanthanide and actinide complexes.37,38 The computational details for the LiCl solution have been described in ref 30, and BP86 was then proven to describe the electrolyte properly. For lanthanum, we

Coordination Sphere of Trivalent Lanthanum

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Figure 3. Evolution of the first coordination sphere of lanthanum along the FPMD simulation. Lanthanum in purple, chloride in blue, oxygen in red and hydrogen in white. Water molecules are represented in gray when they are located in the second solvation shell.

Figure 4. Plot of the La-O distances during the water exchange. t ) 5 ps is the beginning of the production run. Labels O1 and O3 are the same as in Figure 3.

Figure 5. On the left: coordination sphere of trivalent lanthanum in | LiCl | ) 14 mol · L-1 at the end of the FPMD simulation. On the right: top view of the square antiprismatic structure.

have generated a Troullier-Martins norm-conserving pseudopotential39 along with the Kleinman-Bylander decomposition40 for which the lanthanum is described in its ionic form La3+. The electronic wave functions have been expanded in a plane

waves basis set up to the energy cutoff of 100 Ry. A pseudization radii of 2.03 au was employed. We checked the validity of our pseudopotential on a model system, [La(Cl)2(H2O)7]+, whose CPMD optimized geometry was compared to that obtained with Gaussian 0341 (BP86, 6-31++G(2d,2p)) and ADF42 (BP86, ZORA, TZ2P) codes. Structural discrepancies were found to be negligible. We also checked that orbital energy levels from CPMD were consistent with that calculated with the ADF code. The pre-equilibrated geometry from classical MD was introduced as the initial configuration for the first principle simulation. It was carried out in a cubic box of size 10.37 Å with periodic boundary conditions. To ensure an accurate description of structural properties, we have taken µ ) 500 au for the fictitious mass while the time step was 4.0 au (0.096 fs). This should allow for negligible dependency of our results with respect to the fictitious mass µ.43 From our previous study on LiCl,30 we know that the dynamics in highly concentrated LiCl is quite slow. Moreover, the BP86 functional has been shown to increase artificially the structuration of water.44 For these reasons, the temperature was first set to 350 K (instead of 300 K, see ref 30) for 5 ps to make the system equilibrate, and then the trajectories were sampled for 15 ps in the NVE ensemble. The maximally localized Wannier functions45 were collected every 10 steps to compute molecular dipole moments. In the following, the VMD program46 is used for visualizations. Radial distribution functions g(r) are also analyzed with VMD. Corresponding g(r) results are presented from 0 to 5 Å to avoid double-counting due to periodic boundary conditions. 3. Results and Discussion 3.1. Structure. The behavior of the lithium chloride solution in our FPMD simulation is similar to that found in a previous study for the bulk solution (|LiCl| ) 14 M30). The main characteristics of the highly concentrated LiCl solution are found

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Figure 6. Distribution of dipole moments for chloride ions and water molecules within lanthanum first coordination sphere and within the bulk solvent (from FPMD).

back, i.e. ion paring through direct contact between Li+ and Cl- ions, as well as water bridging between Li+ and Clcoordination spheres. Distances are also hardly modified with respect to our previous simulation (see ref 30), with a discrepancy in the order of 0.02 Å, and always below 0.05 Å. The only significant change occurs for coordination numbers. Lithium ions still feature a tetragonal environment, with three stable forms: Li+ + 4H2O, Li + + Cl- + 3H2O and Li + +2Cl+2H2O. Yet, ion-pairing is found to happen more often than in the bulk LiCl solution, with 3 water molecules and 1 chloride ion on average surrounding each lithium cation (vs 3.5 water molecules and 0.5 chloride ions in our previous simulation, ref 30). Radial distribution functions for the La-Cl and the La-O interactions from the FPMD are plotted in Figure 1. The main peaks are detailed in Table 1. On the whole, our simulation is in very good agreement with EXAFS measurements.7 The lanthanum cation is on average surrounded by 2 chloride anions and 6 water molecules, for a total coordination number of 8. The radial distribution function for the La-Cl interaction presents a first peak at 2.88 vs 2.92 Å experimentally. It is rather sharp and exhibits a well-pronounced zero minimum, indicating that chloride ions are tightly bound to lanthanum. Such a low mobility is in line with the strong electrostatic stabilization between the two charged La3+ and Cl- species. The angular distribution of chlorides (θ ) ∠Cl-La-Cl in Figure 2) is rather large, and spreads from 80° to 100°. The mean angle is on the order of 90°. Further chorides ions are found to be below 5 Å, that is to say within the second hydration sphere. The La-O radial distribution function also compares nicely with experimental values. The first maximum (Figure 1, on the right) is centered at 2.55 Å, whereas the experimental distance is 2.57 Å. This peak is well-defined, showing that the first hydration sphere is clearly separated from the second one. 3.2. Relaxation of the Solvation Shell. In Table 1, we have mentioned results from the classical molecular dynamics preliminary step. As expected, as the length of the FPMD simulation is rather short with respect to relaxation times, the coordination numbers of water molecules and chloride ions are hardly modified. In contrast, there is a significant adjustment of La-Cl and La-O distances, that are increased by 0.13 Å during the Car-Parrinello simulation. Still, one rearrangement of water molecules around lanthanum is observed during the FPMD simulation. In Figure 3, we have depicted the evolution of the first coordination sphere of lanthanum during the simulation. A plot of the La-O distances during the water exchange is also given in Figure 4. In the starting configuration (t ) 0 ps), the metal is surrounded by 2 chlorides and 6 water molecules located according to a slightly

distorted square antiprismatic structure. During the equilibration run (t ) 0-5 ps), this configuration tends to get more and more distorted but no exchange between ligands is observed. The oxygen atom O1 is then located outside of the first coordination sphere (Figure 3, A). The production phase then starts and, after 2.5 ps of simulation (t ) 7.5 ps), an additional water molecule (called O1) enters the first coordination sphere of lanthanum (see Figure 4). In Figure 3, sketch B, O1 is now directly bound to lanthanum, while O2 is located in an apical position, for a total coordination number of 9. This transient configuration actually maintains for 2.5 ps, until t ) 10 ps. The strong steric hindrance makes chloride ions come closer to one another, and the ∠Cl-La-Cl angle is then reduced by 20°, down to 70°. Water molecules O3 and O4 also tend to move away from lanthanum, as displayed in sketch C (Figure 3), but only one of them (O3) finally goes out of the first coordination sphere. The eight remaining ligands (2 Cl- + 6H2O) then rearrange their positions and in sketch D, the square antiprismatic configuration is restored. The geometry of the first coordination sphere of lanthanum in the last picoseconds of the simulation is shown in Figure 5: O1 is in place of the initial O2 position and O2 is in place of O3. The sketch on the right should help to visualize the square antiprismatic configuration. Hydrogen atoms are not displayed to make the identification of the coordination polyhedron easier. 3.3. Ions and Water Dipole Moments. The influence of trivalent lanthanum on the electronic structure of water molecules and chloride anions have been studied using maximally localized Wannier orbitals. They provide an unambiguous way to assign dipole moments to ions and molecules. With this method the dipole moment of water molecules in pure water has been previously estimated as being in the order of 3.0 D by Silvestrelli and Parrinello.47,48 The change in the dipole moment distributions for the first shell and the bulk solvent is shown in Figure 6. On the whole, the metal cation has a strong influence on neighboring ligands: the dipole moment of chloride ions is increased from 0.52 D in solution to 1.39 D within lanthanum first coordination sphere. The water dipole moments are similarly moved up by 0.48 D, a value larger than what has been obtained in other studies of solvation of monovalent ions49,50 This is primarly due to the small size and large charge of trivalent lanthanum. The dipole moment of chloride anions is even more affected by trivalent lanthanum as might be expected from its larger polarizability: indeed the ratio between the two dipole moment changes, choride anions or water molecules, is close to the ratio of their polarizability divided by the square of their distance to lanthanum. Lanthanum acquires a dipole moment of 0.15 D on average, showing that the polarizability of the cation cannot be neglected.

Coordination Sphere of Trivalent Lanthanum 4. Conclusion Car-Parrinello molecular dynamics have been successfully applied to the description of the first coordination sphere of trivalent lanthanum in concentrated lithium chloride (|LiCl| ) 14 mol · L-1). To ensure a correct number of chloride ions around lanthanum, the initial structure was taken from classical molecular dynamics. Our first principle simulation reproduces very well experimental interatomic distances. The coordination number between the La3+ ion and water molecules is also well described, while the number of chloride ions around lanthanum is much more dependent on the classical MD step. The solvation shell arranges in a square antiprism around La3+. Distances are strongly modified with respect to the classical simulation, and we also observe exchange of water molecules in the first coordination sphere of the metal cation. This exchange occurs through an intermediate structure comprising 7 water molecules stable for 2.5 ps. Finally, substantial polarization of the choride anions and the water molecules in the first solvation shell of trivalent lanthanum was found, while La3+ is itself polarized with an average 0.15 D dipole moment. This is of course very encouraging for a future application to trivalent plutonium, for which the coordination of chloride ions is still debated. Methods for accelerated dynamics could then provide a solution to the sampling problem of the plutonium-chloride coordination number and help to determine the most probable coordination in conjunction with FPMD. Acknowledgment. The authors would like to thank the Centre de Calcul Recherche et Technologie (CCRT) for a generous allocation of computer time. References and Notes (1) Sillen, L. G.; Martell, A. E. Stability constants of metal-ion complexes; Spec. Publ. No. 17; The Chemical Society: London, 1964. Sillen, L. G.; Martell, A. E. Stability constants of metal-ion complexes; Spec. Publ. No. 25; The Chemical Society: London, 1971. (2) Fangha¨nel, T.; Kim, J. I.; Klenze, R.; Kato, Y. J. Alloys. Compd. 1995, 225, 308. (3) Chopin, G. R. J. Alloys. Compd. 1997, 249, 9. (4) Shiloh, M.; Marcus, Y. J. Inorg. Nucl. Chem. 1966, 28, 2725. (5) Shiloh, M.; Marcus, Y. Isr. J. Chem 1965, 3, 123. (6) Allen, P. G.; Bucher, J. J.; Shuh, D. K.; Edelstein, N. M.; Reich, T. Inorg. Chem. 1997, 36, 4676. (7) Allen, P. G.; Bucher, J. J.; Shuh, D. K.; Edelstein, N. M.; Craig, I. Inorg. Chem. 2000, 39, 595. (8) Petit, L.; Borel, A.; Daul, C.; Maldivi, P.; Adamo, C. Inorg. Chem. 2006, 45, 7382. (9) Atanasov, M.; Daul, C.; Rauzy, C. Chem. Phys. Lett. 2003, 367, 737. (10) Atanasov, M.; Daul, C.; Rauzy, C. Struct. Bonding 2003, 106, 97. (11) Pearson, R. G. Chemical Hardness; Wiley-VCH: New York, 1997. Pearson, R. G. J. Am. Chem. Soc. 1963, 85, 3533. (12) Clavague´ra-Sarrio, C.; Brenner, V.; Hoyau, S.; Marsden, C. J.; Millie´, P.; Dognon, J.-P. J. Phys. Chem. B 2003, 107, 3051. Clavague´ra, C.; Pollet, R.; Soudan, J. M.; Brenner, V.; Dognon, J. P. J. Phys. Chem. B 2005, 109, 7614. (13) Kowall, Th.; Foglia, F.; Helm, L.; Merbach, A. E. J. Am. Chem. Soc. 1995, 117, 3790. (14) Derepas, A.-L.; Soudan, J.-M.; Brenner, V.; Dognon, J.-P.; Millie´, P. J. Comput. Chem. 2002, 23, 1013. (15) Hagberg, D.; Bednarz, E.; Edelstein, N. M.; Gagliardi, L. J. Am. Chem. Soc. 2007, 129, 14136.

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