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Cite this:Phys.Chem.Chem.Phys.,

2014, 16, 3693

Hydration properties of lanthanoid(III) carbonatecomplexes in liquid water determined bypolarizable molecular dynamics simulations†

Fausto Martelli,ab Yannick Jeanvoine,ac Thomas Vercouter,d Cesar Beuchat,e

Rodolphe Vuilleumierfgh and Riccardo Spezia*ac

In this work we have studied the structure and dynamics of complexes formed by three and four

carbonates and a central lanthanoid(III) ion in liquid water by means of polarizable molecular dynamics

simulations. With this aim we have developed a force field employing an extrapolation procedure that

was previously developed for lanthanoid(III) aqua ions and then we have validated it against DFT-based

data. In this way we were able to shed light on properties of the whole series, finding some similarities

and differences across the series, and to help in interpreting experiments on those systems. We found

that the bi-dentate tri-carbonate complexes are the most stable for all the atoms, but a variation of the

number of water molecules in the first ion shell, and the associated exchange dynamics, is observed

from lighter to heavier elements. On the other hand, for four-carbonate systems only one water

molecule is observed in the first shell, with 10–20% probability, for La(III) and Ce(III), while for the rest of

the series it seems impossible for a water molecule to enter the first ion shell in the presence of such an

excess of carbonate ligands. Finally, the good performance of our extrapolation procedure, based on

ionic radii, makes us confident in extending such approaches to study the structure and dynamics of

other systems in solution containing Ln(III) and An(III) ions. This parametrization method results

particularly useful since it does not need expensive quantum chemistry calculations for all the atoms in

the series.

1. Introduction

The structure and dynamics of water around lanthanoid (Ln)ions, mainly at oxidation state III, have been widely studiedboth experimentally and theoretically.1–4 Behavior of Ln(III)in water is in fact related to various fields such as rare earthelements chemistry, environmental impact of pollutants,

radioactive waste remediation and medical imaging.5–7 In thecontext of radioactive waste management, these elements areused as chemical analogues of actinide ions (An).8 Their inter-actions with inorganic anions may control their speciation insolution with the formation of aqueous complexes. The Ln(III)ions can accept several ligands in their first coordination layerby replacing all the hydration molecules. Carbonate ligandshave gained major attention due to environmental and processapplications. Interestingly, reliance on differential lanthanide–carbonate interactions has been proposed as a possible separa-tion procedure for Ln(III) and An(III) ions in solution.9 Up tothree or four carbonate anions can bind to Ln(III) trications inconcentrated carbonate solutions. Several experimental studieshave been carried out in order to determine the exact stoichio-metry though a clear consensus has not yet been reached.

Crystallographic data for Ln(III) carbonate hydrates are avail-able for tri-carbonate ligands,10 and for Nd(III). Runde et al.11 havesuggested the formation of [Nd(CO3)4H2O]5� structure at highcarbonate concentrations. Recently several Ln(III)–carbonate com-plexes have been studied in solution using electrophoretic mobi-lity measurements and time-resolved laser-induced fluorescencespectroscopy (TRLFS).12–14 They concluded that light Ln(III) ions

a CNRS, Laboratoire Analyse et Modelisation pour la Biologie et l’Environnement,

UMR 8587, Franceb Frick Chemistry Laboratory, Department of Chemistry, Princeton University,

Princeton, 08544 USAc Universite d’Evry Val d’Essonne, UMR 8587 LAMBE, Boulevard F. Mitterrand,

91025 Evry Cedex, France. E-mail: riccardo.spezia@univ-evry.fr;

Tel: +33 (0)169 47 01 41d CEA, DEN, DANS, DPC, SEARS, LANIE, F-91191 Gif sur Yvette cedex, Francee Department of Physical Chemistry, University of Geneva, 30 Quai Ernest Ansermet,

CH-1211 Geneva, Switzerlandf Ecole Normale Superieure, Departement de Chimie, 24, rue Lhomond, 75005 Paris,

Franceg UPMC Univ Paris 06, 4, Place Jussieu, 75005 Paris, Franceh UMR 8640 CNRS-ENS-UPMC, France

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3cp54001d

Received 21st September 2013,Accepted 10th December 2013

DOI: 10.1039/c3cp54001d

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can coordinate up to four carbonate ligands while heavier onescoordinate only up to three ligands, in line with the effect of thelanthanoid ion contraction. In contrast, considering availablecrystallographic and spectroscopic data (including UV-Vis, nearinfrared, and infrared), Janicki et al. concluded that in aqueoussolution all Ln(III) ions form tetra-carbonates when carbonateions are not limited.15 Another recent theoretical contribution inthis area was a report by Sinha et al. on [Nd(CO3)4]5� using theParameterized Model 3 (PM3) semi-empirical method.16 Notwith-standing these two studies, the first quantitative and systematictheoretical study undertaken to characterize the structures andbonding of lanthanoid(III) tri- and tetra-carbonates was reportedrecently by Jeanvoine et al.17 They studied different clusters bymeans of Density Functional Theory (DFT) pointing out that: (1)in the gas phase the most stable structure is the full bi-dentate fortri-carbonate complexes, while for the tetra-carbonate complexesit is the full mono-dentate; (2) in water, modeled there as acontinuum – i.e. no explicit water molecules were considered – inboth cases the full bi-dentate complexes are the most stablestructures; (3) the tri-carbonate structure is more stable than thetetra-carbonate one; (4) the Ln(III)–carbonate interaction is mainlyionic, thus allowing use of a simple, physics based, interactionpotential to study such complexes in liquid water by means ofclassical molecular dynamics simulations.

Molecular dynamics (MD) simulations were performedrecently with success to study hydration of lanthanoids(III) inwater or in salts, in particular when polarizable force fields areadopted.18–23 In aqueous solution with non-coordinating coun-terions, the difference in ionic radius for two elements givesrise to a difference in hydration number across the series(9-fold vs. 8-fold for La and Lu, respectively).24 Ln(III)–waterinteractions have been determined to be mainly electrostatic innature, as one might expect given the ‘‘hard’’ characters of bothLn(III) ions and water. As such, the variation in ionic radius isthe main physical quantity that affects hydration properties.25

The fact that ionic radii can dictate the complexation propertieshas also been pointed out for the case of ligands that arepotentially less hard than water, like hexacyanoferrate.26 Albeitcarbonates are ligands softer than water, and it is also possiblethat the metal–ligand interaction may change across the spec-trum of the lanthanoid series, we have recently shown that alsoin this case the interaction is mainly electrostatic and thecontribution of 4f orbitals to Ln/carbonate interaction is neg-ligible.17 Since 4f orbitals are compact around lanthanoids,they rarely contribute to valence bonding; indeed this behaviorrationalizes the importance of the role that ionic radius plays indictating interactions with water as a ligand.27 As we will showin the present study, the same physical picture can be evokedand used to successfully develop a polarizable potential inorder to study the complexes between all the Ln(III) ions inthe series and carbonates in water.

MD simulations allow for an explicit description of thesolvent and inclusion of temperature and entropic effectsthat are so important in the liquid state. Recently, the presenceof Cl�, ClO4

� and NO3� anions in the first shell of Ln(III)

was studied using polarizable force fields,19,28,29 but, with the

aforementioned exceptions, few studies were devoted tostudy complexes in liquid water using molecular dynamicssimulations.

In the present work we have thus developed a force field forclassical molecular dynamics of such complexes in liquidwater. In particular, we have developed a polarizable force fieldfor La(III) (the first ion in the series) interacting with carbonateions and then extrapolated it to Lu(III) following the sameprocedure developed for Ln(III)– and An(III)–water inter-action.30,31 Results obtained from classical molecular dynamicssimulations were validated against DFT results on clusters17

and discussed with respect to DFT-based molecular dynamics.The good performance of the extrapolation procedure to Lu(III),which is based on the picture obtained from a previous study ofelectron density, pointing out the ionic nature of Ln–carbonateinteraction,17 gave us confidence to use the same procedure tostudy the whole series. We have thus extended the polarizableforce field to the whole series and performed moleculardynamics simulations of Ln(III)–carbonate clusters in liquidwater using the water ionic radii recently reported by D’Angeloet al.18 We were then able to study structural and energeticproperties of Ln(III)–carbonate complexes in liquid water. Inparticular, we found that the tri-carbonate structures are themost stable structures in both the gas phase and solution andthat the bi-dentate complexes are spontaneously formed inliquid water when starting from mono-dentate ones, thusconfirming results obtained from calculations done on clus-ters. Furthermore, we point out that for tri-carbonate struc-tures, a variable number of water molecules can enter the firstLn(III) hydration shell: from 4 to 2 moving from lighter toheavier elements. In the case of tetra-carbonate structures, onlyone water molecule can come into the first hydration shell, aswell as for the first two elements of the series, La(III) and Ce(III).

2. Methods2.1 Classical force field

Our main goal is to provide a classical force field in order tostudy liquid systems composed of Ln(III) and carbonate ions inwater by means of classical molecular dynamics simulations(CLMD). With this aim, our classical potential energy functionconsists of the sum of different terms:

Vtot = Velec + V LJwater–water + V LJ

water–carb + V LJcarb–carb + VLn–water + VLn–carb

(1)

where Velec is the electrostatic energy term composed of aCoulomb and a polarization term (when activated) followingThole’s induced dipole model,32 V LJ

water–water, V LJwater–carb and

V LJcarb–carb are the 12-6 Lennard-Jones potential terms describing

the interactions between water and carbonates. In Thole’smodel, each site carries one permanent charge and an induceddipole associated with an isotropic polarizability tensor. Toavoid the polarization catastrophe in Thole’s model, a screen-ing function is employed for dipole–dipole interaction at shortdistances, using the original exponential function, with the

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same parameters used in our previous studies.33 CarbonateLennard-Jones parameters were obtained from the literature34

and for water we used those of the TIP3P water model.35

VLn–water and VLn–carb account for the non-electrostatic Ln–waterand Ln–carbonate interaction potential for which we have useda potential composed of a long range attractive part with a 1/r6

behavior and a short range repulsive part modeled via anexponential function, dealing with the well-known Buckinghampotential

VBuckðrÞ ¼ A expð�BrÞ � C

r6(2)

where r is the distance between Ln and O atoms of water andcarbonate. This expression applied to Ln(III) and An(III) in waterwas shown to be able to correctly reproduce various proper-ties.30,31 This interaction potential, in conjunction with theTIP3P/P model for water, was able, for example, to accuratelyreproduce EXAFS spectra both for Ln(III) and An(III)18,36 andthus for Ln(III)–water interactions we used the same parametersdeveloped previously.18

Parameters of the Buckingham potential can be related toionic radii, as shown recently by our group31 and in previouswork of Madden and co-workers in the case of molten salts.37–39

In particular, we have shown that starting from B and Creference values of an atom of the Ln (or An) series, we canextrapolate values for the whole series. To this end, we havefirst obtained B and C parameters for La(III) in interaction withcarbonates. Here, as previously, we constrained the fit bykeeping A constant since it modulates the height of the barrierthat is never reached for liquid systems at room temperature,and we used the same value,30,33 i.e. 240 000 kcal mol�1. The Band C parameters were obtained in order to reproduce DFTresults in gas and liquid phases. We have explored the perfor-mances of both polarizable and non-polarizable potentials,such that we consider two force fields labeled POL-ff andUPOL-ff, respectively, and corresponding molecular dynamics(POL-CLMD and UPOL-CLMD). Then, assuming the same extra-polation rules for water–Ln(III) and water–An(III) inter-action,18,30,31,36 we have obtained values for Lu(III), and thenfor the whole series. We should point out that this is not a strictderivation, but an extrapolation based on the assumption thatthe ionic radii decrease across the series similarly to whathappens in water. The validity of the extrapolation is checkedby comparing results of the extrapolated force fields withDFT-based calculations. Extrapolation was done for bothPOL-ff and UPOL-ff.

The electrostatic term is composed of partial charges andatomic polarizabilities for POL-ff; for UPOL-ff only partialcharges were used. For water we used TIP3P35 charges andTIP3P/P40 charges and atomic polarizabilities for UPOL-ff andPOL-ff, respectively. For Ln(III) we used: charge q = +3; for ionicpolarizability we employed the values reported and used in ourforce field developed for hydration.30,41 For carbonates, we usedpartial charges reported in the literature34 for the UPOL-ff,while for POL-ff we obtained them via the Lo-PROP procedure42

based on MP2 calculations using an ANO-RCC-VQZP basis

set.43 These calculations were done using the MOLCAS pack-age.44 The same Lo-PROP procedure was used to obtain atomicsite polarizabilities of carbonates. Partial charges and atomicsite polarizabilities used in both UPOL and POL force fields aresummarized Table 1. For intermolecular potential of carbo-nates we used values reported by Bruneval et al.,45 where theMorse potential was replaced by harmonic potential and for theequilibrium distance we used the value suggested for liquidwater.46 These parameters are reported in Table 1. To check theeffect of modifying these parameters on results we have per-formed some simulations with higher values of Kr and Ky,570 kcal mol�1 Å2 and 400 kcal mol�1 rad2 respectively.

2.2 Classical molecular dynamics simulations set-up

CLMD simulations in liquid water were done as follows.A cluster composed of one Ln(III) and 3 or 4 carbonates(CO3)2� was immersed in a box composed of 216 or 512 watermolecules. Box sizes have been obtained with 5 ps of equili-bration in the NpT ensemble with the DL_POLY classic pack-age47 using the UPOL force field. The Berendsen thermostatand barostat were employed48 resulting in box edges of 19.5and 25.05 Å (for 216 and 512 water molecule boxes respectively)for T = 300 K and p = 1 atm. Periodic boundary conditions (PBC)were applied to each simulation box in order to mimic bulkconditions. Long-range interactions were calculated by usingthe smooth particle mesh Ewald method.49 Once the systemequilibrated we switch to the NVE ensemble and use a velocity-Verlet algorithm with a time step of 1 fs. The SHAKE algorithmwas used to constrain bonds and angles of water molecules.50

Trajectories were thus 3 ns long for each system.POL-CLMD simulations were started after UPOL NpT equili-

bration as described previously. In these simulations we employedthe extended Lagrangian method to propagate induced dipoles intime51 that was shown to work properly with Thole’s induceddipole model for similar systems. Note that the dynamics of the

Table 1 Charges and atomic polarizabilities used in both non-polarizable(UPOL-ff) and polarizable (POL-ff) force fields. CC and OC are C and O ofcarbonates, while OW and HW are O and H of water. We also reportintramolecular parameters for carbonates used

UPOL-ff POL-ff

q Q a (Å3)

La +3 +3 1.41Lu +3 +3 0.77OW �0.82 �0.66 0.85HW 0.41 0.33 0.41CC 0.68 0.78 0.52OC �0.89 �0.93 0.71

req (Å) Kr (kcal mol�1 Å2)

C–OC 1.31 383.3

yeq (1) Ky (kcal mol�1 rad2)

OC–C–OC 120.0 200.0

xeq Kx (kcal mol�1 rad2)

OC–C–OC–OC 180.0 300.0

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induced dipole degree of freedom is fictitious, it only servesthe purpose of keeping the induced dipoles close to theirvalues at minimum energy, which would be obtained from theexact solution of the self-consistent equations (SCF) at eachstep. Dipoles and temperature stability were verified along thepresent simulations (induced dipoles obtained with SCF arewithin the oscillations observed using the dipole dynamics)while a more detailed report of the performances of theextended Lagrangian implementation is reported elsewhere.52

Equations of motion were numerically integrated using a 1 fstime step, with the SHAKE algorithm50 to constrain bonds andangles of water molecules. The system was equilibrated at298 K for 5 ps. Production runs were subsequently collectedfor 3 ns.

The 216 water molecule box was used to develop andvalidate the force fields and then final results were checkedwith the 512 water molecules box. No big differences werenoticed in results obtained with two boxes, as previouslyobserved.33,53,54

We have studied the complexation between Ln(III) ions and3 or 4 carbonate ions. The starting points of the dynamicalsimulations are all the possible arrangements of 3 and 4carbonate ions, i.e. mono-dentate (Z1) or bi-dentate (Z2).The general formula we adopted to identify those clusters is:[Ln(Z1-CO3)l(Z

2-CO3)m]k, where l + m = 3 or 4 and k = 3- or5- respectively. Representative illustrations of the clusters con-sidered are reported in Fig. 1. As initial structures in MDsimulations we have used clusters previously optimized atthe DFT level in our group17 and then immersed in explicitwater boxes.

The code MDVRY52 was used for production dynamics withboth UPOL and POL force fields.

2.3 Car–Parrinello molecular dynamics

In order to have a DFT comparison where solvent watermolecules are explicitly taken into account, we performedCar–Parrinello molecular dynamics55 (CPMD) simulations ofLa(III) and Lu(III) clusters with 3 and 4 carbonates in fullbi-dentate binding conformation. We immersed the clusterspreviously optimized with DFT17 in a box of 120 water mole-cules and after an NpT equilibration using classical dynamics(as reported in Section 2.1) in order to set the correct boxdimensions for T = 300 K and p = 1 atm; then we performedNVE simulations. Periodic boundary conditions were employedwith a box length of 15.5 Å as obtained by NpT equilibration.The BLYP functional56,57 was employed with plane waves basisset and a cut-off of 110 Ry. For C, O and H we used standardTroullier–Martins semi-core pseudo-potentials58 used pre-viously in similar CPMD simulations.59–61 For La(III), we useda semi-core Troullier–Martins pseudo potential developedrecently by some of us.27 For Lu(III) we developed a Troullier–Martins pseudo-potential as follows. The reference configu-ration used to generate the PP for Lu was Lu(III). The orbitals5s, 5p, and 5d were included in the PP with cutoffs of 1.01, 1.15and 1.163 au, respectively. 4f orbitals were considered as coreorbitals, and a non-linear core correction was thus employed.

When using pseudo-potentials with plane waves, the semilocalKleinman–Bylander form was used with the p channel as thelocal channel.62 Molecular dynamics simulations were done

Fig. 1 Chemical structures of different Ln(III)–carbonate clusters.

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using a fictious mass of 150 au and a time-step for numericalintegration of 2 au (= 0.0484 fs).

For La(III) with three carbonates we have performed twosimulations with different initial conditions: one obtainedfrom a classical equilibration keeping the complex fixed andrelaxing water molecules around; the other was obtained after aclassical equilibration where the cluster was allowed to movefreely (using the Pol-ff described previously). In the first case wedo not have any water molecule at t = 0 in DFT-based dynamicswhile in the second case we have four molecules – in agreementwith Pol-ff results shown in the following section. Thus we labelthese two simulations CPMD(0) and CPMD(4).

In the case of Lu(III) with three carbonates we have per-formed two simulations with one water molecule in the firstshell at t = 0, called CPMD(1)S1 and CPMD(1)S2. We have alsodone simulations with two water molecules at t = 0 in the firstshell taken from the Pol-ff equilibration. In this case, whenusing the CP Lagrangian, the kinetic energy of electrons quicklydiverged, and thus for this specific simulation we performed aBorn–Oppenheimer dynamics simulation, with an optimizationconvergence of 10�6 and an extrapolation scheme of order 3and a time step of 20 au (= 0.48378 fs). This simulation islabeled BOMD(2).

Trajectories, after an equilibration of 0.5 ps, were thenaccumulated for 2–8 ps depending on the system. CPMDpackage was employed for these simulations (CPMD).63

2.4 DFT optimizations

Finally, based on the structures obtained from simulations inliquid water of La(III) and Lu(III) complexes we have optimizedLn–carbonate complexes where the first shell water moleculeswere treated explicitly and the bulk as a continuum. With thisaim we have used the PBE functional64,65 with an all-electrontriple-z plus two polarization function basis set on all atoms.Relativistic corrections were introduced by the scalar relativisticzero-order regular approximation (ZORA).66,67 Implicit solva-tion was considered via the COSMO68 solvent model withstandard radii except for La (R = 2.42 Å) and Lu (R = 2.24 Å)centers.69 Dispersion corrections were added using the Grimmemethod with D3 parameters.70 We have optimized structures ofLa(III) with three carbonates and four or three water moleculesin the first shell, labeled PBE/COSMO(4) and PBE/COSMO(3),Lu(III) with three carbonates and two or one water moleculesin the first shell, labeled PBE/COSMO(2) and PBE/COSMO(1)and La(III) with four carbonates and one water molecule infirst shell, labeled PBE/COSMO(1). These structures wereselected on the basis of results obtained in bulk water. Thesecalculations were performed using the Amsterdam DensityFunctional program (ADF 2012.01) developed by Baerendsand co-workers.71

3. Results and discussion

Before describing and discussing our results it is useful todefine a nomenclature used here and hereafter for atoms of the

systems studied. Ln is for the generic lanthanoid(III) ion (if notspecified), OW and HW for oxygen and hydrogen atoms of thewater molecules, OC

(n) for oxygen atoms of carbonates that arein the first shell of Ln(III), OC

(f) for the oxygen atoms ofcarbonates that are exposed to the solvent and C for the carbonatoms of carbonates.

3.1 La(III) and Lu(III) force field development and validation

First we have obtained non-electrostatic parameters for theLa(III)–carbonate interaction. With this aim we obtainedLa(III)–OC B and C parameters (see eqn (2)) in order to betterreproduce DFT results obtained with the B3LYP functional.17 Asdone in our previous studies,30,31 we kept fixed the A parameter.Starting from values developed for La(III)–water, we adjusted theB and C parameters in a systematic way in order to providestructural properties for the [La(Z2-CO3)3]3� complex in liquidwater as close as possible to Ln–OC

(n) distances resulting fromDFT-optimization and DFT-based dynamics. In this way weobtained UPOL and POL parameters. In Table 2 we report thefinal parameters that best reproduce known Ln–OC

(n) distancesof the [La(Z2-CO3)3]3� complex. We should note that once weobtained B and C values for UPOL-ff, we only had to adjust theC parameter to obtain a POL-ff that is in agreement with the DFTcalculations. We have then extrapolated the Lu(III) parametersfollowing the procedure developed (and justified) in our previouswork:30,31 A is kept fixed across the series, B is increased as afunction of the ionic radius differences and C is decreasedlinearly as a function of the ionic radius behavior across theseries. With this aim, we have used effective ionic radii obtainedrecently18 and reported in Table 2. Results provided by UPOL-ffand POL-ff for [La(Z2-CO3)3]3�, [Lu(Z2-CO3)3]3�, [La(Z2-CO3)4]5�

and [Lu(Z2-CO3)4]5� complexes are reported in Table 3, wherewe compare them with structural results from DFT optimiza-tion,17 DFT-based dynamics with different initial conditions(i.e. different number of water molecules in the first shell of thecation) and geometry optimizations of clusters with explicitwater molecules in the first shell and the implicit solvationmodel (simulations labeled PBE/COSMO). We can see that ourforce field is able to correctly reproduce in particular Ln–OC

(n)

distances of the different complexes; that was the principalaim of our parametrization. Ln–C and Ln–OC

(f) distances areunderestimated in classical simulations. This is due mainlyto different OC

(n)COC(n) angles and COC

(n) distances of thecarbonates, while COC

(f) distances are almost the same inboth classical and DFT results, as reported in detail in ESI†

Table 2 Interaction parameters of UPOL and POL force fields for theBuckingham potential (eqn (2)) between La3+, Lu3+ and carbonate oxygenatoms. A is fixed at 240 000 kcal mol�1 in all cases. We report also effectiveionic radii as reported by D’Angelo et al.18

B (Å�1) C (Å6 kcal mol�1) Ri (Å)

La3+ (UPOL) 3.47 9257.0 1.250La3+ (POL) 3.47 9157.0 1.250Lu3+ (UPOL) 3.725 6135.5 0.995Lu3+ (POL) 3.725 6035.5 0.995

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(Tables S1 and S2). Furthermore the LnCOC(f) angles seem to

deviate more from linearity in DFT-based simulations while inclassical and DFT optimized geometries they are linear. Inparticular, what is promising for our parametrization proce-dure is that the Lu–OC

(n) distances obtained from classical MDsimulations are in good agreement with DFT ones. We shouldremark that the Lu(III)–carbonate force field is extrapolated andnot adjusted to reproduce DFT results: parameters wereadjusted only to reproduce the structures of tri-carbonatecomplexes with La(III), and they give reasonable results (i.e.without any further adjustment), as well as for tetra-carbonatesystems and for tri- and tetra-carbonate Lu(III) complexes.

We now move to analyze in detail results obtained from MDsimulations. In Fig. 2 and 3 we report radial distributionfunctions (RDFs) between the ions and the oxygen atoms ofcarbonates and water molecules obtained from POL-ff andCPMD simulations for simulations containing three carbo-nates. The La–OC first peak is very well reproduced while thesecond La–OC peak, corresponding to the distance with the‘‘far’’ oxygen atom of the carbonate, is shorter in the classicalsimulations than in the CPMD ones. Note that in classicaldynamics the C–OC bond is modeled using a harmonicpotential where the equilibrium distance is 1.31 Å and all thebonds are equal, while in DFT simulations this is not the case.

This is an intrinsic limit of classical simulations, and weused an equilibrium value in the classical force field of 1.31 Å,

which is reported for C–O distances of carbonates in explicitwater at the Hartree–Fock level;46 this geometry seems themost adapted for simulating free carbonates in water and, inperspective, more complex mixtures of lanthanoid/carbonatesolutions or even crystal growth can be studied with the same(or similar) force field. When the force constants of CQO

Table 3 Structural results for [La(Z2-CO3)3]3�, [La(Z2-CO3)4]5�, [Lu(Z2-CO3)3]3�, [Lu(Z2-CO3)4]5� complexes in bulk water obtained from UPOL-ff,POL-ff, PBE/COSMO and CPMD calculations. We report the maximum of radial distribution functions. Ln–OC

(n) is the distance from the oxygen atoms ofcarbonates in the first shell of Ln, while Ln–OC

(f) is the remaining oxygen atom to Ln distance; Ln–OW is the distance of Ln from water molecules and inparentheses we report the number of water molecules in the first shell (if any)

System Method Ln–OC(n) Ln–OC

(f) Ln–C Ln–OW

[La(Z2-CO3)3]3� UPOL-ff 2.50 4.09 2.82 2.75 (3.91)[La(Z2-CO3)3]3� POL-ff 2.49 4.09 2.77 2.75 (3.76)[La(Z2-CO3)3]3� POL-ff (Ky = 400) 2.49 4.07 2.80 2.76 (3.78)[La(Z2-CO3)3]3� POL-ff (Kr = 570) 2.49 4.06 2.79 2.76 (3.79)[La(Z2-CO3)3]3� DFTa 2.47 4.19 2.93 —[La(Z2-CO3)3]3� CPMD(0) 2.485 4.19 2.93 2.63 (1.20)[La(Z2-CO3)3]3� CPMD(4) 2.54 4.27 3.01 2.68 (3.0)[La(Z2-CO3)3]3� PBE/COSMO(4) 2.52 4.23 2.97 2.73 (3) 3.79 (1)

[La(Z2-CO3)3]3� PBE/COSMO(3) 2.52 4.22 2.95 2.74 (3)

[La(Z2-CO3)4]5� UPOL-ff 2.53 4.09 2.83 2.62 (1.98)[La(Z2-CO3)4]5� POL-ff 2.48 4.01 2.75 2.72 (0.17)[La(Z2-CO3)4]5� DFTa 2.64 4.42 3.12 —[La(Z2-CO3)4]5� CPMD 2.49 4.20 2.97 —[La(Z2-CO3)4]5� PBE/COSMO 2.55 4.24 2.98 2.71 (1.00)

[Lu(Z2-CO3)3]3� UPOL-ff 2.32 3.89 2.62 2.42 (2.99)[Lu(Z2-CO3)3]3� POL-ff 2.29 3.82 2.53 2.50 (2.00)[Lu(Z2-CO3)3]3� DFTa 2.27 3.97 2.71 —[Lu(Z2-CO3)3]3� CPMD 2.29 4.00 2.67 2.30 (1.00)[Lu(Z2-CO3)3]3� BOMD(2) 2.29 4.03 2.73 2.38 (2.00)[Lu(Z2-CO3)3]3� PBE/COSMO(2) 2.30 3.99 2.73 2.50 (2.00)[Lu(Z2-CO3)3]3� PBE/COSMO(1) 2.28 3.96 2.70 2.38 (1.00)

[Lu(Z2-CO3)4]5� UPOL-ff 2.33 3.89 2.63 2.45 (0.86)[Lu(Z2-CO3)4]5� POL-ff 2.33 3.86 2.60 —[Lu(Z2-CO3)4]5� DFTa 2.48 4.20 2.90 —[Lu(Z2-CO3)4]5� CPMD 2.30 4.04 2.75 —

a DFT B3LYP optimization results from Jeanvoine et al.17 All distances are in Å.

Fig. 2 La–OC and La–OW radial distribution functions obtained from POL-ff,CPMD(0) and CPMD(4) simulations for [La(Z2-CO3)3]3� simulations.

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stretching and OCO bending are changed, the results are notlargely modified (as reported in Table 3, Tables S1 and S2,ESI†). We should also note that the force field gives COC

(f)

distances that are in good agreement with DFT ones. Thedifference occurs when oxygen atoms (partially negativelycharged) are in the vicinity of a 3+ ion. As shown by resultsobtained by increasing Kr and Ky that are very similar to whatwas obtained with other parameters, the discrepancy in theCOC

(n) distance and the OC(n)COC

(n) angle should come fromintrinsic limitations of harmonic potentials or more in generalclassical models that do not take into account resonancehybrids. Explicit polarization through atomic site induceddipoles provide more physical results than a simple fixedcharge model, but it is probably not able to catch all aspectsof the interactions involved. This is reflected in differences inhydration of OC

(f), as reported in ESI† (Fig. S11). Similarly towhat was obtained by Leenders et al.,72 the classical force fieldstend to form more structuration between the water moleculesand the carbonates. Furthermore, even if our polarizablepotential gives an improved description of electrostatics withrespect to non-polarizable models, surely it misses the fullcharge transfer effect that is only partially taken into accountby Buckingham parameters (implicitly) and by means ofinduced dipoles. NBO analysis found that, even if small, thereis a partial charge transfer contribution in Ln–carbonate bind-ing.17 Here our aim was to provide a first polarizable classicalpotential able to reliably describe Ln(III)–carbonate systems thatcan be used for further studies with typical advantages over thelimitations of classical MD simulations.

We now move to analyze the structure of (possible) watermolecules in the first shell of Ln(III)–carbonate complexes. InFig. 2 and 3, we report the RDFs between La(III) and Lu(III) andoxygen atoms of water molecules. In the case of [La(Z2-CO3)3]3�

complexes (Fig. 2), from POL-ff simulations we obtained adynamical equilibrium between three and four water moleculesat a distance of 2.75 Å (maximum of RDF). When optimizingclusters with explicit water molecules, we have results verysimilar in distances (average distances are shown in Table 3).

Interestingly we saw that when four waters are in the first shell,three are at 2.73 Å and one is far away – nearly in a second shell.We then performed CPMD simulations with different initialconditions: CPMD(0) where there are no water molecules in thefirst shell at t = 0 and CPMD(4) with 4 water molecules at t = 0.In the CPMD(0) simulations the cluster needs some time toopen and in 3 ps we have two water molecules that are able tocome into the first shell. Thus, from CPMD(0) simulation weobtained a RDF that is different than what was obtained fromPol-ff simulations, but also distances that are much shorterthan what resulted from DFT optimizations. To let watermolecules enter, the cluster must open (as shown by CLaCangles in ESI,† Fig. S1). We thus run a CPMD simulation withfour water molecules at the beginning. In this case one watermolecule leaves quickly and then three water molecules arestable in the first shell for 8 ps. Now the RDF is more inagreement with the Pol-ff in terms of height, integral and alsothe position is now closer (2.68 Å) to Pol-ff and PBE/COSMOresults.

A similar situation is obtained in the case of [Lu(Z2-CO3)3]3�

complexes for which RDFs are shown in Fig. 3. In the case ofPol-ff simulations we have two water molecules at 2.50 Å, inagreement with DFT optimization with two water molecules –PBE/COSMO(2) results in Table 3. In DFT-based dynamics byincreasing the number of water molecules in the first shell theLu–OW distance increases, in agreement with PBE/COSMOresults. When comparing Pol-ff and DFT-based dynamics withtwo water molecules in first shell, we obtain that DFT tends toprovide shorter distances. This discrepancy should result fromdifferences in Lu(III)–water interaction. We should remark thatthe POL-ff Lu(III) water interaction potential was shown to veryaccurately reproduce structural and thermodynamical experi-ments,53 and PBE/COSMO optimizations provide the sameLu(III)–water distance. Furthermore, CLnC angles obtainedfrom POL-ff dynamics and PBE/COSMO optimizations (shownin ESI,† Tables S1 and S2 and Fig. S2 and S4) are similar. Theoptimized geometries are reported in ESI† (Table S3) and canbe used to have a simple static picture of water–carbonatearrangement – more details will be given in Section 3.3. Itcould be that BLYP-based dynamics, while describing wellstructures of complexes, are not highly accurate in describingion–water interaction (that can be better described by a wellparameterized force field), as we have pointed out in the case ofcobalt–cysteine complexes.60,73,74 Furthermore, it is well knownthat BLYP-based dynamics at T = 300 K give an over-structurated water.75 Here we decided to perform dynamics atthis temperature since increasing it (as it is sometimes done)can result in a problematic description of Ln–carbonate com-plexes, which is the main subject of this work.

Finally, we inspect differences between POL-ff and UPOL-ffresults. The Ln–OC

(n), Ln–OC(f) and Ln–C distances are very

similar, in particular for [La(Z2-CO3)3]3�, while they are slightlylonger in UPOL-ff results for the other complexes. We shouldalso note that the extrapolation procedure used to obtain theLu(III)–carbonate force field was developed using a polarizablepotential and thus it is not surprising that it is less accurate in

Fig. 3 Lu–OC and Lu–OW radial distribution functions obtained from POL-ff,CPMD(0) and BOMD(2) simulations for [Lu(Z2-CO3)3]3� simulations.

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the case of a non-polarizable potential. The carbonate structureis also similar (see Tables S1 and S2, ESI†), while the mostnoticeable difference is in tri-dimensional arrangement ofcarbonates around the ion, as shown by the CLnC angledynamics (reported in ESI,† Fig. S2 and S4). As shown pre-viously, these angles are related to the water molecules in thefirst shell of the Ln(III) ion. The main difference between POL-ffand UPOL-ff results was found mainly in the water structureand dynamics. In particular the UPOL-ff simulations providehigher Ln(III) first shell coordination numbers (CN) than POL-ff,as shown in Table 3: 3.91 vs. 3.76 for [La(Z2-CO3)3]3�, 2.99 vs.2.0 for [Lu(Z2-CO3)3]3�, 1.98 vs. 0.17 for [La(Z2-CO3)4]5� and0.86 vs. 0.0 for [Lu(Z2-CO3)4]5�. This is in agreement to whatwas observed in La(III) hydration, where UPOL-ff overestimatesthe number of water molecules in the first shell.33 Furthermore,the dynamics of the first shell water molecules is a property verysensitive to the potential, as largely shown in the case of bareions in liquid water.22,23 In Fig. 4 we show the number of watermolecules in the first shell of La(III) and Lu(III) as a functionof time as obtained from UPOL-ff and POL-ff. We note thatUPOL-ff provides much less exchange than POL-ff and highercoordination numbers (as obtained for La(III) in bulk water).Thus, while UPOL-ff provides results for Ln(III)–carbonatessimilar to POL-ff results, it gives different results for structure

and dynamics of water around the central ion. This differencein the behavior of polarizable and non-polarizable force fieldshas been already noticed in other situations.22,23,33 This shouldbe taken into account if one wanted to use the UPOL-ff modelfor simulating bigger systems in the future.

3.2 Energetic properties

Before studying the energetic properties in the liquid phase, wedetermined using both UPOL-ff and POL-ff the formationenergies of different clusters (i.e. for the different coordinationmotifs shown in Fig. 1) in the gas phase, and compared them toprevious DFT results.17 In Fig. 5 we show results for La(III) andLu(III) as a function of the cluster structures for both tri- andtetra-carbonate complexes. Both POL-ff and UPOL-ff reproducecorrectly the trend obtained from DFT: in the gas phase forthree carbonate complexes the full bi-dentate is the most stablestructure, while for four carbonate complexes the full mono-dentate is the most stable one. The same behavior is found forLa(III) and Lu(III). POL-ff better reproduces the formation energythan UPOL-ff and in particular in the extrapolation to Lu(III).Note that the parameters for Lu(III) were not obtained in orderto reproduce structural properties of Lu(III)–carbonate com-plexes. Parameters were only adjusted for La(III) in order tomatch structural properties of the [La(Z2-CO3)3]3 complex witha ‘minimal’ modification from the La(III)–water parameters.

Concerning the stability of clusters in water, first, weshould remark that when performing simulations where theinitial structure is a mono-dentate species (full or partial, forboth three of four carbonate complexes) we always obtain aftera few picoseconds a full bidentate complex (see a prototypicalmovie in ESI†). We then calculate hydration and formationenthalpies of the stable full bi-dentate species, i.e. [La(Z2-CO3)3]3�,[Lu(Z2-CO3)3]3�, [La(Z2-CO3)4]5� and [Lu(Z2-CO3)4]5� com-plexes. To obtain formation enthalpies in water, we used athermodynamic cycle shown in Fig. 6. Hydration energies areobtained from simulations in the liquid phase, using the

Fig. 4 Number of water molecules in the first shell of Ln(III) ion obtainedfrom UPOL-ff (in red) and POL-ff (in black) for [La(Z2-CO3)3]3� (panel a)and [Lu(Z2-CO3)3]3� (panel b) simulations.

Fig. 5 Gas phase formation energies of [Ln(CO3)3]3� (left) and[Ln(CO3)4]5� (right) clusters (Ln = La, Lu) as a function of the number ofmono-dentate ions (from left to right we move from (Z2-CO3)3 and (Z2-CO3)4 to (Z1-CO3)3 and (Z2-CO3)4, respectively). Energies calculated withUPOL-ff and POL-ff are compared with values obtained from DFT.17

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correction terms described by Garcia and co-workers,76–79 asrecently done by us to obtain hydration enthalpies of Ln(III) andAn(III).31,53,54 Results for the reaction

Ln3+(aq) + nCO3

2�(aq) - [Ln(Z2-CO3)n]3�2n (3)

are reported in Table 4. In the same table we report valuesobtained for the reactions in the gas phase. Note that the gasphase DH overestimates the interaction, but by less than 4% ofthe interaction energy; that is quite surprising since the para-meters were obtained by modifying Ln–water parameters inorder to reproduce La–OC distances in tri-carbonate complexes.Solvation has a small effect on formation enthalpies and theDH POL-ff

aq –DHPOL-ffgas is in the �7/+51 kcal mol�1 range – small

compared to formation enthalpy values of the order of thou-sands of kcal mol�1. Following the simple Born model oneshould expect a strong contribution in solvation for small ions,but, as we have recently shown,54 effective Born radii of highlycharged cations like lanthanoids(III) are much bigger (in the7.2–9.5 Å range) than corresponding ionic radii. This corre-sponds to the fact that a Ln(III) ion is, from a Born point of view,of a size similar to the complex because of the saturation of thedipoles of structured water molecules. On the other hand, theformation of such complexes in liquid water corresponds to adecreasing number of charged atoms exposed to the solventwith respect to free ions.

Furthermore, for both La(III) and Lu(III) systems we foundthat the tri-carbonate complexes are more stable than the tetra-carbonate ones in solution, as was similarly found in the gasphase. This strengthens the picture that the tri-carbonate

species is the most stable complex in solution. Of course othereffects like ionic strength can change the relative stability; herewe just provide enthalpy differences under ideal conditionsthat can be used as a starting point for further evaluationof thermodynamics quantities under different conditions.Another interesting effect is the difference between tri- andtetra-carbonate complexes for La and Lu, represented by thedifference between the two formation enthalpies – DDH(Ln) inthe same Table 4. Moving from gas to solution, the differencebetween the two lanthanoids(III) decreases from 20 kcal mol�1

(40 kcal mol�1 using DFT energies) to only 4 kcal mol�1, that islargely within statistical fluctuations. We should note that inthe gas phase we have a difference of 20 kcal mol�1 betweenDFT and POL-ff energies; the force field could underestimatethe relative energy in the liquid phase, too.

3.3 Extension to the whole Ln(III) series and water exchangedynamics

On the ground of the good performances in the extrapolation ofthe POL-ff from La(III) to Lu(III), we extended it to the wholeseries, and thus performed simulations of [Ln(Z2-CO3)3]3� and[Ln(Z2-CO3)4]5� complexes in liquid water for the whole Ln(III)series (except Pm that is not naturally available and for whichaccurate experimental ionic radii are not present). Extrapolatedparameters and results for [Ln(Z2-CO3)3]3� complexes areshown in Table 5. The Ln–OC distance (i.e. the maximum ofLn–OC RDF) decreases as a function of the ionic radius as wellas the Ln–OW one. In Fig. 7 we show how the Ln–OC distancedecreases across the series – here we represent the series by theinverse of the ionic radius – for both complexes. We note that,while for light atoms the Ln–OC distances of tri- and tetra-carbonate complexes are very similar, decreasing the ionicradius, in the case of tri-carbonate complexes, the ‘contraction’is bigger than for tetra-carbonate ones. This is likely due to thesteric hindrance that is higher for tetra-carbonate complexes sothat a plateau in the distance is obtained for smaller radii. It isinteresting to note that while in both series we employed B andC parameters corresponding to the same decrease of ionic radii

Fig. 6 The thermodynamic cycle used to evaluate formation enthalpies inaqueous solution from hydration enthalpies and gas phase formationenthalpies.

Table 4 Formation enthalpies (see eqn (3)) obtained from POL-ff simula-tions. In water values (aq) are results from the thermodynamic cycle ofFig. 6

DHDFT(gas)

a DHPOL-ff(gas) DHPOL-ff

(aq)

[La(Z2-CO3)3]3� �1228 �1272 �1258[La(Z2-CO3)4]5� �957 �962 �969[Lu(Z2-CO3)3]3� �1346 �1355 �1304[Lu(Z2-CO3)4]5� �1036 �1025 �1011DDH(La) �271 �310 �289DDH(Lu) �310 �330 �293

a DFT B3LYP results from Jeanvoine et al.17 DDH(Ln) are the differencesbetween tri- and tetra-carbonate complex formation enthalpies. Allvalues are in kcal mol�1.

Table 5 Buckingham parameters (see eqn (2)) and structural results forthe [Ln(Z2-CO3)3]3� series in liquid water as obtained from POL-ff simula-tions. Ri is the effective ionic radius as reported by D’Angelo et al.18 and CNis the number of water molecules in the Ln(III) first shell

Ri (Å) B (Å�1) C (kcal mol�1 Å6) rLn–OC(Å) rLn–OW

(Å) CN t (ps)

La 1.250 3.470 9157.0 2.49 2.75 3.76 147.7Ce 1.220 3.475 8789.5 2.50 2.75 3.83 203.6Pr 1.200 3.520 8544.5 2.43 2.70 3.25 92.1Nd 1.175 3.545 8238.2 2.42 2.68 3.15 165.9Sm 1.140 3.580 7809.4 2.40 2.64 3.01 191.1Eu 1.120 3.600 7564.4 2.37 2.64 2.93 110.2Gd 1.105 3.615 7380.6 2.37 2.62 2.89 97.7Tb 1.090 3.630 7196.8 2.35 2.61 2.73 104.7Dy 1.075 3.645 7013.1 2.34 2.59 2.60 69.6Ho 1.055 3.665 6768.0 2.32 2.56 2.28 143.1Er 1.040 3.680 6584.3 2.32 2.57 2.21 172.9Tm 1.025 3.695 6400.5 2.30 2.56 2.14 177.0Yb 1.010 3.710 6216.8 2.29 2.54 2.04 361.9Lu 0.995 3.725 6033.0 2.29 2.53 2.04 591.0

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along the series, the resulting Ln–OC(n) distances do not

decrease with the same slope for tri- and tetra-carbonatecomplexes. We should remark that our Nd–O distance in the[Nd(Z2-CO3)4]5� complex, 2.42 Å, is not far from the reportedX-ray structure of the hydrated crystal, where a value between2.55 and 2.45 Å in the presence of one water molecule isreported.11 Intriguingly, this Ln–O distance is even closer toLa–O or Ce–O distances corresponding to tetra-carbonate com-plexes where one water molecule can come into the first ionhydration shell (Table 6). The structures of carbonates, in termsof bond distances and angles, are similar for all the complexes(see Table S3 in ESI†). Concerning the tridimensional arrange-ment around the ion, the CLnC angles show a slightly differentdynamics, reflecting different water exchange dynamics as wewill discuss in the following paragraph. [Ln(Z2-CO3)3]3� com-plexes fluctuate more from Pr(III) to Ho(III), while they do less atthe end of the series. Similarly for [Ln(Z2-CO3)4]5�, the CLnCangles fluctuate for La(III) and Ce(III) while they do not(or slightly) for other ions. As already remarked, the valuesare similar to what was obtained from PBE/COSMO optimiza-tion with explicit water molecules, and thus these geometriescan provide a simple picture of how carbonates and water are

disposed around the ion. In Fig. 8 we show the optimizedstructures with CN = 4, 3, 2, 1 for prototypical La(III) and Lu(III)complexes – geometries are given in ESI,† Table S3.

We now move to study the number of water molecules (CN)in the first shell of Ln(III) and their exchange dynamics acrossthe series. Results for [Ln(Z2-CO3)3]3� complexes simulationsare reported in Table 5 in terms of distances and average CN.They both decrease across the series, as expected from thelanthanoid contraction. Details of the first shell water mole-cules dynamics for [Ln(Z2-CO3)3]3� complexes across the seriesare reported in Fig. 9, where we show CN as a function of timefor Ln(III) in the beginning, middle and end of the series. Weshould note, with regard to the first shell, that moving fromlight to heavy Ln(III), we first have an equilibrium between 4 and3 water molecules, then in the middle of the series we have3 water molecules as an average and the possibility of bothadding or removing one, and for heavy elements we have2 water molecules with possibly a third molecule coming in.These results may be compared with experimental estimations ofthe number of water molecules in Eu(III) and Dy(III) first coordi-nation shells by time-resolved laser-induced fluorescence spectro-scopy (TRLFS). An average CN of 1.8 was obtained by fluorescencedata fitting for Eu(III) in 1 M Na2CO3,12 while values of 2.1 and 1.9were obtained for Eu(III) and Dy(III) respectively, in 3 M K2CO3.14

Fig. 7 The Ln–Oc(n) distance across the series (as a function of theinverse of the ionic radius), as obtained from POL-ff simulations in liquidwater for both [Ln(Z2-CO3)3]3� and [Ln(Z2-CO3)4]5� complexes.

Fig. 8 Structures of [Ln(Z2-CO3)3]3� and [Ln(Z2-CO3)4]5� complexesobtained from PBE/COSMO geometry optimizations.

Fig. 9 Number of water molecules in the first shell of Ln(III) for[Ln(Z2-CO3)3]3� complexes as a function of time from POL-ff simulations.

Table 6 Structural results for the [Ln(Z2-CO3)4]5� complexes across theLn(III) series in liquid water as obtained from POL-ff simulations

rLn–OC(Å) rLn–OW

(Å) CN

La 2.48 2.75 0.17Ce 2.49 2.75 0.27Pr 2.44 — 0.01Nd 2.43 — —Sm 2.40 — —Eu 2.39 — —Gd 2.38 — —Tb 2.37 — —Dy 2.36 — —Ho 2.35 — —Er 2.35 — —Tm 2.34 — —Yb 2.34 — —Lu 2.33 — —

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Further information on such first shell water molecules dynamicsis obtained by calculating the mean residence time (MRT) ofwater molecules in the first shell of the Ln(III). Here we adoptedthe so-called Impey method;80 we used here a t* of 2 ps as inImpey’s original work. Results are given in Table 5. We note thatfrom La(III) to Dy(III) we do not have a clear behavior of MRTacross the series as was obtained in the case of bare ions inwater.24 This is probably due to the fact that while for the lightelements we have an equilibrium between CN = 4 and CN = 3,then in the middle we have equilibrium between CN = 4, CN = 3and CN = 2 and, at the end, we have the equilibrium only betweenCN = 3 and CN = 2. Upon increasing the atomic number (i.e.moving from light to heavy ions) this low coordination numberbecomes much more probable and thus the time spent by watermolecules in the first shell of Ln(III) is longer. In fact, from Dy(III)to Lu(III) we have a steady increase of MRT (Table 5).

In the case of [Ln(Z2-CO3)4]5� complexes the situation ismuch simpler: only one water molecule is able to enter the firstshell (Table 6). This was only observed for La(III), Ce(III) and,with very low probability, Pr(III), while for the rest of the seriesthe carbonates fulfill the coordination sphere of Ln(III) andthere is no room for water molecules to enter. In Fig. 10 wereport some prototypical structures (snapshots from thedynamics) of [Ln(Z2-CO3)3]3� and [Ln(Z2-CO3)4]5� clusters toshow how such water molecules are spatially arranged in thefirst shell in the presence of three or four carbonates. Weshould note that they are in-between carbonate molecules,similarly to what was obtained from PBE/COSMO optimiza-tions, but the hydrogen atoms now point towards bulk while itwas not always the case in cluster optimization. This clearlycomes from the explicit inclusion of solvent water moleculesoutside the cluster.

4. Conclusions

In this paper we have studied the complexes formed by carbo-nates with ions of the lanthanoids(III) series by means ofpolarizable molecular dynamics simulations, DFT-based molec-ular dynamics simulations and DFT optimizations with explicitwater molecules in the first shell and continuum method(COSMO) to mimic the bulk effect. With this aim we have firstbuilt a polarizable potential able to correctly reproduce DFT-based structure and energetics. Starting from parametersadjusted on La(III), the first atom of the series, we were thenable to extrapolate parameters to the whole series without theneed of electronic structure calculations that are slow andproblematic for open shell Ln(III) of the series. No classicalforce field, with or without polarization, between lanthanoid(III)ions and carbonates is reported in the literature, and thus thepresent work can serve as a reference for future work on theapplication of classical molecular dynamics on systems con-taining such species under different conditions of concen-tration and ionic strength.

Here, we studied complexes formed with three and fourcarbonates. When considering these complexes, differentcoordination motifs are possible: we found that bi-dentatestructures are spontaneously formed when starting from mono-dentate ones, thus confirming the picture obtained from previousPCM calculations.17 Further, the tri-carbonate complexes seem tobe preferred from an enthalpy point of view in the limit of infinitedilution conditions. Of course this result holds under idealconditions, and, for example, the high ionic strength of solutionsneeded to form these complexes can modify the equilibrium.

Thanks to the possibility of performing long simulationswith explicit water molecules provided by the developed forcefield and subsequent classical MD simulations, we were able tostudy whether and how water molecules enter into the firstshell of the Ln(III) ion in the presence of three or four carbo-nates surrounding the ion. We obtained that for tri-carbonatecomplexes there is room for up to four water molecules for lightLn(III) ions, while this decreases to two for heavy ions. Inparticular, MD simulations provided details of water exchangedynamics and how the first shell water molecules residencetime evolves across the series, which could help in interpretingexperimental data like TRLFS data. On the other hand, for tetra-carbonate complexes it is very difficult for a water molecule toenter into the ion’s first shell, and this possibility is onlyallowed for light ions, even with relatively low probability (lessthan 20%).

Finally, the ability of the extrapolation procedure of para-meters for the whole series starting from those for La(III) toreproduce DFT-based structure and energetics for Lu(III) andTRLFS of Eu(III) and Dy(III) paves the way for using suchapproaches for other ligands of interest like silicates or nitrates.

Acknowledgements

We thank Prof. Laura Gagliardi and Dr Pere Miro for usefuldiscussions and Mrs Elizabeth A. Kish for careful reading of the

Fig. 10 Snapshots of Ln–carbonate structures obtained from POL-ff simu-lations in liquid water. From left to right and top to bottom: [Ln(Z2-CO3)3]3�

with 4, 3 and 2 water molecules in the first shell and [Ln(Z2-CO3)4]5� withone water molecule in the first shell.

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3704 | Phys. Chem. Chem. Phys., 2014, 16, 3693--3705 This journal is© the Owner Societies 2014

manuscript. This work was supported by the French NationalResearch Agency (ANR) on project ACLASOLV (ANR-10-JCJC-0807-01) (F. M., Y. J, T. V and R. S.). We acknowledge GENCI(grants x2012071870 and x2013071870) for computing time.

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