Building a polarizable pair interaction potential for lanthanoids(III) in liquid water: A molecular dynamics study of structure and dynamics of the whole series

Modeling Lanthanide Ions in Solution: A Versatile Force Field in Aqueous and Organic Solvents

In this paper, we propose a new nonpolarizable force field for describing the Ln3+ (Ln = lanthanide) series based on a 12-6-4 Lennard-Jones potential. The development of the force field was performed in pure water by adjusting both the ion-oxygen distance and the hydration free energy. This force field accurately reproduces the Ln3+ hydration properties through the series, especially the coordination number that is hardly accessible using a nonpolarizable force field. Then, the validity and the transferability of the current force field were evaluated for two different systems containing Ln3+ in various solvents, namely, 0.1 mol L-1 La(NO3)3 salts in methanol and Eu(NO3)3 salts in solvent organic phases composed of DMDOHEMA molecules in n-heptane. The good agreement between our simulations and the data available in the literature confirms the accuracy of the force field for describing the lanthanide cations in both aqueous and nonaqueous media.

Speciation of La3+-Cl- Complexes in Hydrothermal Fluids from Deep Potential Molecular Dynamics

The stability of rare earth element (REE) complexes plays a crucial role in quantitatively assessing their hydrothermal migration and transformation. However, reliable data are lacking under high-temperature hydrothermal conditions, which hampers our understanding of the association behavior of REE. Here a deep learning potential model for the LaCl3-H2O system in hydrothermal fluids is developed based on the first-principles density functional theory calculations. The model accurately predicts the radial distribution functions compared to ab initio molecular dynamics (AIMD) simulations. Furthermore, species of La-Cl complexes, the dissociation pathway of the La-Cl complexes dissociation process, and the potential of mean forces and corresponding association constants (logK) for LaCln3-n (n = 1-4) are extensively investigated under a wide range of temperatures and pressures. Empirical density models for logK calculation are fitted with these data and can accurately predict logK data from both experimental results and AIMD simulations. The distribution of La-Cl species is also evaluated across a wide range of temperatures, pressures, and initial chloride concentration conditions. The results show that La-Cl complexes are prone to forming in a low-density solution, and the number of bonded Cl- ions increases with rising temperature. In contrast, in a high-density solution, La3+ dominates and becomes the more prevalent species.

Analysis of the First Ion Coordination Sphere: A Toolkit to Analyze the Coordination Sphere of Ions

Rapid and accurate approaches to characterizing the coordination structure of an ion are important for designing ligands and quantifying structure-property trends. Here, we introduce AFICS (Analysis of the First Ion Coordination Sphere), a tool written in Python 3 for analyzing the structural and geometric features of the first coordination sphere of an ion over the course of molecular dynamics simulations. The principal feature of AFICS is its ability to quantify the distortion a coordination geometry undergoes compared to uniform polyhedra. This work applies the toolkit to analyze molecular dynamics simulations of the well-defined coordination structure of aqueous Cr³⁺ along with the more ambiguous structure of aqueous Eu³⁺ chelated to ethylenediaminetetraacetic acid. The tool is targeted for analyzing ions with fluxional or irregular coordination structures (e.g., solution structures of f-block elements) but is generalized such that it may be applied to other systems.

Norm-Conserving 4f-in-Core Pseudopotentials and Basis Sets Optimized for Trivalent Lanthanides (Ln = Ce-Lu)

We present here a set of scalar-relativistic norm-conserving 4f-in-core pseudopotentials, together with complementary valence-shell Gaussian basis sets, for the lanthanide (Ln) series (Ce-Lu). The Goedecker, Teter, and Hutter (GTH) formalism is adopted with the generalized gradient approximation (GGA) for the exchange-correlation Perdew-Burke-Ernzerhof (PBE) functional. The 4f-in-core pseudopotentials are built through attributing 4f-subconfiguration 4fⁿ (n = 1-14) for Ln (Ln = Ce-Lu) into the atomic core region, making it possible to circumvent the difficulty of the description of the open 4fⁿ valence shell. A wide variety of computational benchmarks and tests have been carried out on lanthanide systems including Ln³⁺-containing molecular complexes, aqueous solutions, and bulk solids to validate the accuracy, reliability, and efficiency of the optimized 4f-in-core GTH pseudopotentials and basis sets. The 4f-in-core GTH pseudopotentials successfully replicate the main features of lanthanide structural chemistry and reaction energetics, particularly for nonredox reactions. The chemical bonding features and solvation shells, hydrolysis energetics, acidity constants, and solid-state properties of selected lanthanide systems are also discussed in detail by utilizing these new 4f-in-core GTH pseudopotentials. This work bridges the idea of keeping highly localized 4f electrons in the atomic core and efficient pseudopotential formalism of GTH, thus providing a highly efficient approach for studying lanthanide chemistry in multi-scale modeling of constituent-wise and structurally complicated systems, including electronic structures of the condensed phase and first-principles molecular dynamics simulations.

Direct Observation of Contact Ion-Pair Formation in La3+ Methanol Solution

An approach combining molecular dynamics (MD) simulations and X-ray absorption spectroscopy (XAS) has been used to carry out a comparative study about the solvation properties of dilute La(NO₃)₃ solutions in water and methanol, with the aim of elucidating the still elusive coordination of the La³⁺ ion in the latter medium. The comparison between these two systems enlightened a different behavior of the nitrate counterions in the two environments: while in water the La(NO₃)₃ salt is fully dissociated and the La³⁺ ion is coordinated by water molecules only, the nitrate anions are able to enter the metal first solvation shell to form inner-sphere complexes in methanol solution. The speciation of the formed complexes showed that the 10-fold coordination is preferential in methanol solution, where the nitrate anions coordinate the La³⁺ cations in a monodentate fashion and the methanol molecules complete the solvation shell to form an overall bicapped square antiprism geometry. This is at variance with the aqueous solution where a more balanced situation is observed between the 9- and 10-fold coordination. An experimental confirmation of the MD results was obtained by La K-edge XAS measurements carried out on 0.1 M La(NO₃)₃ solutions in the two solvents, showing the distinct presence of the nitrate counterions in the La³⁺ ion first solvation sphere of the methanol solution. The analysis of the extended X-ray absorption fine structure (EXAFS) part of the absorption spectrum collected on the methanol solution was carried out starting from the MD results and confirmed the structural arrangement observed by the simulations.

The formation of contact ion pairs between the La³⁺ ions and the nitrate anions has been demonstrated in diluted methanol solution using a combined approach using Molecular Dynamics simulations and X-ray absorption spectroscpy.

Ionic Contraction across the Lanthanide Series Decreases the Temperature-Induced Disorder of the Water Coordination Sphere

In liquid, temperature affects the structures of lanthanide complexes in multiple ways that depend upon complex interactions between ligands, anions, and solvent molecules. The relative simplicity of lanthanide aqua ions (Ln³⁺) make them well suited to determine how temperature induces structural changes in lanthanide complexes. We performed a combination of ab initio molecular dynamics (AIMD) simulations and extended X-ray absorption fine structure (EXAFS) measurements, both at 25 and 90 °C, to determine how temperature affects the first- and second-coordination spheres of three Ln³⁺ (Ce³⁺, Sm³⁺, and Lu³⁺) aqua ions. AIMD simulations show first lanthanide coordination spheres that are similar at 25 and 90 °C, more so for the Lu³⁺ ion that remains as eight-coordinate than for the Ce³⁺ and Sm³⁺ ions that change their preferred coordination number from nine (at 25 °C) to eight (at 90 °C). The measured EXAFS spectra are very similar at 25 and 90 °C, for the Ce³⁺, Sm³⁺, and Lu³⁺ ions, suggesting that the dynamical disorder of the Ln³⁺ ions in liquid water is sufficient such that temperature-induced changes do not clearly manifest changes in the structure of the three ions. Both AIMD simulations and EXAFS measurements show very similar structures of the first coordination sphere of the Lu³⁺ ion at 25 and 90 °C.

Predicting lanthanide coordination structures in solution with molecular simulation

The chemical and physical properties of lanthanide coordination complexes can significantly change with small variations in their molecular structure. Further, in solution, coordination structures (e.g., lanthanide-ligand complexes) are dynamic. Resolving solution structures, computationally or experimentally, is challenging because structures in solution have limited spatial restrictions and are responsive to chemical or physical changes in their surroundings. To determine structures of lanthanide-ligand complexes in solution, a molecular simulation approach is presented in this chapter, which concurrently considers chemical reactions and molecular dynamics. Lanthanide ion, ligand, solvent, and anion molecules are explicitly included to identify, in atomic resolution, lanthanide coordination structures in solution. The computational protocol described is applicable to determining the molecular structure of lanthanide-ligand complexes, particularly with ligands known to bind lanthanides but whose structures have not been resolved, as well as with ligands not previously known to bind lanthanide ions. The approach in this chapter is also relevant to elucidating lanthanide coordination in more intricate structures, such as in the active site of enzymes.

Coordination Sphere of Lanthanide Aqua Ions Resolved with Ab Initio Molecular Dynamics and X-ray Absorption Spectroscopy

To resolve the fleeting structures of lanthanide Ln3+ aqua ions in solution, we (i) performed the first ab initio molecular dynamics (AIMD) simulations of the entire series of Ln3+ aqua ions in explicit water solvent using pseudopotentials and basis sets recently optimized for lanthanides and (ii) measured the symmetry of the hydrating waters about Ln3+ ions (Nd3+, Dy3+, Er3+, Lu3+) for the first time with extended X-ray absorption fine structure (EXAFS). EXAFS spectra were measured experimentally and generated from AIMD trajectories to directly compare simulation, which concurrently considers the electronic structure and the atomic dynamics in solution, with experiment. We performed a comprehensive evaluation of EXAFS multiple-scattering analysis (up to 6.5 Å) to measure Ln-O distances and angular correlations (i.e., symmetry) and elucidate the molecular geometry of the first hydration shell. This evaluation, in combination with symmetry-dependent L3- and L1-edge spectral analysis, shows that the AIMD simulations remarkably reproduces the experimental EXAFS data. The error in the predicted Ln-O distances is less than 0.07 Å for the later lanthanides, while we observed excellent agreement with predicted distances within experimental uncertainty for the early lanthanides. Our analysis revealed a dynamic, symmetrically disordered first coordination shell, which does not conform to a single molecular geometry for most lanthanides. This work sheds critical light on the highly elusive coordination geometry of the Ln3+ aqua ions.

Stabilization of hydrated AcIII cation: the role of superatom states in actinium-water bonding

225Ac-based radiopharmaceuticals have the potential to become invaluable in designated cancer therapy. However, the limited understanding of the solution chemistry and bonding properties of actinium has hindered the development of existing and emerging targeted radiotherapeutics, which also poses a significant challenge in the discovery of new agents. Herein, we report the geometric and electronic structural properties of hydrated AcIII cations in the [AcIII(H2O) n ]3+ (n = 4-11) complexes in aqueous solution and gas-phase using density functional theory. We found that nine water molecules coordinated to the AcIII cation is the most stable complex due to an enhanced hydration Gibbs free energy. This complex adopts a closed-shell 18-electron configuration (1S 21P 61D 10) of a superatom state, which indicates a non-negligible covalent character and involves H2O → AcIII σ donation interaction between s-/p-/d-type atomic orbitals of the Ac atom and 2p atomic orbitals of the O atoms. Furthermore, potentially existing 10-coordinated complexes need to overcome an energy barrier (>0.10 eV) caused by hydrogen bonding to convert to 9-coordination. These results imply the importance of superatom states in actinide chemistry generally, and specifically in AcIII solution chemistry, and highlight the conversion mechanism between different coordination numbers.

Analysis of charge density in nonaaquagadolinium(III) trifluoromethanesulfonate - insight into GdIII-OH2 bonding

The experimental charge-density distribution in [Gd(H₂O)₉](CF₃SO₃)₃ has been analysed and compared with the theoretical density functional theory calculations. Although the Gd-OH₂ bonds are mainly ionic, a covalent contribution is detectable when inspecting both the topological parameters of these bonds and the natural bond orbital results. This contribution originates from small electron transfer from the lone pairs of oxygen atoms to empty 5d and 6s spin orbitals of Gd³⁺.

Ion Association in Lanthanide Chloride Solutions

A better understanding of the solution chemistry of the lanthanide (Ln) salts in water would have wide ranging implications in materials processing, waste management, element tracing, medicine and many more fields. This is particularly true for minerals processing, given governmental concerns about lanthanide security of supply and the drive to identify environmentally sustainable processing routes. Despite much effort, even in simple systems, the mechanisms and thermodynamics of LnIII association with small anions remain unclear. In the present study, molecular dynamics (MD), using a newly developed force field, provide new insights into LnCl3 (aq) solutions. The force field accurately reproduces the structure and dynamics of Nd3+ , Gd3+ and Er3+ in water when compared to calculations using density functional theory (DFT). Adaptive-bias MD simulations show that the mechanisms for ion pairing change from dissociative to associative exchange depending upon cation size. Thermodynamics of association reveal that whereas ion pairing is favourable, the equilibrium distribution of species at low concentration is dominated by weakly bound solvent-shared and solvent-separated ion pairs, rather than contact ion pairs, reconciling a number of contrasting observations of LnIII -Cl association in the literature. In addition, we show that the thermodynamic stabilities of a range of inner sphere and outer sphere LnCl x ( 3 - x ) + coordination complexes are comparable and that the kinetics of anion binding to cations may control solution speciation distributions beyond ion pairs. The techniques adopted in this work provide a framework with which to investigate more complex solution chemistries of cations in water.

Solvation structure of lanthanide(iii) bistriflimide salts in acetonitrile solution: a molecular dynamics simulation and EXAFS investigation

Lanthanide³⁺ ions in acetonitrile solutions of bistriflimide salts form 10-fold coordination complexes composed of both solvent molecules and counterions

The folding equilibria of enterobactin enantiomers and their interaction with actinides

The helicity preference of Ent enantiomers was enhanced when binding with Fe³⁺ while disrupted when binding with actinides.

Anion dependent ion pairing in concentrated ytterbium halide solutions

We have studied ion pairing of ytterbium halide solutions. THz spectra (30-400 cm^-1) of aqueous YbCl₃ and YbBr₃ solutions reveal fundamental differences in the hydration structures of YbCl₃ and YbBr₃ at high salt concentrations: While for YbBr₃ no indications for a changing local hydration environment of the ions were experimentally observed within the measured concentration range, the spectra of YbCl₃ pointed towards formation of weak contact ion pairs. The proposed anion specificity for ion pairing was confirmed by supplementary Raman measurements.

Raman spectroscopic characterization of light rare earth ions: La3+, Ce3+, Pr3+, Nd3+ and Sm3+ - hydration and ion pair formation

Raman spectra of aqueous La³⁺, Ce³⁺, Pr³⁺, Nd³⁺ and Sm³⁺ - perchlorate solutions were measured and weak strongly polarized Raman bands were detected at 343 cm^-1, 344 cm^-1, 347 cm^-1, 352 cm^-1 and 363 cm^-1, respectively. The full width at half height for these bands is quite broad (∼50 cm^-1) in the isotropic spectrum and the band width increases with increasing solute concentration. The polarized Raman bands were assigned to the breathing modes of the nona-aqua ions of the mentioned rare earth ions. Published structural results confirmed that these ions exist as nona-hydrates in aqueous solutions [Ln(H₂O)₉]³⁺. The Ln-O bond distances of these rare earth ions correlate well with the band positions of the nona-aqua ions [Ln(OH₂)₉]⁺³ (Ln = La³⁺, Ce³⁺, Pr³⁺, Nd³⁺ and Sm³⁺) and the force constants were calculated for these breathing modes. The strength of the force constants increase with decreasing the Ln-O bond distances (La-O > Ce-O > Pr-O > Nd-O > Sm-O). While the fully hydrated ions are stable in dilute perchlorate solutions (∼0.2 mol L^-1), in concentrated perchlorate solutions outer-sphere ion pairs and contact ion pairs are formed (C > 1.5 mol L^-1). In a hydrate melt at 161 °C of Ce(ClO₄)₃ plus 6H₂O, the contact ion pairs are the dominate species. The Raman bands of the ligated perchlorate and the Ce-O breathing mode of the partially hydrated ion pair at 326 cm^-1 were measured and characterized. In cerium chloride solutions chloro-complex formation was detected over the measured concentration range from 0.270-2.167 mol L^-1. The chloro-complexes in CeCl₃(aq) are weak and diminish rapidly with dilution and disappear at a concentration <0.1 mol L^-1. In a CeCl₃ solution, with additional HCl, a series of chloro-complex species of the type [Ce(OH₂)_9-nCl_n]^+3-n (n = 1, 2) were detected.

Accurate prediction of bulk properties in hydrogen bonded liquids: amides as case studies

In this contribution we show that it is possible to build accurate force fields for small organic molecules allowing the reliable reproduction of a large panel of bulk properties, which are seldom addressed in the same context. Starting from the results obtained in recent studies, we developed a protocol for charge estimation and virtual site generation for the amide class of molecules. The parametrization of electrostatic properties is based on population analysis and orbital localization of quantum mechanical computations rooted in density functional theory and the polarizable continuum model, without any additional external information. The new protocol, coupled to other recent studies in our group targeted at an accurate fitting of internal degrees of freedom, makes available a method for building force fields from scratch (excluding for the moment intermolecular van der Waals interactions) with focus on reproducing the structure and dynamics of hydrogen bonded liquids, yielding results that are in line or better than those delivered by current general force fields. The approach is tested on the demanding series formed by formamide and its two N-methyl derivatives, N-methylformamide and N,N-dimethylformamide. We show that the atomistic structure of the liquids arising from classical molecular dynamics (MD) simulations employing the new force field is in full agreement with X-ray and neutron diffraction experiments and the corresponding spatial distribution functions are in remarkable agreement with the results of ab initio MD simulations. It is noteworthy that the latter result has never been obtained before without using ad hoc (and system dependent) scale factors and that, in addition, our parameter-free procedure is able to reproduce static dielectric constants over a wide range of values without sacrificing the force field accuracy with respect to other observables. Finally, we are able to explain the trend of static dielectric constants followed by the three amides in terms of properties obtained from the simulations, namely hydrogen bond patterns and reorientational lifetimes.

Hydration and ion association of La3+ and Eu3+ salts in aqueous solution

Lanthanide ions affect water out to the third shell and form double solvent-separated and solvent-shared ion pairs.

Lutetium(iii) aqua ion: On the dynamical structure of the heaviest lanthanoid hydration complex

The structure and dynamics of the lutetium(iii) ion in aqueous solution have been investigated by means of a polarizable force field molecular dynamics (MD). An 8-fold square antiprism (SAP) geometry has been found to be the dominant configuration of the lutetium(iii) aqua ion. Nevertheless, a low percentage of 9-fold complexes arranged in a tricapped trigonal prism (TTP) geometry has been also detected. Dynamic properties have been explored by carrying out six independent MD simulations for each of four different temperatures: 277 K, 298 K, 423 K, 632 K. The mean residence time of water molecules in the first hydration shell at room temperature has been found to increase as compared to the central elements of the lanthanoid series in agreement with previous experimental findings. Water exchange kinetic rate constants at each temperature and activation parameters of the process have been determined from the MD simulations. The obtained structural and dynamical results suggest that the water exchange process for the lutetium(iii) aqua ion proceeds with an associative mechanism, in which the SAP hydration complex undergoes temporary structural changes passing through a 9-fold TTP intermediate. Such results are consistent with the water exchange mechanism proposed for heavy lanthanoid atoms.

Identifying Coordination Geometries of Metal Aquaions in Water: Application to the Case of Lanthanoid and Actinoid Hydrates

The angular distribution function (ADF) associated with the oxygen-metal ion-oxygen angle (OMO) of several trivalent lanthanoid and actinoid aquaions has been used to identify the most probable coordination geometry of these aquaions in aqueous solutions. The ADFs extracted from the molecular dynamics trajectories have been compared with continuous distribution functions corresponding to the geometry of a reference polyhedron pattern. The procedure incorporates specific quantum-mechanical information on the aquaion under study. The new method is applied to the analysis of four M(H₂O)_n³⁺ aquaions in water, M = Lu and Cf for n = 8, and M = La and Ac for n = 9. For those that are 8-coordinated, the square antiprism (SA) coordination geometry is preferred. For the 9-fold coordination, the simulation ADFs are more similar to the continuous ADF derived from a Gyro-elongated-SA rather than to the usually proposed trigonal tricapped prism. Advantages of these continuous distributions with respect to the usually employed discrete distributions are emphasized as well as further applications are suggested.

Hydration and ion pair formation in common aqueous La(III) salt solutions--a Raman scattering and DFT study

Raman spectra of aqueous lanthanum perchlorate, triflate (trifluorosulfonate), chloride and nitrate solutions were measured over a broad concentration (0.121-3.050 mol L(-1)) range at room temperature (23 °C). A very weak mode at 343 cm(-1) with a full width at half height at 49 cm(-1) in the isotropic spectrum suggests that the nona-aqua La(III) ion is thermodynamically stable in dilute perchlorate solutions (∼0.2 mol L(-1)) while in concentrated perchlorate solutions outer-sphere ion pairs and contact ion pairs are formed. The La(3+) nona-hydrate was also detected in a 1.2 mol L(-1) La(CF3SO3)3(aq). In lanthanum chloride solutions chloro-complex formation was detected over the measured concentration range from 0.5-3.050 mol L(-1). The chloro-complexes in LaCl3(aq) are fairly weak and disappear with dilution. At a concentration <0.1 mol L(-1) almost all complexes disappeared. In LaCl3 solutions, with additional HCl, a series of chloro-complexes of the type [La(OH2)(9-n)Cln](+3-n) (n = 1-3) were formed. The La(NO3)3(aq) spectra were compared with a spectrum of a 0.409 mol L(-1) NaNO3(aq) and it was concluded that in La(NO3)3(aq) over the concentration range from 0.121-1.844 mol L(-1), nitrato-complexes, [La(OH2)(9-n)(NO3)n](+3-n) (n = 1, 2) were formed. These nitrato-complexes are quite weak and disappear with dilution <0.01 mol L(-1). DFT geometry optimizations and frequency calculations are reported for a lanthanum-nona-hydrate with a polarizable dielectric continuum in order to take the solvent into account. The bond distances and angles for the cluster geometry of [La(OH2)9](3+) with the polarizable dielectric continuum are in good agreement with data from recent structural experimental measurements and high quality simulations. The DFT frequency of the La-O stretching mode at 328.2 cm(-1), is only slightly smaller than the experimental one.

Structural, energetic, and electronic properties of La(III)-dimethyl sulfoxide clusters

By using accurate density functional theory calculations, we have studied the cluster complexes of a La(3+) ion interacting with a small number of dimethyl sulfoxide (DMSO) molecules of growing size (from 1 to 12). Extended structural, energetic, and electronic structure analyses have been performed to provide a complete picture of the physical properties that are the basis of the interaction of La(III) with DMSO. Recent experimental data in the solid and liquid phase have suggested a coordination number of 8 DMSO molecules with a square antiprism geometry arranged similarly in the liquid and crystalline phases. By using a cluster approach on the La(3+)(DMSO)n gas phase isolated structures, we have found that the 8-fold geometry, albeit less regular than in the crystal, is probably the most stable cluster. Furthermore, we provide new evidence of a 9-fold complexation geometric arrangement that is competitive (at least energetically) with the 8-fold one and that might suggest the existence of transient structures with higher coordination numbers in the liquid phase.

Combining the Fluctuating Charge Method, Non-Periodic Boundary Conditions and Meta-Dynamics: Aqua Ions as case studies

We present the current status of development of our code for performing Molecular Dynamics (MD) simulations exploiting a polarizable force field based on the Fluctuating Charge (FQ) method and non-Periodic Boundary Conditions (NPBC). Continuing on the path set in a previous work, we increased the capabilities of the code by implementing a number of new features, including: a non-iterative algorithm for rigid trigonal molecule simulations; two additional temperature coupling schemes; a meta-dynamics based approach for effective free energy evaluations. Although these are well known algorithms, each present in one or more widely used MD packages, they have now been tested, for the first time, in the context of the FQ model coupled with NPBC. As case studies, we considered three aqueous ions of increasing charge, namely Na⁺, Ca²⁺ and La³⁺, at infinite dilution. In particular, by exploiting a computational approach recently proposed by our group and based on the metadynamics technique, we focused on the important role played by solvent polarization on ionic hydration structures, also investigating the free energy landscapes of ion coordination and the water exchange rates. Such an approach, previously tested with standard non-polarizable models, was applied here to evaluate the effects of explicit polarization on water exchange barriers between different solvent coordination structures. Moreover, we have analyzed and discussed in some detail non-linear electrostatic effects arising from solvent polarization while going from a mono- to a di- and trivalent ion.