Influence of Counterions on the Hydration Structure of Lanthanide Ions in Dilute Aqueous Solutions

Does Pb2+ Form Holodirected or Hemidirected Solvation Geometries in Water?

The hydration properties of the Pb2+ ion in aqueous solution have been investigated by using a synergic approach based on Classical and Car-Parrinello molecular dynamics (CPMD) simulations and extended X-ray absorption fine structure (EXAFS) spectroscopy. A definite answer has been given to the main question on the Pb2+ hydration structure, which concerns the formation of either holodirected or hemidirected solvation geometries, such terms referring to the arrangements of the ligands that can be directed either throughout the surface of an encompassing globe around Pb2+ or throughout only part of the globe, respectively. Our CPMD results show that the Pb2+ ion in water forms a hemidirected 4-fold cluster with a well-defined distorted pyramidal geometry. This cluster is directed throughout one side of the first shell globe, while the other side contains either two or three very mobile water molecules that do not form a well-defined geometry around the Pb2+ ion. The Pb2+ first shell structural arrangement determined from the CPMD simulation was confirmed by the EXAFS experimental results. A homodirected Pb2+ first shell complex like the 8-fold SAP structure obtained from the classical MD simulations cannot be reconciled with the EXAFS experimental data. These findings represent a significant step forward in the understanding of the solvation chemistry of the Pb2+ ion, which is fundamental to improving the efficiency of lead removal procedures that are crucial to the safety of water resources.

Physicochemical Characterization and Antimicrobial Properties of Lanthanide Nitrates in Dilute Aqueous Solutions

This work presents the results of studying dilute aqueous solutions of commercial Ln(NO3)3 · xH2O salts with Ln = Ce-Lu using X-ray diffraction (XRD), IR spectroscopy, X-ray absorption spectroscopy (XAS: EXAFS/XANES), and pH measurements. As a reference point, XRD and XAS measurements for characterized Ln(NO3)3 · xH2O microcrystalline powder samples were performed. The local structure of Ln-nitrate complexes in 20 mM Ln(NO3)3 · xH2O aqueous solution was studied under total external reflection conditions and EXAFS geometry was applied to obtain high-quality EXAFS data for solutions with low concentrations of Ln3+ ions. Results obtained by EXAFS spectroscopy showed significant contraction of the first coordination sphere during the dissolution process for metal ions located in the middle of the lanthanide series. It was established that in Ln(NO3)3 · xH2O solutions with Ln = Ce, Sm, Gd, Yb (c = 134, 100, 50 and 20 mM) there are coordinated and, to a greater extent, non-coordinated nitrate groups with bidentate and predominantly monodentate bonds with Ln ions, the number of which increases upon transition from cerium to ytterbium. For the first time, the antibacterial and antifungal activity of Ln(NO3)3 · xH2O Ln = Ce, Sm, Gd, Tb, Yb solutions with different concentrations and pH was presented. Cross-relationships between the concentration of solutions and antimicrobial activity with the type of Ln = Ce, Sm, Gd, Tb, Yb were established, as well as the absence of biocidal properties of solutions with a concentration of 20 mM, except for Ln = Yb. The important role of experimental conditions in obtaining and interpreting the results was noted.

Modeling separation of lanthanides via heterogeneous ligand binding

Individual lanthanide elements have physical/electronic/magnetic properties that make each useful for specific applications. Several of the lanthanides cations (Ln3+) naturally occur together in the same ores. They are notoriously difficult to separate from each other due to their chemical similarity. Predicting the Ln3+ differential binding energies (ΔΔE) or free energies (ΔΔG) at different binding sites, which are key figures of merit for separation applications, will help design of materials with lanthanide selectivity. We apply ab initio molecular dynamics (AIMD) simulations and density functional theory (DFT) to calculate ΔΔG for Ln3+ coordinated to ligands in water and embedded in metal-organic frameworks (MOFs), and ΔΔE for Ln3+ bonded to functionalized silica surfaces, thus circumventing the need for the computational costly absolute binding (free) energies ΔG and ΔE. Perturbative AIMD simulations of water-inundated simulation cells are applied to examine the selectivity of ligands towards adjacent Ln3+ in the periodic table. Static DFT calculations with a full Ln3+ first coordination shell, while less rigorous, show that all ligands examined with net negative charges are more selective towards the heavier lanthanides than a charge-neutral coordination shell made up of water molecules. Amine groups are predicted to be poor ligands for lanthanide-binding. We also address cooperative ion binding, i.e., using different ligands in concert to enhance lanthanide selectivity.

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.

Going beyond Radial Hydration Models: The Hidden Structures of Chloride and Iodide Aqua Ions Revealed by the Use of Lone Pairs

A novel model of hydration for the chloride and iodide ions in water is proposed, which overcomes the limitations of conventional radial models. A new approach, based on a representation of the halide lone pairs, highlighted a subset of first shell water molecules featuring preferential strong interactions with the ion lone pairs, giving rise to tetrahedral hydration structures in both Cl- and I- aqueous solutions. By adopting a novel descriptor correlated to the halide-water interaction energy, we were able to split the conventional first solvation shell into a tight first hydration shell, composed of water molecules strongly interacting with the ions via hydrogen bonds, and a loose first shell containing molecules that are only slightly perturbed by the halide electrostatic charge. The picture emerging from our findings indicates that lone pairs play an important role in the description of systems where hydrogen bonds are the main interactions taking place in the solvation process.

Aqueous Structure of Lanthanide-EDTA Coordination Complexes Determined by a Combined DFT/EXAFS Approach

Sustainable production of rare earth elements (REEs) is critical for technologies needed for climate change mitigation, including wind turbines and electric vehicles. However, separation technologies currently used in REE production have large environmental footprints, necessitating more sustainable strategies. Aqueous, affinity-based separations are examples of such strategies. To make these technologies feasible, it is imperative to connect aqueous ligand structure to ligand selectivity for individual REEs. As a step toward this goal, we analyzed the extended X-ray absorption fine structure (EXAFS) of four lanthanides (La, Ce, Pr, and Nd) complexed by a common REE chelator, ethylenediaminetetraacetic acid (EDTA) to determine the aqueous-phase structure. Reference structures from density functional theory (DFT) were used to help fit the EXAFS spectra. We found that all four Ln-EDTA coordination complexes formed 9-coordinate structures with 6 coordinating atoms from EDTA (4 carboxyl oxygen atoms and 2 nitrogen atoms) and 3 oxygen atoms from water molecules. All EXAFS fits were of high quality (R-factor < 0.02) and showed decreasing average first-shell coordination distance across the series (2.62-2.57 Å from La-Nd), in agreement with DFT (2.65-2.56 Å from La-Nd). The insights determined herein will be useful in the development of ligands for sustainable rare earth elements (REE) separation technologies.

Solution Structures of Europium Terpyridyl Complexes with Nitrate and Triflate Counterions in Acetonitrile

Lanthanide-ligand complexes are key components of technological applications, and their properties depend on their structures in the solution phase, which are challenging to resolve experimentally or computationally. The coordination structure of the Eu³⁺ ion in different coordination environments in acetonitrile is examined using ab initio molecular dynamics (AIMD) simulations and extended X-ray absorption fine structure (EXAFS) spectroscopy. AIMD simulations are conducted for the solvated Eu³⁺ ion in acetonitrile, both with or without a terpyridyl ligand, and in the presence of either triflate or nitrate counterions. EXAFS spectra are calculated directly from AIMD simulations and then compared to experimentally measured EXAFS spectra. In acetonitrile solution, both nitrate and triflate anions are shown to coordinate directly to the Eu³⁺ ion forming either ten- or eight-coordinate solvent complexes where the counterions are binding as bidentate or monodentate structures, respectively. Coordination of a terpyridyl ligand to the Eu³⁺ ion limits the available binding sites for the solvent and anions. In certain cases, the terpyridyl ligand excludes any solvent binding and limits the number of coordinated anions. The solution structure of the Eu-terpyridyl complex with nitrate counterions is shown to have a similar arrangement of Eu³⁺ coordinating molecules as the crystal structure. This study illustrates how a combination of AIMD and EXAFS can be used to determine how ligands, solvent, and counterions coordinate with the lanthanide ions in solution.

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.

Hydration of divalent lanthanides, Sm2+ and Eu2+ : A molecular dynamics study with polarizable AMOEBA force field

The chemistry of divalent lanthanides, Ln2+ , is a growing sub-field of heavy element chemistry owing to new synthetic approaches. However, some theoretical aspects of these unusual cations are currently underdeveloped, especially as they relate to their dynamic properties in solution. In this work, we address the hydration of two of the classical Ln2+ cations, Sm2+ and Eu2+ , using atomic multipole optimized energetic for biomolecular applications (AMOEBA) force fields. These cations have not been parameterized to date with AMOEBA, and few studies are available because of their instability with respect to oxidation in aqueous media. Coordination numbers (CN's) of 8.2 and 8.1 respectively for Sm2+ and Eu2+ , and 8.8 for both Sm3+ and Eu3+ have been obtained and are in good agreement with the few available AIMD and X-ray absorption fine structures studies. The decreased CN of Ln2+ compared with Ln3+ arises from progressive water exchange events that indicates the gradual stabilization of 8-coordinate structures with respect to 9-coordinate geometries. Moreover, the effects of the chloride counter anions on the coordination of Ln2+ cations have been studied at different chloride concentrations in this work. Lastly, water exchange times of Ln2+ cations have been calculated to provide a comprehensive understanding of the behavior of Eu2+ and Sm2+ in aqueous chloride media.

Fate of a Deep Eutectic Solvent upon Cosolvent Addition: Choline Chloride-Sesamol 1:3 Mixtures with Methanol

The changes upon methanol (MeOH) addition in the structural arrangement of the highly eco-friendly deep eutectic solvent (DES) formed by choline chloride (ChCl) and sesamol in 1:3 molar ratio have been studied by means of attenuated total reflection Fourier transform infrared spectroscopy, small- and wide-angle X-ray scattering (SWAXS), and molecular dynamics simulations. The introduction of MeOH into the DES promotes the increase of the number of Cl-MeOH hydrogen bonds (HBs) through the replacement of sesamol and choline molecules from the chloride anion coordination sphere. This effect does not promote the sesamol-sesamol, choline-choline, and sesamol-choline interactions, which remain as negligible as in the pure DES. Differently, the displaced sesamol and choline molecules are solvated by MeOH, which also forms HBs with other MeOH molecules, so that the system arranges itself to keep the overall amount of HBs maximized. SWAXS measurements show that this mechanism is predominant up to MeOH/DES molar ratios of 20-24, while after this ratio value, the scattering profile is progressively diluted in the cosolvent background and decreases toward the signal of pure MeOH. The ability of MeOH to interplay with all of the DES components produces mixtures with neither segregation of the components at nanoscale lengths nor macroscopic phase separation even for high MeOH contents. These findings have important implications for application purposes since the understanding of the pseudophase aggregates formed by a DES with a dispersing cosolvent can help in addressing an efficient extraction procedure.

On the Coordination Chemistry of the lanthanum(III) Nitrate Salt in EAN/MeOH Mixtures

A thorough structural characterization of the La(NO₃)₃ salt dissolved into several mixtures of ethyl ammonium nitrate (EAN) and methanol (MeOH) with EAN molar fraction χ_EAN ranging from 0 to 1 has been carried out by combining molecular dynamics (MD) and X-ray absorption spectroscopy (XAS). The XAS and MD results show that changes take place in the La³⁺ first solvation shell when moving from pure MeOH to pure EAN. With increasing the ionic liquid content of the mixture, the La³⁺ first-shell complex progressively loses MeOH molecules to accommodate more and more nitrate anions. Except in pure EAN, the La³⁺ ion is always able to coordinate both MeOH and nitrate anions, with a ratio between the two ligands that changes continuously in the entire concentration range. When moving from pure MeOH to pure EAN, the La³⁺ first solvation shell passes from a 10-fold bicapped square antiprism geometry where all the nitrate anions act only as monodentate ligands to a 12-coordinated icosahedral structure in pure EAN where the nitrate anions bind the La³⁺ cation both in mono- and bidentate modes. The La³⁺ solvation structure formed in the MeOH/EAN mixtures shows a great adaptability to changes in the composition, allowing the system to reach the ideal compromise among all of the different interactions that take place into it.

The structural properties of the La(NO₃)₃ salt dissolved into EAN/methanol mixtures were characterized by molecular dynamics and X-ray absorption spectroscopy. The La³⁺ solvation shell undergoes significant changes with increasing the ionic liquid content of the mixture, progressively losing methanol molecules to accommodate more and more nitrate anions. The La³⁺ solvation structure shows great adaptability to composition changes, passing from a 10-fold bicapped square antiprism geometry in pure methanol to a 12-coordinated icosahedral complex in EAN.

Coordination of the Co2+ and Ni2+ Ions in Tf2N- Based Ionic Liquids: A Combined X-ray Absorption and Molecular Dynamics Study

Molecular dynamics (MD) simulations and X-ray absorption spectroscopy (XAS) have been combined to study the coordination of the Co2+ and Ni2+ ions in ionic liquids (ILs) based on the bis(trifluoromethylsulfonyl)imide ([Tf2N]-) anion and having different organic cations, namely, 1-butyl-3-methylimidazolium ([C4mim]+), 1,8-bis(3-methylimidazolium-1-yl)octane ([C8(mim)2]2+), N,N,N-trimethyl-N-(2-hydroxyethyl)ammonium ([choline]+), and butyltrimethylammonium ([BTMA]+). Co and Ni K-edge XAS data have been collected on 0.1 mol L-1 Co(Tf2N)2 and Ni(Tf2N)2 solutions and on the metallic salts. MD simulations have been carried out to obtain structural information on the metal ion coordination. The analysis of the extended X-ray absorption fine structure (EXAFS) spectra of the solutions has been carried out based on the atomistic description provided by MD, and the studied ILs have been found to be able to dissolve both the Co(Tf2N)2 and Ni(Tf2N)2 salts giving rise to a different structural arrangement around the metal ions as compared to the solid state. The combined EXAFS and MD results showed that the Co2+ and Ni2+ ions are surrounded by a first solvation shell formed by six [Tf2N]- anions, each coordinating in a monodentate fashion by means of the oxygen atoms. The nature of the IL organic cation has little or no influence on the overall spatial arrangement of the [Tf2N]- anions, so that stable octahedral complexes of the type [M(Tf2N)6]4- (M = Co, Ni) have been observed in all the investigated ILs.

Anatomy of a deep eutectic solvent: structural properties of choline chloride : sesamol 1 : 3 compared to reline

The structural properties of the deep eutectic solvent (DES) formed by choline chloride (ChCl) and sesamol in 1 : 3 ratio have been investigated and compared to those of reline (ChCl : urea 1 : 2). An integrated approach combining small and wide angle X-ray scattering with molecular dynamics simulations has been employed and the simulation protocol has been validated against the experimental data. In the ChCl : sesamol DES, strong hydrogen bonds (HBs) are formed between the chloride anion and the hydroxyl groups of the choline and of sesamol molecules. Conversely, choline-choline, choline-sesamol and sesamol-sesamol interactions are negligible. A more extended interplay between the constituents is observed in reline where, besides the HBs involving the chloride anion, the eutectic formation is favored also by strong choline-urea and urea-urea interactions. The three-dimensional arrangement around the individual components shows that, in the ChCl : sesamol DES, the cholinium cations and the sesamol molecules are packed in such a way to maximize the interactions with the chlorine anion. This structural arrangement may favor the π-π interactions between the sesamol molecules and the aromatic species mediated by the chloride ions, providing an interpretation for the high separation rates previously observed for phenolic DESs towards aromatic compounds.

Solvation structure and dynamics of the dimethylammonium cation diluted in liquid water: A molecular dynamics approach

Classical molecular dynamics simulation techniques were employed to investigate the local solvation structure and related dynamics of the dimethylammonium cation diluted in liquid water at ambient conditions. The translational and orientational order around the dimethylammonium cation was investigated in terms of the corresponding radial and angular distribution functions. The results obtained revealed that the first solvation shell of the dimethylammonium consists mainly of two and, less frequently, three water molecules. The two nearest water neighbors form hydrogen bonds with the ammonium hydrogen atoms of the cation, whereas the third neighbor interacts with the methyl hydrogen atoms as well. The distribution of the trigonal order parameter exhibits a bimodal behavior, signifying the existence of local orientational heterogeneities in the solvation shell of the dimethylammonium cation. The calculated continuous and intermittent residence and hydrogen bond lifetimes for the cation-water pairs have also been found to be longer in comparison with the water-water ones. The very similar self-diffusion coefficients of the dimethylammonium cation and the water molecules in the bulk dilute solution indicate that the translational motions of the cation are mainly controlled by the translational mobility of the surrounding water molecules.

Unraveling the solvation geometries of the lanthanum(iii) bistriflimide salt in ionic liquid/acetonitrile mixtures

La(Tf₂N)₃ in C₈(mim)₂(Tf₂N)₂/acetonitrile mixtures forms 10-fold coordination complexes composed of both acetonitrile molecules and Tf₂N⁻ anions.

Molecular dynamics simulations of Y(iii) coordination and hydration properties

Y mainly exists in ionic rare-earth resources. During rare-earth carbonate precipitation, rare-earth ion loss in the precipitated rare-earth mother liquor often occurs due to CO₃²⁻ coordination and Y(iii) hydration. Microscopic information on the coordination and hydration of CO₃²⁻ and H₂O to Y(iii) has not yet been elucidated. Therefore, in this study, the macroscopic dissolution of Y(iii) in different aqueous solutions of Na₂CO₃ was studied. The radial distribution function and coordination number of Y(iii) by CO₃²⁻ and H₂O were systematically analyzed using molecular dynamics (MD) simulations to obtain the complex ion form of Y(iii) in carbonate solutions. Density functional theory (DFT) was used to geometrically optimize and calculate the UV spectrum of Y(iii) complex ions. This spectrum was then analyzed and compared with experimentally determined ultraviolet-visible spectra to verify the reliability of the MD simulation results. Results showed that Y(iii) in aqueous solution exists in the form of [Y·3H₂O]³⁺ and that CO₃²⁻ is present in the bidentate coordination form. In 0–0.8 mol L⁻¹ CO₃²⁻ solutions, Y(iii) was mainly present as the 5-coordinated complex [YCO₃·3H₂O]⁺. When the concentration of CO₃²⁻ was increased to 1.2 mol L⁻¹, [YCO₃·3H₂O]⁺ was converted into a 6-coordinated complex [Y(CO₃)₂·2H₂O]⁻. Further increases in CO₃²⁻ concentration promoted Y(iii) dissolution in solution in the form of complex ions. These findings can be used to explain the problem of incomplete precipitation of rare earths in carbonate solutions.

Based on MD results, DFT was used to geometrically optimize and calculate the UV spectrum of Y(iii) complex ions. Data validation was further performed using UV-vis experiments to reveal Y(iii) coordination and hydration properties.

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

Hydration and Ion Pair Formation in Aqueous Lu3+- Solution

Aqueous solutions of Lu³⁺- perchlorate, triflate and chloride were measured by Raman spectroscopy. A weak, isotropic mode at 396 cm⁻¹ (full width at half height (fwhh) at 50 cm⁻¹) was observed in perchlorate and triflate solutions. This mode was assigned to the totally symmetric stretching mode of [Lu(OH₂)₈]³⁺, ν₁LuO₈. In Lu(ClO₄)₃ solutions in heavy water, the ν₁LuO₈ symmetric stretch of [Lu(OD₂)₈]³⁺ appears at 376.5 cm⁻¹. The shift confirms the theoretical isotopic effect of this mode. In the anisotropic scattering of aqueous Lu(ClO₄)₃, five bands of very low intensity were observed at 113 cm⁻¹, 161.6 cm⁻¹, 231 cm⁻¹, 261.3 cm⁻¹ and 344 cm⁻¹. In LuCl₃ (aq) solutions measured over a concentration range from 0.105–3.199 mol·L⁻¹ a 1:1 chloro-complex was detected. Its equilibrium concentration, however, disappeared rapidly with dilution and vanished at a concentration < 0.5 mol·L⁻¹. Quantitative Raman spectroscopy allowed the detection of the fractions of [Lu(OH₂)₈]³⁺, the fully hydrated species and the mono-chloro complex, [Lu(OH₂)₇Cl]²⁺. In a ternary LuCl₃/HCl solution, a mixtrure of chloro-complex species of the type [Lu(OH₂)_8−nCl_n]⁺³⁻ⁿ (n = 1 and 2) were detected. DFT geometry optimization and frequency calculations are reported for Lu³⁺- water cluster in vacuo and with a polarizable dielectric continuum (PC) model including the bulk solvent implicitly. The bond distance and angle for [Lu(OH₂)₈]³⁺ within the PC are in good agreement with data from structural experiments. The DFT frequencies for the Lu-O modes of [Lu(OH₂)₈]³⁺ and its deuterated analog [Lu(OD₂)₈]³⁺ in a PC are in fair agreement with the experimental ones. The calculated hydration enthalpy of Lu³⁺ (aq) is slightly lower than the experimental value.