Development of Lennard-Jones and Buckingham Potentials for Lanthanoid Ions in Water

Chemical models for dense solutions

Here we examine the question of the chemical models widely used to describe dense solutions, particularly ionic solutions. First, a simple macroscopic analysis shows that, in the case of weak interactions, taking into account aggregated species amounts to modelling an effective attraction between solutes, although the stoichiometry used does not necessarily correspond to atomic reality. We then use a rigorous microscopic analysis to explain how, in the very general case, chemical models can be obtained from an atomic physical description. We show that there are no good or bad chemical models as long as we consider exact calculations. To obtain the simplest possible description, it is nevertheless advisable to take the speciation criterion that minimises the excess terms. Molecular simulations show that, very often, species can be defined simply by grouping ions which are in direct contact. In some cases, the appearance of macroscale clusters can be predicted.

Structure and mobility of rare earth ions in interlayer space of montmorillonite: a molecular dynamics study

Ion adsorption-type deposits (IADs) are the dominant sources of rare earth elements (REEs), in which REEs are mainly enriched in clay minerals. However, the adsorption mechanism of REEs in the interlayer region of clay minerals is still poorly understood. In this study, by using molecular dynamics (MD) simulations, we explored the interlayer structures and dynamics of REEs-intercalated montmorillonite. La3+ and Lu3+ were used as the model cations for light REEs (LREEs) and heavy REEs (HREEs), respectively. It was found that the most thermodynamically stable state for both LREE- and HREE-montmorillonite was the double-hydration state and the corresponding basal spacing was calculated to be ∼16.1 Å. REE ions are located at the middle plane of the interlayer space and adsorbed on the montmorillonite basal surface through hydrogen bonds between its coordination water and the basal oxygens (i.e. as outer-sphere complexes). La3+ was 9-fold coordinated in the interlayer space with a mono-capped square antiprism coordination shell, while Lu3+ was 8-fold coordinated in a square antiprism cage. The mobility of REEs intercalated in the interlayer was significantly reduced compared to the mobility of REEs in aqueous solutions. The microscopic structures, thermodynamic data, and mobility obtained in the present study can help understand the enrichment and mobilization of REEs in IADs, and provide a molecular level basis for developing more efficient extraction techniques.

Toward a realistic theoretical electronic spectra of metal aqua ions in solution: The case of Ce(H2O)n3+ using statistical methods and quantum chemistry calculations

Accurately predicting spectra for heavy elements, often open-shell systems, is a significant challenge typically addressed using a single cluster approach with a fixed coordination number. Developing a realistic model that accounts for temperature effects, variable coordination numbers, and interprets experimental data is even more demanding due to the strong solute-solvent interactions present in solutions of heavy metal cations. This study addresses these challenges by combining multiple methodologies to accurately predict realistic spectra for highly charged metal cations in aqueous media, with a focus on the electronic absorption spectrum of Ce3+ in water. Utilizing highly correlated relativistic quantum mechanical (QM) wavefunctions and structures from molecular dynamics (MD) simulations, we show that the convolution of individual vertical transitions yields excellent agreement with experimental results without the introduction of empirical broadening. Good results are obtained for both the normalized spectrum and that of absolute intensity. The study incorporates a statistical machine learning algorithm, Gaussian Mixture Models-Nuclear Ensemble Approach (GMM-NEA), to convolute individual spectra. The microscopic distribution provided by MD simulations allows us to examine the contributions of the octa- and ennea-hydrate of Ce3+ in water to the final spectrum. In addition, the temperature dependence of the spectrum is theoretically captured by observing the changing population of these hydrate forms with temperature. We also explore an alternative method for obtaining statistically representative structures in a less demanding manner than MD simulations, derived from QM Wigner distributions. The combination of Wigner-sampling and GMM-NEA broadening shows promise for wide application in spectroscopic analysis and predictions, offering a computationally efficient alternative to traditional methods.

Improved Gaussian basis sets for norm-conserving 4f-in-core pseudopotentials of trivalent lanthanides (Ln = Ce-Lu)

The first-principles quantum chemical computations often scale as Nk (N = basis sets; k = 1-4 for linear scaling, Hartree-Fock or density functional theory methods), which makes the development of accurate pseudopotentials and efficient basis sets necessary ingredients in modeling of heavy elements such as lanthanides and actinides. Recently, we have developed 4f-in-core norm-conserving pseudopotentials and associated basis sets for the trivalent lanthanides [Lu et al., J. Chem. Theory Comput. 19, 82-96 (2023)]. In the present paper, we present a unified approach to optimize high-quality Gaussian basis sets for modeling and simulations of condensed-phase systems. The newly generated basis sets not only capture the low total energy and fairly reasonable condition number of overlap matrix of lanthanide-containing systems, but also exhibit good transferability and reproducibility. These advantages ensure the accuracy of the basis sets while avoiding linear dependency concern of atom-centered basis sets. The performance of the basis sets is further illustrated in lanthanide molecular and condensed-phase systems by using Gaussian-plane wave density functional approach of CP2K. These new basis sets can be of particular interest to model structurally complicated lanthanide molecules, clusters, solutions, and solid systems.

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.

Lanmodulin's EF 2-3 Domain: Insights from Infrared Spectroscopy and Simulations

Lanmodulins are small, ∼110-residue proteins with four EF-hand motifs that demonstrate a picomolar affinity for lanthanide ions, making them efficient in the recovery and separation of these technologically important metals. In this study, we examine the thermodynamic and structural complexities of lanthanide ion binding to a 41-residue domain, EF 2-3, that constitutes the two highest-affinity metal-binding sites in the lanmodulin protein from Methylorubrum extorquens. Using a combination of circular dichroism (CD) spectroscopy, isothermal titration calorimetry (ITC), two-dimensional infrared (2D IR) spectroscopy, and molecular dynamics (MD) simulations, we characterize the metal binding capabilities of EF 2-3. ITC demonstrates that binding occurs between peptide and lanthanides with conditional dissociation constants (Kd) in the range 20-30 μM, with no significant differences in the Kd values for La3+, Eu3+, and Tb3+ at pH 7.4. In addition, CD spectroscopy suggests that only one binding site of EF 2-3 undergoes a significant conformational change in the presence of lanthanides. 2D IR spectroscopy demonstrates the presence of both mono- and bidentate binding configurations in EF 2-3 with all three lanthanides. MD simulations, supported by Eu3+ luminescence measurements, explore these results, suggesting a competition between water-lanthanide and carboxylate-lanthanide interactions in the EF 2-3 domain. These results underscore the role of the core helical bundle of the protein architecture in influencing binding affinities and communication between the metal-binding sites in the full-length protein.

Investigation of Rare Earth Element Binding to a Surface-Bound Affinity Peptide Derived from EF-Hand Loop I of Lanmodulin

Bioinspired strategies have been given extensive attention for the recovery of rare earth elements (REEs) from waste streams because of their high selectivity, regeneration potential, and sustainability as well as low cost. Lanmodulin protein is an emerging biotechnology that is highly selective for REE binding. Mimicking lanmodulin with shorter peptides is advantageous because they are simpler and potentially easier to manipulate and optimize. Lanmodulin-derived peptides have been found to bind REEs, but their properties have not been explored when immobilized on solid substrates, which is required for many advanced separation technologies. Here, two peptides, LanM1 and scrambled LanM1, are designed from the EF-hand loop 1 of lanmodulin and investigated for their binding affinity toward different REEs when surface-bound. First, the ability of LanM1 to bind REEs was confirmed and characterized in solution using circular dichroism (CD), nuclear magnetic resonance (NMR), and molecular dynamics (MD) simulations for Ce(III) ions. Isothermal titration calorimetry (ITC) was used to further analyze the binding of the LanM1 to Ce(III), Nd(III), Eu(III), and Y(III) ions and in low-pH conditions. The performance of the immobilized peptides on a model gold surface was examined using a quartz crystal microbalance with dissipation (QCM-D). The studies show that the LanM1 peptide has a stronger REE binding affinity than that of scrambled LanM1 when in solution and when immobilized on a gold surface. QCM-D data were fit to the Langmuir adsorption model to estimate the surface-bound dissociation constant (Kd) of LanM1 with Ce(III) and Nd(III). The results indicate that LanM1 peptides maintain a high affinity for REEs when immobilized, and surface-bound LanM1 has no affinity for potential competitor calcium and copper ions. The utility of surface-bound LanM1 peptides was further demonstrated by immobilizing them to gold nanoparticles (GNPs) and capturing REEs from solution in experiments utilizing an Arsenazo III-based colorimetric dye displacement assay and ultraviolet-visible (UV-vis) spectrophotometry. The saturated adsorption capacity of GNPs was estimated to be around 3.5 μmol REE/g for Ce(III), Nd(III), Eu(III), and Y(III) ions, with no binding of non-REE Ca(II) ions observed.

Acceleration of Solvation Free Energy Calculation via Thermodynamic Integration Coupled with Gaussian Process Regression and Improved Gelman-Rubin Convergence Diagnostics

The determination of the solvation free energy of ions and molecules holds profound importance across a spectrum of applications spanning chemistry, biology, energy storage, and the environment. Molecular dynamics simulations are powerful tools for computing this critical parameter. Nevertheless, the accurate and efficient calculation of the solvation free energy becomes a formidable endeavor when dealing with complex systems characterized by potent Coulombic interactions and sluggish ion dynamics and, consequently, slow transition across various metastable states. In the present study, we expose limitations stemming from the conventional calculation of the statistical inefficiency g in the thermodynamic integration method, a factor that can hinder the determination of convergence of the solvation free energy and its associated uncertainty. Instead, we propose a robust scheme based on Gelman-Rubin convergence diagnostics. We leverage this improved estimation of uncertainties to introduce an innovative accelerated thermodynamic integration method based on the Gaussian Process regression. This methodology is applied to the calculation of the solvation free energy of trivalent rare-earth elements immersed in ionic liquids, a scenario in which the aforementioned challenges render standard approaches ineffective. The proposed method proves to be effective in computing solvation free energy in situations where traditional thermodynamic integration methods fall short.

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.

Designed Y3+ Surface Segregation Increases Stability of Nanocrystalline Zinc Aluminate

The thermal stability of zinc aluminate nanoparticles is critical for their use as catalyst supports. In this study, we experimentally show that doping with 0.5 mol % Y₂O₃ improves the stability of zinc aluminate nanoparticles. The dopant spontaneously segregates to the nanoparticle surfaces in a phenomenon correlated with excess energy reduction and the hindering of coarsening. Y³⁺ was selected based on atomistic simulations on a 4 nm zinc aluminate nanoparticle singularly doped with elements of different ionic radii: Sc³⁺, In³⁺, Y³⁺, and Nd³⁺. The segregation energies were generally proportional to ionic radii, with Y³⁺ showing the highest potential for surface segregation. Direct measurements of surface thermodynamics confirmed the decreasing trend in surface energy from 0.99 for undoped to 0.85 J/m² for Y-doped nanoparticles. Diffusion coefficients calculated from coarsening curves for undoped and doped compositions at 850 °C were 4.8 × 10^-12 cm²/s and 2.5 × 10^-12 cm²/s, respectively, indicating the coarsening inhibition induced by Y³⁺ results from a combination of a reduced driving force (surface energy) and decreased atomic mobility.

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.

Recalibrating the calcium trap in amino acid carboxyl groups via classical molecular dynamics simulations

In order to use classical molecular dynamics to complement experiments accurately, it is important to use robust descriptions of the system. The interactions between biomolecules, like aspartic and glutamic acid, and dissolved ions are often studied using standard biomolecular force-fields, where the interactions between biomolecules and cations are often not parameterized explicitly. In this study, we have employed metadynamics simulations to investigate different interactions of Ca with aspartic and glutamic acid and constructed the free energy profiles of Ca²⁺-carboxylate association. Starting from a generally accepted, AMBER-based force field, the association was substantially over and under-estimated, depending on the choice of water model (TIP3P and SPC/fw, respectively). To rectify this discrepancy, we have replaced the default calcium parameters. Additionally, we modified the σ_ij value in the hetero-atomic Lennard-Jones interaction by 0.5% to further improve the interaction between Ca and carboxylate, based on comparison with the experimentally determined association constant for Ca with the carboxylate group of L-aspartic acid. The corrected description retrieved the structural properties of the ion pair in agreement with the original biomolecule - Ca²⁺ interaction in AMBER, whilst also producing an association constant comparable to experimental observations. This refined force field was then used to investigate the interactions between amino acids, calcium and carbonate ions during biogenic and biomimetic calcium carbonate mineralisation.

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.

Modeling Gd3+ Complexes for Molecular Dynamics Simulations: Toward a Rational Optimization of MRI Contrast Agents

The correct parametrization of lanthanide complexes is of the utmost importance for their characterization using computational tools such as molecular dynamics simulations. This allows the optimization of their properties for a wide range of applications, including medical imaging. Here we present a systematic study to establish the best strategies for the correct parametrization of lanthanide complexes using [Gd(DOTA)]^- as a reference, which is used as a contrast agent in MRI. We chose the bonded model to parametrize the lanthanide complexes, which is especially important when considering the study of the complex as a whole (e.g., for the study of the dynamics of its interaction with proteins or membranes). We followed two strategies: a so-called heuristic approach employing strategies already published by other authors and another based on the more recent MCPB.py tool. Adjustment of the Lennard-Jones parameters of the metal was required. The final topologies obtained with both strategies were able to reproduce the experimental ion to oxygen distance, vibrational frequencies, and other structural properties. We report a new strategy to adjust the Lennard-Jones parameters of the metal ion in order to capture dynamic properties such as the residence time of the capping water (τ_m). For the first time, the correct assessment of the τ_m value for Gd-based complexes was possible by recording the dissociative events over up to 10 μs all-atom simulations. The MCPB.py tool allowed the accurate parametrization of [Gd(DOTA)]^- in a simpler procedure, and in this case, the dynamics of the water molecules in the outer hydration sphere was also characterized. This sphere was divided into the first hydration layer, an intermediate region, and an outer hydration layer, with a residence time of 18, 10 and 19 ps, respectively, independent of the nonbonded parameters chosen for Gd³⁺. The Lennard-Jones parameters of Gd³⁺ obtained here for [Gd(DOTA)]^- may be used with similarly structured gadolinium MRI contrast agents. This allows the use of molecular dynamics simulations to characterize and optimize the contrast agent properties. The characterization of their interaction with membranes and proteins will permit the design of new targeted contrast agents with improved pharmacokinetics.

Atomistic Insights into Structure and Dynamics of Neodymium(III) Complexation with a Bis-lactam Phenanthroline Ligand in the Organic Phase

Rare-earth elements (REEs) such as neodymium are critical materials needed in many important technologies, and rigid neutral bis-lactam-1,10-phenanthroline (BLPhen) ligands show one of the highest extraction performance for complexing Nd(III) in REE uptake and separation processes. However, the local structure of the complexes formed between BLPhen and Nd(III) in a typical organic solvent such as dichloroethane (DCE) is unclear. Here, we perform first-principles molecular dynamics (FPMD) simulations to unveil the structure of complexes formed by BLPhen with Nd(NO3)3 in the DCE solvent. BLPhen can bind to Nd(III) in either 1:1 or 2:1 fashion. In the 1:1 complex, three nitrates bind to Nd(III) via the bidentate mode in the first solvation shell, leading to the formation of a neutral complex, [Nd(BLPhen)(NO3)3]0, in the organic phase. In contrast, there are two nitrates in the first solvation shell in the 2:1 complex, creating a charged complex, [Nd(BLPhen)2(NO3)2]+. The third nitrate was found to be far away from the metal center, migrating to the outer solvation shell. Our simulations show that the binding pocket formed by the two rigid BLPhen ligands allows ample space for two nitrates to bind to the Nd(III) center from opposite sides. Our findings of two nitrates in the first solvation shell of the 2:1 complex and the corresponding bond distances agree well with the available crystal structure. This study represents the first accurate FPMD modeling of the BLPhen-Nd(III) complexes in an explicit organic solvent and opens the door to more atomistic understanding of REE separations from first principles.

Where Lennard-Jones Potentials Fail: Iterative Optimization of Ion-Water Pair Potentials Based on Ab Initio Molecular Dynamics Data

The use of the Lennard-Jones (LJ) potential in computer simulations of aqueous electrolyte solutions is widespread. The standard approach is to parametrize LJ potential parameters against thermodynamic solution properties, but problems in representing the local structural and dynamic properties of ion hydration shells remain. The r^-12-term in the LJ potential is responsible for this as it leads to overly repulsive ion-water interactions at short range. As a result, the LJ potential predicts blue-shifted vibrational peaks of the cations' rattling mode and too large negative ion hydration entropies. We demonstrate that cation-water effective pair potentials derived from ab initio MD data have softer short-range repulsions and represent hydration shell properties significantly better. Our findings indicate that replacing the LJ potential with these effective pair potentials offers a promising route to represent thermodynamic solution properties and local interactions of specific ions with nonpolarizable force field models.

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.

Lanthanide-dependent coordination interactions in lanmodulin: a 2D IR and molecular dynamics simulations study

The biological importance of lanthanides, and the early lanthanides (La³⁺-Nd³⁺) in particular, has only recently been recognized, and the structural principles underlying selective binding of lanthanide ions in biology are not yet well established. Lanmodulin (LanM) is a novel protein that displays unprecedented affinity and selectivity for lanthanides over most other metal ions, with an uncommon preference for the early lanthanides. Its utilization of EF-hand motifs to bind lanthanides, rather than the Ca²⁺ typically recognized by these motifs in other proteins, has led it to be used as a model system to understand selective lanthanide recognition. Two-dimensional infrared (2D IR) spectroscopy combined with molecular dynamics simulations were used to investigate LanM's selectivity mechanisms by characterizing local binding site geometries upon coordination of early and late lanthanides as well as calcium. These studies focused on the protein's uniquely conserved proline residues in the second position of each EF-hand binding loop. We found that these prolines constrain the EF-hands for strong coordination of early lanthanides. Substitution of this proline results in a more flexible binding site to accommodate a larger range of ions but also results in less compact coordination geometries and greater disorder within the binding site. Finally, we identify the conserved glycine in the sixth position of each EF-hand as a mediator of local binding site conformation and global secondary structure. Uncovering fundamental structure-function relationships in LanM informs the development of synthetic biology technologies targeting lanthanides in industrial applications.

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.

Highly Accurate Many-Body Potentials for Simulations of N2O5 in Water: Benchmarks, Development, and Validation

Dinitrogen pentoxide (N₂O₅) is an important intermediate in the atmospheric chemistry of nitrogen oxides. Although there has been much research, the processes that govern the physical interactions between N₂O₅ and water are still not fully understood at a molecular level. Gaining a quantitative insight from computer simulations requires going beyond the accuracy of classical force fields while accessing length scales and time scales that are out of reach for high-level quantum-chemical approaches. To this end, we present the development of MB-nrg many-body potential energy functions for nonreactive simulations of N₂O₅ in water. This MB-nrg model is based on electronic structure calculations at the coupled cluster level of theory and is compatible with the successful MB-pol model for water. It provides a physically correct description of long-range many-body interactions in combination with an explicit representation of up to three-body short-range interactions in terms of multidimensional permutationally invariant polynomials. In order to further investigate the importance of the underlying interactions in the model, a TTM-nrg model was also devised. TTM-nrg is a more simplistic representation that contains only two-body short-range interactions represented through Born-Mayer functions. In this work, an active learning approach was employed to efficiently build representative training sets of monomer, dimer, and trimer structures, and benchmarks are presented to determine the accuracy of our new models in comparison to a range of density functional theory methods. By assessing the binding curves, distortion energies of N₂O₅, and interaction energies in clusters of N₂O₅ and water, we evaluate the importance of two-body and three-body short-range potentials. The results demonstrate that our MB-nrg model has high accuracy with respect to the coupled cluster reference, outperforms current density functional theory models, and thus enables highly accurate simulations of N₂O₅ in aqueous environments.

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.

Interplay of physically different properties leading to challenges in separating lanthanide cations - an ab initio molecular dynamics and experimental study

Lanthanide elements have well-documented similarities in their chemical behavior, which make the valuable trivalent lanthanide cations (Ln3+) particularly difficult to separate from each other in water. In this work, we apply ab initio molecular dynamics simulations to compare the free energies (ΔGads) associated with the adsorption of lanthanide cations to silica surfaces at a pH condition where SiO- groups are present. The predicted ΔGads for lutetium (Lu3+) and europium (Eu3+) are similar within statistical uncertainties; this is in qualitative agreement with our batch adsorption measurements on silica. This finding is remarkable because the two cations exhibit hydration free energies (ΔGhyd) that differ by >2 eV, different hydration numbers, and different hydrolysis behavior far from silica surfaces. We observe that the similarity in Lu3+ and Eu3+ ΔGads is the result of a delicate cancellation between the difference in Eu3+ and Lu3+ hydration (ΔGhyd), and their difference in binding energies to silica. We propose that disrupting this cancellation at the two end points, either for adsorbed or completely desorbed lanthanides (e.g., via nanoconfinment or mixed solvents), will lead to effective Ln3+ separation.

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.

In Situ/Operando Electrocatalyst Characterization by X-ray Absorption Spectroscopy

During the last decades, X-ray absorption spectroscopy (XAS) has become an indispensable method for probing the structure and composition of heterogeneous catalysts, revealing the nature of the active sites and establishing links between structural motifs in a catalyst, local electronic structure, and catalytic properties. Here we discuss the fundamental principles of the XAS method and describe the progress in the instrumentation and data analysis approaches undertaken for deciphering X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) spectra. Recent usages of XAS in the field of heterogeneous catalysis, with emphasis on examples concerning electrocatalysis, will be presented. The latter is a rapidly developing field with immense industrial applications but also unique challenges in terms of the experimental characterization restrictions and advanced modeling approaches required. This review will highlight the new insight that can be gained with XAS on complex real-world electrocatalysts including their working mechanisms and the dynamic processes taking place in the course of a chemical reaction. More specifically, we will discuss applications of in situ and operando XAS to probe the catalyst's interactions with the environment (support, electrolyte, ligands, adsorbates, reaction products, and intermediates) and its structural, chemical, and electronic transformations as it adapts to the reaction conditions.

Alchemical Binding Free Energy Calculations in AMBER20: Advances and Best Practices for Drug Discovery

Predicting protein-ligand binding affinities and the associated thermodynamics of biomolecular recognition is a primary objective of structure-based drug design. Alchemical free energy simulations offer a highly accurate and computationally efficient route to achieving this goal. While the AMBER molecular dynamics package has successfully been used for alchemical free energy simulations in academic research groups for decades, widespread impact in industrial drug discovery settings has been minimal because of the previous limitations within the AMBER alchemical code, coupled with challenges in system setup and postprocessing workflows. Through a close academia-industry collaboration we have addressed many of the previous limitations with an aim to improve accuracy, efficiency, and robustness of alchemical binding free energy simulations in industrial drug discovery applications. Here, we highlight some of the recent advances in AMBER20 with a focus on alchemical binding free energy (BFE) calculations, which are less computationally intensive than alternative binding free energy methods where full binding/unbinding paths are explored. In addition to scientific and technical advances in AMBER20, we also describe the essential practical aspects associated with running relative alchemical BFE calculations, along with recommendations for best practices, highlighting the importance not only of the alchemical simulation code but also the auxiliary functionalities and expertise required to obtain accurate and reliable results. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative BFE simulations in AMBER20, with a focus on real-world drug discovery applications.

The origins of binding specificity of a lanthanide ion binding peptide

Lanthanide ions (Ln³⁺) show similar physicochemical properties in aqueous solutions, wherein they exist as + 3 cations and exhibit ionic radii differences of less than 0.26 Å. A flexible linear peptide lanthanide binding tag (LBT), which recognizes a series of 15 Ln³⁺, shows an interesting characteristic in binding specificity, i.e., binding affinity biphasically changes with an increase in the atomic number, and shows a greater than 60-fold affinity difference between the highest and lowest values. Herein, by combining experimental and computational investigations, we gain deep insight into the reaction mechanism underlying the specificity of LBT3, an LBT mutant, toward Ln³⁺. Our results clearly show that LBT3-Ln³⁺ binding can be divided into three, and the large affinity difference is based on the ability of Ln³⁺ in a complex to be directly coordinated with a water molecule. When the LBT3 recognizes a Ln³⁺ with a larger ionic radius (La³⁺ to  Sm³⁺), a water molecule can interact with Ln³⁺ directly. This extra water molecule infiltrates the complex and induces dissociation of the Asn5 sidechain (one of the coordinates) from Ln³⁺, resulting in a destabilizing complex and low affinity. Conversely, with recognition of smaller Ln³⁺ (Sm³⁺ to Yb³⁺), the LBT3 completely surrounds the ions and constructs a stable high affinity complex. Moreover, when the LBT3 recognizes the smallest Ln³⁺, namely Lu³⁺, although it completely surrounds Lu³⁺, an entropically unfavorable phenomenon specifically occurs, resulting in lower affinity than that of Yb³⁺. Our findings will be useful for the design of molecules that enable the distinction of sub-angstrom size differences.

Interfacial structure in the liquid-liquid extraction of rare earth elements by phosphoric acid ligands: a molecular dynamics study

Solvent extraction (SX), wherein two immiscible liquids, one containing the extractant molecules and the other containing the solute to be extracted are brought in contact to effect the phase transfer of the solute, underpins metal extraction and recovery processes. The interfacial region is of utmost importance in the SX process, since besides thermodynamics, the physical and chemical heterogeneity at the interface governs the kinetics of the process. Yet, a fundamental understanding of this heterogeneity and its implications for the extraction mechanism are currently lacking. We use molecular dynamics (MD) simulations to study the liquid-liquid interface under conditions relevant to the SX of Rare Earth Elements (REEs) by a phosphoric acid ligand. Simulations revealed that the extractant molecules and varying amounts of acid and metal ions partitioned to the interface. The presence of these species had a significant effect on the interfacial thickness, hydrogen bond life times and orientations of the water molecules at the interface. Deprotonation of the ligands was essential for the adsorption of the metal ions at the interface, with these ions forming a number of different complexes at the interface involving one to three extractant molecules and four to eight water molecules. Although the interface itself was rough, no obvious 'finger-like' water protrusions penetrating the organic phase were seen in our simulations. While the results of our work help us gain fundamental insights into the sequence of events leading to the formation of a variety of interfacial complexes, they also emphasize the need to carry out a more detailed atomic level study to understand the full mechanism of extraction of REEs from the aqueous to organic phases by phosphoric acid ligands.

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.

Evidence for an egg-box-like structure in iron(ii)–polygalacturonate hydrogels: a combined EXAFS and molecular dynamics simulation study

The coordination of Fe(ii) with polygalacturonic acid (polyGalA) in Fe(ii)–polyGalA hydrogels exhibits an octahedral geometry that follows the “egg-box model”.

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

On the coordination of Zn2+ ion in Tf2N− based ionic liquids: structural and dynamic properties depending on the nature of the organic cation

The Zn²⁺ coordination structure changes when the Zn(Tf₂N)₂ salt is dissolved in ionic liquids resulting in more favorable interactions among solvent cations and anions.